Barrier crossing of semiflexible polymers

– We consider the motion of semiflexible polymers in double-well potentials. We calculate shape, energy, and effective diffusion constant of kink excitations, and in particular their dependence on the bending rigidity of the semiflexible polymer. For symmetric potentials, the kink motion is purely diffusive, whereas kink motion becomes directed in the presence of a driving force on the polymer. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or synthetic polyelectrolytes on structured substrates. Introduction. – The Kramers problem [1] of thermally activated escape of an object over a potential barrier is one of the central problems of stochastic dynamics. It has been extensively studied not only for point particles [2], but also for extended objects such as elastic strings which occur in a variety of contexts in condensed-matter physics such as dislocation motion in crystals [3], motion of flux lines in type-II superconductors [4], or charge-density waves [5]. Elastic strings activate over potential barriers by nucleation and subsequent separation of soliton-antisoliton pairs which are localized kink excitations [6, 7]. An analogous problem is the activated motion of a flexible polymer over a potential barrier [8]. However, the thermally activated escape of a semiflexible polymer, which is a filament governed by its bending energy rather than entropic elasticity or tension, remained an open question that we want to address in this paper. Semiflexible polymers such as DNA or actin filaments have a large bending stiffness and, thus, a large persistence length, Lp. On scales exceeding Lp, the orientational order of the polymer segments decays exponentially, and the polymer effectively behaves as a flexible chain with a segment size set by Lp. In contrast, on length scales which are small compared to Lp, the bending energy of the semiflexible polymer strongly affects the behaviour of the polymer. The persistence lengths of the most prominent biopolymers range from 50 nm for DNA [9], to the 10μm range for actin [10,11] or even up to the mm range for microtubules [11] and becomes comparable to typical contour lengths of these polymers. Whereas the adsorption of such semiflexible polymers onto homogeneous adhesive