Temperature dependence of the mean square displacement (MSD) of protein obtained from the incoherent neutron scattering

A variety of models and hypothesis have been proposed to interpreted the temperature dependence of the mean square displacement (MSD) of protein, that is obtained from the neutron scattering measurement, but a consensus seems yet to be achieved. The most controversial point is concerned with the physics behind the abrupt change of gradient of MSD plotted against temperature. The phenomenon is attributed to different physics by different authors, such as glass transition, alpha to bete transition, harmonic to anharmonic transition, coupling of protein and hydrated-water dynamics, and so forth. In this report, we propose a theory to analyse the elastic incoherent neutron scattering (EINS) data of aqueous solutions of protein, based on the generalized Langevin theory combined with the 3D-RISM/RISM equation. The theory gives closed equations for the elastic incoherent structure factor (EISF) and MSD as a function of temperature. Based on the theory, the abrupt change of the gradient of MSD in the temperature dependence is interpreted as an onset of 'solvent-induced elasticity,' or 'free energy elasticity,' with increasing temperature. (author)