Stretching multistate flexible chains and loops.

Polymer loop structure commonly appears in biological phenomena, such as DNA looping and DNA denaturation. When a chain forms a loop, its elastic behavior differs from that of an open chain due to the loss of entropy. In the case of reversible loop formation, interesting behavior emerges related to the multistate nature of the conformations. In this study, we model a multistate reversible loop as a looping Gaussian chain, which can bind (close) reversibly at one or several points to form a loop, or a zipping Gaussian loop, which can zip reversibly to form a double-stranded chain. For each model, we calculate the force-extension relations in the fixed-extension (Helmholtz) and the fixed-force (Gibbs) statistical ensembles. Unlike the single Gaussian chain or loop, the multilevel systems demonstrate qualitatively distinct tensile elasticity and ensemble inequivalence. In addition, we investigate a Gaussian necklace consisting of reversible alternating blocks of the zipped chain and loop and obtain the force-temperature phase diagram. The phase diagram implies a force-induced phase transition from a completely looped (denatured) state to a mixed (bound) state.