Biophys J, July 2000, p. 94-115, Vol. 79, No. 1

A Mathematical Model of Cardiocyte Ca²⁺ Dynamics with a Novel Representation of Sarcoplasmic Reticular Ca²⁺ Control

Department of Kinesiology and Applied Physiology, The University of Colorado Cardiovascular Institute (CUCVI), University of Colorado, Boulder, Colorado 80309-0354 USA

Cardiac contraction and relaxation dynamics result from a set of simultaneously interacting Ca²⁺ regulatory mechanisms. In this study, cardiocyte Ca²⁺ dynamics were modeled using a set of six differential equations that were based on theories, equations, and parameters described in previous studies. Among the unique features of the model was the inclusion of bidirectional modulatory interplay between the sarcoplasmic reticular Ca²⁺ release channel (SRRC) and calsequestrin (CSQ) in the SR lumen, where CSQ acted as a dynamic rather than simple Ca²⁺ buffer, and acted as a Ca²⁺ sensor in the SR lumen as well. The inclusion of this control mechanism was central in overcoming a number of assumptions that would otherwise have to be made about SRRC kinetics, SR Ca²⁺ release rates, and SR Ca²⁺ release termination when the SR lumen is assumed to act as a simple, buffered Ca²⁺ sink. The model was sufficient to reproduce a graded Ca²⁺-induced Ca²⁺ release (CICR) response, CICR with high gain, and a system with reasonable stability. As constructed, the model successfully replicated the results of several previously published experiments that dealt with the Ca²⁺ dependence of the SRRC (Fabiato, 1985, J. Gen. Physiol. 85:247-289), the refractoriness of the SRRC (Cheng et al., 1996, Am. J. Physiol. 270:C148-C159), the SR Ca²⁺ load dependence of SR Ca²⁺ release (Bassani et al., 1995, Am. J. Physiol. 268:C1313-C1329; Gilchrist et al., 1992, J. Biol. Chem. 267:20850-20856), SR Ca²⁺ leak (Wier et al., 1994, J. Physiol. (Lond.). 474:463-471; Bassani and Bers, 1995, Biophys. J. 68:2015-2022), SR Ca²⁺ load regulation by leak and uptake (Ginsburg et al., 1998, J. Gen. Physiol. 111:491-504), the effect of Ca²⁺ trigger duration on SR Ca²⁺ release (Bers et al., 1990, Am. J. Physiol. 258:C944-C954), the apparent relationship that exists between sarcoplasmic and sarcoplasmic reticular calcium concentrations (Shannon and Bers, 1997, Biophys. J. 73:1524-1531), and a variety of contraction frequency-dependent alterations in sarcoplasmic [Ca²⁺] dynamics that are normally observed in the laboratory, including rest potentiation, a negative frequency-[Ca²⁺] relationship, and extrasystolic potentiation. Furthermore, under the condition of a simulated Ca²⁺ overload, an alternans-like state was produced. In summary, the current model of cardiocyte Ca²⁺ dynamics provides an integrated theoretical framework of fundamental cellular Ca²⁺ regulatory processes that is sufficient to predict a broad array of observable experimental outcomes.

Biophys J, July 2000, p. 94-115, Vol. 79, No. 1
© 2000 by the Biophysical Society   0006-3495/00/07/94/22  $2.00

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