Shape Theory via QR decomposition

This work sets the non isotropic noncentral elliptical shape distributions via QR decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference procedure can be studied under exact densities instead under the published approximations and asymptotic densities under isotropic models. An application in Biology is studied under the classical gaussian approach and a two non gaussian models.Comment: 13 page

Shape Theory Via SV Decomposition II

The non isotropic and non central elliptical shape distributions via the Le and Kendall SVD decomposition approach are derived in this paper in the context of invariant polynomials and zonal polynomials. The so termed cone and disk densities here obtained generalise some results of the literature. Finally, some particular densities are applied in a classical data of Biology, and the inference is performed after choosing the best model by using a modified BIC criterion.Comment: 16 page

STRUCTURAL ORIGINS OF PRESSURE EFFECTS IN PROTEINS

The molecular mechanisms of chemical and heat denaturation of proteins are relatively well established; those of pressure unfolding are not. Volume is the conjugate variable of pressure; it is the fundamental thermodynamic variable that governs the pressure sensitivity of proteins. Cavities that are present in the native state and absent in the unfolded state are thought to contribute significantly to the change in volume upon unfolding (∆V). Staphylococcal nuclease was used to examine the role of cavities systematically. The wild-type protein has a small cavity in its hydrophobic core, comparable in volume to a water molecule. Artificial cavities were generated by substitution of internal hydrophobic residues to Ala. Substitutions of small residues with large ones were used to eliminate the natural cavity. Substitutions to polar residues were used to affect the hydration state of cavities. For 27 variants studied, (a) crystal structures, (b) thermodynamic stabilities using chemical denaturation, and (c) ∆V of unfolding measured by pressure denaturation monitored with Trp-fluorescence and NMR spectroscopy were obtained. In general, the cavities did not affect the structure. The cavities were large enough to hold several waters, but these were only detected in the cavities lined with polar groups. The measured ∆V of variants was always larger than for the wild-type. A near-linear correlation between the ∆V measured experimentally and the one calculated from structures illustrate the importance of cavities in pressure sensitivity. A correlation between measured ∆V and thermodynamic stability (∆G°) suggests that 1 kcal/mol is lost per 11 mL/mol of increased void volume. This study demonstrates that cavities contribute significantly towards the pressure sensitivity of proteins and can modulate the hydration and structural fluctuations of proteins

Editorial

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