Path-integral theory of an axially confined worm-like chain

A path-integral formulation is developed for the thermodynamic properties o f a worm-like chain moving on a surface and laterally confined by a harmoni c potential. The free energy of the chain is calculated as a function of it s length and boundary conditions at each end. Distribution functions for ch ain displacements can be constructed by utilizing the Markov property as a function of displacement phi (s) and its derivative d phi (s)/ds along the path. These quantities are also calculated in the presence of pinning sites which impose fixed positive or negative displacements. foreshadowing their application to a model for the regulation of striated muscle.