Experiments in bulk water confirm the existence of two local arrangements of water molecules with different densities, but, because of inevitable freezing at low temperature $T$, can not ascertain whether the two arrangements separate in two phases. To avoid the freezing, new experiments measure the dynamics of water at low $T$ on the surface of proteins, finding a crossover from a non-Arrhenius regime at high $T$ to a regime that is approximately Arrhenius at low $T$. Motivated by these experiments, Kumar et al. [Phys. Rev. Lett. 100, 105701 (2008)] investigated, by Monte Carlo simulations and mean field calculations, the relation of the dynamic crossover with the coexistence of two liquid phases in a cell model for water and predict that: (i) the dynamic crossover is isochronic, i.e. the value of the crossover time $tau_{rm L}$ is approximately independent of pressure $P$; (ii) the Arrhenius activation energy $E_{rm A}(P)$ of the low-$T$ regime decreases upon increasing $P$; (iii) the temperature $T^*(P)$ at which $tau$ reaches a fixed macroscopic time $tau^*geq tau_{rm L}$ decreases upon increasing $P$; in particular, this is true also for the crossover temperature $T_{rm L}(P)$ at which $tau=tau_{rm L}$. Here, we compare these predictions with recent quasi elastic neutron scattering (QENS) experiments performed by X.-Q. Chu {it et al.} on hydrated proteins at different values of $P$. We find that the experiments are consistent with these three predictions.
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