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/.

To obtain insights into the mechanisms underlying the membrane excitation and contraction of cardiac myocytes, we developed a computer model of excitation-contraction coupling (Kyoto model: Jpn. J. Physiol. 53 (2003) 105). This model was further expanded by incorporating pivotal reactions of ATP metabolism; the model of mitochondrial oxidative phosphorylation by Korzeniewski and Zoladz (Biophys. Chem. 92 (2001) 17). The ATP-dependence of contraction, and creatine kinase and adenylate kinase were also incorporated. After minor modifications, the steady-state condition was well established for all the variables, including the membrane potential, contraction, and the ion and metabolite concentrations in sarcoplasmic reticulum, mitochondria and cytoplasm. Concentrations of major metabolites were close to the experimental data. Responses of the new model to anoxia were similar to experimental results of the P-31 NMR study in whole heart. This model serves as a prototype for developing a more comprehensive model of excitation-contraction-metabolism coupling.

The cardiac cell model (Kyoto Model) described in the accompanying paper [1] is developed to simulate membrane excitation and contraction in both ventricular and sinoatrial (SA) node cells using a set of equations common for both cell types. Using the Kyoto model, we aim to clarify the relationship between the role of individual current systems in membrane excitation and their unique gating and conductance properties in the SA node cell. So far, the contribution of various time-and voltage-dependent current systems has been evaluated simply by comparing the magnitude of individual currents or by examining the effects of excluding the particular current system of interest. In the present study, we reconstruct the spontaneous action potential by varying not only the current size, but also the voltage dependency of the channel gating according to the experimental data. Furthermore, we evaluate the contribution of each current system by introducing a new hypothetical equilibrium potential during the course of pacemaker depolarization. The Kyoto model is compared with the models of Wilders et al. [2], Demir et al. [3], and the Oxsoft SA node model (Oxsoft Heart Program; Biologic, Claix, France). METHODSThe methods have been fully described in the accompanying paper [1]. The gating and conductance properties of ion channels are common for both the ventricular and SA node cell versions.The sequential numbers of equations and tables and abbreviations referred to in the present paper indicate those in the accompanying paper [1].

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...

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