Liquid Between Macromolecules in Protein Crystals: Static Versus Dynamics

Protein crystals are so fragile that they often can not be handled by tweezers. Indeed, measurements of the Young modulus, E, of lysozyme crystals resulted in E approx. equals 0.1 - 1 GPa, the lower figures, 0.1 - 0.5 GPa, being obtained from triple point bending of as-grown and not cross-linked crystals sitting in solution. The bending strength was found to be approx.10(exp -2) E. On the other hand, ultrasound speed and Mandelstam-Raman-Brilloin light scattering experiments led to much higher figures, E approx. equals 2.7 GPa. The lower figures for E were found from static or low frequency crystal deformations measurements, while the higher moduli are based on high frequency lattice vibrations, 10(exp 7) - 10(exp 10) 1/s. The physical reason for the about an order of magnitude discrepancy is in different behavior of water filling space between protein molecules. At slow lattice deformation, the not-bound intermolecular water has enough time to flow from the compressed to expanded regions of the deformed crystal. At high deformation frequencies in the ultra- and hypersound waves, the water is confined in the intermolecular space and, on that scale, behaves like a solid, thus contributing to the elastic crystal moduli. In this case, the reciprocal crystal modulus is expected to be an average of the water protein and water compressibilities (reciprocal compressibilities): the bulk modulus for lysozyme is 26 GPa, for water it is 7 GPa. Anisotropy of the crystal moduli comes from intermolecular contacts within the lattice while the high frequency hardness comes from the bulk of protein molecules and water bulk moduli. These conclusions are based on the analysis of liquid flow in porous medium to be presented.