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Modeling the effect of neonatal diabetes mutations on electrical activity and insulin secretion in pancreatic beta cells

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Modeling the effect of neonatal diabetes mutations on electrical activity and insulin secretion in pancreatic beta cells
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Full Text
MODELING THE EFFECT OF NEONATAL DIABETES MUTATIONS ON ELECTRICAL
ACTIVITY AND INSULIN SECRETION IN PANCREATIC BETA CELLS
by
ALEENA NOTARY
B.S. University of Colorado Denver, 2012
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
2015


2015
ALEENA NOTARY
ALL RIGHTS RESERVED


This thesis for the Master of Science degree by
Aleena Michelle Notary
has been approved for the
Bioengineering program
by
Richard Benninger, Chair
Kendall Hunter
Jane Reusch
November 16, 2015


Notary, Aleena Michelle (MS, Bioengineering)
Modeling the Effect of Neonatal Diabetes Mutations on Electrical Activity and Insulin
Secretion in Pancreatic Beta Cells
Thesis directed by Assistant Professor Richard Benninger
ABSTRACT
Diabetes is caused by dysfunctional beta ((B) cells found in the multicellular pancreatic
islet of Langerhans, an essential micro-organ to maintaining glucose homeostasis via
the secretion of insulin. (B cells are highly coupled within the islet, functioning to
coordinate a global response to elevated glucose levels and suppressing insulin
secretion at basal glucose levels. Despite intrinsic heterogeneity in (B cells, the islet
displays network behavior where global activation and suppression are a result of the
intracellular coupling between (B cells by means of gap junctions. Previous work has
shown that under the influence of gap junction coupling there exists a critical number of
inexcitable cells (~15%) that can act as a dominate negative to the system, and
suppress activity in stimulatory glucose conditions. This was done by using an inducible
mutation that renders specific cells inexcitable, producing a functional form of Neonatal
Diabetes Mellitus (NDM), and was simulated by a multi-cellular model for (B cell
electrophysiology. We explore this critical behavior further by altering the level of cell-
cell coupling by removing gap junction expression in mice and simulating an uncoupled
multi-cellular islet with multiple forms of the inactivating (NDM) mutation. We find that
critical behavior is diminished when coupling is removed, and islet electrical activity
can persist into the realm of severe NDM mutation. Further, we add completeness to the
model of the (B cell by accounting for stochastic channel noise and insulin secretion. We
IV


show that critical behavior in physiological parameters, e.g. insulin secretion, and
electrical activity as measured by real time and simulated calcium dynamics and can be
rescued when cell-cell coupling is removed. We present these results as further
characterization of the emergent critical behavior in the islet and uncover possible
treatment methods for Neonatal Diabetes Mellitus, and other monogenic forms of
diabetes.
The form and content of this abstract are approved. I recommend its publication.
Approved: Richard Benninger
v


ACKNOWLEDGEMENTS
A number of people contributed to finishing this work. I would like to sincerely thank
and acknowledge Richard Benninger for his support in guiding this thesis, and
committee members Kendall Hunter and Jane Reusch for providing valuable insight.
Additionally I would like to thank all the current and former members of the Benninger
Lab. Special thanks to Tom Hraha who provided the experimental data that this work
built from, and Matt Westacott for significant assistance on the computational portions
of this thesis. Additional acknowledgement goes to the staff at the Bardo Coffeehouse in
Denver for providing a fantastic place to work and exceptional espresso during my time
in graduate school. Finally, I would like to thank my family, friends and especially my
husband, Daniel, for his unwavering support and commitment throughout my time in
this program.
Special thanks to the University of Colorado at Boulder for providing access to the
JANUS supercomputer cluster, the Advanced Light Microscopy Core at the University of
Colorado Denver and the Barbara Davis Center islet isolation core.
Funding for this research was provided by NIH and NIDDK grants R00DK85145,
R01DK106412, R01DK102950 and JDRF grant 5-CDA-2014-198-A-N. Mouse studies
were performed according to IACUC protocol: B 95814(07)1D.
vi


TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION............................................................1
Diabetes: Motivation, Costand Complications.............................1
Islet of Langerhans Architecture........................................2
Beta Cell Function......................................................5
Gap Junction Coupling..................................................12
Katp Mutations Causing Diabetes........................................14
Percolation Theory in Islet Behavior...................................17
Mathematical Models For the Beta Cell..................................20
Specific Aim...........................................................23
II. MATERIALS AND METHODS..................................................24
Mouse Studies..........................................................24
Coupled Oscillator Model Simulations...................................26
Data Analysis..........................................................32
III. RESULTS...............................................................35
Calcium Imaging Reveals Recovery of Activity for Cx36(-/-) Mice........35
ATP Sensitivity is Reduced, Shows Critical Behavior....................37
Clinical NDM Mutations Examined........................................40
Stochastic Noise in Katp Channel Opening Probability...................42
Insulin Secretion in the Coupled Oscillator Model......................44
IV. DISCUSSION............................................................48
Phase Transition and Global Behavior as Measured by Calcium Dynamics....49
The Effect of Other Channel Parameters.................................53
The Effect of Stochastic Channel Noise in the Presence of NDM Mutations.57
Exocytosis Events Modeled for Various Mutations........................57
Critical Behavior and Networks in Biological Systems...................58
Implications For Diabetes..............................................60
FIGURES........................................................................62
LIST OF REFERENCES.............................................................77
ii


CHAPTER I
INTRODUCTION AND BACKGROUND
Diabetes: Motivation, Costand Complications
Over 200 million people across the globe are diagnosed with diabetes, a disease
marked by chronic hyperglycemia and a host of long term complications including
nerve damage, heart disease risk and kidney failure (Polonsky 2012, Diabetes Care
2002, International Diabetes Federation). Metabolic health and signaling are regulated
through a complex interplay of what we eat and how we expend energy; insulin is
arguably the most important hormone involved in metabolic health as it is the primary
hormone that lowers blood glucose levels as they rise after a meal. Hyperglycemia, a
hallmark of diabetes mellitus, along with insulin resistance occur when insulin
production does not meet the demand to lower blood glucose levels or when peripheral
tissues fail to respond to circulating insulin (Cnop et al. 2005, Diabetes Care 2010,
Diabetes Care 2002).
In 2012, diabetes healthcare accumulated over $245 billion in costs in the United
States alone, up from $174 billion in 2007, and projections estimate that the current 1
in 10 adults who have diabetes in the U.S. will rise to between 1 in 3 and 1 in 5 by 2050
(Boyle et al. 2010, American Diabetes Association 2013). Certainly, finding ways to
reverse this disease is important and will greatly improve the quality of life for millions
of people worldwide.
1


Type 1, Type 2 and Neonatal Diabetes
Diabetes can arise from an inappropriate immune response in which the body
kills insulin producing (B cells (Type 1) or from a chronic tolerance of excess glucose
levels that eventually renders insulin ineffective and exhausts (B cells (Type 2) (Dotta
and Eisenbarth 1989, Miranda et al. 2005, Bell and Polonsky 2001). Additionally, in
infants, neonatal diabetes mellitus (NDM) may present in the first 18 months of life, and
is marked by specific mutations to the insulin producing (B cells that leave them less
sensitive and ill-equipped to secrete sufficient insulin (Lang and Light. 2010, Ashcroft
and Rorsman. 2013, Pearson et al. 2006, Hattersley and Ashcroft. 2005). Other types of
diabetes such as MODY (maturity-onset diabetes of the young) can be found discussed
in the literature, the work presented here will focus on neonatal diabetes mellitus
(NDM) and Type 2 diabetes. Treatment options vary for the different types of diabetes,
but the consistent component behind all types is the insulin producing beta cells found
in the pancreatic islet of Langerhans.
Islet of Langerhans Architecture
The pancreatic Islet of Langerhans are multi-cellular micro organs that lie
dispersed within the pancreas, composed primarily of alpha, beta ((B) and delta cells.
This system is highly integrated with surrounding vasculature and plays a key role in
regulating blood glucose homeostasis. Islets are a spherical aggregation of the 3
primary cell types that work to coordinate a system wide response to blood glucose
changes, a response which is affected and coordinated largely by the architecture
intrinsic to the islet. Approximations in mouse islets have shown that alpha cells make
2


up 21%, (B cells 68% and delta cells 10%, with other endocrine cells (F cells) composing
about 6% of the islet volume (Kim et al. 2009, Ishihara et al. 2013), but studies have
also shown that there is great variability in the overall composition, especially in human
islets (Kim et al. 2009, Brissova, et al. 2005). Varying conditions, such as diabetes or
pregnancy, can result in plasticity of the expression of each cell type, but (B cells are the
majority in humans (~55%) and rodents (Cabrera et al. 2006, Kim et al. 2009).
Alpha cells respond to low glucose levels through the secretion of the peptide
hormone glucagon. Primary cell types interact via their secretagogues, glucagon works
in opposition to insulin by raising overall blood glucose levels. Delta cells secrete
somatostatin as a paracrine signal to inhibit both the secretion of insulin and glucagon.
Ishihara et al showed that insulin secretion from (B cells effects glucagon release from
nearby alpha cells, inhibiting its release when (B cells are active as a way to allow for the
necessary insulin action. Rorsman et al has indicated that glucose is a direct regulator of
alpha cell activity, and neurotransmitter GABA may be involved as well (Rorsman et al.
1989, Gopel et al. 2000). As a consequence of diabetes, the interactions between the
primary cells types are disrupted and inappropriate secretion of glucagon or
somatostatin can contribute to hypoglycemia (Gerich et al. 1973, Alberti et al. 1973).
The architecture in rodents has been well established with (B cells composing much of
the islet core while alpha and delta cells can be scattered, but concentrate mostly to the
periphery of the islet. Human islet architecture has been mostly understood to have
more intermingled cell types rather than distinct areas of specific cells. (Ravier and
Rutter, 2005, MacDonald et al. 2007, Brissova, et al. 2005). In 2010, Bosco et al. found
3


that human islets do contain a more scattered distribution of alpha, delta and (B cells,
but that (B cells tended to cluster and be surrounded by alpha cells, while the center of
the islet contained dense vasculature and glucagon secreting alpha cells. This structure
has been suggested by additional groups since, and some studies such as Kilimnik et al.
have shown morphological and cell type composition changes in the presence of Type 2
diabetes and with changing islet size.
In both humans and rodents, (B cells are highly coupled together via gap junction
channels (Serre-Beinier et al. 2000, Perez-Armendariz et al. 2013, Serre-Beinier et al.
2009) which enable ion sharing and give rise to the sophisticated patterns observed in
insulin secretion and electrical activity (Ravier, et al. 2005, Benninger et al. 2008).
Architecture lends itself directly to cell-cell coupling because cells in close contact with
each other will be more likely to couple via shared ion channels (Wojtusciszyn et al.
2008). Connexin36 is the gap junction in (B cells (Saez et al. 2003, Serre-Beinier et al.
2009, Jain and Lammert, 2009) and is the focus of the coupling aspect of this research,
this will be discussed in further sections. In considering the islets response to elevated
glucose levels, architecture is vitally important. The islet tends to respond globally, that
is, it is unlikely for individual cells to function autonomously and respond without the
entire system responding synchronously as well when the system is coupled (Hraha et
al., 2014, Benninger et al., 2008).
4


/3 Cell Function
Electrical Activity
Beta cells act as glucose sensors and respond to changing glucose levels by
secreting insulin directly into the circulatory system where it is carried to target cells
throughout the body. This general process can be referred to as stimulus-secretion
coupling, or specifically glucose stimulated insulin secretion (GSIS) (MacDonald and
Rorsman 2006, Misler et al. 1992).
Typically the plasma membrane of the (B cell rests at about -70 [mV] (Ashcroft
and Rorsman 1989, Sherman, 1996) at basal blood glucose conditions, <5mM. Potential
of the plasma membrane is determined by the relative ion concentrations in the cytosol
and outside the cell, and can be described by the Nernst equation.
Here, R is the ideal gas constant (J/K mol), T is temperature in units of Kelvin, F
is Faradays constant (C/mol) and z represents the ion charge, +1 for potassium.
Therefore, when no ions are moving across the membrane, the Nernst equation
becomes:
Potassium (K+) ions are the largest contributor to the overall membrane
potential in the (B cell and flow outward through an ATP sensitive potassium channel
(Katp) when the cell is electrically silent. This outward current sets the resting
membrane potential around -70 mV, across the plasma membrane having a thickness of
E = .0591 [V] log10(l) = -59.1 mV
5


~3.5 nm. The size of the results in a large electric field, ~ 20 106 , sensitive to small
m
changes in ion concentrations.
As glucose in the blood increases, it is taken up into the (3 cell by GLUT2
transporters, the glucose is then phosphorylated by glucokinase, and sent into the
mitochondria for metabolism (MacDonald, et al. 2005). Metabolism produces pyruvate,
NADH and ATP. As more glucose is metabolised and the concentration of ATP increases,
the ratio of [ATP]/[ADP] will reach a level sufficient to close the ATP sensitive
potassium channel (Katp) and trigger the depolarization of the plasma membrane
(Ashcroft and Rorsman 1989, Stamper, et al. 2014, MacDonald et al. 2005, Sherman
1996.). This channel closure prohibits the additional outflow of K+ ions through the Katp
channel and triggers a membrane depolarization that promotes the opening of voltage
gated L-type Calcium channels that then allow the influx of Ca2+ ions. L-type calcium
channels open around -45mV (Sherman 1996); their opening is especially important for
insulin secretion because the fusion of granules with the cell membrane is calcium
dependent (MacDonald and Rorsman 2006, Pedersen and Sherman 2009).
Membrane depolarization also triggers voltage dependent K+ channels to open,
allowing an outward rectifying current that acts to repolarize the membrane and
prepare for additional oscillations (Ashcroft and Rorsman 1989, Rorsman and Trube,
2000, Stamper, et al. 2014). The interplay between Katp channel closure, depolarization,
calcium influx and the rectifying K+ current give rise to with bursts of oscillations in
potential (and subsequently, intracellular calcium) followed by a period of electrical
6


silence. This behavior is characteristic of (B cells and is a hallmark of research involving
electric activity and disruptions to that caused by diabetes (see Figure SI for schematic
of GSIS in the (B cell).
Beta cells are known to have intrinsic heterogeneity in their electrophysiology
that causes individual cells to have differing responses when dispersed or uncoupled
(Ashcroft and Rorsman 1989, Speier et al. 2007, Benninger et al. 2014). Heterogeneity
is minimized in fully coupled islets because gap junctions work to coordinate the
response of the islet, thus the islet responds in a critical rather than a gradual manner
to stimuli, e.g. increases in glucose (Ashcroft and Rorsman 1989, Hraha et al. 2014).
Reduced cell-cell coupling is believed to be an early sign of diabetes (Ravier et al. 2005,
Speier et al. 2007, Head et al. 2012), where insulin secretion and calcium dynamics are
also disrupted. In further discussion of this, we will examine methods to model these
effects and examine the interplay between (B cell electric dynamics and cellular
coupling.
ATP Sensitive Potassium Channel (Katp)
Metabolism and cellular electrical activity are uniquely linked in the (B cell by
means of the Katp channel via their response to elevated ATP levels and subsequent
regulation of membrane potential (Ashcroft and Rorsman, 2013). The Katp channel is a
transmembrane protein, composed of 4 Kir6.2 units, encoded by the KCNJ11 gene, in
the transmembrane domain that form a pore with 4 regulatory sulfonylurea receptor
subunits (SUR) on the intracellular side of the membrane encoding the ABCC8 gene
7


(Ashcroft and Gribble, 1999, Ashcroft and Rorsman, 2013). At high glucose levels, ATP
concentrations rise and interact with the Kir6.2 subunit to close the channel and
depolarize the membrane; the adenine nucleotide dependence of this channel is the key
to the metabolic coupling with electrical activity that exists in (3 cells. At low glucose
levels, the Katp channel remains open as ATP/ADP remains low and intracellular
MgATP and MgADP act with the regulatory SUR receptor to promote channel opening
(Ashcroft and Gribble, 1999). This, in conjunction with gap junction coupling, can help
prevent excess insulin secretion at basal glucose levels by keeping the cell electrically
silent (Nguyen, et al. 2014, Benninger et al. 2011).
The Katp channel is key in many diabetes causing mutations. Some mutations are
known to cause overactive Katp channels, that is, they are rendered insensitive to ATP
or otherwise unable to close and trigger a membrane depolarization. Studies examining
gain of function mutations to the Kir6.2 subunit show that hyperactive Katp channels
inhibit cellular activity and thus insulin secretion (Nguyen et al. 2014, McTaggart et al.
2010, Koster et al. 2000). Mutations reducing the ATP sensitivity of the and altering the
regulatory SUR1 subunit on the Katp channel are seen in Neonatal and Type 2 diabetes
with varying degree, ultimately showing reduced insulin secretion (Hattersley and
Ashcroft 2005, Sagen et al. 2004, McTaggart et al. 2010). Many Kir6.2 and SUR1
mutations can cause hyperinsulinism; these are also referred to as loss of function
mutations to the Katp channel. Most often the overall Katp current is reduced and the
cell is overactive, secreting excess insulin even at basal glucose levels (McTaggart et al.
8


2010). This is indicative of the binary effect that the Katp channel has in coupling
metabolism to electrical activity.
Previous work has shown that in a model of neonatal diabetes, sufficient
subpopulations of inactive cells can globally suppress islet activity, though many
functional cells remain (Nguyen et al., 2014, Hraha et al., 2014). Sulfonylureas are used
to treat patients with NDM and (some) Type 2 diabetes (Pearson et al. 2006), acting to
promote Katp channel closure and increase insulin secretion, conversely diazoxide, a
uniform promoter of channel opening can be used to treat hyperinsulinism (McTaggart
et al. 2010).
Insulin Secretion Pathway
Insulin secretion occurs after the (3 cell is stimulated from increasing glucose
levels, and the glucose is metabolized to trigger the influx of calcium ions. The
triggering pathway following calcium influx and leading to insulin secretion has been
studied extensively since the early isolations of islets for study, but there are many
factors at play here and much work remains. One of the more established aspects of the
triggering pathway is the ATP dependent nature, discussed previously, and the calcium
dependence that leads to fusion of insulin granules to the plasma membrane. Insulin
secretion occurs in a biphasic pattern upon a step increase in glucose (Curry et al.
1968), e.g. after eating a large meal, with the first phase showing a sharp increase in
secretion lasting ~5-10 minutes followed by a second phase of sustained secretion
(Palumbo, et al. 2013, Rorsman and Renstrom 2003). Insulin is produced in the
9


endoplasmic reticulum of the (B cell (Rorsman and Renstrom 2003) and is then
processed into membrane bound granules that are kept near the membrane as they
await exocytosis (Rorsman and Renstrom 2003). Each (B cell is estimated to have about
10,000 granules of insulin kept in reserve stores for sustained secretion, with ~200
granules kept near the membrane for immediate release upon cellular stimulation
(Palumbo, et al. 2013, Rorsman and Renstrom 2003, Bratanova-Tochkova, et al. 2002).
It is thought that the first phase of secretion emerges from granules that have
previously been stored near the membrane and are ready for rapid excocytosis, and the
second phase is sustained by newcomer granules that are mobilized from the reserve
stores, and may be part of a highly calcium sensitive pool (Pedersen and Sherman,
2009, Chen, et al. 2008). Loss of the first phase of insulin secretion is recognized as an
early sign of diabetes, and is thus an important physiologic characteristic to study
(Rorsman and Renstrom 2003, Chen et al. 2008, Pedersen and Sherman, 2009).
Sustained stimulatory concentrations of glucose will yield a pulsatile pattern of insulin
secretion as the (B cells continue their characteristic bursting behavior in response to
elevated glucose, triggering the exocytosis events (Pedersen and Sherman 2009,
Benninger et al. 2014, Palumbo et al. 2013). Studies have shown that when gap junction
coupling is not present, the intrinsic heterogeneity in (B cells can alter the insulin
secretion patterns of the islet, namely in reducing the characteristic first phase of
secretion (Head et al. 2012, Benninger et al. 2011, Ravier et al. 2005).
Insulin secretion dynamics have been studied in a number of ways, some
common methods include perfusion, TIRF microscopy and capacitance measurements.
10


Islet perfusion uses a flow culture system to constantly monitor insulin release as a step
increase in glucose is applied, TIRF (total internal reflection microscopy) is used to
examine the granule kinetics near the membrane in cells that express a fluorescent
marker on the insulin granules, this method allows docked and fused vesicles to be
viewed (Wang and Thurmond 2009, Ohara-Imaizumi et al. 2004). Finally, capacitance
measurements are used to detect when a granule fuses with the plasma membrane and
increases the overall membrane area (changing the capacitance of the cell), this is most
often used for detecting the first phase of secretion since both endocytosis and
exocytosis will contribute to this measurement (Wang and Thurmond 2009, Bratanova-
Tochkova et al. 2002).
Examining exocytosis events has revealed that there are distinct pools of insulin
granules kept in different proximities to the membrane. Most models establish that
there is a reserve pool, kept far from the membrane with an "infinite" supply of
granules relative to what is actually required. It has been shown that granules from this
pool are mobilized through glucose dependent (Henequin 2000, Rorsman and
Renstrom 2003) cytoskeleton remodeling (Wang and Thurmond 2009) of the actin
network (Pedersen and Sherman 2009) and moved to a docking area at the membrane
where SNARE proteins are known to facilitate membrane docking while the granules
await fusion and exocytosis (Daniel et al. 1999, Pedersen and Sherman 2009, Barg et al.
2002, Ohara-Imaizumi et al. 2004). Though docking is not established as an absolutely
necessary prerequisite for fusion, it is suggested that the first phase of secretion is
made up almost entirely of docked vesicles, and that the second phase comes from
11


newcomer vesicles that may or may not dock prior to exocytosis (Pedersen and
Sherman, 2009).
Fusion with the membrane leading to exocytosis is heavily dependent on Ca2+
(Barg, et al. 2002, Pedersen and Sherman. 2009, Bratanova-Tochkova, et al. 2002) and
occurs quickly as the first phase of secretion when the (B cells initially become active
and calcium flows into the cell.
Another crucial aspect to this pathway is how other metabolites in addition to
calcium can amplify the response; this is commonly referred to as the amplifying
pathway to insulin secretion. Mobilization of granules is amplified by sustained glucose
concentrations, producing the second phase of insulin secretion (Palumbo et al. 2013,
Rorsman and Renstrom. 2003). Other factors such as cyclic-AMP (camp) produced
during cellular respiration also contribute to amplifying secretion by further mobilizing
granules to prepare for fusion and exocytosis (Gillis et al. 1993, Chen et al. 2008,
Rorsman and Renstrom. 2003).
Gap Junction Coupling
It is established that (B cells are electrically coupled together via gap junctions,
and that these are important for coordinating the islet response and suppressing excess
insulin production at basal glucose levels (Nguyen, et al. 2014, Speier et al. 2007,
Rocheleau et al. 2006). Gap junctions are formed out of connexin molecules that join
together in a cylindrical structure known as a connexon; (B cells meet at these
12


connexons to form a channel between cells whereby metabolites and other signaling
molecules can be exchanged (Stamper et al., 2014, Ravier et al., 2005, Perez-Armendariz
et al. 2013). Connexin36 is the means of coupling between (B cells, and is expressed in
pancreatic (B cells in both rodents and humans (Perez-Armendariz et al. 2013, Serre-
Beinier et al. 2009). This ion exchange allows for sophisticated coordination of
membrane depolarizations, initiated by the Katp channel closure, between (B cells in all
areas of the islet (Jain and Lammert, 2009, Stamper et al. 2014, Ravier et al. 2005, Head
et al. 2012).
Several studies have established that the characteristic coordinated calcium
oscillations are disrupted in rodent islets lacking Cx36 (Ravier et al. 2005, Nguyen et al.
2014, Stamper et al. 2014, Speier et al. 2007). The lack of Cx36 allows the full
expression of intrinsic (B cell heterogeneity (Speier et al. 2007) and cells can function
autonomously instead of in a globally coordinated fashion. This is not desirable in the
case of healthy islets where the global response is key to coordinating the second phase
of insulin secretion and regulating responses (Benninger et al. 2011); diminished
expression of Cx36 is thought to contribute to type 1 and II diabetes where the biphasic
nature of insulin secretion is also lost (Stamper et al. 2014, Rocheleau et al. 2006).
Studies from Pizarro-Delgado et al. and Head et al. have shown an effect on insulin
secretion dynamics through changes to Cx36 expression, with particular changes to the
pulsatile nature and first phase secretion occurring in uncoupled islets that suggest this
to be an important feature of (B cell physiology. Perhaps counter-intuitively, previous
work has hypothesized that removing Cx36 coupling can help overcome the
13


detrimental effect of subpopulations of unhealthy cells as in NDM, and restore some
electrical activity and insulin secretion where the effects of full coupling would
otherwise suppress activity of individual cells (Hraha et al. 2014, Nguyen et al. 2014).
Motivation for this hypothesis is drawn from studies such as Nguyen et al. where a
model of diabetes having Kir6.2 mutations in mice lacking Cx36 expression was shown
to have improved insulin secretion and normal blood glucose levels compared to the
same mutation in fully coupled (Cx36 +/+) mice.
Katp Mutations Causing Diabetes
Neonatal Diabetes
Neonatal diabetes mellitus (NDM) is a monogenic disorder defined by requiring
insulin for diabetes in the first 6 months of life. It may have a transient phenotype
(TNDM), resolving within 18 months, or permanent (PNDM) where the patient requires
lifelong regulation of glucose levels with insulin and may display significant
neurological features of the disease known as DEND symptoms (Pearson et al. 2006).
About 50% of NDM patients have mutations on the KCNJ11 or ABCC8 genes (Hattersley
and Ashcroft. 2005), previously discussed to encode for the Kir6.2 and SUR1 subunits
on the Katp channel in (3 cells (Lang and Light. 2010). The monogenic nature of the
disease means that the mutations are restricted to one allele and therefore take on a
binomial distribution in the subunits it can affect on the Katp channel. For this reason,
heterozygous expression of mutations can have varying degree, occupying 1-3 subunits
of the channel in a binomial distribution (Proks et al. 2004).
14


Mutations that Render the Katp Channel Less Sensitive to ATP
In many cases of NDM, the Katp channel is rendered less sensitive to ATP and/or
the gating mechanisms are affected, thus the cell has a delayed or inhibited response to
glucose uptake and is unable to activate via Katp channel closure (Lang and Light. 2010,
Gloyn et al. 2004, Hattersley and Ashcroft. 2005, Sagen et al. 2004). Several studies to
measure the effect of these mutations show that they occur with varying effect, where
the most dramatic mutations cause complete inactivity of the (3 cell, and thus secrete no
insulin. Electrophysiology findings from many studies and groups have shown NDM
mutations with decreased ATP sensitivity by factors ranging from a mild factor of 1.3 to
a severe mutation with channels that are over 20 times less sensitive to ATP (Gloyn et
al. 2004, Proks et al. 2004, Hattersley and Ashcroft. 2005).
The Katp channel kinetics can be generally described by a dose response curve
for the current response of the channel:
Iratp
a +
1 +
(l~g)
/ [ATP]
\ kl
' 2
H
With ki representing the concentration of ATP at which half of the resulting
2
current is blocked, e.g. overall ATP sensitivity of the cell, and H representing the
steepness of the resulting response curve. A term for residual current at saturating ATP
15


concentrations, a, represents the fraction of current that may remain when ATP is
sufficiently high to close the channel under normal conditions. This is relevant for NDM
mutations because many have been reported to exhibit high residual currents, possibly
due to ATP sensitivities (McTaggart et al. 2010, Hattersley and Ashcroft 2005). Typical
concentrations for half maximal block of the Katp channel have been reported ~7uM
(Gloyn et al. 2004, Proks et al. 2004, Koster et al. 2005) Further details on modeling
these kinetics can be found in the methods section.
The pore forming subunit of the Katp channel (Kir6.2) is a transmembrane
protein, containing the ATP binding site that dictates channel closure on the
intracellular side of the plasma membrane (Pearson et al., 2006). Mutation locations do
not seem to be strictly correlated to the degree of severity that the mutation causes,
many DEND mutations lying near the ATP binding site or away in the side chain of the
Kir6.2 subunit and more mild mutations producing TNDM lying near the ATP binding
site (Pearson, et al. 2006, Lang and Light, 2010). In any case, these gain of function
mutations are known to right shift the ATP dose response curve with varying degree
(Girard et al. 2006, Proks et al. 2005) as all cells are less sensitive to ATP; this is in
contrast to other gain of functions mutations studied where a ratio of cells is expresses
a gain of function mutation to the Katp channel and individually would display a severe
shift in ATP sensitivity (Hraha, et al., 2014).
Many NDM mutations have been expressed in insulin producing cells, or
expressed in mice for study and characterized in terms of their electric properties. In
16


reviewing the literature for several of these mutations, we have consolidated
information based on electrophysiology measurements made in WT and mutant cells
and display a summary of the results in Figure S4. These will be implemented in a
mathematical model of (B cell and islet activity to examine the relative effect of each
mutation, details of which will be discussed in later sections.
Percolation Theory in Islet Behavior
Recent research has investigated the phenomena of percolation theory as it
applies to dynamic, network systems in biology. The islet is among several systems that
functions based on network principles, and has some emergent behavior that results
from the interconnected nature of its constitutive elements, (B cells. Percolation theory
has to do with describing the extent of network connectivity, when a network is highly
connected the resulting signal can reach all edges of the network and is thus, percolated
(Albert and Barabasi 2002, Stamper et al. 2014). We can consider the islet as a system
of interconnected nodes representing (B cells, with each node being connected to its
nearest neighbors. Cells that do not couple together with (B cells such as alpha cells or
dead/inactive (B cells occupy node space but do not conduct any signal. As long as the
percentage of connected nodes is above the critical threshold (~15%), a signal can
percolate across the network. When the percentage of inactive or non-contributing
nodes exceeds this threshold, critical behavior emerges and the signal cannot propagate
properly. In the context of islets, this means that if mutations are present that render
cells inactive, or if a sufficient number of cells has died (Type 1 diabetes) then the islet
will not be able to generate sufficient signal, and no electrical activity will propagate. If
17


we define Pexc as the number of excitable cells, when examining the phase transition
curve as shown in Hraha et al, we can define regimes on the transition as pre-critical
where Pexc > threshold of cells requires for signal propagation, and post-critical where
Pexc < threshold that are useful when talking about where an islet lies in relation to the
expected network behavior.
Phase Transition Behavior in Kir6.2lAN30K185 Mouse Model
The unique components of the (B cell contribute to a robust, coordinated and
dynamic electrical response to glucose changes and thus couples a metabolic output
(insulin) with a system wide electrical response. Due to this, individual (B cell health is
extremely important and small populations of inactive, uncoupled or dead (B cells can
severely inhibit the system response, as well as changes to the intrinsic excitability to
individual cells (Stamper et al. 2014, Hraha et al. 2014). Overactive mutations to the
Katp channel are known in NDM and are hypothesized to cause reduced insulin
secretion: application of these NDM like mutations have been studied in vivo to
elucidate the effect of increasing numbers of inactive cells. Roster, et al. showed that
inducing a mutation that caused a reduction in ATP sensitivity and kept the Katp
channel open (hyperactive) resulted in mice having profound neonatal diabetes, they
suspect due to a lack of insulin secretion. Other groups have developed a tamoxifen
inducible overactive Katp mutation in mice that has both changes to intrinsic channel
opening probability as well as shifted ATP sensitivity (Zhang, et al. 2005, Remedi et al.,
2009), these represent a functional form of neonatal diabetes as they show direct
changes to plasma insulin and reduced calcium signaling due to Katp dysfunction.
18


Increasing the number of cells with overactive channels (inactive cells) should then
decrease the overall excitability of the islet.
We have previously shown the characteristic phase transition behavior in
calcium activity that emerges as the number of inactive cells increases in fully coupled
islets, representing NDM when the number of inexcitable cells reaches >15% (Hraha, et
al., 2014). The application of diazoxide to WT islets additionally shows a functional
NDM form when the applied diazoxide reaches concentrations >100uM, thereby
promoting uniform channel opening across all cells of the islet (Hraha, et al., 2014) and
showing marked decrease in calcium activity in all cells. Similar results have been
shown by computational modeling percolation theory as applied to signal propagation
in the islet (Stamper, et al., 2014), though the specific effect of gap junction coupling on
electrical activity in islets having overactive Katp mutations has not been investigated in
detail.
Connexin36 Synchronizes Islet Response
The phase transition results in calcium activity have been observed in islets
having full Cx36 coupling. Based on previous work showing a recovery of insulin
secretion and normoglycemia in Kir6.2iAN30'K185Q] mice (Nguyen etal. 2014) lacking
expression of Cx36, we hypothesize that a reduction of Cx36 will restore calcium
signaling in islets having severe mutation. By removing the obligation to synchrony, we
believe we can recover function in islets representing functional NDM mutations and
that this has direct application to human NDM that is treatable using sulfonylureas.
19


Mathematical models for the (3 Cell
Several computational models for the (B cell and various aspects of insulin
secretion exist. Here we will examine a model for (B cell activity and components for
modeling insulin secretion as well as stochastic channel noise.
Models for fl Cell Activity
Beta cell activity has been modeled for many years, initially beginning with
simple models showing a few ion currents (Ca2+, K+), that represent glucose induced
electrical activity (Chay and Keizer, 1983. Henquin 1990). Other models have since
been published that include more metabolism and ion concentration changes (Ainscow
and Edwards 2002, Bertram et al. 2000). Most importantly, (B cells show an interesting
electrical burst pattern that is induced by changing glucose concentrations; each model
for (B cell activity shows this consistently by means of including a slowly changing
variable that induces this re-bursting activity. For purposes of study, models such as
these can be used to analyze specific components of the (B cell and quantify the
theoretical whole cell response, based on experimental findings.
We have used a model developed by Cha, et al. that includes metabolism and ER
dynamics in addition to the essential calcium dynamics and glucose dependence for
generating electrical activity. This model was developed based off of the work in
Fridyland et al. and was modified for our use to include a coupling current to represent
gap junction channels. Details of this model and the methods used to adapt it for use in
this work will be discussed in the methods section (Cha et al. 2011, Fridyland et al.
20


2003). We have previously used a boolean model of interconnected nodes to show the
emergent phase transition behavior in the islet when applying an increasing percentage
of inactive cells (Hraha et al. 2014). This model does not encompass (B cell
electrophysiology but does offer insight into the emergent network properties of the
islet, thus it was used as a confirmation of the concept of critical behavior in the islet
but will not be used moving forward in this work.
Modeling Insulin Secretion and Exocytosis Events
Insulin secretion and (B cell activity are absolutely dependent on each other
(Rorsman and Renstrom 2003), and silent (B cells cannot contribute significantly to
insulin secretion. In modeling (B cell activity ion currents and exchanges are taken into
account, but including the exocytosis events of insulin granules is an involved problem
and often isnt included. Still, many studies examining the specific exocytosis events
following the influx of calcium and leading to the secretion of insulin granules have
been published (Chen et al. 2008, Bertuzzi et al. 2007, Pedersen and Sherman, 2009).
Some models, as in Pedersen and Sherman and Chen, et al. include a calcium
micro-domain near the R-type channels in the plasma membrane where the
concentration of calcium ions is much higher and has a more dramatic effect on the
calcium dependent steps in exocytosis. In this work, we use the insulin secretion model
described in these two papers, but without regard to the calcium micro-domain, leaving
the calcium triggered fusion events solely dependent on intracellular calcium. Since this
micro-domain concept is not consistently included in the literature, we do not include it
21


here but instead investigate the total effect that reduced coupling has on insulin
secretion, and leave the model open for additional modifications later.
Stochastic Channel Noise
As described in previous sections, dispersed or uncoupled (B cells exhibit more
random and disturbed patterns of activity compared to coupled cells. Upon channel
sharing via coupling, the signals between (B cells are then shared and synchronized to
burst in rhythmic patterns. In general, ion channels are understood to have some
stochastic changes to their gating properties due to thermal fluctuations or random
noise factors (Jo et al. 2005, Chay and Kang 1988, Goldwyn and Shea-Brown. 2011).
When modeling channel gating, it is expressed as a probability of being open or closed,
and this probability can then have random noise factors that influence how the channel
behaves, especially when uncoupled (Jo et al. 2005). Depending on the amount of noise
and subsequently the number of channels it corresponds to (see methods) noise has
been shown to disrupt oscillatory patterns in membrane potential and induce
membrane potential bursts in uncoupled silent cells. Since coupling is understood to
smooth out individual cell behavior in favor of the whole system response, noise is of
particular interest for uncoupled (B cells, and especially in regard to insulin secretion
because the influence of noise in uncoupled cells could promote additional activity from
otherwise silent (B cells (Benninger et al. 2014). Particular details regarding how we
model this concept can be found in the methods section.
22


Specific Aim
Diabetes is a severe disease affecting many people worldwide. The insulin
producing pancreatic (B cells lie in a very rich and interesting system, proven to be
malleable in treatment. Given the importance of Cx36 coupling and Katp channel
properties in the (B cell, this thesis aims to test the effects of reduced coupling in the
presence of mutations to subpopulations of cells, as well as mutations affecting all cells
uniformly on the overall response of the islet to secrete insulin. By using computation
and experimental means, we investigate the effect that cell-cell coupling has on
intensifying NDM mutations, and to what degree this can be overcome by reducing
coupling and accounting for stochastic channel noise. We assess this by examining
calcium levels and resulting insulin secretion in our coupled oscillator model for the (B
cell, and in experiment by using transgenic mouse lines. This is ultimately useful for
assessing the possible recovery to insulin secretion that could be had for specific
mutations, especially those that are sensitive to oral sulfonylurea therapy, a common
drug used to treat neonatal diabetes.
23


CHAPTER II
METHODS AND MATERIALS
Mouse studies
Ethics statement
Experiments were conducted in accordance with the relevant guidelines and
laws, and were approved by the University of Colorado Institutional Biosafety
Committee and Institutional Animal Care and Use Committee.
Mouse Lines
Creating the gain of function mutation on the Kir6.2 subunit with GFP tag
(Rosa26- Kir6.2lAN30'K185Q] ), (B cell specific, inducible Pdx-Cre, Connexin36 knockout
(Cx36 -/) and the loss of function Katp subunit with GFP tag (KirG^lAAAl) have all been
previously described in (Zhang, et al. 2005, Degen, et al. 2004, Remedi, et al. 2009,
Roster, et al. 2002). Pdx-Cre and Rosa26-Kir6.2 mice were crossed to produce variable
Kir6.2[AN30'K185Q] expression in (B cells. Daily injections of tamoxifen (1-5 daily doses) in
8-16 week old mice (50 mg/g body weight) were administered to induce the variable
Kir6.2[AN30'K185Q] expression. Mice lacking Pdx-Cre or Rosa26-Kir6.2 were used as
controls.
Blood Glucose and Plasma Insulin Measurements
Daily measurements of blood glucose using a glucometer were taken and then
averaged over day 27-29 after tamoxifen induction. Plasma insulin was measured at
24


day 29 from blood samples centrifuged for 15 minutes at 13,900RCF, then assayed
using mouse ultrasensitive insulin ELISA (Alpco).
Insulin Secretion Measurements
After isolation, the islets (5/batch in duplicate) were incubated in 2mM glucose
plus Krebs-Ringer Buffer (128.8 mM NaCl, 5 mM NaHCCb, 5.8 mM KC1,1.2 mM KH2PO4,
2.5mM CaCk, 1.2 mM MgS04,10 mM HEPES, 0.1% BSA, pH 7.4) and then incubated for
60 minutes in Krebs-Ringer Buffer plus 20mM glucose. The medium was then sampled
for secretion, and islets sampled for content after being lysed in 1% TritonX-100 and
frozen overnight at -20C. The samples were then assayed using mouse ultrasensitive
ELISA.
Islet Isolation
Islets were isolated by means of a collagenase injection through the pancreatic
duct, and were handpicked after the pancreas was harvested and digested. Medium to
maintain the islets included RPMI (Invitrogen) plus 10% FBS, 100 U/ml penicillin, 100
pg/ml streptomycin, at 37C under humidified 5% CO2 for 24-48 hours prior to study.
Calcium Imaging
Isolated islets were loaded with 3uM Rhod-2 (Invitrogen), in imaging medium
(125 mM NaCl, 5.7 mM KC1, 2.5 mM CaCk, 1.2 mM MgCk, 10 mM Hepes, 2 mM glucose,
and 0.1% BSA, pH 7.4) for 45 minutes at room temperature, and were held in
polymdimethylsiloxane PDMS microfluidic devices (MacDonald et al. 2000). Rhod-2
25


fluorescence was imaged on a spinning disk confocal (Marianas, 31), excited at 561nm
using a diode laser with a 580-655nm long-pass filter for emission, or a spectral
unmixing confocal (LSM 780) excited at 543nm using a diode laser with a 580-655nm
long-pass filter for emission, both with temperature maintained at 37 C. Images were
acquired 1/sec, 10 minutes after changing glucose concentration (2-20mM).
Coupled Oscillator Model Simulations
This model is based on the Cha-Noma (3 cell model (Cha et al. 2011) and was
expanded to account for cell-cell coupling and some altered Katp channel function. Each
current is described in Cha et al., and contributes to the membrane potential according
to the ODE:
(1)
C V[ ICav + Itrpm + hoc + IbNSC + IrDt + lKCa(SK) + ^fCa(SX) + lK(ATP) + lNaK
+ lNaCa + IpMCA
Gap junction coupling was then simulated by assigning a coupling current
between neighboring cells (i,j), according to a sphere packing algorithm used to
assemble the simulated cluster.
26


(2)
-c*v! = ii + Y^gUuP(yi-vj)
i
Some heterogeneity in coupled was included by randomly assigning gCOuP
according to a distribution from previously published data (SD/mean = 70%)
(Farnsworth et al. 2014).
The Katp channel current was described as:
(3)
Ik (ATP) 9k(ATP) PoK(ATP) (y Vk)
where the open channel probability given by:
(4)
PK(ATP) ~
.os (1+M) + ,9(Mgp)2
[ADP]\2( , A5[ADP] f[ATP]\\
.01 J V1 + .026 + ^ .05 ) )
Changes to Katp Channel
Kir6.2lAN30'K185Q] expression was modeled by modifying the open probability in a
fraction (P exc ) of cells:
(5)
PK(ATP)Mut = Y{P0K(ATP)) + (1 K)
27


Y = 0.5
Diazoxide application and residual current was modeled by again modifying the open
probability, but in all cells according to:
Here, a represents the fraction of current remaining at saturating ATP
concentrations. This was changed only for mutations where the current was reported
and by default is set to zero.
To change the half maximal concentration (ATP sensitivity) and open channel
conductance of the Katp channel, the ATP dependent portion of poK^ATP^ was changed to
reflect the factor of ATP sensitivity decrease. Thus:
(6)
PK(ATP)Mut ~ a + (1 a) PK(ATP)
(7)
28


where k[ represents a factor of increase to the half maximal ATP concentration, and H
2
is the Hill coefficient. By default, H = 1, and was only changed for mutations where the
literature reported a change based on their findings. Here p'0 represents the factor
applied to the open channel conductance, this was changed for some mutations to
reflect the literature. Sources for each mutation simulated can be found in Figure S4.
Insulin Secretion Model
The general form of this model was taken from previously published work
(Pedersen and Sherman 2009) and was adapted to work with our model. Insulin
granules are designated in distinct pools, each with rates of exchange, leading up to a
secretion event. The fusion step was modeled to have calcium dependence by using a
hill equation and choosing an appropriate half maximal concentration to reflect the
expected first phase release of ~20 granules/min per (B cell, and expected second phase
rate of ~5 granules/min per (B cell (Rorsman and Renstrom 2003, Pedersen and
Sherman 2009). Other individual pool rates were adjusted from Pedersen and Sherman
to account for removing the calcium micro-domain and incorporating with our existing
model. Specific rates and parameters can be found in Figure S6.
(8) Reserve Pool:
RES' = rresRES rresRES
29


(9) Docked Pool:
DP' = r_2PP ~ r2DP + rresRES r_resRES
(10) Primed Pool:
PP' = r-tIRP (rt + r_2) PP + r2DP
(11) Immediate Release Pool:
IRP' = ^PP r_i IRP fusion, IRP
(12) Fusion Pool:
FP' = fusion, IRP u2FP
Cafuse
fusion, = fusionMax g +
(13) Release Pool:
RP' = u2 FP u3RP
(14) Membrane Capacitance:
Cap' = .0035 *FP* IRP
30


(15) Granules Secreted per minute:
Granmin = u3 RP 60
(16) Total granules secreted:
Total
'gran
J u3 RP
Individual rates and initial conditions can be found in Figure S6.
Noise Model
Channels are known to have some stochastic noise, where fluctuations in the
open probability occur and can alter the behavior of individual cells. We apply noise to
the Katp current by way of a time varying ODE with a random noise component. Our
model uses 1 explicit Katp current, with the assumption that many Katp channels are
included in the model according to the assigned conductance.
Random noise was generated with the ODE, to allow for a time varying component.
(17)
r = 500 (ms) and =
rand{ )% 3 1
80
generated in C + +
31


This was applied to the open channel probability for the Katp channel such that:
(18)
Ikatp = 9k.atp \P0k(ATP) (1 + P)] (VM Vfc)
where P fluctuates with a mean ~ 0, standard deviation ~ .0489 and acts to make the
channel more likely to be open or closed, depending on the value. If P is negative then
the probability that the channel is open is 0. The number of channels that this noise
represents can be established according to (Jo et al. 2005):
, 1
cr/ = = ~420 channels
N
where a is the standard deviation of P, and N is the number of KATP channels
Data Analysis
Calcium Imaging Data Analysis
Custom MATLAB scripts were used to analyze all images acquired from
fluorescence imaging. First, images were smoothed using a 5x5 average filter (MATLAB
built in function) to remove noise. A quiescent cell was then selected manually from an
area where no significant intensity fluctuations occurred over the duration of the
experiment, ImageJ was used to help identify an appropriate reference cell by looking at
individual cell time courses. The standard deviation for the whole image was calculated
in time to examine which pixels displayed the greatest fluctuations in time. The
variance of the manually selected quiescent cell was then used as a reference to
compare all other pixels to, any pixel then having a variance > 2 standard deviations
32


above the quiescent cells variance was counted as active. Any time courses with
significant motion artifacts were not counted in analysis, and photobleaching was
handled by applying a linear fit. The percentage of cells active is calculated based on the
number of active pixels divided by the islet area in pixels. For each level of Connexin36
expression an average of all the control (0% GFP) islets was used to scale the simulation
fits such that the maximum value was not 1, but reflected the maximum level observed
in islets. All values are reported as the average from all islets imaged from each mouse.
Fraction Active and Duty Cycle Calculations
Again, this analysis was performed with custom MATLAB routines on the output
for each simulation run for different k[ conditions. For all time courses, the fraction the
2
first ~200 time points were excluded until the system had settled. In the model
intracellular calcium fluctuates from ~.09 [uM] to ~.45[uM] when cells are in the quiet
or active phase, respectively. To find the number of cells active, a threshold of .165 [uM]
was applied to find all cells that had Calcium concentrations greater than or equal to the
threshold to be considered active. Duty cycle was calculated using a built-in function in
MATLAB on only the active cells, and is reported as total duty cycle for the simulated
islet:
Total Duty Cycle = Duty Cycle (Active cells)
The same analysis methods were used when noise was added to the model.
33


Insulin Secretion Simulation Analysis
Insulin secretion was analyzed using custom MATLAB scripts. All simulations
were run to produce data representing at least 5 minutes of activity under high glucose.
The total number of granules secreted was calculated according to equation 16 over the
time the simulation ran, this was also normalized to the run time of each simulation for
comparison. First phase secretion was calculated according to equation 16 with only
the first 5 minutes of the resulting time course, and all values are reported as a
percentage of the WT simulations ran for the same random number seed. Second phase
secretion was calculated the same way using data from t=5 min to t=15 minutes.
Students t-test was utilized to calculated significant differences in the results between
simulations, and between our findings from the insulin secretion ELISA.
34


CHAPTER III
RESULTS
Calcium Imaging Reveals Recovery of Activity for Cx36(-/-) Mice
The Kir6.2[AN30'K185Q] mutation as described in (Zhang et al. 2005, Koster et al.
2000) gives a good functional estimation of neonatal diabetes when the mutation is
expressed in >15% of cells (Hraha, et al. 2014). To examine the effect of the
Kir6.2lAN30'K185Q] gain of function mutation on overall islet activity, we performed
calcium imaging on mice having the mutation tagged with GFP, and expressing different
levels of Connexin36 coupling. With insulin secretion being dependent on calcium flux
in the cell as a result of membrane depolarization, examining the changes in
intracellular calcium is a good measure of islet electrical activity. Islets were stained
with calcium sensitive dye (Rhod-2) and imaged at high glucose (20mM) to induce
maximal electric activity. We plot the results showing the area of the islet displaying
calcium activity, against the area of the islet expressing GFP (Fig 1A,B). Analysis shows
that the Cx36 (+/-) islets, expressing ~45% Connexin36 (Farnsworth et al. 2014),
shows a softening in the phase transition (Fig ID) that was observed in previous
experiments (Fig 1C) with fully coupled Cx36 (+/+) islets (Hraha et al. 2014). As
expected, the reduction in coupling promoted additional activity and a right shift in the
transition from active to inactive as shown in Figure 1C-E. Examining a further
reduction of coupling in Cx36 (-/-) mice reveals the recovery of a near linear trend in
35


activity as the number of excitable cells is decreased, but only the mutated cells remain
silent.
Computational Model Agreement
Our coupled oscillator model showed good agreement with experimental results
from the islets expressing Cx36. We examined the agreement with the Cx36 (+/-) and
Cx36 (-/-) to assess if the model is reasonable for predicting beta cell behavior in the
presence of mutations. Islets lacking coupling, Cx36(-/-), showed a trend consistent
with the predicted linear recovery of activity. Islets with 50% coupling had the most
scattered results out of all 3 coupling levels, appearing to behave as though the level of
coupling is slightly higher than ~45%. We note the clear softening of the phase
transition, despite slight deviations of the specific shape from the simulation fit. We
have previously found that the heterozygous expression of Connexin36 (Cx36(+/-))
corresponds to ~45% of actual coupling between beta cells (Farnsworth et al. 2014)
when islets were examined using FRAP to determine the relative percentage of cells
that showed fluorescence recovery after photobleaching. We use a conductance of 50pS
to represent Cx36(+/-) in our simulations (Fig ID), noting that the coupling levels of
major interest are Cx36(+/+) represented by 120pS and Cx36(-/-), OpS.
Insulin Secretion and Cell Activity Follow Similar Pattern
Insulin secretion, blood glucose and plasma insulin were measured from all
islets analyzed for calcium activity. We report values for mice expressing levels of the
36


Kir6.2[AN30'K185Q] mutation on the pre and post-critical side of the transition (Hraha, et
al. 2014), binning at 0% GFP expressed, 0-20% GFP and >20% GFP in order to examine
the changes as coupling is decreased. For both insulin secretion and plasma insulin, a
visible recovery of insulin levels is observed between (+/+) and (-/-) mice, with (+/-)
again showing some scattered results having a higher SEM (Fig 2B,C). T-tests were
performed to test for significant differences between Cx36(+/+), Cx36(+/-) and Cx36(-
/-) on the 20-100% range of GFP (Fig 2B-D). Significant differences were found
between Cx36(+/+) and Cx36(-/-), and Cx36(+/-) and Cx36(-/-) for all cases.
Mice having Kir6.2lAN30'K185Q] mutation produce profound diabetes, having blood
glucose levels between 200 and 600 mg/dl (Fig S2) when Connexin36 expression was
retained, either fully or in the heterozygous expressing mice. In Cx36(-/-) mice, no
diabetic phenotype as measured by blood glucose emerged, all mice had blood glucose
levels <200mg/dl (Fig S2C). Measurements of insulin secretion and plasma insulin
follow this trend as expected, in high GFP expressing mice the amount of insulin
secreted and plasma is significantly reduced in Cx36(+/+) and Cx36(+/-) compared to
Cx36(-/-). This further verifies the diabetic phenotype produced by the functional form
of NDM we observe as measured by calcium activity. Importantly, visual examination of
Figure 2 shows the phase transition pattern as GFP expression moves from pre to post
critical, and significant changes in between Cx36 expression levels in the post critical
data. A dramatic drop in insulin secretion and plasma insulin is observed in Cx36(+/+)
and Cx36(+/-) islets, much greater than that of Cx36(-/-).
37


ATP Sensitivity is Reduced, Shows Critical Behavior
Neonatal diabetes has been established to arise out of primarily Katp channel
dysfunction, namely changes to the gating dynamics or ATP sensitivity. In previous
work we examined the effect of applying diazoxide treatments to Cx36(+/+) and Cx36(-
/-) islets (Hraha et al. 2014). Diazoxide promotes the uniform opening of the Katp
channel in ah cells across the islet, and thus is also a good functional estimation of NDM
mutations. This is unique from the Kir6.2iAN30'K185Q] mutation in that it applies to ah
cells, rather than to a subpopulation (Fig 3B). Applying >50uM of diazoxide brought the
islet into the post critical state and islet activity as measured by calcium imaging ceased
(Hraha et al. 2014). This was modeled, as described in the methods section, for 120pS
and OpS coupling conductance to represent Cx36(+/+) and Cx36(-/-)- Here we add gcoup
= 50pS simulations to represent Cx36(+/-) and see that the activity curve is right
shifted as in the representative Kir6.2iAN30'K185Q] mutation activity curves (Fig 3A,B).
Seeing the phase transition behavior emerge with increasing diazoxide
application, we then explored islet behavior in the model for uniformly shifted ATP
sensitivity, another NDM analogy (Proks et al. 2004). Simulations were run for an islet
consisting of 1000 cells at the 3 different coupling conductance values, with increasing
factors (k[ ) applied to the half maximal concentration of the Katp channel opening
2
probability. Ah simulations were run across 5 simulated islets to examine the
consistency of the transition as k[ was increased.
2
38


As k[ was increased, all cells remained active in islets with 120pS and 50pS
2
coupling until k[ ~4.3 for 120pS and k[ ~5.3 for 50pS (Fig 3F). The duty cycle gradually
2 2
decreased, in all cells, as k[ increased showing that the progressive inefficacy of ATP
2
could be affecting total insulin secretion, though all cells are electrically active. We show
time courses from individual cells having k[ increased up to the pre and post critical
2
regimes to show the decreasing duty cycle and the persistent activity at k[ = 5.3 for the
2
OpS islet (Fig 3 C-E). We infer the "half-maximal" value for cell activity by calculating the
k[ midpoint between the two points where the islet is active and inactive. For OpS, we
2
report the value of k[ for which the model showed 50% (+/- 2%) cells active (Fig 3G).
2
Open Conductance and Hill Coefficient Dependence
In examining the literature reporting electrophysiology measurements
characterizing the Katp channel in mutations, we found some variation in the number of
parameters reported between groups. The channel properties are characterized by a
hill equation with three main parameters (WT = 1), the open channel conductance (p'0 ),
the half maximal binding concentration [k[), and a hill coefficient for the equation. All
2
papers reported WT and mutant half maximal values but open channel conductance
and hill coefficients were not always calculated or fitted in the analysis. For this reason
we deemed it worthwhile to examine the effect of changing the hill coefficient and open
channel conductance values in the model.
39


We found that increasing p'0 alone did not significantly affect the calcium activity,
but that increasing p'0 did have an effect when changed with k[ (Fig 4C, D). We
2
simulated islets having both k[ and p'0 changed to visualize the dual effect of these
2
parameters. These are displayed as heat maps where the color represents the fraction
of cells active, for gcoup = 120pS and OpS (Fig 4A). Figure 4B shows the effect of p'0 on
cell activity when k[ is held near the critical point. Increasing p'0 at this point again
2
produces the phase transition behavior, where increasing p'0 alone does not (Fig 4C).
In our model, the hill coefficient is equal to 1 by default. We examined results
from simulations having increased half maximal binding concentrations will hill
coefficients set at 1.3 and 1.6, based on the commonly reported values in mutations
found in the literature. When increasing the hill coefficient, the calcium activity of the
islet is preserved even as the k[ value increases into the regime of severe mutations (Fig
2
4E, F).
Increasing the hill coefficient seems to offer protection from mutation, in terms
of our model. We decided to continue examining the mutations with only k[ applied in
2
order to be consistent when determining the actual effect of coupling, and because the
half maximal value is consistently reported in all cases, where the hill coefficient can be
a result of mathematical interpretation.
40


Clinical NDM Mutations Simulated
Pearson, et al. examined patients having NDM mutations affecting the Katp
channel to see if application of sulfonylureas could be effective in switching patients off
of daily doses of insulin. They examined a broad spectrum of mutations, those resulting
in TNDM, PNDM, and some showing DEND characteristics. Sulfonylureas promote
uniform Katp channel closure, and thus assist in mutations where ATP sensitivity is
inhibited, present in about 60% of neonatal diabetes patients. They found that patients
with mutations across all parts of the spectrum were able to switch, with the exception
of three severe DEND mutations (Q52R, I296L, L164P). This prompted us to investigate
how coupling specifically could alleviate some of the effect of reduced ATP sensitivity,
since that can also be clinically dealt with using sulfonylureas.
NDM simulations reveal range of mutations affected positively by uncoupling
Neonatal mutations were run for 120pS, 50pS and OpS coupling conductance,
having all reported parameters changed, and again having only k[ changed to reflect
2
the most consistent and often reported channel changes. When all parameters were
changed, we observed in tact calcium activity across the islet for gcoup =120pS and 50pS
when k[ was increased up to ~7 (hetI296L), thus removing coupling did not offer any
2
improvement in activity for some severe mutations, depending on the hill coefficient
(Fig S5). Since the hill coefficient drastically changes the behavior, the duty cycle
showed significant variability with no visible dependence on k[ alone.
2
41


The results for simulations containing only changes in k[ show that for
2
mutations having a k[ of <7, removal of cell-cell coupling (gcoup = OpS) allowed activity
2
to persist where the presence of coupling caused electrical silence (Fig 5). Duty cycle
decreased with increasing k[, indicating that the total duty cycle of the islet (silent cells
2
included) is effected by the ATP sensitivity of the channel. Interestingly, all levels of
coupling showed similar duty cycles for each mutation (Fig 5B), indicating that with the
removal of coupling duty cycle is actually preserved for those cells that are active and
only when the electrically silent cells are included does the duty cycle drop as it would
in the presence of coupling.
Stochastic Noise in Katp Channel Opening Probability
Based on the results where the removal of coupling recovered some activity in
islets that otherwise would be silent, we were motivated to investigate modeling other
processes that may have an amplified effect in the absence of coupling. Channels are
known to have the ability to switch between open and closed states in a stochastic
nature (Jo et al. 2005), but the effect is reduced with coupling. We hypothesized that the
addition of random noise to the Katp channel opening probability could produce
spontaneous activity in otherwise silent cells, and supplement the recovery in activity
that the removal of coupling produces.
42


Noise Induces Activity in Quiescent Cells
We first tested the effects of noise at low (5.5mM) and high glucose (1 ImM),
with gcouP=120pS and OpS. The noise produced additional active cells at low, non-
stimulatory glucose levels when coupling was absent from the system (Fig 6C). Most
cells became active earlier in the presence of noise, when coupling was absent. Noise
was characterized by simulating an islet having 10 different random number seeds set
to generate noise, at 5.5mM glucose, with gCouP=0pS (Fig S7).
Coupling Removes the Effects of Added Noise
When coupling conductance was held at 120pS, the effects of added noise
averaged out and no significant changes to activity or synchronization were observed.
At 5.5mM glucose, no activity was observed either with or without added noise (Fig
6A), llmM glucose showed no increase or decrease in activity, with only a ~3%
increase in duty cycle when noise was added (Fig 6B).
NDM Mutations Simulated with Stochastic Channel Noise
Seeing that stochastic noise is able to induce additional activity in islets lacking
cell-cell coupling, we then applied the same noise to some NDM mutations to examine
how the activity and duty cycle might be improved. We strategically chose to examine
added noise to more severe mutations, and those that showed promise of switching
from oral insulin to sulfonylureas (Pearson et al. 2006) in order to model the maximal
recovery that might be possible from the removal of coupling. Activity was increased in
43


all mutations we modeled with noise at OpS, including I296L, which exhibits DEND
characteristics. We then plot the increase in fraction of cells active and duty cycle
against k[ to show the range of mutations that noise is effectual for (Fig 7A,B). Figure
2
7E shows representative time courses for three cells from three of the mutations
modeled to show the specific effects of noise. These are of special interest because in
patients, H46Y and I296L have been examined in patients with the treatment of
sulfonylureas (Pearson et al. 2009) and here we show modeled electrical activity
improvement with the removal of coupling.
Insulin Secretion in the Coupled Oscillator Model
Based on the interesting results from our simulations increasing k[ and adding
2
noise, we were moved to investigate the impact that these factors could have on insulin
secretion and how this compares to our previous experimental results (Kir6.2iAN30'K185Q]
mice). Using the insulin secretion model previously described, simulations were run for
islets having simulated Kir6.2iAN30'K185Q] expression, and for NDM mutations with
increased k[.
2
Insulin Secretion Critical Behavior in Kir6.2iAN30'K185Q] Model
First, we verified that our model produced reasonable results compared with the
literature (Pedersen and Sherman 2009, Rorsman and Renstrom 2003, Henequin 2000)
(FigS5) in response to a glucose step and calcium step to trigger cell depolarization. We
see a secretion rate of ~20 granules/min for one cell, lasting ~5 minutes to produce the
44


first phase of insulin secretion, and a reduction to ~5 granules/min of sustained
secretion as the second phase (Fig S6 A,B). Having verified the model behavior, we
simulated islets having 10% and 50% cells rendered inexcitable by the Kir6.2lAN30'K185Q]
gain of function mutation (Fig 8A). These values were chosen to represent the pre and
post critical points, respectively, on the phase transition to compare with a WT
condition islet as we did in the Kir6.21AN30'K185Q] mouse lines (Fig 2). We see a reduction
in the total secretion (relative to WT) for the 120pS simulated islet compared to the OpS
simulated islet when the percentage of mutant cells (PMut) = .1 and PMut = .5. The post
critical simulated islet is able to secrete notably more insulin when gcoup = OpS (Fig 8A),
following the trend observed in mice lacking Connexin36 expression (Fig 2B).
Simulating high Kir6.2lAN30'K185Q] mutant expressing islets is computationally expensive,
and could be better characterized in our model at a later time. For now, we note the
marked improvement offered when gcoup = OpS compared to 120pS, and the emergent
critical behavior when gcoup = 120pS, suggesting that this model is reasonable to move
forward with other NDM type simulations.
Increasing k[ Reduces Insulin Secretion
2
Total secretion of NDM mutations is shown in Figure 8, total secretion here
represents the number of granules secreted in the first phase (5 minutes). The secretion
rate and total secretion is k[ dependent (Fig 8B, C), for both OpS and 120pS, when k[ is
2 2
increased by ~3 (V252A), we observe an ~33% drop in total secretion (Fig 8B, C). For
E229K, reducing coupling allows for additional insulin secretion compared to 120pS,
45


this is consistent with Figure 5, showing that E229K does not produce activity at 120pS
but does for OpS.
Channel Noise Uniformly Improves First Phase Insulin Secretion in Uncoupled Islet
We then investigated the addition of channel noise to our model of insulin
secretion, and found that noise offered significant improvement to insulin secretion in
uncoupled islets (Fig 8B). Interestingly, noise offered a uniform k[ dependent shift in
2
insulin secretion, but shifted activity and duty cycle non-uniformly. A manual analysis
of the activity increases shows that in general, silent cells that become active under the
influence of noise have a very short duty cycle (Fig 7A). On the other hand, cells that
were active are caused to "turn on" early, but keep approximately the same average
duty cycle. This leads to an overall greater duty cycle for the whole islet, because more
cells are active, but the total effect on insulin secretion is more linear.
Second Phase of Insulin Secretion is Improved in Simulated NDM Mutants
We also examine the second phase of insulin secretion (t=5-15 minutes), known
to be important to clinicians when the first phase is disrupted in diabetic patients.
Figure 8C shows that the second phase is improved in NDM mutation V252A, though
noise does not offer drastic improvement in this case. The other mutations simulated
show marked improvement with the addition of noise in the system, and retain an
overall higher secretion rate relative to the WT, compared with the first phase results.
This is indicative of the distinct biphasic nature of insulin secretion where the second
46


phase may be sustained even when mutations are present. Further modeling of this
pattern will ultimately be useful to applying our knowledge to a clinical setting.
These results offer interesting insight to the effect that gap junction coupling has
on islet activity and insulin secretion in the presence of different forms of NDM
mutations. Network dynamics and critical behavior in the islet have been previously
established, we aim to unpack more about the dramatic effect that reduced coupling has
on systems such as this, and the possible treatment methods that may arise from a
reduction in coupling.
47


CHAPTER IV
DISCUSSION AND FUTURE WORK
The islet is a very dynamic system, being composed of many oscillatory
components possessing intrinsic heterogeneity and showing unique behavior resulting
from the network interactions that it is built upon. Gap junctions are primarily
responsible for the global nature of the islets response to stimulus (glucose). Fully
coupled islets exhibit quiescence at basal levels of glucose (<5.5mM) compared to
dispersed (B cells showing elevated Ca2+ at basal glucose levels (Speier et al. 2007,
Benninger et al. 2011), and the absence of gap junctions is known to remove synchrony
from the islets response to glucose (Speier et al. 2007, Benninger et al. 2008). Intrinsic (B
cell heterogeneity is known to be a contributor to the varied response observed in the
absence of coupling, where these effects are removed in the presence of coupling
(Benninger et al. 2014). Metabolism and electrical activity are uniquely linked in (B cells
by means of the Katp channel, controlling individual cellular excitability, and the
response of excitable or inexcitable cells can be shared via gap junctions for the
amplification or suppression of the islet response. We have built on previous
experiments examining the unique effect that subpopulations of Kir6.21AN30'K185Q]
expressing cells have on the islet response (Hraha, et al. 2014), the network dynamics
exhibited in the islet, and use predictive mathematical modeling to investigate this
further both with regard to subpopulations and a global shift in excitability.
48


Phase Transition and Global Behavior as Measured by Calcium Dynamics
Previous work has shown that the islet network of (B cells can be described by
network theory principles with specific regard to percolation theory to describe the
robustness of the (B cell network (Hraha et al. 2014, Stamper et al. 2014, Hraha et al.
2014). Having investigated this concept in islets having fully coupled cells, we were
able to further investigate the effect of a reduction in coupling in islets expressing
varying subpopulations of inactive, suppressive cells. Our results from calcium imaging
analysis in Cx36(+/-) and Cx36(-/-) islets show a clear softening in the phase transition
that emerged in Cx36(+/+) islets. As the population of quiescent cells is increased, the
calcium signals throughout the islet tend to decrease until the critical percolation
threshold is reached. The critical threshold marks the point where inordinate
suppression of activity is observed upon negligible changes in the inactive cell
population, producing the phase transition behavior and global shut down of cell
activity. In the Kir6.2lAN30'K185Q] model, we see a range of subpopulation values that can
produce the global quiescence at stimulatory glucose conditions in Cx36(+/+)
expressing islets, ~15-20%. As coupling is reduced, this range is shifted and in Cx36(+/-
) islets, activity is retained until the population of inactive cells exceeds ~25-30% (Fig
1C-E). We see these results verified in the coupled oscillator simulation results where a
2% increase in inactive cells produces a 36% loss of activity for full coupling (120pS)
and the same 2% increase produces only a 2% loss of activity for reduced coupling
(50pS) (Pexc = .2, .22). The largest loss for 50pS is shifted to Pexc = .26, .28 where 16% of
the activity drops off (Fig ID). Conversely, in islets not expressing Cx36, we recover a
near linear decrease in activity (Fig IE). This phenomenon of uncoupling a
49


heterogeneous system to allow heterogeneity to take over is useful when the islet is in
the post critical phase of the transition, and uncoupling provides a significant recovery
of electric function.
Phase Transition in Physiological Characteristics
Our findings from the Kir6.2iAN30'K185Q] model of NDM show that Katp excitability
has the ability to regulate islet function with binary results when under the influence of
gap junction coupling. The imposed "on" or "off" function on the islet implies a global
metabolic effect from the Katp channel that cannot be overcome except by the
uncoupling of cells, allow heterogeneity to take effect. The binary fashion of the islet
response is gradually reduced with a moderate reduction in coupling (Cx36(+/-)) but is
still sufficient to inhibit the percolation of the network once the critical threshold is
exceeded. We propose that the effect seen in these subpopulations of suppressive cells
can be extrapolated to islets having a uniform shift in Katp dynamics on all cells.
Previous experiments showing the phase transition behavior when applying a uniform
Katp channel opener diazoxide to islets motivated further study into this concept (Hraha
et al. 2014). These experiments both analyzed calcium activity and simulation results
modeling diazoxide application as in equation 6 and showed again that a reduction in
Cx36 expression would alleviate the global effects of increasing diazoxide application.
We hypothesize that diazoxide application acts on cells that are inherently less sensitive
to glucose and moves these cells into an inexcitable state (Hraha et al. 2014). In this
work we added simulations for 50pS to examine the shift with reduced coupling Figure
3B. Diazoxide treatment produces a much sharper phase transition than the
50


Kir6.2[AN30'K185Q] mutation, suggesting that perhaps a system wide shift in metabolic
response is quicker to suppress activity than that of subpopulations of suppressive
cells, and perhaps heterogeneity in glucose sensitivity is not the only factor in shifting a
cell into an excitable state.
We have shown that removal of gap junction coupling in the presence of
functional NDM mutations can expunge the phase transition behavior and result in a
more spontaneous, but functional islet system. By manipulating the Katp channel with a
gain of function mutation, we gradually move the islet into a pre and then post-critical
state whereby the electric activity of the islet behaves in a critical manner. Removal of
Cx36 restores the autonomy of each cell, restraining the inactive cells from silencing
active cells. Verifying that the coupled oscillator model is capable of producing this
phase transition behavior at the representative coupling conductances and importantly
is able to encompass both the network behavior of the islet and unique Katp channel
properties of the (3 cell, we thus give confidence to the model as a predictor for general
islet behavior under similar mutations.
Examining k[ Changes Representing Real NDM Mutations
2
Modifying the ki value in our model reproduced characteristic phase transition
2
behavior in simulations with 120pS and 50pS coupling, showing that ATP sensitivity
and intrinsic channel properties are capable of producing global effects. The
Kir6.21AN30'K185Q] gain of function mutation has severe ATP insensitivity and can be
51


regarded as similar to the modeled increase in k[ (Remedi et al. 2009) when k[ is
2 2
increased past the post critical state, ~4.3. The specific effect of decreased ATP
sensitivity on all cells is then shown in our simulation results and suggests that the
heterogeneity intrinsic to all (3 cells is sufficient to overcome, to a point, the binary
behavior that the islet seems to exhibit.
Changes in duty cycle as ATP sensitivity is decreased arise from the right shift to
the dose response curve of the Katp channel, and the oscillatory nature of intracellular
ATP concentrations. We propose that this is somewhat subjective, according to the
particular modeling parameters used, but that the general downward trend in duty
cycle is likely consistent with real cell dynamics. The removal of coupling and
subsequent increase in heterogeneity would then cause the active cells to perhaps
respond more fully, despite the increasing need for ATP to trigger a response. On
average, the duty cycle under wild type conditions for an islet simulated at OpS was
higher than the 120pS islet by ~1%. This would indicate that insulin secretion from an
uncoupled islet may be higher relative to the active secreting cells in a fully coupled
islet. Our previous work examining increasing Kir6.21AN30'K185Q] mutations in Cx36(+/+)
expressing islets has shown how duty cycle decreases as the state of the islet moves to
pre and post critical. Decreases to duty cycle, or burst duration, have been suggested to
result in reduced insulin release (Bertram et al. 2007), we examine this further when
we model exocytosis events in the coupled oscillator model.
52


The Effect of Other Channel Parameters
NDM mutations have been established to have some residual Katp current in the
presence of saturating ATP concentrations (McTaggart et al. 2010). Similar to the
diazoxide application model we simulated, this implies that there may be some
additional detrimental current in the presence of k[ changes. We model this in two
2
mutations where it was reported in the literature (Proks et al. 2005, Masia et al. 2007)
and found that cellular activity was silenced for all levels of coupling, as we suspected.
We leave further investigation of this for future work with the goal that it be applied in
the presence of stochastic noise to assess the severity of its effect, and the ability of
noise to overcome this residual current.
Increasing the hill coefficient in our model showed great protection from k[
2
increases, consistent with the general form of the dose-response curve. For this to have
significant meaning, further research into the specific dose response characteristics of
the Katp channel are needed. The hill coefficient is not an inherently
electrophysiological parameter, and can be quite fluid depending on analysis methods
used (Fig S4). We suggest that this adds confidence to our model as it shows the
expected behavior when increased, and in showing that critical behavior of the islet is
preserved when the hill coefficient is increased, extending the pre-critical regime. It
may be reasonable to investigate possible heterogeneity in the ATP response of the Katp
channel, as the hill coefficient is increased. Perhaps for reduced coupling levels,
53


heterogeneity in Katp current relative to ATP concentrations could be better
understood and offer insight into characterizing NDM mutations.
When we applied increasing factors to p'0 the open channel conductance, on
equation 7, we did not observe any significant change in cellular activity for any of the 3
coupling conductances simulated for p'0 on the interval [1,10], we show data for p'0
increases up to 3 with k[ = 1 and k[ =4 (Figure 4C-D). In theory, increasing p'0 could
2 2
send the Katp channel into a more often open state, thereby possibly acting as k[
2
would, decreasing the activity. Increasing p'0 did cause a slight decrease in duty cycle for
all three coupling conductances, showing that this parameter does not have significant
effects on activity but likely controls some of the frequency aspect of the oscillatory
dynamics. This parameter may play a more significant role in mutations affecting
sulfonylurea sensitivity, but further investigation would be needed. We do establish
that in the presence of increased k[, increasing factors applied to p'0 cause the critical
2
behavior to emerge. This highlights the amplifying effect that the metabolism
components of the Katp channel have on islet activity and the critical role that
metabolism plays in cell electrodynamics, futher hinting to the importance of the Katp
channel in considering therapeutic options. Future work could investigate effects of
decreasing the p'0 parameter to mimic the application of sulfonylureas. This would be
valuable to understanding the combined effects of clinical treatment and uncoupling on
insulin secretion.
54


We have also shown the effect that critical behavior can have on islets containing
NDM mutations, both with adjusted ATP sensitivity and other parameters (FigS3)
modifying cellular excitability. NDM mutations exist on a spectrum of severity most
commonly known to directly affect the ATP sensitivity or channel gating properties of
the Katp channel, mild forms of these mutations can result in Type 2 diabetes
(Hattersley and Ashcroft 2005). The applied k[ factor is not directly correlated to
2
clinical severity (Fig 5, Fig S5) as we have modeled in this work, some severe DEND
producing mutations have a k[ less than some TNDM producing mutations, e.g. DEND
2
producing V59G: k[ = 3.93 or V252A, a TNDM mutation where k[ is higher than several
2 2
PNDM mutations. Thus, k[ alone is not the determining factor for assessing NDM
2
severity, though the general trend does hold (Fig S4). As with any physiological system,
there are many factors to consider and we suggest that open channel conductance or
residual current (a) is likely one of those factors. Additionally, the dynamic aspects of (3
cell behavior suggest that other key players such as glucokinase or camp signaling may
play an amplifying role in the critical behavior. A reduction in the expression of Katp
channels in the presence of NDM mutations has also been implicated as a potential
contributor to reduced islet function (Lin et al. 2006). Thus, the mutations we model
having k[ adjusted do not take possible reduced expression into account and this could
2
explain the few discrepancies between clinical severity and islet activity seen in our
simulations, for example, in V59G.
55


We see that k[ plays the most significant role out of the parameters we have
2
examined and we note that it is the most consistently reported variable in
characterizing these mutations. We show that for NDM mutations modeled with only k[
2
affected, we can examine a range of severity that can be improved by the removal of
cell-cell coupling. The mutations we examine here are heterozygous, these are
mutations that are coexpressed with normal channels in experiment and represent the
real monogenic nature of NDM. Interestingly for all 7 mutations where we examined the
full and heterozygous form (data not shown), those with a greater k[ value in the full
2
form had a greater reduction of k[ in the heterozygous form, holding the pattern where
2
the most severe in each form were the most clinically severe. This could be due to
methods of expression in experiment or a result of the binomial expression pattern that
the mutations can take (Proks et al. 2004). Analysis of the full form of the mutation may
give information about how the mutations were expressed and distributed in
experiment if the k[ values are compared but are not ultimately useful for human
2
disease study. Only heterozygous mutations are known to be expressed in humans and
thus should be used for assessing a range of mutations that might be treatable with
sulfonylureas. When comparing OpS to 120pS we see that the highest improvement in
activity occurs when k[ = 4.3, at the critical point for 120pS when islet activity shuts off.
2
We can establish that this is the beginning of the regime where removal of coupling can
assist in restoring islet function, and where further therapeutic applications should be
studied.
56


The Effect of Stochastic Channel Noise in the Presence ofNDM Mutations
Turning our attention to NDM mutations under the influence of stochastic
channel noise, we see that many showed improvements in activity and total duty cycle
when noise was applied to the model. Noise is an interesting aspect to study as it is
known to exist in (B cells (Jo et al. 2005) (and cells in general) but the actual amount of
inherent noise is not known. In modeling it here we apply the noise with a standard
deviation such that it represents affecting ~25 channels in the cell. Our results indicate
that noise is never detrimental to the system, coupling removes the effects of noise, and
that a range of mutations can be improved by including noise in the model. We show
that we have a more complete model of (B cell behavior by including noise, though more
specifics about the extent and magnitude of noise will be required. Again, the additional
residual current that may affect some NDM mutations was not examined here but we
suspect that it may reduce the improvement that noise offers in some severe cases
(Girard et al. 2006, Proks et al. 2006, Roster et al. 2005).
Exocytosis Events Modeled for Various Mutations
Confirming the phase transition behavior and consistent calcium dynamics in
simulated islets with a variety of mutations, we were motivated to find the
corresponding insulin response to the NDM conditions we modeled. Using the model
described in the methods section, we show insulin secretion results for Kir6.2[AN30'K185Q]
simulated gain of function mutations and additional NDM mutations both with and
without noise.
57


The simulated NDM mutations reveal the distinct behavior of each part of
biphasic insulin secretion. Analysis of the first phase alone reveals that increasing
severity of mutation leads to a marked reduction in secretion. This is consistent with
our knowledge of first phase dynamics in diabetes, where the initial insulin secretion is
impaired (Rorsman and Renstrom 2003, Chen et al. 2008). Analysis of the second
phase reveals that even in the presence of severe mutation, e.g. hetI296L, the second
phase can be quite sustaining when coupling is removed (Fig 8C). Additionally, the
inclusion of channel noise shows the potential improvement to each phase, namely the
second phase where severe mutations retain ~50% secretion relative to the WT islet.
This suggests that patients presenting with a disrupted first phase may be capable of
endogenous insulin secretion if (3 cells could become uncoupled, and perhaps some
balance could be restored to the interaction of primary cell types. Additional work to
examine further long term effects (30 minutes 1 hour) could be done and compare
with experimental insulin secretion data. Treatments such as sulfonylureas or other
monogenic mutations (GK) could also be simulated here. Further development of the
model by including camp signaling and glucose depending mobilization steps will be
useful in the future for examining other metabolic factors, and predicting how specific
diabetic characteristics effect endogenous insulin secretion.
Critical Behavior and Networks in Biological Systems
Several areas of biology are known for the network properties that they exhibit,
e.g. stimulus-secretion, contractile and hormone-secretory coupling. In general, systems
of individual components with shared connectivity may exhibit critical behavior upon
58


removal of or changes to the individual components. Emergent behavior in these
systems has been studied for some time and has shown interesting trends that have
consistency across inherently different systems.
Critical behavior in signaling and cell response is observed in many systems.
Fertility is dependent on the pulsatile secretion of the hormone GnRH (Campbell et al.
2009) and the post-natal remodeling of gonadotropin releasing hormone neurons to
initiate puberty upon their activation (Cotrell et al. 2006). These GnRH neurons are
known to respond in a binary fashion to GABA from before to after maturation,
depending on the explicit opening of the GABA channel and subsequent membrane
depolarization (Han et al. 2002). This is analogous to the closing of the Katp channel
observed in the (3 cell and is an interesting application of network behavior in biological
systems where changing channel kinetics can induce critical behavior. In the heart,
pacemaker cells found in the sinoatrial node exhibit global effects on contractile
myocytes to control synchronized pulsing of the heart (Farenbach et al. 2008). Cardio
myocytes are highly coupled through Cx43 gap junctions where the optimal level of
coupling results in a synchronized signal, but high or low coupling can lead to
arrhythmias (de Boer et al. 2006). Fibroblasts are expressed in the heart and are
upregulated in heart disease, these function as inexcitable cells that may disrupt the
network of myocytes when disease progresses (McArthur et al. 2015) and cause global
suppression or loss of coordination.
59


Connectivity of these excitable systems is crucial and is responsible for dictating the
overall dynamics of the system. During pregnancy, smooth muscle cells in the uterus
begin upregulating the expression of gap junctions to prepare for contractions during
delivery (Sheldon et al. 2014). The increased expression of gap junctions creates a
network allowing for action potential propagation and phasic pulses, without which the
coordinated contractions could not be produced (Sheldon et al. 2014). In brain injuries,
gap junction coupling has been shown to amplify cell injury and cell death, disrupt
calcium dynamics and increase cell death in interconnected cells (Lin et al. 1998). The
absence of gap junctions in these situations does not lead to calcium signal
dysregulation and leads to a decrease in cell death (Lin et al. 1998).
We have shown how gap junction removal specifically alleviates the
consequences of diabetes causing mutations; this concept can be applied to other
systems relying on signaling by means of gap junctions.
Implications For Diabetes
In the islet, gap junction coupling serves two primary purposes. At low glucose
(<5mM), robust gap junction coupling suppresses excess individual cell activity to
prevent unnecessary and unhealthy secretion of insulin. At stimulatory glucose levels
(>5mM), coupling utilizes the shared currents between cells to coordinate a
synchronized response and secrete insulin in the characteristic biphasic manner
(Speier et al. 2007).
60


This thesis work has studied both the general emergent behavior of a coupled
network system and the specific electrophysiology of the islet under various
manipulations. Our examination of the effects of subpopulations of inactive cells and
uniform shifts in excitability on the insulin response of the islet reveals that critical
behavior emerges in both cases of functional NDM mutations. The inclusion of
stochastic channel noise provides additional insight to the possible improvement to
insulin secretion that uncoupling could offer in a clinical setting. Based on patients data
for those treated with sulfonylureas (Pearson et al. 2009), we propose that exploring
these mechanisms in practice along with sulfonylurea therapy could be interesting and
helpful in the case of several of the NDM mutations we have modeled. Effects of other
monogenic defects resulting in NDM, e.g. glucokinase, may be alleviated by the removal
of coupling from the islet. Treatment options may be expanded when coupling is
removed and more combination therapies may be available as the heterogeneity of the
system increases, especially for NDM mutations where sulfonylurea therapies are
ineffective. Our findings further suggest that the nature of uncoupling the system
provides rescue by exposing the intrinsic heterogeneity of the constitutive elements in
the system, and that this is useful not only for diabetes but for the general
understanding of stimulus-secretion coupling and of multicellular excitatory systems in
the body.
61


A
Cx36(+/+)
9colp = 12Ps
Cx36(-/-)
I ^vTv^VWVTw"
* i____________i
0 100 200
sec
I
i kkmM^
9coup
UjUUUUUL
\MV-K~n
Cx36(+/+)
Cx36(-/-)
__jJlJjul_L_^
9tjp = OPS
l
ijjl__dn[
i------1 i
0 100 200
sec
Figure 1: Calcium imaging in islets with varying Cx36 and Kir6.2[AN30K185Q] expression
A) Schematic showing experimental concept. Image of mouse lacking Kir6.2[AN30K185Q]
mutation expression with representative time courses from Cx36(+/+) and Cx36(-/-)
mice. Scale bars represent 20% increase in Rhod2 fluorescence. Time courses from
simulations representing Cx36(+/+), 120pS, and Cx36(-/-), OpS. Scale bars represent
20% increase in simulated [Ca2+]. B) As in A, but for a mouse expressing ~10%
Kir6.2lAN30'K185Q] mutation marked by GFP. Time courses are displayed for simulations
having equivalent number of cells mutated to represent islets. C) Calcium imaging
results from Cx36(+/+) mice with increasing Kir6.2[AN30'K185Q] mutation expressed.
Displayed with simulation results from gcoup =120pS. D) As in C, for Cx36(+/-) islets and
displayed with gCouP=50pS simulation results. E) As in C, for Cx36(-/-) islets displayed
with gcouP=0pS simulation results.
62


A
B
1.5n
**
0% GFP 0-20% GFP 20-100% GFP
Cx36 (+/+)
Cx36 (+/-) 1-5'
0% GFP 0-20% GFP 20-100% GFP
Figure 2: Physiological measurements with regard to Kir6.2lAN30'K185Q\ expression
A) Islet activity as determined by calcium activity shown for ranges of Kir6.2lAN30'K185Q]
mutation expression. 0% GFP indicates control islets with no GFP expression. Data is
shown as a fraction of control, plotted with SEM. B) As in A for insulin secretion as
measured by ELISA assay. C) As in A for plasma insulin levels as measured by ELISA. D)
As in A for blood glucose (day 27-29).
63


A
B
Figure 3: Changes to ATP sensitivity modeled
A) Fraction of cells active for simulations with gcouP=120pS, 50pS, and OpS for increasing
number of inactive cells to simulate Kir6.2lAN30'K185Q] mutation. B) Fraction of cells
active for simulated Diazoxide application by uniform current increase (a) in all cells
for gcouP=120pS, 50pS, and OpS. C-E) Time courses from simulations having increased
k1/2 for gcouP=120pS, 50pS, and OpS respectively. Scale bars represent 20% increase in
simulated [Ca2+]. F) Fraction of cells active and duty cycle for increased k'1/2 in all cells,
for gcouP=120pS, 50pS, and OpS. G) k1/2 value where 50% of cells are active for
gcoup =120pS, 50pS, and OpS, across 5 simulated islets.
64


Figure 4: Effect of other parameters on simulated islet activity
A) Heat map indicating the fraction of cells active for gcouP=120pS with regard to k'1/2
and p'o increase. B) As in A, for gcouP=0pS. C) Plot of the fraction of cells active for k'i/2=l
as p'o increases, for for gCouP=120pS, 50pS, and OpS. D) Plot of the fraction of cells active
for ki/2=4 as p0 increases, for for gCouP=120pS, 50pS, and OpS. E) Fraction of cells active
for gcouP=120pS as k'1/2 increases for increased Hill coefficient (H=l, 1.3,1.6). F) Fraction
of cells active for gCouP=0pS as k'1/2 increases for increased Hill coefficient (H=l, 1.3,1.6).
65


NDM with k'1/2 changes
A
T2D TNDM
PNDM
l-DEND DEND
B
o
>1
O
>.
3
Q
120pS
OpS
T2D TNDM PNDM l-DEND DEND
Figure 5: NDM mutations simulated
A) Fraction of cells active for neonatal mutations simulated with k'1/2 applied to all
mutations, and a applied where reported. B) Showing duty cycle for neonatal mutations
as in panel A. Results are arranged in order of clinical severity, e.g. TNDM = Transient
Neonatal Diabetes Mellitus.
66


5.5mM |
glucose '§
B
11mM |
glucose I
11mM
No Noise
100
sec
Noise
No Noise
Noise
Noise
Figure 6: Stochastic channel noise modeled in low and high glucose concentrations
A) Fraction of cells active and total duty cycle for simulations run at 5.5mM glucose,
with gcouP=120pS with and without stochastic channel noise. B) As in A for llmM
glucose and gCouP=120pS. C) Fraction of cells active and total duty cycle for simulations
run at 5.5mM glucose, with gCouP=0pS with and without stochastic channel noise
showing the increase of activity in the presence of noise. D) As in C, for llmM glucose
and gcouP=0pS. Representative time courses from islet simulated with and without noise
are displayed for all conditions. Scale bars represent 20% increase in simulated [Ca2+].
67


hetH46YW hetl296L'Nl hetE229K(A>
u-
l l-A- (L
r l/v * A r i>^ 1 ~
a (J 4 ft f. * <0 0 a a n. a d f\ ,1 ft ft n O
, n > f, f, r, fi
.A , /! P fi j\ ft r\ !a ...j. J-.j.x.S k.-A J J* _J\ Ji ...
0 100 200 0 160 200 0 100 200
sec
sec
Figure 7: Stochastic channel noise applied to NDM mutations
A) Fraction of cells active and duty cycle plotted with and without noise for increasing
k'1/2 with gcouP=120pS. B) As in A, for gCouP=0pS, with and without noise. C-D) Fraction of
cells active and duty cycle for NDM mutations simulated with k'1/2 applied, with and
without noise. Simulated for gCouP=120pS (C) and gcouP=0pS (D). E) Representative time
courses for 3 NDM mutations at gcouP=0pS to show the effect of added noise on specific
cells. Scale bars represent 20% increase in simulated [Ca2+]. All simulations were run at
llmM glucose.
68


A
9coup = 12Ps
D 9coup =OpS
E
S
c
o
(A
<

B
C
Figure 8: Insulin secretion modeled in NDM mutations with and without channel noise
A) Insulin secretion in simulations representing Kir6.2[AN30'K185Q] [an3o,ki85Q] mutation
expressed in 0%, 10% and 50% of cells for gCouP=120pS and gCouP=0pS, normalized to
simulation run time B) First phase insulin secretion analysis for NDM mutations with
noise, for gcouP=120pS and gCouP=0pS. First phase insulin secretion from NDM mutations,
showing comparison for gcouP=0pS with and without noise in the system. C) Second
phase insulin secretion in NDM mutations (t=5-10 min) for gcouP=0pS, with and without
noise. D) Average first phase response from islet for gcouP=120pS (black) and gCOuP=0pS
(red), time courses are smoothed. E) Average second phase response from islet, marked
at t=5 minutes to denote where the analysis began for panel C.
69


SUPPLEMENTAL FIGURES
p Cell
glucose
SUR1
Figure SI: Schematic ofGSIS in the /? cell
Glucose is metabolized in the mitochondria, closing the Katp channel, producing
membrane depolarization, calcium influx and insulin release.
70


Cx36 (+/+)
B
Cx36 (+/-)
Cx36 (-/-)
re 0.4-
E
% GFP
Cx36 (+/+)
Cx36 (+/-)
Cx36 (-/-)
Cx36 (+/+)
Cx36 (+/-)
Cx36 (-/-)
Figure S2: A) Scatter plots of insulin secretion, plasma insulin and blood glucose verses
GFP expression, taken for Cx6(+/+) mice. B) As in A but for Cx36(+/-) mice. C) As in A
but for Cx36(-/-) mice.
71


A k1/2
a
Pn/iut
9coup = 120pS
Scoup = 50pS
9coup =
Figure S3: Comparison of simulated transition from active to quiescence upon increases to
the simulated mutation. A) Fraction cells active for gCouP=120pS and gCouP= 50pS are
plotted against gcouP=0pS for simulations with increasing k'1/2. B) As in A, for diazoxide
simulations (a). C) As in A, for simulated Kir6.21AN30'K185Q] mutation (PMut = % cells with
mutation). Allows for comparison of activity for all coupling strengths to the trivial
linear case of gcouP = OpS.
72


Mutation K'1/2 P'o Hill Coefficient a Reference
T2D
hetE23K(P) 1.13 1 1.3 nR Villareal et al. 2009
TNDM
het E229K(A) 5.46 1.78 0.95 nR Girard et al. 2006
hetV252A(A) 2.73 1 0.57 nR Girard et al. 2006
PNDM
**hetF35V(A) 2.58 1 0.88 nR Proks et al. 2006
*hetR201C(A) 1.5 1.1 1 nR Proks et al. 2004
**het R201H(A) 1.51 1 1.6 nR Gloyn et al. 2004
**het R50Q(A) 2.87 1 1.37 nR Shimomura et al. 2006
**het H46Y(A) 6.2 1 0.68 nR Girard et al. 2006
hetE292G(A) 6.4 1 0.8 nR Girard et al. 2006
l-DEND
**het V59M(A) 2.42 1 0.94 0.1 Proks et al. 2005
DEND
het G334D(B) 2.99 1 1 0.1 Masia et al. 2007
-het I296L(N) 6.77 1.5 1.3 nR Koster et al. 2005
-hetQ52R(A) 3.28 1.32 1.2 nR Proks et al. 2004
het V59G(A) 3.71 1.32 1.18 nR Proks et al. 2004
Figure S4: Table of parameters reported in the literature for each NDM mutation
simulated, k'1/2 and p'0 are reported as relative to WT measurements. nR = not reported.
Unless noted, all simulations were run having k'1/2 and a changed when reported.
73


A
NDM Mutations (all parameters changed)
T2D TNDM PNDM l-DEND DEND
120pS
B oPs
T2D TNDM PNDM l-DEND DEND
Figure S5: Simulation results from running NDM mutations with all reported parameters
applied to the model for gCouP=120pS and gCouP= OpS. Parameters as shown in Figure S4.
A) Fraction cells active. B) Total duty cycle. Clinical severity is marked as in Figure 5.
74


Figure S6: Modeling insulin secretion dynamics
A) Insulin secretion simulation results in a single, uncoupled cell. A step increase of
intracellular calcium from .01 [uM] to .5[uM] was applied att=5 minutes. B) Insulin
secretion simulation results in a single, uncoupled cell. A step increase of glucose from
3mM to llmM was applied at t=5 minutes. C) Parameters, initial conditions and a
schematic of the exocytosis events modeled according to equations 8-16. Adapted from
Petersen and Sherman 2009.
75


0 9coup -OPS
9 coup -OpS
Figure S7: Noise characterization for 10 random number seeds.
A) Fraction cells active at 5.5mM glucose, with gCouP= OpS. B) Total duty cycle at 5.5mM
glucose, with gCouP= OpS. Noise was generated for a single islet, across 10 random
number seeds to characterize the increase of activity for each run of noise applied to the
system.
76


LIST OF REFERENCES
(2002). Report of the Expert Committee on the Diagnosis and Classification of Diabetes
Mellitus. Dia Care 25, s5-s20.
(2010). Diagnosis and Classification of Diabetes Mellitus. Diabetes Care 33, S62-S69.
Ainscow, E.K., and Rutter, G.A. (2002). Glucose-Stimulated Oscillations in Free Cytosolic
ATP Concentration Imaged in Single Islet (3-Cells Evidence for a Ca2+-Dependent
Mechanism. Diabetes 51, S162-S170.
Albert, R., and Barabasi, A.-L. (2002). Statistical mechanics of complex networks. Rev.
Mod. Phys. 74, 47-97.
Alberti, K.G.M.M., Juel Christensen, N., Engkjser Christensen, S., Prange Hansen, A.,
Iversen, ]., Lundbsek, K., Seyer-Hansen, K., and rskov, H. (1973). Inhibition of Insulin
Secretion by Somatostatin. The Lancet 302,1299-1301.
American Diabetes Association (2013). Economic costs of diabetes in the U.S. in 2012.
Diabetes Care 36,1033-1046.
Ashcroft, F.M., and Gribble, F.M. (1999). ATP-sensitive K+ channels and insulin
secretion: their role in health and disease. Diabetologia 42, 903-919.
Ashcroft, F.M., and Rorsman, P. (1989). Electrophysiology of the pancreatic (3-cell.
Progress in Biophysics and Molecular Biology 54, 87-143.
Ashcroft, F.M., and Rorsman, P. (2013). KATP channels and islet hormone secretion:
new insights and controversies. Nat Rev Endocrinol 9, 660-669.
Barg, S., Eliasson, L., Renstrom, E., and Rorsman, P. (2002). A Subset of 50 Secretory
Granules in Close Contact With 1-Type Ca2+ Channels Accounts for First-Phase Insulin
Secretion in Mouse (3-Cells. Diabetes 51, S74-S82.
Bell, G.I., and Polonsky, K.S. (2001). Diabetes mellitus and genetically programmed
defects in (3-cell function. Nature 414, 788-791.
Benninger, R.K.P., Head, W.S., Zhang, M., Satin, L.S., and 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, 5453-5466.
Benninger, R.K.P., Hutchens, T., Head, W.S., McCaughey, M.J., Zhang, M., Le Marchand, S.J.,
Satin, L.S., and Piston, D.W. (2014). Intrinsic islet heterogeneity and gap junction
coupling determine spatiotemporal Ca2+ wave dynamics. Biophys. J. 107, 2723-2733.
77


Benninger, R.K.P., Zhang, M., Head, W.S., Satin, L.S., and Piston, D.W. (2008). Gap
junction coupling and calcium waves in the pancreatic islet. Biophys. J. 95, 5048-5061.
Bertram, R., Previte, J., Sherman, A., Kinard, T.A., and Satin, L.S. (2000). The phantom
burster model for pancreatic beta-cells. Biophys J 79, 2880-2892.
Bertram, R., Sherman, A., and Satin, L.S. (2007). Metabolic and electrical oscillations:
partners in controlling pulsatile insulin secretion. American Journal of Physiology -
Endocrinology and Metabolism 293, E890-E900.
Bertuzzi, A., Salinari, S., and Mingrone, G. (2007). Insulin granule trafficking in (3-cells:
mathematical model of glucose-induced insulin secretion. American Journal of
Physiology Endocrinology and Metabolism 293, E396-E409.
Bosco, D., Armanet, M., Morel, P., Niclauss, N., Sgroi, A., Muller, Y.D., Giovannoni, L.,
Parnaud, G., and Berney, T. (2010). Unique arrangement of alpha- and beta-cells in
human islets of Langerhans. Diabetes 59,1202-1210.
Boyle, J.P., Thompson, T.J., Gregg, E.W., Barker, L.E., and Williamson, D.F. (2010).
Projection of the year 2050 burden of diabetes in the US adult population: dynamic
modeling of incidence, mortality, and prediabetes prevalence. Popul Health Metr 8, 29.
Bratanova-Tochkova, T.K., Cheng, H., Daniel, S., Gunawardana, S., Liu, Y.-J., Mulvaney-
Musa, J., Schermerhorn, T., Straub, S.G., Yajima, H., and Sharp, G.W.G. (2002). Triggering
and Augmentation Mechanisms, Granule Pools, and Biphasic Insulin Secretion. Diabetes
51, S83-S90.
Brissova, M., Fowler, M.J., Nicholson, W.E., Chu, A., Hirshberg, B., Harlan, D.M., and
Powers, A.C. (2005). Assessment of Human Pancreatic Islet Architecture and
Composition by Laser Scanning Confocal Microscopy. J Histochem Cytochem 53,1087-
1097.
Cabrera, 0., Berman, D.M., Kenyon, N.S., Ricordi, C., Berggren, P.-O., and Caicedo, A.
(2006). The unique cytoarchitecture of human pancreatic islets has implications for
islet cell function. Proc. Natl. Acad. Sci. U.S.A. 103, 2334-2339.
Campbell, R.E., Gaidamaka, G., Han, S.-K., and Herbison, A.E. (2009). Dendro-dendritic
bundling and shared synapses between gonadotropin-releasing hormone neurons.
PNAS 106,10835-10840.
Cha, C.Y., Nakamura, Y., Himeno, Y., Wang, J., Fujimoto, S., Inagaki, N., Earm, Y.E., and
Noma, A. (2011). Ionic mechanisms and Ca2+ dynamics underlying the glucose
response of pancreatic (3 cells: a simulation study. J Gen Physiol 138, 21-37.
78


Chay, T.R., and Kang, H.S. (1988). Role of single-channel stochastic noise on bursting
clusters of pancreatic beta-cells. Biophys J 54, 427-435.
Chay, T.R., and Keizer, J. (1983). Minimal model for membrane oscillations in the
pancreatic beta-cell. Biophys J 42,181-190.
Chen, Y., Wang, S., and Sherman, A. (2008). Identifying the Targets of the Amplifying
Pathway for Insulin Secretion in Pancreatic (3-Cells by Kinetic Modeling of Granule
Exocytosis. Biophys J 95, 2226-2241.
Chimienti, F., Devergnas, S., Favier, A., and Seve, M. (2004). Identification and Cloning of
a (3-CellSpecific Zinc Transporter, ZnT-8, Localized Into Insulin Secretory Granules.
Diabetes 53, 2330-2337.
Cnop, M., Welsh, N., Jonas, J.-C., Jorns, A., Lenzen, S., and Eizirik, D.L. (2005). Mechanisms
of Pancreatic (3-Cell Death in Type 1 and Type 2 Diabetes Many Differences, Few
Similarities. Diabetes 54, S97-S107.
Colomer, C., Ore, L.A.O., Coutry, N., Mathieu, M.-N., Arthaud, S., Fontanaud, P., Iankova, I.,
Macari, F., Thouennon, E., Yon, L., et al. (2008). Functional Remodeling of Gap Junction-
Mediated Electrical Communication between Adrenal Chromaffin Cells in Stressed Rats.
J. Neurosci. 28, 6616-6626.
Cottrell, E.C., Campbell, R.E., Han, S.-K., and Herbison, A.E. (2006). Postnatal Remodeling
of Dendritic Structure and Spine Density in Gonadotropin-Releasing Hormone Neurons.
Endocrinology 147, 3652-3661.
Curry, D.L., Bennett, L.L., and Grodsky, G.M. (1968). Dynamics of insulin secretion by the
perfused rat pancreas. Endocrinology 83, 572-584.
Daniel, S., Noda, M., Straub, S.G., and Sharp, G.W. (1999). Identification of the docked
granule pool responsible for the first phase of glucose-stimulated insulin secretion.
Diabetes 48,1686-1690.
de Boer, T.P., van Veen, T.A.B., Houtman, M.J.C., Jansen, J.A., van Amersfoorth, S.C.M.,
Doevendans, P.A., Vos, M.A., and van der Heyden, M.A.G. (2006). Inhibition of
cardiomyocyte automaticity by electrotonic application of inward rectifier current from
Kir2.1 expressing cells. Med Biol Eng Comput 44, 537-542.
Degen, J., Meier, C., Van Der Giessen, R.S., Sohl, G., Petrasch-Parwez, E., Urschel, S.,
Dermietzel, R., Schilling, K., De Zeeuw, C.I., and Willecke, K. (2004). Expression pattern
of lacZ reporter gene representing connexin36 in transgenic mice. J. Comp. Neurol. 473,
511-525.
79


Dotta, F., and Eisenbarth, G.S. (1989). Type 1 diabetes mellitus: A predictable
autoimmune disease with interindividual variation in the rate of (3 cell destruction.
Clinical Immunology and Immunopathology 50, S85-S95.
Fahrenbach, J.P., Ai, X., and Banach, K. (2008). Decreased intercellular coupling
improves the function of cardiac pacemakers derived from mouse embryonic stem cells.
J Mol Cell Cardiol 45, 642-649.
Farnsworth, N.L., Hemmati, A., Pozzoli, M., and Benninger, R.K.P. (2014). Fluorescence
recovery after photobleaching reveals regulation and distribution of connexin36 gap
junction coupling within mouse islets of Langerhans. J Physiol 592, 4431-4446.
Fridlyand, L.E., Tamarina, N., and Philipson, L.H. (2003). Modeling of Ca2+ flux in
pancreatic (3-cells: role of the plasma membrane and intracellular stores. American
Journal of Physiology Endocrinology and Metabolism 285, E138-E154.
Gembal, M., Gilon, P., and Henquin, J.C. (1992). Evidence that glucose can control insulin
release independently from its action on ATP-sensitive K+ channels in mouse B cells. J
Clin Invest 89,1288-1295.
Gerich, J.E., Langlois, M., Noacco, C., Karam, J.H., and Forsham, P.H. (1973). Lack of
Glucagon Response to Hypoglycemia in Diabetes: Evidence for an Intrinsic Pancreatic
Alpha Cell Defect. Science 182,171-173.
Gillis, K.D., and Misler, S. (1993). Enhancers of cytosolic cAMP augment depolarization-
induced exocytosis from pancreatic B-cells: evidence for effects distal to Ca2+ entry.
Pflugers Arch. 424,195-197.
Girard, C.A.J., Shimomura, K., Proks, P., Absalom, N., Castano, L., Perez de Nanclares, G.,
and Ashcroft, F.M. (2006). Functional analysis of six Kir6.2 (KCNJ11) mutations causing
neonatal diabetes. Pflugers Arch. 453, 323-332.
Gloyn, A.L., Pearson, E.R., Antcliff, J.F., Proks, P., Bruining, G.J., Slingerland, A.S., Howard,
N., Srinivasan, S., Silva, J.M.C.L., Moines, J., et al. (2004). Activating mutations in the gene
encoding the ATP-sensitive potassium-channel subunit Kir6.2 and permanent neonatal
diabetes. N. Engl. J. Med. 350,1838-1849.
Goldwyn JH, Shea-Brown E (2011) The What and Where of Adding Channel Noise to the
Hodgkin-Huxley Equations. PLoS Comput Biol 7(11): el002247.
doi: 10.1371/journal.pcbi. 1002247
Gopel, S.O., Kanno, T., Barg, S., Weng, X.G., Gromada, J., and Rorsman, P. (2000).
Regulation of glucagon release in mouse -cells by KATP channels and inactivation of
TTX-sensitive Na+ channels. J. Physiol. (Lond.) 528, 509-520.
80


Han, S.-K., Abraham, I.M., and Herbison, A.E. (2002). Effect of GABA on GnRH Neurons
Switches from Depolarization to Hyperpolarization at Puberty in the Female Mouse.
Endocrinology 143,1459-1466.
Hansen, J.B. (2006). Towards selective Kir6.2/SUR1 potassium channel openers,
medicinal chemistry and therapeutic perspectives. Curr. Med. Chem. 13, 361-376.
Hattersley, A.T., and Ashcroft, F.M. (2005). Activating Mutations in Kir6.2 and Neonatal
Diabetes New Clinical Syndromes, New Scientific Insights, and New Therapy. Diabetes
54, 2503-2513.
Head, W.S., Orseth, M.L., Nunemaker, C.S., Satin, L.S., Piston, D.W., and Benninger, R.K.P.
(2012). Connexin-36 Gap Junctions Regulate In Vivo First- and Second-Phase Insulin
Secretion Dynamics and Glucose Tolerance in the Conscious Mouse. Diabetes 61,1700-
1707.
Henquin, J.-C. (1990). Glucose-Induced Electrical Activity in (3-Cells: Feedback Control of
ATP-Sensitive K+ Channels by Ca2+. Diabetes 39,1457-1460.
Henquin, J.C. (2000). Triggering and amplifying pathways of regulation of insulin
secretion by glucose. Diabetes 49,1751-1760.
Hraha, T.H., Westacott, M.J., Pozzoli, M., Notary, A.M., McClatchey, P.M., and Benninger,
R.K.P. (2014). Phase Transitions in the Multi-cellular Regulatory Behavior of Pancreatic
Islet Excitability. PLoS Computational Biology 10, el003819.
Ishihara, H., Maechler, P., Gjinovci, A., Herrera, P.-L., and Wollheim, C.B. (2003). Islet (3-
cell secretion determines glucagon release from neighbouring a-cells. Nat Cell Biol 5,
330-335.
Jain, R., and Lammert, E. (2009). Cell-cell interactions in the endocrine pancreas.
Diabetes, Obesity and Metabolism 11,159-167.
Jo, ]., Kang, H., Choi, M.Y., and Koh, D.-S. (2005). How Noise and Coupling Induce
Bursting Action Potentials in Pancreatic (3-Cells. Biophysical Journal 89,1534-1542.
Kilimnik, G., Zhao, B., Jo, ]., Periwal, V., Witkowski, P., Misawa, R., and Hara, M. (2011).
Altered Islet Composition and Disproportionate Loss of Large Islets in Patients with
Type 2 Diabetes. PLoS ONE 6, e27445.
Kim, A., Miller, K., Jo, ]., Kilimnik, G., Wojcik, P., and Hara, M. (2009). Islet architecture.
Islets 1, 129-136.
81


Koster, J.C., Marshall, B.A., Ensor, N., Corbett, J.A., and Nichols, C.G. (2000). Targeted
Overactivity of (B Cell KATP Channels Induces Profound Neonatal Diabetes. Cell 100,
645-654.
Koster, J.C., Remedi, M.S., Dao, C., and Nichols, C.G. (2005). ATP and sulfonylurea
sensitivity of mutant ATP-sensitive K+ channels in neonatal diabetes: implications for
pharmacogenomic therapy. Diabetes 54, 2645-2654.
Koster, J.C., Remedi, M.S., Flagg, T.P., Johnson, J.D., Markova, K.P., Marshall, B.A., and
Nichols, C.G. (2002). Hyperinsulinism induced by targeted suppression of beta cell
KATP channels. Proc Natl Acad Sci U S A 99,16992-16997.
Lang, V., and Light, P.E. (2010). The molecular mechanisms and pharmacotherapy of
ATP-sensitive potassium channel gene mutations underlying neonatal diabetes.
Pharmgenomics Pers Med 3,145-161.
Lin, C.-W., Lin, Y.-W., Yan, F.-F., Casey,}., Kochhar, M., Pratt, E.B., and Shyng, S.-L. (2006).
Kir6.2 Mutations Associated With Neonatal Diabetes Reduce Expression of ATP-
Sensitive K+ channels Implications in Disease Mechanism and Sulfonylurea Therapy.
Diabetes 55,1738-1746.
Lin, J.H.-C., Weigel, H., Cotrina, M.L., Liu, S., Bueno, E., Hansen, A.J., Hansen, T.W.,
Goldman, S., and Nedergaard, M. (1998). Gap-junction-mediated propagation and
amplification of cell injury. Nat Neurosci 1, 494-500.
MacDonald, P.E., and Rorsman, P. (2006). Oscillations, Intercellular Coupling, and
Insulin Secretion in Pancreatic (B Cells. PLoS Biol 4, e49.
MacDonald, P.E., Joseph, J.W., and Rorsman, P. (2005). Glucose-sensing mechanisms in
pancreatic (3-cells. Philosophical Transactions of the Royal Society of London B:
Biological Sciences 360, 2211-2225.
MacDonald, P.E., Marinis, Y.Z.D., Ramracheya, R., Salehi, A., Ma, X., Johnson, P.R.V., Cox,
R., Eliasson, L., and Rorsman, P. (2007). A KATP Channel-Dependent Pathway within a
Cells Regulates Glucagon Release from Both Rodent and Human Islets of Langerhans.
PLoS Biol 5, el43.
Masia, R., Koster, J.C., Tumini, S., Chiarelli, F., Colombo, C., Nichols, C.G., and Barbetti, F.
(2007). An ATP-binding mutation (G334D) in KCNJ11 is associated with a sulfonylurea-
insensitive form of developmental delay, epilepsy, and neonatal diabetes. Diabetes 56,
328-336.
McArthur, L., Chilton, L., Smith, G.L., and Nicklin, S.A. (2015). Electrical consequences of
cardiac myocyte: fibroblast coupling. Biochemical Society Transactions 43, 513-518.
82


McDonald, J.C., Duffy, D.C., Anderson, J.R., Chiu, D.T., Wu, H., Schueller, O.J., and
Whitesides, G.M. (2000). Fabrication of microfluidic systems in poly(dimethylsiloxane).
Electrophoresis 21, 27-40.
McTaggart, J.S., Clark, R.H., and Ashcroft, F.M. (2010). The role of the KATP channel in
glucose homeostasis in health and disease: more than meets the islet. J Physiol 588,
3201-3209.
Miranda, P.J., DeFronzo, R.A., Califf, R.M., and Guyton, J.R. (2005). Metabolic syndrome:
Definition, pathophysiology, and mechanisms. American Heart Journal 149, 33-45.
Misler, S., Barnett, D.W., Gillis, K.D., and Pressel, D.M. (1992). Electrophysiology of
Stimulus-Secretion Coupling in Human (3-Cells. Diabetes 41,1221-1228.
Nguyen, L.M., Pozzoli, M., Hraha, T.H., and Benninger, R.K.P. (2014). Decreasing Cx36
Gap Junction Coupling Compensates for Overactive KATP Channels to Restore Insulin
Secretion and Prevent Hyperglycemia in a Mouse Model of Neonatal. Diabetes 63,1685-
1697.
Ohara-Imaizumi, M., Nishiwaki, C., Kikuta, T., Nagai, S., Nakamichi, Y., and Nagamatsu, S.
(2004). TIRF imaging of docking and fusion of single insulin granule motion in primary
rat pancreatic (3-cells: different behaviour of granule motion between normal and Goto-
Kakizaki diabetic rat (3-cells. Biochem J 381,13-18.
Palumbo, P., Ditlevsen, S., Bertuzzi, A., and De Gaetano, A. (2013). Mathematical
modeling of the glucose-insulin system: A review. Mathematical Biosciences 244, 69-
81.
Pearson, E.R., Flechtner, I., Njplstad, P.R., Malecki, M.T., Flanagan, S.E., Larkin, B.,
Ashcroft, F.M., Klimes, I., Codner, E., Iotova, V., et al. (2006). Switching from Insulin to
Oral Sulfonylureas in Patients with Diabetes Due to Kir6.2 Mutations. New England
Journal of Medicine 355, 467-477.
Pedersen, M.G., and Sherman, A. (2009). Newcomer insulin secretory granules as a
highly calcium-sensitive pool. Proc Natl Acad Sci U S A106, 7432-7436.
Pedersen, M.G., Bertram, R., and Sherman, A. (2005). Intra- and Inter-Islet
Synchronization of Metabolically Driven Insulin Secretion. Biophysical Journal 89,107-
119.
Perez-Armendariz, E.M. (2013). Connexin 36, a key element in pancreatic beta cell
function. Neuropharmacology 75, 557-566.
Pizarro-Delgado, J., Fasciani, I., Temperan, A., Romero, M., Gonzalez-Nieto, D., Alonso-
Magdalena, P., Nualart-Marti, A., Estilles, E., Paul, D.L., Martfn-del-Rfo, R., et al. (2014).
Inhibition of connexin 36 hemichannels by glucose contributes to the stimulation of
83


insulin secretion. American Journal of Physiology Endocrinology and Metabolism 306,
E1354-E1366.
Poil, S.-S., Hardstone, R., Mansvelder, H.D., and Linkenkaer-Hansen, K. (2012). Critical-
State Dynamics of Avalanches and Oscillations Jointly Emerge from Balanced
Excitation/Inhibition in Neuronal Networks. J Neurosci 32, 9817-9823.
Polonsky, K.S. (2012). The Past 200 Years in Diabetes. New England Journal of Medicine
367,1332-1340.
Proks, P., Antcliff, J.F., Lippiat, J., Gloyn, A.L., Hattersley, A.T., and Ashcroft, F.M. (2004).
Molecular basis of Kir6.2 mutations associated with neonatal diabetes or neonatal
diabetes plus neurological features. Proc. Natl. Acad. Sci. U.S.A. 101,17539-17544.
Proks, P., Girard, C., and Ashcroft, F.M. (2005). Functional effects of KCNJ11 mutations
causing neonatal diabetes: enhanced activation by MgATP. Hum. Mol. Genet. 14, 2717-
2726.
Proks, P., Girard, C., Baevre, H., Njplstad, P.R., and Ashcroft, F.M. (2006). Functional
effects of mutations at F35 in the NH2-terminus of Kir6.2 (KCNJ11), causing neonatal
diabetes, and response to sulfonylurea therapy. Diabetes 55,1731-1737.
Ravier, M.A., and Rutter, G.A. (2005). Glucose or Insulin, but not Zinc Ions, Inhibit
Glucagon Secretion From Mouse Pancreatic a-Cells. Diabetes 54,1789-1797.
Ravier, M.A., Giildenagel, M., Charollais, A., Gjinovci, A., Caille, D., Sohl, G., Wollheim, C.B.,
Willecke, K., Henquin, J.-C., and Meda, P. (2005). Loss of connexin36 channels alters
beta-cell coupling, islet synchronization of glucose-induced Ca2+ and insulin
oscillations, and basal insulin release. Diabetes 54,1798-1807.
Remedi, M.S., Kurata, H.T., Scott, A., Wunderlich, F.T., Rother, E., Kleinridders, A., Tong,
A., Briining, J.C., Roster, J.C., and Nichols, C.G. (2009). Secondary Consequences of (3 Cell
Inexcitability: Identification and Prevention in a Murine Model of KATP-Induced
Neonatal Diabetes Mellitus. Cell Metabolism 9,140-151.
Rocheleau, J.V., Remedi, M.S., Granada, B., Head, W.S., Roster, J.C., Nichols, C.G., and
Piston, D.W. (2006). Critical Role of Gap Junction Coupled RATP Channel Activity for
Regulated Insulin Secretion. PLoS Biol 4, e26.
Rorsman P., Trube G. (1986). Calcium and delayed potassium currents in mouse
pancreatic beta-cells under voltage-clamp conditions. J. Physiol. 374:531-550
Rorsman, D.P., and Renstrom, E. (2003). Insulin granule dynamics in pancreatic beta
cells. Diabetologia 46,1029-1045.
84


Rorsman, P., Berggren, P.O., Bokvist, K., Ericson, H., Mohler, H., Ostenson, C.G., and
Smith, P.A. (1989). Glucose-inhibition of glucagon secretion involves activation of
GABAA-receptor chloride channels. Nature 341, 233-236.
Saez, J.C., Berthoud, V.M., Branes, M.C., Martinez, A.D., and Beyer, E.C. (2003). Plasma
Membrane Channels Formed by Connexins: Their Regulation and Functions.
Physiological Reviews 83,1359-1400.
Sagen, J.V., Raeder, H., Hathout, E., Shehadeh, N., Gudmundsson, K., Baevre, H., Abuelo,
D., Phornphutkul, C., Moines, J., Bell, G.I., et al. (2004). Permanent neonatal diabetes due
to mutations in KCNJ11 encoding Kir6.2: patient characteristics and initial response to
sulfonylurea therapy. Diabetes 53, 2713-2718.
Serre-Beinier, V., Bosco, D., Zulianello, L., Charollais, A., Caille, D., Charpantier, E.,
Gauthier, B.R., Diaferia, G.R., Giepmans, B.N., Lupi, R., et al. (2009). Cx36 makes channels
coupling human pancreatic beta-cells, and correlates with insulin expression. Hum. Mol.
Genet. 18, 428-439.
Serre-Beinier, V., Le Gurun, S., Belluardo, N., Trovato-Salinaro, A., Charollais, A.,
Haefliger, J.A., Condorelli, D.F., and Meda, P. (2000). Cx36 preferentially connects beta-
cells within pancreatic islets. Diabetes 49, 727-734.
Sheldon, R.E., Mashayamombe, C., Shi, S.-Q., Garfield, R.E., Shmygol, A., Blanks, A.M., and
Berg, H.A. van den (2014). Alterations in gap junction connexin43/connexin45 ratio
mediate a transition from quiescence to excitation in a mathematical model of the
myometrium. Journal of The Royal Society Interface 11, 20140726.
Sherman, A. (1996). Contributions of modeling to understanding stimulus-secretion
coupling in pancreatic beta-cells. American Journal of Physiology Endocrinology and
Metabolism 271, E362-E372.
Sherman, A., and Rinzel, J. (1991). Model for synchronization of pancreatic beta-cells by
gap junction coupling. Biophys J 59, 547-559.
Shimomura, K., Girard, C.A.J., Proks, P., Nazim, J., Lippiat, J.D., Cerutti, F., Lorini, R., Ellard,
S., Hattersley, A.T., Barbetti, F., et al. (2006). Mutations at the same residue (R50) of
Kir6.2 (KCNJ11) that cause neonatal diabetes produce different functional effects.
Diabetes 55,1705-1712.
Speier, S., Gjinovci, A., Charollais, A., Meda, P., and Rupnik, M. (2007). Cx36-Mediated
Coupling Reduces (3-Cell Heterogeneity, Confines the Stimulating Glucose Concentration
Range, and Affects Insulin Release Kinetics. Diabetes 56,1078-1086.
Stamper, I.J., Jackson, E., and Wang, X. (2014). Phase transitions in pancreatic islet
cellular networks and implications for type-1 diabetes. Phys. Rev. E 89, 012719.
85


Villareal, D.T., Koster, J.C., Robertson, H., Akrouh, A., Miyake, K., Bell, G.I., Patterson, B.W.,
Nichols, C.G., and Polonsky, K.S. (2009). Kir6.2 variant E23K increases ATP-sensitive K+
channel activity and is associated with impaired insulin release and enhanced insulin
sensitivity in adults with normal glucose tolerance. Diabetes 58,1869-1878.
Wang, Z., and Thurmond, D.C. (2009). Mechanisms of biphasic insulin-granule
exocytosis roles of the cytoskeleton, small GTPases and SNARE proteins. J Cell Sci 122,
893-903.
Wojtusciszyn, A., Armanet, M., Morel, P., Berney, T., and Bosco, D. (2008). Insulin
secretion from human beta cells is heterogeneous and dependent on cell-to-cell
contacts. Diabetologia 51,1843-1852.
Zhang, H., Fujitani, Y., Wright, C.V.E., and Gannon, M. (2005). Efficient recombination in
pancreatic islets by a tamoxifen-inducible Cre-recombinase. Genesis 42, 210-217.
86


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