Folding time dependence of the motions of a molecular motor in an amorphous medium

We investigate the dependence of the displacements of a molecular motor embedded inside a glassy material on its folding characteristic time τ_{f}. We observe two different time regimes. For slow foldings (regime I) the diffusion evolves very slowly with τ_{f}, while for rapid foldings (regime II) the diffusion increases strongly with τ_{f}(D≈τ_{f}^{-2}), suggesting two different physical mechanisms. We find that in regime I the motor's displacement during the folding process is counteracted by a reverse displacement during the unfolding, while in regime II this counteraction is much weaker. We notice that regime I behavior is reminiscent of the scallop theorem that holds for larger motors in a continuous medium. We find that the difference in the efficiency of the motor's motion explains most of the observed difference between the two regimes. For fast foldings the motor trajectories differ significantly from the opposite trajectories induced by the following unfolding process, resulting in a more efficient global motion than for slow foldings. This result agrees with the fluctuation theorems expectation for time reversal mechanisms. In agreement with the fluctuation theorems we find that the motors are unexpectedly more efficient when they are generating more entropy, a result that can be used to increase dramatically the motor's motion.