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

Journal Article · · Nature Physics
DOI:https://doi.org/10.1038/nphys3553· OSTI ID:1327648
 [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)
+ Show Author Affiliations

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.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1327648
Journal Information:
Nature Physics, Vol. 12, Issue 2; ISSN 1745-2473
Publisher:
Nature Publishing Group (NPG)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 113 works
Citation information provided by
Web of Science

References (29)

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
Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer journal October 2003
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
The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms journal June 1967
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
  • 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
conference January 2008

Cited By (35)

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
Effectively explore metastable states of proteins by adaptive nonequilibrium driving simulations journal March 2017
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
Weak Galilean invariance as a selection principle for coarse-grained diffusive models 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 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

Similar Records

Non-ergodicity of a globular protein extending beyond its functional timescale
Journal Article · Wed Aug 24 00:00:00 EDT 2022 · Chemical Science · OSTI ID:1327648
+4 more
Self-similar transport in incomplete chaos
Journal Article · Wed Sep 01 00:00:00 EDT 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) · OSTI ID:1327648
Dynamics of Nanoparticles in Entangled Polymer Solutions
Journal Article · Fri Dec 01 00:00:00 EST 2017 · Langmuir · OSTI ID:1327648
+4 more

Related Subjects

59 BASIC BIOLOGICAL SCIENCES