The thermodynamics of reversible cyclization in semiflexible polymers

A recent model of the irreversible kinetics of ring formation in semiflexible polymers [J. Chem. Phys. 116, 399 (2002)] is generalized to the case of equilibrium cyclization, for which the rate constants for the forward and backward reaction are finite. The model is based on the diffusion-reaction formalism of Wilemski and Fixman [J. Chem. Phys. 60, 866 (1974)], and employs a path integral representation of the semiflexible chain (within a certain Gaussian approximation) to derive an expression for the steady state probability of occurrence of open configurations for given values of the chain length N, the reaction radius a, the degree of stiffness z, and the ratio of forward to backward reaction rates k/k(r). The steady state probability is used to calculate the free energy changes for the open-to-close transition. Chain rigidity is found to strongly influence the standard Gibbs free energy and enthalpy for the transition. While flexible chains tend to cyclize by virtue of their entropic elasticity alone, cyclization in semiflexible chains is also governed by the change in enthalpy between the open and closed states. The results are in qualitative agreement with the experimental measurements of Libchaber and co-workers. (C) 2002 American Institute of Physics.