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At least 847 records · Page 47Linked to original sources
PubMed2001

Estimating genotypes with independently sampled descent graphs.

A method for estimating genotypic and identity-by-descent probabilities in complex pedigrees is described. The method consists of an algorithm for drawing independent genotype samples which are consistent with the pedigree and observed genotype. The probability distribution function for samples obtained using the algorithm can be evaluated up to a normalizing constant, and combined with the likelihood to produce a weight for each sample. Importance sampling is then used to estimate genotypic and identity-by-descent probabilities. On small but complex pedigrees, the genotypic probability estimates are demonstrated to be empirically unbiased. On large complex pedigrees, while the algorithm for obtaining genotype samples is feasible, importance sampling may require an infeasible number of samples to estimate genotypic probabilities with accuracy.

Algorithms↗
PubMed1982

Influenza surveillance in England and Wales using routine statistics. Development of 'cusum' graphs to compare 12 previous winters and to monitor the 1980/81 winter.

Surveillance of influenza in England and Wales is made by monitoring weekly data. Principal indices are deaths, sickness-benefit claims (SBC), laboratory reports and observations from general practitioners (GPs). The 12 winter 1968/9 to 1979/80 have been studied to see which indices best described size and timing of influenza epidemics. A method of plotting the data (called cusums) is suggested which makes it easier to see the effect of small epidemics. Cusums for GP statistics and respiratory deaths were found to be the most helpful indices for describing both size and timing of the epidemics, followed by total deaths and SBC, which were less specific to influenza, and influenza deaths, which lagged behind other indices. Deaths certified as pneumonia have been increasing over these years, whereas bronchitis deaths have been decreasing and these indices should not be used separately for monitoring. The laboratory reporting system is important. It confirms the presence of influenza virus in the community and indicates prevalent strains. Because it is a voluntary system with no defined population base the reports are not reliable numerically for estimating relative size of epidemics or for developing cusums. Cusum plots were unanimous in describing the winter of 1980/1 as one of little influenza activity.

Data Collection↗
PubMedDate not supplied

Graph-theoretical analysis of tunneling electron transfer in large polycyclic aromatic hydrocarbon networks.

Effect of a single nitrogen atom substitution to a number of large polycyclic aromatic hydrocarbon (PAH) molecules was calculated systematically, and it was found that especially in parallelogram-type PAH abnormal electron transfer (called tunneling electron transfer, TET) was observed. That is, fairly large amount of pi-electron is withdrawn to an electronegative nitrogen atom from almost the farthest end of a conjugated aromatic hydrocarbon molecule, leaving almost no change in the interior of the molecule. This change can be simulated by the Kekulé structure counting for subgraphs of the parent molecule.

Journal Article↗
PubMedDate not supplied

Global molecular identification from graphs. Neutral and ionized main-group diatomic molecules.

Diophantine equations and inequalities are presented for main-group closed-shell diatomic molecules. Specifying various bond types (covalent, dative, ionic, van der Waals) and multiplicities, it becomes possible to identify all possible molecules. While many of the identified species are probably unstable under normal conditions, they are interesting and present a challenge for computational or experimental analysis. Ionized molecules with net charges of -1, 1, and 2 are also identified. The analysis applies to molecules with atoms from periods 2 and 3 but can be generalized by substituting isovalent atoms. When closed-shell neutral diatomics are positioned in the chemical space (with axes enumerating the numbers of valence electrons of the free atoms), it is seen that they lie on a few parallel isoelectronic series.

Journal Article↗
PubMedDate not supplied

Substructure, subgraph, and walk counts as measures of the complexity of graphs and molecules.

In discussions of unsaturated compounds represented by multigraphs it is necessary to distinguish between the notions of substructure and subgraph. Here the difference is explained and exemplified, and a computer program is introduced which for the first time is able to construct and count all substructures and subgraphs for a colored multigraph (a molecular compound which may contain unsaturation and heteroatoms). Construction of all substructures and subgraphs is computationally demanding; therefore, two alternatives are pointed out for the treatment of large sets of compounds: (i) Often it will suffice to consider counts of substructures/subgraphs up to a certain number of edges only, information which is provided by the program much more rapidly. (ii) It is shown that information equivalent to that gained from substructure or subgraph counts is often far more easily available using walk counts. Some problems and their consequences for substructure/subgraph/walk counts are discussed that arise from the models used in organic chemistry for certain compounds such as aromatics and from the necessity to express qualitative features of molecular structures numerically.

Journal Article↗
PubMedDate not supplied

Wiener-Hosoya index--a novel graph theoretical molecular descriptor.

We describe the construction of a novel molecular descriptor, called the Wiener-Hosoya index, in view of its structural relationship to both the Wiener number W and the Hosoya topological index Z. It is shown that this index has a smaller degeneracy than many simple topological indices, including W, Z, and the connectivity index chi. In a way the index can be viewed as a particular generalization of the Wiener number.

Journal Article↗
PubMedDate not supplied

QSPR modeling of lipid-water partition coefficient by optimization of correlation weights of local graph invariants.

The optimization of correlation weights scheme was applied to model lipid-water partition coefficient (log P) of two sets of diverse functional aliphatic and aromatic compounds. In both cases, the optimized descriptors formulated based on the data of training sets generated statistically acceptable relations for the corresponding training sets, test sets, and combined sets. When the relations of log P values with the optimized molecular descriptors formulated based on the data of the training sets were used for calculation of log P values of the corresponding training sets, rpred2 values were found to be satisfactory (above 0.99) in both cases, which is indicative of the predictive potential of the scheme. The results indicate promising potential of the optimization of a correlation weights scheme in modeling studies.

Journal Article↗
PubMedDate not supplied

SURFCOMP: a novel graph-based approach to molecular surface comparison.

Analysis of the distributions of physicochemical properties mapped onto molecular surfaces can highlight important similarities or differences between compound classes, contributing to rational drug design efforts. Here we present an approach that uses maximal common subgraph comparison and harmonic shape image matching to detect locally similar regions between two molecular surfaces augmented with properties such as the electrostatic potential or lipophilicity. The complexity of the problem is reduced by a set of filters that implement various geometric and physicochemical heuristics. The approach was tested on dihydrofolate reductase and thermolysin inhibitors and was shown to recover the correct alignments of the compounds bound in the active sites.

Journal Article↗
PubMed2000

Graph-theoretic techniques for macromolecular docking

We propose a solution to the problem of docking two macromolecules. We represent each of two proteins as a set of potential hydrogen bond donors and acceptors and use a clique-detection algorithm to find maximally complementary sets of donor/acceptor pairs. Preliminary results are presented which demonstrate the feasibility of the method.

Journal Article↗
PubMed2005

HierS: hierarchical scaffold clustering using topological chemical graphs.

An exhaustive ring-based algorithm, HierS, has been developed in order to provide an intuitive approach to compound clustering for analyzing high-throughput screening results. The recursive algorithm rapidly identifies all possible ring-delimited substructures within a set of compounds. Molecules are grouped by shared ring substructures (scaffolds) so that common scaffolds obtain higher membership. Once all of the scaffolds for a set of compounds are identified, the hierarchical structural relationships between the scaffold structures are established. The complex network of hierarchical relationships is then utilized to navigate compounds in a structurally directed fashion. When the scaffold hierarchy is traversed, over-represented structural features can be rapidly identified so that excess compounds that contain them can be removed without significantly impacting the structural diversity landscape of the compound set. Furthermore, the removed compounds can provide the opportunity to follow-up on active compounds that had previously been discarded because of practical limitations on follow-up capacity. A Web-based interface has been developed that incorporates this algorithm in order to allow for an interactive analysis. In addition, biological data are coupled to scaffolds by the inclusion of activity histograms, which indicate how the compounds in each scaffold class performed in previous high-throughput screening campaigns.

Algorithms↗
PubMedDate not supplied

On invariants of a 2-D proteome map derived from neighborhood graphs.

We consider the problem of the construction of invariants for characterization of 2-D maps, such as 2-D proteome maps, 2-D NMR spectral maps, etc., that in addition to facilitating cataloguing such maps, can be used for comparison of maps and numerical evaluation of their degree of similarity. A novel approach, based on the concept that the nearest neighborhood of points (spots) on a map are sufficiently flexible to allow one not only to vary the number of points used for characterization of the map but also the density of information on their relative positions, is put forward. The method is illustrated with the Coomassie brilliant blue stained 2-D gel electrophoresis patterns of the proteomes from liver cells of healthy male Fisher F344 rats and the rats treated with four peroxisome proliferators.

Animals↗
PubMed2003

A theoretical graph method for search and analysis of critical phenomena in biochemical systems. II. Kinetic models of biochemical oscillators including two and three substances.

Four kinetic models of hypothetical complex reactions containing minimal two-substance or three-substance oscillators were constructed on the basis of the graphical rules suggested in the preceding work. The kinetic models are thought to be a part of one of four general biochemical systems: 1) system of mutual protein phosphorylation/dephosphorylation; 2) autophosphorylation of multisubunit protein; 3) association/dissociation of proteins or protein-containing structures during protein-protein or protein-ligand interaction; and 4) two-substrate enzymatic reaction with substrate inhibition by one substrate. Graphical rules of oscillator association with surrounding medium were considered. The graphical criteria of the oscillation generator elimination and criteria of oscillation damping were obtained. Both damped and undamped oscillations of reaction components were obtained by numerical integration of the mathematical models of these reactions. The areas of changes of model parameters and variables, within which the oscillations exist, were found.

Biological Clocks↗