Motional displacements in proteins: The origin of wave-vector-dependent values

Derya Vural, Liang Hong, Jeremy C. Smith, and Henry R. Glyde
Phys. Rev. E 91, 052705 – Published 14 May 2015

Abstract

The average mean-square displacement, r2, of H atoms in a protein is frequently determined using incoherent neutron-scattering experiments. r2 is obtained from the observed elastic incoherent dynamic structure factor, Si(Q,ω=0), assuming the form Si(Q,ω=0) =exp(Q2r2/3). This is often referred to as the Gaussian approximation (GA) to Si(Q,ω=0). r2 obtained in this way depends on the value of the wave vector, Q considered. Equivalently, the observed Si(Q,ω=0) deviates from the GA. We investigate the origin of the Q dependence of r2 by evaluating the scattering functions in different approximations using molecular dynamics (MD) simulation of the protein lysozyme. We find that keeping only the Gaussian term in a cumulant expansion of S(Q,ω) is an accurate approximation and is not the origin of the Q dependence of r2. This is demonstrated by showing that the term beyond the Gaussian is negligible and that the GA is valid for an individual atom in the protein. Rather, the Q dependence (deviation from the GA) arises from the dynamical heterogeneity of the H in the protein. Specifically it arises from representing, in the analysis of data, this diverse dynamics by a single average scattering center that has a single, average r2. The observed Q dependence of r2 can be used to provide information on the dynamical heterogeneity in proteins.

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  • Received 3 February 2015

DOI:https://doi.org/10.1103/PhysRevE.91.052705

©2015 American Physical Society

Authors & Affiliations

Derya Vural1, Liang Hong2, Jeremy C. Smith2, and Henry R. Glyde1

  • 1Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716-2570, USA
  • 2UT/ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, P. O. Box 2008, Tennessee 37831, USA

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Vol. 91, Iss. 5 — May 2015

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