This proposal addresses three major aspects of research to elucidate the mechanisms underlying cardiac rhythms: (1) single channel gating mechanisms, (2) reconstructing caridac action potentials, and three effects of pharmacological agents on the propagation of action potentials. The general approach is mathematical modeling and correlation of the models with experimental data derived from the physiological studies of others. Specifically, the first part of this proposal deals with the ionic channel activity in heart cells from the viewpoint of non-Markovian Weibull kinetics. Markovian models will be compared with non-Markovian models to determine their relative merits and to determine whether the non-Markovian Weibull model can be classified as a "fractal" model. The second part of the proposal deals with the construction of a minimal unified model for cardiac action potentials using experimental data on action currents obtained by others, so as to study the dynamic role of compartmentalized calcium ions under spontaneous beating conditions, and to construct a mathematical model for the cardiac action potential. The third part of this proposal deals with elucidation of the effect of calcium channel blockers on the action potential propagation. To acheive these objectives the cardiac impulse initiation and propagation will be simulated using the Cray X-MP/48 supercomputer and study how changes in the ionic channel properties would alter the properties of the propagating waves. The availability of advanced scientific computers has greatly expanded the possibility for using mathematical modeling as an approach to study physiological processes. Although models of the heart action potential have been of interest for many years, experimental advances have provided new information that can now be incorporated into more sophisticated models which, in turn, may point to more refined experiments. The ultimate goal of these approaches is to develop a thorough understanding of the electrical phenomena that underly the rythmic activity of the heart.
