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At least 469 records · Page 26Linked to original sources
PubMed2000

Molecular evolution of catalysis.

In this paper, we consider the evolutionary dynamics of catalytically active species with a distinct genotype-phenotype relationship. Folding landscapes of RNA molecules serve as a paradigm for this relationship with essential neutral properties. The landscape itself is partitioned by phenotypes (realized as RNA secondary structures). To each genotype (represented as a sequence) a structure is assigned in a unique way. The set of all sequences which map into a particular structure is modeled as a random graph in sequence space (the so-called neutral network). A catalytic network is realized as a random digraph with maximal out-degree two and secondary structures as vertex sets. A population of catalytic RNA molecules shows significantly different behavior compared to a deterministic description: hypercycles are able to co-exist and out-compete a parasite with superior catalytic support. A "switching" between different dynamic organizations of the network can be observed, dynamical stability of hypercyclic organizations against errors and the existence of an error-threshold of catalysis can be reported.

Animals↗
PubMed2006

Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis.

Previous studies demonstrated that intelligence is significantly related to an impressive array of psychological, social, biological and genetic factors and that working memory (WM) can be considered as a general cognitive resource strongly related with a wide variety of higher order cognitive competencies and intelligence. Also, evaluating the WM of subjects might allow one to test the neural efficiency hypothesis (NEH). WM typically involves functional interactions between frontal and parietal cortices. We recorded EEG signals to study neuronal interactions during one WM test in individuals who had few years of formal education (LE) as compared to individuals with university degrees (UE). The two groups of individuals differed in the scores they obtained in psychological tests. To quantify the synchronization between EEG channels in several frequency bands, we evaluated the "synchronization likelihood" (SL), which takes into consideration nonlinear processes as well as linear ones. SL was then converted into graphs to estimate the distance from "small-world network" (SWN) organization, i.e., an optimally organized network that would give rise to the data. In comparison to LE subjects, those with university degrees exhibited less prominent SWN properties in most frequency bands during the WM task. This finding supports the NEH and suggests that the connections between brain areas of well-educated subjects engaged in WM tasks are not as well-organized in the sense of SWN.

Adult↗
PubMedDate not supplied

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↗
PubMedDate not supplied

Oriented 2-cell embeddings of a graph and their symmetry classification: generating algorithms and case study of the möbius-kantor graph.

We discuss a method to derive all symmetry-distinct oriented 2-cell embeddings of a given graph and classify them based on their symmetry. As an example, we apply the algorithm to the highly symmetrical trivalent Möbius-Kantor graph. Considering the derived 2-cell embeddings as carbon networks leads to some interesting negative curvature carbon allotropes.

Journal Article↗
PubMed2002

A new scheme for electronegativity equalization as a source of electronic descriptors: application to chemical reactivity.

Recently, we have proposed a new unconventional scheme of electronegativity equalization. We assume that atomic electronegativities are equalized in a molecule in the same manner as electrical potentials in the nodes of a closed electrical network, with the molecule being represented by a molecular graph (MG). Computational procedure includes several operations over the matrices associated with MG. The only parameter used is the atomic electronegativity (EN). The method is very fast and easy-to-implement. With the help of the method one can generate a family of electronic descriptors (equalized or "effective" ENs and atomic charges) which are applicable to the treatment of some types of chemical reactivity. Quite good correlations of the descriptors obtained are observed for such thermodynamic and kinetic data as proton affinity and Taft's inductive sigma* constants. The EN equalization scheme suggested can be used as an independent tool for molecular electrostatics modeling, or can be implemented into an integrated QSAR software.

Electricity↗
PubMed2006

Metastable configurations of small-world networks.

We calculate the number of metastable configurations of Ising small-world networks that are constructed upon superimposing sparse Poisson random graphs onto a one-dimensional chain. Our solution is based on replicated transfer-matrix techniques. We examine the denegeracy of the ground state and find a jump in the entropy of metastable configurations exactly at the crossover between the small-world and the Poisson random graph structures. We also examine the difference in entropy between metastable and all possible configurations, for both ferromagnetic and bond-disordered long-range couplings.

Journal Article↗
PubMed2006

A quantitative analysis of secondary RNA structure using domination based parameters on trees.

BACKGROUND: It has become increasingly apparent that a comprehensive database of RNA motifs is essential in order to achieve new goals in genomic and proteomic research. Secondary RNA structures have frequently been represented by various modeling methods as graph-theoretic trees. Using graph theory as a modeling tool allows the vast resources of graphical invariants to be utilized to numerically identify secondary RNA motifs. The domination number of a graph is a graphical invariant that is sensitive to even a slight change in the structure of a tree. The invariants selected in this study are variations of the domination number of a graph. These graphical invariants are partitioned into two classes, and we define two parameters based on each of these classes. These parameters are calculated for all small order trees and a statistical analysis of the resulting data is conducted to determine if the values of these parameters can be utilized to identify which trees of orders seven and eight are RNA-like in structure. RESULTS: The statistical analysis shows that the domination based parameters correctly distinguish between the trees that represent native structures and those that are not likely candidates to represent RNA. Some of the trees previously identified as candidate structures are found to be "very" RNA like, while others are not, thereby refining the space of structures likely to be found as representing secondary RNA structure. CONCLUSION: Search algorithms are available that mine nucleotide sequence databases. However, the number of motifs identified can be quite large, making a further search for similar motif computationally difficult. Much of the work in the bioinformatics arena is toward the development of better algorithms to address the computational problem. This work, on the other hand, uses mathematical descriptors to more clearly characterize the RNA motifs and thereby reduce the corresponding search space. These preliminary findings demonstrate that graph-theoretic quantifiers utilized in fields such as computer network design hold significant promise as an added tool for genomics and proteomics.

Algorithms↗
PubMed2006

Estimating the parameters of a model for protein-protein interaction graphs.

We find accurate approximations for the expected number of three-cycles and unchorded four-cycles under a stochastic distribution for graphs that has been proposed for modelling yeast two-hybrid protein-protein interaction networks. We show that unchorded four-cycles are characteristic motifs under this model and that the count of unchorded four-cycles in the graph is a reliable statistic on which to base parameter estimation. Finally, we test our model against a range of experimental data, obtain parameter estimates from these data and investigate possible improvements in the model. Characterization of this model lays the foundation for its use as a prior distribution in a Bayesian analysis of yeast two-hybrid networks that can potentially aid in identifying false-positive and false-negative results.

Algorithms↗
PubMed2001

Minimum spanning trees on random networks.

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Because of this geometric universality, we are able to characterize the energy of MST using a scaling distribution [P(epsilon)] found using uniform disorder. We show that the MST energy for other disorder distributions is simply related to P(epsilon). We discuss the relationship to invasion percolation, to the directed polymer in a random media, to uniform spanning trees, and also the implications for the broader issue of universality in disordered systems.

Journal Article↗
PubMed2006

Structural properties of planar graphs of urban street patterns.

Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological, and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street patterns of different world cities. Samples are turned into spatial valued graphs. In such graphs, the nodes are embedded in the two-dimensional plane and represent street intersections, the edges represent streets, and the edge values are equal to the street lengths. We evaluate the local properties of the graphs by measuring the meshedness coefficient and counting short cycles (of three, four, and five edges), and the global properties by measuring global efficiency and cost. We also consider, as extreme cases, minimal spanning trees (MST) and greedy triangulations (GT) induced by the same spatial distribution of nodes. The measures found in the real and the artificial networks are then compared. Surprisingly, cities of the same class, e.g., grid-iron or medieval, exhibit roughly similar properties. The correlation between a priori known classes and statistical properties is illustrated in a plot of relative efficiency vs cost.

Journal Article↗
PubMed2005

Biogeographic interpretation of splits graphs: least squares optimization of branch lengths.

Although most often used to represent phylogenetic uncertainty, network methods are also potentially useful for describing the phylogenetic complexity expected to characterize recent species radiations. One network method with particular advantages in this context is split decomposition. However, in its standard implementation this approach is limited by a conservative criterion for branch length estimation. Here we extend the utility of split decomposition by introducing a least squares optimization technique for correcting branch lengths that may be underestimated by the standard implementation. This optimization of branch lengths is generally expected to improve divergence time estimates calculated from splits graphs. We illustrate the effect of least squares optimization on such estimates using the Australasian Myosotis and the Hawaiian silversword alliance as examples. We also discuss the biogeographic interpretation and limitations of splits graphs.

Boraginaceae↗
PubMed2004

A graph model for the evolution of specificity in humoral immunity.

The immune system protects the body against health-threatening entities, known as antigens, through very complex interactions involving the antigens and the system's own entities. One remarkable feature resulting from such interactions is the immune system's ability to improve its capability to fight antigens commonly found in the individual's environment. This adaptation process is called the evolution of specificity. In this paper, we introduce a new mathematical model for the evolution of specificity in humoral immunity, based on Jerne's functional, or idiotypic, network. The evolution of specificity is modeled as the dynamic updating of connection weights in a dynamic graph whose nodes are related to the network's idiotypes. At the core of this weight-updating mechanism are the increase in specificity caused by clonal selection and the decrease in specificity due to the insertion of uncorrelated idiotypes by the bone marrow. As we demonstrate through numerous computer experiments, for appropriate choices of parameters the new model correctly reproduces, in qualitative terms, several immune functions.

Antibody Formation↗
PubMed2003

An assessment of preferential attachment as a mechanism for human sexual network formation.

Recent research into the properties of human sexual-contact networks has suggested that the degree distribution of the contact graph exhibits power-law scaling. One notable property of this power-law scaling is that the epidemic threshold for the population disappears when the scaling exponent rho is in the range 2 < rho < or = 3. This property is of fundamental significance for the control of sexually transmitted diseases (STDs) such as HIV/AIDS since it implies that an STD can persist regardless of its transmissibility. A stochastic process, known as preferential attachment, that yields one form of power-law scaling has been suggested to underlie the scaling of sexual degree distributions. The limiting distribution of this preferential attachment process is the Yule distribution, which we fit using maximum likelihood to local network data from samples of three populations: (i) the Rakai district, Uganda; (ii) Sweden; and (iii) the USA. For all local networks but one, our interval estimates of the scaling parameters are in the range where epidemic thresholds exist. The estimate of the exponent for male networks in the USA is close to 3, but the preferential attachment model is a very poor fit to these data. We conclude that the epidemic thresholds implied by this model exist in both single-sex and two-sex epidemic model formulations. A strong conclusion that we derive from these results is that public health interventions aimed at reducing the transmissibility of STD pathogens, such as implementing condom use or high-activity anti-retroviral therapy, have the potential to bring a population below the epidemic transition, even in populations exhibiting large degrees of behavioural heterogeneity.

Female↗
PubMed2006

Modeling a health telematics network: does the 3LGM2 approach assist in its management and operation ?

Health Telematics Networks (HTN) are characterized by a complex setup and interrelations. Using available tools and methods focusing on mainly one aspect, e.g. its functionality or the network infrastructure leads to a restricted view. The objective of this paper is to assess the applicability of the Revised Three-layer Graph-based Meta Model (3LGM(2))--developed for modeling hospital information systems--towards health telematics networks. Having identified an approach on how to represent the hospitals effectively in the model the 3LGM(2) proved to support strategic management, day-to-day maintenance and documentation.

Germany↗
PubMed2001

Visualizing plant metabolomic correlation networks using clique-metabolite matrices.

MOTIVATION: Today, metabolite levels in biological samples can be determined using multiparallel, fast, and precise metabolomic approaches. Correlations between the levels of various metabolites can be searched to gain information about metabolic links. Such correlations are the net result of direct enzymatic conversions and of indirect cellular regulation over transcriptional or biochemical processes. In order to visualize metabolic networks derived from correlation lists graphically, each metabolite pair may be represented as vertices connected by an edge. However, graph complexity rapidly increases with the number of edges and vertices. To gain structural information from metabolite correlation networks, improvements in clarity are needed. RESULTS: To achieve this clarity, three algorithms are combined. First, a list of linear metabolite correlations is generated that can be regarded as a set of pairs of edges (or as 2-cliques). Next, a branch-and-bound algorithm was developed to find all maximal cliques by combining submaximal cliques. Due to a clique assignment procedure, the generation of unnecessary submaximal cliques is avoided in order to maintain high efficiency. Differences and similarities to the Bron-Kerbosch algorithm are pointed out. Lastly, metabolite correlation networks are visualized by clique-metabolite matrices that are sorted to minimize the length of lines that connect different cliques and metabolites. Examples of biochemical hypotheses are given that can be built from interpretation of such clique matrices. AVAILABILITY: The algorithms are implemented in Visual Basic and can be downloaded from our web site along with a test data set (http://www.mpimp-golm.mpg.de/fiehn/projekte/data-mining-e.html). CONTACT: kose@mpimp-golm.mpg.de

Algorithms↗
PubMed2002

Building and analysing genome-wide gene disruption networks.

MOTIVATION: Microarray experiments comparing expression levels of all genes in yeast for hundreds of mutants allow us to examine properties of gene regulatory networks on a genomic scale. We can investigate questions such as network modularity, connectivity, and look for genes with particular roles in the network structure. RESULTS: We have built genome-wide disruption networks for yeast, using a representation of gene expression data as directed labelled graphs. Nodes represent genes and arcs connect nodes if the disruption of the source gene significantly alters the expression of the target gene. We are interested in features of the resulting disruption networks that are robust over a range of significance cutoffs. The networks show a significant overlap with analogous networks constructed from scientific literature. In disruption networks the number of arcs adjacent to different nodes are distributed roughly according to a power-law, like in many complex systems where the robustness against perturbations is important. The networks are dominated by a single large component and do not have an obvious modular structure. Genes with the highest outdegrees often encode proteins with regulatory functions, whereas genes with the highest indegrees are predominantly involved in metabolism. The local structure of the networks is meaningful, genes involved in the same cellular processes are close together in the network. AVAILABILITY: http://www.ebi.ac.uk/microarray/networks

Chromosome Mapping↗
PubMed1994

Users conceptual views on medical information databases.

As information databases we consider all the kinds of information repositories that are handled by computer systems. When querying very large information databases, the end-users are often faced with the problem to parse their questions efficiently into the query languages of the computer systems. Conceptual graphs were initially designed for natural language analysis and understanding. Due to their closeness to semantic networks, their expressiveness is powerful enough to be applied to knowledge representation and use by computer systems. This work demonstrates that conceptual graphs are a suitable means to model both the information in patient databases and the queries to these databases, and that operations on graphs can compute the pattern matching process needed to provide the answers. A prototype that exploits this model is presented. Experiments have been made with the material furnished by the Unified Medical Language System project (version 2, 1992) of the National Library of Medicine, USA.

Abstracting and Indexing↗
PubMed2004

Molecular triangulation: bridging linkage and molecular-network information for identifying candidate genes in Alzheimer's disease.

A major challenge in human genetics is identifying the molecular basis of common heritable disorders. In contrast to rare single-gene diseases, multifactorial disorders are thought to arise from the combined effect of multiple gene variants, such that any single variant may have only a modest effect on disease susceptibility. We present a method to identify genes that may harbor a significant proportion of the genetic variation that predisposes individuals to a given multifactorial disorder. First, we perform an automated literature analysis that predicts physical interactions (edges) among candidate disease genes (seed nodes, selected on the basis of prior information) and other molecular entities. We derive models of molecular networks from this analysis and map the seed nodes to them. We then compute the graph-theoretic distance (the minimum number of edges that must be traversed) between the seed nodes and all other nodes in the network. We assume that nodes that are found in close proximity to multiple seed nodes are the best disease-related candidate genes. To evaluate this approach, we selected four seed genes, each with a proven role in Alzheimer's disease (AD). The method performed well in predicting additional network nodes that match AD gene candidates identified manually by an expert. We also show that the method prioritizes among the seed nodes themselves, rejecting false-positive seeds that are derived from (noisy) whole-genome genetic-linkage scans. We propose that this strategy will provide a valuable means to bridge genetic and genomic knowledge in the search for genetic determinants of multifactorial disorders.

Algorithms↗