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PubMed2000

Search for isotypism in crystal structures by means of the graph theory

A method for the classification of crystal structures of chemical compounds is proposed, which is based on the representation of the system of interatomic bonds in a crystal as a finite 'reduced' graph. The program IsoTest is described, allowing one to find automatically the topological similarity (isotypism) for large groups of stoichiometrically and structurally different compounds. The analysis of crystal structures of simple and double sulfates and binary inorganic compounds was carried out and numerous examples of topological isotypism of the representatives of these groups of substances were found. It is shown that in many cases the ionic sublattices, constructed according to one of the close packings, can be selected in the sulfate crystal structures.

Journal Article↗
PubMed1997

Handling context-sensitivity in protein structures using graph theory: bona fide prediction.

We constructed five comparative models in a blind manner for the second meeting on the Critical Assessment of protein Structure Prediction methods (CASP2). The method used is based on a novel graph-theoretic clique-finding approach, and attempts to address the problem of interconnected structural changes in the comparative modeling of protein structures. We discuss briefly how the method is used for protein structure prediction, and detail how it performs in the blind tests. We find that compared to CASP1, significant improvements in building insertions and deletions and sidechain conformations have been achieved.

Amino Acid Sequence↗
PubMedDate not supplied

Graph theory and group contributions in the estimation of boiling points.

Estimation of normal boiling points of organic compounds using a group contribution method is known to be unsatisfactory and an attempt has been made to improve the accuracy of the estimations by including chemical graph information in the regressions. This leads to a measurable improvement in the results obtained for both a set of 63 alcohols and also a set of 541 structurally diverse organic compounds. This new approach was found to have better predictive ability than the group contribution approach both in the cross-validation tests and in predicting the normal boiling points for 32 new compounds.

Alcohols↗
PubMed1990

Use of techniques derived from graph theory to compare secondary structure motifs in proteins.

A substructure matching algorithm is described that can be used for the automatic identification of secondary structural motifs in three-dimensional protein structures from the Protein Data Bank. The proteins and motifs are stored for searching as labelled graphs, with the nodes of a graph corresponding to linear representations of helices and strands and the edges to the inter-line angles and distances. A modification of Ullman's subgraph isomorphism algorithm is described that can be used to search these graph representations. Tests with patterns from the protein structure literature demonstrate both the efficiency and the effectiveness of the search procedure, which has been implemented in FORTRAN 77 on a MicroVAX-II system, coupled to the molecular fitting program FRODO on an Evans and Sutherland PS300 graphics system.

Algorithms↗
PubMed2006

Pattern detection in forensic case data using graph theory: application to heroin cutting agents.

Pattern recognition techniques can be very useful in forensic sciences to point out to relevant sets of events and potentially encourage an intelligence-led style of policing. In this study, these techniques have been applied to categorical data corresponding to cutting agents found in heroin seizures. An application of graph theoretic methods has been performed, in order to highlight the possible relationships between the location of seizures and co-occurrences of particular heroin cutting agents. An analysis of the co-occurrences to establish several main combinations has been done. Results illustrate the practical potential of mathematical models in forensic data analysis.

Journal Article↗
PubMed2002

Using graph theory to describe and model chromosome aberrations.

A comprehensive description of chromosome aberrations is introduced that is suitable for all cytogenetic protocols (e.g. solid staining, banding, FISH, mFISH, SKY, bar coding) and for mathematical analyses. "Aberration multigraphs" systematically characterize and interrelate three basic aberration elements: (1) the initial configuration of chromosome breaks; (2) the exchange process, whose cycle structure helps to describe aberration complexity; and (3) the final configuration of rearranged chromosomes, which determines the observed pattern but may contain cryptic misrejoinings in addition. New aberration classification methods and a far-reaching generalization of mPAINT descriptors, applicable to any protocol, emerge. The difficult problem of trying to infer actual exchange processes from cytogenetically observed final patterns is analyzed using computer algorithms, adaptations of known theorems on cubic graphs, and some new graph-theoretical constructs. Results include the following: (1) For a painting protocol, unambiguously inferring the occurrence of a high-order cycle requires a corresponding number of different colors; (2) cycle structure can be computed by a simple trick directly from mPAINT descriptors if the initial configuration has no more than one break per homologue pair; and (3) higher-order cycles are more frequent than the obligate cycle structure specifies. Aberration multigraphs are a powerful new way to describe, classify and quantitatively analyze radiation-induced chromosome aberrations. They pinpoint (but do not eliminate) the problem that, with present cytogenetic techniques, one observed pattern corresponds to many possible initial configurations and exchange processes.

Algorithms↗
PubMed1990

Applications of graph theory to enzyme kinetics and protein folding kinetics. Steady and non-steady-state systems.

Graphic methods have proved to be very useful in enzyme kinetics, as reflected in both raising the efficiency of performing calculations and aiding in the analysis of catalytic mechanisms. The kinetic relations among protein folding states are very similar to those between enzyme-catalyzed species. Therefore, it should be equally useful to provide a visually intuitive relation between kinetic calculations and folding mechanisms for protein folding kinetics, as manifested by the graphic rules in enzyme kinetics. It can actually be anticipated that, due to increasing interest in protein folding, the graphic method will become an important tool in folding kinetics as well. Based on the recent progress made in graphic methods of enzyme kinetics, in this review four graphic rules are summarized, which can be used to deal with protein folding systems as well as enzyme-catalyzed systems. Rules 1-3 are established for deriving the kinetic equations for steady-state processes and Rule 4 for those in the case of non-steady-state processes. In comparison with conventional graphic methods, which can only be applied to a steady-state system, the current rules have the following advantages: (1) Complicated and tedious calculations can be greatly simplified. (2) A lot of wasted labor can be turned away. (3) Final results can be double-checked by a formula provided in each of the graphic rules. (4) Transient kinetic systems can also be treated. The mathematical proof of Rules 1-4 is given in appendices A-D, respectively.

Enzymes↗
PubMed2005

Application of graph theory: prediction of glycogen synthase kinase-3 beta inhibitory activity of thiadiazolidinones as potential drugs for the treatment of Alzheimer's disease.

The relationship of Wiener's index, a distance-based topological descriptor; Zagreb group parameter, M(1), an adjacency-based topological descriptor and eccentric connectivity index,an adjacency-cum-distance based topological descriptor with the glycogen synthase kinase-3 beta inhibitory activity of thiadiazolidinones has been investigated. A training set comprising 28 analogues of substituted thiadiazolidinones was selected for the present investigations. The values of the Wiener's index, Zagreb group parameter, and eccentric connectivity index for each of 28 analogues comprising the data set were computed. Resulting data was analyzed and suitable models developed after identification of active ranges. Subsequently, biological activity was predicted for each analogue involved in the data set using these models, which was then compared with the reported glycogen synthase kinase-3 beta inhibitory activities. Accuracy of prediction was found to vary from a minimum of approximately 83% for model based on Zagreb group parameter to a maximum of approximately 87% for model based on Wiener's index.

Alzheimer Disease↗
PubMed2001

Mining DNA microarray data using a novel approach based on graph theory.

The recent demonstration that biochemical pathways from diverse organisms are arranged in scale-free, rather than random, systems [Jeong et al., Nature 407 (2000) 651-654], emphasizes the importance of developing methods for the identification of biochemical nexuses--the nodes within biochemical pathways that serve as the major input/output hubs, and therefore represent potentially important targets for modulation. Here we describe a bioinformatics approach that identifies candidate nexuses for biochemical pathways without requiring functional gene annotation; we also provide proof-of-principle experiments to support this technique. This approach, called Nexxus, may lead to the identification of new signal transduction pathways and targets for drug design.

Apoptosis↗