Search

Transition paths refer to the time taken by molecules to cross a barrier separating two molecular conformations. In this work, we study how memory, as well as inertial contribution in the dynamics along a reaction coordinate, can affect the distribution of the transition-path time. We use a simple model of dynamics governed by a generalized Langevin equation with a power-law memory along with the inertial term, which was neglected in previous studies, where memory effects were explored only in the overdamped limit. We derive an approximate expression for the transit-time distribution and discuss our results for the short- and long-time limits and also compare it with known results in the high friction (overdamped) limit as well as in the Markovian limit. We have developed a numerical algorithm to test our theoretical results against extensive numerical simulations.

Protein-DNA interactions are important for all biological processes and involve the process of proteins searching for and recognizing specific binding sites on the DNA. Many aspects of the mechanism of the protein search for targets on DNA are not well understood. One important problem is the effect of DNA conformation on the protein search dynamics. Using a theoretical method based on a discrete-state stochastic approach, we obtained an analytical description of the dynamic properties. We investigated a system with two DNA conformers. It was found that the average search time on one DNA conformer via 1D or 3D motions depended on the dynamics of the search process on the other DNA conformer.