Many cellular processes are governed by discrete molecular events that are intrinsically stochastic, e.g., single channel gating, the binding and unbinding of ligand and receptor, and the collective activity of intracellular calcium channels giving rise to "calcium sparks." These subcellular phenomena are typically modeled using Monte Carlo simulation methods. The proposed work begins with the observation that realistic models of cardiac myocytes are required to strategically investigate the generation of cardiac arrhythmias and to develop medical device or drug interventions that can prevent this pathophysiology. Unfortunately, widely used deterministic cardiac myocyte models do not reproduce certain cellular phenomenon in which discrete molecular events and local signaling within subcellular compartments play an essential role. An important example is pathological excitation-contraction (EC) coupling during heart failure that is due in part to aberrant local signaling between small numbers of voltage-gated calcium channels and ryanodine receptors co-localized at the same dyadic cleft, so-called "stochastic functional units" (SFUs). Another example is the phenomenon of "graded release" where the amount of calcium released by internal stores is a gradually increasing function of calcium entry through voltage-gated calcium channels. In these cases deterministic models provide only limited mechanistic insight and stochastic cellular models only include a compact representation of subcellular events that are required to assist experimental design and interpretation. Moreover, Monte Carlo simulations of SFUs are computationally expensive and difficult to apply at the cellular scale. To address those issues, the development of an "ensemble density" approach is proposed where coupled Fokker-Planck-like equations are used to accurately represent SFU activity and the resulting independent probability density of subsarcolemmal calcium concentrations in mathematical models of normal and pathophysiological EC coupling in cardiac myocytes. The ensemble density method will be validated using traditional Monte Carlo techniques and the computational advantage of the method explored. A hierarchy of models will be developed and tested in the context of a joint experimental/theoretical investigation of the stochastic aspects of normal and pathological EC coupling in cardiac myocytes.
To summarize, many cellular processes are involved in single events that occur with a certain probability. These seemingly random events combined determine cellular function. The proposed research will develop methods and representations for the cardiac muscle cell incorporating discrete random events in efficient cellular models. The modeling efforts will be guided and confirmed by experimental work. The development of computationally efficient whole cell models of cardiac myocytes is a step toward realistic tissue and organ level models of the heart.
