title: Moment closure for local control models of calcium-induced calcium release in cardiac myocytes.
abstract: In prior work, we introduced a probability density approach to modeling local control of Ca2+-induced Ca2+ release in cardiac myocytes, where we derived coupled advection-reaction equations for the time-dependent bivariate probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum (SR) [Ca2+] conditioned on Ca2+ release unit (CaRU) state. When coupled to ordinary differential equations (ODEs) for the bulk myoplasmic and network SR [Ca2+], a realistic but minimal model of cardiac excitation-contraction coupling was produced that 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 SR depletion domains. Here we introduce a computationally efficient method for simulating such whole cell models when the dynamics of subspace [Ca2+] are much faster than those of junctional SR [Ca2+]. The method begins with the derivation of a system of ODEs describing the time-evolution of the moments of the univariate probability density functions for junctional SR [Ca2+] jointly distributed with CaRU state. This open system of ODEs is then closed using an algebraic relationship that expresses the third moment of junctional SR [Ca2+] in terms of the first and second moments. In simulated voltage-clamp protocols using 12-state CaRUs that respond to the dynamics of both subspace and junctional SR [Ca2+], this moment-closure approach to simulating local control of excitation-contraction coupling produces high-gain Ca2+ release that is graded with changes in membrane potential, a phenomenon not exhibited by common pool models. Benchmark simulations indicate that the moment-closure approach is nearly 10,000-times more computationally efficient than corresponding Monte Carlo simulations while leading to nearly identical results. We conclude by applying the moment-closure approach to study the restitution of Ca2+-induced Ca2+ release during simulated two-pulse voltage-clamp protocols.
authors.affiliation: Department of Applied Science, College of William and Mary, Williamsburg, Virginia, 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 / Q000378:metabolism*; D020013:Calcium Signaling / Q000502:physiology*; D003198:Computer Simulation; D008564:Membrane Potentials / Q000502:physiology*; D008955:Models, Cardiovascular; D009200:Myocardial Contraction / Q000502:physiology*; D032383:Myocytes, Cardiac / Q000502:physiology*
chemical_list: D002118:Calcium