Motion characterization by self-distribution-function procedure

In the present paper a procedure for the biomolecular motion characterization based on the evaluation of the Mean Square Displacement (MSD), through the Self Distribution Function (SDF), is presented. In particular it will be shown how the MSD, which represents a good observable for the characterization of the dynamical properties in disordered systems, can be decomposed into partial contributions associated to the system dynamical processes within a specific spatial scale. It will be shown how the SDF procedure allows to evaluate both the total MSD and the partial MSDs through the total SFD and the partial SDFs. As a result, the total MSD is the weighed sum of the partial MSD contributions in which the weights are obtained by the fitting procedure of measured EINS intensity data. We apply the SDF procedure at EINS data collected, by the IN13 backscattering spectrometer at the Institute Laue-Langevin, Grenoble, on aqueous mixtures of two homologous disaccharides (sucrose and trehalose) and on dry myoglobin in trehalose environment. It emerges that the hydrogen bond imposed network of the water-trehalose mixture appears to be stronger with respect to that of the water-sucrose mixture and this result can justify the highest bioprotectant effectiveness of trehalose in comparison with sucrose. Furthermore it emerges that, the partial MSD behaviours of sucrose and trehalose are equivalent in the low Q domain (0-1.7) A(-1) whereas they are different in the high Q domain (1.7-4) A(-)(1). This circumstance suggests that the higher structure sensitivity of sucrose in respect to trehalose should be related to the small spatial observation windows.