Harmonically Confined, Semiflexible Polymer in a Channel: Response to a Stretching Force and Spatial Distribution of the Endpoints

Abstract

We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points or radial distribution function is also analyzed.

Stretching a Semiflexible Polymer in a Tube

“…We note that an equivalent expression to Equations (22)–(25) has been derived by Burkhardt [ 25 ] by using a different method. Figure 2 shows the dependence of the range (shadow region) on , , and , from which we can see that as long as the chain is sufficiently long and the confinement is strong enough, we always have , so that Equation (22) can be simplified to …”

“…When the polymer chain simultaneously subjects to tube confinement and force stretch in the deflection regime, as shown by [23,24] and later by [25], the effect of confinement can be approximately equivalent to an additional effective stretching force f c [23] witĥ…”

“…When the polymer chain simultaneously subjects to tube confinement and force stretch in the deflection regime, as shown by [ 23 , 24 ] and later by [ 25 ], the effect of confinement can be approximately equivalent to an additional effective stretching force [ 23 ] with and , where c is a prefactor. Then force-extension relation of the confined polymer chain under stretching force, f , can be described by that of an unconfined chain subjecting to an effective stretching force f + f c .…”

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

“…define the tangential vector and its components. As shown in [32,51], in the case of strong confinement, undulation of the chain due to thermal fluctuation is small so that =1 s    ur [52][53][54], together with Equation (2) leads to…”

“…is the confinement potential per unit length due to the tube wall, and p L is the persistence length of Based on Equation 3, one can obtain the extension of the chain along the tube axis [51]…”