Sound Velocity and Elasticity of Tetragonal Lysozyme Crystals by Brillouin Spectroscopy

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 [110] plane vary between 2.12 ± 0.03 km/s along the [001] direction and 2.31 ± 0.08 km/s along the [110] 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 [110] 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.