Tensile elasticity of a freely jointed chain with reversible hinges

Many biopolymers exhibit reversible conformational transitions within the chain, which affect their bending stiffness and their response to a stretching force (e.g. ds-DNA with denatured bubbles or bundles with reversible cross-links). The simplest theoretical model which captures what such systems have in common is a freely jointed chain (FJC) with reversible hinges. Each hinge can be open, as in the usual FJC or closed, forcing the linked segments to align. This model was analysed in the Helmholtz ensemble by Glatting et al. (Colloid Polym Sci, 1995). In this talk, we analyse it in the Gibbs ensemble. Remarkably, the reversible FJC exhibits ensemble inequivalence. A mean field treatment suggests a continuous phase transition to a fully closed state at a certain force, but the generating function method ("necklace model") shows that there is no phase transition. However, there is a crossover between two states with clearly different response. At the low force (linear response) regime, the reversible FJC has higher tensile compliance than its usual counterpart. On the contrary, at the strong force regime, the tensile compliance of the reversible FJC is much lower than that of the usual FJC.