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

Abstract

The average mean square displacement, r 2 , of H atoms in a protein is frequently determined using incoherent neutron scattering experiments. r 2 is obtained from the observed elastic incoherent dynamic structure factor, Si(Q, ω = 0), assuming the form Si(Q, ω = 0) = exp(− Q 2 r 2 /3). This is often referred to as the Gaussian approximation (GA) to Si(Q, ω = 0). r 2 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 r 2 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 r 2 . 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 r 2 . The observed Q dependence of r 2 can be used to provide information on the dynamical heterogeneity in proteins.

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The fluctuating ribosome: thermal molecular dynamics characterized by neutron scattering

“…where ΔE is instrumental energy resolution, related to the time window through Heisenberg’s uncertainty principle, and < u 2 > is the average time-dependent atomic mean square displacement (MSD)5455 in the limit defined by ΔE , the energy resolution of the spectrometer. (Note that with respect to the radius of gyration of the motion about its center of mass ( R g ), < u 2 > = 2 R g 2 ).…”

Critical structural fluctuations of proteins upon thermal unfolding challenge the Lindemann criterion

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