Abstract
We investigate theoretically the effect of polymer tension on the collective behavior of reversibly binding cross-links. For this purpose, we employ a model of two weakly bending wormlike chains aligned in parallel by a tensile force, with a sequence of inter-chain binding sites regularly spaced along the contours. Reversible cross-links attach and detach at the sites with an affinity controlled by a chemical potential. In a mean-field approach, we calculate the free energy of the system and find the emergence of a free-energy barrier which controls the reversible (un)binding. The tension affects the conformational entropy of the chains which competes with the binding energy of the cross-links. This competition gives rise to a sudden increase in the fraction of bound sites as the tension increases. We show that this transition is related to the cross-over between weak and strong localization of a directed polymer in a pinning potential. The cross-over to the strongly bound state can be interpreted as a mechanism for force-stiffening which exceeds the capabilities of single-chain elasticity and thus available only to reversibly cross-linked polymers.
Highlights
Cells and tissues are sensitive and responsive to mechanical forces
We have studied two reversibly cross-linked, semiflexible filaments under tension and shown that the two filaments are always in a bound state
The sharp transition obtained in mean-field theory is expected to be replaced by a crossover, if fluctuations are taken into account—similar to the cross-over observed in the model of a single stretched polymer in a confining potential
Summary
Cells and tissues are sensitive and responsive to mechanical forces. The constituent filament networks are able to adapt in a differentiated manner to a variety of strain or flow conditions, substrates, and biological functions [1, 2]. The stress fibers are reversibly cross-linked actin bundles extending between focal adhesions which are the sites where cells adhere to the extracellular matrix. They have been the subject of significant experimental and modeling activity in recent years [9,10,11,12,13,14,15,16]. The basis for our model is two identical semiflexible (locally inextensible) polymers which can reversibly bind to each other at spaced contour positions Both polymers have contour length L and are aligned parallel along a given direction x by a tensile force f, see figure 1. Where the functional integral ∫ [y1, y2] comprises all polymer conformations consistent with the boundary conditions, and β := 1 (kB T )
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