Two types of the late Na channels, burst and background, were studied in Purkinje and ventricular cells. In the whole-cell configuration, steady-state Na currents were recorded at potentials (-70 to -80 mV) close to the normal cell resting potential. The question of the contribution of late Na channels to this background Na conductance was investigated. During depolarization, burst Na channels were active for periods (up to approximately 5 s), which exceeded the action potential duration. However, they eventually closed without reopening, indicating the presence of slow and complete inactivation. When, at the moment of burst channel opening, the potential was switched to -80 mV, the channel closed quickly without reopening. We conclude that the burst Na channels cannot contribute significantly to the background Na conductance. Background Na channels undergo incomplete inactivation. After a step depolarization, their activity decreased in time, approaching a steady-state level. Background Na channel openings could be recorded at constant potentials in the range from -120 to 0 mV. After step depolarizations to potentials near -70 mV and more negative, a significant fraction of Na current was carried by the background Na channels. Analysis of the background channel behavior revealed that their gating properties are qualitatively different from those of the early Na channels. We suggest that background Na channels represent a special type of Na channel that can play an important role in the initiation of cardiac action potential and in the TTX-sensitive background Na conductance.

High-frequency arrhythmias leading to fibrillation are often associated with the presence of inhomogeneities (obstacles) in cardiac tissue and reduced excitability of cardiac cells. Studies of antiarrhythmic drugs in patients surviving myocardial infarction revealed an increased rate of sudden cardiac death compared with untreated patients. These drugs block the cardiac sodium channel, thereby reducing excitability, which may alter wavefront-obstacle interactions. In diseased atrial tissue, excitability is reduced by diminished sodium channel availability secondary to depolarized rest potentials and cellular decoupling secondary to intercellular fibrosis. Excitability can also be reduced by incomplete recovery between successive excitations. In all of these cases, wavefront-obstacle interactions in a poorly excitable medium may reflect an arrhythmogenic process that permits formation of reentrant wavelets leading to flutter, fibrillation, and sudden cardiac death. To probe the relationship between excitability and arrhythmogenesis, we explored conditions for new wavelet formation after collision of a plane wave with an obstacle in an otherwise homogeneous excitable medium. Formulating our approach in terms of the balance between charge available in the wavefront and the excitation charge requirements of adjacent medium, we found analytically the critical medium parameters that defined conditions for wavefront-obstacle separation. Under these conditions, when a parent wavefront collided with a primitive obstacle, the resultant fragments separated from the obstacle boundaries, subsequently curled, and spawned new "daughter" wavelets. We identified spatial arrangements of obstacles such that wavefront-obstacle collisions leading to spawning of new wavelets could produce high-frequency wavelet trains similar to fibrillation-like arrhythmias.

No abstract

The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.