A Population Density and Moment-Based Approach to Modeling Domain Calcium-Mediated Inactivation of L-Type Calcium Channels

We present a population density and moment-based description of stochastic domain calcium-mediated inactivation of L-type calcium channels. Our approach accounts for the effect of heterogeneity of local calcium signals on whole cell calcium currents; however, in contrast with prior work by Sherman et al. [Biophys J. 58(4):985, 1990], we do not assume that calcium domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approach using a12-state Markov chain model of an L-type calcium channel [Greenstein and Winslow, Biophys J. 83(6):2918, 2002]. Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell calcium current that agrees or disagrees with the classic result of Sherman et al. when domains dynamics are fast or slow, respectively. We analyze the voltage-dependence of calcium inactivation that occurs via slow heterogeneous domains and find that when channel permeability is held constant, calcium inactivation increases as the domain time constant increases. However, when this parameter study is repeated for fixed maximum domain calcium concentration, 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 several 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