Colored noise, folding rates and departure from Kramers’ behavior

Abstract

Recent experiments have shown that, for several proteins, the dependence of folding and unfolding rates on solvent viscosity does not obey Kramers' theory. Such a departure from standard Kramers' behavior is often attributed to the existence of internal friction, related to the structure of a polypeptide chain. In this paper, we propose an entirely different mechanism leading to violation of Kramers' theory. Using the generalized Langevin equation with time-dependent friction and a C(α)-Go model, we demonstrate that this effect may be caused by the colored Gaussian noise which is characterized by correlation time τ. Surprisingly, the dependence of folding time t(f) on τ is non-trivial: the plot t(f)vs τ exhibits two minima at low and intermediate values of τ. The appearance of one more additional minimum is in sharp contrast to one dimensional barrier crossing dynamics. We argue that it is a generic signature of entropy of activation in a multidimensional problem.

Probing the Viscosity Dependence of Rate: Internal Friction or the Lack of Friction?

“…We expected that the increased deviation with the parameters would correspond to an increase in σ; while σ increases with the barrier curvature, it decreases with the solute–solvent coupling and solute size (Figure a–d). Therefore, deviation from KT or memory friction alone, as previously thought, does not correlate with σ.…”

“…Therefore, the above results, nonzero σ or the fractional value of α in the water bath, indicate that a fit to Ansari’s equation may not provide an estimate of internal friction; rather, it indicates a deviation from Kramers’ behavior only. This deviation has already been shown to depend on the frequency-dependent friction, first by Bagchi and Oxtoby and later by many others. , …”

“…There are only a few studies in the literature that have questioned the interpretation of σ > 0 or α < 1 as internal friction . However, they ascribed the presence of σ to the frequency-dependent friction which, as we will show next, is only partially correct.…”

Effect of elastic colored noise in the hopping dynamics of single molecules in stretching experiments

“…[2]. It was recently shown that, for several proteins, the dependence of folding and unfolding rates on solvent viscosity does not obey Kramers' theory and thus, indicating the necessity to use colored noise descriptions [3]. These descriptions may be implemented through non-Markovian Langevin equations.…”

“…Commonly, experiments using laser optical tweezers (LOT) are implemented in order to produce an external force, which induces conformational changes on the structure of RNA or DNA molecules [2][3][4][5][6][7]. The system considered in these works is made up by a RNA hairpin joined at its ends through two appropriate polymeric arms to two polystyrene beads.…”