TY - JOUR

T1 - Turbulence in protein folding

T2 - Vorticity, scaling and diffusion of probability flows

AU - Andryushchenko, Vladimir A.

AU - Chekmarev, Sergei F.

N1 - Publisher Copyright: © 2017 Andryushchenko, Chekmarev. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - Recently, when studying folding of a SH3 domain, we discovered that the flows of transitions between protein states can be surprisingly similar to turbulent fluid flows. This similarity was not restricted by a vortex pattern of the flow fields but extended to a spatial correlation of flow fluctuations, resulting, in particular, in the structure functions such as in the Kolmogorov theory of homogeneous and isotropic turbulence. Here, we undertake a detailed analysis of spatial distribution of folding flows and their similarity to turbulent fluid flows. Using molecular dynamics simulations, we study folding of another benchmark system—Trp-cage miniprotein, which has different content of secondary structure elements and mechanism of folding. Calculating the probability fluxes of transitions in a three-dimensional space of collective variables, we have found that similar to the SH3 domain, the structure functions of the second and third orders correspond to the Kolmogorov functions. The spatial distributions of the probability fluxes are self-similar with a fractal dimension, and the fractal index decreases toward the native state, indicating that the flow becomes more turbulent as the native state is approached. We also show that the process of folding can be viewed as Brownian diffusion in the space of probability fluxes. The diffusion coefficient plays a role of the key parameter that defines the structures functions, similar to the rate of dissipation of kinetic energy in hydrodynamic turbulence. The obtained results, first, show that the very complex dynamics of protein folding allows a simple characterization in terms of scaling and diffusion of probability fluxes, and, secondly, they suggest that the turbulence phenomena similar to hydrodynamic turbulence are not specific of folding of a particular protein but are common to protein folding.

AB - Recently, when studying folding of a SH3 domain, we discovered that the flows of transitions between protein states can be surprisingly similar to turbulent fluid flows. This similarity was not restricted by a vortex pattern of the flow fields but extended to a spatial correlation of flow fluctuations, resulting, in particular, in the structure functions such as in the Kolmogorov theory of homogeneous and isotropic turbulence. Here, we undertake a detailed analysis of spatial distribution of folding flows and their similarity to turbulent fluid flows. Using molecular dynamics simulations, we study folding of another benchmark system—Trp-cage miniprotein, which has different content of secondary structure elements and mechanism of folding. Calculating the probability fluxes of transitions in a three-dimensional space of collective variables, we have found that similar to the SH3 domain, the structure functions of the second and third orders correspond to the Kolmogorov functions. The spatial distributions of the probability fluxes are self-similar with a fractal dimension, and the fractal index decreases toward the native state, indicating that the flow becomes more turbulent as the native state is approached. We also show that the process of folding can be viewed as Brownian diffusion in the space of probability fluxes. The diffusion coefficient plays a role of the key parameter that defines the structures functions, similar to the rate of dissipation of kinetic energy in hydrodynamic turbulence. The obtained results, first, show that the very complex dynamics of protein folding allows a simple characterization in terms of scaling and diffusion of probability fluxes, and, secondly, they suggest that the turbulence phenomena similar to hydrodynamic turbulence are not specific of folding of a particular protein but are common to protein folding.

KW - Hydrodynamics

KW - Kinetics

KW - Probability

KW - Protein Folding

KW - Proteins/chemistry

KW - PERSPECTIVE

KW - TRP-CAGE

KW - MECHANISMS

KW - MODEL

KW - THERMODYNAMICS

KW - INTEGRATION

KW - BETA-SHEET MINIPROTEIN

KW - KINETICS

KW - MOLECULAR-DYNAMICS SIMULATIONS

KW - ENERGY LANDSCAPE

UR - http://www.scopus.com/inward/record.url?scp=85036619030&partnerID=8YFLogxK

U2 - 10.1371/journal.pone.0188659

DO - 10.1371/journal.pone.0188659

M3 - Article

C2 - 29206845

AN - SCOPUS:85036619030

VL - 12

SP - e0188659

JO - PLoS ONE

JF - PLoS ONE

SN - 1932-6203

IS - 12

M1 - 0188659

ER -