Slow dynamics of supercooled hydration water in contact with lysozyme: examining the cage effect at different length scales

We study by computer simulation the dynamics of hydration water in solution with lysozyme upon approaching the glassy state of water. We calculate the self-density correlation function at different wavelengths to test the Mode Coupling Theory (MCT) of glassy dynamics at different length scales. The results show a strict and clear relation of the behaviour of the structural relaxation with the cage effect. We find a good agreement with the predictions of the MCT in the short and medium scale range, while at increasing length scales the interaction of water molecules with the protein's substrate induces deviations from the MCT behaviour, as found in previous studies. Besides at low temperatures the slow dynamics deviates from MCT due to hopping processes, similar to the bulk, as witnessed by a crossover from a fragile behaviour to a strong behaviour. We show that this deviation is evident at all length scales. Interestingly, we find that in the fragile region the confining cage decreases in radius with temperature while in the strong region it appears stable.