Resolution Effects on the Mean Square Displacement as Obtained by the Self-Distribution-Function Procedure

In the present contribution, a procedure for molecular motion characterization based on the evaluation of the Mean Square Displacement (MSD), through the Self-Distribution Function (SDF), is presented. It is shown how MSD, which represents an important observable for the characterization of dynamical properties, can be decomposed into different partial contributions associated to system dynamical processes within a specific spatial scale. It is also shown how the SDF procedure allows us to evaluate both total MSD and partial MSDs through total and partial SDFs. As a result, total MSD is the weighed sum of partial MSDs in which the weights are obtained by the fitting procedure of measured Elastic Incoherent Neutron Scattering (EINS) intensity. We apply SDF procedure to data collected,by IN13, IN10 and IN4 spectrometers (Institute Laue Langevin), on aqueous mixtures of two homologous disaccharides (sucrose and trehalose) and on dry and hydrated (H2O and D2O) lysozyme with and without disaccharides. 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. This result can justify the higher bioprotectant effectiveness of trehalose. Furthermore, it emerges that partial MSDs of sucrose and trehalose are equivalent in the low Q domain (0÷1.7) Å−1 whereas they are different in the high Q domain (1.7÷4) Å−1. This suggests that the higher structure sensitivity of sucrose should be related to the small spatial observation windows. Moreover, the role of the instrumental resolution in EINS is considered. The nature of the dynamical transition is highlighted and it is shown that it occurs when the system relaxation time becomes shorter than the instrumental energy time. Finally, the bioprotectants effect on protein dynamics and the amplitude of vibrations in lysozyme are presented.