title: Population Density and Moment-based Approaches to Modeling Domain Calcium-mediated Inactivation of L-type Calcium Channels.
abstract: We present a population density and moment-based description of the stochastic dynamics of domain [Formula: see text]-mediated inactivation of L-type [Formula: see text] channels. Our approach accounts for the effect of heterogeneity of local [Formula: see text] signals on whole cell [Formula: see text] currents; however, in contrast with prior work, e.g., Sherman et al. (Biophys J 58(4):985-995, 1990), we do not assume that [Formula: see text] 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 [Formula: see text] channel introduced by Greenstein and Winslow (Biophys J 83(6):2918-2945, 2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell [Formula: see text] current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of [Formula: see text] inactivation that may occur via slow heterogeneous domain [[Formula: see text]]. Next, we find that when channel permeability is held constant, [Formula: see text]-mediated inactivation of L-type channels increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [[Formula: see text]] near open channels; conversely, when the maximum domain [[Formula: see text]] 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.
authors.affiliation: Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA.
authors.forename: Xiao
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA.
authors.forename: Kiah
authors.initials: K
authors.lastname: Hardcastle
authors.affiliation: Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA.
authors.forename: Seth H
authors.initials: SH
authors.lastname: Weinberg
authors.affiliation: Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA. greg@as.wm.edu.
authors.forename: Gregory D
authors.initials: GD
authors.lastname: Smith
mesh_terms: D000465:Algorithms; D002118:Calcium / Q000378:metabolism*; D020746:Calcium Channels, L-Type / Q000378:metabolism*; D006801:Humans; D008390:Markov Chains; D008962:Models, Theoretical; D011156:Population Density
chemical_list: D020746:Calcium Channels, L-Type; D002118:Calcium
keywords: -dependent inactivation; L-type channel; Moment-based model; Population density model