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

Nature Physics volume 12, pages 171174 (2016) | Download Citation


Internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behaviour with effective relaxation times existing over many decades in time, from ps up to 102 s (refs 1,2,3,4). Here, using molecular dynamics simulations, we show that, on timescales from 10−12 to 10−5 s, 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 behaviour persists up to timescales approaching the in vivo lifespan of individual protein molecules.

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Anton computer time was provided by the National Center for Multiscale Modeling of Biological Systems (MMBioS) through Grant P41GM103712-S1 from the National Institutes of Health (NIH) and the Pittsburgh Supercomputing Center (PSC). The Anton machine at PSC was generously made available by D.E. Shaw Research. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC05-00OR22725 and resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. L.H. acknowledges the support from NSF China 11504231. We thank I. M. Sokolov, A. P. Sokolov and F. Noé for fruitful discussions and T. Splettstößer (http://www.scistyle.com) for rendering the 3D protein structure shown in Fig. 1.

Author information


  1. Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA

    • Xiaohu Hu
    • , Micholas Dean Smith
    • , Xiaolin Cheng
    •  & Jeremy C. Smith
  2. Graduate School of Genome Science and Technology, University of Tennessee, Knoxville, Tennessee 37996, USA

    • Xiaohu Hu
  3. Institute of Natural Sciences & Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

    • Liang Hong
  4. Wiesbaden Business School, Rhein-Main University of Applied Sciences, Bleichstr. 44, D-65183 Wiesbaden, Germany

    • Thomas Neusius
  5. Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee 37996, USA

    • Jeremy C. Smith


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X.H. performed and conceived the research, analysed the results and wrote the manuscript. L.H. analysed the results and wrote the manuscript. M.D.S. performed the research. T.N. analysed the results and wrote the manuscript. X.C. analysed the results and wrote the manuscript. J.C.S. conceived the research, analysed the results and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Jeremy C. Smith.

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