Modeling of kinetic processes in biological systems

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Dependence of the mean transition path time on the height of the entropy barrier Transition path of a particle diffusing between points a and b is the final segment of the particle trajectory when it leaves point a and goes to point b without touching point a and vice versa. We studied the mean transition path time in entropy potentials focusing on its dependence of the entropy barrier height. We found that this dependence is highly non-trivial changing from monotonic decrease with the barrier height in high-dimensional spaces to monotonic increase in two dimensions. Dynamics of systems, like molecular motors, that randomly jump between states with different velocities and diffusivities At long times, stochastic dynamics of systems mentioned in the title can be characterized by two parameters: effective drift velocity and diffusivity. We developed a theory that explains how these effective parameters are related to the drift velocities and diffusivities in individual states and the rates of inter-state transitions. Random walk in crowded environment We developed a theory of cyclic random walk in crowded environment and demonstrated that crowding affects main features of the random walk in the absence of crowding. We explained how one can observe the discovered effects in single-molecule experiments. Forward-backward symmetry of the transition path time Conventional consideration of the transition path time assumes conservation of diffusing particles. Because of the detailed balance, the distribution of the transition path possesses the forward-backward symmetry. We generalized the conventional consideration to the case where diffusing particles can be trapped and proved that the detailed balance is fulfilled in the presence of a distributed sink of an arbitrary shape. This allowed us to show that the forward-backward symmetry of the distribution of the transition path time is conserved even in the presence of trapping.