Development of a novel thermodynamical model for sinoatrial node pacemaker cells and bifurcation analysis of the model systems in terms of nonlinear dynamics.

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On the basis of our classical Hodgkin-Huxley type model, we have first developed a novel thermodynamical model for sinoatrial node cells. For the development of the novel model, gating kinetics of ionic channels and dynamics of ion transports by Na^+-K^+ pump and Na^+/Ca^<2+> exchangers were described by time-homogeneous Markovian state models with state transition rate constants being formulated with single exponential functions based on Eyring's absolute reaction rate theory. Furthermore, the dynamics of binding and unbinding of antiarrhythmic drugs were incorporated to the base model. We have also developed the methods and computer programs to investigate bifurcation structures of model systems during changes in parameters. Based on bifurcation theory, we calculated equilibrium points, their stability, and dynamics of limit cycles. Exploring bifurcation structures of model systems allowed us to validate the mathematical models more accurately as well as to elucidate the dynamical me … More chanisms of pacemaker generation.To validate the novel model as well as the classical model, we simulated spontaneous action potentials and ionic current dynamics, and also experimentally examined the effects of antiarrhythmic agents to block L-type Ca^<2+> (I_<Ca,L>) and delayed-rectifier K^+ (I_<Kr>) currents on SA node pacemaking. Moreover, we explored bifurcation structures of model cells during inhibitions of I_<Ca,L> or I_<Kr> by constructing bifurcation diagrams. Our findings are summarized as follows : 1)The novel model is superior to the classical model in mimicking the action potential change during I_<Kr> inhibition. 2)In both the models, blocking I_<Ca,L> or I_<Kr> caused cessation of pacemaker activity via a Hopf bifurcation where an EP was stabilized, suggesting that bifurcation structures of the model systems during I_<Ca,L> or I_<Kr> inhibitions are essentially the same. It was suggested that a classical Hodgkin-Huxley type model is still useful in exploring the mechanisms of pacemaker generation, and can be used for constructing whole heart models. Less