Ca2+ entry-dependent inactivation of L-type Ca current: a novel formulation for cardiac action potential models

Cardiac L-type Ca current (I(Ca,L)) is controlled not only by voltage but also by Ca(2+)-dependent mechanisms. Precise implementation of I(Ca,L) in cardiac action potential models therefore requires thorough understanding of intracellular Ca(2+) dynamics, which is not yet available. Here, we present a novel formulation of I(Ca,L) for action potential models that does not explicitly require the knowledge of local intracellular Ca(2+) concentration ([Ca(2+)](i)). In this model, whereas I(Ca,L) is obtained as the product of voltage-dependent gating parameters (d and f), Ca(2+)-dependent inactivation parameters (f(Ca): f(Ca-entry) and f(Ca-SR)), and Goldman-Hodgkin-Katz current equation as in previous studies, f(Ca) is not a instantaneous function of [Ca(2+)](i) but is determined by two terms: onset of inactivation proportional to the influx of Ca(2+) and time-dependent recovery (dissociation). We evaluated the new I(Ca,L) subsystem in the framework of the standard cardiac action potential model. The new formulation produced a similar temporal profile of I(Ca,L) as the standard, but with different gating mechanisms. Ca(2+)-dependent inactivation gradually proceeded throughout the plateau phase, replacing the voltage-dependent inactivation parameter in the LRd model. In typical computations, f declined to approximately 0.7 and f(Ca-entry) to approximately 0.1, whereas deactivation caused fading of I(Ca,L) during final repolarization. These results support experimental findings that Ca(2+) entering through I(Ca,L) is essential for inactivation. After responses to standard voltage-clamp protocols were examined, the new model was applied to analyze the behavior of I(Ca,L) when action potential was prolonged by several maneuvers. Our study provides a basis for theoretical analysis of I(Ca,L) during action potentials, including the cases encountered in long QT syndromes.