Derivation of Mean-Square Displacements for Protein Dynamics from Elastic Incoherent Neutron Scattering

The derivation of mean-square displacements from elastic incoherent neutron scattering (EINS) of proteins is examined, with the aid of experiments on camphor-bound cytochrome P450cam and complementary molecular dynamics simulations. It is shown that a q(4) correction to the elastic incoherent structure factor (where q is the scattering vector) can be simply used to reliably estimate from the experiment both the average mean-square atomic displacement, of the nonexchanged hydrogen atoms in the protein and its variance, sigma(2). The molecular dynamics simulation results are in broad agreement with the experimentally derived and sigma(2) derived from EINS on instruments at two different energy resolutions, corresponding to dynamics on the similar to 100 ps and similar to 1 ns time scales. Significant dynamical heterogeneity is found to arise from methyl-group rotations. The easy-to-apply q(4) correction extends the information extracted from elastic incoherent neutron scattering experiments and should be of wide applicability.