Modeling of kinetic processes in biological systems

Center For Information Technology

Investigators

Linked publications & trials

Abstract

Diffusion resistance of a constriction zone in a membrane channel The overwhelming majority of membrane channels have complex shapes including constriction zones that affect transport of solutes through the channels. One can quantify the slowdown of channel-facilitated transport due to the presence of the constriction zones in terms of the increase of the channel diffusion resistance. We considered a special case, a constriction zone formed by a thin partition with a hole, located in the middle of a cylindrical channel. The theory is developed that shows how the additional diffusion resistance due to the presence of the partition depends on the geometric parameters of the system. Our theory is corroborated by the comparison of its predictions with the corresponding results obtained from Brownian dynamics simulations. Subtleties in analyzing experimental results on blockage of single channels In experiments on blockage of single membrane channels one can detect only slow blockages, whereas the overwhelming majority of blockage events are too fast to be resolved. As a consequence, one cannot learn about open-blocked equilibrium of the channel from such experiments. We developed a theory that explains how to bypass this difficulty. The theory suggests how one can determine the equilibrium constant between the blocked and open states of the channel from the experiments on blockage of single channels. Effective transport coefficients for transport with fluctuating drift velocity Transport of motor proteins is one of the numerous examples of biological transport with fluctuating drift velocity. At sufficiently long times such transport is characterized by two effective transport coefficients: effective drift velocity and diffusivity. Finding of these quantities is a long-standing problem that has been considered only in special cases of 2 and 3 states. We developed a general theory of transport in such systems. The theory shows how the transport coefficients depend on the drift velocities and diffusivities of the motor protein in individual states and the rates of its transitions between these states. Variational approach to the barrier crossing problem Protein folding and unfolding are frequently described as diffusive crossing of a barrier separating two wells of a bistable potential. The rate of such processes is well known when the barrier separating the wells is high compared to the thermal energy, that is not necessarily the case. Using variational approach to this diffusive barrier crossing problem, we developed a theory that allows one to treat the cases of low and high barriers on equal footing. Comparison of our theoretical predictions with the existing numerical results shows good agreement between the two over the entire range of the barrier height.