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Intrinsic Mean Square Displacements in Proteins

The thermal mean square displacement (MSD) of hydrogen in proteins and its associated hydration water is measured by neutron scattering experiments and used an indicator of protein function. The observed MSD as currently determined depends on the energy resolution width of the neutron scattering instrument employed. We propose a method for obtaining the intrinsic MSD of H in the proteins, one that is independent of the instrument resolution width. The intrinsic MSD is defined as the infinite time value of <r^2> that appears in the Debye-Waller factor. The method consists of fitting a model to the resolution broadened elastic incoherent structure factor or to the resolution dependent MSD. The model contains the intrinsic MSD, the instrument resolution width and a rate constant characterizing the motions of H in the protein. The method is illustrated by obtaining the intrinsic MSD <r^2> of heparan sulphate (HS-0.4), Ribonuclease A and Staphysloccal Nuclase (SNase) from data in the literature.