A population density and moment-based approach to modeling domain Ca-mediated inactivation of L-type Ca channels

We present a population density and moment-based description of the stochastic dynamics of domain Ca2+-mediated inactivation of L-type Ca2+ channels. Our approach accounts for the effect of heterogeneity of local Ca2+ signals on whole cell Ca2+ currents; however, in contrast with prior work, e.g., Sherman et al. (1990), we do not assume that Ca2+ domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov chain model of an L-type Ca2+ channel introduced by Greenstein and Winslow (2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell Ca2+ current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of Ca2+ inactivation that may occur via slow heterogeneous domains. Next, we find that when channel permeability is held constant, Ca2+-mediated inactivation of L-type channel increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [Ca2+] near open channels; conversely, when the maximum domain [Ca2+] is held constant, inactivation decreases as the domain time constant increases. Comparison of simulation results using population densities and moment equations confirms the computational efficiency of the moment-based approach, and enables the validation of two distinct methods of truncating and closing the open system of moment equations. In general, a slow domain time constant requires higher order moment truncation for agreement between moment-based and population density simulations.