Two-state theory of single-molecule stretching experiments

We present a statistical mechanics analysis of the finite-size elasticity of model polymers, consisting of domains which can exhibit transitions between more than one stable state at large applied force. The constant-force (Gibbs) and constant-displacement (Helmholtz) formulations of single molecule stretching experiments are shown to converge in the thermodynamic limit. Monte Carlo simulations of continuous three dimensional polymers of variable length are carried out, based on this formulation. We demonstrate that the experimental force-extension curves for short and long polymers are described by a unique universal model, despite the differences in chemistry and rate-dependence of transition forces.