Özer, Mahmut

Proceedings | 2003 | Mathematical and Computational Applications8 ( 1-3 ) , pp.71 - 78

In this study, phase-plane analysis is carried out for a simplified model of Purkinje cell dendrite in terms of voltage-gated ionic channels involved. State variables, nullclines and equilibrium points of the model are determined, and effects of ionic channel conductance and injected current on the shape of nullclines and the equilibrium points are investigated. In this study, phase-plane analysis is carried out for a simplified model of Purkinje cell dendrite in terms of voltage-gated ionic channels involved. State variables, nullclines and equilibrium points of the model are determined, and effects of ionic channel conductance and . . . injected current on the shape of nullclines and the equilibrium points are investigated Daha fazlası Daha az

Özer, Mahmut

Proceedings | 2003 | Chinese Journal of Physics41 ( 2 ) , pp.206 - 218

The dynamics of a voltage-gated ionic channel is modeled by the conventional Hodgkin-Huxley mathematical formalism. In that formalism, the dynamics of the ionic channel activation and inactivation gates is modeled by a first-order differential equation dependent on the gate variable and the membrane potential. In this study a method, which combines statistical equilibrium theory and the thermodynamics of irreversible processes, is proposed for the study of the relaxation phenomena in the activation and inactivation gates of ionic channels present in the excitable membranes of neurons. In order to study the relaxation phenomena, the . . .assumption is made that the activation and inactivation gate order parameters can be treated as fluxes and forces, in the sense of Onsager's theory of irreversible thermodynamics. The kinetic equations are solved by using the Runge-Kutta method, in order to study the relaxation of the order parameters. It is found that the kinetic equations are characterized by two relaxation times. The kinetic coefficients that relate the fluxes to the forces are determined. Furthermore, it is shown that the obtained relaxation times have the same results as those obtained by using the Hodgkin-Huxley model. These results therefore indicate the validity of the proposed approach Daha fazlası Daha az