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 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 of heparan sulphate
(HS-0.4), Ribonuclease A and Staphysloccal Nuclase (SNase) from data in the
literature