Determination of Dynamical Heterogeneity from Dynamic Neutron Scattering of Proteins

Motional displacements of hydrogen (H) in proteins can be measured using incoherent neutron-scattering methods. These displacements can also be calculated numerically using data from molecular dynamics simulations. An enormous amount of data on the average mean-square motional displacement (MSD) of H as a function of protein temperature, hydration, and other conditions has been collected. H resides in a wide spectrum of sites in a protein. Some H are tightly bound to molecular chains, and the H motion is dictated by that of the chain. Other H are quite independent. As a result, there is a distribution of motions and MSDs of H within a protein that is denoted dynamical heterogeneity. The goal of this paper is to incorporate a distribution of MSDs into models of the H incoherent intermediate scattering function, I(Q,t), that is calculated and observed. The aim is to contribute information on the distribution as well as on the average MSD from comparison of the models with simulations and experiment. For example, we find that simulations of I(Q,t) in lysozyme are well reproduced if the distribution of MSDs is bimodal with two broad peaks rather than a single broad peak.