Stochastic Resonance in Protein Folding Dynamics

Abstract

Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics.

Environmental Fluctuations and Stochastic Resonance in Protein Folding

“…Moreover, the red signal is in phase with T ( t ) for slow modulation frequency ν ≪ k obs , but up to 90° out of phase with T ( t ) for fast modulation frequency ν ≫ k obs as the protein folding reaction cannot track rapid variations in temperature, which is further elaborated elsewhere. [19] …”

“…The suitability of such simple kinetic master equation models [8] has been tested by comparison with Brownian dynamics simulations. [19] …”

“…[11] To see if folding/unfolding can be accelerated by application of artificial thermal noise, we performed molecular dynamics simulations on a small model protein with a temperature-dependent native structure-based model potential. [13, 14] The goal was not to simulate VlsE, which folds far too slowly for realistic simulation with an all-atom force field, but to obtain in general the effect of noise amplitude and correlation time on reaction rate (see Methods and accompanying paper [19] ).…”

“…As discussed in the accompanying paper, [19] stochastic resonance can also be seen via the phase shift Δφ of the red and green signal. The predicted phase shifts with realistic FRET input parameters are small (see accompanying theory paper), but we were able to identify stochastic resonance by comparing the experimental phase shift with a Brownian dynamics simulation.…”

“…[11] This is similar to algorithms proposed by Lemarchand and coworkers, [8] and verified by Brownian dynamics in the accompanying paper in this issue. [19] The new addition to the model is the capability to optimize model parameters by a least-squares algorithm, and the code used in this paper is available in SI. Briefly, the donor and acceptor signals at each driving frequency ω =2 πν were least square fitted to a sine wave…”