Dynamics of a protein and its surrounding environment: A quasielastic neutron scattering study of myoglobin in water and glycerol mixtures

In this quasielastic neutron scattering (QENS) study we have investigated the relation between protein and solvent dynamics. Myoglobin in different water:glycerol mixtures has been studied in the temperature range of 260-320 K. In order to distinguish between solvent and protein dynamics we have measured protonated as well as partly deuterated samples. As commonly observed for bulk as well as for confined water, the dynamics of the surrounding solvent is well described by a jump diffusion model. The intermediate scattering function I(Q,t) from the protein (partly deuterated samples) was analyzed by fitting a single Kohlrausch-Williams-Watts (KWW) stretched exponential function to the data. However, due to the limited experimental time window, two different curve fitting approaches were used. The first one was performed with the assumption that I(Q,t) decays to zero at long times, i.e., it was assumed that all protein relaxations that are observed on the experimental time scale, as well as would be observed on longer time scales, can be described by a single KWW function. In the second approach we instead assumed that both the protein relaxation time tau(p) and the stretching parameter beta(KWW) were Q-independent, i.e., we assumed that the protein dynamics is dominated by more local motions. Advantages and disadvantages of both approaches are discussed. The first approach appears to work best at higher Q-values, indicating a power law relation of the Q-dependent protein dynamics for all samples and temperatures, whereas the second approach seems to work at lower Q-values, where the expected confined diffusion of hydrogen atoms in the protein gives the assumed Q-independent relaxation time. Independent of the chosen approach we find a significant correlation between the average relaxation time of the protein and the diffusion constant (or in this case the related relaxation time) of the solvent. However, the correlation is not perfect since the average relaxation time of the protein is more strongly dependent on the total amount of solvent than the diffusion constant of the solvent itself. Thus, the average relaxation time of the protein decreases not only with increasing solvent mobility, but also with increasing solvent content.