In our companion paper, the physiological functions of pancreatic β cells were analyzed with a new β-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 β cells.

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 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.

Although the Na + /K + pump is one of the key mechanisms responsible for maintaining cell volume, we have observed experimentally that cell volume remained almost constant during 90 min exposure of guinea pig ventricular myocytes to ouabain. Simulation of this finding using a comprehensive cardiac cell model (Kyoto model incorporating Cl − and water fluxes) predicted roles for the plasma membrane Ca 2+ -ATPase (PMCA) and Na + /Ca 2+ exchanger, in addition to low membrane permeabilities for Na + and Cl − , in maintaining cell volume. PMCA might help maintain the [Ca 2+ ] gradient across the membrane though compromised, and thereby promote reverse Na + /Ca 2+ exchange stimulated by the increased [Na + ] i as well as the membrane depolarization. Na + extrusion via Na + /Ca 2+ exchange delayed cell swelling during Na + /K + pump block. Supporting these model predictions, we observed ventricular cell swelling after blocking Na + /Ca 2+ exchange with KB-R7943 or SEA0400 in the presence of ouabain. When Cl − conductance via the cystic fibrosis transmembrane conductance regulator (CFTR) was activated with isoproterenol during the ouabain treatment, cells showed an initial shrinkage to 94.2 ± 0.5%, followed by a marked swelling 52.0 ± 4.9 min after drug application. Concomitantly with the onset of swelling, a rapid jump of membrane potential was observed. These experimental observations could be reproduced well by the model simulations. Namely, the Cl − efflux via CFTR accompanied by a concomitant cation efflux caused the initial volume decrease. Then, the gradual membrane depolarization induced by the Na + /K + pump block activated the window current of the L-type Ca 2+ current, which increased [Ca 2+ ] i . Finally, the activation of Ca 2+ -dependent cation conductance induced the jump of membrane potential, and the rapid accumulation of intracellular Na + accompanied by the Cl − influx via CFTR, resulting in the cell swelling. The pivotal role of L-type Ca 2+ channels predicted in the simulation was demonstrated in experiments, where blocking Ca 2+ channels resulted in a much delayed cell swelling.

A new method was developed to automatically measure the thickness of a single ventricular myocyte of guinea-pig heart. A fine marker was attached on the cell's upper surface and changes in its vertical position were measured by focusing it under the microscope. When the osmolarity of the bath solution was varied, the cell thickness reached a new steady level without any obvious regulatory volume change within the period of observation up to 15 min. The cell thickness was 7.8 ± 0.2 μm ( n = 94) in the control Tyrode solution and was varied to 130.4 ± 3.1% ( n = 10), 119.1 ± 1.1% ( n = 50), 87.2 ± 1.9% ( n = 9), and 75.6 ± 3.2% ( n = 5) of control at 50, 70, 130, and 200% osmolarity, respectively. The application of a Cl − channel blocker, 500 μM anthracene-9-carboxylic acid (9AC) did not modify these osmotic volume changes. We discovered that the application of isoprenaline induced a regulatory volume decrease (RVD) in cells inflated by hypotonic solutions. This isoprenaline-induced RVD was inhibited by antagonizing β-adrenergic stimulation with acetylcholine. The isoprenaline-induced RVD was mimicked by the external application of 8-bromoadenosine 3′:5′-cyclic monophosphate. The RVD was inhibited by blocking the cAMP-dependent Cl − channel (I Cl, cAMP ) with 9AC but was insensitive to 4, 4′-diisothiocyanostilbene-2, 2′-dissulphonate (DIDS). Taken together these data suggest an involvement of I Cl, cAMP activation in the RVD. Whole cell voltage clamp experiments revealed activation of I Cl, cAMP by isoprenaline under the comparable conditions. The cardiac cell volume may be regulated by the autonomic nervous activity.