Individual types of ion channels play a unique role in generating membrane excitation based on their gating and conductance properties. The contribution of a given ion channel has been extensively discussed in original experimental papers. However, the complicated interactions of more than 10 ionic current systems through a common membrane potential make it difficult to clarify their roles in membrane excitability. ; I ext , current applied through the electrode (pA); I ha , hyperpolarization-activated cation current (pA); I Kl , inward rectifier K ϩ current (pA); I KACh , ACh-activated K ϩ current (pA); I KATP , ATP-sensitive K ϩ current (pA); I Kpl , non-specific, voltage-dependent outward current (plateau current) (pA); I Kr , delayed rectifier K ϩ current, rapid component (pA); I Ks , delayed rectifier K ϩ current, slow component (pA); I l , total of background current (time-independent) components (pA); I l(Ca) , Ca 2ϩ -activated background cation current (pA); I Na , Na ϩ current (pA); I NaCa , Na ϩ /Ca 2ϩ exchange current (pA); I NaK , Na ϩ /K ϩ pump current (pA); I net X, whole cell current carried by ion X (pA); I RyR , Ca 2ϩ release through the RyR channel in SR (pA); I SR L, Ca 2ϩ leak from the SR (pA); I SR U, Ca 2ϩ uptake in the SR (pA); I SR T, Ca 2ϩ transfer from the SR uptake site to the release site (pA); I st , sustained inward current (pA); I to , transient outward current (pA); I tot , total current of ion channels and ion exchangers (pA); K mX , Michaelis constant for ion X binding; N, total number of channels; P x , convert factor (pA mM Ϫ1 ); p(X), probability of state X in a multiple states gate; R, gas constant, 8.3143 C mV K Ϫ1 mmol Ϫ1; SA factor, scaling factor for SA node cell sarcoplasmic reticulum (0.03); T, absolute temperature K; T, T*, TCa, TCa*, the 4 states of NL model (1996) ).

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 Ca2+-ATPase (PMCA) and Na+/Ca2+ exchanger, in addition to low membrane permeabilities for Na+ and Cl−, in maintaining cell volume. PMCA might help maintain the [Ca2+] gradient across the membrane though compromised, and thereby promote reverse Na+/Ca2+ exchange stimulated by the increased [Na+]i as well as the membrane depolarization. Na+ extrusion via Na+/Ca2+ exchange delayed cell swelling during Na+/K+ pump block. Supporting these model predictions, we observed ventricular cell swelling after blocking Na+/Ca2+ 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 Ca2+ current, which increased [Ca2+]i. Finally, the activation of Ca2+-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 Ca2+ channels predicted in the simulation was demonstrated in experiments, where blocking Ca2+ channels resulted in a much delayed cell swelling.

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We aim at introducing a Cl- homeostasis to the cardiac ventricular cell model (Kyoto model), which includes the sarcomere shortening and the mitochondria oxidative phosphorylation. First, we examined mechanisms underlying the cell volume regulation in a simple model consisting of Na+/K+ pump, Na+-K+-2Cl- cotransporter 1 (NKCC1), cystic fibrosis transmembrane conductance regulator, volume-regulated Cl- channel and background Na+, K+ and Cl- currents. The high intracellular Cl- concentration of approximately 30 mM was achieved by the balance between the secondary active transport via NKCC1 and passive currents. Simulating responses to Na+/K+ pump inhibition revealed the essential role of Na+/K+ pump in maintaining the cellular osmolarity through creating the negative membrane potential, which extrudes Cl- from a cell, confirming the previous model study in the skeletal muscle. In addition, this model well reproduced the experimental data such as the responses to hypotonic shock in the presence or absence of beta-adrenergic stimulation. Finally, the volume regulation via Cl- homeostasis was successfully incorporated to the Kyoto model. The steady state was well established in the comprehensive cell model in respect to both the intracellular ion concentrations and the shape of the action potential, which are all in the physiological range. The source code of the model, which can reproduce every result, is available from http://www.sim-bio.org/.