Two structural relaxations in protein hydration water and their dynamic crossovers

We study the translational single particle dynamics of hydration water of lysozyme upon cooling by means of molecular dynamics simulations. We find that water close to the protein exhibits two distinct relaxations. By characterizing their behavior upon cooling, we are able to assign the first relaxation to the structural $alpha$-relaxation also present in bulk water and in other glass-forming liquids. The second, slower, relaxation can be ascribed to a dynamic coupling of hydration water motions to the fluctuations of the protein structure. Both relaxation times exhibit crossovers in the behavior upon cooling. For the $alpha$-process, we find upon cooling a crossover from a fragile behavior to a strong behavior at a temperature which is about five degrees higher than that of bulk water. The long-relaxation time appears strictly connected to the protein motion as it shows upon cooling a temperature crossover from a strong behavior with a lower activation energy to a strong behavior with a higher activation energy. The crossover temperature coincides with the temperature of the protein dynamical transition. These findings can help experimentalists to disentangle the different information coming from total correlators and to better characterize hydration water relaxations in different biomolecules.