Quasilongitudinal sound velocities and the second-order elastic moduli of tetragonal hen egg-white lysozyme crystals were determined as a function of relative humidity (RH) by Brillouin scattering. In hydrated crystals the measured sound velocities in the  plane vary between 2.12 ± 0.03 km/s along the  direction and 2.31 ± 0.08 km/s along the  direction. Dehydration from 98% to 67% RH increases the sound velocities and decreases the velocity anisotropy in (110) from 8.2% to 2.0%. A discontinuity in velocity and an inversion of the anisotropy is observed with increasing dehydration providing support for the existence of a structural transition below 88% RH. Brillouin linewidths can be described by a mechanical model in which the phonon is coupled to a relaxation mode of hydration water with a single relaxation time of 55 ± 5 ps. At equilibrium hydration (98% RH) the longitudinal moduli C11 + C12 + 2C66 = 12.81 ± 0.08 GPa, C11 = 5.49 ± 0.03 GPa, and C 33 = 5.48 ± 0.05 GPa were directly determined. Inversion of the measured sound velocities in the  plane constrains the combination C44 + 1/2C13 to 2.99 ± 0.05 GPa. Further constraints on the elastic tensor are obtained by combining the Brillouin quasilongitudinal results with axial compressibilities determined from high-pressure x-ray diffraction. We constrain the adiabatic bulk modulus to the range 2.7-5.3 GPa.
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