To clarify the mechanisms underlying the pancreatic β-cell response to varying glucose concentrations ([G]), electrophysiological findings were integrated into a mathematical cell model. The Ca2+ dynamics of the endoplasmic reticulum (ER) were also improved. The model was validated by demonstrating quiescent potential, burst–interburst electrical events accompanied by Ca2+ 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 Ca2+ 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 Ca2+- or Na+-dependent currents, which were generated by the plasma membrane Ca2+ pump, Na+/K+ pump, Na+/Ca2+ exchanger, and TRPM channel. Accumulation and release of Ca2+ 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.

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.

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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.

Positive chronotropy induced by β1-adrenergic stimulation is achieved by multiple interactions of ion channels and transporters in sinoatrial node pacemaker cells (SANs). To investigate the ionic mechanisms, we updated our SAN model developed in 2003 and incorporated the β1-adrenergic signaling cascade developed by Kuzumoto et al. (2007). Since the slow component of the delayed rectifier K + current (I Ks ) is one of the major targets of the β1-adrenergic cascade, we developed a guinea pig model with a large I Ks . The new model provided a good representation of the experimental characteristics of SANs. A comparison of individual current during diastole recorded before and after β1-adrenergic stimulation clearly showed the negative shift of the L-type Ca 2+ current (I CaL ) takeoff potential, enlargement of the sustained inward current (I st ), and the hyperpolarization-activated nonselective cation current (I ha ) played major roles in increasing the firing frequency. Deactivation of I Ks during diastole scarcely contributed to the time-dependent decrease in membrane K + conductance, which was the major mechanism for slow diastolic depolarization, as indicated by calculating the instantaneous equilibrium potential (lead potential). This was because the activation of I Ks during the preceding action potential was negligibly small. However, I Ks was important in counterbalancing the increase in I CaL and the Na + /Ca 2+ exchange current (I NaCa ), which otherwise compromised the positive chronotropic effect by elongating the action potential duration. Enhanced Ca 2+ release from the sarcoplasmic reticulum failed to induce an obvious chronotropic effect in our model.Key words: β1-adrenergic receptor, cardiac pacemaker model, sinoatrial node, sympathetic nerve stimulation, simulation.Sympathetic stimulation of SA node pacemaker cells (SANs) is essential for increasing heart rate when a larger blood supply is required for the body. The autonomic neurotransmitter, noradrenaline, is released from nerve terminals, binds to the β1-adrenergic receptor, and initiates intracellular signal transduction in SANs, which causes the increased firing frequency of spontaneous action potentials. This positive chronotropy is due to a variety of functional modifications of ion channels and ion transporters. To date, electrophysiological and pharmacological studies have provided experimental evidence to show that ion channels and transporters are modified by the β1-adrenergic stimulation. To clarify the contributions of each current, however, an integrative analysis is required because positive chronotropy is induced by multiple interactions of all ion channels and transporters, which have different kinetics and respond differently to β1-adrenergic stimulation. In 2003, we developed a SAN model that included spontaneous action potential generation and intracellular ion homeostasis, including Ca 2+ dynamics [1,2]. Using this model, we proposed the principal ionic mechanisms underlying the spontaneous action potential. In the...