Modeling of kinetic processes in biological systems

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Theory of milestoning Milestoning is a method that potentially allows significantly enlarge the time range of processes that can be analyzed using molecular dynamics simulations. Its main ides is to use MD simulations to map the original dynamics onto rate equations which then can be used to study the process of interest. Our theory explains physical meaning of the states transitions among which are described by the rate equations. Dynamics of blocking molecules in a membrane channel When a large molecule enters a membrane channel, it blocks the current of small ions through the channels. This phenomenon is studied experimentally in single-channel experiments in the Dr. Bezrukov's group. We developed a two-site model of the blocker lifetime in the channel, which is much simpler than the exact diffusion model and, therefore, useful for the analysis of experimental data on the blockade duration. Forward-backward symmetry of transition path time Transition path is a final part of a diffusion trajectory that starts form point a and is terminated when it comes to point b for the first time, during which the trajectory goes from point a to point be without touching point a. We show that the distribution of the duration of a-to-b transition path is equal to that for the duration of b-to-a transition path. This is a consequence of time-reversal symmetry of diffusion dynamics. Diffusion-limited trapping by rough surfaces We study trapping of diffusing particles by rough non-uniformly absorbing surfaces and show that it is equivalent to that by smooth uniformly absorbing surfaces with properly chosen parameters: effective surface location and its trapping rate. Our theory establishes the relation between these parameters and the parameters of the original surface which is rough and non-uniform.