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

AbstractCardiac 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