Intracellular calicum cycling and control of action potential duration

Cardiac electrophysiology is a field with a rich history of integrative modeling. A particularly important milestone was the development of the first biophysically-based cell model describing interactions between voltage-gated membrane currents, pumps and exchangers, and intracellular calcium (Ca²⁺) cycling processes (DiFrancesco & Noble, Phil. Trans. Roy. Soc. Lond. B 307: 353), and the subsequent elaboration of this model to describe the cardiac ventricular myocyte action potential (Noble et al. Ann. N.Y. Acad. Sci. 639: 334; Luo, C-H and Rudy, Y. Circ. Res.74: 1071). These, and all other integrative models of the myocyte developed to date are of a type known as "common pool" models (Stern, Biophys. J. 63: 497). In such models, Ca²⁺ flux through L-type Ca²⁺ channels (LCCs) and ryanodine sensitive Ca²⁺ release channels (RyRs) in the junctional sarcoplasmic reticulum (JSR) membrane is directed into a common Ca²⁺ compartment. Ca²⁺ within this common pool also serves as activator Ca²⁺ triggering JSR Ca²⁺ release. In a modeling tour de force, Stern demonstrated that common pool models are structurally unstable, exhibiting all-or-none Ca²⁺ release except (possibly) over some narrow range of model parameters. Despite this inability to reproduce experimentally measured properties of graded JSR Ca²⁺ release, common pool models have been very successful in reproducing and predicting a range of myocyte behaviors. This includes properties of interval-force relationships that depend heavily on intracellular Ca²⁺ uptake and release mechanisms (Rice et al. Am. J. Physiol. 278: H913). Given these findings, one may wonder whether or not it is important to incorporate an accurate biophysical description of graded JSR Ca²⁺ release in computational models of the cardiac myocyte.

Stern went on to propose the "local-control" theory of Ca²⁺ release. In this theory, individual LCCs, the set of RyR with which they communicate, and the subspace within which they communicate, defines a functional release unit (FRU). Local control theory holds that while Ca²⁺ release within each FRU may be all or none, the averaged behavior of many independent FRUs reflects the probability of opening of LCCs. We have previously developed a model of the functional release unit (FRU) consisting of one LCC, eight RyR, and the volume in which they are enclosed (Biophys J 77:1871-84). To study the impact of local Ca²⁺ control in the context of the whole cell AP, we have developed a new class of ventricular cell model which combines the stochastic simulation of a large number of independent FRUs with the solution of a system of coupled ordinary differential equations describing the full complement of card