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Synchronization and critical behavior in B-cell networks

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Title:
Synchronization and critical behavior in B-cell networks towards the engineering of the islets of langerhans
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Hraha, Thomas H. ( author )
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Denver, CO
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University of Colorado Denver
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Islands of Langerhans ( lcsh )
Diabetes -- Treatment ( lcsh )
Diabetes -- Treatment ( fast )
Islands of Langerhans ( fast )
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non-fiction ( marcgt )

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The pancreatic islets of Langerhans' are multicellular micro-organs which are integral to maintaining glucose homeostasis through secretion of insulin. Beta cells within islets synchronize their insulin release through cell-cell communication to create large bursts to meet physiological needs. However, in patients with diabetes there is a reduction in this cell-cell coupling which leads to a hindered insulin response.To better characterize the effect of cell-cell coupling in β-cell synchronization, we studied the differences in real-time coupling dynamics between 2D and 3D cell structures. Using a novel system for aggregating β-cells back into 3D structures of defined size, we were able to show that the uncoordinated behavior seen in 2D cell networks is ameliorated by the 3D cell structure. Using this system to aggregate primary islet cells, we found that the resulting `pseudo-islets' had higher viability and functionality compared to normal islets at two week, indicating they may yield higher post-transplant viability and increase transplant effectiveness. Applying these findings to a network model of cell synchronization, we were then able to theoretically show how reductions in the fractal dimension of cell coupling (number of nearest neighbors a cell can coupling with) can lead to a diabetic phenotype. Furthermore, we were able to apply this model in a predictive manner to forecast the existence of a critical point of cell coupling, below which a diabetic phenotype is established. This was then verified through islet with genetic mutations.
Thesis:
Thesis (M.S.)--University of Colorado Denver. Bioengineering
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Includes bibliographic references.
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Department of Bioengineering

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879676352 ( OCLC )
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Full Text
SYNCHRONIZATION AND CRITICAL BEHAVIOR IN (3-CELL
NETWORKS: TOWARDS THE ENGINEERING
OF THE ISLETS OF LANGERHANS
by
THOMAS H. HRAHA
B.S., Colorado State University, 2008
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Bioengineering
2013


This thesis for the Master of Science degree by
Thomas H. Hraha
has been approved for the
Department of Bioengineering
By
Kendall Hunter, Chair
Richard Benninger
Robin Shandas
6/19/2013


Hraha, Thomas H. (M.S., Bioengineering]
Synchronization and Critical Behavior in (3-Cell Networks:
Towards the Engineering of the Islets of Langerhans
Thesis directed by Assistant Professor Richard KP Benninger
ABSTRACT
The pancreatic islets of Langerhans are multicellular micro-organs which are integral to
maintaining glucose homeostasis through secretion of insulin. Beta cells within islets
synchronize their insulin release through cell-cell communication to create large bursts to
meet physiological needs. However, in patients with diabetes there is a reduction in this
cell-cell coupling which leads to a hindered insulin response.
To better characterize the effect of cell-cell coupling in (B-cell synchronization, we studied
the differences in real-time coupling dynamics between 2D and 3D cell structures. Using a
novel system for aggregating (3-cells back into 3D structures of defined size, we were able to
show that the uncoordinated behavior seen in 2D cell networks is ameliorated by the 3D
cell structure. Using this system to aggregate primary islet cells, we found that the resulting
'pseudo-islets had higher viability and functionality compared to normal islets at two week,
indicating they may yield higher post-transplant viability and increase transplant
effectiveness.
Applying these findings to a network model of cell synchronization, we were then able to
theoretically show how reductions in the fractal dimension of cell coupling (number of
nearest neighbors a cell can coupling with) can lead to a diabetic phenotype. Furthermore,
we were able to apply this model in a predictive manner to forecast the existence of a
critical point of cell coupling, below which a diabetic phenotype is established. This was
then verified through islet with genetic mutations.
The form and content of this abstract are approved. I recommend its
publication
m
Approved: Richard KP Benninger


TABLE OF CONTENTS
Chapter
I. INTRODUCTION AND BACKGROUND..................................................1
Introduction.................................................................1
Overview of Glucose-Stimulated Insulin Secretion (GSIS)......................2
Diabetes.....................................................................3
Islet Architecture...........................................................3
Beta Cell Electrophysiology and the Triggering Pathway.......................6
Amplification Pathway and Exocytosis.........................................9
The Insulin Response........................................................12
The Oscillatory Nature of GSIS..............................................13
Cell-Cell Coupling in GSIS..................................................11
Beta Cell Heterogeneity.....................................................14
Overview of Relevant Mathematical Models....................................18
Applications of Transgenic Mouse Model......................................20
Islet Transplantation.......................................................14
Engineering Islets..........................................................27
Lattice-Resistor Network Model of Islet Connectivity........................28
II. MATERIALS AND METHODS.......................................................33
Cell Culture and Aggregate Formation........................................33
Insulin Secretion Assay.....................................................35
Microscopy..................................................................36
Matlab Analysis.............................................................36
Development of Transgenic Models............................................40
Bond Percolation Simulations for Size-Scaling and Dimensionality Comparisons.... 40
High Glucose (Synchronization) Simulations...........................41
Low glucose (Suppression) Simulations ...............................53
Bond Percolation Simulations for Discrete Modeling of Islet Dynamics........54
IV


III. RESULTS PART 1: DIMENSIONALITY AND SIZE-SCALING OF COORDINATED Ca2+
DYNAMICS IN PANCREATIC p-CELL NETWORKS....................................45
[Ca2+]i Dynamics and Insulin Secretion Under Two- and Three-Dimensional
Coupling...................................................................45
Dimension and Size-Dependence of [Ca2+]i Synchronization..................47
Sub-Regions of Synchronization in Two-Dimensional Cell Clusters...........50
Wave Velocity Under Two- and Three-Dimensional Coupling...................51
Dimension and Size-Dependence of Basal [Ca2+]i Suppression.................52
Network Lattice Model of [Ca2+]iDynamics ..................................54
IV. RESULTS PART 2: REAGGREGATION OF PRIMARY ISLET CELLS INTO PSEUDO-
ISLETS OF DEFINED SIZE BY MICROWELL CELL.....................................58
Primary Islet Cells Uniformly Aggregate to Defined Sizes in 3D PEG
Micro well Arrays..........................................................60
Pseudo-Islets Show Comparable Viability and Functionality to Fresh Islets.60
Day 7 and 14 Pseudo-Islets are Better than Age-Matched Normal Islets......62
Summary of Results.........................................................63
V. RESULTS PART 3: PERCOLATION MODELING PREDICTS LOW-GLUCOSE BEHAVIOR
IN Katp CHANNEL GENETIC MUTANTS............................................65
Model Predictions..........................................................66
Cell Activity as a Function of Coupling Conductance in KIR6.2 [AAA] Mice..69
Cell Activity as a Function of Excitability in KIR6.2[AN2-30,K185Q] Mice..70
Summary of Findings........................................................71
VI. DISCUSSION.................................................................72
Dimensionality and Size-Scaling of Coordinated [Ca2+]i Dynamics in p-cells.72
Insufficient p-cell Coupling in Two-Dimensions......................73
Network Model Describes Dimension and Size-Scaling of [Ca2+]i Dynamics 75
Physiological Importance of Dimensionality and Size-Scaling in Network
Architecture........................................................77
Re-Aggregation of Primary Islet Cells into Functional Pseudo-Islet.........79
v


Primary Islet Cells Readily Aggregate to Form 3D Pseudo-Islets
of Defined Size........................................................80
Pseudo-Islets Show Superior Viability and Functionality................82
Applications to Human Work.............................................84
Percolation Modeling Predicts Low-Glucose Behavior in Katp Channel Genetic
Mutants.....................................................................86
Percolation Modeling Accurately Predicts the Increase in Low Glucose
Activity of KIR6.2 [AAA] Islets as a Function of Gap Junction Coupling.88
Percolation Modeling Predicts Critical Behavior in Fasting Insulin Secretion
in KIR6.2[AN2-30,K185Q] Expressing Mice..............................89
Implications of the Model for Overactive Katp Channels...............92
Future Directions...........................................................98
REFERENCES.........................................................................99
vi


CHAPTER 1
INTRODUCTION & BACKGROUND
"The greatest challenge today, not just in cell biology and ecology but in all of science, is the
accurate and complete description of compiex systems. Scientists have broken down many
kinds of systems. They think they know most of the elements and forces. The next task is to
reassemble them, at least in mathematical models that capture the key properties of the entire
ensembles"
Edward Wilson
Introduction
The pancreatic islets of Langerhans are multicellular micro-organs which are
integral to maintaining glucose homeostasis through secretion of the hormones insulin and
glucagon. Normally, the cells of this organ are electrically coupled to produce insulin in
coordinated bursts in response to elevated blood glucose. These insulin bursts are the result
of complex triggering and amplification pathways which are subject to a complex array of
inputs. Impairment of the islets ability to accomplish this leads to hyperglycemia, and is
implicated in the development of type 1 and type 2 diabetes. Many studies indicate that the
pulsatile dynamics of insulin secretion are important for insulin action and maintaining
insulin sensitivity, and insulin pulsatility. Therefore, factors that regulate in-vivo insulin
dynamics are important for regulating glucose homeostasis.
Currently, the best treatment option for type 1 diabetics is islet transplantation.
However, a lack of donor tissue and low post-transplant islet viability are major hurdles
towards making this a widely available option. The engineering of islets from donor tissue,
1


or de novo from stem cells, has the ability to ameliorate this problem. However, these
engineered islets must be shown to display similar physiology and have sufficiently
developed electrical coupling. Therefore, a working model of both the electrophysiogical
coupling of the triggering pathway with integration of components of the amplification
pathway would provide a benchmark to which engineered islets can be compared. In
addition, the tools developed to build these models would be helpful in studying the
development and pathophysiology of diabetes mellitus.
Much work has been done in the last 50 years to understand the electrophysiology
and molecular biology of the (3-cell. However, relatively little is known regarding how these
cells interact with each other to produce such exquisite coordination to maintain glucose
homeostasis. This paradigm also reflects the changes taking place in scientific research in
general; while the last 50 years have been focused on reductionism, or dissecting the
intricacies of biological systems, high level computing and instrumentation will allow the
next 50 years to be focused on how these intricate systems interact to produce life and
disease.
Overview of Glucose-Stimulated Insulin Secretion
Pancreatic (3-cells synthesize and secrete insulin at appropriate rates to maintain
blood glucose levels within a relatively small range. Any alteration in their function has a
profound effect on glucose homeostasis and often leads to disease. This apparently simple
role of the (3-cell in glucose physiology contrasts sharply with the complexity of its
regulation, which is controlled by an intricate array of metabolic, electrophysiological,
hormonal and sometimes pharmacological factors.
2


When blood glucose rises above its normal level of ~5mM, the pancreatic (3-cell
responds by releasing insulin into the blood. Because the Km1 of the (3-cell glucose receptor
GLUT2 is ~20mM, a rise in extracellular glucose in this range causes a proportionate
increase in glucose entry. Glucose-stimulated insulin secretion (GSIS) from (3-cells is
regulated by a series of molecular events including an elevated ATP/ADP ratio following
glucose metabolism, subsequent ATP-sensitive K+ (Katp) channel closure, membrane
depolarization, Ca2+ influx to increase intracellular free-calcium activity ([Ca2+]i), and the
triggering of insulin granule exocytosis. Other important steps independent of this 'Katp-
dependent' or triggering pathway' include cAMP elevations which elevate insulin granule
trafficking to the plasma membrane and augment exocytosis, therefore referred to the
'amplifying pathway (Henquin, 2000).
Glucose concentrations over ~7 mM generate synchronous oscillations in (3-cell
intracellular Ca2+ concentration ([Ca2+]i], which lead to pulsatile insulin secretion. Although
insulin can be secreted through steps independent of Ca2+, primarily through hormonal
control, the fraction of insulin released by this mechanism is only minor fraction of insulin
released in the presence of Ca2+ (Komatsu, etal., 1997). Therefore, the sequence of events
leading to insulin secretion may have Ca2+-independent steps, however the physiological
regulation by glucose is achieved through Ca2+-dependent pathways.
Diabetes
When insulin secretion is absent or impaired, peripheral tissues fail to respond to
insulin, resulting in hyperglycemia leading ultimately to diabetes (MacDonald & Rorsman,
1 Where Km is defined by Michaelis-Menten kinetics to be the substrate concentration at which the
reaction rate (in this case entry rate which is defined by receptor affinity) is half of the maximal.
3


2006). Diabetes affects more than 285 million people worldwide, with type 2 diabetics
making up about 90% of the cases. It has an annual cost of $132 billion to the American
medical system and is associated with several long-term complications including nerve
damage, kidney failure, microcirculatory impairment, and a greater risk for heart disease
and stroke (MacDonald & Rorsman, 2006).
The vast majority of cases of diabetes fall into two broad categories: type 1 and type
2. Type 1, or juvenile-onset, diabetes results from a cellular-mediated autoimmune
destruction of the (3-cells. Though the rate of (3-cell destruction varies between patients, the
resulting impairment is usually large enough to require peripheral insulin injection
(Mellitus, 2006).
In contrast, type II diabetes accounts for greater than 85% of cases. In this variant,
(3-cells persist, but for reasons that remain to be elucidated they fail to secrete insulin in
sufficient quantities to maintain proper blood glucose levels (MacDonald & Rorsman, 2006)
This disruption in secretion seen prior to the onset of type II diabetes (LeRoith, 2002), and
when combined with the development of insulin resistance in peripheral tissues, the results
in chronic hyperglycemia. Thus, understanding the electrophysiological mechanisms
regulating (3 cell function and interactions is crucial towards understanding the
pathogenesis of type II diabetes.
Islet Architecture
The pancreatic islets of Langerhans play a central role in the regulation of blood
glucose homeostasis through the regulated secretion of the hormones insulin and glucagon.
The endocrine tissue of the pancreas is organized as cell clusters approximately 100-400gm
4


in diameter called the islets of Langerhans, which are dispersed throughout the pancreatic
exocrine tissue and receive a rich vascular (blood vessel) supply. Islets are composed of
three main cells types: pancreatic a cell occupy constitute ~15% of the mouse islet mass
and secrete the hormone glucagon in response to low blood glucose. Glucagon increases
blood glucose, thereby opposing the actions of insulin. Pancreatic 6 cells, which constitute
~5% of the mouse islet mass, secrete somatostatin, which acts in a paracrine fashion to
inhibit the secretion of both insulin and glucagon (Reichlin, 1983). Finally, the insulin-
secreting (3 cells are by far the most abundant cell type, comprising ~80% of the islet mass.
Detailed quantitative studies assessing the cell composition (Stefan etal. 1982;
Rahier et al. 1983; Clark et al. 1988) have found that human islets are composed ~70% (3-
cells, 20% a-cells < 15% 6- and other cells. However, more recent studies suggest the there
is a lower number of (3-cells (50-60%) and a higher number of a-cells (30-40%) (Sakuraba
etal. 2002; Street etal. 2004; Brissova etal. 2005).
Although much work has been done with regards to quantifying the cell types in
islets, few have examined the cytoarchitecture across species. In rodent islets, the
predominating (3-cells are clustered mainly in the core of the islet, whereas cells expressing
glucagon (a-cells) and somatostatin (6-cells) are mainly localized to the periphery. In
contrast, human islets have shown to have glucagon- and somatostatin-positive cells
homogeneously scattered throughout the islet, however recent evidence has shown that
this effect may be due to the age of human islets studying, typically being from older
individuals compared to weeks-old mice. This is explained in more detail in the discussion.
To estimate the degree of clustering or segregation of similar cell types in the islet, Cabrera,
etal. quantified the proportion of a- and (3-cells exclusively adjacent to cells of the same
type (homotypic association) or adjacent to cells of other types (heterotypic associations).
5


In mouse islets, they found that 71% of (3-cells showed homotypic associations, whereas in
human islets only 29% showed these associations (Cabrera, etal., 2006). This suggests that
the paracrine effects of other cell types may play a more important role in human islets,
which was further supported by evidence showing that ~86% of 6-cells were found to be
closely opposed to blood vessels.
However, recent evidence suggests that the cytoarchitecture seen in human islets by
Cabrera et al. may be the result of a changing cell composition over time (Bosco et al. 2010;
Kilimnkik et al. 2011). In a better statistically powered study, Bosco, et al. demonstrated
that while larger human islets have a heterogeneous core composed of a- and (3-cells,
smaller human islets maintain the core-mantle structure seen in mice islets. Furthermore,
they found that the a-cells within the core the islet were focused around the edges of the
vasculature and therefore postulate that this architecture in larger islets still facilitates a
folded mantle-core structure around the vasculature (Bosco etal. 2010).
Nevertheless, these aspects of the cellular architecture must be taken into
consideration when applying findings regarding intercellular electrical synchronization and
when attempting to engineer islets de novo. It appears that differences in islet
cytoarchitecture may lead to functional differences in islet behavior, with human islets
having more of a reliance on neuro-endocrine secretions. It is therefore important to
consider the relative proportions and locations of cell types when attempting to engineer
islets using hydrogel scaffolds or when aggregating cells de-novo. Also, the lower
percentage of (3-cells within the human islet may lead to less cell-cell electrical coupling,
although this has never been shown.
6


Beta Cell Electrophysiology and the Triggering Pathway
Pancreatic (3 cells have multiple ion channels which allow for the flow of ions
(mostly Ca2+ and K+) into and out of the cell. Due to the charged nature of these ions, their
flux across the membrane can give rise to sharp changes in voltage (action potentials). In (3-
cells, these action potentials are stimulated through intracellular glucose metabolism.
The cell membrane gives rise to small voltage changes by manipulating the
concentration gradient of ions using selective permeability. If the concentrations of positive
and negative ions on either side of the cell membrane are equal, there will be no difference
in the electrical potential gradient. However, if the membrane was permeable to an ion (K+
in the case of the beta cell) then the inward flux of this ion down its concentration gradient
would create a charge imbalance and therefore a potential gradient. As more K+ ion move
through the channel, the magnitude of the charge difference (or voltage) increases until a
repulsive force caused by excess positive K+ ions leads to an equilibrium. If a membrane is
only permeable to K+ ions (which is the approximate case for the beta cell), then the
electrical potential Ek+ (in volts) is given by the Nernst equation
RT [Ke\
Ek~ZFln M
where Ke and Ki are the extracellular and intracellular concentrations of K+ ions,
respectively; R is the gas constant 1.987 calories / (degree*mol); T is the absolute
temperature in Kelvins (293K for 20C); Z is the +1; and F is the Faraday constant equal to
23,062 cal / (mol*V) or 96,000 coulombs / (mol*V). At 20C, this reduces to:
[Ke]
Ek = 0.059logwj^
7


Therefore, at a 10-fold concentration the magnitude of the difference is 0.059V (or 59mV).
However, since the cytoplasmic side is viewed as negative in this case, this would be -59mV.
The resting membrane potential of the (3-cell is dominated by K+ channels. As a
result, the major ionic movement across the plasma membrane is that of K+ out of the cell,
powered by the concentration gradient This creates a resting membrane potential of the
cell is approximately -70mv. Although this value does not seem very large, given that the
cell membrane is only ~3.5nm thick, this corresponds to ~200,000 volts per cm. To put this
in context, high-voltage power lines generally use a 200,000 volt gradient over a kilometer.
Under low glucose conditions, ATP-sensitive K+ channels (Katp channels) are open,
allowing an outward flux of K+ ions which effectively clamps the beta-cell membrane
potential at the K+ Nernst potential and produces a steady-state cell membrane potential of
70mV (Rorsman, 1997; Henquin, 2000). These channels are tetramers of a complex of
two proteins: a high-affinity sulfonylurea receptor (SUR1) and an inwardly rectifying K+
channel (Kir 6.2). SUR1 provides the pore-forming KIR6.2 with sensitivity to sulfonylureas
and diazoxide, which respectively close and open the channel. The closing action in
response to an elevated ATP:ADP ratio is KIR6.2 -dependent (Henquin, 2000; Ashcroft &
Gribble, 1998).
When the (3-cell is exposed to glucose through the pancreatic vasculature, glucose
enters the cell through GLUT2 transporters and increased cellular metabolism of the sugar
through glycolysis (anaerobic) and oxidative phosphorylation (aerobic) leads to a rise in the
ATP:ADP ratio. Increased levels of ATP bind to the KRI6.2 subunit of the Katp channel and
cause it to close; stopping the influx of K+ ions down their electrical gradient This drives the
membrane towards a more positive potential and once the Katp channels are almost all
(>90%) inhibited, the Katp conductance is unable to balance the background depolarizing
8


influences and the beta cell depolarizes at around -45mV (Rorsman 1997; MacDonald &
Rorsman, 2006; Drews etal., 2010; Misler etal., 1992). When this depolarization is large
enough, L-type voltage-gated calcium channels (VDCC) become activated, allowing the
influx of Ca2+ down the electrical gradient, further driving the membrane potential.
The predominant VDCC isoforms found in (3 cells are composed of four subunits.
Each subunit is composed of six transmembrane a-helices, the fourth of which serves as the
voltage sensors for activation. In response to membrane depolarization, VDCCs undergo an
extremely rapid conformational shift, moving outward and rotating under the influence of
the electric field and initiating a conformational change which opens a highly permeable
pore (Yang & Berggren, 2006).
The resultant increase in [Ca2+]i triggers direct interactions between the exocytotic
proteins situated in the insulin-containing granule membrane and those localized in the
plasma membrane. Eventually, the interaction between exocytotic proteins initiates the
fusion of insulin-containing granules with the plasma membrane resulting in insulin
exocytosis (Yang & Berggen, 2005a; Yang & Berggen, 2005b).
If glucose concentrations remain high, the (3-cell undergoes oscillatory Vm activity.
This is caused by oscillatory changes in ATP and activation of voltage-dependent inward
rectifying K+ (Kv) channels, whose opposing activity creates high frequency oscillations at
high membrane potentials. As the levels of [Ca2+]i increase, Ca2+-activated K+ channels are
opened which are responsible for the repolarizing curve of the Vm trace and reset the cycle
(MacDonald, 2003).
Thus, the Katp channels can be viewed as the transducers of glucose-induced insulin
secretion. This role is easily demonstrated by the use of agents which manipulate the
9


channels behavior. Opening of channels with diazoxide causes membrane repolarization,
lowers [Ca2+]i and inhibits insulin secretion (Henquin, 2000). Subsequent addition of
tolbutamide or sulfonylureas to close the channels leads to a depolarization of the cell and a
resumption in [Ca2+]i -driven insulin release (Henquin, 2000). In addition, recent evidence
has suggested that waves of depolarization through the entire islet originate in areas of high
Katp inhibition (Rochelau et al., 2004).
If Katp are said to be the transducers of glucose-stimulated insulin secretion, then
the VDCCs are the effectors because of their effect on insulin exocytosis. This is supported
by a work in which a point mutation of human VDCC channel rendering constitutively active
makes the (3-cell secrete insulin excessively (Splawski et al., 2004).
A number of additional factors have been found to control (3-cell electrophysiology,
including Cl- and non-selective cation channels, as well as electrogenic pumps such as the
Na+ / K+ ATPase. While the role of these has not been extensively characterized, their
activity has been found to be highly dependent on peripheral systems such as the protein-
kinase C pathway and mitochondrial NADPH production (MacDonald, 2003). Though they
may play an undiscovered critical role, the three channels which regulate the glucose-
induced response (and were discussed above) are the main players in regulating glycemic
control through insulin secretion.
Amplification Pathway and Exocytosis
Although much work has been done to show that insulin exocytosis is clearly Ca2+ -
dependent, recent evidence suggests that increased intracellular [Ca2+]i acts more as an
initiator rather than a determinant of insulin release. For example, removal of extracellular
10


Ca2+ prevents action potential (Liu et al., 2004) and subsequent insulin secretion (Gopel et
al., 2000; Gromada et al., 2004), however, the amplitude of the exocytotic response depends
to a greater extent on the activity of kinases and phosphatases rather than purely [Ca2+]i
(Rorsman, 1997; Milser etal., 1992; Henquin, etal., 2000). This points to another,
'amplifying pathway of insulin secretion that has been found to be mediated by cyclic
adenosine monophosphate (cAMP).
A ubiquitous secondary messenger of most cell types in the body, cAMP is another
critical factor in GSIS. Until recently, little was known about the spatiotemporal dynamics of
cAMP signaling in (3 cells. With the recent advance of novel fluorescent biosensors, complex
spatiotemporal patterns which are Ca2+ dependent and independent are beginning to
emerge. Interestingly, glucose has been found to trigger concurrent oscillations of cAMP and
[Ca2+]i in individual MIN6 cells (Landa etal., 2005; Ni etal., 2010). Since cAMP enhances
exocytosis predominantly via PKA, and is also influenced by hormonal factors (in addition
to [Ca2+]i), it has been suggested that cAMP plays an amplifying role of the Ca2+ signal. In
both humans and rodents, the glucose-induced oscillations in [cAMP]i resemble those of
[Ca2+]i with small initial lowering, followed by pronounced rise and slow oscillations with a
period of 2-10 minutes (Dyachok et al., 2008). Although several studies have found that
depolarization of the cell causes oscillations in [cAMP]i (Dyachok & Gylfe, 2004; Landa et al.,
2005; Ni etal., 2010), the phase relationship between these two signaling factors seems to
depend on the other conditions. Whereas cells stimulated with GLP-1 showed synchronous
oscillations in [cAMP]i and [Ca2+]i (Dyachok etal., 2006), TEA-induced elevations of [Ca2+]i
were associated with decreases of cAMP (Landa et al., 2005), which may be due to over-
activation of Ca2+ -sensitive phosphodiesterase.
11


Glucose-induced generation of cAMP in (3 cells may potentiate insulin secretion by
sensitizing the exocytosis machinery since inhibition of [cAMP]i oscillations markedly
suppress pulsatile insulin secretion without affecting the underlying [Ca2+]i oscillations
(Henquin, 2000). Agents which increase cytoplasmic levels of cAMP potentiate Ca2+ -
stimulated insulin exocytosis almost 10-fold (through a protein kinase A (PKA)-dependent
mechanism) without affecting Ca2+ influx or [Ca2+]i (Ammala et al., 1993). This is thought to
be due to PKA accelerating granule mobilization. Thus, when exocytosis is initiated by
[Ca2+]i a greater number of granules are available for release. Therefore, the Ca2+, ATP:ADP
and cAMP dynamics may lead to triggering and amplification pathways of insulin secretion,
which would explain why cAMP can oscillate even under steady Ca2+ levels.
The principal action of cAMP on exocytosis seems to be exerted at a step distal to
the elevation of [Ca2+]i (Ammala et al., 1993; Gillis and Misler, 1993), involving both PKA-
dependent and -independent mechanisms, the latter most likely mediated by exchange
proteins activated by cAMP (Epac) (Renstrom etal., 1997). Many exocytosis-related
proteins have been identified as substrates for PKA (Seino and Shibasaki, 2005), and the
subcellular targeting of PKA to its effectors via A-kinase anchoring proteins has been found
to be critical for the stimulatory effect of cAMP-elevating agents on insulin secretion (Lester
etal., 1997; Fraser etal., 1998). Capacitance recordings by Eliasson, etal. have indicated
that PKA mediates the slower cAMP-dependent mobilization of insulin granules, while Epac
accounts for the rapid cAMP-dependent potentiation of exocytosis in (3-cells (Eliasson et al.,
2003). Epac has also been reported to increase the number of granule fusion sites and along
with PKA the number of granule-granule fusion events (Kwan etal., 2007).
Interestingly, both sulfonylureas and GLP-1 treatment have been found to improve
in-vivo insulin pulsatility (Porksen, 2002), which is most likely due to the established ability
12


of these drugs to generate oscillations in [Ca2+]t (Grapengeisser, 1990) and cAMP (Dyachok,
2006). Impairment of insulin pulsatility from (3 cells is central to the development of type 2
diabetes, and may reflect a degradation of synchronization in secretory activity rather than
a deficit in (3 cells mass. In addition, since insulin has been suggested to be an important
stimulus for (3 cell proliferation in states of insulin resistance (Henquin, 2000), loss of
pulsatile insulin secretion in prediabetic and diabetic states may also impair the
compensatory expansion of the (3 cell mass (Lang, 1981).
Despite the fact that much work has been done in regards to understanding the
roles of cAMP and [Ca2+]iin individual cells, how these cells come together to form a
coordinated pulse of insulin remains unclear. Despite work in the role of gap junctions in
coordinating electrical activity (Benninger etal., 2008; Benninger etal., 2011; Rochelau et
al., 2004), how cAMP activity coordinates the 'amplifying pathway remains unclear. In fact,
there is a lack of data where cAMP and [Ca2+]i were measured in anything but a single cell. If
islets are ever to be reformed from primary cells or stem cells, these are important
dynamics that need to be established to recreate a functional islet capable of overcoming
diabetes.
The Insulin Response
Pancreatic (3-cells respond to a step increase in the glucose concentration with a
biphasic insulin secretory pattern. This biphasic pattern of insulin secretion was first
observed in the perfused rat pancreas (Grodsky, 1966; Nesher, 1987). Later, it was also
visualized in the portal vein and peripheral blood in human subjects in response to a rapid
elevation of glucose (Cerasi etal., 1972). The response is characterized by a rapid initial
13


phase of insulin release, which is maintained for about 10 minutes, followed by a gradually
increasing second phase, which reaches a plateau after another 25 to 30 minutes (Yang &
Berggen, 2005a). Mouse islets subjected to an abrupt and sustained increase also secrete
insulin biphasically. However, the second phase of insulin release from mouse islets is lower
than that from human and rat islets (Jing, 2005). A loss of the first phase and a reduction of
the second phase of insulin secretion occur in type 2 diabetes characterized by (3-cell
dysfunction (Rorsman & Renstrom, 2003).
This supports other evidence which shows that glucose-induced insulin secretion
dynamics by human islets is very similar to that in rodents in terms of metabolic and Ca2+
dependencies (Ricordi etal., 1998; Grant etal., 1980; Misler, etal., 1992). Therefore, this
supports the use of rodent models in the study of islet electrophysiology, pathology and
diabetes.
Oscillatory Nature ofGSIS
Insulin secretion occurs in a pulsatile fashion, which is driven by the underlying
pulsatile nature of the cell voltage. The opening of Ca2+ channels is intermittent, oscillating
with the membrane potential and therefore resulting in oscillations in [Ca2+]i and in-turn,
oscillations in insulin release (Gilon et al., 1992; Tornheim, 1997).These oscillations occur
with a period of 2-8 minutes in humans (Land et al., 1979) and mice (Nunemaker et al.,
2006), and reflect a balance between the VDCCs (depolarization) and the Kca channel
activity (repolarization) (Ashcroft & Rorsman, 1989). The depolarizing Ca2+ component
dominates at the beginning of the burst, but the Ca2+ influx rapidly leads to increased Kca
channel activity. This occurs via a direct effect on Ca2+-activated Kca channels (Zhang et al.,
14


2005) and also through indirect effect on KAtp channels by lowering the cytoplasmic
ATP:ADP ratio due increased Ca2+ ATPase activity (Kanno etal., 2002). Upon the buildup of
Ca2+, Kca channel activity repolarizes the (3-cell, thereby readying the cell for another burst if
intracellular metabolism remains high.
Glucose produces a concentration-dependent decrease in the period. At glucose
concentrations beyond physiological levels (20mM), constant action potential spiking is
seen, which may be due to a higher rate of glucose metabolism leading to such high
intracellular ATP concentrations that Ca2+ ATPase cannot lower them to increase Kca
conductance enough to lead to repolarization. This is supported by the use of the of Katp
inhibitor tolbutamide, which has been used to treat diabetes for over 50 years. By blocking
Katp channels, membrane potential is suppressed and results in continuous firing
(MacDonald & Rorsman, 2006).
Cell-Cell Coupling in GSIS
In addition to proper electrophysiology in individual (3 cells, communication
between cells is imperative for a proper insulin response. (3-cells within the same pancreatic
islet are electrically coupled by gap junctions (Santos et al., 1991; Eddlestone et al., 1984),
such that the [Ca2+ ]i oscillations within different parts of the islet occur in-phase even
though individual (3-cells show a heterogeneous sensitivity to a given glucose concentration.
This gap junction coupling coordinates the dynamics underlying GSIS and also mediates the
suppression of electrical activity at low blood glucose concentrations. This synchronization
of electrical activity produces coordinated bursts of insulin, which are imperative in
glycemic control.
15


In contrast to continuous secretion, pulsatile insulin release has been shown to be
more effective at lowering blood-glucose (Bratusch-Marrian etal., 1986; Matthews etal.,
1983; Paolisso etal., 1988; Meier etal., 2005), and also maintaining peripheral tissue insulin
sensitivity (Goodner et al., 1988). Several landmark studies have also shown that diabetic
patients require less insulin to maintain normoglycemia if insulin is infused in an oscillatory
manner as opposed to a constant rate. Pulsatile insulin infusion has also been implicated for
use in patients with type 2 diabetes with positive results (Bratusch-Marrain et al., 1986;
Matthews et al., 1987; Paolisso et al., 1988). These oscillations are disrupted in patients
with type II diabetes (ORahilly et al., 1988; Porksen, 2002) as well as obese individuals
(Peiris et al., 1992), and this has been proposed to play a pathogenic role in the progression
of diabetes (OMeara etal., 1993). Therefore, it can be reasoned that this is the result of
downregultion of gap junctions as well as a reduction in (3-cell to (3-cell proximity due to
infiltration of a-cells and other immune cells, which is known to occur in hyperglycemic
conditions (Sorenson et al., 1997; Sheridan etal., 1988).
The gap junction channels which electrically couple (3-cells are formed by six
identical connexin-36 (Cx36) transmembrane proteins, which mediate ionic currents and
the diffusion of small molecules (ref from 3). As a result, Cx36 gap junctions are the sole
means of electrical coupling between (3-cells in the islet (Benninger et al., 2008; Ravier et al.,
2005), and in the absence of Cx36, isolated islets do not exhibit coordination in
[Ca2+]i oscillations (Benninger, 2011) or pulsatile insulin release (Benninger et al., 2011;
Drews et al., 2010; Ravier et al., 2005). When islet architecture is altered, a concomitant
impairment of insulin secretion and [Ca2+]i is observed, which recovers as soon as contact
among cells is re-established (Halban et al., 1982; Bertuzzi et al., 1999). Underscoring the
importance of coupling, (3-cells from intact islets exhibit several-fold the glucose-stimulated
insulin secretion (GSIS) at elevated glucose compared to dispersed (3-cells (Lernmark, 1974;
16


Halban et al., 1982). Recently, we have shown that the dimensionality of the coupling (2D
vs. 3D) alone can explain the better response of highly coupled islets and have developed a
novel simulation-based mathematical model to explain such behavior (Hraha, etal. 2013, in
submission).
Similar to patients with type II diabetes, Cx36 knockout mice were glucose
intolerant and had reduced peak amplitude of the insulin pulse as measured through
plasma insulin levels (Benninger et al., 2008; Head et al., 2012). Since this effect was also
found in the isolated islets ex-vivo, this pathology is thought to be islet-specific. Therefore,
since Cx36 is also the sole means of coupling in humans islets (Serre-Beiner etal., 2009), a
reduction in Cx36 gap junction conductance would help explain the symptoms seen in type
2 diabetics.
Using a model of Cx36 knockout mice, Head and colleagues found that in the
absence of Cx36, the heterogeneity in [Ca2+]i oscillations is indicative of some (3-cells
exhibiting transient repolarizing events even high glucose. This is in contrast to the
sustained elevations in [Ca2+]iin the presence of Cx36. This can help to explain the decrease
in mean [Ca2+]i concentration at high glucose stimulation in the absence of Cx36, and points
to the role of gap junctions in maximizing the effectiveness of the GSIS (Head, et al., 2012).
Gap junction coupling has also been found to coordinate behavior at low blood-
glucose concentrations by having a hyperpolarizing effect. This is a desirable characteristic
because secreting insulin at levels of low blood glucose would drive the system into a
deeper state of hypoglycemia. Benninger etal. has demonstrated a similar [Ca2+]i response
to glucose in Cx36/ islets and isolated (3-cells suggests gap junctions are the predominant
mechanism present to suppress elevations in basal [Ca2+]i that rise due to cellular
heterogeneity in mice expressing a Katp transgene (Benninger etal., 2010). Therefore, an
17


understanding of coupling between (3 cells via gap junctions is imperative for understanding
the pathogenesis of the disease as well as understanding the challenges of creating islets de
novo.
(i-Cell Heterogeneity
The unique feature of the beta cell, essential for its ability to serve as the bodys fuel
sensor, is the presence of Katp channels. As discussed previously, the activity of these
channels sets the membrane potential of the (3-cell and this determines its electrical
sensitivity to blood glucose and therefore its secretory activity. For this reason, the Katp
channel inhibitor sulphonylureas has been used for over 70 years to treat treat type 2
diabetes (Gerstein, 2008).
In contrast to the highly synchronized islet, isolated (3-cells show a considerably
variable glucose response. Isolated (3-cells exhibit heterogenous and irregular responses to
clucose for many variables, including NAD (P)H elevations (Bennett et al. 1996), [Ca2+]i
oscillations (Zhang etal. 2003) and the dynamic range of insulin release (Vanschravendijk,
et al. 1992). This demonstrates that a high degree of electrical coupling exists between (3-
cells in the islet to create synchronous oscillations in [Ca2+]iand insulin release. Recent
evidence has actually suggested that the origin of [Ca2+]i waves in intact islets is actually due
to heterogeneity in (3-cells population (Benninger etal. 2008). Heterogeneity in
[Ca2+]i oscillations occurs in both dissociated (3-cells (Zhang et al. 2003) and islets lacking
gap junctions (Ravier etal., 2005; Benninger etal., 2008). Therefore (3-cells within the islet
are intrinsically heterogeneous in terms of the electrical response to glucose, and gap
junction acts to uniformly suppress any subthreshold response.
18


Overview of Relevant Mathematical Models ofp-cell Electrophysiology
Mathematical modeling is useful in biology to unify theories, fit data to statistical
models, identify mechanisms from disparate data, and to predict tests. Physicists have used
modeling for centuries to explain phenomena, however most biologists are just recently
beginning to employ detailed models to inform their research (Winters, 2012). Because of
its complex dynamics as well as measurable outcomes, the electrophysiology of the (3-cells
lends itself quite readily to mathematical treatment and therefore much work has been
done on the subject.
The Chay-Keizer model is a minimal mathematical model which describes the
bursting behavior of 2-dimensional clusters of pancreatic (3-cells. The model is minimal in
that it includes only the basic set of processes that lead to burst oscillations: voltage-
regulated K+ channels, Ca2+-activated K+ channels, voltage-regulated Ca2+ channels, and
glucose-stimulated efflux of Ca+2 from the cytosol. With these basic processes the model
produces burst oscillations with features like those observed experimentally. The Chay-
Keizer model also describes the evolution of the cytosolic Ca2+ concentration (Chay &
Keizer, 1983).
Although commendable for its ability to simulate (3-cell bursting using simple
dynamics, the Chay-Keizer model is a bit too simplistic to capture all of the complex
dynamics underlying membrane potential. One of the criticisms of the Chay-Keizer model is
that in its original form, it is unable to account for some of the variation in calcium
dynamics; namely that experimental evidence has suggested that calcium levels plateau
quickly, rather than in the stepped fashion seen in the model. Also, it is unable to accurately
account for both high and low frequency [Ca2+]i components (Keizer etal., 1991). This has
been somewhat remedied by the addition of an endoplasmic reticulum component to the
19


[Ca2+]i dynamics. Another qualm was that it does not include a glycolytic component. Since
the bursting patterns of [Ca2+]iis due to intracellular ATP levels, Bertram et al. introduced a
model in which the conductance of Katp channels varied with observed oscillation in
glycolysis (Bertram etal., 2000).
Though the previous models are reported to fit experimental data nicely, they still
do not include components of the model which (as we have seen) explain much of the
behavior seen in (3-cells: coupling, cAMP and heterogeneity. The Bertram group solved one
of these by creating what is called the phantom burster model. The authors considered a
mechanism which allows single cells to fire on both the slow (1-5 seconds) and fast (1-2
minutes) scales (as is seen in experimental data of single cells) (Bertram etal. 2000). Since
there is no pacemaker cells initiating the burst, and instead it is a function of the collective
behavior, it has been termed the phantom-burster.
To introduce coupling, Sherman etal. considered many Chay-Keizer-like cells
coupled together, thereby creating a 'supercell with a very high coupling conductance
(Sherman & Keizer, 1990). Importantly, they demonstrated that coupling a silent cell with a
cell undergoing periodic oscillations may result in bursting at the network level as the
network passes between both solution types. However, the model did not account for any
heterogeneity and needed values of conductance parameters that were much higher than
what has been previously reported.
Heterogeneity in (3-cells is an inherent physiological property that intercellular
coupling must overcome. In their 2008 paper Benninger et al. studied coupled cells based
on the previously mentioned phantom burster model. They introduced heterogeneity into
their network by randomly distributing the electrical coupling strength between adjacent
cells. Therefore, a given cells membrane potential is affected by its surrounding cells
20


potential as a function of heterogeneous coupling strength. Additional heterogeneity was
introduced through Katp sensitivity and metabolic flux (ATP production). They found that
the model predicts traveling waves of calcium levels amongst the network, which was
consistent with experimental data. In addition, it was able to explain how large numbers of
heterogeneous (3-cells can couple to form a coordinated syncytium at both high and low
glucose (Benninger etal., 2008).
Although the effects of gap junction coupling and [Ca2+]i remain to be uncovered,
cAMP nonetheless plays an important part in GSIS and deserves adequate mathematical
treatment to help elucidate its behavior. Recently, Ni, etal. published an extremely elegant
model of cAMP dynamics based off of an [Ca2+]i-cAMP-PKA oscillatory / regulatory circuit.
The model was able to predict the effects of numerous channel inhibitors for different
endpoints, which were confirmed by experimental data (which was also not a trivial
undertaking), ffowever, as impressive as their model was, it was only in single cells and
therefore misses much of the dynamics which underlie cAMP signaling.
Therefore, although the understanding of (3-cell dynamics has been greatly
enhanced from these models, a full working model of GSIS is still a far-off goal. To fully
elucidate the mechanisms underlying GSIS and to create a set of endpoints for which
engineered islets can be based, a full working model is needed.
Applications of Transgenic Mouse Models
In pancreatic (3-cells, the Katp channel is a critical link in the pathway of glucose-
induced insulin release. According to this paradigm, a high intracellular ATP/ADP ratio
inhibits Katp channels, causing membrane depolarization. This induces Ca2+ entry though
21


VDCCs and initiates events leading to subsequent exocytosis. Conversely, a lower ATP/ADP
ratio during a fasting state relieves inhibition of the Katp channels, resulting in membrane
hyperpolarization and suppression of Ca2+ activity. The dependence of channel activity on
intracellular ATP underlies the physiologic role of the Katp channel by coupling the
metabolic status of a cell to electrical activity.
The recent discovery of numerous mutations in pancreatic Katp channel subunits
(both the pore-forming Kir6.2 and SUR1) in human patients with persistent
hyperinsulinemic hypoglycemia of infancy (PHHI) further establishes the link between
suppressed Katp activity and the corollary metabolic disorder of /jyperinsulinism (Huopi, et
al., 2002). PHHI-associated Katp mutations can be classified into two major categories: those
which suppress channel activity without altering cell-surface expression, and biosynthetic
or trafficking defects that reduce or abolish surface expression. In both cases, reduced
Katp channel activity is expected to result in constitutive depolarization, persistently
elevated [Ca2+]i, and unregulated insulin secretion (Huopio, et al., 2002). Although a few
cases can be treated with the Katp channel opener drug diazoxide, but the majority of cases
require surgical removal of almost all of the pancreas (de Lonlay, et al., 2002).
Genetic suppression of the Katp channel has been undertaken previously to better
characterize its role by alteration of the KIR6.2 and SUR1 subunits. Miki et al. developed a
transgenic model expressing a dominant-negative KIR6.2 mutant which perturbs the
structure of the KATP pore forming unit which renders it non-functional (Miki, etal., 1998).
Although these (3-cells from these mice showed reduced Katp currents and an increase in
resting membrane potential, they also showed no glucose-induced insulin secretion and
therefore developed neonatal hyperglycemia and experience extensive (3-cell apoptosis.
22


To circumvent this issue, Koster etal. developed another KIR6.2 mutant which
showed suppressed pancreatic Katp currents as adults, in contrast to neonates (Koster, etal.
2001 PNAS; Koster et al., 2000). In their model, there was ~70% penetrance of the
KIR6.2 [AAA] mutation, meaning transgenic overexpression and incorporation of the
nonfunctional KIR6.2 subunit in approximately 2/3 of (3-cells in a particular islet will exhibit
no measurable KATP channel activity. This reduction in overall Katp conductance lead to
reduced resting membrane potential and a loss of hyperpolarizing. Therefore, these mice
exhibit hypersecretion of insulin leading to a left-shift of the insulin dose-response curve
(Koster, etal., 2000 & 2001). However, since this does not lead to a dominant negative
phenotype with no Katp activity (like in other models), hyperinsulinemia and the onset of
diabetes is markedly delayed.
In contrast to loss-of-function Katp mutants associated with hypersecretion of
insulin, mutations in Katp subunits that reduce sensitivity to inhibitory ATP (gain of
function) give rise to the corollary disease, diabetes. To test this, Koster et al. created
mutants by truncating the 30 N-terminal amino acids (KIR6.2[AN2-30]), and combined this
with a point mutation at amino acid 185 (KIR6.2[K185Q]), hence KIR6.2[AN2-30,K185Q],
This combination results in mutant subunits with a ~30-fold reduction of ATP sensitivity
(Koster, et al., 2000). Since Katp channels are formed as tetramers, each with a SUR1 and
KIR6.2 subunit, overexpression of the KIR6.2 will yield SUR1 as rate-limiting. Therefore,
KIR6.2[AN2-30,K185Q] subunits will be incorporated accordingly and result in a partial
'functional knockin of the transgenic product. The effects of transgenic expression were
profound and included early onset diabetes characterized by reduced serum insulin levels
and dramatically elevated blood glucose (Koster et al, 2000).
23


In addition to KAtp transgenic models, Cx36 knockout mice have also lead to a greater
understanding in how (3-cells suppress and coordinate activity. For example, Benninger, et
al. have found at sub-threshold glucose conditions Cx36-/- had spontaneous Ca2+ activity in
~50% of (3-cells, whereas wild-type islets remained quiescent (Benninger, et al., 2011).
In intact Kir6.2 [AAA] islets, (3-cells exhibit essentially normal [Ca2+]i and insulin
secretion responses to glucose (Rocheleau et al. 2006). Therefore the maintained cell-cell
contacts in these islets acts to suppresses the expected elevations in [Ca2+]i and insulin
release at low glucose due to the Katp mutation. These islets therefore allow us to quantify
and further distinguish how gap junctions and other means of cell-cell communication can
specifically regulate basal electrical activity and insulin secretion in the intact islet They
also allow us to verify and fit our models to better explain how cell-cell contact suppressed
basal [Ca2+]i dynamics and insulin release.
To test this, we can investigate islets in which electrical activity has been perturbed
by the mosaic expression of a loss-of-function or gain-of-function mutations in
Katp channels (Koster et al. 2000; Rocheleau et al. 2006), in addition to Cx36 knockout In
these mouse models, elevations of basal [Ca2+]i and insulin secretion due to the Katp loss-of-
function are suppressed by mechanisms dependent on cell-cell contact in the intact islet
These islets therefore allow us to specifically study how cellular differences in electrical
activity in the intact islet are suppressed by gap junction coupling and other mechanism
dependent on cell-cell contacts, as well as to understand how these mechanisms apply to
mathematical modeling of the islet architecture.
24


Islet Transplantation
Currently, the best treatment option for patients with type 1 diabetes is islet
transplantation from cadaveric donors. Since they are the only cells known to secrete
insulin in response to elevated blood glucose, (3-cells can be transplanted by a variety of
methods to reduce insulin-dependence of diabetic patients. Partial pancreas transplants
were first attempted in the early 1900s. However, it was not until the historic Edmonton
study described 7 type I diabetics who became insulin-independent after as isolated islet
transplant that this procedure initiated a new arena of research. In this study, patients were
injected with isolated whole islet preparations into the portal vein, where the islets lodge in
the vasculature. By being in a high-flow digestion-related system, graft islets are then
capable of physiologically regulating insulin secretion. However, despite the wide-spread
promise of this procedure, many complications remain with regards to its efficacy.
In the United States, it is estimated that there are 12,000 potential islet donors per
year. However, when consent, time and isolation efficiencies are taken into account the
number drops to 3,000 (Rother & Harlan, 2004). Barriers to the effectiveness of transplants
include not only the availability number of donor islets, but also post-transplant graft
viability. Normally, pancreatic islets have a dense capillary network that entails blood
perfusion which is 10 times higher than that of the exocrine pancreas (Fung et al. 2007).
This not only allows the islet to be sensitive to changes in blood glucose, but also maintains
the high metabolic demand of the islets. However, during the process of isolation and in
vitro culture pre-transplant, islet vasculature dedifferentiates or degenerates (Brissova &
Powers 2008). Immediately after transplantation the pancreatic islets are supplied with
oxygen and nutrients solely by diffusion. Therefore, in the early post-transplant setting of
the portal vein the centers of larger islets can become hypoxic and necrotic. It is estimated
25


that 50-70% of the transplanted islets will be lost in the immediate post-transplantation
period (Lehmann et al., 2007; MacGregor et al., 2006), with the hypoxic conditions of the
portal vein combined with the energy status of the islets being major contributor (Ryan et
al., 2002). Consequently, most patients require multiple transplants (2-4 in most instances),
further reducing the number of available pancreata (MacGregor et al., 2006). Taken
together, the statistics show that our current transplant protocols are only ~25% effective
at using the ~6,000 available donors to treat the 1,000,000 type I diabetics in the United
States (Hirshberg etal. 2003). However, by increasing the post-transplant viability of donor
islets the efficacy can be increased.
Other than cadaveric islets, many other potential sources of (3-cells have been
discussed in scientific literature, though the chasm between promise and reality remains
large. Three potential sources that have seen much discussion are expanding (3-cells in-
vitro, other-species transplantation (xenograph) and differentiation of stem cells into (3-
cells. Though research should be maintained, issues with each remain, for example: no
group has been able to reliably propagate isolated islet cells; immunoreactivity and ethical
questions remain around xenographs; and issues remain around the efficacy potential
malignancy of differentiated stem cells (Rother & Harlan, 2004; Hirshberg, et al, 2003;
Shaprio, et al.; 2000). In addition, none of these options address the complex cell
architecture that will be necessary for a proper GSIS. Therefore, it can be argued that
pursuing option which make human islet transplant more effective poses the highest
immediate potential for addressing the islet deficiency.
It has historically been noted that large islets >200pm in diameter do not survive in
culture as well as their smaller counterparts, developing necrotic cores while smaller islets
showed little core damage (MacGregor et al., 2006). Recently, it has also been shown that
26


smaller islets show a much better insulin response (MacGregor et al., 2006; Chan et al.,
1999), and perform better in hypoxic and normoxic culture (Lehmann et al., 2007).
Previous work has also demonstrated that large isolated islets have poor oxygen
utilization, poor survivability following isolation, and secrete less insulin than small islets
when normalized for the same volume (Williams et al. 2009). When diabetic rats were
transplanted with a marginal mass of large islets, none of them became insulin independent.
In contrast, when an equivalent mass of small islets was transplanted into diabetic rats,
80% became insulin independent and remained that way for the 2 month duration of the
experiment (MacGregor etal., 2006).
Subsequently, Lehmann et al. determined that small human islets had a higher
survival rate during both normoxic and hypoxic culture conditions with a preferential loss
of large islets after 48 hours in hypoxic culture. Ultimately, they demonstrated better
performance of human islet transplants with a higher percentage of small versus large islets
(Lehman, et al. 2007).
A Japanese study (Kaihow et al., 1986) reported that small islets far outnumber
large islets in the human pancreata, but constitute only a small percentage of the total islet
volume. Since large islets make up the largest percentage of overall transplant mass, but
also die with the highest probability, it stands to reason that transplants could be made far
more efficient if the large islets could be re-aggregated into smaller islets of optimal size, or
sizes, which allow for proper diffusion of nutrients and maximum insulin response.
27


Engineering Islets
Multiple methods have been reported for aggregating or re-aggregating pancreatic
primary cells and other insulin-secreting tumor cells lines, however most have not given
control of the aggregate size, thus preventing the issues discussed above. Recent work by
Bernard, et al. has shown that using a novel hydrogel-based device, they were able to
reform aggregates of mouse insulinoma cells (MIN6) of controlled sizes ranging from
100pm to 250pm in diameter with high precision. In addition, cell viability showed positive
results using confocal imaging (Bernard, et al. 2012). Using photolithography to create high-
density polyethylene glycol (PEG) microwells of defined precise diameters, cell aggregates
can be formed from dissociated pancreata after culture for ~7 days. Our group has recently
shown that these aggregates have similar Ca2+ dynamics, however caution must be taken.
Despite the promise that such advancements hold, when re-aggregating an organ as
complex and reliant on cell-cell communication as the Islet of Langerhans, data must first
prove that cell coupling and electrophysiology are similar to intact organs. Though popular,
simply measuring insulin release can be a crude way to determine viability. Though
accurate, it is impossible to simulate the different conditions of the transplant environment
However, if we can verify that the inner workings of these organs are intact, we can have
more confidence in the procedure and its promise for the future. Therefore, this data needs
to be backed by mechanistic and mathematical modeling to support further research into
human applications.
28


Percolation Model
Complex network models describe a wide range of systems in nature, and are
increasingly used to describe complex intra- and intercellular behaviors. In recent years,
they have been used with some success to describe how interacting dynamical systems be
they neurons, power stations, weather or (3-cells behave collectively given their individual
dynamics and coupling architecture (Strogatz, 2001).
Random graphs were first studied by famed mathematician Paul Erdos. In their
model, Erdos and Albert Renyi define a random graph as N randomly positioned nodes (or
points) which are connected by n edges (or lines). Two nodes are connected by an edge
with a probability p, and a histogram of the edges per node (or degree distribution) follows
a Poisson distribution (Erdos and Renyi, 1959; Bollobas, 1981). Although seemingly simple,
this models probabilistic properties have led to many breakthroughs in the study of
complex systems.
An interesting finding of random graph theory is the probabilistic clustering
behavior of the nodes at different values of p. Specifically, percolation theory predicts the
existence of a critical probability pc such that below this probability the network is
composed of isolated clusters of nodes, but above pc a phase transition occurs and a giant
cluster begins to span the network. See figure 12A for example of sub-pc clustering and
emergence of the infinite network. Above Pc, this cluster is called an infinite network since it
diverges as the lattice size increases (Albert & Barabasi, 2002).
In contrast to random graph theory, percolation theory starts with a regular d-
dimensional lattice of nodes which can only connect to adjacent nodes. Similar to random
graphs, an edge is present between two adjacent nodes with a probability p and absent with
29


a probability 1-p. For example, in a 2-dimensional square lattice, a node can form edges
with its 4 adjacent nodes and for the 3-dimensional cubic lattice 6 edges can be formed all
with a probability p. An alternative 'site percolation model posits that all edges are present,
but nodes are occupied with probability p. However, in applications to islet and cell
coupling architecture, the bond percolation model is more appropriate since all nodes
(cells) are present, but not electrically coupled (Benninger, et al. 2008).
Since islets are highly vascularized and contain ~20% non-excitable cells, two (3-
cells in close proximity (and potentially adjacent) may not be directly coupled via gap
junctions. In addition, heterogeneity in connexin-36 coupling may lead to adjacent (3-cells
being in different coupling environments. Thus, these aspects of islet architecture lend
themselves to description through a percolation model.
Percolation theory has previously described the properties of randomly coupled
resistor networks and how these properties can alter the behavior of [Ca2+]i in coupled
systems of (3-cells (Benninger, et al. 2008). For instance, the electrical conductance across
an islet or cluster of (3-cells is proportional to the number of unique paths that can traverse
the network. Then a p=0.75 indicates a 75% chance of adjacent (3-cell to (3-cell connections,
and a 25% reduction from maximum conductance of the cell network. As network
connections are increased from some p < pc, the number of paths increases until the system
reaches criticality and an infinite percolating structures forms. Thus, in percolation pc is the
probability below which no percolation can occur and is dependent on the lattice
architecture and dimension.
A principle property of percolation theory is that even the most general percolation
problem in any dimension obeys a scaling relation near the percolation threshold. These
scaling laws are heavily dependent on the architecture and dimension of the node lattice.
30


For example, an element of the scaling hypothesis is that the correlation length (?;) for a
given cluster diverges near the percolation threshold according the following power law:
^(P)~|P-Pel-17 asp^pc
Where the critical probability pc is dependent on the lattice architecture and the
critical exponent v is dimensional-dependent. The correlation length ^ is a measure of the
mean cluster radius and scales with the power law given for cluster size (not shown). Thus,
since their size does not scale with their radius to the dimensional power but rather a
separate power law, finite percolation clusters have been proven to be fractals for p < pc
(Kapitulnick, et al., 1983; Albert & Barbasi, 2002). Further, the percolation probability P,
denoting the probability that a given node is part of the infinite cluster is given by
P~(p~ Vc)P
which scales as a positive power of p pc for p > pc. Therefore, it is 0 for p = pc and increases
for all p > pc. Conversely, the average size of finite clusters ((s)-Q within the percolation
network can be calculated on either side of the pc, and obeys
(s)r~\P ~Pc\~Y
diverging for p -> pc (Stauffer & Aharony, 1994).
Although there are many elegant scaling laws which describe cluster size
distributions, node correlation length, and intra-cluster coupling of percolation lattices -
which have been successfully used to approximate islet electrical coordination (Benninger,
etal. 2008) these laws only hold for p -> pc (Stauffer & Aharony, 1994). Therefore, for
discrete cellular networks with p away from pc, percolation-based simulations (which were
historically used to find most of these scaling laws) offer the best mode of model fitting.
31


Percolation theory was first applied to model the synchronization of islet
electrophysiology in a paper by Benninger, et al. Using connexin-36 homozygous knockout,
heterozygous and wild type mice (which theoretically correspond to p = 0, 0.5 and ~1,
respectively), they were able to demonstrate how disruptions in inter-cell connectivity can
lead to erratic behavior of (3-cells. In both experimental and computational models, a ~50%
decrease in mean coupling conductance was able to disrupt wave propagation and reduce
overall synchrony in (3-cells.
Considering both wave velocity and proportion of cells in the islet showing
synchronized [Ca2+]i dynamics, they found experimental data fit a percolation model of cell
coupling compared to an ohmic model which posits that all cells are coupled and overall
coupling is mediated by individual differences in coupling conductance. Furthermore, their
model found that p = 0.85 optimally fit experimental wild-type data, indicating that under
normal physiological coupling, 85% of neighboring (3-cells are electrically coupled, which is
in sound agreement which previous data on islet coupling (Moreno, et al., 2005) and the
proportion of non- (3-cells in the islet (Brissova, etal. 2004).
Application of percolation theory to (3-cell dynamics also predicts a phase-transition
which can be characterized in both 2D and 3D. For example, since the theoretical Pc =
0.2488 for a 3D cubic lattice (which has been shown to appropriately match coupled (3-cells
in the islet), ~25% of normal physiological coupling will be insufficient to maintain a
synchronized syncytium of (3-cells. Therefore, Ca2+ would not be able to propagate across
the whole islet to coordinate [Ca2+]i oscillations and insulin dynamics atp similar to p = 0 or homozygous knockout Cx36 mice.
Since a loss in insulin pulsatility is often seen in type II diabetics and obese
individuals (Porksen, etal. 2002 ; Peiris, etal. 1992) the effects of coupling probabilities and
32


phase transitions may play a previously understated role in the progression of diabetes as
well as the underlying properties of multicellular dynamical systems in general. In addition,
this model predicts that at alternative dimensions the differences in coupling alone (even at
the same p) can explain the differences in synchronized [Ca2+]i behavior.
33


CHAPTER II
MATERIALS & METHODS
Cell Culture and Aggregate Formation
Mouse insulinoma 6 (MIN6) cells (P28-36) were maintained in DMEM
supplemented with 10% FBS, 1% penicillin-streptomycin, 0.2% fungizone, ImM sodium
pyruvate and 60pM 2-mercaptoethanol. Media was changed 3 times per week and cells
were passaged at~70% confluency. For passage and seeding, MIN6 cells were briefly
washed in Hanks balanced salt solution (HBSS) and then treated with 0.05% trypsin/EDTA.
The trypsin was deactivated with growth media. For 2-dimensional aggregates MIN6 cells
were seeded at ~4,000cells/mm2 in glass bottom dishes (MatTek) which aggregate over 5
days in culture.
Three-dimensional (3D) cell aggregates were formed using hydrogel micro well cell
culture arrays as previously described (Bernard etal., 2012). Briefly, cell microwell arrays
were formed from a prepolymer solution of 10.8 wt% polyethylene glycol (PEG) diacrylate
(Mn~3,000 Da, synthesized as previously described (Lin et al., 2009), 4.2 wt% PEG
monoacrylate (Mn~400 Da), 0.5 wt% 4-(2-hydroxyethoxy)phenyl-(2-hydroxy-2-
propyl)ketone (Irgacure 2959), and HBSS (Figure 1A). Hydrogel microwells were
polymerized to glass slides treated with (3-acryloxypropyl)-trimethoxysilane (Gelest) by
chemical vapor deposition (Kloxin et al., 2010). Well dimensions were defined by
photoinitiation of the prepolymer solution through chrome photomasks (Photo Sciences,
100 pm x 100 pm (wlOO), 200 pm x 200 pm (w200), and 300 pm x 300 pm (w300) wide.
34


A
B
C
O
PEG400A (75 moi%)
o
PEG3000DA (25 mol%)
Figure 1: Formation of hydrogel devices for aggregating MIN6 cells. A) Photocrosslinkable
prepolymer solution (red) consisting of 15 wt% macromere (75mol% PEGA0.4kDa,
25mol% PEGDA3 kDa), 0.5 wt% photoinitiator 12959, and 300 mM methacryloxyethyl
thiocarbonyl Rhodamine B in Hanks balanced salt solution was placed between a glass slide
and a chrome photomask separated by spacers (tan) of defined thickness. B) Microwells
formed after ultraviolet light exposure (350-450 nm) for 60 s had been covalently attached
to the functionalized glass slide. C) Representative confocal image of a microwell device
(width and height = 100 mm) in both the x-y plane (top) and x-z plane (bottom). Scale bars
represent 100 pm. PEGDA, poly(ethylene glycol) diacrylate.
Inc., Torrance, CA) to form wells (Figure IB & C) that were approximately 100 pm deep and
MIN6 cells were seeded into the wells at a density of 520,000 cells/cm2 in wlOO devices and
940,000 cells/cm2 in w200 and w300 devices using centrifugation as described previously
(Bernard et al., 2012). The devices were rotated on an orbital shaker for 2 hours and then
cultured under static conditions in growth media for 5 additional days. 3D aggregates were
removed from the microwell devices using a gentle flow of media and selected for
experiments using a Leica SL30 dissection microscope (Figure 2).
Prior to the formation of primary cell 3D aggregates, fresh isolated islets were
incubated overnight in RPMI (Invitrogen) supplemented with 10% FBS, 1% penicillin-
streptomycin, and 0.2% fungizone. To disperse individual cells, islets were twice digested in
a solution HBSS with 0.05% trypsin for 30 minutes and centrifuged to collect the cells. The
final cell suspension was then seeded on to preformed 100 pm x 100 pm (wlOO), 200 pm x
200 pm (w200) devices and aggregates were formed as explained above.
35


B
C
Figure 2: Formation of MIN6 aggregates. Aggregates of MIN6 cells in poly(ethylene glycol)
microwell devices. Cells were seeded at a density of 3xl06 cells / ml followed by
centrifugation. To visualize, cells were stained with CellTracker Green before seeding and
confocal images were taken 5 days after seeding (A-C) and after removal (D-F). Well widths
are 100pm (A, D), 200pm (B, E) and 300pm (C, F).
Insulin Secretion
Cumulative, static insulin secretion was measured in order to investigate
correlations with the [Ca2+]i behavior. Two and three-dimensional cell aggregates were
formed as described above and cultured for 5 days. MIN6 cell clusters were conditioned in
Krebs-Ringer Buffer (KRB, 128.8 mM NaCl, 5 mM NaHC03, 5.8 mM KC1,1.2 mM KH2P04, 2.5
mM CaCl2,1.2 mM MgS04,10 mM Hepes, 0.1% BSA) containing 2 mM glucose for 1 hour
prior to the glucose stimulation assay. Aggregates were then incubated in KRB containing
either 2 mM glucose (low glucose), 20 mM glucose only (high glucose), or 20 mM glucose
and 20 mM TEA (+TEA) for one hour. Supernatant from each sample was collected and
stored at -70C until testing. Supernatant samples were tested using a sandwich ELISA per
the manufacturers instructions (Mercodia). Total insulin secreted was normalized to basal
secretion levels.
36


Microscopy
To measure [Ca2+]i dynamics, 2- and 3-dimensional aggregates were stained with
4pM Fluo4-AM in imaging medium (125mM NaCl, 5.7mM KC1, 2.5mM CaCD, 1.2mM MgCD,
lOmM Hepes, 2mM glucose, and 0.1% BSA, pH 7.4) at room temperature for 60-90 minutes
before imaging. 2D aggregates were imaged in glass-bottom dishes, and 3D aggregates
were imaged in polydimethylsiloxane (PDMS) microfluidic device, the fabrication of which
has been previously described (Rocheleau, et al., 2004). Real-time imaging was performed
on a Nikon Eclipse Ti equipped with a humidified environmental chamber maintained at
37C. Fluo4 fluorescence was imaged with a 2 Ox 0.8NA objective, using a Xenon-arc lamp
light source (Sutter) and 470/20 filter for excitation and 525/36 filter and a CCD camera
(Andor Clara) for fluorescence detection. Aggregates were allowed to equilibrate after each
treatment for 10 minutes before imaging at 1 frame/s for 15 minutes, with negligible
photobleaching observed.
Matlab Analysis
In signal processing, cross correlation is the measure of similarity between two
waveforms with a time-lag, or phase shift, applied to one of them. To calculate [Ca2*!
coordination of a cell cluster, a cross correlation function was used to determine the level of
similarity of the waveforms generated by the fluorescent intensity of the imaging time
course. The average fluorescent intensity of a selected area of the cell cluster or aggregate
was used as the reference waveform and then the cross correlation was performed between
this reference waveform and the fluorescent intensity waveform of each pixel in the cluster
(Figure 3A). The cross correlation function measures waveform similarity by sliding one
37


wave function across the other and calculating the integral of the overlapping area. At each
interval a cross correlation coefficient is calculated in this way, with 1 indicating perfect
overlap and 0 indicating none. For example, a cross correlation coefficient of 1 would
indicate that a certain pixel is in perfect synchronization with the reference area, whereas a
coefficient of 0 means there is no similarity. The maximum cross correlation coefficient was
used as a measure of similarity and a value above 0.75 was used as a threshold as to
whether a certain cell was correlated with the cell cluster or aggregate as a whole.
Therefore, the total area of the cluster with a cross correlation coefficient above 0.75 was
used as a measurement for the overall correlation, or synchrony.
The information describing cell synchronization and areas of coordination is
represented as a false color hue-saturation-value image where the hue (color) represents
the cross correlation coefficient or period of oscillation, saturation (the amount of color) is
set to one and value (intensity) represents the average fluorescence intensity in order
visualize cell localization.
Based on the presumption that the cumulative standard deviation of the fluorescent
intensity of a silent cell will be much less than that of an active cell, the mean and plus three
times the standard deviation of the 'silent cell fluorescent intensity was compared to the
total standard deviation of the measured fluorescence intensity of each pixel in the rest of
the cluster. If the standard deviation in fluorescence of a pixel was higher, it was deemed to
be active. This was accomplished by a custom-written program which would calculate the
standard deviation of the fluorescent intensity across the entire time course of a selected a
silent cell, then compare that with every pixel within the entire cell cluster. Silent cells were
selected by looking at a cells fluorescent waveform in a software package (Nikon Elements).
38


Figure 3: Explanations of computational methods. A) Cross correlation analysis calculates a
sliding integral of the overlap between the test wave (blue) and the stationary reference
wave (black). The maximum cross correlation coefficient is achieved at the point of
maximum overlap. B) Sample power spectrum from experimental data. Power robustness
was calculated by normalizing the maximum value of the AC component with the maximum
value of the DC component.
Only cells with relatively flat responses were used as the silent cell reference. The
size of each cluster or aggregate, as well as the regions of coordination within them, was
determined by manually tracing the boundaries in a custom written Matlab program, which
then tabulated the pixels within the boundaries. Average cell size in both two dimensional
aggregates and three dimensional clusters were also determined and found to be
approximately 14pm in diameter, which is in agreement with previous work (Ni, et al.
2010). To determine aggregate cell number, the radius was found from the area and then
used to calculate volume using a spherical formula, which was then divided by the volume
of a single cell. Two dimensional cell cluster area was found by dividing the total area of the
cluster by the area of a cell.
To determine whether there is a maximum distance over which cells are coupled, a
Matlab program was written to calculate the Euclidian distance of over which cells in a
cluster were coordinated. A cell within a cluster was isolated by tracing its boundaries and
the average fluorescent intensity was calculated over the entire time course to give a
representative waveform of that cells. A cross correlation was performed between that
39


reference waveform and each other pixel in the cell cluster and a value higher than 0.75
indicated that that pixel was correlated with the reference cells. Therefore, the distance
over which the pixels maintained a coefficient higher than 0.75 was used as a measure of
the correlation distance of the cells.
To extract data regarding phase and period, a Fourier Transform was performed on
the fluorescent intensity profile of each pixel. The power spectrum from the Fourier
Transform tells us how much of the fluorescent signal is at a particular frequency. For
example, in a sine wave where there is one frequency, there would be a single impulse. In a
noisier signal of the same average fluorescence intensity there may be multiple peaks
corresponding to multiple frequencies in the signal, though the area under the spectrum
will be the same. The DC component of the power spectrum, located at the zero frequency,
corresponds to the average value of the signal (Figure 3B), and is typically removed
(Najarian & Splinter, 2012). To measure the robustness, or regularity, of the period in [Ca2+]i
oscillations, the maximum value of the power spectrum with the DC component removed
was normalized to the maximum value of the power spectrum with the DC not removed to
normalize for the variability in fluorescent signal (Figure 3B). The maximum value of the
power spectrum was also used to find the period of oscillation for each pixel, which was
then mapped (using the HSV format explained above) to investigate coordination in
frequency of [Ca2+]i oscillations.
Wave propagation was determined by selecting two cells within a two dimensional
cluster or three dimensional aggregate which were separated by approximately 100pm and
measuring the temporal offset between successive identical parts of a [Ca2+]i wave. The
velocity is calculated in the direction of the wave propagation by dividing the exact spatial
separation by the temporal offset of the [Ca2+]i wave.
40


All statistics were performed in Matlab ( Mathworks, Natick, MA). For comparison of
two means, Students t test was utilized. For comparison of multiple means, ANOVA was
utilized. To compare determine whether linear relationships existed between a variable and
cell number, a linear regression model was used.
Development of KIR2.1 and Connexin-36 Knockout Mice
Mutant KIR6.2 [AAA] constructs containing green fluorescence protein (GFP) were
generated by replacing the tripeptide sequence 132GFG134 of the ion selectivity filter
KIR6.2 with nonpolar alanine residues. After verifying functional expression in a (3-cell lines
through transient transfection, constructs were purified and microinjected into fertilized
mice eggs. Transgenic mice were identified through PCR on using GFP-specific primers
(Roster et al., 2000; Roster etal., 2001). To establish a stable line, one RIR6.2[AAA] founder
was identified and bred back to littermates.
Bond Percolation Simulations for Size-Scaling and Dimensionality Comparisons
Bond percolation is a sub-model of percolation theory in which for a given lattice of
nodes (cells) adjacent nodes are connected (coupled) with a probability p, or not connected
with a probability (1-p). This is in contrast to site percolation, in which all edges are present
but nodes only exist with a probability p. In a 2D or 3D aggregate all cells are present;
however, whether the cells are coupled varies according to size-scaling and dimensionality
laws. Therefore, a bond percolation model was established to model cellular coordination
on a 2D square lattice or 3D cubic lattice where each node (cell) is capable of establishing
connections with its 4 or 6 adjacent neighbors, respectively. The bond percolation lattice
41


Figure 4: Overview of bond percolation lattice. A) Visual representation a cubic lattice with
bonds to all 6 nearest neighbors, representing a p = 1. B) Visualization of the llxllxll
lattice created for the percolation model in Matlab at p = 0, representing the nodes only
without cells. The left panel is a top view demonstrating the equal spacing for edges, which
are not present. C) Visualization of the 5x5x5 lattice created for the percolation model in
Matlab at p = 0, representing the nodes only without cells. The left panel is a top view
demonstrating the equal spacing for edges, which are not present
was developed in Matlab with a matrix of alternating values of 1 (node) and 0 (site for
potential edge bond). Probabilities were randomly assigned to each edge bond point. If the
probability was less than or equal to the assigned percolation probability (p), an edge was
established and the 2 neighboring nodes were deemed coupled. An identification number
was assigned to each individual cluster formed from coupled edges, and the edges were
then removed to establish clusters based solely on node coupling (Figure 4A, second panel).
High Glucose (Synchronization) Simulations
Simulations of high glucose coupling were carried out with a custom MATLAB
routine based on a previously published method (Kapitulnik, et al. 1983). Two dimensional
clusters of 25x25 nodes were populated with edge probabilities based on a Gaussian
42


200 400 600 800 1000 1200 1400
Aggregate Size (Cell Number)
Figure 4: Summary of resistor network model. A) False-color simulation of cluster size for
bond percolation with p below (left) and above (middle) the critical probability. (Right)
Resistor network showing behavior above the critical probability. B) Simulations and
experimental data of oscillation synchronization for values of p at high glucose in 2D. C)
Simulations and experimental data of [Ca2+]i activity for values of p at low glucose in 2D. D)
Simulations and experimental data of [Ca2+]i activity for values of the percent of cells within
a cluster necessary to suppress [Ca2+]i activity of the entire cluster (Sp) in 2D. E)
Simulations and experimental data of oscillation synchronization for values of p at high
glucose in 3D. F) Simulations and experimental data of [Ca2+]i activity for values of p at low
glucose in 3D. G) Simulations and experimental data of [Ca2+]i activity for values of the
percent of cells within a cluster necessary to suppress [Ca2+]i activity of the entire cluster
(Sp) in 2D.
distribution and clusters were formed based on a whether adjacent connections had
assigned probabilities greater than, or equal to, the critical probability (Figure 5A). We next
identified the largest cluster on each of the simulated lattices and selected only those in
which the central lattice site belonged to the cluster. The mass of the percolating area, or
43


M(L), was determined by summing the connected nodes to the central cluster within
squares of area L2 around it. By averaging these over the area of the simulated cluster sizes,
we found the percolation density
p(L) =
M(L)
L2
We then deemed that if any two cells were coupled to the same network, they were
synchronized. Therefore the percolation density is analogous to the synchronized area of
each cluster. For each value of p, 1,000 simulations were run (Figure 5B) and best fit to
experimental data was determined by a chi-square test.
Low Glucose (Suppression) Simulations
In contrast to modeling high glucose [Ca2+]i activity, where all cells within a network
are deemed synchronized, low glucose modeling was based on the principle that a certain
percentage of non-responsive cells can hyperpolarize and suppress the activity of all other
cells in a coupled network. A linear fit to the experimental low glucose data showed a y-
intercept value of 67%, indicating that that there is approximately a 2/3 probability that a
given cell will be active. We then used this probability in a binomial model, which describes
the number of successes k (active cells) in a number of trials n (total cells in a cluster), with
each success having a probability p (67%). Or,
Pr(A = k) = (^j pfe(l p)n~k where
(n\ n'
^k) (n k)\k\
44


After establishing bond percolation clusters as in the high glucose model, the cell
number of each cluster (n) was then determined and the probability of the cell being active
was calculated using the binomial model. For each value of p and k, 2,000 simulations were
run, and best fit to experimental data was determined by a chi-square test (Figure 5E>).
Bond Percolation Simulations for Discrete Modeling of Islet Connectivity
To examine how our mathematical model can predict islet [Ca2+]i and insulin
behavior when the system is perturbed through transgenic mutation of the Katp channel or
Cx36 gap junctions, the simulations of high glucose were run to calculate percent
synchronization as a function of p for varying cell diameters. In addition, the level of
suppression was simulated in the low glucose model for varying levels of p and the
probability of a cell being active for varying network diameters.
45


CHAPTER III
RESULTS: DIMENSIONALITY AND SIZE-SCALING OF COORDINATED
Ca2+ DYNAMICS IN PANCREATIC p-CELL NETWORKS
[Ca2+]i Dynamics and Insulin Secretion Under Two- and Three-Dimensional Coupling
Under normal physiological conditions at high glucose, (3-cells within the islet of
Langerhans undergo robust oscillations in [Ca2+]i. These individual [Ca2+]i oscillations are
synchronized through cell-cell gap junctions and results in a transverse Ca2+ wave across
the islet which coordinates pulsatile insulin secretion (Head, et al., 2012; Macdonald &
Rorsman, 2006). However, the underlying architecture and coupling has been shown to
have large impacts on this synchronized behavior.
In order to investigate how the underlying cellular architecture and electrical
coupling affects the robustness and synchronization of [Ca2+]i dynamics in (3-cells, we
analyzed [Ca2+]i time-courses in 2D cell clusters and 3D aggregates of defined size and
shape. Under 2D coupling, cell clusters generally exhibited irregular bursts of [Ca2+]iathigh
glucose, which became more regular upon addition of the Katp channel inhibitor TEA
(Figure 6A). As quantified from the robustness of the Fourier power spectrum, TEA at high
glucose was found to significantly increase the robustness of the oscillation period
compared to high glucose alone (p<0.01) (Figure 6C). This increase in regularity of the
period was expected given that blockage of the Katp channels has previously been shown to
increase resting membrane potential and therefore render (3-cells more sensitive to changes
in Vm and inter-cellular coupling (Bokvist, et al., 1990)
46


A
MJJJUUi
400 600
Time (Seconds)
2mM Glucose
20mM Glucose
20m M Glucose
+TEA
C
|IZl20mM I
M20mM+TEA|
B
iJUjUUUUULi-a
2mM Glucose
20mM Glucose
20mM Glucose
+TEA
400 600
Time (Seconds)
Figure 6: Robust [Ca2+]i oscillations and insulin release in 3D aggregates. A)
Representative [Ca2+]i oscillations, measured from Fluo-4 fluorescence, averaged over a
2D aggregate. B) As in A, averaged over a 3D aggregate of comparable size. Time-courses
are offset for clarity and vertical scale bar represents 50% change in fluorescence. C)
Mean (s.e.m.) power robustness at 20mM glucose and 20mM glucose +20mM TEA D)
Mean (s.e.m.) insulin release as % of content, normalized to release at 2mM glucose.
Data in C averaged over n=28 (2D) and n=22 (3D) aggregates, and data in D averaged
over n=6 (2D) and n=12 (3D) aggregates. in C, D indicates significant difference
between glucose and glucose+TEA for power robustness (p=0.00015) and insulin
release (p=0.0166).
In contrast, under 3D coupling aggregates exhibited highly regular [Ca2+]i
oscillations both in the presence and absence of TEA (Figure 6B). The robustness of the 3D
oscillations showed no significant differences (p>0.05) upon addition of TEA and was
significantly more robust compared to 2D clusters under high glucose alone, but not 2D
under high glucose with TEA (Figure 6C).
Similarly, the insulin secretion response demonstrated a similar pattern to the
[Ca2+]ioscillation robustness. In 2D aggregates, high glucose with TEA stimulated a
significantly greater insulin secretion compared to high glucose alone. However, the
addition of TEA was not found to have an effect on 3D insulin secretion at high glucose
(Figure 6D). Therefore, this data demonstrates that the aggregation of (3-cells into
47


structures which allow for 3D coupling increases the robustness of the oscillatory [Ca2+]t
response and leads to higher levels of insulin secretion at high glucose.
Dimension and Size-Dependence of[Ca2+], Synchronization
To investigate the spatial variation of [Ca2+]i dynamics, we next measured the
synchronization of [Ca2+]i oscillations in 2D and 3D under high glucose with and without
TEA. In 2D aggregates at high glucose with TEA, oscillations were found to be synchronized
within distinct sub-regions of the cell cluster (Figure 7 A). Compared to the oscillations in a
specific cell, the synchronization of the oscillations in other cells decreased as a function of
increasing distance. Using a cross correlation function, we found that these oscillations
were highly synchronized within a radius of approximately 5 cells. However, at greater
distances there was a sharp decrease with little synchronization observed. The change was
sudden, with adjacent cells showing different oscillatory [Ca2+]i patterns suggesting they are
part of different electrophysiological coupling environments (Figure 7E>). In contrast, 3D
aggregates at high glucose with TEA showed synchronization that was consistent across the
entire cell mass (Figure 7C). Most cells showed synchronized oscillations, independent of
separation distance and position with in the aggregate (Figure 7D).
Given that cells were only synchronized within a limited Euclidean distance (~5
cells) in 2D, we anticipated that smaller 2D aggregates with less than a 5 cell radius would
show a greater proportion of cells that were synchronized. Indeed, 2D cell clusters
consisting of <20 cells were highly synchronized (Figure 7F), with a percentage of
synchronized cells that was not different compared to 3D aggregates (p<0.05) (Figure 7E).
48


A
B
C
G

200 400 600
Time (Seconds)
D
U\JlAAJ\A/\.
UUiAAAAAj
0 200 400 600 800
Time (Seconds)
Figure 7: Size scaling and dimensionality of [Ca2+]i oscillation synchronization. A) False-
color map of the cross-correlation coefficient in a 2D aggregate, relative to a reference
cell (I). B) Fluo4 time-courses in cells at increasing distance from the reference cell (II-
V). C) False-color map of the cross-correlation coefficient in a 3D aggregate, relative to a
reference cell (I). D) Fluo4 time-courses in cells well separated from the reference cell in
3D (II, III). E) Mean (s.e.m.) area of aggregate showing synchronized [Ca2+]i oscillations,
in 2D and 3D aggregates of different size ranges at 20mM glucose +20mM TEA. F)
Scatterplot of synchronization versus aggregate size, for 2D aggregates at 20mM glucose
+20mM TEA. G) As in F for 3D aggregates. in E indicates significant difference in
synchronization of larger 2D aggregates (21-200 and >200) compared to small
aggregates (<20), and a significant difference in synchronization comparing 2D and 3D
aggregates (p<0.001). Linear regression in F, G indicated by solid line, with significant
size dependence in F and G (p < 0.0001).
However, larger 2D aggregates above the critical size showed a significant reduction
in synchronization with increasing size compared to 3D aggregates containing an
equivalent number of cells (p>0.01) (Figure 7E). Interestingly, in larger 2D cell clusters
above the critical size there were multiple clusters of cells which were highly synchronized,
49


A
IV
B
|v^,



%

___AJIaI
0 200 400 600 800
Time (Seconds)
c
D
1 JWUVAAiv
" JUUV/VAAJx.
JVAAAAJVX-I
0 200 400 600 800
Time (Seconds)
Figure 8: Size scaling and dimensionality of [Ca2+]i oscillation synchronization at 20mM
glucose. A) False-color map of the cross-correlation coefficient in a 2D aggregate, relative
to a reference cell (I). B) Fluo4 time-courses in cells at increasing distance from the
reference cell (II-V). C) False-color map of the cross-correlation coefficient in a 3D
aggregate, relative to a reference cell (I). D) Fluo4 time-courses in cells well separated
from the reference cell in 3D (II, III). E) Mean (s.e.m.) area of aggregate showing
synchronized [Ca2+]i oscillations, in 2D and 3D aggregates of different size ranges at
20mM glucose +20mM TEA. F) Scatterplot of synchronization versus aggregate size, for
2D aggregates at 20mM glucose +20mM TEA. G) As in F for 3D aggregates. in E
indicates significant difference in synchronization of larger 2D aggregates (21-200 and
>200) compared to small aggregates (<20), and a significant difference in
synchronization comparing 2D and 3D aggregates (p<0.01).
supporting the notion of a defined distance over which cells can coordinate.
Synchronization in 3D aggregates also showed a size-dependence up to the 300pm
diameter, however the slope of the line was much more shallow (Figure 7G). Similar results
were seen in 2D and 3D aggregates under high glucose alone. However, the radius of
synchronization was found to be far less (~2 cells) (Figure 8).
50


A
B
0 200 400 600 800
Time (Seconds)
C
D
Period Cross Corr.
Figure 9: Localization of synchronized [Ca2+]i oscillations to discrete regions in 2D. A)
False-color map of regions of high cross-correlation coefficient in a 2D aggregate, with
respect to different reference cells. B) Fluo4 time-courses of cells within each area of
synchronization in A. C) False-color map of [Ca2+]i oscillation period in same 2D
aggregate as A. D) Mean (s.e.m.) area of oscillation period (Period) and area of high
cross-correlation coefficient (Cross corr). Data averaged over n=28 clusters. No
significant difference is observed (p=0.3147).
Therefore, this data indicates that not only can cells coordinate over a defined
region, but the size of 2D (3-cell clusters can have a significant impact on [Ca2+]i
synchronization. In addition, the dimensionality of the coupling is critical to properly
synchronize an entire syncytium of electrically excitable cells.
Sub-Regions of Synchronization in Two-Dimensional Cell Clusters
To further investigate the limiting range over which 2D cell clusters can synchronize
[Ca2+]i oscillations, we measured the extent of synchronization at different positions within
cell clusters. Qualitatively, multiple non-overlapping areas of synchronized [Ca2+]i
oscillations and similar period were observed within large cell clusters (Figure 9A).
51


Importantly, regions with similar oscillation period as found from the Fourier power
spectrum overlapped strongly with regions of synchronization as found by our methods.
There was not found to be a difference between the area of synchronization as found by
either method (Figure 9D), validating the 0.75 cross correlation coefficient threshold.
Within the cell cluster, the largest area of synchronization was similar to the largest region
with similar oscillation period, with a mean size of ~28 cells (Figure 9D). In addition,
regions of similar period as defined through Fourier mapping produced similar results
compared to cross correlation mapping independent of which cell within the area was
chosen as the reference (Figure 9 A & C). This indicates that areas of synchronization are
well-defined through local interactions in 2D.
Wave Velocity Under Two- and Three-Dimensional Coupling
Calcium dynamics are synchronized within the islet through intercellular coupling,
where elevations in [Ca2+]i propagate across the islet from regions of higher glucose
sensitivity (Benninger, etal., 2008; Aslanidi et al., 2001; Bertuzzi, et al., 1999). The velocity
of the Ca2+ wave propagation has been linked to (3-cell coupling where reduced coupling
across the islet results in slower waves and less overall [Ca2+]i coordination (Benninger, et
al., 2008). To further characterize the effects of dimensionality on the coupling behavior of
(3-cells, we measured the propagation velocity in 2D and 3D. In 2D aggregates, Ca2+ waves
were confined to the sub-regions of synchronization (~100gm). As characterized by the
temporal offset of peak [Ca2+]ibetween two cells ~100gm apart, the mean wave velocity
was found to be significantly higher in 3D aggregates compared to the 2D sub-regions
(Figure 10A-C). The distribution of wave velocities was also biased to waves >50pm/s in
3D aggregates compared to a bias towards <50pm/s waves in 2D (Figure 10D).
52


Figure 10: Dimensionality affects wave propagation velocity. A) Fluo4 time-course for
two cells within a 2D aggregate separated by ~100pm, at the wave start (black) and
wave end (red). B) As in A, for time-course at the wave start and end within a 3D
aggregate. C) Mean (s.e.m.) wave velocity in 2D and 3D aggregates. D) Histogram of
measured wave velocities in 2D and 3D aggregates. Data averaged over n = 18 (2D) and
n=12 (3D) aggregates. in C indicates significant difference in wave velocity (p<0.001).
Therefore, 2D aggregates show slower propagating Ca2+ waves compared to 3D aggregates,
which further suggests that 2D cells are less coupled and that dimensionality plays an
important role in (1-cell synchronization.
Dimension and Size-Dependence of Basal [Ca2+]t Suppression
Intact islets area also characterized by a uniformly quiescent [Ca2+]iatlow/basal
glucose as a results of the suppressive hyperpolarizing effect of (1-cell coupling (Benninger,
etal., 2011; Speier, etal., 2007). Therefore, given the dependence of [Ca2+]idynamics on size
and dimensionality of the cellular architecture, we next measured whether [Ca2+]i
suppression had a similar dependence at low glucose. Under low glucose conditions (2mM),
2D cell clusters generally exhibited spontaneous, transient [Ca2+]iactivity, whereas 3D
aggregates remain quiescent. Interestingly, large 2D cell clusters consisting of >200 cells
were mostly quiescent, showing similar activity to that measured in 3D aggregates
53


B
100
A
I I 2D
c
Figure 11: Size scaling and dimensionality of [Ca2+]i suppression at low glucose. A) Mean
(s.e.m.) area of aggregate showing transient [Ca2+]i elevations in 2D and 3D aggregates
of different sizes at 2mM glucose. B) Scatterplot of transient [Ca2+]i elevations versus
aggregate size, for 2D aggregates. C) As in B for 3D aggregates. in A indicates significant
difference in transient [Ca2+]i elevations of small 2D aggregates (<20) compared to larger
aggregates (20-200, >200), and a significant difference in elevation comparing 2D and
3D aggregates atmoderate size (20-200, p<0.001), but not veiy large clusters (>200,
p>0.05). Linear regression in B,C indicated by solid line, with significant size dependence
in B (p < 0.001), but not in C (p > 0.05).
(p<0.001)(Figure 11A). However, smaller 2D cell clusters were found to be more active
compared to 3D aggregates of similar cell number and larger 2D cell clusters (p<0.001).
In the smallest 2D aggregates, 67% of the cells showed a transient [Ca2+]i elevation with a
progressive decrease in activity with increasing cluster size, suggesting that (3-cell
suppression is size-dependent 2D (Figure 11B). In contrast, 3D aggregates showed a size-
independent suppression with ~20% active cells over the entire range of sizes measured,
up to 300pm diameter (Figure 11C).
54


A
B
D
_100
£
T3 80
.j3
§ 60
I 40
w
g20
< 0

E
100
? 80
| 60
s
n 40
£
< 20
l-p = 0.360I
300 600 900 1200 1500
Aggregate Size (Cell Number)
-p = Q.323|
<,
300 600 900 1200 1500
Aggregate Size (Cell Number)
Figure 12: Coupled resistor network model of size scaling and dimensionality. A)
Simulated networks for different probabilities of resistive coupling connections (p),
where low numbers of connections give sub-critical behavior with multiple sub regions
of connected units (left) but high numbers of connections give super-critical behavior
with connecting units spanning the entire network (right). B) Simulation and
experimental data of oscillation synchronization for 2 values connection probability p.
Circle represents experiment, solid blue line represents p=0.27 (x2 = 8.01) and solid red
line represents p=0.32 (x2 = 3.89). C) Simulation and experimental data of transient
elevations with p=0.32 (x2 = 12.31). Each line represents an average over n=2000
simulations.
Network Lattice Model of [Ca2+]iDynamics
As previously outlined, a lattice resistor model has been used to accurately describe
the dependence of [Ca2+]idynamics on coupling strength between (3-cells (Benninger, et al.,
2008). Therefore, we next set out to put our results in mathematical context by testing
whether such a model could describe the size and dimensional-dependence of synchronized
[Ca2+]ioscillations and suppression. Our initial methodology centered on using established
power laws which describe the average size of a cluster, the average correlation distance
55


and percolation probability of a random percolation network. However, using this approach
we could not accurately reproduce our experimental results, especially in the 3D case. This
is most likely due to the fact that these power laws only obey the scaling relation near the
percolation threshold, which is pc=0.5 for 2D square and pc=0.2488 for 3D cubic lattices.
Therefore, to circumvent the scaling relations, we simulated partially coupled
resistor networks covering different sizes over 2D and 3D for a given proportion of node
(cell) connectivity. In a 2D network for sub pc (p<0.5) connectivity, multiple small clusters
of connected nodes were generated which were similar to the sub-regions of synchronized
oscillations measured in 2D aggregates (Figure 12A). For higher connectivity (p>0.5) in 2D
and 3D, a single cluster of connected nodes emerged which spanned the whole network.
This network-spanning behavior was similar to the uniform synchronization seen in
3D aggregates at high glucose and suggests that the network model simulations can be
related to [Ca2+]i oscillation synchronization: (3-cells are synchronized if their corresponding
nodes belong to the same connected cluster, with an unbroken path traced between the
nodes.
We next tested whether this network model could quantitatively describe the [Ca2+]i
oscillations synchronization, as well as reconcile the differences seen with regards to
dimension and size. We initially simulated low connectivity 2D networks for varying p. As
predicted by previous percolation work, as p decreases from pc multiple fractal clusters
begin to form (Kapitulnick, etal., 1983). Ap=0.320.005 generated multiple synchronized
clusters with a mean size of 28 nodes, which is similar to the experimentally determined
number of cells in the largest synchronized cluster in 2D networks. Following Kapitulnick,
et al. we then measured the proportion of nodes in the largest synchronized cluster relative
to the total network for varying network sizes (9 to 441 nodes on a square lattice). A
56


p=0.312 (95% Cl: 0.284-0.337) generated a size variation which best fit the experimental
2D synchronization data (Figure 12B)and is in close agreement with the p describing the
number of cells in a 2D synchronized region.
The scaling laws of percolation theory are proven for infinite networks and
therefore become more applicable as the network size becomes very large (n -> oo). Based
on the power law concerning characteristic cluster size
(ns) = \p-pc\~Y
a p=0.253 was found to generate an average cluster size of 28 cells, which is outside of the
95% confidence interval bounds found by simulation. However, when the simulation was
run to best fit data for >250 cells, a p=0.277 generated a best fit Therefore, as cluster size
increase in the 2D model the behavior may better converge to that of the scaling laws.
In the 3D model, a p=0.369 (95% Cl: 0.334-0.423) generated a size variation which
best fit the experimental synchronization data (Figure 12D), which is in sound agreement
with the 2D model as demonstrated by the overlapping 95% confidence intervals.
Therefore, taken together this data shows that the size dependence of multiple independent
parameters representing [Ca2+]i oscillations at high glucose can be quantitatively described
by the lattice resistor network model. Of note is the fact that both cases generated similar p,
indicating the probability of coupling may be conserved across dimensions. However, this
value of p corresponds to sub-critical, fractured percolation in 2D and super-critical
percolation in 3D.
We next tested whether this same network model could also describe the
suppression of spontaneous [Ca2+]i elevations at low glucose. Inexcitable (3-cells can
suppress the activity in excitable (3-cells through gap junctions electrical coupling (Head, et
57


al., 2012), and therefore also lends itself to description through the percolation model. To
determine whether cells were active or silent within the model, we defined a rule were a
threshold proportion of the inexcitable cells within a connected cluster can suppress
activity in all cells in the connected cluster. Based on our experimental measurement that
67% of single cells are active, binomial statistics were used to determine whether there
were sufficient inexcitable cells to reach the suppression threshold. Naturally, as n becomes
large the probability of the entire cluster being quiescent increases.
In both 2D and 3D there was a strong agreement between experimental data and
network model with a threshold of 15% inexcitable cells, whereas the data was best fit by
p=0.378 (95% CI:0.354-0.398) in 2D (Figure 12C) andp=0.323 (95% CI:0.302-0.346) in 3D
(Figure 12E). Therefore, not only can the size-dependence of spontaneous [Ca2+]i
suppression can be quantitatively described by a lattice network architecture, but the
values of the percolation probability were found to be similar to those that describe high
glucose [Ca2+]i oscillations.
58


CHAPTER IV
RESULTS: REAGGREGATION OF PRIMARY ISLET CELLS INTO
PSEUDO-ISLETS' OF DEFINED SIZE BY MICROWELL CELL CULTURE
Primary Islet Cells Uniformly Aggregate to Defined Sizes in 3D PEG Microwell Arrays
Islet transplant is currently the best option in the treatment of type I diabetes.
However, recent work has shown that even though large islets make up the majority of the
transplant mass, limited post-transplant diffusion often causes the islet centers to become
necrotic, which leads to reduced transplant efficacy. Therefore, a method to disperse and
then re-aggregate large primary islets into 'pseudo-islets of smaller dimensions, as well as
similar cellular composition and function, could drastically increase the efficacy of islet
transplants.
Towards this goal, primary murine islets were dispersed by trypsin digestion and
seeded into square PEG microwells with diameters of 100pm and 200pm. After 5 days of in-
vitro culture seeded cells naturally formed tight aggregates within the microwells (Figure
13A). The 3D structure was verified through nuclear staining followed by confocal
microscopy (Figure 13B). Primary cells clustered were relatively uniform in size and with
dimensions that scaled with the microdevice well dimensions. To assess the uniformity and
scalability of primary cell aggregates formed using microwell devices, the aggregate
diameter was measured using confocal laser scanning microscopy combined with further
image analysis. The average aggregate diameters were found to
59


DAPI z-stacks
A Post-Seeding 5 days of culture After Removal C
Device Size Pseudo-islet size (N = 2,
n = 100)
100 pm 60 pm 15 pm
200 pm 95 |im 15 pm
Live/Dead
Figure 13: Primary islet cells form viable 3D pseudo-islets of defined size in PEG
microwells. A) Formation of pseudo-islests. Bright field images taken 1 day after seeding, 5
days in culture and after removal from the devices. B) Table of pseudo-islet sizes for each
PEG micro well diameter. C) Confocal images of pseudo-islets stained with the fluorescent
nucleic acid stain DAPI to demonstrate 3D structure. D-E) Live/Dead staining of D) whole
islets as well as E) 100pm and F) 200pm pseudo-islets on day 7. Green fluorescent cells are
live while dead are red. All scale bars represent 100pm.
depend on the cross sectional area of the micro wells, with wlOO aggregates having a
diameter of 6015pm and w200 aggregates w200 aggregates having a diameter of
10015pm (Figure 13C). Therefore, the diameter of the aggregates was 50-60% of the
microwell diameter. The mean diameter of all normal islets analyzed was 15321pm (n =
21).
60


A
Day 1
Day 7
B
/W\/'vJVw\AArl/\/\VVA/^^ Day 14
0 100 200 300 400 500
Time (Seconds)
Day 7
Day 14
0 100 200 300 400 500
Time (Seconds)
Figure 14: Pseudo-islets show more robust [Ca2+]i oscillations compared to age-matched
normal islets. A) Representative [Ca2+]i oscillations, measured from Fluo-4 fluorescence,
averaged over entire normal islets for on day 1, 7 and 14. B) Representative [Ca2+]i
oscillations, measured from Fluo-4 fluorescence, averaged over pseudo-islets on day 7
and 14, which are days 1 and 7 removed from the micro well devices, respectively. C)
Normalized power robustness for normal islets (bottom line) and pseudo-islets (top
line) on days 1, 7 and 14. Error bars represent SEM, indicates a significant difference
between groups at the same time point and t indicates a significant difference within the
same group compared to the previous time point
Pseudo-Islets Show Comparable Viability and Functionality to Fresh Islets
Islets exist in a unique, highly vascularized environment in-vivo, and generally do
not show optimal function or viability after long-term in-vitro culture. Since the re-
aggregation procedure takes 7 days, the post-aggregation function and viability is of
concern. After 7 days in culture, both the wlOO and w200 sized pseudo-islets demonstrated
similar viability to day 1 normal islets (Figure 14 A, B & C). As a percentage of total cells,
wlOOs and w200s comparable viability to day 1 normal islets (p<0.05)(Figure 14D).
61


Therefore, the re-aggregation procedure was not found to have a significant effect on the
overall viability of primary islet cells.
To examine the function of the pseudo-islets, we used a similar procedure to the
MIN6 aggregates. Time courses of [Ca2+]i dynamics were analyzed for overall
synchronization across the entire cell mass as well as robustness of the oscillation period.
Activity at low glucose was also examined to determine if there was proper electrical
suppression.
At llmM glucose, the [Ca2+]i dynamics of the pseudo-islets was highly synchronized
(~88.354.02%). This was very similar to control Day 1 normal islets (~84.056.03%),
suggesting that functionality and proper gap junction coupling was properly re-established
after 7 days in culture. When grouped by well size, the W200s were found to have a higher
area of synchronization compared to the WlOOs (P<0.05) (Figure 16D), although neither
group was significantly different compared to normal islets (P>0.05). The area of
synchronization for normal islets at day 1 at llmM was also in agreement with previous
results using an analogous method (Benninger, et al.). Pseudo-islets had very regular [Ca2+]i
oscillations which mimicked Day 1 normal islets; when quantified, day 7 pseudo-islets had a
normalized power robustness that was not found to be different than Day 1 normal islets
(0.02480.0003 vs. 0.02320.0048, respectively)(p>0.05)(Figure 15C). Taken together, this
data indicates that after 7 days in culture the islet re-aggregation procedure was able to
maintain proper islet dynamics, comparable to freshly harvested islets.
62


Figure 15: Pseudo-islets show better superior functionality over time. A) False-color map
of the cross-correlation coefficient in a 3D aggregates, relative to a reference cell. B) Area
with synchronized [Ca2+]i dynamics (as defined as the area with a cross correlation
coefficient > 0.75) for normal islets (bottom line) and pseudo-islets (top line) on days 1, 7
and 14. Error bars represent SEM, indicates a significant difference between groups at the
same time point and t indicates a significant difference within the same group compared to
the previous time point. C) Area synchronized found as in B for W100 and W200 pseudo-
islets. indicates a significant difference between groups. D) Islet area active at low glucose.
Day 7 and 14 Pseudo-Islets are Better Than Age-Matched Normal Islets
A major concern in islet transplantation is post-transplant graft survival. It has been
reported that ~50% of islets become necrotic after transplantation. Since this is the issue
we intend to address with this procedure, long-term function is of concern. Therefore, we
compared [Ca2+]i endpoints for Day 7 (1 day removed from the microwell device) pseudo-
islets to batch-matched normal islets which were cultured in parallel for 7 days. We then
did the same comparison on Day 14.
When compared to normal islets one day post-harvest, pseudo-islets one day
removed from the microwell device (day 7) showed much more robust and coordinated
[Ca2+]i oscillations despite the fact that both groups had spent 7 days in culture. At 14 days,
the oscillatory behavior of the pseudo-islets remained synchronized while the normal islets
63


maintained their deteriorated behavior (Figure 15). Indeed, when the robust of the
oscillations were quantified a significant reduction in robustness was seen in day 7 normal
islets compared to day 1 normal islets (p<0.05). In contrast, day 7 and 14 pseudo-islets
were not found to be different from day 1 normal islets (p<0.05).
After 7 days in culture, normal islets were found to have a significantly reduced area
of synchronization compared to Day 1 normal islets (84.056.03% vs. 25.855.82%,
respectively) ( p<0.001) (Figure 16B). However, day 7 pseudo-islets were found to function
similar to normal day 1 islets, with significantly higher synchronization (p<0.001) (Figure
16B). After 14 days in culture, normal islets were still unresponsive with overall
synchronization not significantly different from the normal day 7 islets, which was poor
(p>0.05). Surprisingly, pseudo-islets were found to have comparable synchronization to
Day 7 pseudo-islets and remained markedly better than the normal islets (p<0.001).
At 2mM glucose, Day 7 normal islets had higher transient [Ca2+]i activity compared
to Day 1 normal islets (data not shown). Pseudo-islets at day 7 and 14 were also found to be
comparatively quiescent, showing similar activity at low glucose to normal day 1 islets
(p>0.05) (Figure 17C). Taken together, the high and low glucose data indicates that while
the normal islets were decreasing in function pseudo-islets were maintaining or increasing
functionality. In addition, the low glucose data specifically indicates that gap junctional
conductance may be leading to greater suppression of transient [Ca2+]i activity.
Summary of Results
We found that using precision-controlled PEG microwells to reaggregate normal
islets resulted in viable pseudo-islets with defined shape and size. We then tested their
64


viability by analyzing the synchronization and robustness of their [Ca2+]t dynamics. While
day 1 normal islets demonstrated viability that was in line with previously published
results, day 7 and 14 normal islets showed a significant deterioration in viability.
Conversely, day 7 pseudo-islets (which are one day removed from the microwells) showed
viability and functionality which resembled day 1 normal islets. Pseudo-islets from 100pm
sized wells were also found to be slightly less synchronized than those from 200pm sized
wells. Surprisingly, pseudo-islets continued to show high levels of viability and
functionality at day 14, suggesting that the reaggregation procedure impacts the long-term
behavior of islet cells in some way.
65


Chapter V
RESULTS: PERCOLATION MODELING PREDICTS LOW-GLUCOSE
BEHAVIOR OF Katp CHANNEL GENETIC MUTANTS
In pancreatic (3-cells, the Katp channel is provides a link between cellular
metabolism (intracellular ATP concentration) and membrane potential. In a low glucose
state, the channel is open allowing the outflow of K+ ions. Increased intracellular ATP
causes the Katp channel to close and the accumulation of K+ ions creates an increase in
membrane potential which, when large enough, will activate voltage-gated Ca2+ channels.
This rapid influx of Ca2+ ions causes the membrane to depolarization. At low glucose, the
intracellular concentration of ATP in commonly not sufficient to deactivate enough KATP
channels to sufficiently increase membrane potential, however a heterogeneous
distribution of these channels makes some (3-cells more excitable at a given glucose
concentration than others. Over activity of the highly active cells is overcome by a
hyperpolarizing effect of cell-cell coupling through gap junctions.
As we have previously shown, an increase in gap junction coupling (whether
through larger 2D structures or increasing dimensionality to 3D) produces lower [Ca2+]i
activity at low glucose. We also demonstrated how percolation modeling combined with
binomial statistics can predict how active a given cluster will be. Using genetic mutations
which can decrease
66


A
100
B 100
p = o
p = 0.1
p 0.2
p = 0.3
p = 0.4
p = 0.5
p = 0.6
p = 0.7
p = 0.8
p 0.9
- p = 1.0
p
p
exc
Figure 17: Percolation model predictions for transgenic mouse models. A) Percent of islet
cells active at low glucose as a function of p (gCOup) for variable percentage of excitable cells
in the islet (pexc). B) Percent of islet cells active at low glucose as a function of peXc for
variable p. For both simulations the step size was 0.05 with an n=500 and the percentage of
cells necessary to suppress the entire islet was 15%.
(loss-of-function) or increase (gain-of-function) Katp function, we set to further test the
percolation model by using a forward model2.
Model Predictions
Using previously acquired data from mice expressing transgenes for Cx36 and the
Katp channel, we were able to compared perturbed experimental systems to our theoretical
model. As previously shown, mosaic expression of the KIR6.2[AAA] transgene, which
renders the pore-forming subunit of the Katp channel non-functional, makes 70% of the cells
functional knockouts (Koster et al. 2001). In terms of our model this means 70% of cells will
be active at low glucose. These mice were crossed with Cx36 knockout mice to yield
different levels of gap junction conductance (gcoup), which is represented by the percolation
probability p in our model.
2 A forward model is based on prediction, in contrast to the reverse paradigm where the model is fit
to the data retrospectively. Since the reverse model was used in chapter 1 to fit the model
parameters, we now use the same tool to predict the behavior when the wild type system is
perturbed.
67


Figure 18: Percolation modeling fits experimental data from Katp loss-of-function islets. A)
Plot of percent cells active versus p for peXc = 0.7, corresponding to the theoretical cells
active for KIR6.2[AAA] islets. The data was normalized to a wild type p = 0.45, represented
by the area within the box. B) Normalized model plot C) Scatterplot of percent of cells
active at low glucose in mice as a function of coupling conductance (gCOup) from Cx36
knockout mice with further gap junction inhibition. D) Fit of model to experimental data.
For C and D, points represent the mean SEM.
Predictive activity of the KIR6.2[AAA] knockout islets from these mice at different
levels of coupling conductance (or levels of Cx36 knockout) were simulated through the low
glucose percolation model using a 3D cubic lattice of diameter 11. This diameter was chosen
based off the average islet having a diameter of ~150gm and the average cell having a
diameter of ~10-20pm. Therefore, an average islet is 10 cells across, but since the model
requires there to be a central cell in each lattice 11 was chosen. The threshold of quiescent
cells to silence a cluster was set at 15%, which was previously found to provide the best fit
for the MIN6 data. Although the effect of this parameter was not found to have a very
substantial effect on parameter fit, it is within the 10-30% range as previously reported. For
each simulation on this lattice the predictive activity was found for each p (gcoup) at different
levels of cell excitability (pexc). Since incorporation of the KIR6.2[AAA] trangsgene renders
70% of cells in the islet active, pexc = 0.7 for this transgenic model. The resolution (or step
68


size) for each variable was 0.05 and simulations were run for n=500. The standard
deviation of the predictions for each simulation was low, varying by less than 10% of the
mean (corresponding to <1% SEM).
For a given peXc below 85%, the model showed the percent active cells in the islet
would also decrease as a function of p (Figure 17A). However, when peXc>0.85 there are not
enough quiet cells to suppress the activity (since 15% are required) of the overactive (3-cells
and the islets become constitutively active. In our experimental model where pexc = 0.7, this
predicts that when gCOup = 0 the islet will be 70% active and this will decrease as gCOup is
increased.
The model was then run as a function of pexc for variable p to describe the behavior
of a gain-of-function Katp mutant In mice expressing the KIR6.2[AN2-30,K185Q]-GFP
transgene, the Katp channel becomes ~30 times less sensitive to ATP and is therefore
overactive. This creates a hyperpolarizing current in expressing (3-cells so that membrane
potential never increases enough to activate the voltage-dependent Ca2+ channels. This
inhibits [Ca2+]i activity and renders them under-active. The expression of the KIR6.2[AN2-
30,K185Q]-GFP transgene is inducible and dependent on the dosage of the inducing agent
tamoxifen and can be quantified by GFP penetrance. Therefore, this gives us a model to
predict low glucose activity as a function of pexc for a given p.
For levels of p (or gCOup) below pc the percent of active cells at low glucose increased
linearly as pexc was increased. This is expected given that the many small clusters seen when
p pc = 0.2488 the behavior
becomes
69


A
B C
Figure 19: Percolation modeling fits experimental data from KATP gain-of-function islets.
A) Theoretical plot of percent cells active at low glucose as a function of percent of cells
excitable for previous estimations of p for wild type islets. B) Scatterplot of plasma insulin
versus the fraction of excitable for KIR6.2[AN2-30,K185Q] expressing islets. C) Fit of model
to experimental data.
markedly different The percent active cells remain relatively quiescent at low peXc and
critical behavior appears atpeXc -> 0.8, where above this level of activity the islets overcome
any suppressive effects and become highly active. For p = 0.3-0.4, there were still enough
uncoupled cells to increase the percent cells active as Pexc was increased up to the critical
point, but for p > 0.4 the percent cells active remained very low until pexc ~ 0.8 (Figure 17B).
Cell Activity as a Function of Coupling Conductance in KIR6.2 [AAA] Mice
In KIR6.2[AAA] mice ~70% of (3-cells are constitutively active and therefore a model
parameter from our simulations of pexc = 0.7 should fit the experimental data best (Figure
18A). However, since wild type islets do not have a p = 1, but a value somewhere between
0.3-0.4 as was shown in MIN6 aggregates and previously for high glucose synchronization
(Benninger et al. 2008), the simulation data is normalized to wild type conductance (Figure
18B). A wild type conductance of p = 0.45 was found to best match the experimental data
and if plotted in Figure 18B. When plotted, percent cells active at low glucose follows a
trend very similar to that of the normalized simulation plot (Figure 17C), and when plotted
70


with the theoretical data they match very closely (Figure 17D). Only one data point was
found to have a SEM which did not include the theoretical line. The model was also able to
capture the behavior of the experimental system at low gCOup (p) and high. In addition, it
nicely explains the rapid drop in percent cells active follows by more asymptotic behavior.
Cell Activity as a Function of Excitability in KIR6.2[AN2-30,K185Q] Mice
Simulations of gCOup for varying percent cells active found that for a p within the
range of what was previously found (p = 0.3-0.4), there would be low activity in the islet up
to the point where ~80% of the cells are active. However, when activity goes beyond that
point there will be a transition accompanied by a rapid increase in the percent cells active
(Figure 19A). This increase corresponds to the number of cells required to suppress
transient activity at low glucose (15% in our model), and the simulations will therefore be
very sensitive to this parameter. For instance, if this threshold was set to 25% instead of
15% the critical point would occur around 70-75% instead. As the number of active cells
increases, there will be a point above which there are not enough quiescent cells by
percentage to suppress. In our model this point was 85% (100%-15%). When using plasma
insulin in fasting mice as a measure of islet activity at low glucose, the data was found to
follow a similar patter as that described by the model for p between 0.3 and 0.4 (Figure
18B). Though incomplete in the 60-90% range, as activity of the (3-cells increases through
reductions of inducible KIR6.2[AN2-30,K185Q] expression plasma insulin normalized to
wild type levels shows low levels of activity combined with a sudden increase. When plotted
with the theoretical data, there is sound agreement at low percent cells active and the
location of the phase transition (Figure 19C).
71


Summary of Findings
After fitting our model of islet connectivity to the MIN6 2D/3D data retrospectively,
we wanted to test if we could predict the behavior of wild type islets as parameters of the
model were perturbed. The model found that for increasing values of p (when peXc = 0.7)
there would be a sigmoidal-like decrease in the percent cells active at low glucose. Using
data acquired from transgenic variants we were able to fit data from Katp loss-of-function
KIR6.2 [AAA] (which have ~70% of cells active) very well when normalizing to a p = 0.45.
When simulations were run as a function of peXc for variable p, the range of p values which
were found to approximate MIN6 aggregates had a small size dependent increase in activity
up to a critical point at ~80%, above which the islets became highly active. Similarly, the
experimental data was found to fit the theoretical data. Taken together, these results
demonstrate that the experimental data from transgenic mice can be fit using the same
percolation model, albeit with a p for wild type conductance which was slightly higher than
the MIN6 aggregates.
72


CHAPTER VI
DISCUSSION AND FUTURE DIRECTIONS
Dimensionality and Size-Scaling of Coordinated [Ca2+]i Dynamics in p-cel Is
The importance of cell-cell communication is a recurring theme in physiology and is
integral to the proper function of multiple biological systems. In the pancreas, the islets of
Langerhans show coordinated [Ca2+]i oscillations and propagating Ca2+ waves at elevated
glucose mediated by Cx36 gap junctions. These electrical dynamics are critical for the
underlying dynamics of insulin release and glucose homeostasis. In addition, gap junction
coupling also coordinates a suppressive effect at low glucose, preventing non-essential
insulin release which has been shown to be a contributing factor to the progression of type
II diabetes (Benninger, etal. 2011; Tisch etal. 1996).
Utilizing a hydrogel microwell array to generate 3D (3-cell aggregates of defined size,
we examined the dependence of [Ca2+]i dynamics on size and dimension by comparing the
[Ca2+]i dynamics to 2D cell cluster sheets. Previous work has modeled the islet architecture
as a partially coupled lattice resistor network to quantify the dependence of these dynamics
on the level of gap junction coupling. Since this model was established for multiple network
mesh sizes and dimensions, we were able to take it a step further to quantify multiple
aspects of size-scaling and dimensionality of (3-cell [Ca2+]i dynamics.
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Insufficient fi-cell Coupling in Two-Dimensions
In our model, when MIN6 (3-cells were coupled within a 3D architecture, they
showed significantly more robust [Ca2+]i dynamics compared to a 2D architecture. This
included more robust oscillations, increased oscillation synchrony between cells and faster
Ca2+ wave propagation across the cell structure. Within this 3D architecture, MIN6 cells
showed similar responses to previously reported values for intact islets, with similar wave
velocities (72pm/s6 vs. 69pm/s5, respectively) and oscillation synchronization (962%
vs. 912%, respectively) (Benninger, etal., 2008). Since the MIN6 aggregates are composed
of solely coupled (3-cells, compared to intact islets which are ~80% (3-cells and ~20% non-
coupled cells, this could explain the increase in both wave velocity and synchronization.
However, the closeness of the two values can be reconciled with our percolation mode.
Since both systems would be estimated to have behavior above the critical probability, a
20% reduction in resistors or cells would have a negligible effect on total synchronization.
This is exhibited by figure 5E, in which there is a distinct transition from p=0.2 to p=0.3
(pc=0.2488) and with only a ~15% change over a range of p=0.3-1.0. The closeness of the
values also indicates that MIN6 aggregates can serve as a sufficient model system in which
to examine the effects of coupling.
When the coupling architecture is reduced to 2D, the behavior of the cell cluster
becomes qualitatively similar to islets showing a loss of coupling. There is a marked
reduction in synchronized oscillations which are restricted to defined sub-regions,
propagating Ca2+ waves slow (Benninger, etal., 2008), and basal [Ca2+]i activity is elevated
(Benninger, et al., 2011). In intact islets, patch-clamp data has shown (3-cells are electrically
coupled to ~6 neighboring cells (Zhang, et al., 2008). Since this the degree of connectivity
for each node in a simple cubic lattice, this architecture is suitable to model islets.
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Therefore, by reducing the dimensionality from 3D to 2D there is a ~33% decrease in total
coupling to adjacent neighbors by reducing each node degree from 6 to 4. However, this
effect becomes magnified when considering the range of which cells can couple. We
experimentally determined that MIN6 cells can couple over a 5 cell radius. Therefore, over
this range 2D allows for 5 times fewer cells with which a given cell can interact over this
range (52=5 vs. 53=125).
This is supported by the percolation model, in which the critical probability is ~25%
less in 3D than in 2D (pc=0.2488 vs. pc=0.5, respectively), meaning that 25% more
connections can be uncoupled to have a fully coupled electrical syncytium. This may also
help to explain why a disproportionately low reduction in synchronization is seen in 3D
islet networks following a >50% reduction in coupling (Benninger et al. 2008). If the p falls
further below pc in an islet through gap junction knockout and/or inhibition, there will be a
sharp decrease in overall synchronization.
In MIN6 cells, the K+ channel inhibitor TEA is conventionally used to increase
resting membrane potential, which creates more regular oscillation patterns. In fact, this
cell line was developed primarily for these properties. Therefore, we also measured size
and dimensionality scaling under treatment with high glucose alone as a control condition.
Since [Ca2+]i patterns were similar in the presence and absence of TEA, this suggests that the
size-scaling and dimensional behavior seen is more a function of intercellular dynamics
rather than intracellular events. However, upon increasing the dimension from 2D to 3D
with glucose alone, we found that there was a significant increase in period robustness of
the oscillations. This indicates that the 3D coupling architecture is vital affects MIN6 cells in
such a way where they becomes more sensitized to adjacent depolarizations at high glucose.
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At low glucose, 3D aggregates showed suppression of transient [Ca2+]t activity which
was size invariant In contrast, suppression improved with increasing cell number in 2D
aggregates, which is opposite to the size-scaling seen at high glucose. Therefore, there is not
an ideal size at which 2D aggregates can form a proper balance between high glucose
synchronization and low glucose suppression: as the cluster increases in size it becomes
better able to suppress transient [Ca2+]i activity but loses overall synchronization. This can
be qualitatively explained by considering the mechanisms of gap junction-mediated
suppression and synchronization. To be show similar synchronization behavior, cells must
be effectively coupled. In 2D aggregates cells at opposite ends of a cluster are very unlikely
to be within the same coupling environment. However, for cells in an aggregate to be
suppressed, the must only be in contact to a sufficient number of inactive cells. Cells at
opposite ends of a large cluster do not themselves need to be connected to be quiescent As
the cluster increases in size, the proportion of inactive cells increases and the network
dynamics allow for suppression to propagate over larger distances. This reveals a
fundamental and unexpected difference in the way in which cell-cell connections play a role
in the suppression of [Ca2+]i at low glucose compared to the synchronization of [Ca2+]i
oscillations at high glucose.
Network Model Describes Dimension and Size-Scaling of[Ca2+]t dynamics
To gain a better theoretical understanding of how these different behaviors emerge
from the coupling architecture, we simulated (3-cell coupling within a lattice resistor
network model. By examining network properties based on the probability of adjacent
coupling, these simulations could describe multiple aspects of the size-scaling of [Ca2+]i
dynamics, including the size of synchronized regions in 2D and 3D, the effect on dimension
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on synchronization and the change in suppression in 2D and 3D. Importantly, these models
were fit with one network connectivity parameter (p) to describe the proportion of
functional cell-cell interactions. The suppression utilized an additional parameter (Sp) to
describe the percent of inactive cells necessary to suppress the connected cluster.
In percolation theory, there are a critical percentage of connections (defined by pc)
for which a phase transition occurs and overall coupling spans the full network. This critical
probability pc=0.2488 for 3D cubic networks and pc=0.5 for 2D square networks. In our
simulation models, a phase transition is clearly visible for finite size networks >100 cells,
where there is a sharp jump in synchronization when p>pc (Figure 5). Given the similar p
which fit the 2D and 3D experimental data best (p=0.312 vs. p=0.369, respectively), 3D (3-
cell networks are super-critical where coupling spans the entire network and 2D (3-cell
networks are sub-critical, where coupling is localized to defined sub-regions which do not
span the network. This further explains how 3D aggregates are able to show high levels of
synchronization and propagating Ca2+ waves over the entire cell structure, but large 2D
clusters show very low synchronization. The fractal clustering behavior of random
percolation networks in the sub-critical phase closely mimics that of coupled (3-cell clusters,
which further supports the use of the network model (compare Figures 5E and 9C). In
addition, the model supports the idea that through the coupling architecture, a
characteristic probability alone can explain the coupling and synchronization behavior of
electrically coordinated cellular networks.
Overall, these model results demonstrate how separating details of cellular
dynamics from the system architecture can be used to discover general properties by which
cellular interactions govern the behavior of multicellular systems, which could be broadly
applicable.
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Physiological Importance of Dimensionality and Size-Scaling in Cellular
Network Architecture
Size and dimensionality play an integral role in the regulation of electrical activity in
(3-cell aggregates. Aggregates with higher dimensionality show a more coordinated [Ca2+]i
response at high glucose and enhanced suppression of [Ca2+]i activity at low glucose. This
can therefore explain the higher insulin secretion in 3D aggregates in our model, and also
explain the higher dynamic range of non-diabetic islets. Although we did not investigate the
size-dependence of insulin secretion, it has been shown to be size invariant in the 3D
aggregates (Bernard, Lin & Anseth, 2013). Furthermore, previous studies have shown that
confluent MIN6 cells (large cell clusters) show reduced insulin compared to non-confluent
MIN6 (small cell clusters) (Konstantinova, et al., 2007). In context of our data of [Ca2+]i
dynamics and insulin secretion, this indicates a key role that the underlying cellular
architecture plays in determining the efficacy of the glucose-stimulated insulin response.
The 3D aggregates we created through hydrogel microwells behave very similarly to
intact islets, which demonstrate the utility of the 3D architecture. Compared to 2D cell
clusters, 3D aggregates were able to show robust and synchronized oscillations without the
addition of TEA. Human islets have been proposed to have a number of different
architectures (Cabrera, etal., 2006; Bosco, etal., 2010), however defects which alter the
systems architecture and reduce the dimensionality over which coupling occurs would be
expected to lead to dysfunction that is similar to a loss of gap junction coupling (Head, et al.,
2012). Indeed, a loss in insulin pulsatility is often seen in type II diabetics (ORahilly et al.
1988; Porksenetal. 2002; Menge etal. 2011) and obese individuals (Periris etal. 1992),
which could potentially be the result of downregulation of gap junction proteins as well as a
reduction in cell-cell contact through inflammation and a-cell infiltration. These events are
known to occur in hyperglycemic conditions which are associated with the symptoms of
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type II diabetes (Rahier et al. 1983; Allagnat et al. 2005). Furthermore, it has been shown
that during pregnancy, an increase in gap junctional coupling is observed in islets,
coinciding with increased islet size and enhanced insulin secretion (Sorenson et al. 1997;
Sheridan etal. 1988).
Excitable cells in the human body have a small finite conductance that is dictated by
the coupling architecture of the gap junctions. Through this architecture, cells are able to
synchronize behavior across large distance through these low-conductance channels. For
example, electrical synchronization allows for our hearts to beat, muscles to move and
glucose levels to be maintained. These findings add insight into how the body is able to
achieve the optimal cellular architecture for life.
Currently the most promising treatment for type I diabetes is islet transplant and
these results are also important to consider for generating alternate sources of (3-cells for
islet transplantation. While cellular coupling will be important to enhance insulin release,
our data suggests that the architecture will also be important. Transplantation of 2D sheets
of (3-cells, as has been recently suggested, will provide insufficient coupling for well-
regulated insulin dynamics. Rather, a robust 3D architecture is necessary. This also has
important implication when seeding (3-cells onto scaffolds (Pedraza et al. 2012; Kodama et
al. 2009), since those scaffolds which promote the formation of higher-dimensional
structures will likely show enhance function. It will also be important to consider if other
factors such as revascularization, nutrient diffusion and hypoxia are dependent on
architecture. For example, it has been shown that transplanting smaller 3D islets better
reverses diabetes compared to large 3D islets in both mouse and human models (Lehman et
al. 2007). Nevertheless, our method of controlled aggregation to generate 3D aggregates of
79


controlled size (Bernard, Lin & Anseth, 2013) could be used to re-aggregate primary islets
to optimal sizes or creating islets from differentiated stem cells.
Intercellular coordination via [Ca2+]i oscillation is not unique to the islet and applies
to other neuroendocrine cell systems. For example, robust and enhanced pulsatile growth-
hormone (GH) secretion results from the coupling between GH cells and the coordination of
[Ca2+]i (Bonnefort et al. 2005; Hodson etal. 2012); where remodeling of the coupling
architecture regulates GH release in puberty (Bonnefort et al. 2005). Gap junctions couple
chromaffin cells in the adrenal medulla which synchronize [Ca2+]i transients and regulate
catecholamine release (Martin et al. 2001); where stress responses evokes a remodeling of
electrical coupling to enhance chromaffin cell excitability (Colomer et al. 2008; Hill et al.
2012). Therefore, our findings are not only applicable for the islet and may have the ability
to predict architecture and gap junction coupling changes in the pathology of other diseases.
Re-Aggregation of Primary Islet Ceils into Functional Pseudo-Islets
In the transplant environment, whole pancreas grafts are not realistic because of
rejection and functionality issues, and islet isolation procedures are thus necessary. In
addition, time delays to engraftment make culture inevitable. It has previously been shown
that the unique architecture of islets cells and vasculature is not maintained in cultured or
transplanted islets (Bosco, et al., 2010). This is not surprising given the insults sustained
during isolation, digestion, shaking and subsequent culture. Therefore, to improve the
quality to transplant tissue methods are needed to avoid these pitfalls. Here, we have
shown that long-term viability and functionality of normal islets is poor (to which the
isolation procedure may have contributed), but show that using PEG microwells to re-
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aggregate primary cells results into pseudo-islets of defined sizes leads to long-term
functionality and viability resembling freshly isolated islets.
Efforts to improve islet transplantation have begun to focus more on improved
survival rates of the transplanted islets as an adjunct to isolation techniques and
immunosuppression (Lehman, et al. 2008). It is estimated that ~50% of whole islet
transplants become necrotic, with a larger proportion of larger islets being affected. Despite
high numbers of transplanted islets, the functional capacity of the graft remains around 20-
40% (Ryan et al. 2001). Normally, pancreatic islets have a blood perfusion that is 10 times
higher than in exocrine pancreas, resulting in a significantly higher oxygen tension (Fung et
al. 2007). During the process of isolation and in vitro culture the islet vasculature
dedifferentiates or degenerates, rendering nutrient and oxygen availability to be based
solely on the limits of diffusion. Even islets which revascularize show oxygen tension that is
10 times lower that in native pancreas (Carlsson et al. 2004).
We propose a new, previously neglected parameter to improve islet function: islet
size. Islet size has been shown to be of importance for in vitro and in vivo function (Lehman
et al. 2007), and may also influence many other factors such as higher percentages of (3-
cells, higher insulin secretion per unit mass, better oxygenation and more favorable
outcomes (Lehman etal. 2007; MacGregor etal. 2006; Fungetal. 2007). Smaller islets have
also been shown to have a significantly reduced diffusion barrier, easing the effects of
hypoxia and nutrient accessibility (Mattsson etal. 2002; OSullivan etal. 2010). This is
supported by previous work showing that smaller islets have a more robust insulin
response and had better outcomes after engraftment (Macgregor et al. 2006). Therefore, by
re-aggregating larger islets into pseudo-islets of optimal islet size, the efficacy of transplants
can be significantly improved.
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Primary Islet Cells Readily Aggregate Form 3D Pseudo-Islets of Defined Size
Primary mouse islet cells have been shown to reaggregate after dispersion, however
these methods have mostly been cumbersome and inaccurate (Cavalleri et al. 2007;
OSullivan etal. 2010; Ramachandran etal. 2013). Here, we show that using
photolithography to form precisely sized PEG microwells, we can repeatedly form pseudo-
islets of defined size (Figure 14A). For both the 100pm and 200pm well diameters, pseudo-
islets were found to have a diameter which was ~50% of the microwell diameter (Figure
14B). This is expected given one of the mechanisms through which the wells create pseudo-
islets of defined size by limiting and evenly distributing the number of cells within the well.
These cells then create 3D aggregates of lesser diameters, which are similar to the
diameters of MIN6 aggregates formed using the same method (Bernard, Lin & Anseth,
2012). More importantly, the standard error for both well diameters was only found to be
15-25% of the pseudo-islet diameter (Figure 14B), indicating a high level of control
regarding size. This size control is comparable with the diameters of MIN6 aggregates using
the same method (Bernard, Lin & Anseth, 2012) and superior to flat culture aggregation
(OSullivan et al. 2010), hanging drop aggregation (Cavalleri et al. 2007) and other
micromold-guided techniques (Hwang etal. 2011; OSullivan etal. 2010). Although the
optimal size for transplanted islets still needs to be addressed, given the emphasis on islet
size in transplant viability control over this aspect will be of high importance for in-vivo
trials.
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Pseudo-Islets Show Superior Viability and Functionality Compared to
Age-Matched Islets
Directly removed from the microwells, pseudo-islets were found to have a defined
3D shape (Figure 14C) and high levels of viability (Figure 14D-F). Importantly, they also had
coordinated (Figure 16A & B) and robust (Figure 15A-C) [Ca2+]i dynamics which were
similar to freshly isolated islets (Figure 15C), indicating that 5 days in culture was sufficient
for intercellular gap junction coupling to develop. Gap junction coupling plays an important
role not only in coordinating insulin secretion at high glucose, but also suppressing insulin
secretion at low glucose which can also have a detrimental effect (Benninger et al. 2011).
As shown by [Ca2+]i activity at low glucose (Figure 16C), pseudo-islets were found to have
similar suppression to freshly isolated islets.
Interestingly, we found that pseudo-islets continued to maintain highly
synchronized and robust [Ca2+]i dynamics up to two weeks (day 14) in culture, while
cultured normal islets continued to deteriorate (Figure 15C; Figure 16B). In addition, the
suppression of [Ca2+]i activity was found to be similar to both fresh islets and day 7 pseudo
islets (Figure 16C). This is surprising given normal islets 7 days post-harvest showed
deteriorated dynamics, but pseudo-islets 7 days post-removal from the microwells showed
no such deterioration of their [Ca2+]i dynamics.
Although we were not able to determine whether the improvements seen in pseudo-
islets were based solely on changes in islet size, this could possibly explain some of the
differences seen between the two groups at day 7. While control normal islets remained in
culture under potentially hypoxic and nutrient-poor conditions, cells from pseudo-islets
were dissociated and therefore under more optimal culture conditions. This notion is
supported by the fact that even small normal islets exhibited poor viability and functionality
83


after 7 days. In addition, pseudo-islets were then aggregated to smaller sizes, allowing for
better nutrient diffusion and higher oxygen tension when functionality was assessed
through [Ca2+]i imaging.
ffowever, size differences do not seem to explain the high viability and function of
the pseudo-islets at day 14. At this time point the pseudo-islet cells had been in culture for
14 days, and were 7 days post-removal from the microwell devices the same timeframe
over which the normal islets of comparable size were found to deteriorate (data not
shown). This suggests that some aspect of the dispersion / aggregation procedure is
increasing function and viability. Future work will aim to elucidate this mechanism, but two
probable explanations are either molecular switching or a reworking of the islet
architecture into a more beneficial organization.
In rodents, dissociated islet cells have previously been shown to reaggregate in
culture to form pseudoislets with a core-mantle organization similar to that of normal
mouse islets (Cavalleri et al. 2007; Ramachandran et al. 2013). This indicates that in
rodents, information that decides the islet architecture is foremost provided by islet cells
themselves (Cirulli etal. 1993; Rouiller etal. 1991). Therefore, the intracellular mechanism
which controls cell aggregation may also be causing the cells to circumvent the cell death
seen in normal islets in culture. Indeed, a study by Beattie et al. found that dedifferentiation
of human fetal pancreatic cells is reversed by reaggregation (Beattie etal. 2000).
As supported by previous work in the literature as well as this thesis, islet
architecture plays a hugely important role in islet behavior, and a relative increase in alpha-
cells present in the central core of the islet has been reported in many animal models of
type 2 diabetes, pregnancy and obesity (Epstein et al. 1989; Bates et al. 2008; Rahier et al.
1983; Clark et al. 1988). This is often described as "disorganized islet architecture based on
84


"the prototype structure (Kharouta etal. 2009). However, it is also thought that the
architecture accompanied with increased a-cell fractions may lead to more efficient cell-cell
communication resulting in enhanced endocrine function such as increased sensitivity to
changes of external glucose concentrations (Cabrera et al. 2006; Kharouta et al. 2009). This
is supported by mouse islets containing (3-cells over expressing the glucagon receptor were
found to have increased (3-cell mass (Gelling et al. 2009).
Therefore, this offers an alternate explanation for the increased function and
viability: the reaggregation procedure may allow the incorporation of a-cells into the (3-cell
mantle thereby increasing content without disrupting gap junction connections between (3-
cells. Since the cells were taken from healthy mice, an increase in the a-cell:(3-cell ratio
associated with obesity and diabetes will not be seen. In addition, if we assume that normal
islets have a similar coupling environment to MIN6 aggregates, our percolation model can
still explain how there would not be a reduction in overall [Ca2+]i synchronization. For
example, if there was a theoretical 20% decrease in (3-cell coupling from the infiltration of
a-cells (since a-cells constitute ~20% of the islet), this would only reduce the p to 0.36*(1-
0.2)=0.288, which is still well above the critical threshold
Applications to Human Work
Although our findings in a mouse model are promising, there is currently not an
epidemic of murine diabetes in the United States. To realize its full potential, our work
needs to be applied to human transplant islets. As in the murine model, the architecture of
the human pseudo-islets will prove to play an important role in defining their function,
viability and behavior.
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Recent evidence has shown marked differences in the cellular organization of islets
in humans compared to mice. In addition to human islets having a lower percentage of (3-
cells, Cabrera, et al. have demonstrated that mice have a (3-cell core surrounded by an a-cell
mantle (mantle-core), while human islets may have a higher proportion of these cells that
are intermixed. Therefore, human islets may have much lower (3-cell coupling and may be
characterized by a lower p. For example, the Cabrera, et al. study also showed that
synchronization of [Ca2+]i dynamics was absent in human islets, but present in isolated sub-
regions. Conversely, the study has not been repeated with human islets and a ~30%
reduction in (3-cell coupling would not be enough to justify a phase-transition to sub-critical
percolation according to our model (corresponding to ap = 0.252 > pc = 0.2488).
However, observations by Bosco, et al. in the only statistically well-powered study
to date have found that small human islets (40-60gm) do indeed show a segregated mantle-
corer architecture with a-cells localized to the mantle and (3-cells predominantly forming
the core (Bosco, et al., 2010). In larger islets (60+pm) a-cells were found in the mantle, but
also within the islet adjacent to vascularized areas. They therefore proposed a model in
which (3-cells exist as sheets with a-cell edges, which fold around the vasculature of the islet
as it becomes larger than the defined sheet diameter (Bosco et al. 2010). Since smaller islets
have diameters less than the sheet diameter, the mantle-core architecture is conserved.
It is interesting to note that islets obtained from older patients in many under-
powered architecture studies (Cabrera, etal. 2005; Brissova, 2005) have shown similar
architectures to murine models of diabetes (Kim etal. 2009), and smaller islets from the
same patients often have mantle-core structures. Indeed, it has been suggested that the
heterogeneous architecture seen in older humans may represent a reorganization of the
architecture over time one that potentially contributes to diabetes (Butler etal. 2003).
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This suggests that the architecture seen in older human islets (which is the most widely
available tissue for both research and transplant) may be an effect of aging rather than
normal composition. Therefore, reaggregating donor tissue may not only create smaller,
more viable islets, but reassembling the cyto-architecture to a more non-diseased state may
also serve to further improve outcomes.
Therefore, if the reaggregation procedure is found to reorganize the islet
architecture in a way which makes transplant tissue from older patients function better,
this could pose to greatly increase the effectiveness of the donor-recipient matching. Future
experiments in both human and mouse models are currently being planned to test this.
However, even if reaggregation is unable to increase function in islets cells from aged
donors, the increase in smaller islets with higher viability as reported here may increase the
grafts chance of surviving the hypoxic insult of the portal vein.
Percolation Modeling Predicts Low-Glucose Behavior of Katp Channel Genetic Mutants
In pancreatic (3-cells, the Katp channel provides a link between cellular and
membrane potential. In a low glucose state, the channel is open allowing the outflow of K+
ions. Increased intracellular ATP causes the Katp channel to close and the accumulation of K+
ions creates an increase in membrane potential which, when large enough, will activate
voltage-gated Ca2+ channels and cause a membrane depolarization. Conversely, at low
glucose the intracellular concentration of ATP is not sufficient to inhibit enough Katp
channels to adequately increase membrane potential. However, a heterogeneous
distribution of these channels makes some (3-cells more excitable at a given glucose
87


concentration than others. Over-activity of the highly active cells is overcome by a
hyperpolarizing effect of cell-cell coupling through gap junctions.
As we have previously shown, an increase in gap junction coupling (whether
through larger 2D structures or increasing dimensionality to 3D) produces lower [Ca2+]i
activity at low glucose. We also demonstrated how percolation modeling combined with
binomial statistics can predict how active a given cluster will be given a threshold number
of inexcitable cells being able to suppress the activity of the cluster. To better understand
this important mechanism and further validate our model, we used transgenic mice
expressing altered or deficient pancreatic Katp channels that exhibit (3-cell dysfunction.
Transgenic mice with overactive Katp channels (KIR6.2[AN2-30,K185Q] transgene)
show neonatal diabetes due to permanent hyperpolarization of the cell membrane,
demonstrating the Katp channels ability to suppress insulin secretion (Koster et al. 2000).
These mice demonstrate a particularly accelerated progression from hyperinsulinemia to
diabetes as might occur in the most severe (i.e., completely Katp channel deficient) versions
of human hyperinsulinemia. Conversely, KIR6.2[AAA] mice differ significantly from the
knockout mice in that whereas Katp channels are essentially absent from 70% of beta cells,
they are present at near-normal density in the remainder. Thus, the phenotype is a partial
(i.e., cell-by-cell) knockout. Because of a partial syncytium in the islet (cells are electrically
coupled to one another), these mice should still exhibit a Katp dependence of insulin
secretion, but with the set point of electrical activity, and hence secretion, shifted toward
lower glucose concentration (Koster etal. 2002).
Previously, we have shown that in a single (3-cell (or very small group of (3-cells)
were coupling can be considered negligent, heterogeneity of glucose sensitivities leads to a
67% probability that a given MIN6 cell in 2D will be active at low glucose. However, when
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coupling was incorporated by analyzing larger 2D cell clusters a marked size-scaling effect
was seen. Elevation of the dimension was also shown to have a highly suppressive effect
given the same probability of being active. Given the unique architecture of the islet,
extrapolation of our MIN6 findings is difficult without knowing a set point of Katp activity.
Therefore, using KIR6.2 [AAA] mutant mice provides a model in which it is known that
~70% of cells do not have functioning Katp channels and will thus be active at low glucose.
The use of KIR6.2[DN30K185Q] provides a more thorough model because the level of Katp
function can be varied and also quantified by GFP penetrance.
Percolation Modeling Accurately Predicts the Increase in Low Glucose Activity of
KIR6.2[AAA] Islets as a Function of Gap Junction Coupling
In the absence of gap junction coupling, our model showed that KIR6.2 [AAA] islets
will theoretically have 70% activity. Being that there will be no gap junction coupling to
suppress excitable cells at low glucose, this makes sense. For Cx36-/- islets expressing the
KIR6.2[AAA] transgene, this was the approximate case. Since Cx36-/- still have small levels
of gap junction conductance (Benninger et al. 2008), the lowest values gCOup will
theoretically have percent of cells active at low glucose that is slightly less than 70%.
Indeed, there was less of a reduction than a linear trend might suggest, but was in
agreement with the model with peXc = 0.7.
Normalizing the coupling conductance to a p=0.45 was found to provide the optimal
fit for the KIR6.2[AAA]/Cx36 data. This was higher than the optimal p=0.36 seen in the
MIN6 low glucose model, but may have been inflated by the large step size of the simulation.
For example, a step size of 0.01 instead of 0.05 will lead to a better approximation and may
lower the p of optimal fit. In addition, differences would be expected between MIN6
89


aggregates and intact islets given they have different development and cellular composition.
This might also suggest an approximation for the true p of a WT islet as being between 0.4
and 0.45.
Our model was able to predict how a loss in gap junction coupling can lead to
elevated [Ca2+]i activity at basal glucose levels in KIR6.2[AAA] mice. These results show that
the coupling of Katp activity via gap junctions results a suppressive activity at low glucose
which is similar to wild-type islets, even though up to ~70% are constitutively active.
Furthermore, we were also able to predict a critical point of excitable cells (80%), above
which suppressive coupling becomes nonexistent islets become constitutively active. This
further supports that glucose control of [Ca2+]i activity is gap junction dependent and
validates them as means by which cells suppress a state of hyperinsulinemia in a fasting
state.
Percolation modeling predicts critical behavior in fasting insulin secretion in
KIR6.2[AN2-30,K185Q] mice
In KIR6.2[AN2-30,K185Q] transgenic mice, the level of expression can be induced by
tamoxifen injections and quantified through GFP fluorescence. This ability to variably make
levels of the Katp channels in (3-cells insensitive to ATP gives us a model in which we can
study the effect of variable percent of excitable cells (pexc). The transgene is tagged with GFP
and higher levels of GFP fluorescence indicate greater expression of the KIR6.2[AN2-
30,K185Q] transgene and therefore a lower peXc. The percent of excitable cells (x-axis in
Figuresl9A-C) compared to a wild-type islet thus represents one minus the fraction of GFP
fluorescence. At zero fluorescence, the islet is wild-type, and at maximal fluorescence the
islet is maximally suppressed.
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In ranges of p (or in this case, lattice connectivity) which were found to approximate
MIN6 aggregates (0.3-0.4), the model predicted that at low levels ofpeXc (high GFP
fluorescence), there would be slight increases in the percent of cells active at low glucose up
to peXc ~ 0.6 (Figure 19A). ffowever, as peXc approaches 85% there are not enough quiescent
cells in the system to suppress the other active cells and the model shows a sharp increase
in low glucose activity. The plasma insulin data agreed nicely with this predication, showing
a rapid increase in this area, ffowever, a lack of data in the range of pexc = 0.6-0.9 made the
true critical point difficult to predict. Since the dose-response of KIR6.2[AN2-30,K185Q] can
be tailored to focus on this region, we hope to gain more data and better approximate this
threshold in the future. Nonetheless, the existence of a critical point in the experimental
data, which we were able to predict with relative accuracy, further verifies that the true
threshold of quiescent cells necessary to suppress the entire islet is between 10-40%.
The diabetic phenotype is characterized by an increase in non-(3-cells in the islet
core combined with a decrease in (3-cell mass, which could explain the decrease in gap
junction coupling and insulin sensitivity. Indeed, development of overt diabetes (chronic
hyperglycemia) is a long process has been found to occur when the overall functional beta-
cell mass drops below a threshold necessary to maintain euglycemia (10-30% of total beta-
cell mass in various species; Gepts 1965; Kjerns etal. 2001; Larsen etal. 2003; Sreenan etal.
1999; Bonner-Weir et al 1983). This is supported by previous from Rochelau et al, which
showed that within intact KIR6.2 [AAA] islets, (f-cells exhibit essentially normal [Ca2+]i
activity and insulin release. This suggests that the maintained cell-cell contact suppresses
the expected elevations in these two factors at low glucose given the Katp mutation
(Rochelau et al. 2006). Since it is known that 70% of these cells are constitutively active, we
can state that the level of quiescent cells necessary to suppress the coupled islet it <30%,
91


which is consistent with our data. Combined with our current findings, we can therefore
further tailor the approximation of cells necessary to suppress coupling to 10-30%.
Using the same model of KIR6.2[AAA]/Cx36 mice as the present work, Benninger et
al. found that despite elevations in [Ca2+]i activity at low glucose following complete
knockout of Cx36, there was not a concomitant increase in insulin secretion (Benninger et
al. 2010). This suggests supports the work by Rochelau et al. suggesting that some level of
gap junctional coupling is preventing activity at low glucose. Our model of KIR6.2 [AN2-
30,K185Q] mice shows that this is most likely because 70% penetrance of the transgene still
corresponds to sub-critical suppression, meaning that there were sufficient quiescent cells
to suppress the increase insulin secretion. However, our data predicts that if this level of
penetrance was increased to >80% there would be a concomitant increase in insulin
release.
In the KIR6.2[AN2-30,K185Q] model we used fasting plasma insulin as an
approximation to low glucose activity of the islets, which is represented as percent of cells
active in our model. However, the model was built and validated to predict [Ca2+]i activity in
isolated islets. Therefore, although the plasma insulin data was found to correlate well with
model predictions at an experimentally predicated range of p, we suspect that when [Ca2+]i
activity is quantified there will be better agreement More specifically, plasma insulin can
vary even with maximal [Ca2+]i activity and the experimental data will show a sharper
increase in activity compared to the plasma insulin.
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Implications of the Model for Overactive Katp Channels
The ability of cells to communicate with one another via gap junctions in the intact
islet of Langerhans is important for the enhancement and coordination of glucose-
stimulated insulin secretion as well as for uniform suppression of insulin secretion at low
glucose. While isolated (3-cells exhibit transient [Ca2+]i activity which is thought to be based
on a heterogeneous distribution of Katp channels, intact islets (some with up to 70% basal
activity) show uniform quiescence at low glucose. Although this behavior has been shown to
be a gap junction-dependent (Benninger etal. 2010), we have further explored this
mechanism by applying a model based on percolation theory.
These results have implication in the understanding of diabetic phenotypes
resulting from Katp dysfunction. Neonatal diabetes is caused from overactive Katp channels
and leads to an inability to secrete insulin. Our data shows that cell-cell coupling can create
a hyperpolarized state in all cells if Katp activity is low enough in a small percentage of cells.
More ambitiously, our model predicts that when less than 15-30% of (3-cells exhibit Katp
hyperactivity, the entire islet becomes overactive and may potentially lead to a diabetic
phenotype. Furthermore, our model predicts that when gCOup falls below ~25% of wild type
levels, the reduction in coupling abolishes this suppressive effect (Figure 17B). Thus,
normal percentages of active cells as found from our model (~67%) can lead to a several-
fold increase in basal plasma insulin. For example, our model predicts that when coupling
falls to 20% of wild type, ~67% excitable cells will secrete four times the insulin as the 35%
coupling conductance which fit the model. If coupling falls to 10% of wild type, this insulin
secreted will be ~6.5 fold higher.
It has previously been reported that elevating cAMP under low glucose conditions
cause a rise in insulin secretion in Cx36-/- mice, buthas a negligible effect in Cx36+/+ mice.
93


This result demonstrates that gap junctions can robustly suppress elevations in basal
insulin secretion induced by secretagogues that act independently of Ca2+ (Benninger et al.
2010). Since plasma insulin was found to scale approximately with our model of [Ca2+]i
activity, evaluating the effects of cAMP on insulin secretion by the models approximation
will be an active area of research by our group. In addition, these data suggest that
glucagon-like peptide 1 based treatments (which elevate cAMP and therefore prime insulin
secretion) will be less effective at low levels of gap junction coupling since the elevated
basal release will decrease the dynamic range of GSIS.
This mechanism may also explain an evolutionary drive to organize these secretory
cells into a unique electrical syncytium. Such a mechanism provides a protective effect
against hypoglycemia if individual cell properties change under pathological or
physiological stimuli. Since elevations in basal insulin and a decrease in (3-cell coupling have
been shown to occur in obese individuals as well as type II diabetics (Bonner-Weier &
Turner, 2008; Rahier et al. 2003; Porksen et al. 2002), our model further supports these
pathological changes as occurring in-tandem and also makes clinically-relevant predictions
about how a pathological phenotype can rapidly progress as regions of criticality are
approached.
Future Directions
Given the surprising results seen in day 14 pseudo-islets, this gives promise to the
potential for increasing the efficacy of human transplants. Future work in this arena needs
to focus on not only further validating the procedure through application to a mouse model
of diabetes, but also reaggregating human transplant islets to determine if function can
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Full Text

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SYNCHRONIZATION AND CRITICAL BEHAVIOR IN CELL NETWORKS: TOWARDS THE ENGINEERING OF THE ISLETS OF LANGERHANS b y THOMAS H HRAHA B.S., Colorado State University, 2008 A t hesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Bioengineering 2013

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ii This thesis for the Master of Science degree by Thomas H. Hraha has been approved for the Department of Bioengineering By Kendall Hunter, Chair Richard Benninger Robin Shandas 6/19/2013

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iii Hraha, Thomas H. (M.S., Bioengineering) Cell Networks: Towards the Engineering of the Islets of Langerhans Thesis directed by Assistant Professor Richard KP Benninger ABSTRACT organs which are integral to maintaining glucose homeostasis through secretion of insulin. Beta cells within islets synchronize their insulin release through cell cell communication to create large bursts to meet physiological needs. However, in patients with diabetes there is a reduction in this cell cell coupling which le ads to a hindered insulin response. To better characterize the effect of cell cell coupling in cell synchronization, we studied the differences in real time coupling dynamics between 2D and 3D cell structures. Using a novel system for aggregating cells back into 3D structures of defined size, we were able to show that the uncoordinated behavior seen in 2D cell networks is ameliorated by the 3D cell structure. Using this system to aggregate primary islet cells, we found that the resulting had higher viability and functionality compared to normal islets at two week, indicating they may yield higher post transplant viability and increase transplant effectiveness. Applying these findings to a network model of cell synchronization, we were th en able to theoretically show how reductions in the fractal dimension of cell coupling (number of nearest neighbors a cell can coupling with) can lead to a diabetic phenotype. Furthermore, we were able to apply this model in a predictive manner to forecast the existence of a critical point of cell coupling, below which a diabetic phenotype is established. This was then verified through islet with genetic mutations. The form and content of this abstract are approved. I recommend its publication Approved: Richard KP Benninger

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iv TABLE OF CONTENTS Chapter I. INTRODUCTION AND BACKGROUND ................................ ................................ ............................... 1 Introduction ................................ ................................ ................................ ................................ ................ 1 Overview of Glucose Stimulated Insulin S ecretion (GSIS) ................................ ...................... 2 Diabetes ................................ ................................ ................................ ................................ ........................ 3 Islet Architecture ................................ ................................ ................................ ................................ ...... 3 Beta Cell E lectrophysiology a nd the Triggering P athway ................................ ....................... 6 Amplification Pathway and E xocytosis ................................ ................................ ............................ 9 The Insulin R esponse ................................ ................................ ................................ ........................... 12 The Oscillatory N ature of GSIS ................................ ................................ ................................ ......... 13 Cell Cell C oupling in GSIS ................................ ................................ ................................ .................... 11 Beta Cell H eterogeneity ................................ ................................ ................................ ....................... 14 Overview of Relevant Mathematical M odels ................................ ................................ .............. 18 Application s of Transgenic Mouse M odel ................................ ................................ .................... 20 Islet T ransplant ation ................................ ................................ ................................ ............................ 14 Engineering I slets ................................ ................................ ................................ ................................ .. 27 Lattice Resistor Network Model of Islet C onnectivity ................................ ............................ 28 II. MATERIALS AND METHODS ................................ ................................ ................................ ............. 33 Cell Culture and Aggregate F ormation ................................ ................................ .......................... 33 Insulin Secretion A ssay ................................ ................................ ................................ ........................ 35 Microscopy ................................ ................................ ................................ ................................ ................ 36 Matlab Analysis ................................ ................................ ................................ ................................ ....... 36 Development of Transgenic Models ................................ ................................ ............................... 40 Bond Percolation Simulations for Size Scaling and Dimensionality C omparisons .... 40 High Glucose (Synchronization) S imulations ................................ ............................ 41 Low glucose (Suppression) S imulations ................................ ................................ ..... 53 Bond Percolation Simulations for Discrete Modeling of Islet D ynamics ....................... 54

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v III. RESULT S PART 1: DIMENSIONALITY AND SIZE SCALING OF COORDINATED Ca 2+ DYNAMICS IN PANCREATIC CELL NETWORKS ................................ ................................ .... 45 [Ca 2+ ] i Dynamics and Insulin Secretion Under Two and Three Dimensional C oupling ................................ ................................ ................................ ................................ .................... 45 Dimension and S ize D ependence of [Ca 2+ ] i S ynchronization ................................ .............. 47 Sub Regions of S ynchroni zation in Two Dimensional Cell C lusters ................................ 50 Wave V elocity U nder T wo and T hree D imensional C oupling ................................ ........... 51 Dimension and S ize D ependence of B asal [Ca 2+ ] i S uppression ................................ ......... 52 Network L attice M odel of [Ca 2+ ] i D ynamics ................................ ................................ ............... 54 IV. ................................ ................................ ... 58 Primary Islet Cells Uniformly Aggregate to Defined Sizes in 3D PEG Microwell A rrays ................................ ................................ ................................ ................................ ... 60 Pseudo Islets Show C omparable Viability and Functionality to Fresh I slets ............... 60 Day 7 and 14 Pseudo Islets are Better than Age Matched Normal I slets ...................... 62 Summary of R esults ................................ ................................ ................................ .............................. 63 V. RESULTS PART 3: PERCOLATION MODELING PREDICTS LOW GLUCOSE BEHAVIOR IN K ATP CHANNEL GENETIC MUTANTS ................................ ................................ ........................ 65 Model P redictions ................................ ................................ ................................ ................................ .. 66 Cell Activity as a Function of Coupling Conductance in KIR6.2[AAA] M ice ................... 69 Cell Activity as a Function of E xcitability in 30,K185Q] M ice ................... 70 Summary of F indings ................................ ................................ ................................ ............................ 71 VI. DISCUSSION ................................ ................................ ................................ ................................ .............. 72 Dimensionality and Size Scaling of C oordinated [Ca 2+ ] i D cells .............. 72 cell Coupling in Two D imensions ................................ ...................... 73 Network Model Describes Dimension and Size S caling of [Ca 2+ ] i D ynamics 75 Physiological Importance of Dimensionality and Size Scaling in Network A rchitecture ................................ ................................ ................................ .............................. 77 Re Aggregation of Primary Islet Cells into Functional Pseudo I slet ............................... 79

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vi Primary Islet Cells Readily Aggregate to Form 3D Pseudo Islets of Defined S ize ................................ ................................ ................................ .............................. 80 Pseudo Islets Show Superior Viability and F unctionalit y ................................ .......... 82 Applications to Human W ork ................................ ................................ ................................ 84 Percolation Modeling Predicts Low Glucose Behavior in K ATP Channel G enetic M utants ................................ ................................ ................................ ................................ ..................... 86 Percolation Modeling Accurately Predicts the Increase in Low Glucose A ctiv ity of KIR6.2[AAA] Islets as a Function of Gap Junction C oupling .......... 88 Percolation Modeling Predicts Critical Behavior in Fasting Insulin Secretion 30,K185Q] Expressing M ice ................................ ................................ 89 Implications of the Model for O veractive K ATP C hannels ................................ ....... 92 Future Directions ................................ ................................ ................................ ................................ ... 98 REFERENCES ................................ ................................ ................................ ................................ ........................... 99

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1 CHAPTER 1 INTRODUCTION & BACKGROUND accurate and complete description of complex systems. Scientists have broken down many kinds of systems. They think they know most of the elements and forces. The next task is to reassemble them, at least in mathematical models that capture the key properties of the entire Edward Wilson Introduction multicellular micro organs which are integral to maintaining glucose homeostasis through secretion of the hormones insulin and glucagon. Normally, the cells of this organ are electrically coupled to produce insulin in coordinated bursts in response to elev ated blood glucose. These insulin bursts are the result of complex triggering and amplification pathways which are subject to a complex array of inputs. Impairment of the islets ability to accomplish this leads to hyperglycemia, and is implicated in the de velopment of type 1 and type 2 diabetes. Many studies indicate that the pulsatile dynamics of insulin secretion are important for insulin action and maintaining insulin sensitivity, and insulin pulsatility. Therefore, factors that regulate in vivo insulin dynamics are important for regulating glucose homeostasis. Currently, the best treatment option for type 1 diabetics is islet transplantation. However, a lack of donor tissue and low post transplant islet viability are major hurdles towards making this a widely available option. The engineering of islets from donor tissue,

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2 or de novo from stem cells, has the ability to ameliorate this problem. However, these engineered islets must be shown to display similar physiology and have sufficiently developed elect rical coupling. Therefore, a working model of both the electrophysiogical coupling of the triggering pathway with integration of components of the amplification pathway would provide a benchmark to which engineered islets can be compared. In addition, the tools developed to build these models would be helpful in studying the development and pathophysiology of diabetes mellitus. Much work has been done in the last 50 years to understand the electrophysiology cell. However, rela tively little is known regarding how these cells interact with each other to produce such exquisite coordination to maintain glucose homeostasis. This paradigm also reflects the changes taking place in scientific research in general; while the last 50 year s have been focused on reductionism, or dissecting the intricacies of biological systems, high level computing and instrumentation will allow the next 50 years to be focused on how these intricate systems interac t to produce life and disease. Overview of Glucose Stimulated Insulin Secretion cells synthesize and secrete insulin at appropriate rates to maintain blood glucose levels within a relatively small range. Any alteration in their function has a profound effect on glucose homeostasis and often leads to disease. This apparently simple cell in glucose physiology contrasts sharply with the complexity of its regulation, which is controlled by an intricate array of metabolic, electrophysiological, hormonal and sometimes pharmacol ogical factors.

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3 cell responds by releasing insulin into the blood. Because the Km 1 cell glucose receptor GLUT2 is ~20mM, a rise in extracellular glucose in this range cause s a proportionate increase in glucose entry. Glucose cells is regulated by a series of molecular events including an elevated ATP/ADP ratio following glucose metabolism, subsequent ATP sensitive K + (K ATP ) channel closure, membrane depolarization, Ca 2+ influx to increase intracellular free calcium activity ([Ca 2+ ] i ), and the ATP tions which elevate insulin granule trafficking to the plasma membrane and augment exocytosis, therefore referred to the Henquin, 2000 ). Glucose concentrations cell intracellular Ca 2+ concentration ([Ca 2+ ] i ), which lead to pulsatile insulin secretion. Although insulin can be secreted through steps independent of Ca 2+ primarily through hormonal control, the fracti on of insulin released by this mechanism is only minor fraction of insulin released in the presence of Ca 2+ (Komatsu, et al., 1997). Therefore, the sequence of events leading to insulin secretion may have Ca 2+ independent steps, however the physiological regulation by glucose is achieved through Ca 2+ dependent pathways. Diabetes When insulin secretion is absent or impaired, peripheral tissues fail to respond to insulin, resulting in hyperglycemia leading ultimately to diabetes (MacDonald & Rorsman, 1 Where K m is defined by Michaelis Menten kinetics to be the substrate concentratio n at which the reaction rate (in this case entry rate which is defined by receptor affinity) is half of the maximal.

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4 2006). Diabetes affects more than 285 million people worldwide, with type 2 diabetics making up about 90% of the cases. It has an annual cost of $132 billion to the American medical system and is associated with several long term complications including nerve da mage, kidney failure, microcirculatory impairment, and a greater risk for heart disease and stroke (MacDonald & Rorsman, 2006). The vast majority of cases of diabetes fall into two broad categories: type 1 and type 2. Type 1, or juvenile onset, diabetes re sults from a cellular mediated autoimmune cell destruction varies between patients, the resulting impairment is usually large enough to require peripheral insulin injection (Mellitus, 2006). In contrast, typ e II diabetes accounts for greater than 85% of cases. In this variant, cells persist, but for reasons that remain to be elucidated they fail to secrete insulin in sufficient quantities to maintain proper blood glucose levels (MacDonald & Rorsman, 2006) T his disruption in secretion seen prior to the onset of type II diabetes (LeRoith, 2002), and when combined with the development of insulin resistance in peripheral tissues, the results in chronic hyperglycemia. Thus, understanding the electrophysiological mechanisms pathogenesis of type II diabetes. Islet A rchitecture The pancreatic islets of Langerhans play a central role in the regulation of blood glucose homeostasis through the regulated secretion of the hormones insulin and glucagon. The endocrine tissue of the pancreas is organized as cell clusters approximately 100 400m

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5 in diameter called the islets of Langerhans, which are dispersed throughout the pancreatic exocrine ti ssue and receive a rich vascular (blood vessel) supply. Islets are composed of and secrete the hormone glucagon in response to low blood glucose. Glucagon increases bl ~5% of the mouse islet mass, secrete somatostatin, which acts in a paracrine fashion to inhibit the secretion of both insulin and glucagon (Reichlin, 1983). Finally, the insulin Detailed quantitative studies assessing the cell composition (Stefan et al. 1982; Rahier et al. 1983; Clark et al. 1988) have found that human islets and other cells. However, more recent studies suggest the there cells (50 cells (30 40%) (Sakuraba et al. 2002; Street et al. 2004; Brissova et al. 2005). Although much work has been done with regards to quantifying the cell types in islets, few have examined the cytoarchitecture across species. In rodent islets, the cells are clustered mainly in the core of the islet, whereas cells express ing cells) are mainly localized to the periphery. In contrast, human islets have shown to have glucagon and somatostatin positive cells homogeneously scattered throughout the islet, however recent evidence has shown that this effect may be due to the age of human islets studying, typically being from older individuals compared to weeks old mice. This is explained in more detail in the discussion. To estimate the degree of clustering or segregation of similar cell type s in the islet, Cabrera, cells exclusively adjacent to cells of the same type (homotypic association) or adjacent to cells of other types (heterotypic associations).

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6 cells showed homotypic associations, whereas in human islets only 29% showed these associations (Cabrera, et al., 2006). This suggests that the paracrine effects of other cell types may play a more important role in human islets, which was further supporte cells were found to be closely opposed to blood vessels. However, recent evidence suggests that the cytoarchitecture seen in human islets by Cabrera et al. may be the result of a changing cell composition over time (Bos co et al. 2010; Kilimnkik et al. 2011). In a better statistically powered study, Bosco, et al. demonstrated cells, smaller human islets maintain the core mantle structure seen in mice islets. Furthermore, cells within the core the islet were focused around the edges of the vasculature and therefore postulate that this architecture in larger islets still facilitates a core structure around the vasculature (Bosco et al. 2010). Nevertheless, these aspects of the cellular architecture must be taken into consideration when applying findings regarding intercellular electrical synchronization and when attempting to engineer islets de novo It appears that differences in islet cytoarchitecture may lead to functional differences in islet behavior, with human islets having more of a reliance on neuro endocrine secretions. It is therefore important to consider the relative proportions and locations of cell types when attempting to engineer islets using hydrogel scaffolds or when aggregating cells de novo. Also, the lower cells within the human islet may lead to less cell cell electrical coupling, although this has never been shown.

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7 Beta Ce ll Electrophysiology and the T riggerin g P athway (mostly Ca 2+ and K + ) into and out of the cell. Due to the charged nature of these ions, their cells, these action potentials are stimulated through intracellular glucose metabolism. The cell membrane gives rise to small voltage changes by manipulating the concentration gradient of ions using selective permeability. If the concentrations of positive and negative ions on either side of the cell membrane are equal, there will be no diff erence in the electrical potential gradient. However, if the membrane was permeable to an ion (K+ in the case of the beta cell) then the inward flux of this ion down its concentration gradient would create a charge imbalance and therefore a potential gradi ent. As more K+ ion move through the channel, the magnitude of the charge difference (or voltage) increases until a repulsive force caused by excess positive K+ ions leads to an equilibrium. If a membrane is only permeable to K+ ions (which is the approxim ate case for the beta cell), then the electrical potential E k+ (in volts) is given by the Nernst equation where K e and K i are the extracellular and intracellular concentrations of K+ ions, respectively; R is the gas constant 1.987 calories / (degree*mol); T is the absolute temperature in Kelvins (293K for 20C); Z is the +1; and F is the Faraday constant equal to 23,062 cal / (mol*V) or 96,000 coulombs / (mol*V). At 20C, this reduces to:

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8 Therefore, at a 10 fold concentration the magnitude of the difference is 0.059V (or 59mV). However, since the cytoplasmic side is viewed as negative in this case, this would be 59mV. cell is dominated by K+ channels. As a result, the major ionic movement across the plasma membrane is that of K+ out of the cell, powered by the concentration gradient. This creates a resting me mbrane potential of the cell is approximately 70mv. Although this value does not seem very large, given that the cell membrane is only ~3.5nm thick, this corresponds to ~200,000 volts per cm. To put this in context, high voltage power lines generally use a 200,000 volt gradient over a kilometer. Under low glucose conditions, ATP sensitive K + channels (K ATP channels) are open, allowing an outward flux of K + ions which effectively clamps the beta cell membrane potential at the K + Nernst potential and produc es a steady state cell membrane potential of ~ 70mV (Rorsman, 1997; Henquin, 2000). These channels are tetramers of a complex of two proteins: a high affinity sulfonylurea receptor (SUR1) and an inwardly rectifying K+ channel (Kir 6.2). SUR1 provides the pore forming KIR6.2 with sensitivity to sulfonylureas and diazoxide, which respectively close and open the channel. The closing action in response to an elevated ATP:ADP ratio is KIR6.2 dependent (Henquin, 2000; Ashcroft & Gribble, 1998). cell is exposed to glucose through the pancreatic vasculature, glucose enters the cell through GLUT2 transporters and increased cellular metabolism of the sugar through glycolysis (anaerobic) and oxidative phosphorylation (aerobic) leads to a rise in the ATP:AD P ratio. Increased levels of ATP bind to the KRI6.2 subunit of the K ATP channel and cause it to close; stopping the influx of K + ions down their electrical gradient. This drives the membrane towards a more positive potential and once the K ATP channels are almost all (>90%) inhibited, the K ATP conductance is unable to balance the background depolarizing

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9 influences and the beta cell depolarizes at around 45mV (Rorsman 1997; MacDonald & Rorsman, 2006; Drews et al., 2010; Misler et al., 1992). When this depol arization is large enough, L type voltage gated calcium channels (VDCC) become activated, allowing the influx of Ca2+ down the electrical gradient, further driving the membrane potential. r subunits. helices, the fourth of which serves as the voltage sensors for activation. In response to membrane depolarization, VDCCs undergo an extremely rapid conformational shift, moving outward and rotatin g under the influence of the electric field and initiating a conformational change which opens a highly permeable pore (Yang & Berggren, 2006). The resultant increase in [Ca 2+ ] i triggers direct interactions between the exocytotic proteins situated in the insulin containing granule membrane and those localized in the plasma membrane. Eventually, the interaction between exocytotic proteins initiates the fusion of insulin containing granules with the plasma membrane resulting in insulin exocytosis (Yang & Ber ggen, 2005a; Yang & Berggen, 2005b). cell undergoes oscillatory Vm activity. This is caused by oscillatory changes in ATP and activation of voltage dependent inward rectifying K + (K v ) channels, whose opposing a ctivity creates high frequency oscillations at high membrane potentials. As the levels of [Ca 2+ ] i increase, Ca 2+ activated K+ channels are opened which are responsible for the repolarizing curve of the V m trace and reset the cycle (MacDonald, 2003) Thus, the K ATP channels can be viewed as the transducers of glucose induced insulin secretion. This role is easily demonstrated by the use of agents which manipulate the

PAGE 16

10 channels behavior. Opening of channels with diazoxide causes membrane repolarization, lowers [Ca 2+ ] i and inhibits insulin secretion (Henquin, 2000). Subsequent addition of tolbutamide or sulfonylureas to close the channels leads to a depolarization of the cell and a resumption in [Ca 2+ ] i driven insulin release (Henquin, 2000). In addition, recen t evidence has suggested that waves of depolarization through the entire islet originate in areas of high K ATP inhibition (Rochelau et al., 2004). If K ATP are said to be the transducers of glucose stimulated insulin secretion, then the VDCCs are the effect ors because of their effect on insulin exocytosis. This is supported by a work in which a point mutation of human VDCC channel rendering constitutively active cell secrete insulin excessively ( Splawski et al., 2004). cell electrophysiology, including Cl and non selective cation channels, as well as electrogenic pumps such as the Na + / K + ATPase. While the role of these has not been extensively characterized, their activity has been found to be highly dependent on peripheral systems such as the protein kinase C pathway and mitochondrial NADPH production (MacDonald, 2003). Though they may p lay an undiscovered critical role, the three channels which regulate the glucose induced response (and were discussed above) are the main players in regulating glycemic control through insulin secretion. Amplification Pathway and Exocytosis Although much work has been done to show that insulin exocytosis is clearly Ca 2+ dependent, recent evidence suggests that increased intracellular [Ca 2+ ] i acts more as an initiator rather than a determinant of insulin release. For example, removal of extracellular

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11 Ca 2+ prevents action potential (Liu et al., 2004) and subsequent insulin secretion (Gopel et al., 2000; Gromada et al., 2004), however, the amplitude of the exocytotic response depends to a greater extent on the activity of kinases and phosphatases rather than purely [Ca 2+ ] i (Rorsman, 1997; Milser et al., 1992; Henquin, et al., 2000). This points to another, adenosine monophosphate (cAMP). A ubiquitous secondary messenger of most cell types in the body, cAMP is another critical factor in GSIS. Until recently, little was known about the spatiotemporal dynamics of spatiotemporal patterns which are Ca 2+ dependent and independent are beginning to emerge. Interestingly, glucose has been found to trigger concurrent oscillations of cAMP and [Ca 2+ ] i in individual MIN6 cells (Landa et al., 2005; Ni et al., 2010). Since cAMP enhances exocytosis predominantly via PKA, and is also influenced by hormonal factors (in addition to [Ca 2+ ] I ), it has been suggested that cAMP plays an amplifying role of the Ca 2+ signal. In both humans and rodents, the glucose induced oscillations in [cAMP] i resemble those of [Ca 2+ ] i with small initial lowering, followed by pronounced rise and slow oscillations with a period of 2 10 minutes (Dyachok et al., 2008). Although several studies have found that depolarization of the cell causes oscillations in [cAMP] i (Dyachok & G ylfe, 2004; Landa et al., 2005; Ni et al., 2010), the phase relationship between these two signaling factors seems to depend on the other conditions. Whereas cells stimulated with GLP 1 showed synchronous oscillations in [cAMP] i and [Ca 2+ ] i (Dyachok et al. 2006), TEA induced elevations of [Ca 2+ ] i were associated with decreases of cAMP (Landa et al., 2005), which may be due to over activation of Ca2+ sensitive phosphodiesterase.

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12 Glucose n by sensitizing the exocytosis machinery since inhibition of [cAMP]i oscillations markedly suppress pulsatile insulin secretion without affecting the underlying [Ca2+]i oscillations (Henquin, 2000). Agents which increase cytoplasmic levels of cAMP potenti ate Ca 2+ stimulated insulin exocytosis almost 10 fold (through a protein kinase A (PKA) dependent mechanism) without affecting Ca 2+ influx or [Ca 2+ ] i (Ammala et al., 1993). This is thought to be due to PKA accelerating granule mobilization. Thus, when exo cytosis is initiated by [Ca 2+ ] i a greater number of granules are available for release. Therefore, the Ca2+, ATP:ADP and cAMP dynamics may lead to triggering and amplification pathways of insulin secretion, which would explain why cAMP can oscillate even u nder steady Ca2+ levels. The principal action of cAMP on exocytosis seems to be exerted at a step distal to the elevation of [Ca 2+ ] i (Ammala et al., 1993; Gillis and Misler, 1993), involving both PKA dependent and independent mechanisms, the latter most l ikely mediated by exchange proteins activated by cAMP (Epac) (Renstrom et al., 1997). Many exocytosis related proteins have been identified as substrates for PKA (Seino and Shibasaki, 2005), and the subcellular targeting of PKA to its effectors via A kinas e anchoring proteins has been found to be critical for the stimulatory effect of cAMP elevating agents on insulin secretion (Lester et al., 1997; Fraser et al., 1998). Capacitance recordings by Eliasson, et al. have indicated that PKA mediates the slower c AMP dependent mobilization of insulin granules, while Epac accounts for the rapid cAMP dependent potentiation of exocytosis in cells (Eliasson et al., 2003). Epac has also been reported to increase the number of granule fusion sites and along with PKA the number of granule granule fusion events (Kwan et al., 2007). Interestingly, both sulfonylureas and GLP 1 treatment have been found to improve in vivo insulin pulsatility (Porksen, 2002), which is most likely due to the established ability

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13 of these dru gs to generate oscillations in [Ca 2+ ] i (Grapengeisser, 1990) and cAMP (Dyachok, diabetes, and may reflect a degradation of synchronization in secretory activity r ather than pulsatile insulin secretion in prediabetic and diabetic states may also impair the Despite the fact that much work has been done in regards to understanding the roles of cAMP and [Ca 2+ ] i in individual cells, how these cells come together to form a coordinated pulse of insulin remains unclear. Despite work in the role of gap junctions in coordinating electrical activity (Benninger et al., 2008; Benninger et al., 2011; Rochelau et In fact, there is a lack of data where cAMP and [Ca 2+ ] i were measured in anything but a single cell. If islets are ever to be reformed from primary cells or stem cells, these are important dynamics that need to be established to recreate a functional isle t capable of overcoming diabetes. The Insulin Response cells respond to a step increase in the glucose concentration with a biphasic insulin secretory pattern. This biphasic pattern of insulin secretion was first observed in the perfused rat pancreas (Grodsky, 1966; Nesher, 1987). Later, it was also visualized in the portal vein and peripheral blood in human subjects in response to a rapid elevation of glucose (Cerasi et al., 1972). The response is characterized by a rapid initial

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14 phase of ins ulin release, which is maintained for about 10 minutes, followed by a gradually increasing second phase, which reaches a plateau after another 25 to 30 minutes (Yang & Berggen, 2005a). Mouse islets subjected to an abrupt and sustained increase also secrete insulin biphasically. However, the second phase of insulin release from mouse islets is lower than that from human and rat islets (Jing, 2005). A loss of the first phase and a reduction of the second phase of insulin secretion occur in type 2 diabetes cha cell dysfunction (Rorsman & Renstrom, 2003). This supports other evidence which shows that glucose induced insulin secretion dynamics by human islets is very similar to that in rodents in terms of metabolic and Ca2+ dependencies (Ricordi et al., 1998; Grant et al., 1980; Misler, et al., 1992). Therefore, this supports the use of rodent models in the study of islet electrophysiology, pathology and diabetes. Oscillatory Nature of GSIS Insulin secretion occurs in a pulsatile fashion, which is driven by the underlying pulsatile nature of the cell voltage. The opening of Ca 2+ channels is intermittent, oscillating with the membrane potential and therefore resulting in oscillations in [Ca 2+ ] i and in turn, oscillations in insulin release (Gilon et al., 1992; Tornheim, 1997).These oscillations occur with a period of 2 8 minutes in humans (Land et al., 1979) and mice (Nunemaker et al., 2006), and reflect a balance between the VDCCs (depolarization) and the K Ca channel activity (repolarization) (Ashcro ft & Rorsman, 1989). The depolarizing Ca 2+ component dominates at the beginning of the burst, but the Ca 2+ influx rapidly leads to increased K Ca channel activity. This occurs via a direct effect on Ca 2+ activated K Ca channels (Zhang et al.,

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15 2005) and also through indirect effect on K ATP channels by lowering the cytoplasmic ATP:ADP ratio due increased Ca2+ ATPase activity (Kanno et al., 2002). Upon the buildup of Ca 2+ K Ca cell, thereby readying the cell for another burst i f intracellular metabolism remains high. Glucose produces a concentration dependent decrease in the period. At glucose concentrations beyond physiological levels (20mM), constant action potential spiking is seen, which may be due to a higher rate of glucos e metabolism leading to such high intracellular ATP concentrations that Ca 2+ ATPase cannot lower them to increase K Ca conductance enough to lead to repolarization. This is supported by the use of the of K ATP inhibitor tolbutamide, which has been used to tr eat diabetes for over 50 years. By blocking K ATP channels, membrane potential is suppressed and results in continuous firing (MacDonald & Rorsman, 2006). Cell Cell Coupling in GSIS ion cells within the same pancreatic islet are electrically coupled by gap junctions (Santos et al., 1991; Eddlestone et al., 1984), such that the [Ca 2+ ] i oscillations within different parts of the islet occur in phase even cells show a heterogeneous sensitivity to a given glucose concentration. This gap junction coupling coordinates the dynamics underlying GSIS and also mediates the s uppression of electrical activity at low blood glucose concentrations. This synchronization of electrical activity produces coordinated bursts of insulin, which are imperative in glycemic control.

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16 In contrast to continuous secretion, pulsatile insulin rel ease has been shown to be more effective at lowering blood glucose (Bratusch Marrian et al., 1986; Matthews et al., 1983; Paolisso et al., 1988; Meier et al., 2005), and also maintaining peripheral tissue insulin sensitivity (Goodner et al., 1988). Several landmark studies have also shown that diabetic patients require less insulin to maintain normoglycemia if insulin is infused in an oscillatory manner as opposed to a constant rate. Pulsatile insulin infusion has also been implicated for use in patients wi th type 2 diabetes with positive results (Bratusch Marrain et al., 1986; Matthews et al., 1987; Paolisso et al., 1988). These oscillations are disrupted in patients (Peiris et al., 1992), and this has been proposed to play a pathogenic role in the progression cell proximity due to cells and other immune cells, which is known to occur in hyperglycemic conditions (Sorenson et al., 1997; Sheridan et al., 1988). cells are formed by six identi cal connexin 36 (Cx36) transmembrane proteins, which mediate ionic currents and the diffusion of small molecules (ref from 3). As a result, Cx36 gap junctions are the sole cells in the islet (Benninger et al., 2008; R avier et al., 2005), and in the absence of Cx36, isolated islets do not exhibit coordination in [Ca 2+ ] i oscillations (Benninger, 2011) or pulsatile insulin release (Benninger et al., 2011; Drews et al., 2010; Ravier et al., 2005). When islet architecture is altered, a concomitant impairment of insulin secretion and [Ca 2+ ] i is observed, which recovers as soon as contact among cells is re established (Halban et al., 1982; Bertuzzi et al., 1999). Underscoring the cells from intact is lets exhibit several fold the glucose stimulated cells (Lernmark, 1974;

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17 Halban et al., 1982). Recently, we have shown that the dimensionality of the coupling (2D vs. 3D) alone can explai n the better response of highly coupled islets and have developed a novel simulation based mathematical model to explain such behavior (Hraha, et al. 2013, in submission). Similar to patients with type II diabetes, Cx36 knockout mice were glucose intolera nt and had reduced peak amplitude of the insulin pulse as measured through plasma insulin levels (Benninger et al., 2008; Head et al., 2012). Since this effect was also found in the isolated islets ex vivo, this pathology is thought to be islet specific. T herefore, since Cx36 is also the sole means of coupling in humans islets (Serre Beiner et al., 2009), a reduction in Cx36 gap junction conductance would help explain the symptoms seen in type 2 diabetics. Using a model of Cx36 knockout mice, Head and colle agues found that in the absence of Cx36, the heterogeneity in [Ca 2+ ] i cells exhibiting transient repolarizing events even high glucose. This is in contrast to the sustained elevations in [Ca 2+ ] i in the presence of Cx36. This can help to explain the decrease in mean [Ca 2+ ] i concentration at high glucose stimulation in the absence of Cx36, and points to the role of gap junctions in maximizing the effectiveness of the GSIS (Head, et al., 2012). Gap junction coupling has als o been found to coordinate behavior at low blood glucose concentrations by having a hyperpolarizing effect. This is a desirable characteristic because secreting insulin at levels of low blood glucose would drive the system into a deeper state of hypoglycem ia. Benninger et al. has demonstrated a similar [Ca 2+ ] i response to glucose in Cx36 cells suggests gap junctions are the predominant mechanism present to suppress elevations in basal [Ca 2+ ] i that rise due to cellular heterogeneity in mice expressing a K ATP transgene (Benninger et al., 2010). Therefore, an

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18 the pathogenesis of the disease as well as understanding the challenges of creating isle ts de novo. Cell Heterogeneity sensor, is the presence of K ATP channels. As discussed previously, the activity of these channels sets the membrane potential of t cell and this determines its electrical sensitivity to blood glucose and therefore its secretory activity. For this reason, the K ATP channel inhibitor sulphonylureas has been used for over 70 years to treat treat type 2 diabetes (Gerstein, 2008). In cells show a considerably cells exhibit heterogenous and irregular responses to clucose for many variables, including NAD(P)H elevations (Bennett et al. 1996), [Ca 2 + ] i oscillations (Zhang et al. 2003) and the dynamic range of insulin release (Vanschravendijk, cells in the islet to create synchronous oscillations in [Ca 2+ ] i and insulin release. Recent evidence has actually suggested that the origin of [Ca 2+ ] i waves in intact islets is actually due cells population (Benninger et al. 2008). Heterogeneity in [Ca 2+ ] i cel ls ( Zhang et al. 2003 ) and islets lacking gap junctions ( Ravier et al., 2005 ; Benninger et al., 2008 cells wi thin the islet are intrinsically heterogeneous in terms of the electrical response to glucose, and gap junction acts to uniformly suppress any subthreshold response.

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19 cell Electrophysiology Mathematical modeli ng is useful in biology to unify theories, fit data to statistical models, identify mechanisms from disparate data, and to predict tests. Physicists have used modeling for centuries to explain phenomena, however most biologists are just recently beginning to employ detailed models to inform their research (Winters, 2012). Because of cells lends itself quite readily to mathematical treatment and therefore much work has been d one on the subject. The Chay Keizer model is a minimal mathematical model which describes the bursting behavior of 2 cells. The model is minimal in that it includes only the basic set of processes that lead to burst oscillations: voltage regulated K+ channels, Ca 2+ activated K + channels, voltage regulated Ca 2+ channels, and glucose stimulated efflux of Ca+2 from the cytosol. With these basic processes the model produces burst oscillations with features like those obse rved experimentally. The Chay Keizer model also describes the evolution of the cytosolic Ca 2+ concentration (Chay & Keizer, 1983). cell bursting using simple dynamics, the Chay Keizer model is a bit too si mplistic to capture all of the complex dynamics underlying membrane potential. One of the criticisms of the Chay Keizer model is that in its original form, it is unable to account for some of the variation in calcium dynamics; namely that experimental evid ence has suggested that calcium levels plateau quickly, rather than in the stepped fashion seen in the model. Also, it is unable to accurately account for both high and low frequency [Ca 2+ ] i components (Keizer et al., 1991). This has been somewhat remedie d by the addition of an endoplasmic reticulum component to the

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20 [Ca 2+ ] i dynamics. Another qualm was that it does not include a glycolytic component. Since the bursting patterns of [Ca 2+ ] i is due to intracellular ATP levels, Bertram et al. introduced a model in which the conductance of K ATP channels varied with observed oscillation in glycolysis (Bertram et al., 2000). Though the previous models are reported to fit experimental data nicely, they still do not include components of the model which (as we have seen) explain much of the cells: coupling, cAMP and heterogeneity. The Bertram group solved one of these by creating what is called the phantom burster model. The authors considered a mechanism which allows single cells to fire on both t he slow (1 5 seconds) and fast (1 2 minutes) scales (as is seen in experimental data of single cells) (Bertram et al. 2000). Since there is no pacemaker cells initiating the burst, and instead it is a function of the collective behavior, it has been termed the phantom burster. To introduce coupling, Sherman et al. considered many Chay Keizer like cells (Sherman & Keizer, 1990). Importantly, they demonstrated that couplin g a silent cell with a cell undergoing periodic oscillations may result in bursting at the network level as the network passes between both solution types. However, the model did not account for any heterogeneity and needed values of conductance parameters that were much higher than what has been previously reported. cells is an inherent physiological property that intercellular coupling must overcome. In their 2008 paper Benninger et al. studied coupled cells based on the previously mentioned phantom burster model. They introduced heterogeneity into their network by randomly distributing the electrical coupling strength between adjacent cells. Therefore, a given cells membrane potential is affected by its surrounding cells

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21 potential as a function of heterogeneous coupling strength. Additional heterog eneity was introduced through K ATP sensitivity and metabolic flux (ATP production). They found that the model predicts traveling waves of calcium levels amongst the network, which was consistent with experimental data. In addition, it was able to explain h ow large numbers of cells can couple to form a coordinated syncytium at both high and low glucose (Benninger et al., 2008). Although the effects of gap junction coupling and [Ca 2+ ] i remain to be uncovered, cAMP nonetheless plays an importan t part in GSIS and deserves adequate mathematical model of cAMP dynamics based off of an [Ca 2+ ] i cAMP PKA oscillatory / regulatory circuit. The model was able to predict the effects of numerous channel inhibitors for different endpoints, which were confirmed by experimental data (which was also not a trivial undertaking). However, as impressive as their model was, it was only in single cells and therefore misses m uch of the dynamics which underlie cAMP signaling. cell dynamics has been greatly enhanced from these models, a full working model of GSIS is still a far off goal. To fully elucidate the mechanisms underlying GSI S and to create a set of endpoints for which engineered islets can be based, a full working model is needed. Applications of Transgenic Mouse Models cells, the K ATP channel is a critical link in the pathway of glucose induced insulin r elease. According to this paradigm, a high intracellular ATP/ADP ratio inhibits Katp channels, causing membrane depolarization. This induces Ca 2+ entry though

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22 VDCCs and initiates events leading to subsequent exocytosis. Conversely, a lower ATP/ADP ratio du ring a fasting state relieves inhibition of the Katp channels, resulting in membrane hyperpolarization and suppression of Ca2+ activity. The dependence of channel activity on intracellular ATP underlies the physiologic role of the K ATP channel by coupling the metabolic status of a cell to electrical activity. The recent discovery of numerous mutations in pancreatic K ATP channel subunits (both the pore forming Kir6.2 and SUR1) in human patients with persistent hyperinsulinemic hypoglycemia of infancy (PHHI) further establishes the link between suppressed K ATP activity and the corollary metabolic disorder of hyper insulinism (Huopi, et al., 2002). PHHI associated K ATP mutations can be classified into two major categories: those which suppress channel activity w ithout altering cell surface expression, and biosynthetic or trafficking defects that reduce or abolish surface expression. In both cases, reduced K ATP channel activity is expected to result in constitutive depolarization, persistently elevated [Ca 2+ ] i an d unregulated insulin secretion (Huopio, et al., 2002). Although a few cases can be treated with the K ATP channel opener drug diazoxide, but the majority of cases require surgical removal of almost all of the pancreas (de Lonlay, et al., 2002). Genetic sup pression of the K ATP channel has been undertaken previously to better characterize its role by alteration of the KIR6.2 and SUR1 subunits. Miki et al. developed a transgenic model expressing a dominant negative KIR6.2 mutant which perturbs the structure of the KATP pore forming unit which renders it non functional (Miki, et al., 1998). cells from these mice showed reduced K ATP currents and an increase in resting membrane potential, they also showed no glucose induced insulin secretion and t cell apoptosis.

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23 To circumvent this issue, Koster et al. developed another KIR6.2 mutant which showed suppressed pancreatic K ATP currents as adults, in contrast to neonates (Koster, et al 2001 PNAS; Koster et al., 2000). In their model, there was ~70% penetrance of the KIR6.2[AAA] mutation, meaning transgenic overexpression and incorporation of the cells in a particular islet will exh ibit no measurable KATP channel activity. This reduction in overall K ATP conductance lead to reduced resting membrane potential and a loss of hyperpolarizing. Therefore, these mice exhibit hypersecretion of insulin leading to a left shift of the insulin do se response curve (Koster, et al., 2000 & 2001). However, since this does not lead to a dominant negative phenotype with no K ATP activity (like in other models), hyperinsulinemia and the onset of diabetes is markedly delayed. In contrast to loss of functio n K ATP mutants associated with hypersecretion of insulin, mutations in K ATP subunits that reduce sensitivity to inhibitory ATP (gain of function) give rise to the corollary disease, diabetes. To test this, Koster et al. created mutants by truncating the 30 N 30]), and combined this with a point mu 30,K185Q]. This combination results in mutant subunits with a ~30 fold reduction of ATP sensitivity (Koster, et al., 2000). Since K ATP channels are formed as tetramers, each with a SUR1 and KIR6.2 subunit, overexpression of the KIR6.2 will yield SUR1 as rate limiting. Therefore, 30,K185Q] subunits will be incorporated accordingly and result in a partial The effects of transgenic expression were profound and included early onset diabetes characterized by reduced serum insulin levels and dramatically elevated blood glucose (Koster et al, 2000).

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24 In addition to K ATP transgenic models, Cx36 knockout mice have also lead to a greater understandin cells suppress and coordinate activity. For example, Benninger, et al. have found at sub threshold glucose conditions Cx36 / had spontaneous Ca2+ activity in cells, whereas wild type islets remained quiescent (Benninger, et al., 2011) cells exhibit essentially normal [Ca 2+ ] i and insulin secretion responses to glucose ( Roche leau et al. 2006 ). Therefore the maintained cell cell contacts in these islets acts to suppresses the expected elevations in [Ca 2+ ] i and insulin release at low glucose due to the K ATP mutation. These islets therefore allow us to quantify and further distin guish how gap junctions and other means of cell cell communication can specifically regulate basal electrical activity and insulin secretion in the intact islet. They also allow us to verify and fit our models to better explain how cell cell contact suppre ssed basal [Ca 2+ ] i dynamics and insulin release. To test this, we can investigate islets in which electrical activity has been perturbed by the mosaic expression of a loss of function or gain of function mutations in K ATP channels ( Koster et al. 2000 ; Rocheleau et al. 2006 ), in addition to Cx36 knockout. In these mouse models, elevations of basal [Ca 2+ ] i and insulin secretion due to the K ATP loss of function are suppressed by mechanisms dependent on cell cell contact in the intact islet. These islets t herefore allow us to specifically study how cellular differences in electrical activity in the intact islet are suppressed by gap junction coupling and other mechanism dependent on cell cell contacts, as well as to understand how these mechanisms apply to mathematical modeling of the islet architecture.

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25 Islet Transplantation Currently, the best treatment option for patients with type 1 diabetes is islet transplantation from cadaveric donors. Since they are the only cells known to secrete insulin in respon cells can be transplanted by a variety of methods to reduce insulin dependence of diabetic patients. Partial pancreas transplants stud y described 7 type I diabetics who became insulin independent after as isolated islet transplant that this procedure initiated a new arena of research. In this study, patients were injected with isolated whole islet preparations into the portal vein, where the islets lodge in the vasculature. By being in a high flow digestion related system, graft islets are then capable of physiologically regulating insulin secretion. However, despite the wide spread promise of this procedure, many complications remain wit h regards to its efficacy. In the United States, it is estimated that there are 12,000 potential islet donors per year. However, when consent, time and isolation efficiencies are taken into account the number drops to 3,000 (Rother & Harlan, 2004). Barrier s to the effectiveness of transplants include not only the availability number of donor islets, but also post transplant graft viability. Normally, pancreatic islets have a dense capillary network that entails blood perfusion which is 10 times higher than that of the exocrine pancreas (Fung et al. 2007). This not only allows the islet to be sensitive to changes in blood glucose, but also maintains the high metabolic demand of the islets. However, during the process of isolation and in vitro culture pre tran splant, islet vasculature dedifferentiates or degenerates (Brissova & Powers 2008). Immediately after transplantation the pancreatic islets are supplied with oxygen and nutrients solely by diffusion. Therefore, in the early post transplant setting of the p ortal vein the centers of larger islets can become hypoxic and necrotic. It is estimated

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26 that 50 70% of the transplanted islets will be lost in the immediate post transplantation period (Lehmann et al., 2007; MacGregor et al., 2006), with the hypoxic condi tions of the portal vein combined with the energy status of the islets being major contributor (Ryan et al., 2002). Consequently, most patients require multiple transplants (2 4 in most instances), further reducing the number of available pancreata (MacGre gor et al., 2006). Taken together, the statistics show that our current transplant protocols are only ~25% effective at using the ~6,000 available donors to treat the 1,000,000 type I diabetics in the United States (Hirshberg et al. 2003). However, by incr easing the post transplant viability of donor islets the efficacy can be increased. cells have been discussed in scientific literature, though the chasm between promise and reality remains larg cells in vitro, other cells. Though research should be maintained, issues with each remain, for example: no group has been able to reliably propagate isolated islet cells; immunoreactivity and ethical questions remain around xenographs; and issues remain around the efficacy potential malignancy of differentiated stem cells (Rother & Harlan, 2004; Hirshberg, e t al, 2003; Shaprio, et al.; 2000). In addition, none of these options address the complex cell architecture that will be necessary for a proper GSIS. Therefore, it can be argued that pursuing option which make human islet transplant more effective poses t he highest immediate potential for addressing the islet deficiency. It has historically been noted that large islets >200m in diameter do not survive in culture as well as their smaller counterparts, developing necrotic cores while smaller islets showed little core damage (MacGregor et al., 2006). Recently, it has also been shown that

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27 smaller islets show a much better insulin response (MacGregor et al., 2006; Chan et al., 1999), and perform better in hypoxic and normoxic culture (Lehmann et al., 2007). Previous work has also demonstrated that large isolated islets have poor oxygen utilization, poor survivability following isolation, and secrete less insulin than small islets when normalized for the same volume (Williams et al. 2009). When diabetic rats were transplanted with a marginal mass of large islets, none of them became insulin independent. In contrast, when an equivalent mass of small islets was transplanted into diabetic rats, 80% became insulin independent and remained that way for the 2 month duration of the experiment (MacGregor et al., 2006). Subsequently, Lehmann et al. determined that small human islets had a higher survival rate during both normoxic and hypoxic culture conditions with a preferential loss of large islets after 48 hours in hypoxic culture. Ultimately, they demonstrated better performance of human islet transplants with a higher percentage of small versus large islets (Lehman, et al. 2007). A Japanese study (Kaihow et al., 1986) reported that small islets far outnumber large islets in the human pancreata, but constitute only a small percentage of the total islet volume. Since large islets make up the largest percentage of overall transplant mass, but also die with the highest probability, it stands to reason that transplants c ould be made far more efficient if the large islets could be re aggregated into smaller islets of optimal size, or sizes, which allow for proper diffusion of nutrients and maximum insulin response.

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28 Engineering Islets Multiple methods have been reported for aggregating or re aggregating pancreatic primary cells and other insulin secreting tumor cells lines, however most have not given control of the aggregate size, thus preventing the issues discussed above. Recent work by Bernard, et al. has shown that using a novel hydrogel based device, they were able to reform aggregates of mouse insulinoma cells (MIN6) of controlled sizes ranging from 100m to 250m in diameter with high precision. In addition, cell viability showed positive results using confocal im aging (Bernard, et al. 2012). Using photolithography to create high density polyethylene glycol (PEG) microwells of defined precise diameters, cell aggregates can be formed from dissociated pancreata after culture for ~7 days. Our group has recently shown that these aggregates have similar Ca 2+ dynamics, however caution must be taken. Despite the promise that such advancements hold, when re aggregating an organ as complex and reliant on cell cell communication as the Islet of Langerhans, data must first pro ve that cell coupling and electrophysiology are similar to intact organs. Though popular, simply measuring insulin release can be a crude way to determine viability. Though accurate, it is impossible to simulate the different conditions of the transplant e nvironment. However, if we can verify that the inner workings of these organs are intact, we can have more confidence in the procedure and its promise for the future. Therefore, this data needs to be backed by mechanistic and mathematical modeling to suppo rt further research into human applications.

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29 Percolation Model Complex network models describe a wide range of systems in nature, and are increasingly used to describe complex intra and intercellular behaviors. In recent years, they have been used with some success to describe how interacting dynamical systems be cells behave collectively given their individual dynamics and coupling architecture (Strogatz, 2001). Random graphs were first studied by famed ma thematician Paul Erdos. In their model, Erdos and Albert Renyi define a random graph as N randomly positioned nodes (or points) which are connected by n edges (or lines). Two nodes are connected by an edge with a probability p, and a histogram of the edges per node (or degree distribution) follows a Poisson distribution (Erdos and Renyi, 1959; Bollobas, 1981). Although seemingly simple, this models probabilistic properties have led to many breakthroughs in the study of complex systems. An interesting findin g of random graph theory is the probabilistic clustering behavior of the nodes at different values of p. Specifically, percolation theory predicts the existence of a critical probability p c such that below this probability the network is composed of isolat ed clusters of nodes, but above p c a phase transition occurs and a giant cluster begins to span the network. See figure 12A for example of sub p c clustering and emergence of the infinite network. Above P c this cluster is called an infinite network since i t diverges as the lattice size increases (Albert & Barabasi, 2002). In contrast to random graph theory, percolation theory starts with a regular d dimensional lattice of nodes which can only connect to adjacent nodes. Similar to random graphs, an edge is p resent between two adjacent nodes with a probability p and absent with

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30 a probability 1 p. For example, in a 2 dimensional square lattice, a node can form edges with its 4 adjacent nodes and for the 3 dimensional cubic lattice 6 edges can be formed all wi but nodes are occupied with probability p. However, in applications to islet and cell coupling architecture, the bond percolation model is more appropriate since all nodes (cells) are present, but not electrically coupled (Benninger, et al. 2008). Since islets are highly vascularized and contain ~20% non cells in close proximity (and potentially adjacent) may not be directly coupled via gap junctions. In addition, heterogeneity in connexin cells being in different coupling environments. Thus, these aspects of islet architecture lend themselves to description through a percolation model. Percolation theory ha s previously described the properties of randomly coupled resistor networks and how these properties can alter the behavior of [Ca 2+ ] i in coupled cells (Benninger, et al. 2008). For instance, the electrical conductance across an islet or clust cells is proportional to the number of unique paths that can traverse cell connections, and a 25% reduction from maximum conductance of the cell network. As network connectio ns are increased from some p < p c the number of paths increases until the system reaches criticality and an infinite percolating structures forms. Thus, in percolation pc is the probability below which no percolation can occur and is dependent on the latt ice architecture and dimension. A principle property of percolation theory is that even the most general percolation problem in any dimension obeys a scaling relation near the percolation threshold. These scaling laws are heavily dependent on the architec ture and dimension of the node lattice.

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31 given cluster diverges near the percolation threshold according the following power law: Where the critical probability p c is dependent on the lattice architecture and the critical exponent v is dimensional mean cluster radius and scales with the power law given for cluster size (not sho wn). Thus, since their size does not scale with their radius to the dimensional power but rather a c (Kapitulnick, et al., 1983; Albert & Barbasi, 2002). Further, the percolation probability P, denoting the probability that a given node is part of the infinite cluster is given by which scales as a positive power of p p c c Therefore, it is 0 for p = p c and increases for all p > p c Conversely, the average size of finite clusters within the percolation network can be calculated on either side of the p c and obeys Although there are many elegant scaling laws which describe clu ster size distributions, node correlation length, and intra cluster coupling of percolation lattices which have been successfully used to approximate islet electrical coordination (Benninger, et al. 2008) c (Stauffer & Aha rony, 1994). Therefore, for discrete cellular networks with p away from pc, percolation based simulations (which were historically used to find most of these scaling laws) offer the best mode of model fitting.

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32 Percolation theory was first applied to model the synchronization of islet electrophysiology in a paper by Benninger, et al. Using connexin 36 homozygous knockout, heterozygous and wild type mice (which theoretically correspond to p = 0, 0.5 and ~1, respectively), they were able to demonstrate how dis ruptions in inter cell connectivity can cells. In both experimental and computational models, a ~50% decrease in mean coupling conductance was able to disrupt wave propagation and reduce cells. Consideri ng both wave velocity and proportion of cells in the islet showing synchronized [Ca 2+ ] i dynamics, they found experimental data fit a percolation model of cell coupling compared to an ohmic model which posits that all cells are coupled and overall coupling is mediated by individual differences in coupling conductance. Furthermore, their model found that p = 0.85 optimally fit experimental wild type data, indicating that under cells are electrically coupled, which is in sound agreement which previous data on islet coupling (Moreno, et al., 200 5) and the proportion of non cells in the islet (Brissova, et al. 2004). cell dynamics also predicts a phase transition which can be characterized in both 2D and 3D. For example, since the theoretical Pc = 0.2488 fo cells in the islet), ~25% of normal physiological coupling will be insufficient to maintain a cells. Therefore, Ca 2+ would not be able to propagate acro ss the whole islet to coordinate [Ca2+]i oscillations and insulin dynamics at p


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33 phase transitions may play a previously understated role in the progression of diabetes as well as the underlying properties of multicellular dynamical systems in general. In addition, thi s model predicts that at alternative dimensions the differences in coupling alone (even at the same p) can explain the differences in synchronized [Ca 2+ ] i behavior.

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34 CHAPTER II MATERIALS & METHODS Cell Culture and Aggregate Formation Mouse insulinoma 6 (MIN6) cells (P28 36) were maintained in DMEM supplemented with 10% FBS, 1% penicillin streptomycin 0.2% fungizone, 1mM sodium pyruvate and 60M 2 mercaptoethanol. Media was changed 3 times per week and cells were passaged at ~70% confl uency. For passage and seeding, MIN6 cells were briefly washed in Hanks balanced salt solution (HBSS) and then treated with 0.05% trypsin/EDTA. The trypsin was deactivated with growth media. For 2 dimensional aggregates MIN6 cells were seeded at ~4,000cell s/mm 2 in glass bottom dishes (MatTek) which aggregate over 5 days in culture. Three dimensional (3D) cell aggregates were formed using hydrogel microwell cell culture arrays as previously described (Bernard et al., 2012). Briefly, cell microwell arrays w ere formed from a prepolymer solution of 10.8 wt% polyethylene glycol (PEG) diacrylate (M n ~3,000 Da, synthesized as previously described (Lin et al., 2009), 4.2 wt% PEG monoacrylate (M n ~400 Da), 0.5 wt% 4 (2 hydroxyethoxy)phenyl (2 hydroxy 2 propyl)ketone (Irgacure 2959), and HBSS (Figure 1A). Hydrogel microwells were polymerized to glass slides treated with (3 acryloxypropyl) trimethoxysilane (Gelest) by chemical vapor deposition (Kloxin et al., 2010). Well dimensions were defined by photoinitiation of t he prepolymer solution through chrome photomasks (Photo Sciences, 100 m x 100 m (w100), 200 m x 200 m (w200), and 300 m x 300 m (w300) wide.

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35 Figure 1: Formation of hydrogel devices for aggregating MIN6 cells. A) Photocrosslinkable prepolymer solution (red) consisting of 15 wt% macromere (75mol% PEGA0.4kDa, 25mol% PEGDA3 kDa), 0.5 wt% photoinitiator I2959, and 300 mM methacryloxyethyl lass slide and a chrome photomask separated by spacers (tan) of defined thickness. B) Microwells formed after ultraviolet light exposure (350 450 nm) for 60 s had been covalently attached to the functionalized glass slide. C) Representative confocal image of a microwell device (width and height = 100 mm) in both the x y plane (top) and x z plane (bottom). Scale bars represent 100 m. PEGDA, poly(ethylene glycol) diacrylate. Inc., Torrance, CA) to form wells (Figure 1B & C) that were approximately 100 m de ep and MIN6 cells were seeded into the wells at a density of 520,000 cells/cm 2 in w100 devices and 940,000 cells/cm 2 in w200 and w300 devices using centrifugation as described previously (Bernard et al., 2012). The devices were rotated on an orbital shake r for 2 hours and then cultured under static conditions in growth media for 5 additional days. 3D aggregates were removed from the microwell devices using a gentle flow of media and selected for experiments using a Leica SL30 dissection microscope (Figure 2) Prior to the formation of primary cell 3D aggregates, fresh isolated islets were incubated overnight in RPMI (Invitrogen) supplemented with 10% FBS, 1% penicillin streptomycin and 0.2% fungizone. To disperse individual cells, islets were twice digest ed in a solution HBSS with 0.05% trypsin for 30 minutes and centrifuged to collect the cells. The final cell suspension was then seeded on to preformed 100 m x 100 m (w100), 200 m x 200 m (w200) devices and aggregates were formed as explained above.

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36 Figure 2: Formation of MIN6 aggregates. Aggregates of MIN6 cells in poly(ethylene glycol) microwell devices. Cells were seeded at a density of 3x10 6 cells / ml followed by centrifugation. To visualize, cells were stained with CellTracker Green before seedi ng and confocal images were taken 5 days after seeding (A C) and after removal (D F) Well widths are 100m (A, D) 200m (B, E) and 300m (C, F) Insulin Secretion Cumulative, static insulin secretion was measured in order to investigate correlations with the [Ca 2+ ] i behavior. Two and three dimensional cell aggregates were formed as described above and cultured for 5 days. MIN6 cell clusters were conditioned in Krebs Ringer Buffer (KRB, 128.8 mM NaCl, 5 mM NaHCO 3 5.8 mM KCl, 1.2 mM KH 2 PO 4 2.5 mM Ca Cl 2 1.2 mM MgSO 4 10 mM Hepes, 0.1% BSA) containing 2 mM glucose for 1 hour prior to the glucose stimulation assay. Aggregates were then incubated in KRB containing either 2 mM glucose (low glucose), 20 mM glucose only (high glucose), or 20 mM glucose an d 20 mM TEA (+TEA) for one hour. Supernatant from each sample was collected and stored at 70C until testing. Supernatant samples were tested using a sandwich ELISA per to basal secretion levels.

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37 Microscopy To measure [Ca 2+ ] i dynamics, 2 and 3 dimensional aggregates were stained with 4M Fluo4 AM in imaging medium (125mM NaCl, 5.7mM KCl, 2.5mM CaCl 2 1.2mM MgCl 2 10mM Hepes, 2mM glucose, and 0.1% BSA, pH 7.4) at room te mperature for 60 90 minutes before imaging. 2D aggregates were imaged in glass bottom dishes, and 3D aggregates were imaged in polydimethylsiloxane (PDMS) microfluidic device, the fabrication of which has been previously described ( Rocheleau, et al., 2004 ) Real time imaging was performed on a Nikon Eclipse Ti equipped with a humidified environmental chamber maintained at 37C. Fluo4 fluorescence was imaged with a 20x 0.8NA objective, using a X enon arc lamp light source (Sutter) and 470/20 filter for excitation and 525/36 filter and a CCD camera (Andor Clara) for fluorescence detection. Aggregates were allowed to equilibrate after each treatment for 10 minutes before imaging at 1 frame/s for 15 minutes, with negligible photobleaching observed. Matlab Analysis In signal processing, cross correlation is the measure of similarity between two waveforms with a time lag, or phase shift, applied to one of them. To calculate [Ca 2+] i coordination of a cell cluster, a cross correlation function was used to determine the level of similarity of the waveforms generated by the fluorescent intensity of the imaging time course. The average fluorescent intensity of a selected area of the cell cluster or aggregate was used as the reference waveform and then the cross correlation was performed between this reference waveform and the fluorescent intensity waveform of each pixel in the cluster (Figure 3A). The cross correlation function measures w aveform similarity by sliding one

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38 wave function across the other and calculating the integral of the overlapping area. At each interval a cross correlation coefficient is calculated in this way, with 1 indicating perfect overlap and 0 indicating none. For example, a cross correlation coefficient of 1 would indicate that a certain pixel is in perfect synchronization with the reference area, whereas a coefficient of 0 means there is no similarity. The maximum cross correlation coefficient was used as a measur e of similarity and a value above 0.75 was used as a threshold as to whether a certain cell was correlated with the cell cluster or aggregate as a whole. Therefore, the total area of the cluster with a cross correlation coefficient above 0.75 was used as a measurement for the overall correlation, or synchrony The information describing cell synchronization and areas of coordination is represented as a false color hue saturation value image where the hue (color) represents the cross correlation coefficient or period of oscillation, saturation (the amount of color) is set to one and value (intensity) represents the average fluorescence intensity in order visualize cell localization. Based on the presumption that the cumulative standard deviation of the fluor escent intensity of a silent cell will be much less than that of an active cell, the mean and plus three total standard deviation of the measured fluorescence inten sity of each pixel in the rest of the cluster. If the standard deviation in fluorescence of a pixel was higher, it was deemed to be active. This was accomplished by a custom written program which would calculate the standard deviation of the fluorescent in tensity across the entire time course of a selected a silent cell, then compare that with every pixel within the entire cell cluster. Silent cells were selected by looking at a cells fluorescent waveform in a software package (Nikon Elements).

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39 Figure 3: Explanations of computational methods. A) Cross correlation analysis calculates a sliding integral of the overlap between the test wave (blue) and the stationary reference wave (black). The maximum cross correlation coefficient is achieved at the point of maximum overlap. B ) Sample power spectrum from experimental data. Power robustness was calculated by normalizing the maximum value of the AC component with the maximum value of the DC component. Only cells with relatively flat responses were used as the silent cell reference. The size of each cluster or aggregate, as well as the regions of coordination within them, was determined by manually tracing the boundaries in a custom written Matlab program, which then tabulated the pixels within the b oundaries. Average cell size in both two dimensional aggregates and three dimensional clusters were also determined and found to be approximately 14m in diameter, which is in agreement with previous work (Ni, et al. 2010). To determine aggregate cell numb er, the radius was found from the area and then used to calculate volume using a spherical formula, which was then divided by the volume of a single cell. Two dimensional cell cluster area was found by dividing the total area of the cluste r by the area of a cell. To determine whether there is a maximum distance over which cells are coupled, a Matlab program was written to calculate the Euclidian distance of over which cells in a cluster were coordinated. A cell within a cluster was isolated by tracing its boundaries and the average fluorescent intensity was calculated over the entire time course to give a representative waveform of that cells. A cross correlation was performed between that

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40 reference waveform and each other pixel in the cell cluster and a va lue higher than 0.75 indicated that that pixel was correlated with the reference cells. Therefore, the distance over which the pixels maintained a coefficient higher than 0.75 was used as a measure of the correlation distance of the cells. To extract data regarding phase and period, a Fourier Transform was performed on the fluorescent intensity profile of each pixel. The power spectrum from the Fourier Transform tells us how much of the fluorescent signal is at a particular frequency. For example, in a sin e wave where there is one frequency, there would be a single impulse. In a noisier signal of the same average fluorescence intensity there may be multiple peaks corresponding to multiple frequencies in the signal, though the area under the spectrum will b corresponds to the average value of the signal (Figure 3B), and is typically removed (Najarian & Splinter, 2012). To measure the robustness, or regularity, of the period i n [Ca 2+ ] i oscillations, the maximum value of the power spectrum with the DC component removed was normalized to the maximum value of the power spectrum with the DC not removed to normalize for the variability in fluorescent signal (Figure 3B). The maximum value of the power spectrum was also used to find the period of oscillation for each pixel, which was then mapped (using the HSV format explained above) to investigate coordination in frequency of [Ca 2+ ] i oscillations. Wave propagation was determined by selecting t wo cells within a two dimensional cluster or three dimensional aggregate which were separated by approximately 100m and measuring the temporal offset between successive identical parts of a [Ca 2+ ] i wave. The velocity is calculated in the direction of the wave propagation by dividing the exact spatial separation by the temporal offset of the [Ca 2+ ] i wave.

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41 All statistics were performed in Matlab ( Mathworks, Natick, MA). For comparison of means, ANOVA was utilized. To compare determine whether linear relationships existed between a variable and cell number, a linear regression model was used. Development of KIR2.1 and Connexin 36 Knockout Mice Mutant KIR6.2[AAA] constructs containing green fluorescence protein (GFP) were generated by replacing the tripeptide sequence 132GFG134 of the ion selectivity filter cell lines through transient transfection, construct s were purified and microinjected into fertilized mice eggs. Transgenic mice were identified through PCR on using GFP specific primers (Koster et al., 2000; Koster et al., 2001). To establish a stable line, one KIR6.2[AAA] founder was identified and bred b ack to littermates. Bond Percolation Simulations for Size Scaling and Dimensionality Comparisons Bond percolation is a sub model of percolation theory in which for a given lattice of nodes (cells) adjacent nodes are connected (coupled) with a probability p or not connected with a probability (1 p ) This is in contrast to site percolation, in which all edges are present but nodes only exist with a probability p In a 2D or 3D aggregate all cells are present; however, whether the cells are coupled varies a ccording to size scaling and dimensionality laws. Therefore, a bond percolation model was established to model cellular coordination on a 2D square lattice or 3D cubic lattice where each node (cell) is capable of establishing connections with its 4 or 6 ad jacent neighbors, respectively. The bond percolation lattice

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42 Figure 4 : Overview of bond percolation lattice. A) Visual representation a cubic lattice with bonds to all 6 nearest neighbors representing a p = 1. B) Visualization of the 11x11x11 lattice created for the percolation model in Matlab at p = 0, representing the nodes only without cells. The left panel is a top view demonstrating the equal spacing for edges, which are not present. C) Visualization of the 5 x5x5 lattice created for the percolation model in Matlab at p = 0, representing the nodes only without cells. The left panel is a top view demonstrating the equal spacing for edges, which are not present. was developed in Matlab with a matrix of alternati ng values of 1 (node) and 0 (site for potential edge bond). Probabilities were randomly assigned to each edge bond point. If the probability was less than or equal to the assigned percolation probability ( p ), an edge was established and the 2 neighboring nodes were deemed coupled. An identification number was assigned to each individual cluster formed from coupled edges, and the edges were then removed to establish clusters based solely on node coupling (Figure 4A, second panel). High Glucose (Synchroniz ation) Simulations Simulations of high glucose coupling were carried out with a custom MATLAB routine based on a previously published method (Kapitulnik, et al. 1983). Two dimensional clusters of 25x25 nodes were populated with edge probabilities based on a Gaussian

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43 Figure 4: Summary of resistor network model. A) False color simulation of cluster size for bond percolation with p below (left) and above (middle) the critical probability. (Right) Resistor network showing behavior above the critical probability. B) Simulations and experimental data of oscillation synchronization for values of p at high glucose in 2D. C) Simulations and experimental data of [Ca 2+ ] i activity for values of p at low glucose in 2D. D) Si mulations and experimental data of [Ca 2+ ] i activity for values of the percent of cells within a cluster necessary to suppress [Ca 2+ ] i activity of the entire cluster (Sp) in 2D. E) Simulations and experimental data of oscillation synchronization for values of p at high glucose in 3D. F) Simulations and experimental data of [Ca 2+ ] i activity for values of p at low glucose in 3D. G) Simulations and experimental data of [Ca 2+ ] i activity for values of the percent of cells within a cluster necessary to suppress [C a 2+ ] i activity of the entire cluster (Sp) in 2D. distribution and clusters were formed based on a whether adjacent connections had assigned probabilities greater than, or equal to, the critical probability (Figure 5A). We next identified the largest clus ter on each of the simulated lattices and selected only those in which the central lattice site belonged to the cluster. The mass of the percolating area, or

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44 M(L), was determined by summing the connected nodes to the central cluster within squares of area L 2 around it. By averaging these over the area of the simulated cluster sizes, we found the percolation density We then deemed that if any two cells were coupled to the same network, they were synchronized. Therefore the percolation density is analogous to the synchronized area of each cluster. For each value of p, 1,000 simulations were run (Figure 5B) and best fit to experimental data was determined by a chi square test. Low Glucose (Suppression) Simulations In contrast to modeling high glucose [Ca 2+ ] i activity, where all cells within a network are deemed synchronized, low glucose modeling was based on the princi ple that a certain percentage of non responsive cells can hyperpolarize and suppress the activity of all other cells in a coupled network. A linear fit to the experimental low glucose data showed a y intercept value of 67%, indicating that that there is ap proximately a 2/3 probability that a given cell will be active. We then used this probability in a binomial model, which describes the number of successes k (active cells) in a number of trials n (total cells in a cluster), with each success having a proba bility p (67%). Or, where

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45 After establishing bond percolation clusters as in the high glucose model, the cell number of each cluster (n) was then determined and the probability of the cell being active was calculated using the binomial model. For each value of p and k, 2,000 simulations were run, and best fit to experimental data was determined by a chi square test (Figure 5B). Bond Percolation Simulations for Discrete Modeling of Islet Connectivity To exam ine how our mathematical model can predict islet [Ca 2+ ] i and insulin behavior when the system is perturbed through transgenic mutation of the K ATP channel or Cx36 gap junctions, the simulations of high glucose were run to calculate percent synchronization as a function of p for varying cell diameters. In addition, the level of suppression was simulated in the low glucose model for varying levels of p and the probability of a cell being active for varying network diameters.

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46 CHAPTER III RESULTS: DIMENSIONALITY AND SIZE SCALING OF COORDINATED Ca 2+ DYNAMICS IN PANCREATIC CELL NETWORKS [Ca 2+ ] i Dynamics and Insulin Secretion Under Two and Three Dimensional C oupling cells within the islet of Langerhans undergo robust oscillations in [Ca 2+ ] i These individual [Ca 2+ ] i oscillations are synchronized through cell cell gap junctions and results in a transverse Ca2+ wave across the islet which coordinates pulsatile insulin secretion (Head, et al., 2012; Macdonald & Rorsman, 2006). However, the underlying architecture and coupling has been shown to have large impacts on this synchronized behavior. In order to investigate how the underlying cellular architecture and electrical coupling affects the robustness and synchronization of [Ca 2+ ] i cells, we analyzed [Ca 2+ ] i time courses in 2D cell clusters and 3D aggregates of defined size and shape. Under 2D coupling, cell clusters generally exhibited irregular bursts of [Ca 2+ ] i at high gluco se, which became more regular upon addition of the K ATP channel inhibitor TEA (Figure 6A) As quantified from the robustness of the Fourier power spectrum, TEA at high glucose was found to significantly increase the robustness of the oscillation period co mpared to high glucose alone (p<0.01) (Figure 6C). This increase in regularity of the period was expected given that blockage of the K ATP channels has previously been shown to cells more sensitive to changes in V m and inter cellular c oupling (Bokvist, et al., 1990)

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47 In contrast, under 3D coupling aggregates exhibited highly regular [Ca 2+ ] i oscillations both in the presence and absence of TEA (Figure 6B). The robustness of the 3D oscillations showed no significant differences (p>0.05) upon addition of TEA and was significantly more robust compared to 2D clusters under high glucose alone, but not 2D under high glucose with TEA (Figure 6C). Similarly, the insulin secretion response demonstrated a similar pattern to the [Ca 2+ ] i oscillation robustness. In 2D aggregates, high glucose with TEA stimulated a significantly greater insulin secretion compared to high glucose alone. However, the addition of TEA was not found to have an effect on 3D insulin secretion at high glucose (Figur cells into Figure 6 : Robust [Ca 2+ ] i oscillations and insulin release in 3D aggregates. A) Representative [Ca 2+ ] i oscillations, measured from Fluo 4 fluorescence, averaged over a 2D aggregate. B) As in A, averaged over a 3D aggregate of comparable size. Time courses are offset for clarity and vertical scale bar represents 50% change in fluorescence. C) Mean (s.e.m.) power robustness at 20mM glucose and 20mM glucose +20mM TEA. D) Mean (s.e.m.) insulin release as % of content, normalized to release at 2mM glucose. Data in C averaged over n=28 (2D) and n=22 (3D) aggregates, and data in D averaged over n=6 (2D) and n=12 (3D) aggregates. in C, D indicates significant difference between glucose and glucose+TEA for power robustness (p=0.00015) and insulin release (p=0.0166).

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48 structures which allow for 3D coupling increases the robustness of the oscillatory [Ca 2+ ] i response and leads to higher levels of insulin secretion at high glucose. Dimension and Size D ependence of [Ca 2+ ] i S ynchronization To investigate the spatial variation of [Ca 2+ ] i dynamics, we next measured the synchronization of [Ca 2+ ] i oscillations in 2D and 3D under high glucose with and without TEA. In 2D aggregates at high glucose with TEA, oscillations were found to be synchronized within distinct sub regions of the cell cluster (Figure 7A). Compared to the oscillations in a specific cell, the synchronization of the oscillations in other cells decreased as a function of increasing dista nce. Using a cross correlation function, we found that these oscillations were highly synchronized within a radius of approximately 5 cells. However, at greater distances there was a sharp decrease with little synchronization observed. The change was sudde n, with adjacent cells showing different oscillatory [Ca 2+ ] i patterns suggesting they are part of different electrophysiological coupling environments (Figure 7B). In contrast, 3D aggregates at high glucose with TEA showed synchronization that was consiste nt across the entire cell mass (Figure 7C). Most cells showed synchronized oscillations, independent of separation distance and position with in the aggregate (Figure 7D). Given that cells were only synchronized within a limited Euclidean distance (~5 cell s) in 2D, we anticipated that smaller 2D aggregates with less than a 5 cell radius would show a greater proportion of cells that were synchronized. Indeed, 2D cell clusters consisting of <20 cells were highly synchronized (Figure 7F), with a percentage of synchronized cells that was not different compared to 3D aggregates (p<0.05) (Figure 7E).

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49 However, larger 2D aggregates above the critical size showed a significant reduction in synchronization with increasing size compared to 3D aggregates containing an equivalent number of cells (p> 0.01) (Figure 7E). Interestingly, in larger 2D cell clusters above the critical size there were multiple clusters of cells which were highly synchronized, V IV III II I 1 0 0 1 I II III Figure 7 : Size scaling and dimensionality of [Ca 2+ ] i oscillation synchronization. A) False color map of the cross correlation coefficient in a 2D aggregate, relative to a reference cell (I). B) Fluo4 time courses in cells at increasing distance from the reference cell (II V). C) Fal se color map of the cross correlation coefficient in a 3D aggregate, relative to a reference cell (I). D) Fluo4 time courses in cells well separated from the reference cell in 3D (II, III). E) Mean (s.e.m.) area of aggregate showing synchronized [Ca 2+ ] i o scillations, in 2D and 3D aggregates of different size ranges at 20mM glucose +20mM TEA. F) Scatterplot of synchronization versus aggregate size, for 2D aggregates at 20mM glucose +20mM TEA G) As in F for 3D aggregates. in E indicates significant differ ence in synchronization of larger 2D aggregates (21 200 and >200) compared to small aggregates (<20), and a significant difference in synchronization comparing 2D and 3D aggregates (p<0.001). Linear regression in F, G indicated by solid line, with signific ant size dependence in F and G (p < 0.0001).

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50 supporting the notion of a defined distance over which cells can coordinate. Synchronization in 3D aggregates also showed a size dependence up to the 300m diameter, however the slope of the line was much more shallow (Figure 7G). Similar results were seen in 2D and 3D aggregates under high glucose alone. However, the radius of synchronization was found to be far less (~2 cells) (Figure 8). I IV III II 1 0 I III II 1 0 Figure 8 : Size scaling and dimensionality of [Ca 2+ ] i oscillation synchronization at 20mM glucose. A) False color map of the cross correlation coefficient in a 2D aggregate, relative to a reference cell (I). B) Fluo4 time courses in cells at increasing distance from the reference cell (II V). C) False color map of the cross correlation coefficient in a 3D aggregate, relative to a reference cell (I). D) Fluo4 time courses in cells well separated from the referenc e cell in 3D (II, III). E) Mean (s.e.m.) area of aggregate showing synchronized [Ca 2+ ] i oscillations, in 2D and 3D aggregates of different size ranges at 20mM glucose +20mM TEA. F) Scatterplot of synchronization versus aggregate size, for 2D aggregates at 20mM glucose +20mM TEA G) As in F for 3D aggregates. in E indicates significant difference in synchronization of larger 2D aggregates (21 200 and >200) compared to small aggregates (<20), and a significant difference in synchronization comparing 2D and 3D aggregates (p<0.01).

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51 Therefore, this data indicates that not only can cells coordinate over a defined cell clusters can have a significant impact on [Ca2+]i synchronization. In addition, the dimen sionality of the coupling is critical to properly synchronize an entire syncytium of electrically excitable cells. Sub Regions of Synchronization in Two Dimensional Cell C lusters To further investigate the limiting range over which 2D cell clusters can synchronize [Ca 2+ ] i oscillations, we measured the extent of synchronization at different positions within cell clusters. Qualitatively, multiple non overlapping areas of synchronized [Ca 2+ ] i oscillations and similar period were observed within large cell c lusters (Figure 9A). I II II I IV 150s 300s Figure 9 : Localization of synchronized [Ca 2+ ] i oscillations to discrete regions in 2D. A) False color map of regions of high cross correlation coefficient in a 2D aggregate, with respect to different reference cells. B) Fluo4 time courses of cells within each area o f synchronization in A. C) False color map of [Ca 2+ ] i oscillation period in same 2D aggregate as A. D) Mean (s.e.m.) area of oscillation period (Period) and area of high cross correlation coefficient (Cross corr). Data averaged over n=28 clusters. No significant difference is observed (p=0.3147).

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52 Importantly, regions with similar oscillation period as found from the Fourier power spectrum overlapped strongly with regions of synchronization as found by our methods. There was not found to be a difference between the area of synch ronization as found by either method (Figure 9D), validating the 0.75 cross correlation coefficient threshold. Within the cell cluster, the largest area of synchronization was similar to the largest region with similar oscillation period, with a mean size of ~28 cells (Figure 9D). In addition, regions of similar period as defined through Fourier mapping produced similar results compared to cross correlation mapping independent of which cell within the area was chosen as the reference (Figure 9 A & C). This indicates that areas of synchronization are well defined through local interactions in 2D. Wave Velocity Under Two and Three Dimensional C oupling Calcium dynamics are synchronized within the islet through intercellular coupling, where elevations in [Ca 2+ ] i propagate across the islet from regions of higher glucose sensitivity (Benninger, et al., 2008; Aslanidi et al., 2001; Bertuzzi, et al., 1999). The velocity of the Ca 2+ cell coupling where reduced coupling across th e islet results in slower waves and less overall [Ca 2+ ] i coordination (Benninger, et al., 2008). To further characterize the effects of dimensionality on the coupling behavior of cells, we measured the propagation velocity in 2D and 3D. In 2D aggregates, Ca2+ waves were confined to the sub regions of synchronization (~100m). As characterized by the temporal offset of peak [Ca 2+ ] i between two cells ~100m apart, the mean wave velocity was found to be significantly higher in 3D aggregates compared to the 2 D sub regions (Figure 10A C). The distribution of wave velocities was also biased to waves >50m/s in 3D aggregates compared to a bias towards <50m/s waves in 2D (Figure 10D).

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53 There fore, 2D aggregates show slower propagating Ca2+ waves compared to 3D aggregates, which further suggests that 2D cells are less coupled and that dimensionality plays an cell synchronization. Dimension and Size Dependence of B asal [Ca 2+ ] i S uppression Intact islets area also characterized by a uniformly quiescent [Ca 2+ ] i at low/basal cell coupling (Benninger, et al., 2011; Speier, et al., 2007). Therefore, given the dependence of [Ca 2+ ] i dynamics on size and dimensionality of the cellular architecture, we next measured whether [Ca 2+ ] i suppression had a similar dependence at low glucose. Under low glucose conditions (2mM), 2D cell clusters generally exhibited spontaneo us, transient [Ca 2+ ] i activity, whereas 3D aggregates remain quiescent. Interestingly, large 2D cell clusters consisting of >200 cells were mostly quiescent, showing similar activity to that measured in 3D aggregates Figure 10 : Dimensionality affects wave propagation velocity. A) Fluo4 time course for two cells within a 2D aggregate separated by ~100m, at the wave start (black) and wave end (red). B) As in A, for time course at the wave start and end within a 3D aggregate. C) Mean (s.e.m.) wave velocity in 2D and 3D aggregates. D) Histogram of measured wave velocities in 2D and 3D aggregates. Data averaged over n = 18 (2D) and n=12 (3D) aggregates. in C indicates significant difference in wave velocity (p<0.001).

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54 (p<0.001)(Figure 11A). However, smaller 2D cell clusters were found to be more active compared to 3D aggregates of similar cell number and larger 2D cell clusters (p<0.001). In the smallest 2D aggregates, 67% of the cell s showed a transient [Ca 2+ ] i elevation with a cell suppression is size dependent 2D (Figure 11B). In contrast, 3D aggregates showed a size independent suppression with ~20% ac tive cells over the entire range of sizes measured, up to 300m diameter (Figure 11C). Figure 11: Size scaling and dimensionality of [Ca 2+ ] i suppression at low glucose. A) Mean (s.e.m.) area of aggregate showing transient [Ca 2+ ] i elevations in 2D and 3D aggregates of different sizes at 2mM glucose. B) Scatterplot of transient [Ca 2+ ] i elevations versu s aggregate size, for 2D aggregates. C) As in B for 3D aggregates. in A indicates significant difference in transient [Ca 2+ ] i elevations of small 2D aggregates (<20) compared to larger aggregates (20 200, > 200), and a significant difference in elevation comparing 2D and 3D aggregates at moderate size (20 200, p<0.001), but not very large clusters (>200, p>0.05). Linear regression in B,C indicated by solid line, with significant size dependence in B (p < 0.0 01), but not in C (p > 0.05).

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55 Network Lattice M odel of [Ca 2+ ] i D ynamics As previously outlined, a lattice resistor model has been used to accurately describe the dependence of [Ca 2+ ] i cells (Benninger, et al., 2008). Therefore, we next set out to put our results in mathematical context by testing whether such a model could describe the size and dimensional dependence of synchronized [Ca 2+ ] i oscillations and suppression. Our initial methodology centered on using established power laws which describe the average size of a cluster, the average correlation distance Figure 12: Coupled resistor network model of size scaling and dimensionality. A) Simulated networks for different probabilities of resistive coupling connections ( p ), where low numbers of connections give sub critical behavior with multiple sub regions of connected units (left) but high numbers of connections give super critical behav ior with connecting units spanning the entire network (right). B) Simulation and experimental data of oscillation synchronization for 2 values connection probability p. Circle represents experiment, solid blue line represents p 2 = 8.01) and solid r ed line represents p 2 = 3.89). C) Simulation and experimental data of transient elevations with p 2 = 12.31). Each line represents an average over n=2000 simulations.

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56 a nd percolation probability of a random percolation network. However, using this approach we could not accurately reproduce our experimental results, especially in the 3D case. This is most likely due to the fact that these power laws only obey the scaling relation near the percolation threshold, which is p c =0.5 for 2D square and p c =0.2488 for 3D cubic lattices. Therefore, to circumvent the scaling relations, we simulated partially coupled resistor networks covering different sizes over 2D and 3D for a give n proportion of node (cell) connectivity. In a 2D network for sub p c (p<0.5) connectivity, multiple small clusters of connected nodes were generated which were similar to the sub regions of synchronized oscillations measured in 2D aggregates (Figure 12A). For higher connectivity (p>0.5) in 2D and 3D, a single cluster of connected nodes emerged which spanned the whole network. This network spanning behavior was similar to the uniform synchronization seen in 3D aggregates at high glucose and suggests that th e network model simulations can be related to [Ca 2+ ] i cells are synchronized if their corresponding nodes belong to the same connected cluster, with an unbroken path traced between the nodes. We next tested whether this netwo rk model could quantitatively describe the [Ca 2+ ] i oscillations synchronization, as well as reconcile the differences seen with regards to dimension and size. We initially simulated low connectivity 2D networks for varying p. As predicted by previous perco lation work, as p decreases from p c multiple fractal clusters begin to form (Kapitulnick, et al., 1983). A p=0.320.005 generated multiple synchronized clusters with a mean size of 28 nodes, which is similar to the experimentally determined number of cells in the largest synchronized cluster in 2D networks. Following Kapitulnick, et al. we then measured the proportion of nodes in the largest synchronized cluster relative to the total network for varying network sizes (9 to 441 nodes on a square lattice). A

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57 p=0.312 (95% CI: 0.284 0.337) generated a size variation which best fit the experimental 2D synchronization data (Figure 12B)and is in close agreement with the p describing the number of cells in a 2D synchronized region. The scaling laws of percolation th eory are proven for infinite networks and on the power law concerning characteristic cluster size a p=0.253 was found to generate an average cluster size of 28 cells, which is outside of the 95% confidence interval bounds found by simulation. However, when the simulation was run to best fit data for >250 cells, a p=0.277 generated a best fit. Therefore, as cluster size increase in the 2D model the behavior may better converge to that of the scaling laws. In the 3D model, a p=0.369 (95% CI: 0.334 0.423) generated a size variation which best fit the experimental synchronization data (Figure 12D), which is in sound agreement with the 2D model as demonstrated b y the overlapping 95% confidence intervals. Therefore, taken together this data shows that the size dependence of multiple independent parameters representing [Ca 2+ ] i oscillations at high glucose can be quantitatively described by the lattice resistor netw ork model. Of note is the fact that both cases generated similar p, indicating the probability of coupling may be conserved across dimensions. However, this value of p corresponds to sub critical, fractured percolation in 2D and super critical percolation in 3D. We next tested whether this same network model could also describe the suppression of spontaneous [Ca 2+ ] i cells can cells through gap junctions electrical coupling (Head, et

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58 al., 2012), and therefore also lends itself to description through the percolation model. To determine whether cells were active or silent within the model, we defined a rule were a threshold proportion of the inexcitable cells within a connected cluste r can suppress activity in all cells in the connected cluster. Based on our experimental measurement that 67% of single cells are active, binomial statistics were used to determine whether there were sufficient inexcitable cells to reach the suppression th reshold. Naturally, as n becomes large the probability of the entire cluster being quiescent increases. In both 2D and 3D there was a strong agreement between experimental data and network model with a threshold of 15% inexcitable cells, whereas the data was best fit by p=0.378 (95% CI:0.354 0.398) in 2D (Figure 12C) and p=0.323 (95% CI:0.302 0.346) in 3D (Figure 12E). Therefore, not only can the size dependence of spontaneous [Ca 2+ ] i suppression can be quantitatively described by a lattice network archite cture, but the values of the percolation probability were found to be similar to those that describe high glucose [Ca 2+ ] i oscillations.

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59 CHAPTER IV RESULTS: REAGGREGATION OF PRIMARY ISLET CELLS INTO CELL CULTURE Primary Islet Cells Uniformly Aggregate to Defined Sizes in 3D PEG Microwell A rrays Islet transplant is currently the best option in the treatment of type I diabetes. However, recent work has shown that even though large islets make up the majority of the transplant mass, limited post transplant diffusion often causes the islet centers to become necrotic, which leads to reduced transplant efficacy. Therefore, a method to disperse and then re islets similar cellular composition and function, could drastically increase the efficacy of islet transplants. Towards this goal, primary murine islets were dispersed by trypsin digestion and seeded into square PEG microwells with diameters of 100m and 200m. After 5 days of in vitro culture seeded cells naturally formed tight aggregates within the microwells (Figure 13A). The 3D structure was verified through nuclear staining followed by confocal microscopy (Figure 13B). Prim ary cells clustered were relatively uniform in size and with dimensions that scaled with the microdevice well dimensions. To assess the uniformity and scalability of primary cell aggregates formed using microwell devices, the aggregate diameter was measure d using confocal laser scanning microscopy combined with further image analysis. The average aggregate diameters were found to

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60 Figure 13 : Primary islet cells form viable 3D pseudo islets of defined size in PEG microwells. A) Formation of pseudo islests. Bright field images taken 1 day after seeding, 5 days in culture and after removal from the devices. B) Table of pseudo i slet sizes for each PEG microwell diameter. C) Confocal images of pseudo islets stained with the fluorescent nucleic acid stain DAPI to demonstrate 3D structure. D E) Live/Dead staining of D) whole islets as well as E) 100m and F) 200m pseudo islets on d ay 7. Green fluorescent cells are live while dead are red. All scale bars represent 100m. depend on the cross sectional area of the microwells, with w100 aggregates having a diameter of 6015m and w200 aggregates w200 aggregates having a diameter of 100 15m (Figure 13C). Therefore, the diameter of the aggregates was 50 60% of the microwell diameter. The mean diameter of all normal islets analyzed was 15321m (n = 21). After Removal 5 days of culture Post Seeding DAPI z stacks

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61 Pseudo Islets Show Comparable Viability and Functionality to Fresh I slets Islets exist in a unique, highly vascularized environment in vivo, and generally do not show optimal function or viability after long term in vitro culture. Since the re aggregation procedure takes 7 d ays, the post aggregation function and viability is of concern. After 7 days in culture, both the w100 and w200 sized pseudo islets demonstrated similar viability to day 1 normal islets (Figure 14 A, B & C). As a percentage of total cells, w100s and w200s comparable viability to day 1 normal islets (p<0.05)(Figure 14D). Figure 14: Pseudo islets show more robust [Ca 2+ ] i oscillations compared to age matched normal islets. A) Representative [Ca 2+ ] i oscillations, measured from Fluo 4 fluorescence, averaged over entire normal islets for on day 1, 7 and 14. B) Representative [Ca 2+ ] i osci llations, measured from Fluo 4 fluorescence, averaged over pseudo islets on day 7 and 14, which are days 1 and 7 removed from the microwell devices, respectively. C) Normalized power robustness for normal islets (bottom line) and pseudo islets (top line) o n days 1, 7 and 14. Error bars represent SEM, indicates a significant difference same group compared to the previous time point.

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62 Therefore, the re aggregation procedure was not found to have a significant effect on the overall viability of primary islet cells. To examine the function of the pseudo islets, we used a s imilar procedure to the MIN6 aggregates. Time courses of [Ca 2+ ] i dynamics were analyzed for overall synchron ization across the entire cell mass as well as robustness of the oscillation period. Activity at low glucose was also examined to determine if there was proper electrical suppression. At 11mM glucose, the [Ca 2+ ] i dynamics of the pseudo islets was highly synchronized (~88.354.02%). This was very similar to control Day 1 normal islets (~84.056.03%), suggesting that functionality and proper gap junction coupling was properly re established after 7 days in culture. When grouped by well size, the W200s were found to have a higher area of synchronization compared to the W100s (P<0.05) (Figure 16D), although neither group was significantly different compared to normal islets (P>0.05). The area of synchronization for nor mal islets at day 1 at 11mM was also in agreement with previous results using an analogous method (Benninger, et al.). Pseudo islets had very regular [Ca 2+ ] i oscillations which mimicked Day 1 normal islets; when quantified, day 7 pseudo islets had a normal ized power robustness that was not found to be different than Day 1 normal islets (0.02480.0003 vs. 0.02320.0048, respectively)(p>0.05)(Figure 15C). Taken together, this data indicates that after 7 days in culture the islet re aggregation procedure was a ble to maintain proper islet dynamics, comparable to freshly harvested islets.

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63 Figure 15 : Pseudo islets show better superior functionality over time. A) False color map of the cross correlation coefficient in a 3D aggregates, relative to a reference cell. B) Area with synchronized [Ca 2+ ] i dynamics (as defined as the area with a cross correlation coefficient > 0.75) for normal islets (bottom line) and pseudo islets (top line) on days 1, 7 and 14. Error bars represent SEM, indicates a significant difference between groups at the same time the previous time point. C) Area synchronized found as in B for W100 and W200 pseudo islets. indicates a significant difference between groups. D) Islet area active at low g lucose. Day 7 and 1 4 Pseudo Islets are Better Than Age Matched Normal I slets A major concern in islet transplantation is post transplant graft survival. It has been reported that ~50% of islets become necrotic after transplantation. Since this is the is sue we intend to address with this procedure, long term function is of concern. Therefore, we compared [Ca 2+ ] i endpoints for Day 7 (1 day removed from the microwell device) pseudo islets to batch matched normal islets which were cultured in parallel for 7 days. We then did the same comparison on Day 14. When compared to normal islets one day post harvest, pseudo islets one day removed from the microwell device (day 7) showed much more robust and coordinated [Ca 2+ ] i oscillations despite the fact that both groups had spent 7 days in culture. At 14 days, the oscillatory behavior of the pseudo islets remained synchronized while the normal islets Normal Islets Pseudo Islets Day 1 Day 7 Day 14

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64 maintained their deteriorated behavior (Figure 15). Indeed, when the robust of the oscillations were quantified a si gnificant reduction in robustness was seen in day 7 normal islets compared to day 1 normal islets (p<0.05). In contrast, day 7 and 14 pseudo islets were not found to be different from day 1 normal islets (p<0.05). After 7 days in culture, normal islets wer e found to have a significantly reduced area of synchronization compared to Day 1 normal islets (84.056.03% vs. 25.855.82%, respectively) ( p<0.001) (Figure 16B). However, day 7 pseudo islets were found to function similar to normal day 1 islets, with s ignificantly higher synchronization (p<0.001) (Figure 16B). After 14 days in culture, normal islets were still unresponsive with overall synchronization not significantly different from the normal day 7 islets, which was poor (p>0.05). Surprisingly, pseudo islets were found to have comparable synchronization to Day 7 pseudo islets and remained markedly better than the normal islets (p<0.001). At 2mM glucose, Day 7 normal islets had higher transient [Ca 2+ ] i activity compared to Day 1 normal islets (data not shown). Pseudo islets at day 7 and 14 were also found to be comparatively quiescent, showing similar activity at low glucose to normal day 1 islets (p>0.05) (Figure 17C). Taken together, the high and low glucose data indicates that while the normal islets were decreasing in function pseudo islets were maintaining or increasing functionality. In addition, the low glucose data specifically indicates that gap junctional conductance may be leading to greater suppression of transient [Ca 2+ ] i activity. Summary of R esults We found that using precision controlled PEG microwells to reaggregate normal islets resulted in viable pseudo islets with defined shape and size. We then tested their

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65 viability by analyzing the synchronization and robustness of their [Ca 2+ ] i dynamics. While day 1 normal islets demonstrated viability that was in line with previously published results, day 7 and 14 normal islets showed a significant deterioration in viability. Conversely, day 7 pseudo islets (which are one day removed from the microwells) showed viability and functionality which resembled day 1 normal islets. Pseudo islets from 100m sized wells were also found to be slightly less synchronized than those from 200m sized wells. Surprisingly, pseudo islets continued to show high levels of viability and functionality at day 14, suggesting that the reaggregation procedure impacts the long term behavior of islet cells in some way.

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66 Chapter V RESULTS: PERCOLATION MODELING PREDICTS LOW GLUCOSE BEHAVIOR OF K ATP CHANNEL GENETIC MUTANTS cells, the K ATP channel is provides a link between cellular metabolism (intracellular ATP concentration) and membrane potential. In a low glucose state, the channel is open allowing the outflow of K+ ions. Increased intr acellular ATP causes the K ATP channel to close and the accumulation of K + ions creates an increase in membrane potential which, when large enough, will activate voltage gated Ca 2+ channels. This rapid influx of Ca 2+ ions causes the membrane to depolarizati on. At low glucose, the intracellular concentration of ATP in commonly not sufficient to deactivate enough KATP channels to sufficiently increase membrane potential, however a heterogeneous cells more excitable a t a given glucose concentration than others. Over activity of the highly active cells is overcome by a hyperpolarizing effect of cell cell coupling through gap junctions. As we have previously shown, an increase in gap junction coupling (whether through l arger 2D structures or increasing dimensionality to 3D) produces lower [Ca 2+ ] i activity at low glucose. We also demonstrated how percolation modeling combined with binomial statistics can predict how active a given cluster will be. Using genetic mutations which can decrease

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67 Figure 17 : Percolation model predictions for transgenic mouse models. A) Percent of islet cells active at low glucose as a function of p (g coup ) for variable percentage of excitable cells in the islet (p exc ). B) Percent of islet cells active at low glucose as a function of p exc for variable p. For both simulations the step size was 0.05 with an n=500 and the percentage of cells necessary to suppress the entire islet was 15%. (loss of function) or increase (gain of function) K ATP function, we set to further test the percolation model by using a forward model 2 Model Predictions Using previously acquired data from mice expressing transgenes for Cx36 and the K ATP channel, we were able to compared perturbed experim ental systems to our theoretical model. As previously shown, mosaic expression of the KIR6.2[AAA] transgene, which renders the pore forming subunit of the K ATP channel non functional, makes 70% of the cells functional knockouts (Koster et al. 2001). In ter ms of our model this means 70% of cells will be active at low glucose. These mice were crossed with Cx36 knockout mice to yield different levels of gap junction conductance (g coup ), which is represented by the percolation probability p in our model. 2 A forward model is based on prediction, in contrast to the reverse paradigm where the model is fit to the data retrospectively. Since the reverse model was used in chapter 1 to fit the model parameters, we now use the same tool to predict the behavior when the wild type system is perturbed.

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68 Figure 18 : Percolation modeling fits experimental data from K ATP loss of function islets. A) Plot of percent cells active versus p for p exc = 0.7, corresponding to the theoretical cells active for KIR6.2[ AAA] islets. The data was normalized to a wild type p = 0.45, represented by the area within the box. B) Normalized model plot. C) Scatterplot of percent of cells active at low glucose in mice as a function of coupling conductance (g coup ) from Cx36 knockou t mice with further gap junction inhibition. D) Fit of model to experimental data. For C and D, points represent the mean SEM. Predictive activity of the KIR6.2[AAA] knockout islets from these mice at different levels of coupling conductance (or levels of Cx36 knockout) were simulated through the low glucose percolation model using a 3D cubic lattice of diameter 11. This diameter was chosen based off the average islet having a diameter of ~150m and the average cell having a diameter of ~10 20m. Therefo re, an average islet is 10 cells across, but since the model requires there to be a central cell in each lattice 11 was chosen. The threshold of quiescent cells to silence a cluster was set at 15%, which was previously found to provide the best fit for the MIN6 data. Although the effect of this parameter was not found to have a very substantial effect on parameter fit, it is within the 10 30% range as previously reported. For each simulation on this lattice the predictive activity was found for each p (g cou p ) at different levels of cell excitability (p exc ). Since incorporation of the KIR6.2[AAA] trangsgene renders 70% of cells in the islet active, p exc = 0.7 for this transgenic model. The resolution (or step

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69 size) for each variable was 0.05 and simulations were run for n=500. The standard deviation of the predictions for each simulation was low, varying by less than 10% of the mean (corresponding to <1% SEM). For a given p exc below 85%, the model showed the percent active cells in the islet would also decr ease as a function of p (Figure 17A). However, when p exc >0.85 there are not enough quiet cells cells and the islets become constitutively active. In our experimental model where p exc = 0.7, this predicts that when g coup = 0 the islet will be 70% active and this will decrease as g coup is increased. The model was then run as a function of p exc for variable p to describe the behavior of a gain of function K ATP mutant. In mice expressing 30,K185Q] GFP transgene, the K ATP channel becomes ~30 times less sensitive to ATP and is therefore cells so that membrane potential never increases enough to activate the vol tage dependent Ca 2+ channels. This inhibits [Ca 2+ ] i activity and renders them under 30,K185Q] GFP transgene is inducible and dependent on the dosage of the inducing agent tamoxifen and can be quantified by GFP penet rance. Therefore, this gives us a model to predict low glucose activity as a function of p exc for a given p. For levels of p (or g coup ) below p c the percent of active cells at low glucose increased linearly as p exc was increased. This is expected given th at the many small clusters seen when p

pc = 0.2488 the behavior becomes

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70 Figure 19 : Percolation modeling fits experimental data from KATP gain of function islets. A) Theoretical plot of percent cells active at low glucose as a function of percent of cells excitable for previous estimations of p for wild type islets. B) Scatterplot of plasma insulin 30,K185Q] expressing i slets. C) Fit of model to experimental data. markedly different. The percent active cells remain relatively quiescent at low p exc and critical behavior appears at p exc any suppressive effects and become highly active. For p = 0.3 0.4, there were still enough uncoupled cells to increase the percent cells active as Pexc was increased up to the critical point, but for p > 0.4 the percent cells active remained very low until p exc ~ 0.8 (Figure 17B) Cell Activity as a Function of Coupling Conductance in KIR6.2[AAA] M ice cells are constitutively active and therefore a model parameter from our simulations of p exc = 0.7 should fit the experimental data best (Figure 18A). However, since wild type islets do not have a p = 1, but a value somewhere between 0.3 0.4 as was shown in MIN6 aggregates and previously for high glucose synchronization (Benninger et al. 2008), the simulation data is normalized to wild type conductance ( Figure 18B). A wild type conductance of p = 0.45 was found to best match the experimental data and if plotted in Figure 18B. When plotted, percent cells active at low glucose follows a trend very similar to that of the normalized simulation plot (Figure 17 C), and when plotted

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71 with the theoretical data they match very closely (Figure 17D). Only one data point was found to have a SEM which did not include the theoretical line. The model was also able to capture the behavior of the experimental system at low g coup (p) and high. In addition, it nicely explains the rapid drop in percent cells active follows by more asymptotic behavior. C ell Activity as a Function of E xcitability in 30,K185Q] M ice Simulations of g coup for varying percent cells active found that for a p within the range of what was previously found (p = 0.3 0.4), there would be low activity in the islet up to the point where ~80% of the cells are active. However, when activity goes beyond that point there will be a transition accompanie d by a rapid increase in the percent cells active (Figure 19A). This increase corresponds to the number of cells required to suppress transient activity at low glucose (15% in our model), and the simulations will therefore be very sensitive to this paramet er. For instance, if this threshold was set to 25% instead of 15% the critical point would occur around 70 75% instead. As the number of active cells increases, there will be a point above which there are not enough quiescent cells by percentage to suppres s. In our model this point was 85% (100% 15%). When using plasma insulin in fasting mice as a measure of islet activity at low glucose, the data was found to follow a similar patter as that described by the model for p between 0.3 and 0.4 (Figure 18B). Tho ugh incomplete in the 60 cells increases through 30,K185Q] expression plasma insulin normalized to wild type levels shows low levels of activity combined with a sudden increase. When plotte d with the theoretical data, there is sound agreement at low percent cells active and the location of the phase transition (Figure 19C).

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72 Summary of F indings After fitting our model of islet connectivity to the MIN6 2D/3D data retrospectively, we wanted to test if we could predict the behavior of wild type islets as parameters of the model were perturbed. The model found that for increasing values of p (when p exc = 0.7) there would be a sigmoidal like decrease in the percent cells active at low glucose. Usin g data acquired from transgenic variants we were able to fit data from K ATP loss of function KIR6.2[AAA] (which have ~70% of cells active) very well when normalizing to a p = 0.45. When simulations were run as a function of p exc for variable p, the range o f p values which were found to approximate MIN6 aggregates had a small size dependent increase in activity up to a critical point at ~80%, above which the islets became highly active. Similarly, the experimental data was found to fit the theoretical data. Taken together, these results demonstrate that the experimental data from transgenic mice can be fit using the same percolation model, albeit with a p for wild type conductance which was slightly higher than the MIN6 aggregates.

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73 CHAPTER VI DISCUSSION AND FUTURE DIRECTIONS Dimensionality and Size Scaling of C oordinated [Ca 2+ ] i D cells The importance of cell cell communication is a recurring theme in physiology and is integral to the proper function of multiple biological systems. In the pancreas, the islets of Langerhans show coordinated [Ca 2+ ] i oscillations and propagating Ca2+ waves at elevated glucose mediated by Cx36 gap junctions. These electrical dynamics are critical for the underlying dynamics of insulin release an d glucose homeostasis. In addition, gap junction coupling also coordinates a suppressive effect at low glucose, preventing non essential insulin release which has been shown to be a contributing factor to the progression of type II diabetes (Benninger, et al. 2011; Tisch et al. 1996). cell aggregates of defined size, we examined the dependence of [Ca 2+ ] i dynamics on size and dimension by comparing the [Ca 2+ ] i dynamics to 2D cell cluster sheets. Previous work has modeled the islet architecture as a partially coupled lattice resistor network to quantify the dependence of these dynamics on the level of gap junction coupling. Since this model was established for multiple network mesh sizes and dimensions, we were able to take it a step further to quantify multiple aspects of size cell [Ca 2+ ] i dynamics.

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74 cell Coupling in Two D imensions cells were coupled within a 3D architecture, they sh owed significantly more robust [Ca 2+ ] i dynamics compared to a 2D architecture. This included more robust oscillations, increased oscillation synchrony between cells and faster Ca2+ wave propagation across the cell structure. Within this 3D architecture, MI N6 cells showed similar responses to previously reported values for intact islets, with similar wave velocities (72m/s6 vs. 69m/s5, respectively) and oscillation synchronization (962% vs. 912%, respectively) (Benninger, et al., 2008). Since the MIN6 aggregates are composed cells and ~20% non coupled cells, this could explain the increase in both wave velocity and synchronization. However, the closeness of the two values can be recon ciled with our percolation mode. Since both systems would be estimated to have behavior above the critical probability, a 20% reduction in resistors or cells would have a negligible effect on total synchronization. This is exhibited by figure 5E, in which there is a distinct transition from p=0.2 to p=0.3 (p c =0.2488) and with only a ~15% change over a range of p=0.3 1.0. The closeness of the values also indicates that MIN6 aggregates can serve as a sufficient model system in which to examine the effects of coupling. When the coupling architecture is reduced to 2D, the behavior of the cell cluster becomes qualitatively similar to islets showing a loss of coupling. There is a marked reduction in synchronized oscillations which are restricted to defined sub reg ions, propagating Ca2+ waves slow (Benninger, et al., 2008), and basal [Ca 2+ ] i activity is elevated (Benninger, et al., 2011). In intact islets, patch cells are electrically coupled to ~6 neighboring cells (Zhang, et al., 2008). Sinc e this the degree of connectivity for each node in a simple cubic lattice, this architecture is suitable to model islets.

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75 Therefore, by reducing the dimensionality from 3D to 2D there is a ~33% decrease in total coupling to adjacent neighbors by reducing e ach node degree from 6 to 4. However, this effect becomes magnified when considering the range of which cells can couple. We experimentally determined that MIN6 cells can couple over a 5 cell radius. Therefore, over this range 2D allows for 5 times fewer c ells with which a given cell can interact over this range (5 2 =5 vs. 5 3 =125). This is supported by the percolation model, in which the critical probability is ~25% less in 3D than in 2D (p c =0.2488 vs. p c =0.5, respectively), meaning that 25% more connection s can be uncoupled to have a fully coupled electrical syncytium. This may also help to explain why a disproportionately low reduction in synchronization is seen in 3D islet networks following a >50% reduction in coupling (Benninger et al. 2008). If the p falls further below pc in an islet through gap junction knockout and/or inhibition, there will be a sharp decrease in overall synchronization. In MIN6 cells, the K+ channel inhibitor TEA is conventionally used to increase resting membrane potential, which creates more regular oscillation patterns. In fact, this cell line was developed primarily for these properties. Therefore, we also measured size and dimensionality scaling under treatment with high glucose alone as a control condition. Since [Ca 2+ ] i patte rns were similar in the presence and absence of TEA, this suggests that the size scaling and dimensional behavior seen is more a function of intercellular dynamics rather than intracellular events. However, upon increasing the dimension from 2D to 3D with glucose alone, we found that there was a significant increase in period robustness of the oscillations. This indicates that the 3D coupling architecture is vital affects MIN6 cells in such a way where they becomes more sensitized to adjacent depolarization s at high glucose.

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76 At low glucose, 3D aggregates showed suppression of transient [Ca 2+ ] i activity which was size invariant. In contrast, suppression improved with increasing cell number in 2D aggregates, which is opposite to the size scaling seen at high g lucose. Therefore, there is not an ideal size at which 2D aggregates can form a proper balance between high glucose synchronization and low glucose suppression: as the cluster increases in size it becomes better able to suppress transient [Ca 2+ ] i activity but loses overall synchronization. This can be qualitatively explained by considering the mechanisms of gap junction mediated suppression and synchronization. To be show similar synchronization behavior, cells must be effectively coupled. In 2D a ggregates cells at opposite ends of a cluster are very unlikely to be within the same coupling environment. However, for cells in an aggregate to be suppressed, the must only be in contact to a sufficient number of inactive cells. Cells at opposite ends of a large cluster do not themselves need to be connected to be quiescent. As the cluster increases in size, the proportion of inactive cells increases and the network dynamics allow for suppression to propagate over larger distances. This reveals a fundamen tal and unexpected difference in the way in which cell cell connections play a role in the suppression of [Ca 2+ ] i at low glucose compared to the synchronization of [Ca 2+ ] i oscillations at high glucose. Network Model Describes Dimension and Size S caling of [Ca 2+ ] i dynamics To gain a better theoretical understanding of how these different behaviors emerge cell coupling within a lattice resistor network model. By examining network properties based on the probabil ity of adjacent coupling, these simulations could describe multiple aspects of the size scaling of [Ca 2+ ] i dynamics, including the size of synchronized regions in 2D and 3D, the effect on dimension

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77 on synchronization and the change in suppression in 2D and 3D. Importantly, these models were fit with one network connectivity parameter (p) to describe the proportion of functional cell cell interactions. The suppression utilized an additional parameter (S p ) to describe the percent of inactive cells necessary t o suppress the connected cluster. In percolation theory, there are a critical percentage of connections (defined by p c ) for which a phase transition occurs and overall coupling spans the full network. This critical probability p c =0.2488 for 3D cubic networ ks and p c =0.5 for 2D square networks. In our simulation models, a phase transition is clearly visible for finite size networks >100 cells, where there is a sharp jump in synchronization when p>p c (Figure 5). Given the similar p which fit the 2D and 3D expe cell regions which do not span the netw ork. This further explains how 3D aggregates are able to show high levels of synchronization and propagating Ca 2+ waves over the entire cell structure, but large 2D clusters show very low synchronization. The fractal clustering behavior of random percolati on networks in the sub cell clusters, which further supports the use of the network model (compare Figures 5E and 9C). In addition, the model supports the idea that through the coupling architecture, a charac teristic probability alone can explain the coupling and synchronization behavior of electrically coordinated cellular networks. Overall, these model results demonstrate how separating details of cellular dynamics from the system architecture can be used t o discover general properties by which cellular interactions govern the behavior of multicellular systems, which could be broadly applicable.

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78 Physiological Importance of Dimensionality and Size S caling in C ellular Network A rchitecture Size and dimensionality play an integral role in the regulation of electrical activity in cell aggregates. Aggregates with higher dimensionality show a more coordinated [Ca 2+ ] i response at high glucose and enhanced suppression of [Ca 2+ ] i activity at low glucose. This can therefore explain the higher insulin secretion in 3D aggregates in our model, and also explain the higher dynamic range of non diabetic islets. Although we did not investigate the size dependence of insulin secretion, it has been shown to be size invariant in the 3D aggregates (Bernard, Lin & Anseth, 2013). Furthermore, previous studies have shown that confluent MIN6 cells (large cell clusters) show reduced insulin compared to non confluent MIN6 (small cell clusters) (Kons tantinova, et al., 2007). In context of our data of [Ca 2+ ] i dynamics and insulin secretion, this indicates a key role that the underlying cellular architecture plays in determining the efficacy of the glucose stimulated insulin response. The 3D aggregates we created through hydrogel microwells behave very similarly to intact islets, which demonstrate the utility of the 3D architecture. Compared to 2D cell clusters, 3D aggregates were able to show robust and synchronized oscillations without the addition of TEA. Human islets have been proposed to have a number of different architectures (Cabrera, et al., 2006; Bosco, et al., 2010), however defects which alter the systems architecture and reduce the dimensionality over which coupling occurs would be expected to lead to dysfunction that is similar to a loss of gap junction coupling (Head, et al., 1988; Porksen et al. 2002; Menge et al. 2011) and obese individuals ( Periris et al. 1992), which could potentially be the result of downregulation of gap junction proteins as well as a reduction in cell cell infiltration. These events are known to occur in hyperglycemic conditions whi ch are associated with the symptoms of

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79 type II diabetes (Rahier et al. 1983; Allagnat et al. 2005). Furthermore, it has been shown that during pregnancy, an increase in gap junctional coupling is observed in islets, coinciding with increased islet size and enhanced insulin secretion (Sorenson et al. 1997; Sheridan et al. 1988). Excitable cells in the human body have a small finite conductance that is dictated by the coupling architecture of the gap junctions. Through this architecture, cells are able to sy nchronize behavior across large distance through these low conductance channels. For example, electrical synchronization allows for our hearts to beat, muscles to move and glucose levels to be maintained. These findings add insight into how the body is abl e to achieve the optimal cellular architecture for life. Currently the most promising treatment for type I diabetes is islet transplant and cells for islet transplantation While cellular coupling will be important to enhance insulin release, our data suggests that the architecture will also be important. Transplantation of 2D sheets cells, as has been recently suggested, will provide insufficient coupling for well reg ulated insulin dynamics. Rather, a robust 3D architecture is necessary. This also has cells onto scaffolds (Pedraza et al. 2012; Kodama et al. 2009), since those scaffolds which promote the formation of higher dimension al structures will likely show enhance function. It will also be important to consider if other factors such as revascularization, nutrient diffusion and hypoxia are dependent on architecture. For example, it has been shown that transplanting smaller 3D is lets better reverses diabetes compared to large 3D islets in both mouse and human models (Lehman et al. 2007). Nevertheless, our method of controlled aggregation to generate 3D aggregates of

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80 controlled size (Bernard, Lin & Anseth, 2013) could be used to re aggregate primary islets to optimal sizes or creating islets from differentiated stem cells. Intercellular coordination via [Ca 2+ ] i oscillation is not unique to the islet and applies to other neuroendocrine cell systems. For example, robust and enhanced pulsatile growth hormone (GH) secretion results from the coupling between GH cells and the coordination of [Ca 2+ ] i (Bonnefort et al. 2005; Hodson et al. 2012); where remodeling of the coupling architecture regulates GH release in puberty (Bonnefort et al. 2005). Gap junctions couple chromaffin cells in the adrenal medulla which synchronize [Ca 2+ ] i transients and regulate catecholamine release (Martin et al. 2001); where stress responses evokes a remodeling of electrical coupling to enhance chromaffin cell e xcitability (Colomer et al. 2008; Hill et al. 2012). Therefore, our findings are not only applicable for the islet and may have the ability to predict architecture and gap junction coupling changes in the pathology of other diseases. Re Aggregation of Primary Islet Cells into Functional Pseudo I slets In the transplant environment, whole pancreas grafts are not realistic because of rejection and functionality issues, and islet isolation procedures are thus necessary. In addition, time delays to engraftme nt make culture inevitable. It has previously been shown that the unique architecture of islets cells and vasculature is not maintained in cultured or transplanted islets (Bosco, et al., 2010). This is not surprising given the insults sustained during isol ation, digestion, shaking and subsequent culture. Therefore, to improve the quality to transplant tissue methods are needed to avoid these pitfalls. Here, we have shown that long term viability and functionality of normal islets is poor (to which the isol ation procedure may have contributed), but show that using PEG microwells to re

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81 aggregate primary cells results into pseudo islets of defined sizes leads to long term functionality and viability resembling freshly isolated islets. Efforts to improve islet transplantation have begun to focus more on improved survival rates of the transplanted islets as an adjunct to isolation techniques and immunosuppression (Lehman, et al. 2008). It is estimated that ~50% of whole islet transplants become necrotic, with a larger proportion of larger islets being affected. Despite high numbers of transplanted islets, the functional capacity of the graft remains around 20 40% (Ryan et al. 2001). Normally, pancreatic islets have a blood perfusion that is 10 times higher than i n exocrine pancreas, resulting in a significantly higher oxygen tension (Fung et al. 2007). During the process of isolation and in vitro culture the islet vasculature dedifferentiates or degenerates, rendering nutrient and oxygen availability to be based s olely on the limits of diffusion. Even islets which revascularize show oxygen tension that is 10 times lower that in native pancreas (Carlsson et al. 2004). We propose a new, previously neglected parameter to improve islet function: islet size. Islet size has been shown to be of importance for in vitro and in vivo function (Lehman cells, higher insulin secretion per unit mass, better oxygenation and more favorable outco mes (Lehman et al. 2007; MacGregor et al. 2006; Fung et al. 2007). Smaller islets have also been shown to have a significantly reduced diffusion barrier, easing the effects of ). This is supported by previous work showing that smaller islets have a more robust insulin response and had better outcomes after engraftment (Macgregor et al. 2006). Therefore, by re aggregating larger islets into pseudo islets of optimal islet size, th e efficacy of transplants can be significantly improved.

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82 Primary Islet Cells Readily Aggregate Form 3D Pseudo Islets of Defined S ize Primary mouse islet cells have been shown to reaggregate after dispersion, however these methods have mostly been cumbersom e and inaccurate (Cavalleri et al. 2007; photolithography to form precisely sized PEG microwells, we can repeatedly form pseudo islets of defined size (Figure 14A). For both the 10 0m and 200m well diameters, pseudo islets were found to have a diameter which was ~50% of the microwell diameter (Figure 14B). This is expected given one of the mechanisms through which the wells create pseudo islets of defined size by limiting and evenl y distributing the number of cells within the well. These cells then create 3D aggregates of lesser diameters, which are similar to the diameters of MIN6 aggregates formed using the same method (Bernard, Lin & Anseth, 2012). More importantly, the standard error for both well diameters was only found to be 15 25% of the pseudo islet diameter (Figure 14B), indicating a high level of control regarding size. This size control is comparable with the diameters of MIN6 aggregates using the same method (Bernard, Li n & Anseth, 2012) and superior to flat culture aggregation micromold optimal size for transplan ted islets still needs to be addressed, given the emphasis on islet size in transplant viability control over this aspect will be of high importance for in vivo trials.

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83 Pseudo Islets Show Superior Viability and Functionality Compared to Age Matched I s lets Directly removed from the microwells, pseudo islets were found to have a defined 3D shape (Figure 14C) and high levels of viability (Figure 14D F). Importantly, they also had coordinated (Figure 16A & B) and robust (Figure 15A C) [Ca 2+ ] i dynamics whic h were similar to freshly isolated islets (Figure 15C), indicating that 5 days in culture was sufficient for intercellular gap junction coupling to develop. Gap junction coupling plays an important role not only in coordinating insulin secretion at high gl ucose, but also suppressing insulin secretion at low glucose which can also have a detrimental effect (Benninger et al. 2011). As shown by [Ca 2+ ] i activity at low glucose (Figure 16C), pseudo islets were found to have similar suppression to freshly isolated islets. Interestingly, we found that pseudo islets continued to maintain highly synchronized and robust [Ca 2+ ] i dynamics up to two weeks (day 1 4) in culture, while cultured normal islets continued to deteriorate (Figure 15C; Figure 16B). In addition, the suppression of [Ca 2+ ] i activity was found to be similar to both fresh islets and day 7 pseudo islets (Figure 16C). This is surprising given norm al islets 7 days post harvest showed deteriorated dynamics, but pseudo islets 7 days post removal from the microwells showed no such deterioration of their [Ca 2+ ] i dynamics. Although we were not able to determine whether the improvements seen in pseudo i slets were based solely on changes in islet size, this could possibly explain some of the differences seen between the two groups at day 7. While control normal islets remained in culture under potentially hypoxic and nutrient poor conditions, cells from p seudo islets were dissociated and therefore under more optimal culture conditions. This notion is supported by the fact that even small normal islets exhibited poor viability and functionality

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84 after 7 days. In addition, pseudo islets were then aggregated t o smaller sizes, allowing for better nutrient diffusion and higher oxygen tension when functionality was assessed through [Ca 2+ ] i imaging. However, size differences do not seem to explain the high viability and function of the pseudo islets at day 14. At this time point the pseudo islet cells had been in culture for 14 days, and were 7 days post removal from the microwell devices the same timeframe over which the normal islets of comparable size were found to deteriorate (data not shown). This suggests t hat some aspect of the dispersion / aggregation procedure is increasing function and viability. Future work will aim to elucidate this mechanism, but two probable explanations are either molecular switching or a reworking of the islet architecture into a m ore beneficial organization. In rodents, dissociated islet cells have previously been shown to reaggregate in culture to form pseudoislets with a core mantle organization similar to that of normal mouse islets (Cavalleri et al. 2007; Ramachandran et al. 2 013). This indicates that in rodents, information that decides the islet architecture is foremost provided by islet cells themselves (Cirulli et al. 1993; Rouiller et al. 1991). Therefore, the intracellular mechanism which controls cell aggregation may als o be causing the cells to circumvent the cell death seen in normal islets in culture. Indeed, a study by Beattie et al. found that dedifferentiation of human fetal pancreatic cells is reversed by reaggregation (Beattie et al. 2000). As supported by previou s work in the literature as well as this thesis, islet architecture plays a hugely important role in islet behavior, and a relative increase in alpha cells present in the central core of the islet has been reported in many animal models of type 2 diabetes, pregnancy and obesity (Epstein et al. 1989; Bates et al. 2008; Rahier et al.

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85 the cell fractions may lead to more efficient cell cell communication resulting in enhanced endocrine function such as increased sensitivity to changes of external glucose concentrations (Cabrera et al. 2006 ; Kha routa et al. 2009). This cells over expressing the glucagon receptor were cell mass (Gelling et al. 2009). Therefore, this offers an alternate explanation for the increased function and v cell c cell ratio associated with obesity and diabetes will not be seen. In addition, if we assume that normal islets have a similar coupling environment to MIN6 aggregates, our percolation model can still explain how there would not be a reduction in over all [Ca 2+ ] i synchronization. For cell coupling from the infiltration of cells constitute ~20% of the islet), this would only reduce the p to 0.36*(1 0.2)=0.288, which is still well abov e the critical threshold Applic ations to Human W ork Although our findings in a mouse model are promising, there is currently not an epidemic of murine diabetes in the United States. To realize its full potential, our work needs to be applied to human transplant islets. As in the murine model, the architecture of the human pseudo islets will prove to play an important role in defining their function, viability and behavior.

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86 Recent evidence has shown marked differences in the cellular organization of isl ets cell mantle (mantle core), while human islets may have a higher proportion o f these cells that cell coupling and may be characterized by a lower p. For example, the Cabrera, et al. study also showed that synchronization of [Ca 2+ ] i dynamics was absent in human islets, bu t present in isolated sub regions. Conversely, the study has not been repeated with human islets and a ~30% cell coupling would not be enough to justify a phase transition to sub critical percolation according to our model (corresponding to a p = 0.252 > p c = 0.2488). However, observations by Bosco, et al. in the only statistically well powered study to date have found that small human islets (40 60m) do indeed show a segregated mantle cells localized to the mantl cells predominantly forming cells were found in the mantle, but also within the islet adjacent to vascularized areas. They therefore proposed a model in cell edges, which fold around the vasculature of the islet as it becomes larger than the defined sheet diameter (Bosco et al. 2010). Since smaller islets have diameters less than the sheet diameter, the mantle core architecture is conserved. It is interes ting to note that islets obtained from older patients in many under powered architecture studies (Cabrera, et al. 2005; Brissova, 2005) have shown similar architectures to murine models of diabetes (Kim et al. 2009), and smaller islets from the same patien ts often have mantle core structures. Indeed, it has been suggested that the heterogeneous architecture seen in older humans may represent a reorganization of the architecture over time one that potentially contributes to diabetes (Butler et al. 2003).

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87 T his suggests that the architecture seen in older human islets (which is the most widely available tissue for both research and transplant) may be an effect of aging rather than normal composition. Therefore, reaggregating donor tissue may not only create s maller, more viable islets, but reassembling the cyto architecture to a more non diseased state may also serve to further improve outcomes. Therefore, if the reaggregation procedure is found to reorganize the islet architecture in a way which makes trans plant tissue from older patients function better, this could pose to greatly increase the effectiveness of the donor recipient matching. Future experiments in both human and mouse models are currently being planned to test this. However, even if reaggregat ion is unable to increase function in islets cells from aged donors, the increase in smaller islets with higher viability as reported here may increase the grafts chance of surviving the hypoxic insult of the portal vein. Percolation Modeling Predicts Low Glucose B ehavior of K ATP Channel Genetic M utants cells, the K ATP channel provides a link between cellular and membrane potential. In a low glucose state, the channel is open allowing the outflow of K + ions. Increased intracellular ATP causes the K ATP channel to close and the accumulation of K + ions creates an increase in membrane potential which, when large enough, will activate voltage gated Ca 2+ channels and cause a membrane depolarization. Conversely, at low glucose the intracellula r concentration of ATP is not sufficient to inhibit enough K ATP channels to adequately increase membrane potential. However, a heterogeneous cells more excitable at a given glucose

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88 concentration than others. Over activity of the highly active cells is overcome by a hyperpolarizing effect of cell cell coupling through gap junctions. As we have previously shown, an increase in gap junction coupling (whether through larger 2D structures or increasing dimensionality to 3D) produces lower [Ca 2+ ] i activity at low glucose. We also demonstrated how percolation modeling combined with binomial statistics can predict how active a given cluster will be given a threshold number of inexcitable cells being able to suppress the a ctivity of the cluster. To better understand this important mechanism and further validate our model, we used transgenic mice expressing altered or deficient pancreatic K ATP cell dysfunction. Transgenic mice with overactive K ATP ch 30,K185Q] transgene) show neonatal diabetes due to permanent hyperpolarization of the cell membrane, demonstrating the K ATP channels ability to suppress insulin secretion (Koster et al. 2000). These mice demonstrate a particularly accel erated progression from hyperinsulinemia to diabetes as might occur in the most severe (i.e., completely K ATP channel deficient) versions of human hyperinsulinemia. Conversely, KIR6.2[AAA] mice differ significantly from the knockout mice in that whereas K A TP they are present at near normal density in the remainder. Thus, the phenotype is a partial (i.e., cell by cell) knockout. Because of a partial syncytium in the islet (cells are electrically couple d to one another), these mice should still exhibit a K ATP dependence of insulin secretion, but with the set point of electrical activity, and hence secretion, shifted toward lower glucose concentration (Koster et al. 2002). Previously, we have shown that i cells) were coupling can be considered negligent, heterogeneity of glucose sensitivities leads to a 67% probability that a given MIN6 cell in 2D will be active at low glucose. However, when

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89 coupling was incorpora ted by analyzing larger 2D cell clusters a marked size scaling effect was seen. Elevation of the dimension was also shown to have a highly suppressive effect given the same probability of being active. Given the unique architecture of the islet, extrapolat ion of our MIN6 findings is difficult without knowing a set point of K ATP activity. Therefore, using KIR6.2[AAA] mutant mice provides a model in which it is known that ~70% of cells do not have functioning K ATP channels and will thus be active at low gluco se. The use of KIR6.2[DN30K185Q] provides a more thorough model because the level of K ATP function can be varied and also quantified by GFP penetrance. Percolation Modeling Accurately Predicts the Increase in Low Glucose Activity of KIR6.2[AAA] Islets as a Function of Gap Junction C oupling In the absence of gap junction coupling, our model showed that KIR6.2[AAA] islets will theoretically have 70% activity. Being that there will be no gap junction coupling to suppress excitable cells at low glucose, this makes sense. For Cx36 / islets expressing the KIR6.2[AAA] transgene, this was the approximate case. Since Cx36 / still have small levels of gap junction conductance (Benninger et al. 2008), the lowest values g coup will theoretically have percent of cells active at low glucose that is slightly less than 70%. Indeed, there was less of a reduction than a linear trend might suggest, but was in agreement with the model with p exc = 0.7. Normalizing the coupling conductance to a p=0.45 was found to provide the optimal fit for the KIR6.2[AAA]/Cx36 data. This was higher than the optimal p=0.36 seen in the MIN6 low glucose model, but may have been inflated by the large step size of the simulation. For example, a step size of 0.01 instead of 0.05 will lead to a bett er approximation and may lower the p of optimal fit. In addition, differences would be expected between MIN6

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90 aggregates and intact islets given they have different development and cellular composition. This might also suggest an approximation for the true p of a WT islet as being between 0.4 and 0.45. Our model was able to predict how a loss in gap junction coupling can lead to elevated [Ca 2+ ] i activity at basal glucose levels in KIR6.2[AAA] mice. These results show that the coupling of K ATP activity via g ap junctions results a suppressive activity at low glucose which is similar to wild type islets, even though up to ~70% are constitutively active. Furthermore, we were also able to predict a critical point of excitable cells (~80%), above which suppressive coupling becomes nonexistent islets become constitutively active. This further supports that glucose control of [Ca 2+ ] i activity is gap junction dependent and validates them as means by which cells suppress a state of hyperinsulinemia in a fasting state. Percolation modeling predicts critical behavior in fasting insulin secretion in 30,K185Q] mice 30,K185Q] transgenic mice, the level of expression can be induced by tamoxifen injections and quantified through GFP fluorescence. This ability to variably make levels of the K ATP cells insensitive to ATP gives us a model in which we can study the effect of variable percent of excitable cells (p exc ). The transgene is tagged with GFP and higher levels of GFP fluorescence 30,K185Q] transgene and therefore a lower p exc The percent of excitable cells (x axis in Figures19A C) compared to a wild type islet thus represents one minus the fraction of GFP fluorescence. At zero fluores cence, the islet is wild type, and at maximal fluorescence the islet is maximally suppressed.

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91 In ranges of p (or in this case, lattice connectivity) which were found to approximate MIN6 aggregates (0.3 0.4), the model predicted that at low levels of p exc (high GFP fluorescence), there would be slight increases in the percent of cells active at low glucose up to p exc ~ 0.6 (Figure 19A). However, as p exc approaches 85% there are not enough quiescent cells in the system to suppress the other active cells and the model shows a sharp increase in low glucose activity. The plasma insulin data agreed nicely with this predication, showing a rapid increase in this area. However, a lack of data in the range of pexc = 0.6 0.9 made the true critical point difficult to p redict. Since the dose 30,K185Q] can be tailored to focus on this region, we hope to gain more data and better approximate this threshold in the future. Nonetheless, the existence of a critical point in the experimental data, which w e were able to predict with relative accuracy, further verifies that the true threshold of quiescent cells necessary to suppress the entire islet is between 10 40%. The diabetic phenotype is characterized by an increase in non cells in the islet core co cell mass, which could explain the decrease in gap junction coupling and insulin sensitivity. Indeed, development of overt diabetes (chronic hyperglycemia) is a long process has been found to occur when the overall functional be ta cell mass drops below a threshold necessary to maintain euglycemia (10 30% of total beta cell mass in various species; Gepts 1965; Kjerns et al. 2001; Larsen et al. 2003; Sreenan et al. 1999; Bonner Weir et al 1983). This is supported by previous from R ochelau et al, which cells exhibit essentially normal [Ca 2+ ] i activity and insulin release. This suggests that the maintained cell cell contact suppresses the expected elevations in these two factors at low g lucose given the K ATP mutation (Rochelau et al. 2006). Since it is known that 70% of these cells are constitutively active, we can state that the level of quiescent cells necessary to suppress the coupled islet it <30%,

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92 which is consistent with our data. C ombined with our current findings, we can therefore further tailor the approximation of cells necessary to suppress coupling to 10 30%. Using the same model of KIR6.2[AAA]/Cx36 mice as the present work, Benninger et al. found that despite elevations in [C a 2+ ] i activity at low glucose following complete knockout of Cx36, there was not a concomitant increase in insulin secretion (Benninger et al. 2010). This suggests supports the work by Rochelau et al. suggesting that some level of gap junctional coupling i 30,K185Q] mice shows that this is most likely because 70% penetrance of the transgene still corresponds to sub critical suppression, meaning that there were sufficient quiescent cells to suppres s the increase insulin secretion. However, our data predicts that if this level of penetrance was increased to >80% there would be a concomitant increase in insulin release. 30,K185Q] model we used fasting plasma insulin as an approximati on to low glucose activity of the islets, which is represented as percent of cells active in our model. However, the model was built and validated to predict [Ca 2+ ] i activity in isolated islets. Therefore, although the plasma insulin data was found to corr elate well with model predictions at an experimentally predicated range of p, we suspect that when [Ca 2+ ] i activity is quantified there will be better agreement. More specifically, plasma insulin can vary even with maximal [Ca 2+ ] i activity and the experim ental data will show a sharper increase in activity compared to the plasma insulin.

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93 Implications of the Model for O veractive K ATP C hannels The ability of cells to communicate with one another via gap junctions in the intact islet of Langerhans is important for the enhancement and coordination of glucose stimulated insulin secretion as well as for uniform suppression of insulin secretion at low cells exhibit transient [Ca 2+ ] i activity which is thought to be based on a heter ogeneous distribution of K ATP channels, intact islets (some with up to 70% basal activity) show uniform quiescence at low glucose. Although this behavior has been shown to be a gap junction dependent (Benninger et al. 2010), we have further explored this m echanism by applying a model based on percolation theory. These results have implication in the understanding of diabetic phenotypes resulting from K ATP dysfunction. Neonatal diabetes is caused from overactive K ATP channels and leads to an inability to secrete insulin. Our data shows that cell cell coupling can create a hyperpolarized state in all cells if K ATP activity is low enough in a small percentage of cells. More ambitiously, our model predicts that when less than 15 cells exhibit K ATP hyperactivity, the entire islet becomes overactive and may potentially lead to a diabetic phenotype. Furthermore, our model predicts that when g coup falls below ~25% of wild type levels, the reduction in coupling abolis hes this suppressive effect (Figure 17B). Thus, normal percentages of active cells as found from our model (~67%) can lead to a several fold increase in basal plasma insulin. For example, our model predicts that when coupling falls to 20% of wild type, ~67 % excitable cells will secrete four times the insulin as the 35% coupling conductance which fit the model. If coupling falls to 10% of wild type, this insulin secreted will be ~6.5 fold higher. It has previously been reported that elevating cAMP under low glucose conditions cause a rise in insulin secretion in Cx36 / mice, but has a negligible effect in Cx36+/+ mice.

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94 This result demonstrates that gap junctions can robustly suppress elevations in basal insulin secretion induced by secretagogues that act ind ependently of Ca 2+ (Benninger et al. 2010). Since plasma insulin was found to scale approximately with our model of [Ca 2+ ] i will be an active area of research by our group. In addition, these data suggest that glucagon like peptide 1 based treatments (which elevate cAMP and therefore prime insulin secretion) will be less effective at low levels of gap junction coupling since the elevated basal release will decrease th e dynamic range of GSIS. This mechanism may also explain an evolutionary drive to organize these secretory cells into a unique electrical syncytium. Such a mechanism provides a protective effect against hypoglycemia if individual cell properties change und er pathological or cell coupling have been shown to occur in obese individuals as well as type II diabetics (Bonner Weier & Turner, 2008; Rahier et al. 2003; Porksen et al. 2002), our model further supports these pathological changes as occurring in tandem and also makes clinically relevant predictions about how a pathological phenotype can rapidly progress as regions of criticality are approached. Future Directions Given the sur prising results seen in day 14 pseudo islets, this gives promise to the potential for increasing the efficacy of human transplants. Future work in this arena needs to focus on not only further validating the procedure through application to a mouse model o f diabetes, but also reaggregating human transplant islets to determine if function can

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95 indeed be increased. A major part of this work is revealing the mechanism through which the increased viability was achieved. cell s could help to explain the differences seen. cells) has been known to potentiate glucose induced insulin secretion through what is thought to be a cAMP dependent effect (Huypens et al 2000; Pipeleers et al. 1985; Samols, M arri & Marks 1965; Kawai et al. 1995). Insulin release cells at high glucose has also been found to be significantly diminished by the addition of a glucagon receptor antagonist (Huypens et al. 2000). This has been thought to explain why patie nts with type 2 diabetes commonly have a mutation in the glucagon receptor gene (Hager et al. 1995). Taken together, this suggests that there is a minimal cells in a glucose competent state. Glucagon b cells causes an increase in cAMP levels and factors which cell survival and avoid apoptosis cell destructi on (Lee et al. 2011). Furthermore, cAMP promotes beta cell survival via a process mediated through the transcription factor CREB (Jhala et al. 2003). Under in cell containing mantl cell core, resulting in a paracrine pathway for glucagon interactions (Jansson 1994; Nyman et al. 2008). However, isolated islets do not have such vasculature and therefore the glucose potentiating and anti apoptotic properties o f glucagon may not be fully realized and that may be leading to the deterioration of the normal islets at day 7. By reorganizing the islet cells in a heterogeneous manner, we may cell and thus increasing viability and function. To investigate this effect, future experiments will first

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96 need to identify the pseudo islet architecture as being heterogeneous or mantle core cells. Then, the expression of cA MP with regards to glucagon binding will need to be established in ex vivo normal islets as well as pseudo islets. Expression of cAMP can be accomplished through cAMP biosensors (Kim et al. 2010; Dyachok et al. 2006) and correlated with glucagon levels thr ough ELISA or immunofluorescence. While the aggregation procedure poses to greatly improve transplant outcomes, it can also give us a platform to continue to apply our model to the pathogenesis of diabetes. As previously stated, the diabetic phenotype is characterized by an increase in non cells cell mass, which could explain the decrease in gap junction coupling and insulin sensitivity. Indeed, development of overt diabetes (chronic hyperglycemia) is a lon g process has been found to occur when the overall functional beta cell mass drops below a threshold necessary to maintain euglycemia (10 30% of total beta cell mass in various species; Gepts 1965; Kjerns et al. 2001; Larsen et al. 2003; Sreenan et al. 199 9; Bonner Weir et al 1983). By incorporating inert microbeads or defined fractions of Cx36 / islet cells, we can test this hypothesis and determine the true cells necessary to maintain insulin homeostasis. Also, since hum an islets have been reported to have distinct areas of [Ca 2+ ] i coordination, which may be the result of islet reorganization, we can also use this model to explain whether a different architecture is responsible for the differences seen between species or the progression of a diabetic phenotype as humans age. Transgenic KIR6.2[AAA] mice allow us to look at an islet where 70% of the cells are active at low glucose. We show that in our low glucose model with a probability of being excitable of pexc = 0.7, the predicted p (or g coup ) fits the experimental data quite nicely.

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97 Importantly, it is very accurate at the high and low ranges. However, this system can only shed light on the 70% activity for varying levels of p, which are created through Cx36 transgenic kn ockout combined with inhibitors. By reaggregating KIR6.2[AAA]/Cx36 mice with Cx36 mice lacking the KIR6.2 mutation we can achieve variable levels of pexc<0.7. This will allow us to further characterize and validate the model with higher level perturbations This model can also be added upon by incorporating a simple model of intracell electrodynamics combined with a coupling term to model how decreasing p affects the overall [Ca 2+ ] i dynamics at physiological levels of coupling. This model could also predi ct changes in gap junction conductance with the progression of diabetes. In addition, if the cells follows a fractal pattern, which is partially supported by the Bosco, et al. paper desc ribing the islet as being based on a repeated unit of cell architecture. Using our model, we could possibly explain this behavior and the effects of dimensionality. cell network or about the conditions which u cell network and help to understand how changes in cytoarchitecture can affect the coordination of [Ca 2+ ] i dynamics. Multiple papers have described how synchronized and chaoti c behavior can emerge in coupled oscillator networks, with many predicting coupling conditions and specific predictions regarding topology (Huang et al. 2008; Sherman 2011). For example, a paper by Huang et al. predicts that optimal synchronization in comp lex clustered networks evolves from many weak coupling of highly coupled clusters, which may explain why human islets have a different architecture from mice (Huang et al. 2008) which is not surprising given that their islets are generally the same size despite the huge cell oscillatory

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98 behavior; however none have had the proper experimental models to validate theoretical predictions. Since we have a variety of mouse models with ion channel mutations as well as a method for aggregating different proportions of these cells into functional pseudo islets, we have the unique capability to test many of our complex mathematical models. In our simulations, we model a heterogeneous and spherical org an (in terms of cellular composition) as a homogenous cube. Since we have proven that small perturbations in architecture can have significant impacts on behavior, this is an area where the model can be improved. Using a spherical lattice may impact behavi or around the boundaries since the surface area of the cube is ~125% that of a sphere. Site percolation can be cells, which are currently incorporated into the model by further reductions in p. Also, using site percolation also might allow us to predict some of the effects of cellular reorganization on [Ca 2+ ] i dynamics. Pseudo islets were found to behave differently in long term culture and a reorganization of cellular dynamics may be a cause. If this is indeed the case, the combined site/bond percolation model may be able to account for the behavior through decreased vasculature and other architectural effects. Application of complex network theory in biology is a new and emerging field which is allowing us to u nderstand structural properties and functional behavior of systems at scales inaccessible to classical approaches which explain behavior as the summation of its individual components. For example, a recent paper has already described that the network archi tecture of the islet follows scale free principles, which predicts that there are highly connected cells which dominate the behavior of the whole cluster (Hastings et al. 2013 ), while another paper posits that the network follows a small world architectur e which is defined by many connected small clusters (Stozer et al. 2013). However informative, neither

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99 model used validated techniques for measuring cell cell coupling and both studies where done in 2D. By utilizing our model with confocal microscopy or ot her 3D techniques and genetic variants, we can build a working model of islet connectivity and provide compelling evidence for the true network topology.

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100 REFERENCES Albert, R., & Barabsi, A. L. (2002). Statistical mechanics of complex networks. Reviews of modern physics 74 (1), 47. mml, C., Ashcroft, F. M., & Rorsman, P. (1993). Calcium independent potentiation of cells. Nature, 363, 356 358 Allagnat, F., Martin, D., Condorelli, D. F. Waeber, G., & Haefliger, J. A. (2005). Glucose represses connexin36 in insulin secreting cells. Journal of cell science 118(22), 5335 5344. Ashcroft FM, Rorsman P (1989) Electrophysiology of the pancreatic beta cell. Prog Biophys Mol Biol 54: 87 143. A shcroft, F. M., & Gribble, F. M. (1999). ATP sensitive K+ channels and insulin secretion: their role in health and disease. Diabetologia 42 (8), 903 919. Barabsi, A. L., & Albert, R. (1999). Emergence of scaling in random networks. S cience, 286(5439), 509 512. Bates, H. E., Sirek, A. S., Kirly, M. A., Yue, J. T., Montes, D. G., Matthews, S. G., & Vranic, M. (2008). Adaptation to mild, intermittent stress delays development of hyperglycemia in the Zucker diabetic Fatty rat independent of food intake: role of habituation of the hypothalamic pituitary adrenal axis. Endocrinology 149(6), 2990 3001. Beattie, G. M., Leibowitz, G., Lopez, A. D., Levine, F., & Hayek, A. (2000). Protection from cell death in cultured human fetal pancreatic cells. Cell transplantat ion 9(3), 431. Benninger, R. K., Zhang, M., Head, W. S., Satin, L. S., & Piston, D. W. (2008). Gap junction coupling and calcium waves in the pancreatic islet. Biophysical journal 95 (11), 5048 5061. Benninger, R. K., Head, W. S., Zhang, M., Satin, L. S., & Piston, D. W. (2011). Gap junctions and other mechanisms of cell cell communication regulate basal insulin secretion in the pancreatic islet. The Journal of physiology 589 (22), 5453 5466. Bratusch Marrain, P. R., Komjati, M., & Waldhusl, W. K. (1986). Efficacy of pulsatile versus continuous insulin administration on hepatic glucose production and glucose utilization in type I diabetic humans. Diabetes 35 (8), 922 926. Bertram, R., Previte, J., Sherman, A., Kinard, T. A., & Satin, L. S. (2000). The Phan tom Burster Model for Pancreatic Cells. Biophysical journal 79 (6), 2880 2892.

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