Dynamics of a polymer surmounting a potential barrier: The Kramers problem for polymers

Abstract

We study the dynamics of a flexible polymer under a Kramers potential using the multidimensional barrier crossing theory. The activation free energy of the polymer evaluated by a lattice statistics yields the crossing rate as a function of chain length, temperature, and potential parameters. It is found that a long chain has an enhanced crossing rate due to the extended conformation of low free energy it has at the barrier, while a short chain has the crossing dynamics of a Brownian particle. A chain of intermediate length can exhibit a minimum in the crossing rate as chain length varies. For any range of chain lengths and potential parameters, the crossing rate is larger than that of a polymer in the globular state, due to the internal degrees of freedom of the unfolded flexible chain. Our results can be applied to macromolecular separation and DNA electrophoresis.

Effective equations for reaction coordinates in polymer transport

“…[51] and reference therein). Important results have been derived also for polymeric chains [35,36,42]. We want to stress that our aim here is not to improve such results: we are interested in analyzing the ability of a data-driven approach to reconstruct an activated dynamics.…”

“…In this work, we revisit the Kramers' problem for a polymer in a double well [35,36] by using the evolution equations of proper RCs characterizing the slow dynamics of the chain. We model the polymer as a one-dimensional harmonic chain (the so-called Rouse chain).…”

Exploring the dynamics of dimer crossing over a Kramers type potential

“…In the last few decades considerable attention has been given to understand the thermally activated escape rate of polymers trapped in a potential well. [7][8][9][10][11][12] In particular Sebastian et al 2 and Sung et al 3,4 computed the crossing rate of a polymer as a function of the number of monomers, and the strength of interaction between individual monomers. They found that indeed the escape rate was a nontrivial function of these parameters.…”

“…1,[3][4][5][6] However, their transport and response properties are difficult to understand since they are multicomponent systems with features that depend on their size, flexibility, and shape. In the last few decades considerable attention has been given to understand the thermally activated escape rate of polymers trapped in a potential well.…”

Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier

“…[20][21][22][23][24][25][26][27] Experimental examples of systems of this sort include polymer translocation, 28,29 where a polymer is crossing a membrane through a pore 30 or narrow µm-scale channels with traps. 31 Recent experiments by Liu et al involve the escape of a DNA molecule from an entropic cage.…”