ABSTRACT Cardiac L-type Ca current (I^sub Ca,L^) is controlled not only by voltage but also by Ca^sup 2+^ -dependent mechanisms. Precise implementation of I^sub Ca,L^ in cardiac action potential models therefore requires thorough understanding of intracellular Ca^sup 2+^ dynamics, which is not yet available. Here, we present a novel formulation of I^sub Ca,L^ for action potential models that does not explicitly require the knowledge of local intracellular Ca^sup 2+^ concentration ([Ca^sup 2+^]^sub i^). In this model, whereas I^sub Ca,L^ is obtained as the product of voltage-dependent gating parameters (d and f), Ca^sup 2+^-dependent inactivation parameters (f^sub Ca^: f^sub Ca-entry^ and f^sub Ca-SR^), and Goldman-Hodgkin-Katz current equation as in previous studies, f^sub Ca^ is not a instantaneous function of [Ca^sup 2+^]^sub i^ but is determined by two terms: onset of inactivation proportional to the influx of Ca^sup 2+^ and time-dependent recovery (dissociation). We evaluated the new I^sub Ca,L^ subsystem in the framework of the standard cardiac action potential model. The new formulation produced a similar temporal profile of I^sub Ca,L^ as the standard, but with different gating mechanisms. Ca^sup 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 ~0.7 and f^sub Ca-entry^ to ~0.1, whereas deactivation caused fading of I^sub Ca,L^ during final repolarization. These results support experimental findings that Ca^sup 2+^ entering through I^sub 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^sub Ca,L^ when action potential was prolonged by several maneuvers. Our study provides a basis for theoretical analysis of I^sub Ca,L^ during action potentials, including the cases encountered in long QT syndromes.
INTRODUCTION
Voltage-dependent L-type Ca channels (I^sub Ca,L^) play vital roles for cardiac functions, including pacemaker activity in nodal cells, trigger for Ca^sup 2+^ -induced Ca^sup 2+^ release (CICR), and control of cardiac contractility (Bers and Perez-Reyes, 1999). I^sub Ca,L^ also contributes to maintenance of the plateau or elongated depolarization of cardiac action potentials. Because I^sub Ca,L^ is important to our understanding of cardiac functions in physiological as well as pathological conditions, mechanisms of its modulation have been studied extensively (McDonald et al., 1994).
Addendum: After the original manuscript was submitted, a set of papers appeared describing how beta-adrenergic stimulation modulates Ca^sup 2+^ - and voltage-dependent inactivation, including their relative contributions (Findlay, 2002a,b). Their voltage-inactivation curve was similar to that used in this study, when myocytes were under beta-adrenergic stimulation.
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Yuji Hirano and Masayasu Hiraoka
Department of Cardiovascular Diseases, Medical Research Institute, Tokyo Medical and Dental University, 1-5-45, Yushima, Bunkyo-ku, Tokyo 113-8510, Japan
Submitted April 11, 2002, and accepted for publication August 29, 2002.
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@mri.tmd. ac.jp.
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