Thermal motion in protein crystals estimated using laser-generated ultrasound and Young's modulus measurements

The measurement of the longitudinal speed of sound in crystals of ribonuclease-A and in human haemoglobin using laser-generated ultrasound is reported. Average values of 1784 (72) m s^-1 and 1828 m s^-1 were obtained. As a control the speed of sound transmitted through a compacted disc of lysozyme powder was measured as 2004(23)ms^-1. The measured longitudinal acoustic velocities and the transverse velocity, estimated from a knowledge of Young's modulus, were used to estimate the acoustic contribution to the mean-square displacements of protein molecules as determined by X-ray crystallography. It was found that thermally induced acoustic vibrations make a significant contribution to the total atomic disorder, estimated to be in the range 0.04-0.11 Ų for the proteins studied. Such single-crystal estimates are required for calculation of the acoustic component of the diffuse scattering in protein crystal X-ray diffraction.