A super-Arrhenius-to-Arrhenius dynamic crossover phenomenon has been observed in the translational (x-relaxation time and in the inverse of the self-diffusion constant both experimentally and by simulations for lysozyme hydration water in the temperature range of T-L = 223 +/- 2 K. MD simulations are based on a realistic hydrated powder model, which uses the TIP4P-Ew rigid molecular model for the hydration water. The convergence of neutron scattering, nuclear magnetic resonance and molecular dynamics simulations supports the interpretation that this crossover is a result of the gradual evolution of the structure of hydration water from a high-density liquid to a low-density liquid form upon crossing of the Widom line above the possible liquid-liquid critical point of water.