An Integrative Model of the Cardiac Ventricular Myocyte Incorporating Local Control of Ca2+ Release

Abstract

The local control theory of excitation-contraction (EC) coupling in cardiac muscle asserts that L-type Ca(2+) current tightly controls Ca(2+) release from the sarcoplasmic reticulum (SR) via local interaction of closely apposed L-type Ca(2+) channels (LCCs) and ryanodine receptors (RyRs). These local interactions give rise to smoothly graded Ca(2+)-induced Ca(2+) release (CICR), which exhibits high gain. In this study we present a biophysically detailed model of the normal canine ventricular myocyte that conforms to local control theory. The model formulation incorporates details of microscopic EC coupling properties in the form of Ca(2+) release units (CaRUs) in which individual sarcolemmal LCCs interact in a stochastic manner with nearby RyRs in localized regions where junctional SR membrane and transverse-tubular membrane are in close proximity. The CaRUs are embedded within and interact with the global systems of the myocyte describing ionic and membrane pump/exchanger currents, SR Ca(2+) uptake, and time-varying cytosolic ion concentrations to form a model of the cardiac action potential (AP). The model can reproduce both the detailed properties of EC coupling, such as variable gain and graded SR Ca(2+) release, and whole-cell phenomena, such as modulation of AP duration by SR Ca(2+) release. Simulations indicate that the local control paradigm predicts stable APs when the L-type Ca(2+) current is adjusted in accord with the balance between voltage- and Ca(2+)-dependent inactivation processes as measured experimentally, a scenario where common pool models become unstable. The local control myocyte model provides a means for studying the interrelationship between microscopic and macroscopic behaviors in a manner that would not be possible in experiments.

An Ionically Based Mapping Model with Memory for Cardiac Restitution

“…On the order of 200 beats are required for the concentration to build up to its steady state. Figure 3(c) shows this gradual build up of concentration for the mapping model (2,3) that approximately describes the behavior of the ionic model 14 , as we now discuss.…”

“…For the map (26), which is derived from the ODE's (21,22), it is shown in Mitchell and Schaeffer (2003) that this threshold behavior follows from asymptotic analysis of the 14 Incidentally, the APD's in Figure 7 are on the order of 5% longer than the values graphed in Figure 3. This discrepancy provides an estimate for the degree of accuracy of the aymptotic approximation.…”

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

“…Along with human ventricular models, which are discussed in detail below, ventricular models have been developed for guinea pig (Luo and Rudy 1991, Nordin 1993, Luo and Rudy 1994, Noble et al 1998, Faber and Rudy 2000, canine , Fox et al 2002, Greenstein and Winslow 2002, Cabo and Boyden 2003, Hund and Rudy 2004, Flaim et al 2006, rabbit (Puglisi and Bers 2001, Shannon et al 2004, Mahajan et al 2008, rat (Pandit et al 2001), and mouse (Bondarenko et al 2004, Wang andSobie 2008). The existence of species-specific ventricular models is a significant improvement over earlier, more generic ventricular models and recognises the differences in current contributions across species.…”

Stochastic hybrid modeling of intracellular calcium dynamics

“…Mathematical models of cytosolic calcium dynamics were developed for both excitable [33][34][35][36][37] cells and nonexcitable 27,33,38 cells. Many of these models deal with spatial distribution of calcium by employing two-or threedimensional partial-differential equations.…”