Reduced Persistence Length and Fluctuation-Induced Interactions of Directed Semiflexible Polymers on Fluctuating surfaces

We consider directed semiflexible polymers embedded in a fluctuating surface which is governed by either surface tension or bending rigidity. The attractive interactions induced by the fluctuations of the surface reduce the rigidity of the polymers. In particular, it is shown that for arbitrarily stiff parallel polymers, there is a characteristic separation below which they prefer to bend rather than stay linear. The out-of plane fluctuations of the polymer, screen out the long-range fluctuation-induced forces, resulting in only a short-ranged effective attraction. 87.20, 82.65D, 34.20 Typeset using REVTEX 1 Fluid membranes with linear inclusions have shown a variety of interesting phenomenon. These inclusions can be incorporated by a polymrization of membranes containing unsaturated amphiphiles using UV irradiation [1]. Also, some (partially) hydrophobic polymers that are water soluble can become immersed or multiply anchored to the interior of a bilayer due to hydrophobic attractions [1]. Thermal fluctuations, or the elastic structure of the membrane, in conjunction with the constraint that inclusions are attached to the surface, affect structural properties of the polymers. For example, it has been shown that [2], depending on the value of rigidity parameters, elastic properties of the membrane may stabilize or destabilze the straight configuration of semiflexible polymers. Thermal fluctuations have been shown to induce an effective nematic-like orientational interaction between different segments of a polymer [3]. Polymers in turn, restricts membrane fluctuations and alter its behavior. It was found that cross-linked polymerization could promote wrinkling of the membranes [4], while linear polymerization causes the membrane to bulge and bud [5]. The long distance orientational interaction between rod-like inclusions due to thermal surface fluctuations were examined in Ref. [6]. There, it was assumed that the rods are much more rigid than the ambient membrane. In the limit that the separation R between rods is much greater than their length L, the interaction falls off as kBT (L/R) ; similar to the attractive interaction between disk-like inclusions [7]. It was also shown that the interactions have the non-trivial orientational dependence of squared dipolar interactions for inclusions on a film, and squared quadrupolar interactions on a membrane. For parallel rods at close separation, R ≪ L, the behavior is similar to the Casimir interaction between parallel plates [8], resulting in an interaction proportional to kBT (L/R). If the distances between the external objects, as well as their characteristic sizes, are larger than the membrane thickness, one can forget about the microscopic details of the membrane. In this limit, the membrane is well-described by the elastic Hamiltonian [9],