Thermodynamic modeling of a phase transformation in protein filaments with mechanical function

Protective egg capsules from whelks (intertidal marine gastropods) were recently demonstrated to derive their impressive mechanical behavior-reminiscent of the pseudoelastic behavior in some alloy systems from a reversible phase transition of component protein building blocks from a compact alpha-helical conformation to a more extended softer conformation, called beta*. This behavior was previously modeled under equilibrium conditions, demonstrating that the transition from the alpha- to beta*-phase could account for the pronounced yield plateau and reversibility; however, a theoretical understanding of the non-equilibrium behaviors of the egg capsule (e. g. strain rate dependence and hysteresis) requires a new approach. Here, we modify the previously proposed model in order to address the time-dependent behaviors of the whelk egg capsule biopolymer. Our results indicate that hysteresis during cyclic loading originates from a mismatch between the speed of the mechanical driving force and the rate at which the phase transition occurs. Furthermore, the characteristic curved shape of the stress-strain plot arises from a nonlinear relationship between the transformation rate and the amount of applied load. These results have important implications for our understanding of the mechanics of biological polymers and may have implications for the design of biomimetic pseudoelastic polymers.