Casimir interactions in semiflexible polymers

Abstract

We investigate the Casimir or fluctuation-induced interaction between two cross-linkers bound to the same semiflexible filament. The calculation is complicated by the appearance of second-order derivatives in the bending Hamiltonian for such filaments, which requires a careful evaluation of the the path integral formulation of the partition function in order to arrive at the physically correct continuum limit and properly address ultraviolet divergences. Doing so based on the previous work of Kleinert [Kleinert, J. Math. Phys. 27, 3003 (1986)], we find that cross-linkers interact along a filament with an attractive logarithmic potential proportional to thermal energy. The proportionality constant depends on whether and how the cross-linkers constraint the relative angle between the two filaments to which they are bound. We comment on the implications of this Casimir interaction for equilibrium distribution of labile cross-linkers in semiflexible biopolymer, e.g., F-actin, networks, and bundles.