Similarity distance distribution

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. 

Freed et al. [42,43], among others [44,45] have performed RG perturbation calculations of conformational properties of star chains. The results are mainly valid for low functionality stars. A general conclusion of these calculations is that the EV dependence of the mean size can be expressed as the contribution of two terms. One of them contains much of the chain length dependence but does not depend on the polymer architecture. The other term changes with different architectures but varies weakly with EV. Kosmas et al. [5] have also performed similar perturbation calculations for combs with branching points of different functionalities (that they denoted as brushes). Ohno and Binder [46] also employed RG calculations to evaluate the form of the bead density and center-to-end distance distribution of stars in the bulk and adsorbed in a surface. These calculations are consistent with their scaling theory [27]. 

Figure 1 shows Fourier transforms of EXAFS spectra of a few samples prepared. The radial distribution functions of these samples are different from that of nickel oxide or cobalt oxide [7]. All the Fourier transforms showed two peaks at similar distances (phase uncorrected) the peak between 1 and 2 A is ascribed to the M-0 bond (M divalent cation) and the peak between 2 and 3 A is ascribed to the M-O-M and M-O-Si bonds. The similar radial distribution functions in Figure 1 indicate that the local structures of X-ray absorbing atoms (Ni, Co, and Zn) are similar. No other bonds derived from metal oxides (nickel, cobalt and zinc oxides) were observed in the EXAFS Fourier transforms of the samples calcined at 873 K, which suggests that the divalent cations are incorporated in the octahedral lattice. 

This appears not to be the case. On average, the crystal field forces have a distortion effect. This was realized from some of the earliest analyses of hydrogen-bond lengths [52]. It arises from two factors one is the influence of many-atom effects, such as cooperativity. The second is the fact that all other atom-pair interactions are striving toward the equilibrium minimum. Since hydrogen-bonded functional groups tend to protrude from molecules, this results in an overall distortion. The most obvious example of this difference is that between the values for the H 0 distances of 1.7 to 1.8 A observed in the ices and 2.0 A for the water dimer (see Thble 4.3). Similarly, the distribution for two-center OwH O bonds in the hydrates of small molecules, discussed in Part IV, has a mean value of 1.80 A, in agreement with the ices. 

The peak positions are important information for an RDF descriptor. Two RDF descriptors that exhibit the same peak positions must have the same distance distribution in the molecule and, thus, a similar basic structure. The differences in the RDF descriptor can then be attributed to the atomic properties. When atomic properties are used that are independent of the chemical neighborhood, this kind of comparison is useful to find initial models, which contain similar skeletons and which can be optimized through alteration of atom types and shifting operations. The tolerance of the method can be chosen optionally. The initial model chosen and the criterion for similarity of the RDF descriptors determine the strategy for optimization. 

Sample purity The matter of sample purity is somewhat more complex than might be thought at first. The effect of an impurity on the diffraction pattern depends on its mole fraction in the sample vapor and on its scattering power relative to that of the material of interest. (The structure-sensitive scattering from a molecule is approximately proportional to n//Z,Z//r//.) However, the effect of an impurity on the desired structure determination need not bear much relation to its effect on the diffraction pattern. If the impurity has a distance distribution sufficiently different from that of the substance of interest, the peaks of the D(r) curve will be resolved accordingly, the parameter values of the two molecules will be essentially uncorrelated and the desired results unaffected. On the other hand, small amounts of an impurity with a distance spectrum similar to the substance of interest can seriously disturb the results. It is perhaps worth noting that the... 

Nilakantan et described a similarity measure based also on the interatomic distances between all sets of three nonhydrogen atoms, using a bit-string representation of molecular shape. It is also possible to consider doublets or quadruplets of nonhydrogen atoms (the doublets give rise to similarity measures which are related to the distance-distribution measure described by Pepperrell and Willett see also Ref. 86). 

Similarly, the total phase-shift function 4>ij k) can be extracted. These functions can then be used to analyze the EXAFS of the compound under investigation. If a standard compound is chosen so that its electronic and chemical properties are close to that of the compound under investigation, then the influence of some usually unknown factors, such as, e.g., Sq or Aj(A), and of some simplifying assumptions made during the derivation of the EXAFS formula, such as, e.g., that of plane waves or that of a Gaussian distance distribution, is minimized. Instead of an absolute value of relative value Ao], describing the difference in devi-... 

Studies on the complex between the elongation factor EF-Tu. GTP (M 46,000 Rq 2.5 nm) with aminoacylated tRNA (nucleotides 24,500) benefit from the closer similarity in size of the two components [379-381]. X-ray titrations show that a 1 1 complex is formed, and the Rq of 3.6 nm and the distance distribution functions suggested that an extended complex is formed [380]. Subsequent neutron studies have, however, proposed that EF-Tu exists in a monomer-dimer equilibrium. The Rq values of 2.0 nm for monomeric EF-Tu, 2.3 nm for aminoacylated tRNA, and 2.6 nm for the ternary complex have led to the alternative proposition of a compact structure for this complex [381]. 

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