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Birch's law, prescribing a linear dependence of elastic wave speed on the density in a given material, is an important tool in understanding the composition and thermodynamic conditions of the planetary interior. However, data from direct measurements of elastic wave speed usually have too much of scatter to permit a precise test of this law. Here, we use data from experimental measurements as well as ab initio density-functional-theory based calculations existing in the literature, supplemented by our own data of the latter type for elemental solids, for such a test. Using many such datasets, we show that, although Birch's law is satisfied fairly well in all the cases, the product of elastic wave speed and one-third power of density satisfies linear dependence on density consistently and more accurately than the speed alone. This opens the possibility of more reliable extrapolation of low density velocity data to the higher densities—the primary application of Birch's law.

Pressure-induced perturbation of protein structure leading to its folding-unfolding is an important yet not fully understood phenomenon. The key point here is the role of water and its coupling with protein conformations as a function of pressure. In the current work, using extensive molecular dynamics simulation at 298K we systematically examine the coupling between protein conformations and water structure for pressures 1 bar, 5, 10, 15, and 20 kbar, starting from (partially) unfolded structures of the protein Bovine Pancreatic Trypsin Inhibitor (BPTI). We also calculate localized thermodynamics at those pressures as a function of protein-water distance. Our findings show that both protein-specific and generic effects of pressure are operating. In particular, we found that (1) The amount of in- crease in water density near the protein depends on the protein structural heterogeneity, (2) the intra-protein hydrogen bond decreases with pressure while the water-water hydrogen bond per water in the first solvation shell (FSS) increases. Protein-water hydrogen bonds were also found to increase with pressure, (3) with pressure hydrogen bonds in the FSS get twisted, (4) Water's tetrahedrality in the FSS decreases with pressure but it is dependent on the local environment. Thermodynamically, at higher pressure, the structural perturbation of BPTI is mainly due to pressure-volume work, while the entropy decreases with the increase of pressure due to higher translational and rotational rigidity of waters in the FSS. The local and subtle effects of pressure, found in this work, are likely to be typical of pressure-induced protein structure perturbation.

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