Barrier Crossing Problems in Biopolymer Dynamics

Abstract

In a living cell, biopolymers play central roles from storing genetic information to forming cellular structures. The study on the dynamics of the biopolymers is important for basic understanding of numerous living processes as well as for practical applications. In this thesis, we address several problems on thermal noise induced barrier crossing of biopolymers. First, we consider the escape of polymers from a metastable Kramers potential. To implement the slow rate processes in computer simulations, we extend path integral hyperdynamics method to the cases of polymers. Since the polymers can change their conformations upon response to external potential, the free energy barrier of the polymer is found to be much lower than that of the globular limit of the chain. Concurrently, the crossing rates are much higher than that of the globular limit, with strongly depending on the characteristics of the chain, such as stretching and bending stiffness. This result suggests a possibility of efficient separation of biopolymers.In cellular environments, in addition to equilibrium thermal fluctuation, there are also nonequilibrium fluctuations. We study their essential effects on two biological processes, polymer translocation and semiflexible polymer looping. In the process of polymer translocation through a nanopore, it was shown that the process becomes a thermal activation process when the polymer-pore attraction is strong enough. We find that dichomically flipping noise can significantly accelerate the process at an optimal flipping rate. The looping of biopolymers is important for many biological functions, such as in gene regulations. We study the effects of static and fluctuating tensions by using Brownian dynamics simulations and analytical calculations. We find that, because of the cooperativity of the polymer chain, a minute tension of 0.1 pN scale can dramatically change the looping time. In the presence of dichotimically flipping tensions, the looping time can be much faster at an optimal flipping rates of the tension.Double-stranded DNA (dsDNA) is a fairly stiff molecules with a persistence length of about 150 bp or 50 nm at the physiological condition. However, recent experiments have shown that it can readily bent on short length scales. To elucidate the mechanism of the high bending flexibility, we study bending induced bubble nucleation by using theoretical models. For uniformly bent case, as the bending increases above a critical value the bubble emerges abruptly. Concurrently the deformation free energy becomes lower than that of bubble-free DNA. For non-uniformly bent case, since the bubble can release the bending stress of dsDNA part the deformation free energy is further reduced. We also study the characteristics of the bubble by considering the net free energy cost of bubble formation. The bubble is found to be transient in uniformly bent case. On the other hand, the bubble is found to be trapped with a finite life in nonuniformly bent case.