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Ca²⁺ Entry-Dependent Inactivation of L-Type Ca Current: A Novel Formulation for Cardiac Action Potential Models

Department of Cardiovascular Diseases, Medical Research Institute, Tokyo Medical and Dental University, 1-5-45, Yushima, Bunkyo-ku, Tokyo 113-8510, Japan

Correspondence: Address reprint requests to Yuji Hirano, MD, PhD, Dept. of Cardiovascular Diseases, Medical Research Institute, Tokyo Medical and Dental University, 1-5-45, Yushima, Bunkyo-ku, Tokyo 113-8510, Japan. Tel.: 81-3-5803-5830; Fax: 81-3-5684-6295; E-mail: hirano.card{at}mri.tmd.ac.jp.

Cardiac L-type Ca current (I_Ca,L) is controlled not only by voltage but also by Ca²⁺-dependent mechanisms. Precise implementation of I_Ca,L in cardiac action potential models therefore requires thorough understanding of intracellular Ca²⁺ 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 Ca²⁺ concentration ([Ca²⁺]_i). In this model, whereas I_Ca,L is obtained as the product of voltage-dependent gating parameters (d and f), Ca²⁺-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 [Ca²⁺]_i but is determined by two terms: onset of inactivation proportional to the influx of Ca²⁺ 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. Ca²⁺-dependent inactivation gradually proceeded throughout the plateau phase, replacing the voltage-dependent inactivation parameter in the LRd model. In typical computations, f declined to 0.7 and f_Ca-entry to 0.1, whereas deactivation caused fading of I_Ca,L during final repolarization. These results support experimental findings that Ca²⁺ 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.

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