i CYCLIC AMP COORDINATION UNDERLIES ELECTRICAL OSCILLATORY ROBUSTNESS IN C E L L NE T W O R KS By CHRISTOPHER L. WILSON BS, University of Colorado, 2011 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 2014
ii This thesis for the Master of Science degree by Christopher L. W ilson has been approved for the Bioengineering Program By Richard Benninger, Chair Tim Lei Robin Shandas 11/21/2014
iii Wilson, Christopher L. (M .S., Bioen g i n e e r i n g ) Cyclic AMP Coordination Underlies Electrical Oscillatory cell N etworks T h e s i s d i r e c t ed by A s s i stant Pr o f e s s o r Ri ch a r d K P B e n nin g er ABSTRACT The pancreatic islets of Langerhans are micro organs which participate in maintenance of glucose homeostasis through the sec retion of the hormones insulin and glucagon. The beta cells which compromise the majority of the islet secrete insulin in response to glucose elevation via cell depolarization and calcium elevations. Beta cells are electrically coupled via gap junctions, and therefore undergo coordinated depolarizations when healthy. This electrical ac tivity is modulated by the second messenger cAMP. cAMP levels in the beta cell are thought to be primarily controlled by incretin hormones released by the intestine following a meal. To further develop the behavior of cAMP signaling within coupled beta cells, we studied real time dynamics of a glucose stimulated beta cell network using a FRET based biosensor. To study the effect of incretin hormone stimulation, we used the GLP 1 analog E xendin 4. cAMP oscillations were found to be coordinated and cell coordination and duty cycle improved with Exendin 4 treatment. These findings were applied to a coupled cell model of oscillatory depolarization. We were able to then show that increases in adenylyl cyclase activity are responsible for increasing the robustness and duration of depolarization events, improving cell synchronization probability, even when not accounting for effects cAMP may have on gap junction coupling. Previous FRAP results suggest cAMP elevations contribute little gap junction conductance in unstressed islets ; these simulations suggest the effect of this is minor when compared to increasing the stability of voltage waveforms. In support of this, methods were developed to utilize a rhodopsin/GPCR optogenetic construct in ex vivo islets and cell line models. It was found that it is beneficial to bathe them in the cofactor all trans retinal, and cAMP levels can be simultaneously detected using a translocation based biosensor. In addition, confocal microscopes can be used to selectively excite specific cells to even more precisely determine the nature of cAMPs effect on beta cell coordination. The form and content of this abstract are approved. I recommend its public ation. Approved: Richard KP Benninger
iv Declaration of original work By Christopher L. Wilson This page is to assert that my master thesis was independently composed and authored by myself, using solely the referred sources and support from my adviser, fellow students, and the Department of Bioengineering Of particular note are the cAMP biosensors used (Zhang et al, Tengholm et al) and parts of code used in the model were developed elsewhere. We developed a new way to detect translocation using the bios ensor developed by Tengholm et al. The portions of the model that we contributed were including a cAMP handling module (Ni et al., 2011) to an existing electrical oscillator model (Bertram et al., 2004), and forming this model into a coupled 2D network.
v TABLE OF CONTENTS CHAPTER I. INTRODUCTION AND BACKGROUND ................................ .................... 1 Introduction ................................ ................................ ................................ ..... 1 Diabetes Mellitus ................................ ................................ ............................. 2 The Islets of Langerhans ................................ ................................ ................. 3 Insulin Secretion ................................ ................................ .............................. 5 Electrical Coupling and Coordination ................................ ............................. 6 ................................ ............................. 8 Incretin Hormones ................................ ................................ ......................... 11 Biosensors ................................ ................................ ................................ ..... 13 Mathematical Models ................................ ................................ .................... 16 II. MATERIALS AND METHODS ................................ ................................ .. 19 Cell Culture ................................ ................................ ................................ ... 19 Gene Cloning, Transfection, and Staining ................................ .................... 20 Microscopy ................................ ................................ ................................ .... 21 Image Processing ................................ ................................ ........................... 22 Matlab Analysis ................................ ................................ ............................. 23 Modeling and Simulation ................................ ................................ .............. 25 Microfluidics ................................ ................................ ................................ 33 Optogenetics ................................ ................................ ................................ .. 35 III. CELL MODEL CELL LINES ................................ ................................ ................. 38
vi [cAMP] Dynamics in Glucose Stimulated MIN6 Cells ................................ 38 Effects of GLP 1 Analog on [c AMP] and [Ca 2+ ] Dynamics ......................... 39 Effects of [cAMP] Elevation within Single Cells ................................ ......... 40 Effects of [cAMP] Elevation on Coordinated Cell Networks ....................... 45 Intracellular Relationships Underlie Network Behavior ............................... 50 Additional Metrics and Control of Result Confounding ............................... 53 Restricting the Dataset Retains Results ................................ ......................... 55 Treating Clusters as Repeated Measures Retains Results ............................. 61 IV. RESULTS PART 2: IN SILICO MODEL PREDICTS CAMP PROVIDES IMPROVED NETWORK COORDINATION BY INCREASING INDIVIDUAL CELL OSCILLATORY ROBUSTNESS ............................. 62 Single Cell Mo del Predicts [cAMP] dependent Duty Cycle and Stability .... 62 Multicellular Network Model Predicts Findings from MIN6 Model ............ 66 Effects of Intracellular Synchronization is Difficult to Observe In Silico ..... 69 Comparative effects of [cAMP] dependent Oscillatory Sta bility vs. Coupling Conductance ................................ ................................ ................................ .. 73 V. RESULTS PART 3: DETECTING OSCILLATIONS PRODUCED BY A CELL MODEL ............. 76 [cAMP] Oscillations Driven by Selective Illumination in MIN6 Cells ........ 76 Detection using Colocalization and Binary Mask Algorithms ...................... 78 Effects of Optogenetic Driven [cAMP] Elevations on Neighboring Cells ... 79 VI. DISCUSSION AND FUTURE DIRECTIONS ................................ ............. 81 cell Model Cell Lines ........................ 81 In Silico Model Predicts cAMP Provides Improved Network Coordination by I ncreasing Individual Cell Oscillatory Robustness ................................ ....... 84
vii Cell Model ................................ ................................ ................................ .... 86 Future Directions ................................ ................................ ........................... 88 REFERENCES ................................ ................................ .............................. 92 APPENDIX ................................ ................................ ................................ 100
1 CHAPTER I INTRODUCTION AND BACKGROUND Introduction Diabetes is a n endocrine disease that affects nearly 4 0 million people in the United States and is the 7 th leading cause of death. It also affects an estimated 382 million people worldwide, and i ncidence is growing rapidly. Diabetes is characterized as insufficient regulation of glucose homeostasis. Glucose is regulated primarily by micro organs in the pancreas, the islets of Langer hans, via the hormones insulin and glucagon. It is generally accepted that dy sfunction or destruction of the islet s of Langerhans contributes to progression of the disease. Deepening understanding of the mechanisms underlying islet physiology are a key step towards improving therapies and possibly even curing this disease. Fig u r e 1 1 : Worldwide prevalence of Diabetes. Source: IDF.org
2 Diabetes Mellitus Early descriptions of diabetes mellitus defined it as a disease characterized by excessive urination or Diabetes that was sweet tasting or attracted insects or Mellitus. Early physicians also quickly noted that the disease came in two forms, one where younger people succumbed to the disease quickly, and another where older, usually overweight people succumbed slowly. Today these forms are commonly referred to as type 1 and type 2, respectively. Among the scientific community, these types are perhaps more accurately designated as autoimmune destructive diabetes, and insulin resistant diabetes. Type 1, or autoimmune destructive diabetes, as the name implies, results from des truction of beta cells within the islets of Langerhans, rendering an individual unable to secrete any insulin in response to elevated blood glucose. Type 2 appears to result from a myriad of interrelated phenomena, but persons with type 2 diabetes consiste ntly show impaired insulin secretion, as well as impaired response to insulin by peripheral tissues, especially the liver. Fig u r e 1 2 : Percentage of US population with Diabetes from 1958 to present. CDC.gov
3 The principal driving factor for studyin g this disease is not only the h undreds of millions of people worldwide w ho have Diabetes, but the distressing rate at which incidence has increased. As shown in figure 2, there even appears to be a remark ably notic e able inflection point in the mid 90s where incidence has nearly doubled. Indeed, there is a strong association between type 2 diabetes and increasing rates of obesity, but incidence of type 1 diabetes is increasing as well. The Islet s of Langerhans The islets of L angerhans are micro organs distributed throughout the pancreas, as shown in figure 3. In healthy individuals, they comprise approximately 1 2 % of the mass of the pancreas equivalent to roughly 1 million islets in total The remainder is mainly exocrine tissue, which serves to secr ete digestive enzymes into the intestines. Fig u r e 1 3 : The pancreas, with islets of Langerhans distributed throug h out Source: A.D.A.M Consumer Health The islet is comprised of a variety of cell types, all of which appear to have endocrine function. The cells charged with secreting insulin are the beta cells, which
4 comprise roughly 7 0% of the cells in the islet in humans (Cabrera et al., 2005) counter regulatory hormone, glucagon, is secreted by alpha cells, which comprise s another 2 0%. Th e remainder of the islet is composed of other, sparsely distributed endocrine cells, which secrete hormones like somatostatin and ghrelin. Somatostatin, secreted by delta cells, is known to regulate the secretion of both insulin and glucagon, but the natur e of its role is poorly understood. Ghrelin is secreted by epsilon cells, which were only discovered recently, and is implicated in the control of hunger. Fig u r e 1 4 : The islet of Langerhans and surrounding tissue, with prominent cell types labeled. Source: Pearson Publishing With such an interesting array of cell types, t here i s a strong belief that the cytoarchitecture of the islet plays a critical role in its physiology (Cabrera et al, 2006) Compellingly, the distribution of these cell types in rodents, the most common animal model for studying islets is noticeably different from the distribution in humans. Rodent gathered at the periphery. In humans, these cell types a re much more interspersed.
5 Insulin Secretion In the beta cell, insulin release is primarily regulated by blood glucose levels. The primary signaling pathway for insulin secretion is described in figure 4. Glucose enters the beta cell through glucose transporter 2, which is also expressed in the brain and liver Upon entering it is phosphorylated by glucokinase, rendering entry into the cell irreversible; all glucose that enters the cell therefore undergoes glycolysis. The rate of glycolysis, followed by the citric acid cycle and oxidative phosphorylation, dictates the ATP/ADP ratio within the cytosol. Sufficient levels of ATP increases closure probability of ATP gated potassium channels (kATP), which initiates depolarization of the cell (Craig et al., 2008) Full depolarization, and insulin exocytosis is then primarily triggered by voltage dependent L type calcium channels (VDCC) but other ions like sodium and chloride also participate (Newgard and McGarry, 1995) However, c alcium concentration is the primary signal in triggering insulin release. The endoplasmic reticulum also plays a large role in regulating intracellular calcium levels, where c alcium ATPases, or SERCAs pump calcium out the cytosol. Other second messengers mediate calcium release from the endoplasmic reticulum. After depolarization, voltage dependent potassium channels open, generating fast action potentials. E levated calcium levels signal a return to repolarization by opening c alcium sensitive BK channels potassium channels with espe cially large conductance. Repetitive depolarization and rep olarization results in electrical oscillations, and oscillatory insulin secretion
6 Fig u r e 1 5 : Schematic of a beta cell and the primary insulin secretion signaling pathway Source: translational medicine.com Electrical Coupling and Coordination An extremely important characteristic of beta cells is that they are electrically coupled to attingent beta cells (Eddlestone et al., 1984) The same behavior is not believed to occur in th e other cell types of the islet. Electrical coupling in beta cells is mediated by gap junctions. Gap junctions are pores that directly connect the cytosol of attingent cells, and allow selective components to pass through. They also participate in the electrical connections of cardiomyocytes and neurons. Gap junctions are formed when two complementary complexes from each cell are joined; these have been given the term connexons. Conne xons are formed from 6 subunits called co nnexins. Conformational changes of connexins from intracellular signals give the gap junction the ability to open and close in response to external stimuli.
7 Fig u r e 1 6 : Schematic of a typical gap junction and its constituent connexons, connexins, and connexin transmembrane structure Electrical coupling mediated by these gap junctions results in a network of beta cells whose electrical oscillations, and therefore insulin secretion coordinate s (Benninger et al., 2008) Much work has been done to thoro ughly characterize and model the nature and behavior of these networks. Most importantly, t he end result is that the islets of Langerhans, in healthy individuals, secrete insulin in a pulsatile manner. In addition, all islets across the pancreas are able to coordinate with each other, resulting in systemic insulin oscillations. The mechanism through wh ich this occurs is unclear, but many believe it is a result of neuronal control. More importantly, however, pulsatile insulin secretion has been shown to be a key player in dictating systemic insulin delivery by regulating hepatic insulin extraction (Meier et al, 2005). In individuals with type 2 diabetes, systemic oscillations are often not found, and this can usually be attributed to a loss of networking function at the islet level.
8 The existence of signal ing pathway s other than the primary electrical one described previously were initially postulated because of variances in insulin secretion given elevated glucose. To clarify, under normal conditions, insulin secretion varies in a highly glucose dependent manner. How ever, this dependence appeared to vary, like when islets are treated with sulfonylureas, now a common type 2 drug that is known to interact with the ATP dependent potassium channels (kATP) Islets treated with sulfonylureas still secrete insulin in a gluco se dependent manner, but secretion is amplified under high glucose conditions. Hence, t 2 diabetes, first because it was often not found in type 2 animal models, and also with indirect evidence that it is not present in human type 2 patients (Henquin, 2000). It is now believed that this adenine monophosphate (cAMP) In fact, the relationship between cAMP and sulfonylureas was demonstrated by showing that cAMP interacts with the sulfonylurea SUR1 receptors that modulate kATP channel activ ity (Eliasson et al, 2003). cAMP is a ubiquitous second messenger present in most cell types, most notably to mediate the response to G protein coupled receptors (GPCRs). cAMP is produced in the cytosol from ATP from a family of enzymes called adenylyl cyc lases (AC).
9 Fig u r e 1 7 : Schematic of cAMP signaling in the beta cell cAMP has a direct effect on the beta cell s electrical activity by mediating phosphorylation of ion channels such as ryanodin e receptor (RyaR), which potentiates release of calcium from the ER, enhancing depolarization and intracellular calcium levels The mechanism through which this happens is believed to be primarily directed by intracellular calcium levels, and is appropriately called calcium induced calcium r elease (Holz et al, 1999) cAMP also activates multiple proteins associated with the complex exocytosis process (Gillis et al, 1993 ) All of the processes through which cAMP amplifies calcium dependent insulin exocytosis are still being explored and appears to be very complicated. Something that is understood, however, is that insulin granule docking can be characterized into three main groups. Insulin gran ules that are shuttled from formation to exist that reside docked to the membrane, but exocytosis never occurs. These are known recruited and shuttled to the membrane, but pause
10 cAMP regulates the trafficking of all of these granule pools ultimately resulting in increased insulin release through a pathway mediated by Excha nge Protein activated by cAMP (EPAC), and RAP1, both through their GTPase activity (Seino et al, 2010) The actual molecular process of this appears to be very complex, involving precise timing and effects on trafficking, priming, and docking of insulin se cretory granules. cAMP also potentiates VDCCs through activation of PKA (Ammala et al, 1993). N ot central to the insulinotropic effects of cAMP, but highlighting the importance placed on its connection with calcium signaling, t here are special A kinase anc horing proteins in the beta cell that facilitate PKA binding to these voltage dependent L type Ca 2+ channels (Fraser et al., 1998) So far, cAMP appears to be intimately involved in every part of the : modulation of the kATP channel, mo dulation of voltage dependent calcium release, modulation of calcium induced calcium release and even insulin granule transport, docking and exocytosis. In addition to being a key factor in mediating proper insulin secretion, t here is also evidence that c AMP plays a role in modifying gene transcription in islet cells cAMP Response Binding Element, or CREB, is a transcription factor that binds selectively to cAMP response elements, thereby inducing transcription selectively to stimulus by cAMP. While origi nally discovered in hypothalamic cells, i ts importance to the islet is highlighted by the fact that it was originally discovered as a transcription factor of somatostatin (Montminy and Bilezikjian, 1987). It has later been discovered that CREB is involved in the machinery behind transcribing insulin, therefore cAMP potentiates insulin transcription. cAMP and growth factor signaling pathways have long been thought to act in opposing fashion in the regulation of metabolism and cellular proliferation but the
11 hallmark effect of this transcription factor so far is suppressing beta cell apoptosis, and even promoting islet cell proliferation (Jhala et al,. 2003). Some of the more recent discoveries pertaining to cAMP signaling in the islet involve it s kinetics cAMP has been shown to oscillate in glucose stimulated beta cells. The origin of cAMP oscillations is believed to be from the combined factors of calcium ac tivity on phosphodiesterases as well as metabolic activity which of course generates the substrate for AC conversion from ATP to cAMP (Jung et al., 2000 ) These oscillations have been shown to be correlated with insulin secretion, so it stands to reason th at the oscillations are a key contributor in directing insulin secretion (Dyachok et al., 2008). Incretin Hormones The incretin effect was first used to describe the fact that oral glucose load produces a greater insulin response than an isoglycemic intra venous glucose infusion (Fazafeos, 2011). This difference has been attributed to the gastrointestinal peptides GLP The primary mediators of Gs and Gi GPCRs and therefore cAMP changes due to exernal st imuli in the beta cell are catecholamines, primarily epinephrine, and the incretins, primarily glucagon like peptide 1 and gastric inhibitory polypeptide (GLP 1 & GIP ). Catecholamines serve to activate inhibitory GPCRs, quenching the cAMP pathway in the be ta cell, reducing insulin secretion and raising blood glucose, an intuitive characteristic of the fight or flight response. Incretins like GLP 1 are secreted by specialized intestinal cells following a meal GLP 1 is the most powerful endogenous insulin stimulating hormone. Aside from its effect on the islet, this hormone is involved in slowing gastric emptying and suppressing appetite as well as a laundry list of effects
12 on other systems (Campbell et al., 20 13) Once in the bloodstream, GLP 1 is rapidly degraded by dipeptidyl pepdidase 4 (DPP4); therefore, cessation of secretion terminates the effects rapidly. Currently, both DPP4 inhibitors, and long acting GLP 1 analogs have been approved for use by the FDA Fig u r e 1 8 : Various physiological effects of GLP 1 The most well known GLP 1 analog is Exendin 4, which is prescribed under various names such as Exenatide (Amylin Pharmaceuticals). Exendin 4 is a hormone naturall y present in the saliva of the G ila monster, a lizard from the southwestern Uni ted States. It was first isolated by John Eng in 1992 as part of an exploratory project isolating possible therapeutic compounds from reptiles. Interestingly, it was later found that the G ila monster uses this hor mone to regulate growth of the entire pancreas during meals, because it only eats 5 10 times annually. Because of this, in addition to stimulating insulin secretion, it also stimulates growth of pancreatic exocrine tissue in humans. This is cause for conce rn because inappropriate pancreatic growth can cause blockages in pancreatic ducts, and has been shown to lead to pancreatitis and even pancreatic cancer
13 Fig u r e 1 9 : A Gila Monster and the XRC structure of Exendin 4, which is derived from its saliva These potential side effects, and therefore used of Exendin as a therapeutic is hotly debated however, its usefulness in studying GLP 1 pathways, and the role of cAMP in the islet is not, especially considering its advantages in shelf life and GLP 1R af finity. Despite the debate, cAMP regulators such as Exenatide and Sitagliptin, a DPP4 inhibitor, are very good potential drug targets. While they are generally used as secondary treatments to metformin, they lack the hypoglycemic risks associated with sulf onylureas and hepatitis risks associated with TZDs. Biosensors There are numerous commercially available [Ca 2+ ] i indicators. Generally, these d yes work by having an aromatic conformational change when binding to calcium, which results in a change in fluorescence properties. Carboxylic acid groups are esterified to an acetoxymethyl group, which allows the dye to permeate the cell membrane. Upon entering the cell, the abundant esterases remove this group, yielding the active dye and keeping it in the cell until more complex degradation occurs.
14 Fig u r e 1 10 : Schematic of staining a cell with an acetoxymethyl ester calcium dye These dyes come in a huge variety of available spec tra, but Fura 2 AM was used primarily, because it fluoresces in the ultraviolet spectra, which proves useful when trying to detect other things. It also has the ability to make ratio measurements, where ratio of 340nm/380nm emission is directly correlated to the intracellular calcium concentration, regardless of confounding factors. Unfortunately, t here is no similar ly effective small molecule biosensor to detect cAMP. One of the most common strategies employed to measure cAMP, as well as other second messengers is Forster Resonance Energy Transfer (FRET).
15 Fig u r e 1 11 : Jablonski diagram of FRET When there is a strong spectral overlap between the emission of one fluor ophore and the excitation of another instead of emitting a photon, the higher energy fluorophore will donate an exciton to the lower, which ultimately results in emission by the lower energy fluorophore. The quantum efficiency of this process has an r 6 relationship so it is very sensitive to distance. Fig u r e 1 1 2 : Spectral overlap of cyan fluorescent protein and yellow fluorescent protein
16 FRET is ideally suited to the spectral overlap of CFP and YFP. If the distance between these can be controlled b y a parent protein either by conformational change or translocation, FRET becomes a proxy for the parent proteins activity. Fig u r e 1 13 : Schematic of the conformational change motif in FRET biosensors EPAC1 an effector protein of cAMP, undergo a conformational change when bound to cAMP, have already been developed into several FRET biosensors. All use CFP and YFP at the termini. Fig u r e 1 14 : Amino acid sequence of ICUE2 a n EPAC derived, FRET based cAMP biosensor Mathematical Models Modeling in biology is a useful tool to develop understanding of phenomena and predict tests in a much quicker fashion than experiment. This practice has been common in physics for centuries. If a model is able to explain an experimental observation, there
17 a good chance the logic used to generate the model satisfactorily describes the biological system. The islet of Langerhans lends itself to modeling particularly well, because its dynamics can be described in a system of ordinary differential equations. Extensive work has been done on this subject. Some of the earlier work on this matter was developed by Chay & Keizer, now primarily known for the homonymous Chay Keizer model. This was a minimal model that includes only voltage regulated potassium channe ls, calcium activated potassium channels, voltage dependent calcium channels, and a forced glucose stimulated efflux of calcium from the cytosol. A large portion of beta cell physiology was still not understood at the time, but this model was able to produ ce the characteristic bursting and oscillations seen experimentally (Chay & Keizer, 1983) In a manner conforming to almost all mathematical models, this one was quick to draw criticisms for its inadequacies. Primarily, the model failed to include a glycol ytic handling component, even though calcium oscillations are generated by elevated intracellular ATP levels secondary to glucose metabolism. This portion of modeling has been larg ely developed by Bertram and Sherman who first introduced a model where the conductance of ATP dependent potassium channels varied with observed oscillatio ns in glycolysis, then later added a glycolysis handling module based on one developed for skeletal muscle phosphofruct okinase kinetics. (Bertram and Sherman 2004; Smolen, 199 5) These models fail to incorporate what is now the well established synchronized electrical behavior shown in both islets and be ta cell lines. A model was stablished and studied a model based on the previously described Bertram model which incorporated this network behavior (Benninger et al., 2008) In order to mimic natural cellular
18 heterogeneity, various properties of each cell, including electrical coupling conductance to neighbors, were randomly distributed in each cell. They found that the model pre dicted moving waves of calcium elevations, and corroborated this theory with experimental data. The model was also able to show that large networks of heterogeneous cells can still form a coordinated syncytium under multiple glucose conditions. Despite it s experimentally well documented role in augmenting insulin secretion most published islet and beta cell models c ompletely ignore cAMP signaling Ni et al. proposed a model to include this. In this model, they developed a coupled oscillator based off a Calcium/cAMP/PKA regulatory circuit. The model was successfully able to recreate the downstream effects of several ion channel inhibitors in greater detail than previous model s. They also predicted that the oscillatory response of PKA allowed for more complex downstream effects than simple activation. Fridlyand et al. also performed some computational analysis on th e effects of second messengers in beta cells, and focused the ir analysis on cAMP effects on granule docking. Even with limited information on the detailed mechanics of insulin granule docking, they were able to recreate familiar experimental outcomes of insulin secretion with this model based on some assumptions of cAMP effects on insulin granule trafficking and docking (Fridlyand et al., 2011) Even with these excellent models predicting cAMP effects at the single cell level there is scant published data on cAMP behavior in a network model l ike the one described by Benning er et al. Modeling the behavior of cAMP kinetics at the network level therefore is an opportunity to discover new mechanisms of islet physiology.
19 CHAPTER II MATERIALS AND METHODS Cell Culture The primary aim of this project was to investigate whether cAMP dynamics are coordinated in beta cell networks, and the effects that this may have on regulation of insulin secretion. MIN6 cells are a commonly used cell line originally developed by targeted expression of the simian virus 40 T antigen gene i n mouse insulinomas. They retained glucose stimulated insulin secretion and morphological characteristics of pancreatic beta cells. More importantly, they have retained gap junction coupling that is critical to studying network coordination. However, they do not retain MHC class 1 or class 2 expression that is critical for studying immunol ogical pathways underlying type 1 diabetes. More recently, it has been shown that some cells within clusters express glucagon and somatostatin, so it may be a better islet model than originally thought (Nakashima) MIN6 cells are grown in a special variant of DMEM that includes beta mercaptoethanol to promote clustering. MIN6 cells were first grown from DMSO solution liquid nitrogen stocks. Cells were centrifuged in Eppendo rf tubes, resuspended in fresh media, then plated on Corning Cell 3 days during growth. Cell growth and verification of proper clustering morphology was ex amined when media was changed. At 70% con fluence, c ells were released from the flask for splitting into larger flasks or plating for experiment by bathing a solution of 0.05% trypsin, incubating for 15 20 seconds, followed by repeated percussing of the flask until cells detached.
20 Gene Cloning, Transfection and Staining All Plasmid DNA used was currently available in the Benninger lab, but was initially acquired from generous donors or addgene.org. Plasmid DNA was transformed to a bacterial glycerol stock using commercially available competent e. coli cells. Competent cells were placed on ice with a solu tion of beta mercaptoethanol, LB broth, and the DNA of interest for 20 minutes. Next they were heat shocked at 42C for 45 seconds and placed back on ice for 2 minutes. The bacteria were then in cubated in LB broth for 45 minutes. Finally, the bacteria were plated on LB agar plates and incubated overnight. All plasmids used in these experiments contained antibiotic resistance to ampicillin. Agar plate colonies were incubated in LB broth overnight, and then stocked at 80C in a 50% glycerol solution. Prior to experiment, LB broth was inoculated by the appropriate glycerol stock and incubated a shaking incubator for 16 hours. P lasmid DNA was purified from the broth using the QIAGEN minispin prep. Th is procedure uses a series of buffers to lyse the bacteria, remove cell debris, then purify all plasmid DNA in a miniature chromatography column powered by centrifuge. The concentration resulting DNA product was measured using a NanoDrop spectrophotometer. Purity was verified using the ratio of the absorbance at 260/280nm For cAMP imaging, 2 days prior to experiment cells were transfected using the reagent Lipofectamine 2000 (Life Technologies) and 250 ng ICUE3 lyn DNA per well. Sterile, serum free, antibiotic free media was used for transfections. Conical microcentrifuge tubes were prepared first with Lipofectamine and the DNA separately, and left to sit for 5 minutes, per manufacturer recommendations. They were then
21 combined, an d agitated to promote DNA loading, and incubated for 30 minutes. then incubated for 48 hours in the prepared transfection media. Following this period, cells were examin ed for adequate expression and health before proceeding. I mmediately prior to calcium imaging cells were stained with 2 micromolar Fura 2 AM for 45 minutes. Cells were then examined for glucose responsiveness before proceeding further with experiments. Mi croscopy As described previously MIN6 Cells were removed from culture flasks and plated on 8 well chamberslides with #1.5 coverglass (LabTek) and allowed to form clusters. For imaging, cells were immersed in BMHH imaging buffer with 1% bovine serum albumi n. A solution containing 20 mM glucose was used to stimulate MIN6 cells. 20 mM tetraethylammonium was also used to trigger cell depolarizations. Cells were imaged on an epifluorescence microscope through a 0.75 NA/20X Plan Apo objective. Images were genera lly taken that attempted to maximize the number of expressing cells within the field of view but observation of active calcium oscillations was also used to select which images to acquire MIN6 Cells were excited at 430/24 nm and emissions at 470/24 nm a nd 530/24 nm were captured, representing CFP excitation, CFP emission, and YFP emission, respectively. Fura 2 has ratiometric imaging capability to determine absolute concentrations, but only 380 nm excitation was used 340 nm excitation was skipped to improve temporal resolution and because absolute concentrations were of secondary interest to qualitative temporal dynamics Frame rate was generall y limited to 0.33/s by
22 the speed of filterset changes and acquisition times. To maximize signal, the ratio of CFP emission to YFP emission is used to analyze FRET. Image Processing Expressing cells were analyzed individually using the imfreehand function in roipoly so that it could be removed in analysis. The average pixel value over the background signal region was subtracted from the entire image and resulting negative pixels were reduced to zero Fig u r e 2 1 : FRET channel image with an expressing cell in an imfreehand ROI and a b ackground region in an roipoly ROI The signal from each acquisition channel from the entire region of interest was then averaged, and a linear photobleach correc tion was applied. The final CFP/YFP ratio (FRET/cAMP) and Fura 2 (Calcium) signals were then normalized and compared.
23 Before experiments were conducted, four bi osensor opti ons were explored ICUE3, ICUE3 lyn, EPAC cAMPS, and jEPAC escribed previously, a l l involved the same CFP/YFP concept but were constructed slightly differently. To verify the response of the biosensors, cells were prepared as described previously, omitting the calcium dye step. During FRET imaging, cells were bathed in imaging solution with mixture of IBMX and forskolin. IMBX inhibits phosphodiestera ses, enzymes that degrade cAMP, and forskolin activates adenylyl cyclases. Each cell imaged was examined both for its response to an increase in cAMP with addition of IMBX / forskolin, as well as it s response to a washout of IBMX/forskolin with normal imagin g solution. Fig u r e 2 2 : Verification of FRET response and suitability Left) Normalized FRET signal after addition of IBMX/Forskolin. Solution was added at time indicated by arrow Right) Normalized FRET signal after washout of IBMX/Forskolin. Null solution added at time indicated by arrow. This procedure was repeated several times for each biosensor. ICUE3 lyn was accepted because it was able to show a consistent response with good temporal resolution, but was selected primarily because its plasma membrane localization allowed expressing cells to be more easily distinguished at lower levels of expression. Overexpression is a concern because there is a possibility of quenching cAMP signals due to binding the biosensor.
24 Matlab Analysis Images were processed into calcium and cAMP signals as previously described. Once these signals were gathered, their relationships were a primary interest of this project. The following represents an example of two cells in the same cluster for the purposes of explain ing this analysis. Fig u r e 2 3 : Example of processed images Left) CFP excitation/YFP emission channel, with two expressing cells seen on the upper right Right) Normalized FRET and Fura 2 signal s from each cell seen on the right To analyze the degree to which these signals were coordinated, the normalized cross correlation of the calcium and cAMP signals was taken within each expressing cell The cross correlation was also taken between like signals of all possible pairs of expres sing cells. For continuous functions f and g the cross correlation is defined as : Equation 1: The cross correlation function
25 Fig u r e 2 4 : Example of cross correlations calculated from timecourses in figure 17 Left) Normalized cross correlation of calcium signals Right) Normalized cross correlation of cAMP signals While a great deal of information can be extracted from the cross correlations, t he most interesting part of the cross correlation is the maximum value especially for the purpose of this project. The maximum represents where, and to what degree the signals overlap the best. Maximum values exceeding 0.75 to 0.8 for calcium signals can be considered to be highly coordinated, where if the signals were examin ed visually they are not very distinguishable. It usually indicates that all depolarization events occur in a very synchronous manner. The maximum value will decrease as depolarization events become less linked across the timecourse. A cross correlation re presenting strong coordination of cAMP is not as well defined, because cAMP coordination has not been as thoroughly investigated. The degree to which the maximum deviates from the exact middle of the cross correlation vector is known as lag. This will also be examined later. Modeling and Simulation To deepen understanding of the pro cess underlying this behavior, an in silico model was developed in Matlab. Previously developed code was used to mode l glucose
26 handling, which, like a real cell, simulates cell depolarization via closure of kATP channels and the resulting effects on calcium handing This model was first investigated at the single cell level. The initial condition s were randomly seeded and enough simulations were run to match the sample size of experimental data. Figure 2 5: Model Schematic All simulations were systems of initial value ode15s function. This is a variable order pseudo variable step solver specifically suited to solving stiff initial value problems. The original Bertram and Sherman model was not stiff, but addition of cAMP handling created stiff conditions not suitable for more traditional solvers Ode15s is based off of order 1 5 which are geared toward stiff problems :
27 Equatio ns 2 6 : Backward difference formulas of order 1 5 like those used in ode15s equations. For each step, an estimate of the error is made, in this case it is on the order of the step size to the power of the order of the backward difference formula used. 1 st order is preferentially used, but when the error estimate is large, the solver advances to larger orders until error is reduced t o an acceptable level. The solver also allows for changes in step size, but generally uses a constant step size. The Matlab code used for the model is included in an appendix. The equation used for membrane potential is: Equation 7 : Membrane potential The right hand side includes a value for membrane capacitance; the left hand side includes all ion currents handled by this model. I K is a voltage dependent Potassium current, I Ca is a voltage dependent calcium current, I K(Ca) is a calcium activated potassium current, and I K(ATP) is an ATP sensitive potassium current. These current s are described by the following equations : Equation s 8 11 : Equations for ion channel currents
28 g Ca and g k are constant conductances for these types of channels g K (Ca) and g k(ATP) are represented by the following equations: Equation 12 13 : Equations for channel conductances In equation 12 being a calcium dependent channel, this conductance is an increasing sigmoidal function of cytosolic calcium concentration. The remainder of the se equation s represent the difference between the cell voltage and the resting potassium voltage, or the absolute voltage driving this current. Calcium levels were handled assuming a constant fraction of free to total cytosolic calcium (0.1) and using the combination of fluxes from both the plasma membrane and the endoplasmic reticulum. g k(ATP) is dependent on a normalized conductance function for this type of channel, which the foundation for this models link between voltage behavior and glucose metabolism (Magnus and Keizer, 1998): Equation 13: K ATP channel conductance function Going back to equation 8 and 8 the terms n and m are defined by the following:
29 Equation 1 5 17 : Additional conductance functions for voltage gated potassium and calcium channels N is an arbitrary I k activation variable, where n is a time constant activation is not considered instantaneous and is the equilibrium value of n as a function of V described in equation 16. Equation 17 describes the equilibrium function for VDCC activation. The time dependent equation s describing free cytosolic calcium are : Equation 18 22 : Free cytosolic calcium equations where, in equation 18 f cyt is the fraction of free to total cytosolic Ca 2+ J mem is the Ca 2+ flux across the plasma membrane, and J er is the Ca 2+ flux out of the endoplasmic reticulum The membrane flux includes contributions from the plasma membrane calcium ATPase (PMCA), which removes calcium from the cytosol, and the flux contribution from the voltage dependent calcium current. The ER component included a constant (SERCA). The metabolic component of the model was modified from an earlier model for glycolytic oscil lations in muscle extracts (Smolen et al., 1995). The key player in producing oscillations is the Smolen model is the oscillations in the allostery of
30 phosphofructokinase. The metabolic portion of the model consists of the following equations: Equation 23 26 : Equations describing glycolytic handling for nucleotide concentrations where, in equation 23 and 24 G6P represents glucose 6 phosphate, FBP represents fructose bisphosphate, and R GK R PFK, and R GPDH are the catalytic rates for glucokinase, phosphofructokinase, and glycerol 3 phosphate dehydrogenase, respectively. Fructose 6 phosphate is assumed to be in equilibrium wit h glucose 6 phosphate. The glycerol 3 phosphate dehydrogenase reaction rate is dependent on fructose bisphosphate concentration. The PFK reaction is regulated by the binding of activators, AMP and FBP, and an inhibitor, ATP. The equations describing this a re iterative, and therefore very lengthy. Therefore, they can be found in the appendix as Matlab code and are commented concentrations are described by the following: Equation 27 28 : Rates of adenine nucleotide changes The cAMP portion of the model was taken from an earlier model without complex glycolytic bursting modes (Ni et al., 2011). cAMP concentrations were handled
31 as the sum of adenylyl cyclase and phosphodiesterase flux contributions. Adenylyl cyclase activity was modeled using Michaelis Menten kinetics of the adenylyl cyclase 6 isoform and is dependent on intracellular calcium concent ration. Phosphodiesterase rates were modeled as the sum of simple first order degredation with respect to cAMP (Equation 30 ), and simplified calmodulin de pendent degredation (Equation 31 ), where calmodulin actively bound by 3 or 4 calcium ions participates in phosphodiesterase activation ) Equation 29 32 : Equations describing cAMP behavior A significant part of the addition to this model, t he relationship between cAMP and calcium was completed through PKA. PKA which was used to modulate the flux of calcium through the plasma membrane j mem in equation 18 PKA was h andled using the fact that four cAMP molecules bind to PKA to trigger Upon binding 4 cAMP molecules, each catalytic subunit is released one at a time, so concentrations of active PKA, P KA with one catalytic subunit attached, and just a regulatory subunit are handled in this module.
32 Equation 33 37 : Equations describing PKA behavior As the primary addition to this model, simulations of the previously described model were carried out in coupled netwo rks in order to mimic the coordinated nature of insulin secretion. To investigate net work coordination of the 2D MIN6 cell network five by five networks were generated. Each cell in the network was assigned a number from 1:25 in order to be handled as a v ector in Matlab, and coupling relationships were generated based on this. For example cell 1, in the top left corner of the following figure 2 6 is coupled to cell 2 to the right of it and cell 6 below it These relationships were maintained as a binary a rray of contacts. That is, row one of this array contains a 1 in column 2 and column 6, and zeros elsewhere. The coupling conductances associ ated with each coupling relationship were then randomly generated prior to each simulation ( Diago nal coupling relationships were not considered. Fig u r e 2 6 : Schematic of network simulation geometry To drive these relationships, an additional factor, I coup was included in equation 6 describing membrane voltage I coup was simply calculated as the randomly generated coupling conductance for the particular cell couple, multiplied by the difference in
33 voltage. In the analysis of these simulations, 5 random cells were selected with each initialization to mimic the nature of transient transfection. Equation 38 : Calculation of electrical coupling currents Microfluidics Microfluidics have proven useful in the past to expand the capabilities of imaging experiments on actively insulin secreting islets. The small channel features inherent in microfluidic devices particularly allow for investigation of the step responses of islets to changes of solution. There are a myriad of possible targets of investigation, from glucose concentrations to ion channel blockers. In one particular example, it was shown that calcium oscillations will propagate from regions of high glucose concentration towards regions of low glucose concentration (Benninger et al., 2008;Rocheleau et al., 2006 ) In general, microfluidics are manufactured using photolithography. A photoactivatable polymer, SU 8, is spin coated onto a silicon wafer substrate, and covered with a photomask and exposed to UV radiation, then cured to produce permanent features. This requires a clea nroom, and equipment that is often not available at a biomedical research facility. In order to address the need to develop microfluidics easily, and without the need for a cleanroom facility, methods to use 3D printing to manufacture microfluidics were in vestigated Previously used device designs were used, as well as patterns to determine the functional resolution of the 3D printer for this application; lines of varying heights, widths, and spacing were used for this.
34 Fig u r e 2 7 : Example of SolidWorks microfluidic master destined for 3D printing While a working device was made, the application of this method proved to be limited, because features generated from the 3D printer deviated from designs due to issues with resolution, and the way that 3D printers deposit material. Channels tended to be two, or even three times wider than intended. More intricate features than channels are therefore nearly impossible to generate. However, over time the resolution of this technology will certainly improve, and may even play a leading role in prototyping microscopic technologies. Fig u r e 2 8 : Confocal images of a microfluidic generated from a 3D printed master
35 The fact that insulin shows oscillations at the whole body level in response to glucose elevation raises the question as to whether inter islet signaling plays a role in this. While it is generally thought that innervation plays a role in this coordination much is still not understood about this behavior that is seemingly critical to proper peripheral response to glucose. In addition, casual observation of neighboring islets have shown them to be coordinated with each other, and of course, these are not in nervated. In an effort to address the need fo r clarifying this, a microfluidic device was made that allows islets to be arranged in series, and simultaneously imaged. The traditional photolithography method was used to make this device. Data is still bein g collected. Fig u r e 2 9 : Photograph of a silicon master of a microfluidic device prepared with SU 8 photolithography Optogenetics Currently a very hot topic in the field of neuroscience, optogenetics are starting to be explored in the islet of Langerhans; naturally so, their electrical behavior has resulted in deriving many experimental practices from neuroscience. As the name implie s, optogenetics is the practice of introducing light activated protein function in
36 genetically defined cells The attractive thing about this is that no stimuli can be controlled as precisely as light. The most commonly used optoge netics are from a family of channel rhodo ps ins, which are derived from their original purpose as sensory photoreceptors in unicellular green algae These are cation permeable channels that open in response to light. However, for the purposes of this thesis, working with an optogene tic construct that can mimic the pathway of GLP 1 is more useful. Deisseroth et al. developed a family of optogenetics to be used for non ionic second messengers, and one of them, Opto 2 AR, generates cAMP. Fig u r e 2 10 : Schematic of the optogenetic con struct Opto 2 AR Opto 2 AR, as shown above, was generated by removing the 4 intracellular segments of the seven transmembrane domain receptor Rhodopsin, which is responsible for transducing light signals in the eye. These intracellular segments were replaced with 2 adrenergic receptor. The result is a complex that has been shown to elevate cAMP in HEK cells upon illumination with a CFP filterset. Unfortunately, having to use CFP illumination to activate this construct pr ohibits the ability to use a CFP/YFP FRET construct to detect cAMP when the construct should be left inactive. An alternative construct is used in this case. This construct was developed by Tengholm et al, and was developed to improve dynamic range of cAMP signals when used with a Total Internal Reflection Fluorescence (TIRF) system. Additional contributions on my part were made s o that this construct can be used on epifluorescence and confocal microscopes.
37 Fig u r e 2 1 1 : Schematic of the translocation CFP CAAX YFP CFP YFP utilizes the fact that PKA dissociates from its regulatory subunit in the presence of elevated cAMP. Very simply, under low cAMP conditions, the regulatory and catalytic subunits remain bound, and YFP is localized to the membrane. Under high cAMP conditions, YFP dissociates to the cytosol, and greatly reduces signal in a TIRF system. Fig u r e 2 12 : Example of images obtained from a TIRF system using the translocation CFP YFP
38 CHAPTER III CELL MODEL CELL LINE [ cAMP ] Dynamics in Glucose Stimulated MIN6 Cells One of the initial objectives of this project was to confirm that the nature of the c AMP dynamics observed were in reasonably close agreement with published data and possibly develop deeper insight Detecting cAMP oscillations in vivo was obviously paramount to further describing the relationship between cAMP, insu lin release, and ultimately glucose homeostasis. Fig u r e 3 1 : Concurrent imaging timecourses of Calcium and cAMP within a glucose stimulated MIN6 Cell As described previously by Dyachok et al., it was observed that in glucose stimulated beta cells, cAMP oscillations develop in an antiphasic manner to calcium oscillations. Expanding on this, cAMP appears to take a skewed triangular waveform,
39 with gradual elevations followed by rapid degradation occurring during cell depolarizations. This type of waveform was very consistent throughout all experimental runs. However, under some circumstances this synchronization between calcium and cAMP was broken. Occasionally, cAMP elevations would plateau before depolar izations, presumably because a maximal concentration was reached. The other inconsistency found was that cAMP degradation did not always occur during a depolarization. While a ready made explanation for these inconsistencies, the ramifications of them will be discussed later. Effects of GLP 1 Analog on [cAMP] and [Ca 2+ ] Dynamics As highlighted previously, Exendin 4 is an analog of GLP 1, which activates a G stimulatory pathway in beta cells. Naturally, the expectation was to observe alterations in cAMP dynamics in cells treated with Exendin 4 Several observations were found quickly from qualitative analysis of imaging timecourses. Fig u r e 3 2 : Concurrent imaging timecourses of Calcium and cAMP within a glucose and Exendin 4 stimulated MIN6 Cell
40 First, rather than the quick depolarization/repolarization events that are typically observed in MIN6 cells stimulated by glucose alone, calcium waves are significantly protracted in cells treated with Exendin 4. In fact, these calci um waves much more closely mimic calcium waveforms observed in primary tissue derived beta cells. These calcium waves also appear to process in a much more regular manner. Calcium depolarizations observed in MIN6 cells treated with glucose alone often appe ared to be highly irregular and random events, where calcium waves in Exendin 4 treated cells develop a more predictable period. Finally, and perhaps most importantly, depolarization more consistently resulted in simultaneous cAMP degradation. Effects of [cAMP ] Elevation within Single Cells Under conditions of glucose stimulation in healthy individuals, beta cells within the islet of Langerhans coordinate together to produce well synchronized calcium waves which coordinate pulsatile insulin secretion. W hile the uncoordinated beta cell is an ineffective mediator of glucose homeostasis, the behavior at the single cell level is the basis for what ultimately drives the behavior of the entire network. Insulin secretion, in particular insulin vesicle exocytosis, occurs with intracellular calcium as the primary driving factor. Therefore, the duration of calcium elevations is a major determinant in the overall amount of insulin release. Again, q ualitative observations on the nature of th is were quickly observed during image analysis, as shown most recently in figures 26 and 27. In order to quantify the relationship between incretin hormone stimulation and this phenomena, calcium signals of exendin 4 treated and untreated cells were analyz ed an compared The first qualitative observation that Exendin 4 treatment mediates
41 calcium duty cycle protraction was used as the basis for quantifying the effect, shown in figure 28. Fig u r e 3 4 : Comparison of Calcium Duty Cycle by Exendin 4 treatment (p=0.00037) The duty cycle was calculated as the fractional period during which normalized calcium signals were above half their maximum. Under Exendin 4 treatment, this value is estimated to be 2.9% to 9.5% larger than in when untreated at the 95% confidence level. Using a Welch t test assuming unequal differences, t his dif ference was found to be highly significant with a p value of 3.7e 4. actual islets response to glucose stimulation, a fe w reasonable conclusions can be made. Most importantly, if a cell initiates depolarization, increase duration of the depolarization improved the probability that the depolarization will be communicated with its neighbors through gap junction coupling.
42 Movi ng on cAMP signals have been shown to be antiphasic to calcium signals. Observation of experimental data does not show that this is a strict link, as often depolarizations do not result in rapid cAMP degradation, shown again in figure 29 The role of the synchronization between calcium and cAMP has not been well established. Fig u r e 3 5 : Calcium and cAMP timecourses in a single cell. Arrow highlights proposed disconnect between these signals. In order to clarify the role of this relationship, t he maximum negative cross correlation value between calcium and cAMP in individual cells was taken ; Due to the established antiphasic nature of these signals positive cross correlations were assumed to be erroneous. Antiphasic Calcium/cAMP synchronization wa s greatly enhanced by Exendin 4 treatment by an estimated 5.7% to 18.9% at the 95% confidence level (p=2.6 e 4). this synchronization is controlled by incretins, and there fore plays a role in elevating insulin exocytosis.
43 Fig u r e 3 6 : Comparison of Calcium/cAMP antiphasic synchronization by Exendin 4 treatment (p=0.00026) Given the strong relationship between incretin stimulation and therefore adenylyl cyclase activa tion on both of these metrics, it was anticipated that there would be a relationship between the synchronization of calcium and cAMP, and the duty cycle of calcium. This relationship was established using a simple l inear model as shown in figure 3 7.
44 Fig u r e 3 7 : Linear model of Duty cycle vs intracellular Calcium/cAMP Synchronization with 95% confidence intervals ( p=6.2e 6;R 2 =0.2 ) By appearance, there is a rough relationship between duty cycle enhancement, and the antiphasic Calcium/cAMP signal behavior. However, it explains the var iance in duty cycle much better than exendin 4 treatment alone (R 2 =0.2 vs 0.12 ). It now stands to reason that this antiphasic synchronization behavior serves to mediate duty cycle protraction. While both extremes are not observed, t his simple linear relationship es timates that a fully synchronized cell is electrically active an additional 23% of the time, w hen compared to an uns ynchronized cell. roughly translates to a 2 3 fold increase in insulin exocytosis.
45 Effects of [cAMP] Elevation on Coordinated Cell Networks While insulin secretion modulation occurs at the cellular level, insulin is secreted by the islet, therefore we need to consider beta cell function at the network level.T he effects on a coordinated cell network are much more pronounced and therefore play a closer, more direct role in the a ctual mediating of glucose homeostasis Similar methods as described in the previous section were used to analyze the role of cAMP dynamics on the behavior of coord inated beta cell networks. Of primary interest was the effect of cAMP elevation on the pul satile coordination of insulin secretion in the beta cell network. Calcium signals were used as a proxy insulin secretion. Strictly speaking, insulin secretion depends on both calcium and cAMP, but investigating how cAMP impacts calcium dynamics because ca lcium is the primary triggering signal. For each set of images, all ICUE3 lyn expressing cells were analyzed, and all possible pairwise cross correlations of calcium signals were taken.
46 Fig u r e 3 8 : Distributions of pairwise calcium cross correlations by Exendin 4 treatment ( p=8.4e 6) Figure 32 illustrates significant enhancement in calcium coordination between treated cells test assuming unequal variances yields a p value of 8.4x10 6 While this value has little physical significance, the e stimated improvement in calcium signal cross corre lation lies somewhere between .099 and .24 7 at the 95% confidence level Again, using calcium as a proxy for insulin secretion, this roughly translates to a 50% im provement in the coordination of insulin secretion. Improvement in coordination r esults in improved islet pulsatility. This behavior is critical because a lack of coordination results in diminished pulsatile release, an d ultimately insulin intolerance. Conversely improved coordination can drive inter islet behaviors that ultimately render a more effective physiological response to peripheral tissues particularly the liver coordination of cAMP oscillations. Expo unding on this may reveal previously missed insight on the nature of insulin release. Experimentally, pairwise coordination of cAMP oscillations is readily observed in some cells, but the link overall appears to be poor compared to calcium coordination. Th is is consistent with a theory that cAMP
47 Fig u r e 3 9 : Distributions of pairwise cAMP cross correlations by Exendin 4 treatment ( p =0.0019 ) As with calcium, cAMP signal cross correlations were compared between Exendin 4 treated and untreated cell clusters. Overall, cAMP cross correlations are lower than calcium cross correlations, but it is important to remember that the cAMP signal power is s ignificantly lower, and the oscillations are generally broader and less descript. The same comparison between Exendin treatments shows a more modest improvement in cAMP coordination than with calcium. The mean improvement in cross correlation lies somewher e between .033 and .144 at the 95% confidence level. How this improvement arises remains unclear, because it may be directly due to improved calcium coordination, which drives cAMP oscillations at the single cell level, or it may be due to a yet undiscover ed mechanism such as a cAMP permeable gap junction or a paracrine signal In order to investigate how cAMP coordination may arise, a linear model between pairwise calcium cross correlations and their concomitant cAMP cross correlations was developed.
48 Fig u r e 3 10 : Regression of pairwise calcium cross correlation vs pairwise cAMP cross c orrelation ( p=2.2e 16 ) Calcium coordination and cAMP coordination between cells was found to be highly correlated (R 2 = 0.4045, p=2.2e 16). The sl ope of this linear model is 0.87 and this probably provides a clearer picture for how well linked these oscillations are. Based on this model, cAMP coordination appear s to be dri ven by calcium coordination, where the connection is imperfect and the link breaks down from cel l to cell. Given the observed link between calcium and cAMP at the single cell level, and a fairly well developed theory behind intracellular cAMP oscillations, this relationship was expected at the network lev el. However, something that is not trivial is whether GLP 1R stimulation improves the link between calcium and cAMP at the network level. Another linear regression was developed, this time including a term for Exendin 4 treatment.
49 Fig u r e 3 11 : Regression of pairwise calcium cross correlation vs pairwise cAMP cross c orrelation by Exendin 4 treatment ( p=2.2e 16 ) The R 2 f or this model improves a decent amount to 0.45. The multiple linear regression coefficients for this model result in an estimated slope of 0.63 for untreated cells, and 0.85 for treated cells. T here is a clear distinction between the two groups in this model, and as seen in figure 35 the esti mated relationship between calcium and cAMP approaches, but does not reach 1:1 in Exendin 4 treated cells. Exendin 4 treatment not only results in improved intracellular calcium/cAMP synchronization, but also improves synchronization between the two second messengers at the network level. In other words stimulation of the incretin hormone pathway results in both increased insulin release, and increased network wide synchronization of calcium and cAMP. G iven what is known about calcium and cAMP roles in ins ulin granule docking, it stands to reason that improved calcium / cAMP synchronization at the network level plays a role in elevated insulin se cretion and pulsatility (Idevall Hagren et al., 2010)
50 Intracellular Relationships Underlie Network Behavior Expanding on this, as well as going back to what is happen ing at the single cell level, it was next explored how well intracellular synchronization of calcium and cAMP predicted network coordination. Fig u r e 3 12 : Regression of pairwise calcium cross correlation vs pairwise mean of intracellular calcium/cAMP cross correlation ( p=7.9e 8 ) In order to do this, the cross correlation between the calcium and cAMP imaging tim e courses from individual cells, as described in the previous section, were averaged pairwise. Because of the well defined range of cross correlations, this average was simply taken as the mean between the two. No problems appeared to arise from this methodology. Despite the fact that this regression was not anticipated to produce a signi ficant result based on qualitative observation or current physiological explanation for this behavior, it surprisingly produced a highly significant result. The estimate of the slope of this relationship is 0.72, with an R 2 value of 0.18. Not only is it tr ue that c ells
51 that are more internally coordinated tend to be more electrically coupled to their neighbors but synchronization between calcium and cAMP at the single cell level seems to be a critically important mediator of network calcium coordination, a nd therefor pulsatile insulin secretion! Next, the same thought process was tested for cAMP network coordination, in the same manner. As shown in figure x, cAMP coordination also appears to improve with internal coupling, but like the effect of Exendin treatment on cAMP coordination, the result is much less dramatic. Fig u r e 3 13 : Regression of pairwise cAMP cross correlation vs pairwise mean of intracellular calcium/cAMP cross correlation (p=1.3e 5 ;R 2 =0.12 ) The slope of this relationship drops from 0.72 with calcium to a paltry 0.43. This lends further credence to the theory that cAMP oscillations and coordination is driven by calcium oscillations and coordination. Similar behavior is seen in both, but for the case of cAMP, fidelity is lost compared to calcium in almost any manner of anal ysis.
52 Finally, to investigate the possibility of interaction or mediation between the previously discussed metrics, a full multiple linear model for calcium cross correlation was regressed from all pr ior metrics using a stepwise Akaike information criterium (AIC) selection algorithm in R. Exendin treatment was included as a binary factor, so the estimate is the total estimated improvement in calcium cross correlation on treated cells. The resulting parameter estim ates were very similar to what was found using simpler models. Table 1: Parameter estimates for multiple linear regression of calcium cross correlation Parameter Estimate cAMP Coordination 0.73 Exendin Treatment (binary) 0.07 Calcium/cAMP Synchronization 0.29 The overall fit of this model was very good, with an R 2 of 0.475. There was nothing game changing about the parameter selections, with the only parameter left out being the effect modification of Exendin treatment on cAMP coordinatio n. The parameter estimate on the mean calcium/cAMP synchronization was reduced substantially, but its effect is still highly significant, and a stricter selection cut off would have removed Exendin treatment from this model before this parameter.
53 Addi tional Metrics and Control of Result Confounding While the previous results are seemingly signi ficant and meaningful, there were a account for cluster geometry and the loc ation of transfected cells. Distance between cells was used to control for this; given the large number of samples taken, it was assumed that effects of cell connectivity would be sufficiently captured by the pixel distance between ROIs even though this b ehavior is much more complicated in reality Fig u r e 3 14 : Regression of pairwise calcium cross correlation vs pairwise distance between cells (p=2.2e 5;b= 2.8e 4;R 2 =0.11) One of the reasons this test was done was as a sanity check. Calcium coordination inconsistent with distance would be cause for concern. Fortunately, this model behaves as expected based on more rigorous theories of beta cell networking (Hraha et al., 2014) and an R 2 of only 0.11 leaves a lot of additional variance available for explanation by other factors like those examined previously. More importantly
54 however, including pair distance in an AIC selection algorithm changes p values and parameter estimates of those o The same investigation was then applied to cAMP. Unlike for calcium, there was a little more to be gained from this than a sanity check, because theory behind cAMP c oordination has not been as well developed as with calcium coordination. Fig u r e 3 15 : Regression of pairwise cAMP cross correlation vs pairwise distance between cells (p=3.7e 7;b= 2.4e 4;R 2 =0.16) cAMP coordination vs. distance regressed with a very similar slope to calcium, whi ch was mildly unexpected. It appears while the overall distribution of cAMP coordination is lower, the decreasing trend in coordination over distance appears to have a very close relationship to the trend with calcium. The R 2 for this model is slightly bet ter at 0.16, but the variance of cAMP cross correlations is much lower to begin with.
55 R estricting the Dataset Retains Results The quality of signals was also a concern. Given the nature of experiment, a significant portion of the calcium and cAMP signals analyzed were noisy, and resulted in cross correlations with maximum values different from direct overlap. Naturally, significant qualitative analysis was only drawn from the best imaging timecourses. Therefore, Cell Cell Coordination was also exa mined removing data points containing cross correlation lag. Lag is defined as the deviation, in indices, that the maximum cross correlation has from the center of the cross correlation vector. First, the relationship between calcium cross correlation lag and cAMP correlation lag was examined. Fig u r e 3 16 : Regression of pairwise calcium correlation lag vs cAMP correlation lag of the same pair (p=0.001;R 2 =0.06) Calcium cross correlation lags were associated with cAMP cross correlation lags at a significant level (p=0.0018). This reduces concerns of erroneous cross correlations, and advances the idea that non zero cross correlation lags are produced by regular sig nals
56 that happen to overlap better out of phase. Cells that are sufficiently fa r apart yet are still coordinat ed may also produce this effect. The very mild relationship is not concerning, because most of the data points are very centrally located, and pro vide little leverage to the regression. Fig u r e 3 17 : Distributions of pairwise calcium cross correlations by Exendin 4 treatment with cross correlations containing lag removed (p=0.007) The same result is produced with this data set as with the full data set despite significant reduction in sample size Both control and treatme nt show improved coordination. However, t he result is especially dramatic with 75% of E xendin treated cells having a cross correlation greater than 0.8, which is generally cons idered to be an indicator of excellent coordination
57 Fig u r e 3 18 : D istributions of pairwise cAMP cross correlations by Exendin 4 treatment with cross correlations containing lag removed (p=0.009) Removing cross correlations with lag also produced the same r esult for cAMP signals This result is not qui te as dramatic as with calcium, but both groups also show significant improvement with the reduced dataset and again the improvement in treated cells appears to be slightly better. However, even with E xe ndin treatment, it still appears that cAMP coordination is not as robust as calcium coordination. Again, this could be due to the characteristics of the cAMP signal, but observation of imaging timecourses does indicate a generally poorer link.
58 Fig u r e 3 19 : Linear regression of calcium cross correlation vs cAMP cross correlation with cross correlations containing lag removed (p=0.003) Calcium and cAMP are still significantly coordinated when removing lag data. The slope of this relationship has reduced somewhat, but that appears to be because a significant portion of poorly correlated signals have been removed, as expected. Along the same lines calcium coordination appears to have improved more than cAMP coordi nation, which also reduces the estimate of slope The reduced R 2 can also be explained by the removal of low calcium /low cAMP data, which were more clustered than these data.
59 Fig u r e 3 20 : Linear regression of calcium cross correlation vs cAMP cross correlation with cross correlations containing lag removed (p=0.01;R 2 =0.17) Again, inclusion of non zero lag data does not appear to have confounded the result that calcium coordination is improved by a more robust intracellular connection betwee n calciu m and cAMP. Similarly to the previous figure, t he only noticeable differences is that there are f ar fewer low calcium coordination values and some fewer calcium/cAMP synchronization values. However, the summary here is that while calcium coordination can b e strong in the absence of intracellular synchronization, poor calcium coordination is not observed with strong intracellular synchronization, so even with In my opinion, this is an improved result, where the full dataset does contain data of poor calcium coordination and strong intracellular synchronization.
60 Fig u r e 3 21 : Linear regression of calcium cross correlation vs cAMP cross correlation with cross correlations containing lag removed (p=0.06 ;R 2 =0.1) This model supports evidence that cAMP coordination is also improved by a strong antiphasic synchronization because the positive trend is still present but is not significant at the 95% confidence level. In my estimation, significant reduction in sample size, coupled with naturally less coordinated cAMP signals, and generally poorer cAMP signal quality ultimately led to this, and it is not a cause for concern. A final identified concern was that individual clusters of cells may have naturally better or worse activity or coordination, and that clusters with more transfected cells present would apply a larger effect on the prior statistics. A repeated measures mixed model jumps out as the most appropriate way to include the effect of cluster. That is, the same linear models were made with the full data set, but including which cluster the pair belonged to as a repeated measure. Of course, for the models that just used t tests,
61 depen dent measures t tests were used instead. The statistics discussed previously are contained in the following table, rather than recounting the analysis for a third time. Treating Clusters as Repeated Measures Retains Results Table 2 : Summary of repeated m easures models Model P Value Estimate of Slope Calcium Correlation~Exendin.Treatment 0.0089 N/A cAMP Correlation~Exendin.Treatment 0.165 N/A Calcium Correlation~cAMP.Correlation 2.2x10 16 0.85 Calcium Correlation~Intracellular Synchronization 2.2x10 16 0.96 cAMP Correlation~Intracellular Synchronization 2.2x10 16 0.53 The results of these models are remarkably similar to the simple models, even more so than expected from casually observing that some clusters that appeared to be better coordinated than others. In fact, there even appears to be an improvement in some mean intracellular synchronization between calcium and cAMP, which is now nearly 1:1. Curiously, cAMP correlation is no longer significantly altered by Exendin treatment. Initially this was concerning, but results discussed in the next chapter bear singular resemblance to this result.
62 CHAPTER IV RESULTS: IN SILICO MODEL PREDICTS CAMP PROVIDES IMPROVED NETWORK C OORDINATION BY INCREASING INDIVIDUAL CELL OSCILLATORY ROBUSTNESS While the experimental results provide good insight in the behavior and responsibility of cAMP oscillations and coordination in beta cell networks, the linear models generated ar e useful for clarifying data and advancing hypotheses, but not sufficient t o ful ly explain the underlying mechanisms. Simulations fill this gap, because the results of them are easily traced back to the original methodology of coding. Experiments are easil y modified and evaluated by changing parameters and the equations that describe relationships. A similar statistical approach is taken in this section as the previous one, and in some cases the p values reported are extreme due to low variance in simulatio ns. However, this is simply to report output from the statistical package, R, and not to imply elevated confidence in the value. P values of less than 0.05 are taken to be significant in all cases. Single Cell Model Predicts [cAMP] dependent Duty Cycle a nd Stability In the following results, a model was generated from previously published b eta cell models by Bertram and Sherman for glucose handling and calcium oscillations, and by Ni et al. for cAMP and PKA handling. Initial conditions were randomly seeded using the normrnd() function in Matlab to generate heterogeneity in these simulations. The parameter for the maximum conversion rate of adenylyl cyclase (Vmax) was used as a proxy for GsPCR hormone stimulation. Init ially, modeling was commenced in an attempt
63 to mimic results through validation and reiteration. However, the first compilation was able to reproduce most of the trends observed in vivo. Results include related results from experimental data for reference when applicable. Fig u r e 4 1 : Comparison of Calcium Duty Cycle in In Vivo vs. Simulation. Left ) Duty Cycle distributions in In Vivo experiments for cells treated and not treated with Exendin 4 (p=3.7e 4) Right ) Cross Correlation distributions of Simulati ons by Vmax of A denylyl Cyclase (p=2e 16; Anova ) In simulation, as in the MIN6 model, increasing the conversion rate of ATP to cAMP also results in a more prolonged duty cycle. Interestingly, in the simulation there appears to be saturation type behavior where a sharp change i n duty cycle occurs between an adenylyl cyclase Vmax of 1.5x10 4 an d 3x10 4 micromolar/s. Duty cycle values level off beyond that rate In contrast, saturation behavior has no t been shown in vivo, but the binary increase is readily apparent. An additional but separate simulation was conducted to investigate this transition phase. Additional experiments with intermediate concentrations of Exendin 4 are possible, but given the variance in results a great deal of additional data would b e required to show a significant trend.
64 Fig u r e 4 2 : Simulation Results for Duty Cycle over a narrowed range of AC Vmax. (b=1.8e3 %/uM/s; p=2e 16) Figure 47 highlights this proposed transition phase of duty cycle in response to an increased ATP to cAMP conversion rate. Over this range, the duty cycle doubles with a double of Vmax. Because it is known that duty cycle varies over this range, these data were used later to analy ze whether there is a relationship bet ween duty cycle and synchronization between Calcium and cAMP oscillations in simulation like the one found in the MIN6 model As with the experimental model, the next metric that was investigated was how hormone stimu lation, or in this case Vmax, affected the synchronization between calcium and cAMP.
65 Fig u r e 4 3 : Comparison of within cell Calcium/cAMP correlations in In Vivo vs. Simulation. Left ) Cross correlation distributions in In Vivo experiments for cells treated and not treated with Exendin 4 (p=2.5e 4) Right ) Cross Correlation distributions of Simulations by Vmax of Adenylyl Cyclase (pmax=4.7e 14, Pairwise T test, Bonferroni correction) In creasing the conversion rate of ATP to cAMP in simulation results in a highly p redictable improvement in the synchronizatio n be tween Calcium and cAMP oscillations For high values of Vmax, synchronization appears to approach unity. This is in agreement wit h data collected in vivo but the same degree of variance in simulation was not achieved This turns out to be important later when analyzing the effects of calcium/cAMP synchronization.
66 Fig u r e 4 4 : On the role of Antiphasic calcium/cAMP coordination i n duty cycle protraction. A) Duty Cycle vs. calcium/cAMP cross correlations in In Vivo experiments all cells (b= 0.24; Adj R 2 =0.19; p=6.8e 6) B) Cross Correlation distributions of Simulations by Vmax of Adenylyl Cyclase (b= 6.42; Adj R 2 =0.94; p=2e 16) In simulation as well as in vivo t here is evidence that robust coordination between calcium and cAMP drives increases in calcium duty cycle. In vivo this evidence is modest, but significant. Simulation agrees with experiment in a drama tic way however; 94 percent of the variance in duty cycle over the previously discussed Despite decidedly non linear trends in both duty cycle and calcium/cAMP synchronizati on vs Vmax, this relationship displa ys convincing linearity Both experiment and simulation lend strong evidence that the depolarized, high calcium state of the beta cell is stabilized by antiphasic cAMP behavior. Multicellular Network Model Predicts Findings from MIN6 Model In order to i nvestigate comparable metrics of network coordination in silico the single cell model was coupled together to form a 5x5 two dimensional square network.
67 This is reasonably close to the typical cluster size seen in the previously discussed MIN6 experiments Coupling was imposed by including a term in the voltage differential equation for coupling current, which was defined as the difference in the voltages between coupled cells multiplied by a conductance. Coupling conductances were randomly seeded using th e normrnd() function in Matlab. Of primary interest was once again the effect of elevating cAMP on calcium coordination. In order to closely mimic experimental results, and the random nature of transient transfection, for each simulation, 5 cells were rand omly selected from each cluster. For each level of Vmax, the random selections were retained once to calculate pairwise cross correlations Fig u r e 4 5 : cAMP stimulation and calcium network coordination. Left ) Dist ribution of calcium cross correlations as a proxy for electrical coordination in In Vivo experiments by Exendin Treatment (p=8.3e 6) Right ) Cross Correlation distributions of Simulations by Vmax of Adenylyl Cyclase (b=384; Adj R 2 =0.11; p=2e 16) The model corroborates evidence of improved electrical coordination resulting from G stimulatory pathways. Furthermore, because the model does not incorporate any
68 effects cAMP may have on gap junction coupling or other juxtacrine signaling, this behavior i s likely realized in part merely through improved oscillatory robustness and duty cycle protraction in individual cells. Fig u r e 4 6 : cAMP network coordination. A) Distribution of cAMP cross correlations as a proxy for electrical coordination in In Vi vo experiments by Exendin Treatment (p=1.9e 3) B) Cross Correlation distributions of Simulations by Vmax of Adenylyl Cyclase (p=0.223) The s coordination improves with increased Gs activati on. However, there does appear to be an improving trend above the Vmax value of 3e 4 micromolar/s. It is possible that the model just fails to explain this phenomena. As seen in the repeated measures model, the improvement in cAMP coordination may be an artifact of bias form particular clusters. In my estimation, at a Vmax of 1.5e 4, the calcium duty cycle is shortened, therefore the cAMP duty cycle is protracted in a c onjugate manner, resulting in an aberrant increase in cross correlation. Experimentally, with less Gs activation, protract ed cAMP duty cycles are not observed
69 Effects of Intracellular Synchronization is Difficult to Observe In Silico Fig u r e 4 7 : Mean intracellular Ca/cAMP correlation vs network Calcium Coordination Left ) Scatter of Calcium cross correlations with paired mean Ca/cAMP cross correlations In Vivo (b=0.26; Adj R 2 =0.18; p=7.9e 8) Right ) Simulated scatter of calcium cross correlations with paired mean Ca/cAMP cross correlations; Trendlines by Vmax of Adenylyl Cyclase (blue; p=0.09) and Overall (red; b=0.028; Adj R 2 =0.025; p=0.025 ) The result that individual cells with stronger intracellular Calcium/cAMP antiphasic behavior were more couple to their neighbors was still found in the model, but the fit is very poor. In fact, there is no significant relationshi p if Vmax of Adenylyl Cyclase were included in a multiple linear model. This can probably be explained by almost complete lack of variance in mean Calcium/cAMP cross correlation within groups of Adenylyl Cyclase activity. This behavior is not heterogenized well enough by the model. However, conceptually, improved intracellular antiphasic behavior is a mediator of adenylyl cyclase act This would occur mainly due to duty cycle protraction and increased regularity and robustness of oscillations, so gap junction coupling currents have more time to take effect by either depolarizing or hyperpolarizing a neighboring cell.
70 Fig u r e 4 8 : Mean intracellular Ca/cAMP correlation vs network cAMP Coordination A) Scatter of cAMP cross correlations with paired mean Ca/cAMP cross correlations In Vivo (b=0.29; Adj R 2 =0.12; p=1.3e 5) B) Simulated scatter of calcium cross correlations with paired mean Ca/cAMP cross correlations; Trendlines by Vmax of Adenylyl Cyclase (blue; p=0.12) and Overall (red; b= 0.023; Adj R 2 =0.017; p=0.06) Like the result for calcium, this is also not a strong result. In fact, the opp osite effect is now seen in simulation. Again, it c an be explained by low variance combined with lack of overall cAMP trend across the varying adenylyl cyclase activities
71 Fig u r e 4 9 : Calcium network coordination vs. cAMP network coordination with effect modification. A) Scatter of calcium cross correlations with paired cAMP cross 2 =0.44; p=2.2e 16) B) Simulated scatter of calcium cross correlat ions with paired cAMP cross 2 =0.98; p=2.2e 16) Despite there not appearing to be an association between cAMP coordination and AC stimulation in simulation, there is still a strong, nearly 1:1 correlation between calcium coordination and cAMP coordination. The effect modification of Exendin treatment on this relationship is also conserved. Unfortunately, other effect modifications seen in simulations is minimal, probably due to the degree of clustering in within cell cross correlations, and distance was ignored for simulations. Distance was not address ed as it was in vitro because a ll cell distances are perfectly paired in simulations so there is no possibility of confounding Likewise, all simulations sampled the same number of cells, so individual simulations could not skew the results the way that ex perimental image stacks with larger numbers of expressing cells could have. Repeated measures models were also not necessary, because every cluster was of the same size.
72 Finally, a full multiple linear model to predict calcium coordination was selected Even though all behaviors are technically mediated through modulation of AC Vmax, it is able to demonstrate that all of these metrics are important for network coordination in simulation with high confidence. Table 3 : Summary of multiple linear regressio n of simulation data. Coefficient Estimate P Value Intercept 1.7 2 x 10 16 cAMP Coordination 0.75 2 x 10 16 Calcium/cAMP Synchronization 1.9 2 x 10 16 Vmax AC 2.85 x 10 3 0.06 Vmax AC*cAMP Coordination 4.49 x 10 2 2 x 10 16 Vmax AC*Calcium/cAMP Synchronization 2.54 x 10 3 0.09 Vmax ends up having a negative effect on this model, but overall it slightly improves calcium coordination from its effect modification on cAMP coordination and intracellular synchronization Most importantly this result advances the notion that electrical coordination is mediated by cAMP elevations through improved intracellular calcium/cAMP synchronization. is clearly seen with high significance here. T he adjusted R 2 for this model is 0.9964, and the p 16.
73 Comparative effects of [cAMP] dependent Oscillatory Stability vs. Coupling Conductance Fig u r e 4 10 : Gap junction permeability under treatment with cytokines and Exendin 4 Previous experiments conducted to establish cAMP dependent gap junction conductance yielded interesting results that were immediately relevant to this study. Murine islets were treat ed with various combinations of cytokines, PKA and EPAC modulators, and exendin 4, then analyzed for gap junction conductance by FRAP, i.e. photobleaching a section of the islet and measuring fluorescence recovery of the cationic dye rhodamine 123 In this experiment it was shown that gap junction conductance recovery from exendin 4 is significant in cytokine treated cells, which were used as a type 2 diabetic model (Farnsworth & Walters) Other results not shown indicate that this behavior is mediated through PKA. However, in a healthy islet, no such improvement in gap junction conductance was shown, which is inconsistent with my experimental results that calcium coordination improves unde r GLP 1R stimulation Taken together, these data suggest no change in gap junction conductance is warranted for this behavior.
74 Fig u r e 4 11 : A c omparison of the effects on Calcium coordination by adenylyl cyclase activity and coupling conductance Left ) Simulated Calcium cross correlations by Adenylyl Cyclase activity (p =0.025 ) Right ) Simulated Calcium cross correlations by gap junction coupling conductance (b=0.93 ; Adj R 2 =0.13 ; p =1.74e 05 ) Because of this inconsistency, a new series of simulations were conducted to analyze the contribution of cAMP to network coordination. Again, 5x5 cell networks were seeded, and six simulations were run under identical conditions, varying only Vmax of adenylyl cyclase and the electrical conductance of gap junctions. Do ubling the Vmax of adenylyl cyclase, which appears to happen normally with incretin stimulation, results in a significant increase in calcium coordination and generates other results consistent with experiments In contrast, normally observed gap junction conductance changes of 10% results in insignificant changes in calcium coordination. At increases of 75%, coordination improvements become significant, so in stressed or diseased islets this level of improvement appears to be a significant contributing fa ctor. Whether this occurs due to direct signal transduction or through gap junction upregulation is still not understood. However there is strong evidence that in healthy individuals, improved electrical coordination in the islet due to incretin stimulation occurs in lieu of gap junction activation or upregulation. Rather, I propose that a significant role of cAMP oscillations
75 in the islet of Langerhans is to provide improved robustness and stability to electrical oscillations, thereby improving t he stability and coordination of network oscillations as a whole.
76 CHAPTER V RESULTS: DETECTING OSCILLATIONS PRODUCED BY A CAMP CELL MODEL [cAMP] Oscillations Driven by Selec tive Illumination in MIN6 Cells The use of optogenetic constructs that are able to modify elec trical behavior, namely the channel rhodopsins, are used extensively in neurophysiology research and are starting to be used in the islet of Langerhans to drive insulin secretion (Westacott). Given that electrical activity of the alone is insufficient to address all of the physiological stim uli and responses of the islet, developing use of a cAMP based biosensor for the islet is a logical next step.
77 Fig u r e 5 1 : A video of YFP channel during serial activation and deactivation of a G stimulatory optogenetic, accompanied with commensurate timecourse positions. (Epifluorescence 60x 1.4NA Plan Apo Objective) A) Initial state of the cell, prior to any activation B) First activation of construct results in YFP translocation to cytosol, or decreased colocalization C) Full recovery o f colocalization during refractory period D) Subsequent activations result in similar levels of translocation While cAMP oscillations naturally occur as a consequence of coupling to electrical and calcium oscillations, it has been shown that they can also be driven naturally by optogenetic constructs. Oscillations were not observed under the same conditions in cells transfected with the biosensor, and not the optogenetic construct. The dynamic range from maximal cAMP to minimal cAM P using this construct appears to be around 12 15%. Observations indicate that increases from minimal cAMP t o maximal cAMP can be driven on the order of one minute, which is similar to IBMX/Forskolin additions, as well as cAMP increases seen in cAMP oscill ations. However, while cAMP degradation upon cell depolarization appears to take only moments in vivo cAMP degradation in this case take substantially longer. Fortunately, this may not be the case in glucose stimulated cells.
78 Detection using Colocalization and Binary Mask Algorithms Fig u r e 5 2 : A comparison of analysis results in one analyzed cell. Binary mask method is shown in green; Colocalization method is shown in blue. Time regions of optogenetic illumination are shown in cyan. Timecourses indicate normalized colocalization, i.e. inverse of cAMP levels. Both methods developed generated good dynamic range and signal to noise in most cells analyzed, and each method confirms the conceptual validity of the other. Each cell analyzed showed qualitatively identical responses, as shown, in figure 7. Generally, images analyzed using colocalization had greater dynamic range, and less noisy signals. Images analyzed with the binary mask had noisier signals and less dynamic range. Being some what intuitive this is a good result. However, computations on a stack of 300 to 400 images sometimes took in excess of 20 minutes using colocalization, and it would not be possible using Matlab on a computer with less than 8 Gb of memory given the same i mage resolution Alternatively, the binary mask method takes only a few moments. In fact, as a general practice, the binary mask method can be used to confirm results, then colocalization can be used to improve them.
79 Effects of Optogenetic Driven [cAMP] Elevations on Neighboring Cells While this has not been fully explored, and data is incomplete at the moment, methods have been developed to analyze the effect of localized and targeted optogenetic stimulation of adenylyl cyclase in a beta cell network. The same transfection protocol can be used, with the same optogenetic and translocating biosensor. Instead of using an epifluorescence microscope, a confocal is used to illuminate the optogenetic in specific regions using a bleaching function while the e ntire field of view or cell cluster can be imaged for a calcium dye and the cAMP biosensor. Given the const raints in laser options, two photon Fura 2 excitation is being explored. Fig u r e 5 3 : bleaching ROI highlighted
80 Fig u r e 5 4 : Overlaid YFP and Fura 2 Images with bleaching ROI highlighted
81 CHAPTER VI DISCUSSION AND FUTURE DIRECTIONS cAMP cell Model Cell Lines The complex cascade and interplay of cellular signaling is a theme in the study and behavior of almost every physiological system. The control of glucose homeostasis is no exception. The discovery of cAMP oscillations in glucose stimulated beta cells (Dyachok et al., 2006) is surely a product of an evolutionarily refined mechanism for controlling glucose homeostasis, and not a vestigial artifact. Indeed, inhibition of adenylyl cyclases in beta cells di srupts both cAMP oscillations and insulin secretion, highlighting the importance of this pathway (Dyachok et al., 2008). While it is now understood that cAMP regulates the degree t o which individual secrete insulin in response to glucose, we suspected that this behavior becomes more complex at the network level. Combined with the fact that gap junction coupling regulates pulsatile insulin secretion (Benninger et al., 2011) we hypothesized both that cAMP oscillations are coordinated between electrically coup led cells, and that this coupling plays a role in both enhancing insulin secretion from individual cells, as well as regulating coupling itself. Using a FRET based biosensor, the cAMP oscillations antiphasic to calcium previously described were re discovered in cultured MIN6 cells. Based on the appearance of these cAMP signals, there appears to be a definitive basic mechanism behind these oscillations. Adenylyl cyclases constitutively convert cytosolic ATP to cAMP under hyperpolarized conditions, an d upon depolarization, elevated intracellular both activates phosphodiesterase degradation of cAMP and inhibits adenylyl cyclase. Different classes
82 of adenylyl cyclases within the islet confer the ability to fine tune this oscillatory signal to a variety o f inputs, from me tabolic, to hormones, and even to drugs (Hodson et al., 2014; Shinmura et al., 2013; Roger et al., 2011 ; Jung et al., 2000 ) By imaging multiple biosensor expressing cells in the sam e clusters, we were able to identify cAMP oscillations that were coordinated. cAMP coordination showed significant correlation with calcium coordination, and cAMP cross correlation values were generally less than calcium cross correlation values. Therefore, we predict that coordination in cAMP is mediated by g ap junction coupling. However, the presence of some still undiscovered cAMP coupling mechanism is still a possibility. A dramatic change in the nature of the calcium waveform with Exendin 4 stimulation was observed. These waveforms are generally more aki n to those seen in whole islet cells, and app ear to have a more regular period Analysis confirmed that Exendin treatment leads to a dramatic increase in calculated calcium duty cycle. Exendin treatment also improves the antiphasic synchronization between calcium and cAMP oscillations. The improvement in duty cycle and the improvement in synchronization were highly correlated. In fact, synchronization was better able to predict changes in duty cycle than exendin treatment alone, suggesting that duty cycle p rotraction is mediated by the interplay of these two signals. This le a d s to the idea that cAMP plays a role in creating a more stable electrical behavior in individual cells Ostensibly, more stable and robust oscillations in single cells will generate a m ore robust and regular oscillatory pattern in a syncytium of cells. The business of network coordination was then revisited. Stimulation by Exendin 4 significantly improves calcium coordination in MIN6 cell networks. Intuitively, cAMP coordination was hig hly correlated with calcium coordination. Expanding on this, a more interesting result was that this correlation was improved with Exendin treatment. This suggests that improvement in calcium coordination is highly related to increasing
83 coordination of cAMP oscillations. While it was discussed earlier that we believe calcium coordination drives cAMP coordination, I believe that this improved correlation between calcium and cAMP coordination manifest s itself in terms of oscillatory robustness. When cAMP a nd calcium are more synchronized across a network, the probability of single cells disrupting coordination diminishes. Elaborating, noise and inconsistency generated from cellular heterogeneity is mitigated in this way. This theory was corroborated when we examined the relationship between this synchronization and network coordination. Reason could have anticipated the correlation between cAMP and calcium coordination, but intracellular signaling synchronization as a predictor is a more abstract concept Be cause a pair of cells only has one calcium cross correlation, but two intracellular cross correlations, the mean of the two intracellular cross correlations was used. We demonstrated that this antiphasic synchronization between calcium and cAMP is a signif icant predictor of calcium coordination. Therefore, antiphasic cAMP oscillations are critical for the development of sustained electrical coupling, development of a unified network, and ultimately proper insulin secretion. Finally, multiple efforts were made to verify that these results are significant when accounting for possible bias and confounding. Multiple linear regression models were made to verify that the results discussed previously, especially the relationship between intracellular synchronizat ion and network coordination, were not found to be insignificant when taken together with other factors. Next, i t was thought that cross correlations with non zero lags could be erroneous, so analyses were repeated removing data points containing cross cor relation lag in either pairwise calcium or cAMP signals. In all cases but one, the results were corroborated with this data set. The only exception was that the association with intracellular synchronization and cAMP network coordination was not found to b e significant at the 95% confidence level (p=0.06). Finally, analysis was repeated to account for the fact that some clusters of cells were
84 inherently better coordinated than others by including cluster as a random effect in repeated measures models. Chang es in cAMP coordination were not found to be significant. In MIN6 cells, calcium oscillations show coordination mediated by gap junction coupling, but the calcium events are sporadic, and very short lived. It is also probably true that the normal cAMP osc illatory behavior is different compared to primary tissue. Adenylyl cyclases 6 and 9 are well expressed in MIN6 cells (Shinmura et al., 2013), but the expression profile of all classes is different. Adding GLP 1 pathway stimulation to this cell line appear s to recover the ability to produce robust and sustained oscillations that are normally seen in primary tissue In Silico Model Predicts cAMP Provides Improved Network Coordination by Increasing Individual Cell Oscillatory Robustness The importance of modeling physiological systems as a relatively new practice, its impact is just beginning to scratch the surface. The islet of Langerhans is an ideal system to break ground on this approach to studying physiology due in part to the finite cellular scale o f the islet microorgan. We attempted to break new ground on the modeling of this system by including a cAMP/PKA oscillatory circuit in a coordinated network model. Previous models studied by Ni et al. and Bertram and Sherman as well as concepts to model coordinated networks described by Benninger et al were used to develop this model. In order to mimic the system seen from the MIN6 cell line, the network was modeled as a two dimensional 5x5 square network. Initial conditions were randomly initialized, including coupling conductances. Using identical initial conditions and coupling conducances, values of interest were varied. To mimic the nature of transient transfection, cells from these
85 simulations were randomly selected. Ag ain, to minimize confounding, the same random cells were used for each initialization. We were able to show a great amount of agreement between the results of this model and experimental data. Within individual cells, the idea that there exists a relatio nship between the synchronization of calcium and cAMP signals and duty cycle protraction. Again, this relationship appears to better explain the data than the activity of adenylyl cyclase alone. While not observed in vitro, there also appears to be a trans ition phase where duty cycle increases occur. The model was also able to show that calcium coordination improved with increased GLP 1 stimulation. However, the same increase in cAMP coordination was not shown, but this was also found to be possibly erroneo us with the repeated measures models. Given the correlation between cAMP coordination and calcium coordination, a full expla n ation at the moment why this may be the case is elusive In a similar fashion the model was able to corroborate evidence that intra cellular synchronization has an effect on calcium coordination, but not cAMP coordination. The between the groups of synchronization values for this to be found highly significant. The effect modification of adenylyl cyclase activity on the correlation between cAMP and calcium coordination was reproduced by the model. As possibly the most complex interaction that was defended by this model, it appears to be a genuine beh avior. Perhaps the most interesting thing about this model is that these results were found without including any effect on coupling conductance. Previous FRAP studies, conducted by Farnsworth and Walters, demonstrate that there is diminished gap junctio n conductance in islets stressed with inflammatory cytokines. They also demonstrated that this gap junction conductance can be recovered by Exendin treatment. This action was linked to PKA combining these experiments with selective PKA activators and inhib itors. However, in unstressed islets, improvement in gap junction conductance was not
86 observed. The ob servation of improved calcium coordination in the presence of GLP 1 contradicts this result. As such we resimulated, varying gap junction conductance with in the ranges seen in FRAP experiments, and found that gap junction conductance increases played a role in increasing calcium coordination only at extreme levels, like those seen in recovery of stressed cells. However, modest increases in gap junction cond uctance played less of a factor than physiologically modest increases in adenylyl cyclase activity. Therefore, cAMP signaling itself appears to play a role in coordinating the islet of Langerhans. We propose that this occurs by forming an oscillatory circu it with calcium and stabilizing electrical oscillations. Given the results taken from simulation and experimental data, it appears that the cAMP oscillatory circuit is present in vivo to stabilize electrical oscillations both under incretin stimulation a nd under glucose stimulation alone. Incretin stimulation serves to both enhance this effect, as well as act to enhance secretion itself. Subsequent depolarizations are more regular and robust, so even in the absence of gap junction coupling, cAMP behavior improves the probability that coordinated cells remain coordinated over repeated periods of oscillations. Ultimately, this lies at the core of the peripheral response. Cell Model New forms of therapies, devices, and pharmaceuticals are always emerging. Treatment of Diabetes has been a prime target of these approaches for decades, but a common theme behind their limitations has always remained. As described previously, the physiological response to glucose requires dynamic, temporally precise activation of the insulin secretory machinery in the pancreas. In normal beta cells, these oscillations
87 are d riven by the normal cell physiology, but in unhealthy cells, the behavior may become lost. We developed a method to utilize an optogenetic construct to elevate cAMP generation in a beta cell line. In support of this, a new method to utilize and analyze r esults from a translocation based cAMP biosensor were developed. The results of activating the optogenetic were an effect similar to bathin g the cells in IBMX/forskolin, but in a much more precise manner; plus, it removed the clumsy process of aspirating a nd replacing solutions. Given that the construct utilizes adenylyl cyclase, the absolute levels of cAMP generated are likely much more physiologically relevant. In addition, we were able to generate forced cAMP oscillation s under low glucose conditions. As a necessity given the tools at our disposal, we were able to develop two new methods of analyzing images using a translocation based biosensor. The first, a method based on the colocalization of the CFP and YFP subunits of the biosensor produces finer ti mecourses and a better signal to noise ratio. I believe that this method represents a more accurate depiction of actual cAMP dynamics. I recommend t hat it be used in cases of low signal, as is often the case in the cAMP oscillations produced in response to glucose stimulation. The main issue with this method is computational time. The second method is one were the plasma membrane region is estimated by a combination of ROIs and intensity thresholding, and YFP intensity there is taken as a proxy for cAMP. Th e success found with this method was surprising due to its simplicity, and could definitely be useful to quickly crunch through experimental data, especially when there are no expected outcomes. At the moment, the implications of these results appear to be in the form of opening up new avenues of researching islet cell physiology. The construct allows for much more finite control of cAMP elevations than bathing in hormone analogs, especially temporally. We are currently investigating whether targeting of sp ecific
88 expressing cells within a network using confocal microscopy will have an impact on the electrical behavior of neighboring cells. Future Directions The work described in this thesis approached a problem that was formerly under investigated. Due to the technical challenges associated with measuring cAMP dynamics, its role in insulin secretion is poorly understood. In addition, a lack of in vivo data has limited efforts in modeling this system including cAMP effects. With minimal understanding of this cellular process, even less work has been done to in vestigate how cAMP plays a role in coordinated insulin secretion. The results both from cell li ne and simulation experiments suggest that cAMP stabilizes electrical oscillations, essentially minimizing phase differences between coupled oscillators, improving network coordination. It also strongly indicates that cAMP oscillations are driven by the pr imary electrical oscillations. This has not been shown before. Using a GPCR based optogenetic in beta cell lines while simultaneously detecting cAMP dynamics has also not been shown. Whether this construct will be useful clinically for engineering islets i n the future remains to be seen, but this tool should be invaluable in continuing work on studying cAMP in beta cell networks. Given the experimental results obtained on MIN6 cells, a natural next step on this investigation would be to use primary tissue. Islets of Langerhans isolated from murine pancreata are the workhorse of islet physiology research. The same biosensors and optogenetic contstructs can be transfected into primary tissue using adenovirus vectors. At the moment, protocols have not been per fected for applying this to our experiments, but t he hope is that these experiments not only will confirm results from cell line experiments, but also compound on them by adding the wrinkle of a third dimension. In
89 addition, the correct amount of DNA load should be fairly transmutable. On the same token, the model developed can be used as a basis for a three dimensional islet model. This likely would work as a progression from a square geometry, to a cubic geometry, to a spherical geometry, in addition to i terations on the code within the model itself. We are only beginning to scratch the surface of a wealth of information that could be obtained researching the islet of Langerhans with optogenetics. In the future, experiments on activating the constructs in specific regions can also be expanded to primary tissue. Conceptually, this type of experiment could be done in a similar manner to the way FRAP experiments are used to evaluate gap junction conductance. Half of an onstruct, while leaving the other half dark. Differences between the regions could then be evaluated. An exciting, and not inconceivable result would be that calcium waves propagate from regions of optogenetic activation to inactive regions, much like they do from regions of high glucose to low glucose (Benninger et al., 2008). In addition, and perhaps most excitingly, the mere antiapoptotic nature of the GLP 1 pathway means that this optogenetic construct could be used in islet replacement therapy, even in the near future. It would require very little modification to the current procedure, as doctors should be able to selectively illuminate the transplant while its progression is being monitored without disrupting other systems, and with minimal risk of in sulin overdose Another benefit of primary tissue is that the role of cAMP can be investigated on a large variety of beta cell specific mutants. As discussed previously, cAMP signaling modulates the open probability of kATP channels through SUR1 (Eliasso n et al., 2003). Mutant variants of this channel, namely the Kir6.2 subunit, are available in mouse models already housed by our vivarium. In fact, this is one of the most important risk alleles in neonatal diabetes, a form where rather than being destroye d or slowly diseased, the islets It
90 remains to be seen whether increasing the synchronization of cAMP to electrical oscillations can be s hown to be correlated to rescuin g overall activity. Similarly to what was simulated, mutants can also be used to roughly dictate gap junction conductance. Connexin 36 mutants are also available, and increasing the proportion of mutant expression to wild type expression will result in a d ecrease in gap junction conductance. It is also possible to use gap junction inhibitors. Either way, simulation results showing that cAMP synchronization plays a larger role in revving up islet coordination under GLP 1 stimulation than gap junction express ion or activation can be corroborated. Great insight has been gained on the role of cAMP in electrical coordination and oscillatory robustness, but the actual effects on insulin secretion remains to be seen. These experiments can be revisited, including c apturing dynamic information on the coordination of insulin release. Insulin can be imaged by utilizing the fact that insulin is packed into granules with Zinc. Zinc indicator for monitoring induced exocytotic relase, or ZIMIR, is a newly developed indicat or that displays robust fluorescent enhancement upon zinc chelation, with high selectivity against other ions like calcium and magnesium. Using a microscope setup of sufficient resolution, individual exocytotic events can be visualized this way (Li et al., 2011). It will be interesting to see whether the observed effects on calcium and coordination will be mirrored by insulin secretion. It also stands to reason that oscillations in metabolism under glucose stimulation also plays a role in this complex osc illatory circuit. Recently, it has been demonstrated that adenylyl cyclase 5 plays a role in coupling the cAMP oscillatory circuit to beta cell metabolism (Hodson et al., 2014). Methods to image cellular metabolism, such as two photon NADH imaging could be coupled to these experiments to further investigate the link betweek cAMP oscillations and cellular metabolism. Information obtained from these experiments can also be used in the context of other investigations. Currently, only the overall GLP 1 pathway has been investigated
91 However, cAMP is controlled by a family of adenylyl cyclases. The role of each class of adenylyl cyclase in the process of oscillations is unknown, and different classes may be responsible for different phases of the waveform. Also, cAMP oscillations promote oscillations in the activity of PKA and EPACs, and it is not currently understood how downstream signal transduction of these effectors plays an almost certain role in improving oscillatory robustness.
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100 APPENDIX Model Intialization Code %Generate cAMP Model Coefficients global size dim x y z xx yy zz gK VK gCa vCa taun ... fcyt kPMCA kSERCA pleak fer sigmav kappa Kd alpha taua ... Vacm Ki K3c K4c Kdeg kpde Kone Ktwo Kthr Kfou K5f K5b K6f K6b ... Kpkaca R_GK gKATPbar gKCabar k_gamma Cm Atot v_gamma r r1 ... K1 K2 K3 K4 famp fmt ffbp fbt fatp Kdd Ktd Ktt ... contacts Gcoup n_contacts Vm n Cai CaER ADP FBP G6P cAMP c4R2 PKA ... InVars %Specify dimensions size = 5; %edge length dim = 2; %dimension xx= size+1; yy= size+1; if dim==2 zz=0; elseif dim==3; zz= size+1; else error( 'Invalid dim' ) end for ni = 1:size^dim loadbar=waitbar(ni/(size^dim)); %Original Bertram Model Coefficients gK=2700; %Potassium Channel Co nductance VK= 75; %Baseline Potassium Voltage gCa=1000; %Calcium Channel Conductance vCa=26; %Baseline Calcium Voltage taun=20; %Potassium Channel Opening Probability Constant fcyt=0.01; kPMCA=0.2; kSERCA=0.4; %SERCA Pump Constant pleak=0.0002; %ER leak constant fer=0.01; sigmav=31; kappa=0.005; Kd=0.5; alpha=4.50e 6; taua=300000; %cAMP Module coefficients Vacm = 0.0012; %Maximal activity of Adenylyl Cyclase Ki = 0.2; %inhibitory constant for Calcium binding to AC K3c = 0.072; %RR K of calmodulin ca3 activated PDE degradation of cAMP K4c = 2.13; %same as K3c, but for ca4 state of calmoduling Kdeg = 0.01; %Ca independent cAMP degradation rate by PDE
101 kpde = 1; %PDE Degradation Constant %PKA coefficients Kone = 1.64; Ktwo = 1.64; Kthr = 0.68; Kfou = 2.31; %cAMP to PKA binding coefficients K5f = 60; K5b = 18; K6f = 60; K6b = 18; %dis/association rates for PKA catalytic subunits Kpkaca = 3000; %Constant attributing PKA's modulation of Calcium activity %Parameters for metabolic bursting modes R_GK=0.2; gKATPbar=25000; gKCabar=100; k_gamma=10 ; Cm=5300; %LET Atot =3000; %Glycolytic input to mitochondrial ADP equation v_gamma =2.2; r(ni) =1; r1 =0.35; % Glycolytic parameters K1 =30; K2 =1; K3 =50000; K4 =1000; famp =0.02; fmt =20; ffbp =0.2; fbt =20; fatp =20; %KATP open probability Kdd =17; Ktd =26; Ktt =1; %Cell Arrangement x(ni)=xx; y(ni)=yy; z(ni)=zz; xx=xx+2; if xx>(size 1) xx= size+1; yy=yy+2; if yy>(size 1) yy= size+1; zz=zz+2; end end for nii=1:length(x) contacts(ni,nii)=((1.25*(r(ni)+r(nii))^2)>=(x(ni) x(nii))^2+(y(ni) y(nii))^2+(z(ni) z(nii))^2); contacts(nii,ni)=contacts(ni,nii); if contacts(ni,nii)==1 Gcoup(ni,nii)=normrnd(0.2,0.8);
102 if Gcoup(ni,nii)<0 Gcoup(ni,nii)=0; end Gcoup(nii,ni)=Gcoup(ni,nii); end end end close(loadbar) n_contacts=(1:(size^dim))*0; fo r i=1:(size^dim) contacts(i,i)=0; Gcoup(i,i)=0; n_contacts(i)=sum(double(contacts(i,:))); end %Initialized Concentrations, voltage, and time dependent parameters Vm=zeros([length(x),1]); n=zeros([length(x),1]); Cai=zeros([length(x),1]); CaER= zeros([length(x),1]); ADP=zeros([length(x),1]); FBP=zeros([length(x),1]); G6P=zeros([length(x),1]); cAMP=zeros([length(x),1]); c4R2=zeros([length(x),1]); PKA=zeros([length(x),1]); for ni=1:length(x) Vm(ni,1)= 60+normrnd(0,6); %Membrane Potential, mV Cai(ni,1)=0.1+normrnd(0,.01); %Concentration of Calcium, mM CaER(ni,1)=185+normrnd(0,18.5); %Concentration of Calcium in the ER, mM ADP(ni,1)=780+normrnd(0,78); %Concentration of ATP, mM FBP(ni,1)=40+normrnd(0,4); %Fructose Bisphosphate, mM G6P(ni,1)=200+ normrnd(0,20); %Glucose 6 Phospate, mM cAMP(ni,1)=0.2+normrnd(0,.02); %Concentration of cAMP c4R2(ni,1)=0.5+normrnd(0,.05); %Concentration of 4 catalytic 2 regulatory PKA PKA(ni,1)=0.2+normrnd(0,.02); %Concentration of active PKA end InVars=[Vm,n,Cai,CaE R,ADP,FBP,G6P,cAMP,c4R2,PKA]; Model Simulation Code function [vars] = cAMPModelFinal( ) global InVars x tic [time,vars]=ode15s(@cAMPODE,1:1000000,InVars); %Time in ms %Output Plots voltage=vars(:,1:length(x));
103 calcium= vars(:,(length(x)*2+1):length(x)*3); cAMP=vars(:,(length(x)*7+1):length(x)*8); figure subplot(3,1,1) plot(time,voltage(:,1), 'b' ) subplot(3,1,2) plot(time,calcium(:,1), 'g' ) subplot(3,1,3) plot(time,cAMP(:,1), 'r' ) toc end function [outVars] = cAMPODE(~,v) global x gK VK gCa vCa taun ... fcyt kPMCA kSERCA pleak fer sigmav kappa Kd alpha taua ... Vacm Ki K3c K4c Kdeg kpde Kone Ktwo Kthr Kfou K5f K5b K6f K6b ... Kpkaca R_GK gKATPbar gKCabar k_gamma Cm Atot v_gamma r r1 ... K1 K2 K3 K4 famp fmt ffbp fbt fatp Kdd Ktd Ktt ... contacts Gcoup %Constants from Initialization for ni=1:length(x) %Endoplasmic Reticulum Calcium Flux JSERCA = kSERCA *v(length(x)*2+ni); Jleak = pleak *(v(length(x)*3+ni) v(length(x)*2+ni)); Jer = Jleak JSERCA ; %Ion Currents Ik =gK *v(length(x)+ni)*(v(ni) VK ); minf =1/(1+exp( (20+v(ni) )/12)); ICa =gCa *minf *(v(ni) vCa ); gKCa =gKCabar /(1+(Kd /v(length(x)*2+ni))^2); IKCa =gKCa *(v(ni) VK ); %LET Jmem = (alpha *ICa +kPMCA *v(length(x)*2+ni)); %Glycolytic input to mitochondrial ADP equation ninf =1/(1+exp( (16+v(ni) )/5)); % Glycolytic expressions F6P = 0.3*v(length(x)*6+ni); %Nucleotide concentrations rad = sqrt((v(length(x)*4+ni) Atot )^2 4*v (length(x)*4+ni)^2); ATP = 0.5*(Atot v(length(x)*4+ni)+rad );
104 AMP = v(length(x)*4+ni)^2/ATP ; %PhosphoFructoKinase Calculations topa1=0; bottom1=1; weight1=ATP ^2/K4 ; topa2=topa1; bottom2=bottom1+weight1; weight2=F6P ^2/K3 ; topa3=topa2+weight2; bottom3=bottom2+weight2; % (0,0,1,1) weight3=(F6P *ATP )^2/(fatp *K3 *K4 ); topa4=topa3+weight3; bottom4=bottom3+weight3; % (0,1,0,0) weight4=v(length(x)*5+ni)/K2 ; topa5=topa4; bottom5=bottom4+weight4; % (0,1,0,1) weight5=(v(length(x)*5+ni)*ATP ^2)/(K2 *K4 *fbt ); topa6=topa5; bottom6=bottom5+weight5; % (0,1,1,0) weight6=(v(length(x)*5+ni)*F6P ^2)/(K2 *K3 *ffbp ); topa7=topa6+weight6; bottom7=bottom6+weight6; % (0,1,1,1) weight7=(v(length(x)*5+ni)*F6P ^2*ATP ^2)/(K2 *K3 *K4 *ffbp *fbt *fatp ); topa8=topa7+weight7; bottom8=bottom7+weight7; % (1,0,0,0) weight8=AMP /K1 ; topa9=topa8; bottom9=bottom8+weight8; %(1,0,0,1) weight9=(AMP *ATP ^2)/(K1 *K4 *fmt ); topa10=topa9; bottom10=bottom9+weight9; % (1,0,1,0) weight10=(AMP *F6P ^2)/(K1 *K3 *famp ); t opa11=topa10+weight10; bottom11=bottom10+weight10; % (1,0,1,1) weight11=(AMP *F6P ^2*ATP ^2)/(K1 *K3 *K4 *famp *fmt *fatp ); topa12=topa11+weight11; bottom12=bottom11+weight11; % (1,1,0,0) weight12=(AMP *v(length(x)*5+ni))/(K1 *K2 ); topa13=topa12; bottom1 3=bottom12+weight12; % (1,1,0,1) weight13=(AMP *v(length(x)*5+ni)*ATP ^2)/(K1 *K2 *K4 *fbt *fmt ); topa14=topa13;
105 bottom14=bottom13+weight13; % (1,1,1,0) -the most active state of the enzyme weight14=(AMP *v(length(x)*5+ni)*F6P ^2)/(K1 *K2 *K3 *ffbp *famp ); topa15=topa14; topb=weight14; bottom15=bottom14+weight14; % (1,1,1,1) weight15=(AMP *v(length(x)*5+ni)*F6P ^2*ATP ^2)/(K1 *K2 *K3 *K4 *ffbp *famp *fbt *fmt *fatp ); topa16=topa15+weight15; bottom16=bottom15+weight15; % Phosphofructokinase rate %lambda, Vmax as in Smolen95, Eq. 3 lambda=0.06; Vmax=2; R_PFK =Vmax*(lambda*topa16 + topb)/bottom16; %KATP open probability mgADP =0.165*v(length(x)*4+ni); ADP3m =0.135*v(length(x)*4+ni); ATP4m =0.05*ATP ; topo =0.08*(1+2*mgADP /Kdd )+ 0.89*(mgADP /Kdd )^ 2; bottomo =(1+mgADP /Kdd )^2 (1+ADP3m /Ktd +ATP4m /Ktt ); oinf =topo /bottomo ; gKATP =gKATPbar *oinf ; IKATP =gKATP *(v(ni) VK ); R_GPDH = 0.2*sqrt(v(length(x)*5+ni)); gamma = v_gamma *(R_GPDH /(k_gamma +R_GPDH )); %cAMP module Jac = Vacm /(Ki +v (length(x)*2+ni)); JPDE = (K3c *v(length(x)*2+ni)^3+K4c *v(length(x)*2+ni)^4)*v(length(x)*7+ni); JPDEi = Kdeg *v(length(x)*7+ni); %PKA module R2C2 = 1; c4R2C2 = Kone *Ktwo *Kthr *Kfou *v(length(x)*7+ni)^4*R2C2; c4R2C = v(length(x)*9+ni) 2*v(length(x)*8+ni); chiPKA = (1+Kpkaca *v(length(x)*9+ni)); %PKA's effect on VDCC's, change to a probability function above. %Coupling Module % Icoup Icoup =0; downstream=find(contacts(ni,:)); for di=1:length(downstream) Icoup =Icoup +Gcoup(ni,downstream(di))*(v(ni) v(downstream(di))); end % %Differential Equations vprime(ni) = (Ik +ICa +IKCa +IKATP+Icoup )/Cm ; %voltage nprime(ni) = (ninf v(length(x)+ni))/taun ; %condu ctance modifier
106 CaPrime(ni) =fcyt *(Jmem *chiPKA +Jer ); %calcium caerPrime(ni) = fer *sigmav *Jer ; %calcium in ER? ADPprime(ni) = (ATP v(length(x)*4+ni)*exp((r(ni) + gamma )*(1 v(length(x)*2+ni)/r1 )))/taua ; %Adenosine diphosphate FBPprime(ni) =k appa *(R_PFK 0.5*R_GPDH ); %Fructose bisphosphate G6Pprime(ni) =kappa *(R_GK R_PFK ); %Glucose 6 Phosphate cAMPprime(ni) = Jac kpde *(JPDE +JPDEi ); %Cyclic AMP c4R2prime(ni) = K6f *c4R2C K6b *v(length(x)*9+ni)*v(length(x)*8+ni); %complex of 4 cA MP molecules bound %to 2 R subunits of PKA PKAprime(ni) = K5f *c4R2C2 K5b *v(length(x)*9+ni)*c4R2C +K6f *c4R2C K6b *v(length(x)*9+ni)*v(length(x)*8+ni); %active %PKA end %Syntax for ODE15s Output outVars(1:length(x))=vprime; outVars( 1+length(x):2*length(x))=nprime; outVars(1+2*length(x):3*length(x))=CaPrime; outVars(1+3*length(x):4*length(x))=caerPrime; outVars(1+4*length(x):5*length(x))=ADPprime; outVars(1+5*length(x):6*length(x))=FBPprime; outVars( 1+6*length(x):7*length(x))=G6Pprime; outVars(1+7*length(x):8*length(x))=cAMPprime; outVars(1+8*length(x):9*length(x))=c4R2prime; outVars(1+9*length(x):10*length(x))=PKAprime; outVars=outVars(:); end