Ensemble inequivalence and negative extensibility in a strongly stretched wormlike chain with fluctuating bending stiffness

Many semiflexible polymers exhibit fluctuations in the local bending stiffness along their contour. This may be due to intrinsic conformational changes (e.g., denaturation bubble formation in double stranded DNA or helix-coil transition in polypeptides) or the reversible adsorption and desorption of molecules from the polymer's environment (e.g., DNA-protein interactions or hybridization of oligonucleotides). In this article, we analyze the tensile elasticity of a strongly stretched wormlike chain, which consists of N concatenated segments, where each segment can be in one of two states, A or B, which differ in bending stiffness. We call this model the reversible wormlike chain (rWLC) model. In the Gibbs (fixed-force, isotensional) ensemble, we obtain analytic expressions for the force-extension relation and the mean fraction of B segments. We show that, under certain conditions, there is a tension-induced crossover from a mostly A to a mostly B rWLC. In the Helmholtz (fixed-extension, isometric) ensemble, we obtain analytic expressions up to a summation. We show that, for finite N, there is marked ensemble inequivalence. Remarkably, in the Helmholtz ensemble, the rWLC can exhibit negative extensibility and multiple peaks.