A kinetic model for voltage-gated ion channels in cell membranes based on the path integral method

Erdem R., Ekiz C.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, vol.349, no.1-2, pp.283-290, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 349 Issue: 1-2
  • Publication Date: 2005
  • Doi Number: 10.1016/j.physa.2004.10.016
  • Journal Name: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.283-290
  • Keywords: voltage-gated ion channels, kinetic model, path integral method, MEAN-FIELD MODEL, SPINODAL DECOMPOSITION, METASTABLE STATES, DYNAMICS
  • Akdeniz University Affiliated: No

Abstract

A kinetic model of cell membrane ion channels is proposed based on the path integral method. From the Pauli-type master equations valid on a macroscopic time scale, we derive a first-order differential equation or the kinetic equation which governs temporal evolution of the channel system along the paths of extreme probability. Using known parameters for the batrachotoxin (BTX)-modified sodium channels in squid giant axon, the time dependence of the channel activation and the voltage dependence of the corresponding time constants (tau) are examined numerically. It is found that the channel activation relaxes to the steady (or equilibrium)-state values for a given mernbrane potential and the corresponding time constant reaches a maximum at a certain potential and thereafter decreases in magnitude as the membrane potential increases. A qualitative comparison between these results and the results of Hodgkin-Huxley theory, path probability method and thermodynamic models as well as the cut-open axon technique is presented. Good agreement is achieved. (C) 2004 Elsevier B.V. All rights reserved.