The effects of static electric field on the dynamics of lysozyme and its hydration water have been investigated by means of incoherent quasi-elastic neutron scattering (QENS). Measurements were performed on lysozyme samples, hydrated respectively with heavy water (D2O) to capture the protein dynamics, and with light water (H2O), to probe the dynamics of the hydration shell, in the temperature range from 210 $<$ T $<$ 260 K. The hydration fraction in both cases was about $sim$ 0.38 gram of water per gram of dry protein. The field strengths investigated were respectively 0 kV/mm and 2 kV/mm (2 10$^6$ V/m) for the protein hydrated with D2O and 0 kV and 1 kV/mm for the H2O hydrated counterpart. While the overall internal protons dynamics of the protein appears to be unaffected by the application of electric field up to 2 kV/mm, likely due to the stronger intra-molecular interactions, there is also no appreciable quantitative enhancement of the diffusive dynamics of the hydration water, as would be anticipated based on our recent observations in water confined in silica pores under field values of 2.5 kV/mm. This may be due to the difference in surface interactions between water and the two adsorption hosts (silica and protein), or to the existence of a critical threshold field value Ec $sim$ 2-3 kV/mm for increased molecular diffusion, for which electrical breakdown is a limitation for our sample.
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