Nonlinear dynamics of a cellular Ryanodine channel

Dynamics of calcium ions releasing is studied in the framework of a simple electron-conformal model of a cellular Ryanodine channel, a giant protein molecule playing an important role in many biochemical processes. Taking into account only two coupled degrees of freedom (external conformal and internal electron ones), we introduce a Hamiltonian of a cellular Ryanodine channel belonging to the class of spin-boson Hamiltonians. The corresponding equations of motion constitute a nonlinear five-dimensional dynamical system with two isolated integrals of motion. Hamiltonian chaos may arise in that system as a result of a transversal intersection of stable and unstable manifolds of an unperturbed separatrix. The maximal Lyapunov exponent computed is positive in a certain range of values of control parameters. Poincare sections computed demonstrate typical patterns of Hamiltonian chaos with coexisting domains of regular and chaotic motion corresponding to regular and chaotic oscillations of the internal state of the cellular Ryanodine channel. An intermittency of those oscillations is found numerically and explained in terms of a stickiness effect of trajectories to the boundaries of stability islands in the phase space. Thus, even a single cellular Ryanodine channel is able to work in different regimes (regular, chaotic and weakly chaotic) depending on the values of the control parameters.