Motional displacements in proteins incorporating dynamical diversity

The average mean square displacement (MSD), $\langle r^2 \rangle$, of hydrogen \textit{H} in proteins is measured using incoherent neutron scattering methods. The observed MSD shows a marked increase in magnitude at a temperature $T_D$ $\simeq$ 240 K. This is widely interpreted as a dynamical transition to large MSDs which make function possible in proteins. However, when the data is interpreted in terms of a single averaged MSD, the extracted $\langle r^2 \rangle$ depends on the neutron momentum transfer, $\hbar Q$, used in the measurement. We have shown recently that this apparent dependence on $Q$ arises because the dynamical diversity of the \textit{H} in the protein is neglected[2]. We present models of the dynamical diversity of \textit{H} in Lysosyme that when used in the analysis of simulated neutron data lead to consistent, $Q$ independent values for the average MSD and for the diversity model.\\ 2. D. Vural and L. Hong, J. C. Smith and H. R. Glyde. {\it Phys. Rev. E} {\bf 91}, 052705 (2015).