Model of beta-cell mitochondrial calcium handling and electrical activity. II. Mitochondrial variables

Computational Model of Complex Calcium Dynamics: Store Operated Ca2+ Channels and Mitochondrial Associated Membranes in Pancreatic Acinar Cells

This proposed model explores the intricate Ca2+ dynamics within the pancreatic acinar cells (PACs) by emphasizing the role of store-operated Ca2+ entry (SOCE) and the mitochondrial-associated membranes (MAMs) in the secretory region (apical) of the PACs. Traditionally, Ca2+ releases from the endoplasmic reticulum (ER) via calcium-induced calcium release (CICR). It has been shown to be important in regulating functions such as secretion of digestive enzymes in PACs. However, this model posits that upon the depletion of Ca2+ in the ER, the signaling protein stromal interaction molecule (STIM1) is activated. Activated STIM1, then facilitates the opening of Orai channels, allowing Ca2+ influx through the store-operated calcium channels (SOCCs). The model highlights the complexity of the Ca2+ dynamics, and the importance of SOCE and MAMs in the PACs Ca2+ homeostasis. The numerical and bifurcation analysis illustrate how changes in agonist concentrations can lead to the diverse Ca2+ oscillation patterns, such as thin to broader oscillations, sinusoidal patterns, and baseline fluctuations, driven by the feedback mechanisms involving Ca2+ and inositol 1,4,5 trisphosphate (IP3). This understanding could have broader implications for cellular physiology and the development of therapies targeting Ca2+ signaling pathways.

Calcium oscillations optimize the energetic efficiency of mitochondrial metabolism

Energy transduction is central to living organisms, but the impact of enzyme regulation and signaling on its thermodynamic efficiency is generally overlooked. Here, we analyze the efficiency of ATP production by the tricarboxylic acid cycle and oxidative phosphorylation, which generate most of the chemical energy in eukaryotes. Calcium signaling regulates this pathway and can affect its energetic output, but the concrete energetic impact of this cross-talk remains elusive. Calcium enhances ATP production by activating key enzymes of the tricarboxylic acid cycle while calcium homeostasis is ATP-dependent. We propose a detailed kinetic model describing the calcium-mitochondria cross-talk and analyze it using nonequilibrium thermodynamics: after identifying the effective reactions driving mitochondrial metabolism out of equilibrium, we quantify the mitochondrial thermodynamic efficiency for different conditions. Calcium oscillations, triggered by extracellular stimulation or energy deficiency, boost the thermodynamic efficiency of mitochondrial metabolism, suggesting a compensatory role of calcium signaling in mitochondrial bioenergetics.

Ca2+ release or Ca2+ entry, that is the question: what governs Ca2+ oscillations in pancreatic β cells?

The standard model for Ca2+ oscillations in insulin-secreting pancreatic β cells centers on Ca2+ entry through voltage-activated Ca2+ channels. These work in combination with ATP-dependent K+ channels, which are the bridge between the metabolic state of the cells and plasma membrane potential. This partnership underlies the ability of the β cells to secrete insulin appropriately on a minute-to-minute time scale to control whole body plasma glucose. Though this model, developed over more than 40 years through many cycles of experimentation and mathematical modeling, has been very successful, it has been challenged by a hypothesis that calcium-induced calcium release from the endoplasmic reticulum through ryanodine or inositol trisphosphate (IP3) receptors is instead the key driver of islet oscillations. We show here that the alternative model is in fact incompatible with a large body of established experimental data and that the new observations offered in support of it can be better explained by the standard model.

Kinetic Mathematical Modeling of Oxidative Phosphorylation in Cardiomyocyte Mitochondria

Oxidative phosphorylation (OXPHOS) is an oxygen-dependent process that consumes catabolized nutrients to produce adenosine triphosphate (ATP) to drive energy-dependent biological processes such as excitation-contraction coupling in cardiomyocytes. In addition to in vivo and in vitro experiments, in silico models are valuable for investigating the underlying mechanisms of OXPHOS and predicting its consequences in both physiological and pathological conditions. Here, we compare several prominent kinetic models of OXPHOS in cardiomyocytes. We examine how their mathematical expressions were derived, how their parameters were obtained, the conditions of their experimental counterparts, and the predictions they generated. We aim to explore the general landscape of energy production mechanisms in cardiomyocytes for future in silico models.

Computational Model of the Effect of Mitochondrial Dysfunction on Excitation–Contraction Coupling in Skeletal Muscle

It has become well established that mitochondria not only regulate myoplasmic calcium in skeletal muscle, but also use that calcium to stimulate oxidative phosphorylation (OXPHOS). While experimental approaches have allowed for imaging of mitochondrial calcium and membrane potentials in isolated fibers, capturing the role of mitochondria and the impact of mitochondrial impairments on excitation–contraction coupling (ECC) remains difficult to explore in intact muscle. Computational models have been widely used to examine the structure and function of skeletal muscle contraction; however, models of ECC to date lack communication between the myoplasm and mitochondria for regulating calcium and ATP during sustained contractions. To address this, a mathematical model of mitochondrial calcium handling and OXPHOS was integrated into a physiological model of ECC incorporating action potential propagation, calcium handling between the sarcoplasmic reticulum (SR) and the myoplasm, and crossbridge cycling. The model was used to examine the protective role of mitochondria during repeated stimulation and the impact of mitochondrial dysfunction on ECC resulting from progressive OXPHOS inhibition. Pathological myoplasmic calcium accumulation occurred through distinct mechanisms in the model in the case of either electron transport chain, F1F0 ATP synthase, or adenine nucleotide transporter impairments. To investigate the effect of each impairment on force, a model of calcium-stimulated apoptosis was utilized to capture dysfunction-induced reductions in muscle mass, driving whole muscle force loss. The model presented in this study can be used to examine the role of mitochondria in the regulation of calcium, ATP, and force generation during voluntary contraction.

Theoretical approaches used in the modelling of reversible and irreversible mitochondrial swelling in vitro

Existing theoretical approaches were considered that allow modelling of mitochondrial swelling (MS) dynamics. Simple phenomenological kinetic models were reviewed. Simple and extended biophysical and bioenergetic models that ignore mechanical properties of inner mitochondrial membrane (IMM), and similar models that include these mechanical properties were also reviewed. Limitations of these models we considered, as regards correct modelling of MS dynamics. It was found that simple phenomenological kinetic models have significant limitations, due to dependence of the kinetic parameter values estimated by fitting of the experimental data on the experimental conditions. Additionally, such simple models provide no understanding of the detailed mechanisms behind the MS dynamics, nor of the dynamics of various system parameters during MS. Thus, biophysical and bioenergetic models ignoring IMM mechanical properties can't be used to model the transition between reversible and irreversible MS. However, simple and extended biophysical models that include IMM mechanical properties allow modelling the transition to irreversible swelling. These latter models are still limited due to significantly simplified description of biochemistry, compared to those of bioenergetic models. Finally, a strategy of model development is proposed, towards correct interpretation of the mitochondrial life cycle, including the effects of MS dynamics.

Computational modeling of mitochondrial K+- and H+-driven ATP synthesis

ATP synthase (F1Fo) is a rotary molecular engine that harnesses energy from electrochemical-gradients across the inner mitochondrial membrane for ATP synthesis. Despite the accepted tenet that F1Fo transports exclusively H+, our laboratory has demonstrated that, in addition to H+, F1Fo ATP synthase transports a significant fraction of ΔΨm-driven charge as K+ to synthesize ATP. Herein, we utilize a computational modeling approach as a proof of principle of the feasibility of the core mechanism underlying the enhanced ATP synthesis, and to explore its bioenergetic consequences. A minimal model comprising the 'core' mechanism constituted by ATP synthase, driven by both proton (PMF) and potassium motive force (KMF), respiratory chain, adenine nucleotide translocator, Pi carrier, and K+/H+ exchanger (KHEmito) was able to simulate enhanced ATP synthesis and respiratory fluxes determined experimentally with isolated heart mitochondria. This capacity of F1Fo ATP synthase confers mitochondria with a significant energetic advantage compared to K+ transport through a channel not linked to oxidative phosphorylation (OxPhos). The K+-cycling mechanism requires a KHEmito that exchanges matrix K+ for intermembrane space H+, leaving PMF as the overall driving energy of OxPhos, in full agreement with the standard chemiosmotic mechanism. Experimental data of state 4➔3 energetic transitions, mimicking low to high energy demand, could be reproduced by an integrated computational model of mitochondrial function that incorporates the 'core' mechanism. Model simulations display similar behavior compared to the experimentally observed changes in ΔΨm, mitochondrial K+ uptake, matrix volume, respiration, and ATP synthesis during the energetic transitions at physiological pH and K+ concentration. The model also explores the role played by KHEmito in modulating the energetic performance of mitochondria. The results obtained support the available experimental evidence on ATP synthesis driven by K+ and H+ transport through the F1Fo ATP synthase.

Understanding mitochondria and the utility of optimization as a canonical framework for identifying and modeling mitochondrial pathways

The goal of this paper is to provide an overview of our current understanding of mitochondrial function as a framework to motivate the hypothesis that mitochondrial behavior is governed by optimization principles that are constrained by the laws of the physical and biological sciences. Then, mathematical optimization tools can generally be useful to model some of these processes under reasonable assumptions and limitations. We are specifically interested in optimizations via variational methods, which are briefly summarized. Within such an optimization framework, we suggest that the numerous mechanical instigators of cell and intracellular functioning can be modeled utilizing some of the principles of mechanics that govern engineered systems, as well as by the frequently observed feedback and feedforward mechanisms that coordinate the multitude of processes within cells. These mechanical aspects would need to be coupled to governing biochemical rules. Of course, biological systems are significantly more complex than engineered systems, and require considerably more experimentation to ascertain and characterize parameters and subsequent behavior. That complexity requires well-defined limitations and assumptions for any derived models. Optimality is being motivated as a framework to help us understand how cellular decisions are made, especially those that transition between physiological behaviors and dysfunctions along pathophysiological pathways. We elaborate on our interpretation of optimality and cellular decision making within the body of this paper, as we revisit these ideas in the numerous different contexts of mitochondrial functions.

Computational Modeling of Mitochondria to Understand the Dynamics of Oxidative Stress

Mitochondria are complex organelles that use catabolic metabolism to produce ATP which is the critical energy source for cell function. Oxidative phosphorylation by the electron transport chain, which receives reducing equivalents (NADH and FADH₂) from the tricarboxylic acid cycle, also produces reactive oxygen species (ROS) as a by-product at complex I and III. ROS play a significant role in health and disease. In order to better understand this process, a computational model of mitochondrial energy metabolism and the production of ROS has been developed. The model demonstrates the process regulating ROS production and removal and how different energy substrates can affect ROS production.

Symbiosis of Electrical and Metabolic Oscillations in Pancreatic β-Cells

Insulin is secreted in a pulsatile pattern, with important physiological ramifications. In pancreatic β-cells, which are the cells that synthesize insulin, insulin exocytosis is elicited by pulses of elevated intracellular Ca²⁺ initiated by bursts of electrical activity. In parallel with these electrical and Ca²⁺ oscillations are oscillations in metabolism, and the periods of all of these oscillatory processes are similar. A key question that remains unresolved is whether the electrical oscillations are responsible for the metabolic oscillations via the effects of Ca²⁺, or whether the metabolic oscillations are responsible for the electrical oscillations due to the effects of ATP on ATP-sensitive ion channels? Mathematical modeling is a useful tool for addressing this and related questions as modeling can aid in the design of well-focused experiments that can test the predictions of particular models and subsequently be used to improve the models in an iterative fashion. In this article, we discuss a recent mathematical model, the Integrated Oscillator Model (IOM), that was the product of many years of development. We use the model to demonstrate that the relationship between calcium and metabolism in beta cells is symbiotic: in some contexts, the electrical oscillations drive the metabolic oscillations, while in other contexts it is the opposite. We provide new insights regarding these results and illustrate that what might at first appear to be contradictory data are actually compatible when viewed holistically with the IOM.

Brain energetics, mitochondria, and traumatic brain injury

We review current thinking about, and draw connections between, brain energetics and metabolism, and between mitochondria and traumatic brain injury. Energy is fundamental to proper brain function. Its creation in a useful form for neurons and glia, and consistently in response to the brain's high energy needs, is critical for physiological pathways. Dysfunction in the mechanisms of energy production is at the center of neurological and neuropsychiatric pathologies. We examine the connections between energetics and mitochondria - the organelle responsible for almost all the energy production in the cell - and how secondary pathologies in traumatic brain injury result from energetic dysfunction. This paper interweaves these topics, a necessity since they are closely coupled, and identifies where there exist a lack of understanding and of data. In addition to summarizing current thinking in these disciplines, our goal is to suggest a framework for the mathematical modeling of mechanisms and pathways based on optimal energetic decisions.

Reversible and irreversible mitochondrial swelling in vitro

Mitochondrial activity as regards ATP production strongly depends on mitochondrial swelling (MS) mode. Therefore, this work analyzes reversible and irreversible MS using a detailed biophysical model. The reported model includes mechanical properties of the inner mitochondrial membrane (IMM). The model describes MS dynamics for spherically symmetric, axisymmetric ellipsoidal and general ellipsoidal mitochondria. Mechanical stretching properties of the IMM were described by a second-rank rigidity tensor. The tensor components were estimated by fitting to the earlier reported results of in vitro experiments. The IMM rigidity constant of ca. 0.008 dyn/nm was obtained for linear deformations. The model also included membrane bending effects, which were small compared to those of membrane stretching. The model was also tested by simulation of the earlier reported experimental data and of the system dynamics at different initial conditions, predicting the system behavior. The transition criteria from reversible to irreversible swelling were determined and tested. The presently developed model is applicable directly to the analysis of in vitro experimental data, while additional improvements are necessary before it could be used to describe mitochondrial swelling in vivo. The reported theoretical model also provides an idea of physically consistent mechanism for the permeability transport pore (PTP) opening, which depends on the IMM stretching stress. In the current study, this idea is discussed briefly, but a detailed theoretical analysis of these ideas will be performed later. The currently developed model provides new understanding of the detailed MS mechanism and of the conditions for the transition between reversible and irreversible MS modes. On the other hand, the current model provides useful mathematical tools, that may be successfully used in mitochondrial biophysics research, and also in other applications, predicting the behavior of mitochondria in different conditions of the surrounding media in vitro or cellular cyto(sarco)plasm in vivo. These mathematical tools are based on real biophysical processes occurring in mitochondria. Thus, we note a significant progress in the theoretical approach, which may be used in real biological systems, compared to the earlier reported models. Significance of this study derives from inclusion of IMM mechanical properties, which directly impact the reversible and irreversible mitochondrial swelling dynamics. Reversible swelling corresponds to reversible IMM deformations, while irreversible swelling corresponds to irreversible deformations, with eventual membrane disruption. The IMM mechanical properties are directly dependent on the membrane biochemical composition and structure. The IMM deformationas are induced by osmotic pressure created by the ionic/neutral solute imbalance between the mitochondrial matrix media and the bulk solution in vitro, or cyto(sarco)plasm in vivo. The novelty of the reported model is in the biophysical mechanism detailing ionic and neutral solute transport for a large number of solutes, which were not taken into account in the earlier reported biophysical models of MS. Therefore, the reported model allows understanding response of mitochondria to the changes of initial concentration(s) of any of the solute(s) included in the model. Note that the values of all of the model parameters and kinetic constants have been estimated and the resulting complete model may be used for quantitative analysis of mitochondrial swelling dynamics in conditions of real in vitro experiments.

Stretching tension effects in permeability transition pores of inner mitochondrial membrane

Presently a mechanism of permeability transition pore (PTP) opening was proposed and discussed. This mechanism is based on mechanical stretching of inner mitochondrial membrane (IMM) caused by mitochondrial swelling (MS). The latter is induced by osmotic pressure generated by solute imbalance between the matrix and the surrounding cyto(sarco)plasm. Modelled by the Monte-Carlo method, an IMM fragment of 350 simulated biological molecules exhibited formation of micro-domains containing two protein and seven phospholipid molecules. The energies (-0.191 eV per molecule) in these micro-domains were significantly larger than those (-0.375 eV per molecule) of other parts of the IMM fragment. Stretching forces applied to such domains expanded them much more than other parts of the IMM fragment. We identify these micro-domains as the PTPs. Both linear and nonlinear functions were used for the strain-stress relation of the IMM fragment, with nonlinear effects more important at large IMM stretching strains. Thus, two main factors are incorporated into the PTP opening mechanism: (1) presence of micro-domains in the IMM structure and (2) IMM stretching stress caused by MS. Taking into account both of these factors, the equation for the probability of PTP opening was deduced, with matrix Ca²⁺ and H⁺ ionic concentrations as its parameters. Note that the equation deduced was similar to an earlier reported empirical equation describing PTP opening dynamics. This correspondence provides support to the presently proposed mechanism. Thus, a new look at the PTP opening mechanism is provided, of interest to various research areas related to mitochondrial biophysics.

Effect of crista morphology on mitochondrial ATP output: A computational study

Folding of the mitochondrial inner membrane (IM) into cristae greatly increases the ATP-generating surface area, S _IM, per unit volume but also creates diffusional bottlenecks that could limit reaction rates inside mitochondria. This study explores possible effects of inner membrane folding on mitochondrial ATP output, using a mathematical model for energy metabolism developed by the Jafri group and two- and three-dimensional spatial models for mitochondria, implemented on the Virtual Cell platform. Simulations demonstrate that cristae are micro-compartments functionally distinct from the cytosol. At physiological steady states, standing gradients of ADP form inside cristae that depend on the size and shape of the compartments, and reduce local flux (rate per unit area) of the adenine nucleotide translocase. This causes matrix ADP levels to drop, which in turn reduces the flux of ATP synthase. The adverse effects of membrane folding on reaction fluxes increase with crista length and are greater for lamellar than tubular crista. However, total ATP output per mitochondrion is the product of flux of ATP synthase and S _IM which can be two-fold greater for mitochondria with lamellar than tubular cristae, resulting in greater ATP output for the former. The simulations also demonstrate the crucial role played by intracristal kinases (adenylate kinase, creatine kinase) in maintaining the energy advantage of IM folding.

Calcium-dependent insulin resistance in hepatocytes: mathematical model

Hepatocyte insulin resistance is one of the early factors of developing type II diabetes. If insulin resistance is treated early, type II diabetes could be prevented. In recent years, scientists have been conducting extensive research on the underlying issues on a cellular and molecular level. It was found that the modulation of IP₃-receptors, the mitochondrial ability to form the mitochondria-associated membranes (MAMs) and the endoplasmic reticulum stress during Ca²⁺ signaling play a key role in hepatocyte being able to maintain euglycemia and provide metabolic flexibility. However, researchers cannot agree on what factor is the key one in resulting in insulin resistance. In this work, we propose a mathematical model of Ca²⁺ signaling. We included in the model all the major contributors of a proper Ca²⁺ signaling during both the fasting and the postprandial state. Our modeling results are in good agreement with available experimental data. The analysis of modeling results suggests that MAMs dysfunction alone cannot result in abnormal Ca²⁺ signaling and the wrong modulation of IP₃-receptors is a more definite reason. However, both the MAMs dysfunction and the IP₃ signaling dysregulation combined can lead to a robust Ca²⁺ signal and improper glucose release. In addition, our model results suggest a strong dependence of Ca²⁺ oscillations pattern on morphological characteristics of the ER and the mitochondria.

A mathematical model for persistent post-CSD vasoconstriction

Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.

Endothelium as a Therapeutic Target in Diabetes Mellitus: From Basic Mechanisms to Clinical Practice

Endothelium plays an essential role in human homeostasis by regulating arterial blood pressure, distributing nutrients and hormones as well as providing a smooth surface that modulates coagulation, fibrinolysis and inflammation. Endothelial dysfunction is present in Diabetes Mellitus (DM) and contributes to the development and progression of macrovascular disease, while it is also associated with most of the microvascular complications such as diabetic retinopathy, nephropathy and neuropathy. Hyperglycemia, insulin resistance, hyperinsulinemia and dyslipidemia are the main factors involved in the pathogenesis of endothelial dysfunction. Regarding antidiabetic medication, metformin, gliclazide, pioglitazone, exenatide and dapagliflozin exert a beneficial effect on Endothelial Function (EF); glimepiride and glibenclamide, dipeptidyl peptidase-4 inhibitors and liraglutide have a neutral effect, while studies examining the effect of insulin analogues, empagliflozin and canagliflozin on EF are limited. In terms of lipid-lowering medication, statins improve EF in subjects with DM, while data from short-term trials suggest that fenofibrate improves EF; ezetimibe also improves EF but further studies are required in people with DM. The effect of acetylsalicylic acid on EF is dose-dependent and lower doses improve EF while higher ones do not. Clopidogrel improves EF, but more studies in subjects with DM are required. Furthermore, angiotensin- converting-enzyme inhibitors /angiotensin II receptor blockers improve EF. Phosphodiesterase type 5 inhibitors improve EF locally in the corpus cavernosum. Finally, cilostazol exerts favorable effect on EF, nevertheless, more data in people with DM are required.

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.

Decoding the regulatory mechanism of glucose and insulin induced phosphatidylinositol 3,4,5-trisphosphate dynamics in β-cells

In MIN6 pancreatic β-cells, glucose and insulin act in a synergistic manner to regulate the dynamics of Phosphatidylinositol (3,4,5)-trisphosphate (PIP₃). However, the precise regulatory mechanism behind such an experimentally observed synergy is poorly understood. In this article, we propose a phenomenological mathematical model for studying the glucose and insulin driven PIP₃ activation dynamics under various stimulatory conditions to unfold the mechanism responsible for the observed synergy. The modeling study reveals that the experimentally observed oscillation in PIP₃ dynamics with disparate time scales for different external glucose doses is mainly orchestrated by the complex dynamic regulation of cytosolic Ca²⁺ in β-cells. The model accounts for the dose-dependent activation of PIP₃ as a function of externally added insulin, and further shows that even in the absence of Ca²⁺ signaling, externally added glucose can still maintain a basal level of endogenous insulin secretion via the fatty acid metabolism pathway. Importantly, the model analysis suggests that the glucose mediated ROS (reactive oxygen species) activation often contributes considerably to the synergistic activation of PIP₃ by glucose and insulin in a context dependent manner. Under the physiological conditions that keep β-cells in an insulin responsive state, the effect of glucose induced ROS signaling plays a moderate role in PIP₃ activation. As β-cells approach an insulin resistant state, the glucose induced ROS signaling significantly affects the PIP₃ dynamics. Our findings provide a plausible mechanistic insight into the experimentally observed synergy, and can lead to novel therapeutic strategies.

Bioluminescence Assays for Monitoring Chondrogenic Differentiation and Cartilage Regeneration

Since articular cartilage has a limited regeneration potential, for developing biological therapies for cartilage regeneration it is important to study the mechanisms underlying chondrogenesis of stem cells. Bioluminescence assays can visualize a wide range of biological phenomena such as gene expression, signaling, metabolism, development, cellular movements, and molecular interactions by using visible light and thus contribute substantially to elucidation of their biological functions. This article gives a concise review to introduce basic principles of bioluminescence assays and applications of the technology to visualize the processes of chondrogenesis and cartilage regeneration. Applications of bioluminescence assays have been highlighted in the methods of real-time monitoring of gene expression and intracellular levels of biomolecules and noninvasive cell tracking within animal models. This review suggests that bioluminescence assays can be applied towards a visual understanding of chondrogenesis and cartilage regeneration.

COEXISTENCE OF THREE OSCILLATORY MODES OF INSULIN SECRETION: MATHEMATICAL MODELING AND RELEVANCE TO GLUCOSE REGULATION

Insulin secretion in pancreatic [Formula: see text]-cells exhibits three oscillatory modes with distinct period ranges, called fast, slow, and ultradian modes. To unveil the mechanism underlying such oscillatory behaviors and their roles in blood glucose regulation, we propose a combined model for the glucose–insulin regulation system, incorporating both the cell-level insulin secretion mechanism and inter-organ interactions in the blood glucose regulation. Special emphasis is placed on the identification of the mechanism of the slow oscillation and its role associated with the whole-body glucose regulation. Via extensive numerical simulations, we obtain macroscopic behaviors of the three types of insulin/glucose oscillations in the whole-body as well as microscopic behaviors of the membrane potential and the calcium concentration in the [Formula: see text]-cell. Finally, optimal regulatory strategies for the blood glucose level are discussed on the basis of the quantitative information obtained from the mathematical modeling and numerical simulations.

Ca2+ Effects on ATP Production and Consumption Have Regulatory Roles on Oscillatory Islet Activity

Pancreatic islets respond to elevated blood glucose by secreting pulses of insulin that parallel oscillations in β-cell metabolism, intracellular Ca(2+) concentration, and bursting electrical activity. The mechanisms that maintain an oscillatory response are not fully understood, yet several models have been proposed. Only some can account for experiments supporting that metabolism is intrinsically oscillatory in β-cells. The dual oscillator model (DOM) implicates glycolysis as the source of oscillatory metabolism. In the companion article, we use recently developed biosensors to confirm that glycolysis is oscillatory and further elucidate the coordination of metabolic and electrical signals in the insulin secretory pathway. In this report, we modify the DOM by incorporating an established link between metabolism and intracellular Ca(2+) to reconcile model predictions with experimental observations from the companion article. With modification, we maintain the distinguishing feature of the DOM, oscillatory glycolysis, but introduce the ability of Ca(2+) influx to reshape glycolytic oscillations by promoting glycolytic efflux. We use the modified model to explain measurements from the companion article and from previously published experiments with islets.

Phase Analysis of Metabolic Oscillations and Membrane Potential in Pancreatic Islet β-Cells

Metabolism in islet β-cells displays oscillations that can trigger pulses of electrical activity and insulin secretion. There has been a decades-long debate among islet biologists about whether metabolic oscillations are intrinsic or occur in response to oscillations in intracellular Ca(2+) that result from bursting electrical activity. In this article, the dynamics of oscillatory metabolism were investigated using five different optical reporters. Reporter activity was measured simultaneously with membrane potential bursting to determine the phase relationships between the metabolic oscillations and electrical activity. Our experimental findings suggest that Ca(2+) entry into β-cells stimulates the rate of mitochondrial metabolism, accounting for the depletion of glycolytic intermediates during each oscillatory burst. We also performed Ca(2+) clamp tests in which we clamped membrane potential with the KATP channel-opener diazoxide and KCl to fix Ca(2+) at an elevated level. These tests confirm that metabolic oscillations do not require Ca(2+) oscillations, but show that Ca(2+) plays a larger role in shaping metabolic oscillations than previously suspected. A dynamical picture of the mechanisms of oscillations emerged that requires the restructuring of contemporary mathematical β-cell models, including our own dual oscillator model. In the companion article, we modified our model to account for these new data.

Electrical stimulation drives chondrogenesis of mesenchymal stem cells in the absence of exogenous growth factors

Electrical stimulation (ES) is known to guide the development and regeneration of many tissues. However, although preclinical and clinical studies have demonstrated superior effects of ES on cartilage repair, the effects of ES on chondrogenesis remain elusive. Since mesenchyme stem cells (MSCs) have high therapeutic potential for cartilage regeneration, we investigated the actions of ES during chondrogenesis of MSCs. Herein, we demonstrate for the first time that ES enhances expression levels of chondrogenic markers, such as type II collagen, aggrecan, and Sox9, and decreases type I collagen levels, thereby inducing differentiation of MSCs into hyaline chondrogenic cells without the addition of exogenous growth factors. ES also induced MSC condensation and subsequent chondrogenesis by driving Ca2+/ATP oscillations, which are known to be essential for prechondrogenic condensation. In subsequent experiments, the effects of ES on ATP oscillations and chondrogenesis were dependent on extracellular ATP signaling via P2X4 receptors, and ES induced significant increases in TGF-β1 and BMP2 expression. However, the inhibition of TGF-β signaling blocked ES-driven condensation, whereas the inhibition of BMP signaling did not, indicating that TGF-β signaling but not BMP signaling mediates ES-driven condensation. These findings may contribute to the development of electrotherapeutic strategies for cartilage repair using MSCs.

Interplay Between Intracellular Ca(2+) Oscillations and Ca(2+)-stimulated Mitochondrial Metabolism

Oscillations of cytosolic Ca(2+) concentration are a widespread mode of signalling. Oscillatory spikes rely on repetitive exchanges of Ca(2+) between the endoplasmic reticulum (ER) and the cytosol, due to the regulation of inositol 1,4,5-trisphosphate receptors. Mitochondria also sequester and release Ca(2+), thus affecting Ca(2+) signalling. Mitochondrial Ca(2+) activates key enzymes involved in ATP synthesis. We propose a new integrative model for Ca(2+) signalling and mitochondrial metabolism in electrically non-excitable cells. The model accounts for (1) the phase relationship of the Ca(2+) changes in the cytosol, the ER and mitochondria, (2) the dynamics of mitochondrial metabolites in response to cytosolic Ca(2+) changes, and (3) the impacts of cytosol/mitochondria Ca(2+) exchanges and of mitochondrial metabolism on Ca(2+) oscillations. Simulations predict that as expected, oscillations are slowed down by decreasing the rate of Ca(2+) efflux from mitochondria, but also by decreasing the rate of Ca(2+) influx through the mitochondrial Ca(2+) uniporter (MCU). These predictions were experimentally validated by inhibiting MCU expression. Despite the highly non-linear character of Ca(2+) dynamics and mitochondrial metabolism, bioenergetics were found to be robust with respect to changes in frequency and amplitude of Ca(2+) oscillations.

Modeling K,ATP--dependent excitability in pancreatic islets

In pancreatic ?-cells, K,ATP channels respond to changes in glucose to regulate cell excitability and insulin release. Confirming a high sensitivity of electrical activity to K,ATP activity, mutations that cause gain of K,ATP function cause neonatal diabetes. Our aim was to quantitatively assess the contribution of K,ATP current to the regulation of glucose-dependent bursting by reproducing experimentally observed changes in excitability when K,ATP conductance is altered by genetic manipulation. A recent detailed computational model of single cell pancreatic ?-cell excitability reproduces the ?-cell response to varying glucose concentrations. However, initial simulations showed that the model underrepresents the significance of K,ATP activity and was unable to reproduce K,ATP conductance-dependent changes in excitability. By altering the ATP and glucose dependence of the L-type Ca(2+) channel and the Na-K ATPase to better fit experiment, appropriate dependence of excitability on K,ATP conductance was reproduced. Because experiments were conducted in islets, which contain cell-to-cell variability, we extended the model from a single cell to a three-dimensional model (10×10×10 cell) islet with 1000 cells. For each cell, the conductance of the major currents was allowed to vary as was the gap junction conductance between cells. This showed that single cell glucose-dependent behavior was then highly variable, but was uniform in coupled islets. The study highlights the importance of parameterization of detailed models of ?-cell excitability and suggests future experiments that will lead to improved characterization of ?-cell excitability and the control of insulin secretion.

Vascular responses of the extremities to transdermal application of vasoactive agents in Caucasian and African descent individuals

PURPOSE

Individuals of African descent (AFD) are more susceptible to non-freezing cold injury than Caucasians (CAU) which may be due, in part, to differences in the control of skin blood flow. We investigated the skin blood flow responses to transdermal application of vasoactive agents.

METHODS

Twenty-four young males (12 CAU and 12 AFD) undertook three tests in which iontophoresis was used to apply acetylcholine (ACh 1 w/v %), sodium nitroprusside (SNP 0.01 w/v %) and noradrenaline (NA 0.5 mM) to the skin. The skin sites tested were: volar forearm, non-glabrous finger and toe, and glabrous finger (pad) and toe (pad).

RESULTS

In response to SNP on the forearm, AFD had less vasodilatation for a given current application than CAU (P = 0.027-0.004). ACh evoked less vasodilatation in AFD for a given application current in the non-glabrous finger and toe compared with CAU (P = 0.043-0.014) with a lower maximum vasodilatation in the non-glabrous finger (median [interquartile], AFD n = 11, 41[234] %, CAU n = 12, 351[451] %, P = 0.011) and non-glabrous toe (median [interquartile], AFD n = 9, 116[318] %, CAU n = 12, 484[720] %, P = 0.018). ACh and SNP did not elicit vasodilatation in the glabrous skin sites of either group. There were no ethnic differences in response to NA.

CONCLUSION

AFD have an attenuated endothelium-dependent vasodilatation in non-glabrous sites of the fingers and toes compared with CAU. This may contribute to lower skin temperature following cold exposure and the increased risk of cold injuries experienced by AFD.

Calcium and Metabolic Oscillations in Pancreatic Islets: Who's Driving the Bus?*

Pancreatic islets exhibit bursting oscillations in response to elevated blood glucose. These oscillations are accompanied by oscillations in the free cytosolic Ca2+ concentration (Cac ), which drives pulses of insulin secretion. Both islet Ca2+ and metabolism oscillate, but there is some debate about their interrelationship. Recent experimental data show that metabolic oscillations in some cases persist after the addition of diazoxide (Dz), which opens K(ATP) channels, hyperpolarizing β-cells and preventing Ca2+ entry and Ca2+ oscillations. Further, in some islets in which metabolic oscillations were eliminated with Dz, increasing the cytosolic Ca2+ concentration by the addition of KCl could restart the metabolic oscillations. Here we address why metabolic oscillations persist in some islets but not others, and why raising Cac restarts oscillations in some islets but not others. We answer these questions using the dual oscillator model (DOM) for pancreatic islets. The DOM can reproduce the experimental data and shows that the model supports two different mechanisms for slow metabolic oscillations, one that requires calcium oscillations and one that does not.

Mitochondrial reactive oxygen species (ROS) and ROS-induced ROS release

Byproducts of normal mitochondrial metabolism and homeostasis include the buildup of potentially damaging levels of reactive oxygen species (ROS), Ca(2+), etc., which must be normalized. Evidence suggests that brief mitochondrial permeability transition pore (mPTP) openings play an important physiological role maintaining healthy mitochondria homeostasis. Adaptive and maladaptive responses to redox stress may involve mitochondrial channels such as mPTP and inner membrane anion channel (IMAC). Their activation causes intra- and intermitochondrial redox-environment changes leading to ROS release. This regenerative cycle of mitochondrial ROS formation and release was named ROS-induced ROS release (RIRR). Brief, reversible mPTP opening-associated ROS release apparently constitutes an adaptive housekeeping function by the timely release from mitochondria of accumulated potentially toxic levels of ROS (and Ca(2+)). At higher ROS levels, longer mPTP openings may release a ROS burst leading to destruction of mitochondria, and if propagated from mitochondrion to mitochondrion, of the cell itself. The destructive function of RIRR may serve a physiological role by removal of unwanted cells or damaged mitochondria, or cause the pathological elimination of vital and essential mitochondria and cells. The adaptive release of sufficient ROS into the vicinity of mitochondria may also activate local pools of redox-sensitive enzymes involved in protective signaling pathways that limit ischemic damage to mitochondria and cells in that area. Maladaptive mPTP- or IMAC-related RIRR may also be playing a role in aging. Because the mechanism of mitochondrial RIRR highlights the central role of mitochondria-formed ROS, we discuss all of the known ROS-producing sites (shown in vitro) and their relevance to the mitochondrial ROS production in vivo.

Characterization of the effect of the mitochondrial protein Hint2 on intracellular Ca(2+) dynamics

Hint2, one of the five members of the superfamily of the histidine triad AMP-lysine hydrolase proteins, is expressed in mitochondria of various cell types. In human adrenocarcinoma cells, Hint2 modulates Ca(2+) handling by mitochondria. As Hint2 is highly expressed in hepatocytes, we investigated if this protein affects Ca(2+) dynamics in this cell type. We found that in hepatocytes isolated from Hint2(-/-) mice, the frequency of Ca(2+) oscillations induced by 1 μM noradrenaline was 150% higher than in the wild-type. Using spectrophotometry, we analyzed the rates of Ca(2+) pumping in suspensions of mitochondria prepared from hepatocytes of either wild-type or Hint2(-/-) mice; we found that Hint2 accelerates Ca(2+) pumping into mitochondria. We then resorted to computational modeling to elucidate the possible molecular target of Hint2 that could explain both observations. On the basis of a detailed model for mitochondrial metabolism proposed in another study, we identified the respiratory chain as the most probable target of Hint2. We then used the model to predict that the absence of Hint2 leads to a premature opening of the mitochondrial permeability transition pore in response to repetitive additions of Ca(2+) in suspensions of mitochondria. This prediction was then confirmed experimentally.

Modeling the intracellular organization of calcium signaling

Calcium (Ca²⁺) is a key signaling ion that plays a fundamental role in many cellular processes in most types of tissues and organisms. The versatility of this signaling pathway is remarkable. Depending on the cell type and the stimulus, intracellular Ca²⁺ increases can last over different periods, as short spikes or more sustained signals. From a spatial point of view, they can be localized or invade the whole cell. Such a richness of behaviors is possible thanks to numerous exchange processes with the external medium or internal Ca²⁺ pools, mainly the endoplasmic or sarcoplasmic reticulum and mitochondria. These fluxes are also highly regulated. In order to get an accurate description of the spatiotemporal organization of Ca²⁺ signaling, it is useful to resort to modeling. Thus, each flux can be described by an appropriate kinetic expression. Ca²⁺ dynamics in a given cell type can then be simulated by a modular approach, consisting of the assembly of computational descriptions of the appropriate fluxes and regulations. Modeling can also be used to get insight into the mechanisms of decoding of the Ca²⁺ signals responsible for cellular responses. Cells can use frequency or amplitude coding, as well as take profit of Ca²⁺ oscillations to increase their sensitivity to small average Ca²⁺ increases.

Metabolism-secretion coupling and mitochondrial calcium activities in clonal pancreatic β-cells

Pancreatic β-cells are the only cells capable of lowering blood glucose by secreting insulin. The β-cell continuously adjusts its secretory activity to substrate availability in order to keep blood glucose levels within the physiological range--a process called metabolism-secretion coupling. Glucose is readily taken up by the β-cell and broken down into intermediates that fuel oxidative metabolism inside the mitochondria to generate ATP. The resulting increase in the ATP/ADP ratio causes closure of plasma membrane KATP channels, thereby depolarizing the cell and triggering the opening of voltage-gated Ca²⁺ channels. Consequential oscillations of cytosolic Ca²⁺ not only mediate the exocytosis of insulin granules but are also relayed to other subcellular compartments including the mitochondria, where Ca²⁺ is required to accelerate mitochondrial metabolism in response to nutrient stimulation. The mitochondrial Ca²⁺ uptake machinery plays a fundamental role in this feed-forward mechanism that guarantees sustained insulin secretion and, thus, represents a promising therapeutic target for type 2 diabetes.

Mathematical models of electrical activity of the pancreatic β-cell: a physiological review

Mathematical modeling of the electrical activity of the pancreatic β-cell has been extremely important for understanding the cellular mechanisms involved in glucose-stimulated insulin secretion. Several models have been proposed over the last 30 y, growing in complexity as experimental evidence of the cellular mechanisms involved has become available. Almost all the models have been developed based on experimental data from rodents. However, given the many important differences between species, models of human β-cells have recently been developed. This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

Modeling mitochondrial function and its role in disease

Many neurodegenerative diseases involve defects in mitochondrial function. These defects often arise from mutations carried in the genes that code mitochondrial proteins. Many of these defective proteins are involved in mitochondrial energy metabolism which is one of the primary roles of the mitochondria. However, others proteins have other roles that are related to signaling or mitochondrial structure. The interaction of the mitochondrial proteins is complex. Understanding these complex dynamics requires the use of computational models. Studies have started to exploit such models, but much further work is necessary to understand mitochondrial function and its role in neurodegenerative disease.

Slow oscillations of KATP conductance in mouse pancreatic islets provide support for electrical bursting driven by metabolic oscillations

We used the patch clamp technique in situ to test the hypothesis that slow oscillations in metabolism mediate slow electrical oscillations in mouse pancreatic islets by causing oscillations in KATP channel activity. Total conductance was measured over the course of slow bursting oscillations in surface β-cells of islets exposed to 11.1 mM glucose by either switching from current clamp to voltage clamp at different phases of the bursting cycle or by clamping the cells to -60 mV and running two-second voltage ramps from -120 to -50 mV every 20 s. The membrane conductance, calculated from the slopes of the ramp current-voltage curves, oscillated and was larger during the silent phase than during the active phase of the burst. The ramp conductance was sensitive to diazoxide, and the oscillatory component was reduced by sulfonylureas or by lowering extracellular glucose to 2.8 mM, suggesting that the oscillatory total conductance is due to oscillatory KATP channel conductance. We demonstrate that these results are consistent with the Dual Oscillator model, in which glycolytic oscillations drive slow electrical bursting, but not with other models in which metabolic oscillations are secondary to calcium oscillations. The simulations also confirm that oscillations in membrane conductance can be well estimated from measurements of slope conductance and distinguished from gap junction conductance. Furthermore, the oscillatory conductance was blocked by tolbutamide in isolated β-cells. The data, combined with insights from mathematical models, support a mechanism of slow (∼5 min) bursting driven by oscillations in metabolism, rather than by oscillations in the intracellular free calcium concentration.

Modeling the ATP production in mitochondria

We revisit here the mathematical model for ATP production in mitochondria introduced recently by Bertram, Pedersen, Luciani, and Sherman (BPLS) as a simplification of the more complete but intricate Magnus and Keizer's model. We identify some inaccuracies in the BPLS original approximations for two flux rates, namely the adenine nucleotide translocator rate JANT and the calcium uniporter rate Juni. We introduce new approximations for such flux rates and then analyze some of the dynamical properties of the model. We infer, from exhaustive numerical explorations, that the enhanced BPLS equations have a unique attractor fixed point for physiologically acceptable ranges of mitochondrial variables and respiration inputs, as one would indeed expect from homeostasis. We determine, in the stationary regime, the dependence of the mitochondrial variables on the respiration inputs, namely the cytosolic concentration of calcium Cac and the substrate fructose 1,6-bisphosphate FBP. The same dynamical effects of calcium and FBP saturations reported for the original BPLS model are observed here. We find out, however, a novel nonstationary effect, which could be, in principle, physiologically interesting: some response times of the model tend to increase considerably for high concentrations of calcium and/or FBP. In particular, the larger the concentrations of Cac and/or FBP, the larger the necessary time to attain homeostasis.

Store-operated calcium entry could prevent continuous spiking of membrane potential to sustain normal intracellular calcium oscillations and normal potential bursting in pancreatic β-cells

We propose a dynamical store-operated calcium entry (SOCE) model to analyze the complex role of SOCE in modulating calcium oscillations and electrical activity in pancreatic β-cells and provide a new mathematical insight. Using this model, we simulate the SOCE role in a number of cases with different SOCE conductances. When the SOCE conductance is set to 0 or very small (5 pS), our numerical simulation conforms to the experimental observation that endoplasmic reticulum (ER) calcium can sustain normal calcium oscillations and the depletion of ER calcium transforms the normal calcium oscillations into a sustained calcium increase with oscillations of much higher frequency and much smaller amplitude, and transforms the normal membrane potential oscillations to a pattern of continuous spiking. When the SOCE conductance is increased to 20 pS and the ER calcium is depleted, our numerical simulation conforms to the other experimental observation that the normal calcium and potential oscillations are sustained and augmented a little bit. Moreover, the oscillation frequency is increased a very little bit. A further increase of the conductance to 35 pS slows down the oscillation a little bit. This numerical evidence suggests that a sufficiently large SOCE can prevent the continuous spiking of membrane potential to sustain the normal calcium oscillations and the normal membrane potential bursting. A careful examination of our simulated dynamics of the ATP/ADP ratio, the ATP-sensitive outward K(+) current, and the voltage-gated inward Ca(2+) current reveals that intracellular periodic Ca(2+) peaks perhaps resulted from SOCE might play a role in stabilizing the membrane potential at its resting level (avoiding the continuous spiking) for a certain period of time by accelerating ATP consumption, reducing the ratio ATP/ADP, opening the ATP-sensitive potassium channel, and repolarizing the membrane potential.

Mathematical model of metabolism and electrophysiology of amino acid and glucose stimulated insulin secretion: in vitro validation using a β-cell line

We integrated biological experimental data with mathematical modelling to gain insights into the role played by L-alanine in amino acid-stimulated insulin secretion (AASIS) and in D-glucose-stimulated insulin secretion (GSIS), details important to the understanding of complex β-cell metabolic coupling relationships. We present an ordinary differential equations (ODEs) based simplified kinetic model of core metabolic processes leading to ATP production (glycolysis, TCA cycle, L-alanine-specific reactions, respiratory chain, ATPase and proton leak) and Ca(2+) handling (essential channels and pumps in the plasma membrane) in pancreatic β-cells and relate these to insulin secretion. Experimental work was performed using a clonal rat insulin-secreting cell line (BRIN-BD11) to measure the consumption or production of a range of important biochemical parameters (D-glucose, L-alanine, ATP, insulin secretion) and Ca(2+) levels. These measurements were then used to validate the theoretical model and fine-tune the parameters. Mathematical modelling was used to predict L-lactate and L-glutamate concentrations following D-glucose and/or L-alanine challenge and Ca(2+) levels upon stimulation with a non metabolizable L-alanine analogue. Experimental data and mathematical model simulations combined suggest that L-alanine produces a potent insulinotropic effect via both a stimulatory impact on β-cell metabolism and as a direct result of the membrane depolarization due to Ca(2+) influx triggered by L-alanine/Na(+) co-transport. Our simulations indicate that both high intracellular ATP and Ca(2+) concentrations are required in order to develop full insulin secretory responses. The model confirmed that K(+) ATP channel independent mechanisms of stimulation of intracellular Ca(2+) levels, via generation of mitochondrial coupling messengers, are essential for promotion of the full and sustained insulin secretion response in β-cells.

Dual-color system for simultaneously monitoring intracellular Ca(2+) and ATP dynamics

Although Ca(2+) regulates energy metabolism through diverse pathways, there have been no methods to monitor both Ca(2+) dynamics and metabolic activity simultaneously. Here we report a novel system for simultaneously monitoring intracellular Ca(2+) and ATP levels using a blue-emitting photoprotein and a red-emitting beetle luciferase. Using this system, we monitored the dynamic changes simultaneously in both intracellular Ca(2+) and ATP levels during chondrogenesis. We have found that both intracellular Ca(2+) and ATP levels oscillated and their oscillations have a nearly antiphase relationship with each other. The dual-color monitoring system is useful for studying the relationship between Ca(2+) dynamics and energy metabolic pathways.

The endothelium: influencing vascular smooth muscle in many ways

The endothelium, although only a single layer of cells lining the vascular and lymphatic systems, contributes in multiple ways to vascular homeostasis. Subsequent to the 1980 report by Robert Furchgott and John Zawadzki, there has been a phenomenal increase in our knowledge concerning the signalling molecules and pathways that regulate endothelial - vascular smooth muscle communication. It is now recognised that the endothelium is not only an important source of nitric oxide (NO), but also numerous other signalling molecules, including the putative endothelium-derived hyperpolarizing factor (EDHF), prostacyclin (PGI(2)), and hydrogen peroxide (H(2)O(2)), which have both vasodilator and vasoconstrictor properties. In addition, the endothelium, either via transferred chemical mediators, such as NO and PGI(2), and (or) low-resistance electrical coupling through myoendothelial gap junctions, modulates flow-mediated vasodilatation as well as influencing mitogenic activity, platelet aggregation, and neutrophil adhesion. Disruption of endothelial function is an early indicator of the development of vascular disease, and thus an important area for further research and identification of potentially new therapeutic targets. This review focuses on the signalling pathways that regulate endothelial - vascular smooth muscle communication and the mechanisms that initiate endothelial dysfunction, particularly with respect to diabetic vascular disease.

Cardiac mitochondrial network excitability: insights from computational analysis

In the heart, mitochondria form a regular lattice and function as a coordinated, nonlinear network to continuously produce ATP to meet the high-energy demand of the cardiomyocytes. Cardiac mitochondria also exhibit properties of an excitable system: electrical or chemical signals can spread within or among cells in the syncytium. The detailed mechanisms by which signals pass among individual elements (mitochondria) across the network are still not completely understood, although emerging studies suggest that network excitability might be mediated by the local diffusion and autocatalytic release of messenger molecules such as reactive oxygen species and/or Ca(2+). In this short review, we have attempted to described recent advances in the field of cardiac mitochondrial network excitability. Specifically, we have focused on how mitochondria communicate with each other through the diffusion and regeneration of messenger molecules to initiate and propagate waves or oscillations, as revealed by computational models of mitochondrial network.

Synchronized ATP oscillations have a critical role in prechondrogenic condensation during chondrogenesis

The skeletal elements of embryonic limb are prefigured by prechondrogenic condensation in which secreted molecules such as adhesion molecules and extracellular matrix have crucial roles. However, how the secreted molecules are controlled to organize the condensation remains unclear. In this study, we examined metabolic regulation of secretion in prechondrogenic condensation, using bioluminescent monitoring systems. We here report on ATP oscillations in the early step of chondrogenesis. The ATP oscillations depended on both glycolysis and mitochondrial respiration, and their synchronization among cells were achieved via gap junctions. In addition, the ATP oscillations were driven by Ca(2+) oscillations and led to oscillatory secretion in chondrogenesis. Blockade of the ATP oscillations prevented cellular condensation. Furthermore, the degree of cellular condensation increased with the frequency of ATP oscillations. We conclude that ATP oscillations have a critical role in prechondrogenic condensation by inducing oscillatory secretion.

Mathematical models for insulin secretion in pancreatic β-cells

Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β-, and δ-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

The low conductance mitochondrial permeability transition pore confers excitability and CICR wave propagation in a computational model

Mitochondria have long been known to sequester cytosolic Ca(2+) and even to shape intracellular patterns of endoplasmic reticulum-based Ca(2+) signaling. Evidence suggests that the mitochondrial network is an excitable medium which can demonstrate independent Ca(2+) induced Ca(2+) release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca(2+) handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction that also have bioenergetic components. In this paper, we extend the modular Magnus-Keizer computational model for respiration-driven Ca(2+) handling to include a permeability transition based on a channel-like pore mechanism. We demonstrate both excitability and Ca(2+) wave propagation accompanied by depolarizations qualitatively similar to those reported in cell and isolated mitochondria preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function across the mitochondrial network. Our model provides the tools for predictions about the internal physiology that leads to this qualitatively different Ca(2+) excitability seen in mitochondria.