title: [Deterministic chaos in the dynamics of biomembrane ion channel current].
abstract: Within the framework of the theory of deterministic chaos, a nonlinear first-order differential equation with delay and relaxation with periodic influence on channel current for the parameter of order (deviation of channel current from the equilibrium value) was obtained. The numerical solutions of the equation indicate a chaotic dynamics of the order parameter and conformation potential of the channel protein with positive Lyapunov indices. By integration in the time interval between the "jumps" of ions through energy barriers of the channel protein, a mapping was obtained that also results in chaotic solutions realized in experiments. Basic kinetic characteristics of ionic channels for the mapping were obtained: the probability for the channel to be in the open state, P0, and the mean duration of a pack of current pulses depending on controlling parameters. Algorithms for constructing bifurcation diagrams with the transition to chaos and for determining Lyapunov indices and Kholmogorov entropy, pulsation spectra, and other parameters of chaotic dymanics were developed.
authors.forename: G P
authors.initials: GP
authors.lastname: Bystraĭ
authors.forename: A S
authors.initials: AS
authors.lastname: Vorokh
authors.forename: S V
authors.initials: SV
authors.lastname: Andreev
mesh_terms: D002462:Cell Membrane / Q000737:chemistry* / Q000378:metabolism; D007473:Ion Channels / Q000737:chemistry* / Q000378:metabolism; D017136:Ion Transport / Q000502:physiology; D007700:Kinetics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D013816:Thermodynamics
chemical_list: D007473:Ion Channels