Contributions of mathematical modeling of beta cells to the understanding of beta-cell oscillations and insulin secretion

Model of Calcium Dynamics Regulating [Formula: see text], ATP and Insulin Production in a Pancreatic [Formula: see text]-Cell

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ([Formula: see text]) and adenosine triphosphate (ATP) in various cells including pancreatic [Formula: see text]-cells. The calcium signaling mechanisms regulating [Formula: see text], ATP and insulin responsible for various functions of [Formula: see text]-cells are still not well understood. Any disturbance in these mechanisms can alter the functions of [Formula: see text]-cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation for calcium dynamics and a system of first-order differential equations for [Formula: see text], ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of [Formula: see text]-production and degradation, ATP production and insulin secretion on calcium dynamics in a [Formula: see text]-cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of [Formula: see text], ATP and insulin levels in a [Formula: see text]-cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of [Formula: see text], ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in [Formula: see text], ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K^＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca^2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

Hubs, diversity, and synchronization in FitzHugh-Nagumo oscillator networks: Resonance effects and biophysical implications

Using the FitzHugh-Nagumo equations to represent the oscillatory electrical behavior of β-cells, we develop a coupled oscillator network model with cubic lattice topology, showing that the emergence of pacemakers or hubs in the system can be viewed as a natural consequence of oscillator population diversity. The optimal hub to nonhub ratio is determined by the position of the diversity-induced resonance maximum for a given set of FitzHugh-Nagumo equation parameters and is predicted by the model to be in a range that is fully consistent with experimental observations. The model also suggests that hubs in a β-cell network should have the ability to "switch on" and "off" their pacemaker function. As a consequence, their relative amount in the population can vary in order to ensure an optimal oscillatory performance of the network in response to environmental changes, such as variations of an external stimulus.

Assessing Different Temporal Scales of Calcium Dynamics in Networks of Beta Cell Populations

Beta cells within the pancreatic islets of Langerhans respond to stimulation with coherent oscillations of membrane potential and intracellular calcium concentration that presumably drive the pulsatile exocytosis of insulin. Their rhythmic activity is multimodal, resulting from networked feedback interactions of various oscillatory subsystems, such as the glycolytic, mitochondrial, and electrical/calcium components. How these oscillatory modules interact and affect the collective cellular activity, which is a prerequisite for proper hormone release, is incompletely understood. In the present work, we combined advanced confocal Ca2+ imaging in fresh mouse pancreas tissue slices with time series analysis and network science approaches to unveil the glucose-dependent characteristics of different oscillatory components on both the intra- and inter-cellular level. Our results reveal an interrelationship between the metabolically driven low-frequency component and the electrically driven high-frequency component, with the latter exhibiting the highest bursting rates around the peaks of the slow component and the lowest around the nadirs. Moreover, the activity, as well as the average synchronicity of the fast component, considerably increased with increasing stimulatory glucose concentration, whereas the stimulation level did not affect any of these parameters in the slow component domain. Remarkably, in both dynamical components, the average correlation decreased similarly with intercellular distance, which implies that intercellular communication affects the synchronicity of both types of oscillations. To explore the intra-islet synchronization patterns in more detail, we constructed functional connectivity maps. The subsequent comparison of network characteristics of different oscillatory components showed more locally clustered and segregated networks of fast oscillatory activity, while the slow oscillations were more global, resulting in several long-range connections and a more cohesive structure. Besides the structural differences, we found a relatively weak relationship between the fast and slow network layer, which suggests that different synchronization mechanisms shape the collective cellular activity in islets, a finding which has to be kept in mind in future studies employing different oscillations for constructing networks.

Modelling of energy-driven switch for glucagon and insulin secretion

We present a mathematical model of the energy-driven metabolic switch for glucagon and insulin secretion from pancreatic alpha and beta cells, respectively. The energy status related to hormone secretion is studied for various glucose concentrations. Additionally, the physiological response is studied with regards to the presence of other metabolites, particularly the free-fatty acids. At low glucose, the ATP production in alpha cells is high due to free-fatty acids oxidation in mitochondria, which enables glucagon secretion. When the glucose concentration is elevated above the threshold value, the glucagon secretion is switched off due to the contribution of glycolytic ATP production, representing an "anaerobic switch". On the other hand, during hypoglycemia, the ATP production in beta cells is low, reflecting a "waiting state" for glucose as the main metabolite. When glucose is elevated above the threshold value, the oxidative fate of glucose in mitochondria is the main source of energy required for effective insulin secretion, i.e. the "aerobic switch". Our results show the importance of well-regulated and fine-tuned energetic processes in pancreatic alpha and beta cells required for efficient hormone secretion and hence effective blood glucose regulation. These energetic processes have to be appropriately switched on and off based on the sensing of different metabolites by alpha and beta cells. Our computational results indicate that disturbances in cell energetics (e.g. mitochondrial dysfunction), and dysfunctional metabolite sensing and distribution throughout the cell might be related to pathologies such as metabolic syndrome and diabetes.

Electrophysiological models of the human pancreatic δ-cell: From single channels to the firing of action potentials

Minimal mathematical models were developed to describe the electrophysiological properties of human δ-cells. Markov models of single channels were first developed based on the analysis of electrophysiological data. Monte Carlo simulations of voltage-clamp experiments were performed in an iteratively optimization procedure to estimate the number of channels required to reproduce the main characteristics of the macroscopic currents recorded experimentally. A membrane model of the firing of action potentials was then developed based on the kinetic schemes of single channels and the number of channels estimated. We showed that macroscopic currents of human δ-cells can be reproduced by minimal models of single channels when the appropriate number of channels is considered. In addition, our simulations suggest that human δ-cells are capable of generating action potentials through the interaction of the ionic currents involved. Finally, we determined the relative contribution of the currents underlying the firing of action potentials in human pancreatic δ-cells, which allowed us to propose a qualitative model of an action potential in terms of the underlying ionic currents.

Integrated multiscale mathematical modeling of insulin secretion reveals the role of islet network integrity for proper oscillatory glucose-dose response

The integrated multiscale mathematical model we present in this paper is built on two of our previous ones: a model of electrical oscillation in β-cells connected to neighboring cells within a three-dimensional (3D) network, and a model of glucose-induced β-cell intracellular insulin granule trafficking and insulin secretion. In order to couple these two models, we assume that the rate at which primed and release-ready insulin granules fuse at the cell membrane increases with the intracellular calcium concentration. Moreover, by assuming that the fraction of free K_ATP-channels decreases with increasing glucose concentration, we take into account the effect of glucose dose on membrane potential and, indirectly via the effect on the potential, on intracellular calcium. Numerical analysis of our new model shows that a single step increase in glucose concentration yields the experimentally observed characteristic biphasic insulin release. We find that the biphasic response is typically oscillatory in nature for low and moderate glucose concentrations. The plateau fraction (the time that the β-cells spend in their active firing phase) increases with increasing glucose dose, as does the total insulin secretion. At high glucose concentrations, the oscillations tend to vanish due to a constantly elevated membrane potential of the β-cells. Our results also demonstrate how insulin secretion characteristics in various glucose protocols depend on the degree of β-cell loss, highlighting the potential impact from disease. In particular, both the secretory capacity (average insulin secretion rate per β-cell) and the oscillatory response diminish as the islet cell network becomes compromised.

Computational modeling of the effect of temperature variations on human pancreatic β-cell activity

The effect of temperature variations on the pancreatic β-cell activity and the role of different model compartments in temperature sensing have been investigated using a computational modeling approach. The results of our study show that temperature variations by several degrees can change the dynamical states of the β-cell system. In addition, temperature variations can alter the characteristic features of the membrane voltage, which correlates with insulin secretion. Simulation results show that the ion channels such as the L-type calcium, the hERG potassium, sodium channels and the glycolysis pathway are the possible sites for sensing temperature variation. Results indicate that for a small temperature change, even though the frequency and amplitude of electrical activity are altered, the area under the membrane potential curve remains almost unchanged, which implies the existence of a thermoregulatory mechanism for preserving the amount of insulin secretion. Furthermore, the computational analysis shows that the β-cell electrical activity exhibits a bursting pattern in physiological temperature (37 °C) while in vitro studies reported almost the spiking activity at lower temperatures. Since hormone-secreting systems work more efficient in bursting mode, we propose that the pancreatic β-cell works better in the physiological temperature compared with the reference temperature (33 °C).

Investigation of the role of ion channels in human pancreatic β-cell hubs: A mathematical modeling study

In many cellular networks, the structure of the network follows a scale-free organization, where a limited number of cells are strongly coupled to other cells. These cells are called hub cells and their critical roles are well accepted. Despite their importance, there have been only a few studies investigating the characteristic features of these cells. In this paper, a computational approach is proposed to study the possible role of different ion channels in distinguishing between the hub and non-hub cells. The results show that the P/Q-type and T-type calcium channels may have an especial role in the β-cell hubs because the high-level expressions of these channels make a pancreatic β-cell more potent to force other coupled cells to follow it. In addition, in order to consider the variation of the coupling strength with voltage, a novel mathematical model is proposed for the gap junction coupling between the pancreatic β-cells. The proposed approach is validated based on the data from the literature.

Beta-cell hubs maintain Ca2+ oscillations in human and mouse islet simulations

Islet β-cells are responsible for secreting all circulating insulin in response to rising plasma glucose concentrations. These cells are a phenotypically diverse population that express great functional heterogeneity. In mice, certain β-cells (termed 'hubs') have been shown to be crucial for dictating the islet response to high glucose, with inhibition of these hub cells abolishing the coordinated Ca2+ oscillations necessary for driving insulin secretion. These β-cell hubs were found to be highly metabolic and susceptible to pro-inflammatory and glucolipotoxic insults. In this study, we explored the importance of hub cells in human by constructing mathematical models of Ca2+ activity in human islets. Our simulations revealed that hubs dictate the coordinated Ca2+ response in both mouse and human islets; silencing a small proportion of hubs abolished whole-islet Ca2+ activity. We also observed that if hubs are assumed to be preferentially gap junction coupled, then the simulations better adhere to the available experimental data. Our simulations of 16 size-matched mouse and human islet architectures revealed that there are species differences in the role of hubs; Ca2+ activity in human islets was more vulnerable to hub inhibition than mouse islets. These simulation results not only substantiate the existence of β-cell hubs, but also suggest that hubs may be favorably coupled in the electrical and metabolic network of the islet, and that targeted destruction of these cells would greatly impair human islet function.

δ-cells and β-cells are electrically coupled and regulate α-cell activity via somatostatin

Key points

We used a mouse expressing a light‐sensitive ion channel in β‐cells to understand how α‐cell activity is regulated by β‐cells.

Light activation of β‐cells triggered a suppression of α‐cell activity via gap junction‐dependent activation of δ‐cells.

Mathematical modelling of human islets suggests that 23% of the inhibitory effect of glucose on glucagon secretion is mediated by β‐cells via gap junction‐dependent activation of δ‐cells/somatostatin secretion.

Abstract

Glucagon, the body's principal hyperglycaemic hormone, is released from α‐cells of the pancreatic islet. Secretion of this hormone is dysregulated in type 2 diabetes mellitus but the mechanisms controlling secretion are not well understood. Regulation of glucagon secretion by factors secreted by neighbouring β‐ and δ‐cells (paracrine regulation) have been proposed to be important. In this study, we explored the importance of paracrine regulation by using an optogenetic strategy. Specific light‐induced activation of β‐cells in mouse islets expressing the light‐gated channelrhodopsin‐2 resulted in stimulation of electrical activity in δ‐cells but suppression of α‐cell activity. Activation of the δ‐cells was rapid and sensitive to the gap junction inhibitor carbenoxolone, whereas the effect on electrical activity in α‐cells was blocked by CYN 154806, an antagonist of the somatostatin‐2 receptor. These observations indicate that optogenetic activation of the β‐cells propagates to the δ‐cells via gap junctions, and the consequential stimulation of somatostatin secretion inhibits α‐cell electrical activity by a paracrine mechanism. To explore whether this pathway is important for regulating α‐cell activity and glucagon secretion in human islets, we constructed computational models of human islets. These models had detailed architectures based on human islets and consisted of a collection of >500 α‐, β‐ and δ‐cells. Simulations of these models revealed that this gap junctional/paracrine mechanism accounts for up to 23% of the suppression of glucagon secretion by high glucose.

We used a mouse expressing a light‐sensitive ion channel in β‐cells to understand how α‐cell activity is regulated by β‐cells.

Light activation of β‐cells triggered a suppression of α‐cell activity via gap junction‐dependent activation of δ‐cells.

Mathematical modelling of human islets suggests that 23% of the inhibitory effect of glucose on glucagon secretion is mediated by β‐cells via gap junction‐dependent activation of δ‐cells/somatostatin secretion.

Interaction between pancreatic β cell and electromagnetic fields: A systematic study toward finding the natural frequency spectrum of β cell system

Interaction between biological systems and environmental electric or magnetic fields has gained attention during the past few decades. Although there are a lot of studies that have been conducted for investigating such interaction, the reported results are considerably inconsistent. Besides the complexity of biological systems, the important reason for such inconsistent results may arise due to different excitation protocols that have been applied in different experiments. In order to investigate carefully the way that external electric or magnetic fields interact with a biological system, the parameters of excitation, such as intensity or frequency, should be selected purposefully due to the influence of these parameters on the system response. In this study, pancreatic β cell, the main player of blood glucose regulating system, is considered and the study is focused on finding the natural frequency spectrum of the system using modeling approach. Natural frequencies of a system are important characteristics of the system when external excitation is applied. The result of this study can help researchers to select proper frequency parameter for electrical excitation of β cell system. The results show that there are two distinct frequency ranges for natural frequency of β cell system, which consist of extremely low (or near zero) and 100-750 kHz frequency ranges. There are experimental works on β cell exposure to electromagnetic fields that support such finding.

Gap-junction coupling and ATP-sensitive potassium channels in human β-cell clusters: Effects on emergent dynamics

The importance of gap-junction coupling between β cells in pancreatic islets is well established in mouse. Such ultrastructural connections synchronize cellular activity, confine biological heterogeneity, and enhance insulin pulsatility. Dysfunction of coupling has been associated with diabetes and altered β-cell function. However, the role of gap junctions between human β cells is still largely unexplored. By using patch-clamp recordings of β cells from human donors, we previously estimated electrical properties of these channels by mathematical modeling of pairs of human β cells. In this work we revise our estimate by modeling triplet configurations and larger heterogeneous clusters. We find that a coupling conductance in the range 0.005-0.020 nS/pF can reproduce experiments in almost all the simulated arrangements. We finally explore the consequence of gap-junction coupling of this magnitude between β cells with mutant variants of the ATP-sensitive potassium channels involved in some metabolic disorders and diabetic conditions, translating studies performed on rodents to the human case. Our results are finally discussed from the perspective of therapeutic strategies. In summary, modeling of more realistic clusters with more than two β cells slightly lowers our previous estimate of gap-junction conductance and gives rise to patterns that more closely resemble experimental traces.

Modeling spatial distribution of oxygen in 3d culture of islet beta-cells

Three-dimensional (3D) scaffold culture of pancreatic β-cell has been proven to be able to better mimic physiological conditions in the body. However, one critical issue with culturing pancreatic β-cells is that β-cells consume large amounts of oxygen, and hence insufficient oxygen supply in the culture leads to loss of β-cell mass and functions. This becomes more significant when cells are cultured in a 3D scaffold. In this study, in order to understand the effect of oxygen tension inside a cell-laden collagen culture on β-cell proliferation, a culture model with encapsulation of an oxygen-generator was established. The oxygen-generator was made by embedding hydrogen peroxide into nontoxic polydimethylsiloxane to avoid the toxicity of a chemical reaction in the β-cell culture. To examine the effectiveness of the oxygenation enabled 3D culture, the spatial-temporal distribution of oxygen tension inside a scaffold was evaluated by a mathematical modeling approach. Our simulation results indicated that an oxygenation-aided 3D culture would augment the oxygen supply required for the β-cells. Furthermore, we identified that cell seeding density and the capacity of the oxygenator are two critical parameters in the optimization of the culture. Notably, cell-laden scaffold cultures with an in situ oxygen supply significantly improved the β-cells' biological function. These β-cells possess high insulin secretion capacity. The results obtained in this work would provide valuable information for optimizing and encouraging functional β-cell cultures. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 33:221-228, 2017.

Mathematical Modeling of Interacting Glucose-Sensing Mechanisms and Electrical Activity Underlying Glucagon-Like Peptide 1 Secretion

Intestinal L-cells sense glucose and other nutrients, and in response release glucagon-like peptide 1 (GLP-1), peptide YY and other hormones with anti-diabetic and weight-reducing effects. The stimulus-secretion pathway in L-cells is still poorly understood, although it is known that GLP-1 secreting cells use sodium-glucose co-transporters (SGLT) and ATP-sensitive K+-channels (K(ATP)-channels) to sense intestinal glucose levels. Electrical activity then transduces glucose sensing to Ca2+-stimulated exocytosis. This particular glucose-sensing arrangement with glucose triggering both a depolarizing SGLT current as well as leading to closure of the hyperpolarizing K(ATP) current is of more general interest for our understanding of glucose-sensing cells. To dissect the interactions of these two glucose-sensing mechanisms, we build a mathematical model of electrical activity underlying GLP-1 secretion. Two sets of model parameters are presented: one set represents primary mouse colonic L-cells; the other set is based on data from the GLP-1 secreting GLUTag cell line. The model is then used to obtain insight into the differences in glucose-sensing between primary L-cells and GLUTag cells. Our results illuminate how the two glucose-sensing mechanisms interact, and suggest that the depolarizing effect of SGLT currents is modulated by K(ATP)-channel activity. Based on our simulations, we propose that primary L-cells encode the glucose signal as changes in action potential amplitude, whereas GLUTag cells rely mainly on frequency modulation. The model should be useful for further basic, pharmacological and theoretical investigations of the cellular signals underlying endogenous GLP-1 and peptide YY release.

Mathematical modeling of heterogeneous electrophysiological responses in human β-cells

Electrical activity plays a pivotal role in glucose-stimulated insulin secretion from pancreatic β-cells. Recent findings have shown that the electrophysiological characteristics of human β-cells differ from their rodent counterparts. We show that the electrophysiological responses in human β-cells to a range of ion channels antagonists are heterogeneous. In some cells, inhibition of small-conductance potassium currents has no effect on action potential firing, while it increases the firing frequency dramatically in other cells. Sodium channel block can sometimes reduce action potential amplitude, sometimes abolish electrical activity, and in some cells even change spiking electrical activity to rapid bursting. We show that, in contrast to L-type Ca2+-channels, P/Q-type Ca2+-currents are not necessary for action potential generation, and, surprisingly, a P/Q-type Ca2+-channel antagonist even accelerates action potential firing. By including SK-channels and Ca2+ dynamics in a previous mathematical model of electrical activity in human β-cells, we investigate the heterogeneous and nonintuitive electrophysiological responses to ion channel antagonists, and use our findings to obtain insight in previously published insulin secretion measurements. Using our model we also study paracrine signals, and simulate slow oscillations by adding a glycolytic oscillatory component to the electrophysiological model. The heterogenous electrophysiological responses in human β-cells must be taken into account for a deeper understanding of the mechanisms underlying insulin secretion in health and disease, and as shown here, the interdisciplinary combination of experiments and modeling increases our understanding of human β-cell physiology.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

A biophysical model of electrical activity in human β-cells

Electrical activity in pancreatic β-cells plays a pivotal role in glucose-stimulated insulin secretion by coupling metabolism to calcium-triggered exocytosis. Mathematical models based on rodent data have helped in understanding the mechanisms underlying the electrophysiological patterns observed in laboratory animals. However, human β-cells differ in several aspects, and in particular in their electrophysiological characteristics, from rodent β-cells. Hence, from a clinical perspective and to obtain insight into the defects in insulin secretion relevant for diabetes mellitus, it is important to study human β-cells. This work presents the first mathematical model of electrical activity based entirely on published ion channel characteristics of human β-cells. The model reproduces satisfactorily a series of experimentally observed patterns in human β-cells, such as spiking and rapid bursting electrical activity, and their response to a range of ion channel antagonists. The possibility of Human Ether-a-Go-Go-related- and leak channels as drug targets for diabetes treatment is discussed based on model results.

Modeling mechanisms of cell secretion

Secretion is a fundamental cellular process involving the regulated release of intracellular products from cells. Physiological functions such as neurotransmission, or the release of hormones and digestive enzymes, are all governed by cell secretion. Anomalies in the processes involved in secretion contribute to the development and progression of diseases such as diabetes and other hormonal disorders. To unravel the mechanisms that govern such diseases, it is essential to understand how hormones, growth factors and neurotransmitters are synthesized and processed, and how their signals are recognized, amplified and transmitted by intracellular signaling pathways in the target cells. Here, we discuss diverse aspects of the detailed mechanisms involved in secretion based on mathematical models. The models range from stochastic ones describing the trafficking of secretory vesicles to deterministic ones investigating the regulation of cellular processes that underlie hormonal secretion. In all cases, the models are closely related to experimental results and suggest theoretical predictions for the secretion mechanisms.

Diabetes: Models, Signals, and Control

The control of diabetes is an interdisciplinary endeavor, which includes a significant biomedical engineering component, with traditions of success beginning in the early 1960s. It began with modeling of the insulin-glucose system, and progressed to large-scale in silico experiments, and automated closed-loop control (artificial pancreas). Here, we follow these engineering efforts through the last, almost 50 years. We begin with the now classic minimal modeling approach and discuss a number of subsequent models, which have recently resulted in the first in silico simulation model accepted as substitute to animal trials in the quest for optimal diabetes control. We then review metabolic monitoring, with a particular emphasis on the new continuous glucose sensors, on the analyses of their time-series signals, and on the opportunities that they present for automation of diabetes control. Finally, we review control strategies that have been successfully employed in vivo or in silico, presenting a promise for the development of a future artificial pancreas and, in particular, discuss a modular architecture for building closed-loop control systems, including insulin delivery and patient safety supervision layers. We conclude with a brief discussion of the unique interactions between human physiology, behavioral events, engineering modeling and control relevant to diabetes.