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 Ca-mediated inactivation of L-type Ca channels. Our approach accounts for the effect of heterogeneity of local Ca signals on whole cell Ca currents; however, in contrast with prior work, e.g., Sherman et al. (1990), we do not assume that Ca 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 Ca channel introduced by Greenstein and Winslow (2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell Ca current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of Ca inactivation that may occur via slow heterogeneous domains. Next, we find that when channel permeability is held constant, Ca-mediated inactivation of L-type channel increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [Ca] near open channels; conversely, when the maximum domain [Ca] 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.