A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes.

Mathematical models were developed to reconstruct the action potentials (AP) recorded in epicardial and endocardial myocytes isolated from the adult rat left ventricle. The main goal was to obtain additional insight into the ionic mechanisms responsible for the transmural AP heterogeneity. The simulation results support the hypothesis that the smaller density and the slower reactivation kinetics of the Ca(2+)-independent transient outward K(+) current (I(t)) in the endocardial myocytes can account for the longer action potential duration (APD), and more prominent rate dependence in that cell type. The larger density of the Na(+) current (I(Na)) in the endocardial myocytes results in a faster upstroke (dV/dt(max)). This, in addition to the smaller magnitude of I(t), is responsible for the larger peak overshoot of the simulated endocardial AP. The prolonged APD in the endocardial cell also leads to an enhanced amplitude of the sustained K(+) current (I(ss)), and a larger influx of Ca(2+) ions via the L-type Ca(2+) current (I(CaL)). The latter results in an increased sarcoplasmic reticulum (SR) load, which is mainly responsible for the higher peak systolic value of the Ca(2+) transient [Ca(2+)](i), and the resultant increase in the Na(+)-Ca(2+) exchanger (I(NaCa)) activity, associated with the simulated endocardial AP. In combination, these calculations provide novel, quantitative insights into the repolarization process and its naturally occurring transmural variations in the rat left ventricle.

Parasympathetic modulation of sinoatrial node pacemaker activity in rabbit heart: a unifying model.

We have extended our compartmental model [Am. J. Physiol. 266 (Cell Physiol. 35): C832-C852, 1994] of the single rabbit sinoatrial node (SAN) cell so that it can simulate cellular responses to bath applications of ACh and isoprenaline as well as the effects of neuronally released ACh. The model employs three different types of muscarinic receptors to explain the variety of responses observed in mammalian cardiac pacemaking cells subjected to vagal stimulation. The response of greatest interest is the ACh-sensitive change in cycle length that is not accompanied by a change in action potential duration or repolarization or hyperpolarization of the maximum diastolic potential. In this case, an ACh-sensitive K+ current is not involved. Membrane hyperpolarization occurs in response to much higher levels of vagal stimulation, and this response is also mimicked by the model. Here, an ACh-sensitive K+ current is involved. The well-known phase-resetting response of the SAN cell to single and periodically applied vagal bursts of impulses is also simulated in the presence and absence of the beta-agonist isoprenaline. Finally, the responses of the SAN cell to longer continuous trains of periodic vagal stimulation are simulated, and this can result in the complete cessation of pacemaking. Therefore, this model is 1) applicable over the full range of intensity and pattern of vagal input and 2) can offer biophysically based explanations for many of the phenomena associated with the autonomic control of cardiac pacemaking.

Phase sensitivity and entrainment in a modeled bursting neuron.

A model of neuron R15 in Aplysia was used to study the mechanisms determining the phase-response curve (PRC) of the cell in response to both extrinsic current pulses and modeled synaptic input and to compare entrainment predictions from PRCs with those from actual simulations. Over the range of stimulus parameters studied, the PRCs of the model exhibited minimal dependence upon stimulus amplitude, and a strong dependence upon stimulus duration. State-space analysis of the effect of transient current pulses provided several important insights into the relationship between the PRC and the underlying dynamics of the model, such as a correlation between the prestimulus concentration of Ca2+ and the poststimulus phase of the oscillation. The system nullclines were also found to provide well-defined limits upon the perturbatory extent of a hyperpolarizing input. These results demonstrated that experimentally applied current pulses are sufficient to determine the shape of the PRC in response to a synaptic input, provided that the duration of the current pulse is of a duration similar to that of the evoked synaptic current. Furthermore, we found that predictions of phase-locked 1:m entrainment from PRCs were valid, even when the duration of the periodically applied pulses were a significant portion of the control limit cycle.

Characterization of a hyperpolarization-activated inward current in cultured pacemaker cells from the sinoatrial node.

The perforated-patch, whole-cell voltage-clamp technique was used to characterize a hyperpolarization-activated inward current (if) in cultured pacemaker cells isolated from the rabbit sinoatrial (S-A) node. A modified Tyrode solution was used to block interfering currents. After correcting for uncompensated series resistance, leakage current and liquid-junction potentials between the pipette and bath, we obtained the following values for the maximum conductance and reversal potential of (i(f)): 16.2 +/- 2.8 nS or 0.26 +/- 0.07 nS/pF (0.37 +/- 0.10 mS/cm2); and -27.7 +/- 1.2 mV (n = 10). In the modified Tyrode solution, the threshold for activation of i(f) and the half-activation potential and slope factor for Boltzmann fits were -66 +/- 1 mV (n = 53), -77.2 +/- 2.0 mV and 4.2 +/- 0.4 mV (n = 16), respectively. The time course of i(f) was best fit by a sum of two exponentials. Between -110 and -5 mV, time constants ranged from 0.06 to 0.42 s for the rapid component and from 0.65 to 4.39 s for the slow component. Using these characteristics of i(f) and a short segment of spontaneous firing as the membrane potential, we computed the expected time course of i(f) during normal pacemaker activity. It reached a maximum of -3 pA during the diastolic depolarization and +4 pA during the action potential. We conclude that most of the characteristics of i(f) in cultured S-A node cells are similar to those measured previously in freshly isolated pacemaker cells.

A mathematical model of a rabbit sinoatrial node cell.

A mathematical model for the electrophysiological responses of a rabbit sinoatrial node cell that is based on whole cell recordings from enzymatically isolated single pacemaker cells at 37 degrees C has been developed. The ion channels, Na(+)-K+ and Ca2+ pumps, and Na(+)-Ca2+ exchanger in the surface membrane (sarcolemma) are described using equations for these known currents in mammalian pacemaker cells. The extracellular environment is treated as a diffusion-limited space, and the myoplasm contains Ca(2+)-binding proteins (calmodulin and troponin). Original features of this model include 1) new equations for the hyperpolarization-activated inward current, 2) assessment of the role of the transient-type Ca2+ current during pacemaker depolarization, 3) inclusion of an Na+ current based on recent experimental data, and 4) demonstration of the possible influence of pump and exchanger currents and background currents on the pacemaker rate. This model provides acceptable fits to voltage-clamp and action potential data and can be used to seek biophysically based explanations of the electrophysiological activity in the rabbit sinoatrial node cell.