Folding-Unfolding Transition of Active Polymer on the Reconfiguration of Bidirectional Tangential Active Force

Abstract

The role of active stress on the conformational dynamics of a polymer has drawn significant interest due to its potential applications in understanding the energy landscape of protein structures, buckling of biopolymers, genomic spatial organization and their large-scale coherent dynamics. We present a model of bidirectional active force that acts along the polymer’s tangent, with its direction stochastically reversing between head-to-tail and tail-to-head orientations. The active polymer shows a structural transition from a random coil-like state to a compressed state with variations in the active force, directional (polarity) reversal rate, and their fraction. Furthermore, the polymer reswells and stretches more than its passive limit for a large active force. The polymer’s radius of gyration follows the ideal chain-like scaling relation, R_g²∼N_m^2ν with an exponent ν ≈ 1/2, in both the compressed and swelled states. The bidirectional active force drives dynamical transitions, where the effective diffusivity abruptly shifts from a linear to quadratic increase. Similarly, in the regime of large activity, the linear decrease of the longest relaxation time of the polymer changes behavior to a power-law behavior Pe^–4/3 with Péclet number. We have shown that the active polymer’s conformational, relaxation, and diffusive behaviors display a transition from an active polar linear polymer model (APLP) to an active Brownian particle (ABP) polymer model with the increase in the fraction of the opposite polarity and their reconfiguration time.