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, <Δr(2)> of the nonexchanged hydrogen atoms in the protein and its variance, σ(2). The molecular dynamics simulation results are in broad agreement with the experimentally derived <Δr(2)> and σ(2) derived from EINS on instruments at two different energy resolutions, corresponding to dynamics on the ∼100 ps and ∼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.