skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

Abstract

Here, internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behavior with effective relaxation times existing over many decades in time, from ps up to ~102s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10–12 to 10–5s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behavior persists up to timescales approaching the in vivo lifespan of individual protein molecules.

Authors:
 [1];  [2];  [3];  [4];  [3];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
  2. Shanghai Jiao Tong Univ., Shanghai (China)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. Rhein-Main Univ. of Applied Sciences, Weisbaden (Germany)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1327648
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Nature Physics
Additional Journal Information:
Journal Volume: 12; Journal Issue: 2; Journal ID: ISSN 1745-2473
Publisher:
Nature Publishing Group (NPG)
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES

Citation Formats

Hu, Xiaohu, Hong, Liang, Smith, Micholas Dean, Neusius, Thomas, Cheng, Xiaolin, and Smith, Jeremy C. The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time. United States: N. p., 2015. Web. doi:10.1038/nphys3553.
Hu, Xiaohu, Hong, Liang, Smith, Micholas Dean, Neusius, Thomas, Cheng, Xiaolin, & Smith, Jeremy C. The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time. United States. https://doi.org/10.1038/nphys3553
Hu, Xiaohu, Hong, Liang, Smith, Micholas Dean, Neusius, Thomas, Cheng, Xiaolin, and Smith, Jeremy C. 2015. "The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time". United States. https://doi.org/10.1038/nphys3553. https://www.osti.gov/servlets/purl/1327648.
@article{osti_1327648,
title = {The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time},
author = {Hu, Xiaohu and Hong, Liang and Smith, Micholas Dean and Neusius, Thomas and Cheng, Xiaolin and Smith, Jeremy C.},
abstractNote = {Here, internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behavior with effective relaxation times existing over many decades in time, from ps up to ~102s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10–12 to 10–5s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behavior persists up to timescales approaching the in vivo lifespan of individual protein molecules.},
doi = {10.1038/nphys3553},
url = {https://www.osti.gov/biblio/1327648}, journal = {Nature Physics},
issn = {1745-2473},
number = 2,
volume = 12,
place = {United States},
year = {Mon Nov 23 00:00:00 EST 2015},
month = {Mon Nov 23 00:00:00 EST 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 113 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Nonexponential protein relaxation: dynamics of conformational change in myoglobin.
journal, June 1993


Bunching Effect in Single-Molecule T4 Lysozyme Nonequilibrium Conformational Dynamics under Enzymatic Reactions
journal, May 2010


Observation of a Power-Law Memory Kernel for Fluctuations within a Single Protein Molecule
journal, May 2005


Synergistic effects of substrate-induced conformational changes in phosphoglycerate kinase activation
journal, January 1997


Subdiffusion in time-averaged, confined random walks
journal, July 2009


1 f noise and other slow, nonexponential kinetics in condensed matter
journal, April 1988


The energy landscapes and motions of proteins
journal, December 1991


The energy landscape in non-biological and biological molecules
journal, September 1998


Hierarchical analysis of conformational dynamics in biomolecules: Transition networks of metastable states
journal, April 2007


Configurational subdiffusion of peptides: A network study
journal, February 2011


Proteins: Coexistence of Stability and Flexibility
journal, May 2008


Anomalies in the vibrational dynamics of proteins are a consequence of fractal-like structure
journal, July 2010


Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
journal, January 2014


Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
journal, November 1990


Noisy continuous time random walks
journal, September 2013


Aging and nonergodicity beyond the Khinchin theorem
journal, July 2010


Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions
journal, April 2013


Quantification of protein half-lives in the budding yeast proteome
journal, August 2006


A hierarchy of timescales in protein dynamics is linked to enzyme catalysis
journal, November 2007


Rate processes with dynamical disorder
journal, May 1990


Single-Molecule Enzymatic Dynamics
journal, December 1998


Fluctuating Enzymes:  Lessons from Single-Molecule Studies
journal, December 2005


Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited
journal, December 2005


Stretched exponential decay and correlations in the catalytic activity of fluctuating single lipase molecules
journal, February 2005


Nonexponential protein relaxation: Dynamics of conformational change in myoglobin [Correction]
journal, September 1993


Fluctuating Enzymes: Lessons from Single-Molecule Studies
journal, April 2006


Proteins: Coexistence of Stability and Flexibility
conference, January 2008

  • Reuveni, Shlomi; Granek, Rony; Klafter, Joseph
  • 3rd International ICST Conference on Performance Evaluation Methodologies and Tools, Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
  • https://doi.org/10.4108/icst.valuetools2008.4241

Works referencing / citing this record:

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation
journal, August 2018


Optimal reaction coordinates: Optimal reaction coordinates
journal, August 2016


Computed Free Energies of Peptide Insertion into Bilayers are Independent of Computational Method
journal, March 2018


The effects of pressure on the energy landscape of proteins
journal, February 2018


Ligand-Induced Conformational Dynamics of A Tyramine Receptor from Sitophilus oryzae
journal, November 2019


Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion
journal, July 2016


Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing
journal, January 2018


Fluctuations of random walks in critical random environments
journal, January 2018


Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model selection applied to stochastic-diffusivity data
journal, January 2018


Viscoelastic subdiffusion in a random Gaussian environment
journal, January 2018


Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding
journal, October 2017


Perspective: Identification of collective variables and metastable states of protein dynamics
journal, October 2018


Enhanced diffusion, swelling, and slow reconfiguration of a single chain in non-Gaussian active bath
journal, March 2019


Unveiling diffusive states from center-of-mass trajectories in glassy dynamics
journal, July 2019


Strange interfacial molecular dynamics
journal, September 2019


Growing timescales and lengthscales characterizing vibrations of amorphous solids
journal, July 2016


Slow domain reconfiguration causes power-law kinetics in a two-state enzyme
journal, January 2018


Weak Galilean invariance as a selection principle for coarse-grained diffusive models
journal, May 2018


Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
journal, April 2018


Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers
journal, October 2018


Molecular dynamics recipes for genome research
journal, February 2017


Dynamics of a family of cyan fluorescent proteins probed by incoherent neutron scattering
journal, March 2019


Aging is a log-Poisson process, not a renewal process
journal, August 2018


Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity
journal, March 2019


Critical Fluctuations in the Native State of Proteins
journal, February 2017


Gradual Crossover from Subdiffusion to Normal Diffusion: A Many-Body Effect in Protein Surface Water
journal, June 2018


Growing timescales and lengthscales characterizing vibrations of amorphous solids
text, January 2015


Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation
preprint, January 2016


Aging is a log-Poisson Process, not a Renewal Process
text, January 2018


Relaxation Functions of Ornstein-Uhlenbeck Process with Fluctuating Diffusivity
text, January 2019


Conformational Dynamics of a Single Protein Monitored for 24 h at Video Rate
journal, September 2018


The effects of pressure on the energy landscape of proteins
journal, February 2018


The fluctuating ribosome: thermal molecular dynamics characterized by neutron scattering
journal, November 2016


Long-range correlation in protein dynamics: Confirmation by structural data and normal mode analysis
journal, February 2020