Structure statistical analysis

With experimental quantification of mesoscale structures, statistical analysis based on nonequilibrium distribution may require novel mathematical skills to unravel the complex dependence of stress-strain relation on the mass exchange between phases. The structure-dependent energy analysis may help elucidate the dependence between energy dissipation and structural parameters, and how to relate such structural-dependent analysis and the nonlinear nonequilibrium thermodynamics remains a challenge, especially for the scale-dependent granular flow or fluidization systems. 

CODESSA (we tested Version 2.6) stands for comprehensive descriptors for structural and statistical analysis. It is a conventional QSAR/QSPR program. 

To gain the most predictive utility as well as conceptual understanding from the sequence and structure data available, careful statistical analysis will be required. The statistical methods needed must be robust to the variation in amounts and quality of data in different protein families and for structural features. They must be updatable as new data become available. And they should help us generate as much understanding of the determinants of protein sequence, structure, dynamics, and functional relationships as possible. 

Mixmre models have come up frequently in Bayesian statistical analysis in molecular and structural biology [16,28] as described below, so a description is useful here. Mixture models can be used when simple forms such as the exponential or Dirichlet function alone do not describe the data well. This is usually the case for a multimodal data distribution (as might be evident from a histogram of the data), when clearly a single Gaussian function will not suffice. A mixture is a sum of simple forms for the likelihood ... 

Analysis and prediction of side-chain conformation have long been predicated on statistical analysis of data from protein structures. Early rotamer libraries [91-93] ignored backbone conformation and instead gave the proportions of side-chain rotamers for each of the 18 amino acids with side-chain dihedral degrees of freedom. In recent years, it has become possible to take account of the effect of the backbone conformation on the distribution of side-chain rotamers [28,94-96]. McGregor et al. [94] and Schrauber et al. [97] produced rotamer libraries based on secondary structure. Dunbrack and Karplus [95] instead examined the variation in rotamer distributions as a function of the backbone dihedrals ( ) and V /, later providing conformational analysis to justify this choice [96]. Dunbrack and Cohen [28] extended the analysis of protein side-chain conformation by using Bayesian statistics to derive the full backbone-dependent rotamer libraries at all... 

GW Carter Ir. Entropy, likelihood and phase determination. Structure 3 147-150, 1995. RL Dunbrack Ir, EE Cohen. Bayesian statistical analysis of protein sidecham rotamer preferences. Protein Sci 6 1661-1681, 1997. 

The parameters Ci, t2 were postulated to be dependent only upon the substrate, and d, d2, upon the solvent. A large body of kinetic data, embodying many structural types and leaving groups, was subjected to a statistical analysis. In order to achieve a unique solution, these arbitrary conditions were imposed cj = 3.0 C2 for MeBr Cl = C2 = 1.0 for f-BuCl 3.0 Ci = C2 for PhsCF. Some remarkably successful correlations [calculated vs. experimental log (fc/fco)l were achieved, but the approach appeared to lack physical significance and was not much used. Many years later Peterson et al. - showed a correspondence between Eqs. (8-69) and (8-74) in particular, the very simple result di + d, = T was found. 

Scientific information—the contextual interpretation of experimental data—is published as free text. The same applies to the annotation of experimental results, genes, proteins, and compounds and the description of medical conditions. This clearly indicates that scientific information is not structured, which creates a major challenge for its reuse, management, and statistical analysis. This fact has largely been recognized, and much research... 

Green, B. F. (1952). Latent structure class analysis and its relation to factor analysis. Journal of American Statistical Association, 47, 71-76. 

Meyer, J. E. W. and Schulz, G. E. (1997). Energy profile of maltooligosaccharide permeation through maltoporin as derived from the structure and from statistical analysis of saccharide-protein interactions, Protein Set, 6, 1084—1091. 

Our statistical analysis reveals a large improvement from cc-pCV(DT)Z to cc-pCV(TQ)Z see Fig. 1.4. In fact, the cc-pCV(TQ)Z calculations are clearly more accurate than their much more expensive cc-pcV6Z counterparts and nearly as accurate as the cc-pcV(56)Z extrapolations.The cc-pCV(TQ)Z extrapolations yield mean and maximum absolute errors of 1.7 and 4.0 kJ/mol, respectively, compared with those of 0.8 and 2.3 kJ/mol at the cc-pcV(56)Z level. Chemical accuracy is thus obtained at the cc-pCV(TQ)Z level, greatly expanding the range of molecules for which ab initio electronic-structure calculations will afford thermochemical data of chemical accuracy. 

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