Average solution structure 262 Subject

Two copies of the atoms comprising each pseudo-atom were obtained, displaced by 4 A in the z-direction and individually immersed in a pre-equilibrated box of T1P3 water. The charges were maintained, and hence the only set of atoms with a net charge were the five atoms comprising the phosphate (PHO/PHP) bead, with a net —1 charge per set of atoms. If necessary, the system was neutralized with Na+ ions and subjected to the same simulation protocol as before. First 100 ps of NPT dynamics was performed, with snapshots of the last 20 ps (every 2 ps) saved. The ten snapshots were then superimposed on each other and the average MD solution structure obtained as previously discussed. 

Careful analysis of electron-density maps usually reveals many ordered water molecules on the surface of crystalline proteins (Plate 4). Additional disordered water is presumed to occupy regions of low density between the ordered particles. The quantity of water varies among proteins and even among different crystal forms of the same protein. The number of detectable ordered water molecules averages about one per amino-acid residue in the protein. Both the ordered and disordered water are essential to crystal integrity, and drying destroys the crystal structure. For this reason, protein crystals are subjected to X-ray analysis in a very humid atmosphere or in a solution that will not dissolve them, such as the mother liquor. 

The analysis of the resonant solution scattering data demands a different representation of the Debye Equation (30). If the macromolecular structure would have a spherical appearance, then the formalism of isomorphous replacement in single crystal diffraction outlined in the preceding section would apply. This is not surprising as the rotation of a spherical structure could not be noticed anyhow. In more complicated, asymmetric macromolecular structures it is the spherical average of the structure which can be subjected to the phase analysis described above. As this state-... 

Brenner (1980) has explored the subject of solute dispersion in spatially periodic porous media in considerable detail. Brenner s analysis makes use of the method of moments developed by Aris (1956) and later extended by Horn (1971). Carbonell and Whitaker (1983) and Koch et al. (1989) have addressed the same problem using the method of volume averaging, whereby mesoscopic transport coefficients are derived by averaging the basic conservation equations over a single unit cell. Numerical simulations of solute dispersion, based on lattice scale calculations of the Navier-Stokes velocity fields in spatially periodic structures, have also been performed (Eidsath et al., 1983 Edwards et al., 1991 Salles et al., 1993). These simulations are discussed in detail in the Emerging Areas section. 

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