A role of PLC/PKC-dependent pathway in GLP-1-stimulated insulin secretion.

Glucagon-like peptide-1 (GLP-1) is an endogenous glucose-lowering hormone and GLP-1 receptor agonists are currently being used as antidiabetic drugs clinically. The canonical signalling pathway (including cAMP, Epac2, protein kinase A (PKA) and KATP channels) is almost universally accepted as the main mechanism of GLP-1-stimulated insulin secretion. This belief is based on in vitro studies that used nanomolar (1-100 nM) concentrations of GLP-1. Recently, it was found that the physiological concentrations (1-10 pM) of GLP-1 also stimulate insulin secretion from isolated islets, induce membrane depolarization and increase of intracellular [Ca2+] in isolated ß cells/pancreatic islets. These responses were unaffected by PKA inhibitors and occurred without detectable increases in intracellular cAMP and PKA activity. These PKA-independent actions of GLP-1 depend on protein kinase C (PKC), involve activation of the standard GLP-1 receptor (GLP1R) and culminate in activation of phospholipase C (PLC), leading to an elevation of diacylglycerol (DAG), increased L-type Ca2+ and TRPM4/TRPM5 channel activities. Here, we review these recent data and contrast them against the effects of nanomolar concentrations of GLP-1. The differential intracellular signalling activated by low and high concentrations of GLP-1 could provide a clue to explain how GLP-1 exerts different function in the central nervous system and peripheral organs.

GLP-1 stimulates insulin secretion by PKC-dependent TRPM4 and TRPM5 activation.

Strategies aimed at mimicking or enhancing the action of the incretin hormone glucagon-like peptide 1 (GLP-1) therapeutically improve glucose-stimulated insulin secretion (GSIS); however, it is not clear whether GLP-1 directly drives insulin secretion in pancreatic islets. Here, we examined the mechanisms by which GLP-1 stimulates insulin secretion in mouse and human islets. We found that GLP-1 enhances GSIS at a half-maximal effective concentration of 0.4 pM. Moreover, we determined that GLP-1 activates PLC, which increases submembrane diacylglycerol and thereby activates PKC, resulting in membrane depolarization and increased action potential firing and subsequent stimulation of insulin secretion. The depolarizing effect of GLP-1 on electrical activity was mimicked by the PKC activator PMA, occurred without activation of PKA, and persisted in the presence of PKA inhibitors, the KATP channel blocker tolbutamide, and the L-type Ca(2+) channel blocker isradipine; however, depolarization was abolished by lowering extracellular Na(+). The PKC-dependent effect of GLP-1 on membrane potential and electrical activity was mediated by activation of Na(+)-permeable TRPM4 and TRPM5 channels by mobilization of intracellular Ca(2+) from thapsigargin-sensitive Ca(2+) stores. Concordantly, GLP-1 effects were negligible in Trpm4 or Trpm5 KO islets. These data provide important insight into the therapeutic action of GLP-1 and suggest that circulating levels of this hormone directly stimulate insulin secretion by ß cells.

A human ventricular myocyte model with a refined representation of excitation-contraction coupling.

Cardiac Ca(2+)-induced Ca(2+) release (CICR) occurs by a regenerative activation of ryanodine receptors (RyRs) within each Ca(2+)-releasing unit, triggered by the activation of L-type Ca(2+) channels (LCCs). CICR is then terminated, most probably by depletion of Ca(2+) in the junctional sarcoplasmic reticulum (SR). Hinch et al. previously developed a tightly coupled LCC-RyR mathematical model, known as the Hinch model, that enables simulations to deal with a variety of functional states of whole-cell populations of a Ca(2+)-releasing unit using a personal computer. In this study, we developed a membrane excitation-contraction model of the human ventricular myocyte, which we call the human ventricular cell (HuVEC) model. This model is a hybrid of the most recent HuVEC models and the Hinch model. We modified the Hinch model to reproduce the regenerative activation and termination of CICR. In particular, we removed the inactivated RyR state and separated the single step of RyR activation by LCCs into triggering and regenerative steps. More importantly, we included the experimental measurement of a transient rise in Ca(2+) concentrations ([Ca(2+)], 10-15 µM) during CICR in the vicinity of Ca(2+)-releasing sites, and thereby calculated the effects of the local Ca(2+) gradient on CICR as well as membrane excitation. This HuVEC model successfully reconstructed both membrane excitation and key properties of CICR. The time course of CICR evoked by an action potential was accounted for by autonomous changes in an instantaneous equilibrium open probability of couplons. This autonomous time course was driven by a core feedback loop including the pivotal local [Ca(2+)], influenced by a time-dependent decay in the SR Ca(2+) content during CICR.

Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models.

Mathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis technique, which is applicable to any complicated cell model formulated as a system of ordinary differential equations, to quantitatively evaluate contributions of respective model components to the model dynamics in the intact situation. The present technique employs a novel mathematical index for decomposed dynamics with respect to each differential variable, along with a concept named instantaneous equilibrium point, which represents the trend of a model variable at some instant. This article also illustrates applications of the method to comprehensive myocardial cell models for analysing insights into the mechanisms of action potential generation and calcium transient. The analysis results exhibit quantitative contributions of individual channel gating mechanisms and ion exchanger activities to membrane repolarization and of calcium fluxes and buffers to raising and descending of the cytosolic calcium level. These analyses quantitatively explicate principle of the model, which leads to a better understanding of cellular dynamics.

Steady-state solutions of cell volume in a cardiac myocyte model elaborated for membrane excitation, ion homeostasis and Ca2+ dynamics.

The cell volume continuously changes in response to varying physiological conditions, and mechanisms underlying volume regulation have been investigated in both experimental and theoretical studies. Here, general formulations concerning cell volume change are presented in the context of developing a comprehensive cell model which takes Ca(2+) dynamics into account. Explicit formulas for charge conservation and steady-state volumes of the cytosol and endoplasmic reticulum (ER) are derived in terms of membrane potential, amount of ions, Ca(2+)-bound buffer molecules, and initial cellular conditions. The formulations were applied to a ventricular myocyte model which has plasma-membrane Ca(2+) currents with dynamic gating mechanisms, Ca(2+)-buffering reactions with diffusive and non-diffusive buffer proteins, and Ca(2+) uptake into or release from the sarcoplasmic reticulum (SR) accompanied by compensatory cationic or anionic currents through the SR membrane. Time-dependent volume changes in cardiac myocytes induced by varying extracellular osmolarity or by action potential generation were successfully simulated by the novel formulations. Through application of bifurcation analysis, the existence and uniqueness of steady-state solutions of the cell volume were validated, and contributions of individual ion channels and transporters to the steady-state volume were systematically analyzed. The new formulas are consistent with previous fundamental theory derived from simple models of minimum compositions. The new formulations may be useful for examination of the relationship between cell function and volume change in other cell types.

Analyzing electrical activities of pancreatic ß cells using mathematical models.

Bursts of repetitive action potentials are closely related to the regulation of glucose-induced insulin secretion in pancreatic ß cells. Mathematical studies with simple ß-cell models have established the central principle that the burst-interburst events are generated by the interaction between fast membrane excitation and slow cytosolic components. Recently, a number of detailed models have been developed to simulate more realistic ß cell activity based on expanded findings on biophysical characteristics of cellular components. However, their complex structures hinder our intuitive understanding of the underlying mechanisms, and it is becoming more difficult to dissect the role of a specific component out of the complex network. We have recently developed a new detailed model by incorporating most of ion channels and transporters recorded experimentally (the Cha-Noma model), yet the model satisfies the charge conservation law and reversible responses to physiological stimuli. Here, we review the mechanisms underlying bursting activity by applying mathematical analysis tools to representative simple and detailed models. These analyses include time-based simulation, bifurcation analysis and lead potential analysis. In addition, we introduce a new steady-state I-V (ssI-V) curve analysis. We also discuss differences in electrical signals recorded from isolated single cells or from cells maintaining electrical connections within multi-cell preparations. Towards this end, we perform simulations with our detailed pancreatic ß-cell model.

Time-dependent changes in membrane excitability during glucose-induced bursting activity in pancreatic ß cells.

In our companion paper, the physiological functions of pancreatic ß cells were analyzed with a new ß-cell model by time-based integration of a set of differential equations that describe individual reaction steps or functional components based on experimental studies. In this study, we calculate steady-state solutions of these differential equations to obtain the limit cycles (LCs) as well as the equilibrium points (EPs) to make all of the time derivatives equal to zero. The sequential transitions from quiescence to burst-interburst oscillations and then to continuous firing with an increasing glucose concentration were defined objectively by the EPs or LCs for the whole set of equations. We also demonstrated that membrane excitability changed between the extremes of a single action potential mode and a stable firing mode during one cycle of bursting rhythm. Membrane excitability was determined by the EPs or LCs of the membrane subsystem, with the slow variables fixed at each time point. Details of the mode changes were expressed as functions of slowly changing variables, such as intracellular [ATP], [Ca(2+)], and [Na(+)]. In conclusion, using our model, we could suggest quantitatively the mutual interactions among multiple membrane and cytosolic factors occurring in pancreatic ß cells.

Ionic mechanisms and Ca2+ dynamics underlying the glucose response of pancreatic ß cells: a simulation study.

To clarify the mechanisms underlying the pancreatic ß-cell response to varying glucose concentrations ([G]), electrophysiological findings were integrated into a mathematical cell model. The Ca(2+) dynamics of the endoplasmic reticulum (ER) were also improved. The model was validated by demonstrating quiescent potential, burst-interburst electrical events accompanied by Ca(2+) transients, and continuous firing of action potentials over [G] ranges of 0-6, 7-18, and >19 mM, respectively. These responses to glucose were completely reversible. The action potential, input impedance, and Ca(2+) transients were in good agreement with experimental measurements. The ionic mechanisms underlying the burst-interburst rhythm were investigated by lead potential analysis, which quantified the contributions of individual current components. This analysis demonstrated that slow potential changes during the interburst period were attributable to modifications of ion channels or transporters by intracellular ions and/or metabolites to different degrees depending on [G]. The predominant role of adenosine triphosphate-sensitive K(+) current in switching on and off the repetitive firing of action potentials at 8 mM [G] was taken over at a higher [G] by Ca(2+)- or Na(+)-dependent currents, which were generated by the plasma membrane Ca(2+) pump, Na(+)/K(+) pump, Na(+)/Ca(2+) exchanger, and TRPM channel. Accumulation and release of Ca(2+) by the ER also had a strong influence on the slow electrical rhythm. We conclude that the present mathematical model is useful for quantifying the role of individual functional components in the whole cell responses based on experimental findings.

Minor contribution of cytosolic Ca2+ transients to the pacemaker rhythm in guinea pig sinoatrial node cells.

The question of the extent to which cytosolic Ca(2+) affects sinoatrial node pacemaker activity has been discussed for decades. We examined this issue by analyzing two mathematical pacemaker models, based on the "Ca(2+) clock" (C) and "membrane clock" (M) hypotheses, together with patch-clamp experiments in isolated guinea pig sinoatrial node cells. By applying lead potential analysis to the models, the C mechanism, which is dependent on potentiation of Na(+)/Ca(2+) exchange current via spontaneous Ca(2+) release from the sarcoplasmic reticulum (SR) during diastole, was found to overlap M mechanisms in the C model. Rapid suppression of pacemaker rhythm was observed in the C model by chelating intracellular Ca(2+), whereas the M model was unaffected. Experimental rupturing of the perforated-patch membrane to allow rapid equilibration of the cytosol with 10 mM BAPTA pipette solution, however, failed to decrease the rate of spontaneous action potential within ∼30 s, whereas contraction ceased within ∼3 s. The spontaneous rhythm also remained intact within a few minutes when SR Ca(2+) dynamics were acutely disrupted using high doses of SR blockers. These experimental results suggested that rapid disruption of normal Ca(2+) dynamics would not markedly affect spontaneous activity. Experimental prolongation of the action potentials, as well as slowing of the Ca(2+)-mediated inactivation of the L-type Ca(2+) currents induced by BAPTA, were well explained by assuming Ca(2+) chelation, even in the proximity of the channel pore in addition to the bulk cytosol in the M model. Taken together, the experimental and model findings strongly suggest that the C mechanism explicitly described by the C model can hardly be applied to guinea pig sinoatrial node cells. The possible involvement of L-type Ca(2+) current rundown induced secondarily through inhibition of Ca(2+)/calmodulin kinase II and/or Ca(2+)-stimulated adenylyl cyclase was discussed as underlying the disruption of spontaneous activity after prolonged intracellular Ca(2+) concentration reduction for >5 min.

Characterization of the cardiac Na+/K+ pump by development of a comprehensive and mechanistic model.

A large amount of experimental data on the characteristics of the cardiac Na(+)/K(+) pump have been accumulated, but it remains difficult to predict the quantitative contribution of the pump in an intact cell because most measurements have been made under non-physiological conditions. To extrapolate the experimental findings to intact cells, we have developed a comprehensive Na(+)/K(+) pump model based on the thermodynamic framework (Smith and Crampin, 2004) of the Post-Albers reaction cycle combined with access channel mechanisms. The new model explains a variety of experimental results for the Na(+)/K(+) pump current (I(NaK)), including the dependency on the concentrations of Na(+) and K(+), the membrane potential and the free energy of ATP hydrolysis. The model demonstrates that both the apparent affinity and the slope of the substrate-I(NaK) relationship measured experimentally are affected by the composition of ions in the extra- and intracellular solutions, indirectly through alteration in the probability distribution of individual enzyme intermediates. By considering the voltage dependence in the Na(+)- and K(+)-binding steps, the experimental voltage-I(NaK) relationship could be reconstructed with application of experimental ionic compositions in the model, and the view of voltage-dependent K(+) binding was supported. Re-evaluation of charge movements accompanying Na(+) and K(+) translocations gave a reasonable number for the site density of the Na(+)/K(+) pump on the membrane. The new model is relevant for simulation of cellular functions under various interventions, such as depression of energy metabolism.

A novel method to quantify contribution of channels and transporters to membrane potential dynamics.

The action potential, once triggered in ventricular or atrial myocytes, automatically proceeds on its time course or is generated spontaneously in sinoatrial node pacemaker cells. It is induced by complex interactions among such cellular components as ion channels, transporters, intracellular ion concentrations, and signaling molecules. We have developed what is, to our knowledge, a new method using a mathematical model to quantify the contribution of each cellular component to the automatic time courses of the action potential. In this method, an equilibrium value, which the membrane potential is approaching at a given moment, is calculated along the time course of the membrane potential. The calculation itself is based on the time-varying conductance and the reversal potentials of individual ion channels and electrogenic ion transporters. Since the equilibrium potential moves in advance of the membrane potential change, we refer to it as the lead potential, V(L). The contribution of an individual current was successfully quantified by comparing dV(L)/dt before and after fixing the time-dependent change of a component of interest, such as the variations in the open probability of a channel or the turnover rate of an ion transporter. In addition to the action potential, the lead-potential analysis should also be applicable in all types of membrane excitation in many different kinds of cells.

A model of Na+/H+ exchanger and its central role in regulation of pH and Na+ in cardiac myocytes.

A new kinetic model of the Na(+)/H(+) exchanger (NHE) was developed by fitting a variety of major experimental findings, such as ion-dependencies, forward/reverse mode, and the turnover rate. The role of NHE in ion homeostasis was examined by implementing the NHE model in a minimum cell model including intracellular pH buffer, Na(+)/K(+) pump, background H(+), and Na(+) fluxes. This minimum cell model was validated by reconstructing recovery of pH(i) from acidification, accompanying transient increase in [Na(+)](i) due to NHE activity. Based on this cell model, steady-state relationships among pH(i), [Na(+)](I), and [Ca(2+)](i) were quantitatively determined, and thereby the critical level of acidosis for cell survival was predicted. The acidification reported during partial blockade of the Na(+)/K(+) pump was not attributed to a dissipation of the Na(+) gradient across the membrane, but to an increase in indirect H(+) production. This NHE model, though not adapted to the dimeric behavioral aspects of NHE, can provide a strong clue to quantitative prediction of degree of acidification and accompanying disturbance of ion homeostasis under various pathophysiological conditions.

Modeling the cardiac Na(+)/H (+) exchanger based on major experimental findings.

Na(+)-H(+) exchanger (NHE) is the main acid extruder in cardiac myocytes. We review the experimental findings of ion-dependency of NHE activity, and the mathematical modeling developed so far. In spite of extensive investigation, many unsolved questions still remain. We consider that the precise description of NHE activity with mathematical models elucidates the roles of NHE in maintaining ionic homeostasis, especially under pathophysiological conditions.

Electrophysiological modelling of pulmonary artery smooth muscle cells in the rabbits--special consideration to the generation of hypoxic pulmonary vasoconstriction.

In vascular smooth muscle cells, it has been suggested that membrane potential is an important component that initiates contraction. We developed a mathematical model to elucidate the quantitative contributions of major ion currents [a voltage-gated L-type Ca2+ current (ICaL), a voltage-sensitive K+ current (IKV), a Ca2+-activated K+ current (IKCa) and a nonselective cation current (INSC)] to membrane potential. In order to typify the diverse nature of pulmonary artery smooth muscle cells (PASMCs), we introduced parameters that are not fixed (variable parameters). The population of cells with different parameters was constructed and the cells that have the electrophysiological properties of PASMCs were selected. The contributions of each membrane current were investigated by sensitivity analysis and modification of the current parameters. Consequently, IKV and INSC were found to be the most important currents that affect the membrane potential. The occurrence of depolarisation in hypoxic pulmonary vasoconstriction (HPV) was also examined. In hypoxia, IKV and IKCa were reduced, but the consequent depolarisation in simulation was not enough to initiate contractions. If we add an increase of INSC (2.5-fold), the calculated membrane potential was enough to induce contraction. From the results, we conclude that the balance of various ion channel activities determines the resting membrane potential of PASMCs and our model was successful in explaining the depolarisation in HPV. Therefore, this model can be a powerful tool to investigate the various electrical properties of PASMCs in both normal and pathological conditions.