Folds density

B( ) is variously called the reciprocal form factor, the p-space form factor, and the internally folded density. B(s) is the basis of a method for reconstructing momentum densities from experimental data [145,146], and it is useful for the r-space analysis of Compton profiles [147-151]. The B(s) function probably first arose in an examination of the connection between form factors and the electron momentum density [129]. The B f) function has been rediscovered by Howard et al. [152]. 

Since the momentum density is related to the reciprocal form factor or internally folded density by a Fourier transform, Eq. (5.29), there are sum rules that connect moments of momentum with the spherical average of B f) defined by... 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

Polypropylene molecules repeatedly fold upon themselves to form lamellae, the sizes of which ate a function of the crystallisa tion conditions. Higher degrees of order are obtained upon formation of crystalline aggregates, or spheruHtes. The presence of a central crystallisation nucleus from which the lamellae radiate is clearly evident in these stmctures. Observations using cross-polarized light illustrates the characteristic Maltese cross model (Fig. 2b). The optical and mechanical properties ate a function of the size and number of spheruHtes and can be modified by nucleating agents. Crystallinity can also be inferred from thermal analysis (28) and density measurements (29). 

Fig. 22.6. A schematic drawing of a largely crystalline polymer like high-density polyethylene. At the top the polymer has melted and the chain-folded segments hove unwound.

With mostly unambiguous data, this protocol has been successfully used for proteins with up to 160 residues [62]. Although virtually all structures converge to the correct fold for small proteins, we observe that approximately one-third of the structures are misfolded for larger proteins, or for low data density, or many ambiguities (see, e.g.. Ref. 63). We have also used this protocol for most structure calculations with the automated NOE assignment method ARIA discussed in the next section. 

Figure 8.3 The DNA-binding protein Cro from bacteriophage lambda contains 66 amino acid residues that fold into three a helices and three P strands, (a) A plot of the Ca positions of the first 62 residues of the polypeptide chain. The four C-terminal residues are not visible in the electron density map. (b) A schematic diagram of the subunit structure. a helices 2 and 3 that form the helix-turn-helix motif ate colored blue and red, respectively. The view is different from that in (a), [(a) Adapted from W.F. Anderson et al., Nature 290 754-758, 1981. (b) Adapted from D. Ohlendorf et al., /. Mol. Biol. 169 757-769, 1983.]...

The phosducin polypeptide chmn, of some 240 amino acids, is folded into two domains (Figure 13.16). The N-terminal domain is mostly a-helical and appears to be quite flexible since only a weak electron density is obtained in the structure determination. The actual path of the polypeptide chain from the end of helix to the beginning of helix Ba is tentative due to slight disorder. This region is close to serine 73 at the beginning of Ba, which also becomes disordered on phosphorylation. 

There are at least four kinds of information available from an Auger spectrum. The simplest and by far most frequently used is qualitative information, indicating which elements are present within the sampling volume of the measurement. Next there is quantitative information, which requires a little more care during acquisition to make it extractable, and a little more effort to extract it, but which tells how much of each of the elements is present. Third, there is chemical information which shows the chemical state in which these elements are present. Last, but by far the least used, there is information on the electronic structure of the material, such as the valance-band density of states that is folded into the line shape of transitions involving valance-band electrons. There are considerations to keep in mind in extracting each of these kinds of information. 

Although the elastomer phase is essentially in particulate form, the tensile strength of the blend can be increased five-fold by increasing the cross-link density from zero to that conventionally used in vulcanisation processes, whilst tension set may be reduced by over two-thirds. Since the thermoplastic polyolefin phase may be completely extracted by boiling decalin or xylene, there is apparently no covalent chemical bonding of elastomer and thermoplastic phases. 

The relationship of anode current density with electrode potential for mild steel in dilute aqueous soil electrolytes has been studied by Hoar and Farrer. The study shows that in conditions simulating the corrosion of mild steel buried in soil the logarithm of the anode current density is related approximately rectilinearly to anode potential, and the increase of potential for a ten-fold increase of current density in the range 10 to 10 A/cm is between 40 and 65 mV in most conditions. Thus a positive potential change of 20 mV produces a two- to three-fold increase in corrosion rate in the various electrolyte and soil solutions used for the experiments. 

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