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Propagation of information in MetaNet graph models.

Information flow in metabolic networks has been studied with a graph model which represents the biochemical transformations occurring in the system under investigation. The "signal strength", an algebraic expression which estimates the probability that an intermediate metabolite is bound to a given enzyme, has been used to derive the "signal transmittance", the fraction of the informational signal at one intermediate that reaches another intermediate. The transmittance has been used to derive the "response ratio", the sensitivity of the rate of change of information at one metabolite consequent to a perturbation at another metabolite. Because the graphical representation corresponds to the biochemical events presumed to occur in the network, these quantities can be used to design experiments to confirm or falsify the hypotheses underlying the model and aid in understanding the regulatory properties of the system. The technique is illustrated by an example model, and its predictions are shown to be sensitive to modest structural changes in the network.

Animals↗

Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems.

The purpose of this article is to stress the implications that the consideration of nonlinearity has upon the extension and strength of connectivity, if this is understood as a characterization of the degree of interrelation between parts of the system. This objective is reached within the QP formalism for non-linear ODEs. The formalism is developed in a graph-theoretic setting, with the help of which the connectionist aspect of non-linearity becomes apparent. Topology-preserving transformations involve an exchange between the degree of non-linearity and the strengths of interactions, thus assembling systems of apparently different nature into classes of equivalence. We argue that, if we have in mind a classification of systems according to behavior, these classes of equivalence should be given their proper singularity. We characterize globally the connectivity of a class with an index, although we point out during the discussion that the mathematical conception of the complex idea of connectivity is still incomplete.

Linear Models↗

Constructing a useful tool for characterizing amino acid conformers by means of quantum chemical and graph theory indices.

The aim of this work is to construct a tool to assist in the prediction of peptidic properties resulting from the exchange of two amino acids in a proteic chain. In the past others have used experimental properties for this purpose. However, the nature of these data sets severely limits their access to important properties pertaining to secondary structure, and hence the indices used cannot characterize different backbone conformers like alpha helix and beta strands, or side-chain conformations like gauche +, gauche - and trans. In this study we explore the importance of backbone and side-chain angles with regard to conformer similarity measured with theoretical properties calculated in an ab initio manner. For each of the 20 genetically encoded amino acids, we studied five conformers that correspond to alpha helical and beta strand structures, with three different side chain conformations for each, defined solely by their angles phi, psi and chi1. This methodology allowed each of the 108 conformers to be represented by a mathematical object without ambiguity. The peptidic chain was emulated using two capping models to simulate the effect of nearest neighbors. These are OHC-Xaa-NH2 and Ala-Xaa-Ala, where Xaa is the conformer of interest. We then calculated 40 ab initio quantum chemical and graph theory indices for each backbone-side-chain conformer to obtain a characterization and classification scheme. We found that: (1) while backbone structure is very important to conformer similarity, side-chain conformations do not cluster together in a top-level manner; (2) amino acids with pi electrons group together independent of backbone conformation.

Amino Acids↗

Study of synaptic plasticity via random graphs.

The dynamical random graphs associated with a certain class of biological neural networks are introduced and studied. We describe the phase diagram revealing the parameters of a single neuron and of the synaptic strengths which allow formation of the stable strongly connected large groups of neurons. It is shown that the cycles are the most stable structures when the Hebb rule is implemented into the dynamics of the network of excitatory neurons. We discuss the role of cycles for the synchronization of the neuronal activity.

Neural Networks, Computer↗

Topology and graph theory applied to cortical anatomy may help explain working memory capacity for three or four simultaneous items.

Cognitive experimentation suggests that at any single instant only three or four items ("chunks") are simultaneously prominent as a working memory (WM) trace, if we disregard the rehearsal component of WM. The reason for small WM capacity may concern combinatorial manageability. How might the neural representations of these few coactive chunks occupy a spatially distributed set of areas of the sheet-like cortex, while providing both order and flexibility to associate items in WM? Each attribute of each simultaneously active WM item must have broad access to the representational facilities of the cortical sheet, comprising tens of thousands of modular "cortical columns." The two hypothesized neural levels of WM during any moment of cognition comprise (a) "binding" together of many distributed attribute representations within each respective WM chunk, and (b) combinatorial play among three or four WM chunk-representations. Anatomical and functional evidence of cortical unity through its depth suggests that cortex may be viewed as essentially planar in its distribution of activations. Thus, a moment's WM is hypothesized here to reside in myriad activated cortical planar "patches," each subdivided into up to four amoeboid "subpatches." Two different lines of topological reasoning suggest orderly associations of such representations. (1) The four-color principle of map topology, and the related K(4) is planar theorem of graph theory, imply that if a small cortical area is dynamically subdivided into no more than four, discretely bounded planar subareas, then each such segment has ample free access to each of the others. (2) A hypothetical alternative to such associative adjacency of simultaneously active cortical representations of chunk-attributes is associative overlap, whereby, in dense cortical neuropil, activated subpatches behave like Venn diagrams of intersecting sets. As the number of Venn-like coactive subpatches within a patch increases, maintaining ad hoc associativity among all combinations requires exponentially proliferating intersections. Beyond four, serpentine subpatch shapes are required, which could easily lead to pathologies of omission or commission. As hypothesized by many researchers, the binding of the widely distributed cortical modules that represent a given chunk may involve synchrony or coherence of a single EEG frequency. Elsewhere, I have conjectured that such a binding frequency for a single chunk may bear a harmonic relationship with the additional EEG frequencies that are simultaneously binding the other WM chunks. Other possible mechanisms of binding have also been hypothesized. Whatever the mechanism, the many attributes of a moment's complement of three or four WM chunks must generally have an accidental relationship with the spatial distribution of the cortical feature analyzers that must be activated to represent those attributes. Therefore, the cortex may need, and have, comprehensive anatomical connections of each of its modules for representing an attribute (or of small redundant module groupings) with every other. If such whole-part cortico-cortical connections are somehow exploited not only to fully represent each cognitive chunk in its bound-together attributes, but also to bring the major business of intensive WM information processing down to the level of local circuits, in the sorts of topological patterning hypothesized here, there may be two adaptive results: (1) Time and other economies would be achieved in the reduction of activity in distant cortico-cortical connections to lower-energy global orchestration, or binding processes. (2) The piecemeal local topological limit to four subpatches would be writ large, across the entire cortex, preventing an unconstrained combinatorial explosion of associations among all attributes of all three or four simultaneously active chunks. Such hypothetical convergence to foci in local subpatch interactions might take place primarily in association cortex, and/or it might involve temporary shifts in response properties in some cortical subpat might involve temporary shifts in response properties in some cortical subpatches. Quantitative studies of the densely packed cortical fine structure, by Braitenberg and Schüz, and others, seem potentially consistent with this vision of cortical function in cognition.

Animals↗

Graph matching vs mutual information maximization for object detection.

Labeled Graph Matching (LGM) has been shown successful in numerous object vision tasks. This method is the basis for arguably the best face recognition system in the world. We present an algorithm for visual pattern recognition that is an extension of LGM ('LGM+'). We compare the performance of LGM and LGM+ algorithms with a state of the art statistical method based on Mutual Information Maximization (MIM). We present an adaptation of the MIM method for multi-dimensional Gabor wavelet features. The three pattern recognition methods were evaluated on an object detection task, using a set of stimuli on which none of the methods had been tested previously. The results indicate that while the performance of the MIM method operating upon Gabor wavelets is superior to the same method operating on pixels and to LGM, it is surpassed by LGM+. LGM+ offers a significant improvement in performance over LGM without losing LGM' s virtues of simplicity, biological plausibility, and a computational cost that is 2-3 orders of magnitude lower than that of the MIM algorithm.

Algorithms↗

Addition patterns, codes and contact graphs for fullerene derivatives.

The mathematical concept of the d-code and its associated contact graph give a model for sterically constrained addition patterns in fullerene derivatives C60Xm and C70Xm. In combination with simple electronic arguments, the stoichiometries, symmetries, and location of addends can be predicted, yielding a small number of candidates for further study. For example, sterically and optimal solutions C60Xm with pairwise separation of d bonds between addends are found at m(d) = 24(2), 12(3), 6(4,5), 2(6 to 9). The solution for C60X24 is unique, and the model selects 12 candidates for C60X12 from a starting set of 11661527060 possibilities.

Carbon↗

Knowledge representation and retrieval using conceptual graphs and free text document self-organisation techniques.

Hospitals generate and store a large amount of clinical data each year, a significant portion of which is in free text format. Conventional database storage and retrieval algorithms are incapable of effectively processing free text medical data. The rich information and knowledge buried in healthcare records are unavailable for clinical decision-making. We examined a number of techniques for structuring and processing free text documents to effective and efficient for information retrieval and knowledge discovery. One critical success criterion is that the complexity of the techniques must be polynomial both in space and time for them to be able to cope with very large databases. We used conceptual graphs (CG) to capture the structure and semantic information/knowledge contained within the free text medical documents. Ordering and self-organising techniques (lattice techniques and knowledge space) were used to improve organisation of concepts from standard medical nomenclatures and large sets of free text medical documents. Pair-wise union of CG was performed to identify the common generalisation structure and a lattice structure of these CG documents. A combination of all three techniques allowed us to organise a set of 9000 discharge summaries into a generalisation hierarchy that supported efficient and rich information/knowledge retrieval.

Classification↗

A single calibration graph for the direct determination of ascorbic and dehydroascorbic acids by electrogenerated luminescence based on Ru(bpy)(3)2+ in aqueous solution

Ascorbic (H2A) and dehydroascorbic (DA) acids were for the first time directly determined in a single chromatographic run by means of the tris(2,2'-bipyridine)ruthenium(II) (Ru(bpy)(3)2+) based electrogenerated chemiluminescence (ECL) detection. For the first time, it was demonstrated that DA, a nonelectroactive compound, is ECL active and is responsible for the ECL behavior of H2A. This fact, together with the lack of a DA standard, suggested the use of a calibration graph obtained for H2A, for determining both analytes. The proven ECL activity of DA, together with literature data relative to the standard redox potentials of the different species coming from H2A, led to a reconsideration of the proposed ECL reaction mechanism for H2A. The role of the OH- ion in the reaction mechanism of the two analytes appeared to be crucial. H2A and DA could be separated by a suitable C18-reversed-phase HPLC column using an aqueous 30 mM H3PO4 solution as the mobile phase. The optimal ECL response was achieved by polarizing the working electrode at 1.150 Vvs SCE (standard calomel electrode) (oxidation diffusion limiting potential for both H2A and Ru(bpy)(3)2+). The Ru(bpy)(3)2+ solution, at pH 10 for carbonate buffer, was mixed to the eluent solution in a postcolumn system, obtaining, still at pH 10, the final 0.25 mM Ru(bpy)(3)2+ concentration. The detection limit found for the two analytes was 1 x 10(-7) M. The method was successfully applied to the determination of the analytes in a commercially available orange fruit juice.

Journal Article↗

Two-dimensional arrays in the analysis of trends in series of molecules: strongly subspectral molecular graphs, formula periodic tables, and number of resonance structures

Two-dimensional arrays consisting of strongly subspectral molecular graphs and formula periodic tables for polycyclic aromatic hydrocarbons are briefly reviewed. New two-dimensional arrays for free-radical benzenoid hydrocarbons are presented with general analytical expressions for counting their number of resonance structures (SC). The structural origin of the coefficients to these analytical expressions is discussed.

Journal Article↗

Graph theoretical descriptors of two-dimensional chirality with possible extension to three-dimensional chirality.

We report on construction of a graph theoretical descriptor of chirality for two-dimensional benzenoid hydrocarbons. For achiral molecules the index is zero, while for chiral molecules it takes a positive or negative value for a molecule and one for its mirror image. Hence, we also have obtained a descriptor that measures chirality on an absolute scale, i.e., it assigns to a molecule a positive (or a negative) value without ever requiring information on the enantiomer of the molecule considered or any other pair of standards. In addition, we have briefly outlined how this is the 2-D approach extended to characterization of chiral objects in 3-D space, at least in the case of n-alkane rotamers.

Journal Article↗

Correlation of graph-theoretical parameters with biological activity.

Ośmialowski and Kaliszan calculated graph-theoretical indices for substituted isonicotinic hydrazides and used simple and multiple regression to search (unsuccessfully) for correlations with biological activity. The present paper describes successful searches for correlation in the same data set using principal component analysis (PCA) with multivariate outlier testing and also using stepwise multiple regression. Following PCA, correlation with biological activity always appeared in the second principal component, not the first, that is, after projection of the data points into the (n - 1)-space orthogonal to the first principal component axis. In that space, the principal component score was a more accurate predictor of biological activity than were equations provided by multiple regression or stepwise multiple regression using the underlying variables. A multivariate outlier test identified one observation as discordant, and removing that observation improved prediction further.

Data Interpretation, Statistical↗

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↗

DNA solution of a graph coloring problem.

The graph-theoretic parameter that has probably received the most attention over the years is the chromatic number. As is well-known, the coloring problem is an NP-Complete problem. In this paper, it has been solved by means of molecular biology techniques. The algorithm is highly parallel and has satisfactory fidelity. This work shows further evidence for the ability of DNA computing to solve NP-Complete problems.

Base Sequence↗

Cyclical conjunction: an efficient operator for the extraction of cycles from a graph.

The structural characteristics of a molecule, namely size, bond type and number, cycles, shape, and functional groups, will largely determine its physicochemical properties and biological activity. Extraction of data such as the complete structural information of a molecule's ring system is complex (NP-complete) and has traditionally involved high computational cost. The present study proposes a new operator for the extraction of cycles from a graph. Based on an initial cycle set, the operator employs a reduced number of operations in an iterative process of error-free cycle extraction, hence greatly reducing computational cost. Algorithm efficiency has been enhanced by designing new data structures suited to cycle storage, useful not only for interactive solutions but also for applications managing large volumes of information such as descriptor calculation, QSPR/QSAR, matching, clustering, screening, and filtering. Validation was performed by applying the algorithm to a test suite of chemical compounds of varying complexity.

Journal Article↗