Magnesium gating of cardiac gap junction channels.

We aimed to study kinetics of modulation by intracellular Mg(2+) of cardiac gap junction (Mg(2+) gate). Paired myocytes of guinea-pig ventricle were superfused with solutions containing various concentrations of Mg(2+). In order to rapidly apply Mg(2+) to one aspect of the gap junction, the non-junctional membrane of one of the pair was perforated at nearly the connecting site by pulses of nitrogen laser beam. The gap junction conductance (G(j)) was measured by clamping the membrane potential of the other cell using two-electrode voltage clamp method. The laser perforation immediately increased G(j), followed by slow G(j) change with time constant of 3.5 s at 10 mM Mg(2+). Mg(2+) more than 1.0 mM attenuated dose-dependently the gap junction conductance and lower Mg(2+) (0.6 mM) increased G(j) with a Hill coefficient of 3.4 and a half-maximum effective concentration of 0.6 mM. The time course of G(j) changes was fitted by single exponential function, and the relationship between the reciprocal of time constant and Mg(2+) concentration was almost linear. Based on the experimental data, a mathematical model of Mg(2+) gate with one open state and three closed states well reproduced experimental results. One-dimensional cable model of thirty ventricular myocytes connected to the Mg(2+) gate model suggested a pivotal role of the Mg(2+) gate of gap junction under pathological conditions.

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 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.

Simulation analysis of intracellular Na+ and Cl- homeostasis during beta 1-adrenergic stimulation of cardiac myocyte.

To quantitatively understand intracellular Na+ and Cl- homeostasis as well as roles of Na+/K+ pump and cystic fibrosis transmembrane conductance regulator Cl- channel (ICFTR) during the beta1-adrenergic stimulation in cardiac myocyte, we constructed a computer model of beta1-adrenergic signaling and implemented it into an excitation-contraction coupling model of the guinea-pig ventricular cell, which can reproduce membrane excitation, intracellular ion changes (Na+, K+, Ca2+ and Cl-), contraction, cell volume, and oxidative phosphorylation. An application of isoproterenol to the model cell resulted in the shortening of action potential duration (APD) after a transient prolongation, the increases in both Ca2+ transient and cell shortening, and the decreases in both Cl- concentration and cell volume. These results are consistent with experimental data. Increasing the density of ICFTR shortened APD and augmented the peak amplitudes of the L-type Ca2+ current (ICaL) and the Ca2+ transient during the beta1-adrenergic stimulation. This indirect inotropic effect was elucidated by the increase in the driving force of ICaL via a decrease in plateau potential. Our model reproduced the experimental data demonstrating the decrease in intracellular Na+ during the beta-adrenergic stimulation at 0 or 0.5 Hz electrical stimulation. The decrease is attributable to the increase in Na+ affinity of Na+/K+ pump by protein kinase A. However it was predicted that Na+increases at higher beating rate because of larger Na+ influx through forward Na+/Ca2+ exchange. It was demonstrated that dynamic changes in Na+ and Cl- fluxes remarkably affect the inotropic action of isoproterenol in the ventricular myocytes.

Modeling the calcium gate of cardiac gap junction channel.

We addressed the question how Ca2+ transients affect gap junction conductance (Gj) during action potential (AP) propagation by constructing a dynamic gap junction model coupled with a cardiac cell model. The kinetics of the Ca2+ gate was determined based on published experimental findings that the Hill coefficient for the [Ca2+]i-Gj relationship ranges from 3 to 4, indicating multiple ion bindings. It is also suggested that the closure of the Ca2+ gate follows a single exponential time course. After adjusting the model parameters, a two-state (open-closed) model, assuming simultaneous ion bindings, well described both the single exponential decay and the [Ca2+]i-Gj relationship. Using this gap junction model, 30 cardiac cell models were electrically connected in a one-dimensional cable. However, Gj decreased in a cumulative manner by the repetitive Ca2+ transients, and a conduction block was observed. We found that a reopening of the Ca2+ gate is possible only by assuming a sequential ion binding with one rate limiting step in a multistate model. In this model, the gating time constant (T) has a bell-shaped dependence on [Ca2+]i, with a peak around the half-maximal concentration of [Ca2+]i. Here we propose a five-state model including four open states and one closed state, which allows normal AP propagation; namely, the Gj is decreased -15% by a single Ca2+ transient, but well recovers to the control level during diastole. Under the Ca(2+)-overload condition, however, the conduction velocity is indeed decreased as demonstrated experimentally. This new gap junction model may also be useful in simulations of the ventricular arrhythmia.