title: A probability density approach to modeling local control of calcium-induced calcium release in cardiac myocytes.
abstract: We present a probability density approach to modeling localized Ca2+ influx via L-type Ca2+ channels and Ca2+-induced Ca2+ release mediated by clusters of ryanodine receptors during excitation-contraction coupling in cardiac myocytes. Coupled advection-reaction equations are derived relating the time-dependent probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum [Ca2+] conditioned on "Ca2+ release unit" state. When these equations are solved numerically using a high-resolution finite difference scheme and the resulting probability densities are coupled to ordinary differential equations for the bulk myoplasmic and sarcoplasmic reticulum [Ca2+], a realistic but minimal model of cardiac excitation-contraction coupling is produced. Modeling Ca2+ release unit activity using this probability density approach avoids the computationally demanding task of resolving spatial aspects of global Ca2+ signaling, while accurately representing heterogeneous local Ca2+ signals in a population of diadic subspaces and junctional sarcoplasmic reticulum depletion domains. The probability density approach is validated for a physiologically realistic number of Ca2+ release units and benchmarked for computational efficiency by comparison to traditional Monte Carlo simulations. In simulated voltage-clamp protocols, both the probability density and Monte Carlo approaches to modeling local control of excitation-contraction coupling produce high-gain Ca2+ release that is graded with changes in membrane potential, a phenomenon not exhibited by so-called "common pool" models. However, a probability density calculation can be significantly faster than the corresponding Monte Carlo simulation, especially when cellular parameters are such that diadic subspace [Ca2+] is in quasistatic equilibrium with junctional sarcoplasmic reticulum [Ca2+] and, consequently, univariate rather than multivariate probability densities may be employed.
authors.affiliation: Department of Applied Science, College of William and Mary, Williamsburg, Virginia 23187, USA.
authors.forename: George S B
authors.initials: GS
authors.lastname: Williams
authors.forename: Marco A
authors.initials: MA
authors.lastname: Huertas
authors.forename: Eric A
authors.initials: EA
authors.lastname: Sobie
authors.forename: M Saleet
authors.initials: MS
authors.lastname: Jafri
authors.forename: Gregory D
authors.initials: GD
authors.lastname: Smith
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D002118:Calcium / Q000008:administration & dosage / Q000378:metabolism*; D015220:Calcium Channels / Q000502:physiology*; D020013:Calcium Signaling / Q000502:physiology*; D003198:Computer Simulation; D008955:Models, Cardiovascular; D015233:Models, Statistical; D009200:Myocardial Contraction / Q000502:physiology*; D032383:Myocytes, Cardiac / Q000187:drug effects / Q000502:physiology*; D016008:Statistical Distributions
chemical_list: D015220:Calcium Channels; D002118:Calcium