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At least 217 records · Page 12Linked to original sources
PubMed2006

Observing local and global properties of metabolic pathways: 'load points' and 'choke points' in the metabolic networks.

MOTIVATION: The local and global aspects of metabolic network analyses allow us to identify enzymes or reactions that are crucial for the survival of the organism(s), therefore directing us towards the discovery of potential drug targets. RESULTS: We demonstrate a new method ('load points') to rank the enzymes/metabolites in the metabolic network and propose a model to determine and rank the biochemical lethality in metabolic networks (enzymes/metabolites) through 'choke points'. Based on an extended form of the graph theory model of metabolic networks, metabolite structural information was used to calculate the k-shortest paths between metabolites (the presence of more than one competing path between substrate and product). On the basis of these paths and connectivity information, load points were calculated and used to empirically rank the importance of metabolites/enzymes in the metabolic network. The load point analysis emphasizes the role that the biochemical structure of a metabolite, rather than its connectivity (hubs), plays in the conversion pathway. In order to identify potential drug targets (based on the biochemical lethality of metabolic networks), the concept of choke points and load points was used to find enzymes (edges) which uniquely consume or produce a particular metabolite (nodes). A non-pathogenic bacterial strain Bacillus subtilis 168 (lactic acid producing bacteria) and a related pathogenic bacterial strain Bacillus anthracis Sterne (avirulent but toxigenic strain, producing the toxin Anthrax) were selected as model organisms. The choke point strategy was implemented on the pathogen bacterial network of B.anthracis Sterne. Potential drug targets are proposed based on the analysis of the top 10 choke points in the bacterial network. A comparative study between the reported top 10 bacterial choke points and the human metabolic network was performed. Further biological inferences were made on results obtained by performing a homology search against the human genome. AVAILABILITY: The load and choke point modules are introduced in the Pathway Hunter Tool (PHT), the basic version of which is available on http://www.pht.uni-koeln.de.

Bacillus↗
PubMedDate not supplied

A mathematical approach to the connectivity between the cortical visual areas of the macaque monkey.

The visual cortex of the macaque monkey is divided into many distinct visual information processing areas. In many cases, anatomical and physiological results allow one to determine the presence or the absence of neuronal connections from one area to another. We have approached the topology of this neuronal network within the mathematical framework of graph theory. At first, we studied the unknown part of the network, i.e. the part where anatomical and physiological results are lacking. Relying on a specific topological property of the network established on the known part, we developed an interpolation algorithm for reducing the level of uncertainty concerning the unknown part. From these results, we then constructed a connectional model of the neuronal network for the entire cortical visual system. Subsequently, a topological analysis of this model, with the help of factorial analysis and clustering technics, shows its structural properties and singular vertices. This analysis suggests the existence of two distinct classes of areas, one in the parietal part of the cortex and the other in the temporal part, which are connected to each other via relay areas, especially involving the frontal eye field. These results may help to understand the functional role of particular cortical areas in vision and, more generally, to explore how visual information flows within the visual cortex.

Algorithms↗
PubMed2001

BIND--The Biomolecular Interaction Network Database.

The Biomolecular Interaction Network Database (BIND; http://binddb. org) is a database designed to store full descriptions of interactions, molecular complexes and pathways. Development of the BIND 2.0 data model has led to the incorporation of virtually all components of molecular mechanisms including interactions between any two molecules composed of proteins, nucleic acids and small molecules. Chemical reactions, photochemical activation and conformational changes can also be described. Everything from small molecule biochemistry to signal transduction is abstracted in such a way that graph theory methods may be applied for data mining. The database can be used to study networks of interactions, to map pathways across taxonomic branches and to generate information for kinetic simulations. BIND anticipates the coming large influx of interaction information from high-throughput proteomics efforts including detailed information about post-translational modifications from mass spectrometry. Version 2.0 of the BIND data model is discussed as well as implementation, content and the open nature of the BIND project. The BIND data specification is available as ASN.1 and XML DTD.

Binding, Competitive↗
PubMed2003

Topological structure analysis of the protein-protein interaction network in budding yeast.

Interaction detection methods have led to the discovery of thousands of interactions between proteins, and discerning relevance within large-scale data sets is important to present-day biology. Here, a spectral method derived from graph theory was introduced to uncover hidden topological structures (i.e. quasi-cliques and quasi-bipartites) of complicated protein-protein interaction networks. Our analyses suggest that these hidden topological structures consist of biologically relevant functional groups. This result motivates a new method to predict the function of uncharacterized proteins based on the classification of known proteins within topological structures. Using this spectral analysis method, 48 quasi-cliques and six quasi-bipartites were isolated from a network involving 11,855 interactions among 2617 proteins in budding yeast, and 76 uncharacterized proteins were assigned functions.

Algorithms↗
PubMed2004

ACLAME: a CLAssification of Mobile genetic Elements.

The ACLAME database (http://aclame.ulb.ac.be) is a collection and classification of prokaryotic mobile genetic elements (MGEs) from various sources, comprising all known phage genomes, plasmids and transposons. In addition to providing information on the full genomes and genetic entities, it aims to build a comprehensive classification of the functional modules of MGEs at the protein, gene and higher levels. This first version contains a comprehensive classification of 5069 proteins from 119 DNA bacteriophages into over 400 functional families. This classification was produced automatically using TRIBE-MCL, a graph-theory-based Markov clustering algorithm that uses sequence measures as input, and then manually curated. Manual curation was aided by consulting annotations available in public databases retrieved through additional sequence similarity searches using Psi-Blast and Hidden Markov Models. The database is publicly accessible and open to expert volunteers willing to participate in its curation. Its web interface allows browsing as well as querying the classification. The main objectives are to collect and organize in a rational way the complexity inherent to MGEs, to extend and improve the inadequate annotation currently associated with MGEs and to screen known genomes for the validation and discovery of new MGEs.

Bacteriophages↗
PubMed1985

Significance of nucleotide sequence alignments: a method for random sequence permutation that preserves dinucleotide and codon usage.

The similarity of two nucleotide sequences is often expressed in terms of evolutionary distance, a measure of the amount of change needed to transform one sequence into the other. Given two sequences with a small distance between them, can their similarity be explained by their base composition alone? The nucleotide order of these sequences contributes to their similarity if the distance is much smaller than their average permutation distance, which is obtained by calculating the distances for many random permutations of these sequences. To determine whether their similarity can be explained by their dinucleotide and codon usage, random sequences must be chosen from the set of permuted sequences that preserve dinucleotide and codon usage. The problem of choosing random dinucleotide and codon-preserving permutations can be expressed in the language of graph theory as the problem of generating random Eulerian walks on a directed multigraph. An efficient algorithm for generating such walks is described. This algorithm can be used to choose random sequence permutations that preserve (1) dinucleotide usage, (2) dinucleotide and trinucleotide usage, or (3) dinucleotide and codon usage. For example, the similarity of two 60-nucleotide DNA segments from the human beta-1 interferon gene (nucleotides 196-255 and 499-558) is not just the result of their nonrandom dinucleotide and codon usage.

Base Sequence↗
PubMed1990

Structural resemblance between the families of bacterial signal-transduction proteins and of G proteins revealed by graph theoretical techniques.

The first application of a novel technique for the identification of common folding motifs in proteins is presented. Using techniques derived from graph theory, developed in order to compare secondary structure motifs in proteins, we have established that there is a striking resemblance in the tertiary fold of the Salmonella typhimurium Che Y chemotaxis protein and that of the GDP-binding domain of Escherichia coli elongation factor Tu (EF Tu). These two protein structures are representatives of two major macromolecular classes: CheY is a signal-transduction protein with sequence homologies to a wide range of bacterial proteins involved in regulation of chemotaxis, membrane synthesis and sporulation; whilst EF Tu is one of a family of guanosine-nucleotide-binding proteins which include the ras oncogene proteins and signal-transducing G proteins. The similarity we have found extends far beyond the previously recognized resemblances of each protein's fold to that of a generic nucleotide-binding domain. The lack of significant sequence homology between the two classes of proteins may mean that the common fold of the two proteins constitutes a particularly stable folding motif. However, an alternative possibility is that the strong three-dimensional structural resemblance may be indicative of a remote shared common ancestry between the bacterial signal-transduction proteins and the GDP-binding proteins.

Algorithms↗
PubMed2003

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Cardiology↗
PubMed2003

The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Cardiology↗
PubMed2003

The conceptual basis of mathematics in cardiology IV: statistics and model fitting.

This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Cardiology↗
PubMed2025

Design Rules for Expanding PAM Compatibility in CRISPR-Cas9 from the VQR, VRER and EQR variants.

Expanding the range of Protospacer Adjacent Motifs (PAMs) recognized by CRISPR-Cas9 is essential for broadening genome-editing applications. Here, we combine molecular dynamics simulations with graph-theory and centrality analyses to dissect the principles of PAM recognition in three Cas9 variants - VQR, VRER, and EQR - that target non-canonical PAMs. We show that efficient recognition is not dictated solely by direct contacts between PAM-interacting residues and DNA, but also by a distal network that stabilizes the PAM-binding domain and preserves long-range communication with REC3, a hub that relays signals to the HNH nuclease. A key role emerges for the D1135V/E substitution, which enables stable DNA binding by K1107 and preserves key DNA phosphate locking interactions via S1109, securing stable PAM engagement. In contrast, variants carrying only R-to-Q substitutions at PAM-contacting residues, though predicted to enhance adenine recognition, destabilize the PAM-binding cleft, perturb REC3 dynamics, and disrupt allosteric coupling to HNH. Together, these findings establish that PAM recognition requires local stabilization, distal coupling, and entropic tuning, rather than a simple consequence of base-specific contacts. This framework provides guiding principles for engineering Cas9 variants with expanded PAM compatibility and improved editing efficiency.

Journal Article↗
PubMed1998

Software for constructing and verifying pedigrees within large genealogies and an application to the Old Order Amish of Lancaster County.

This paper describes PedHunter, a software package that facilitates creation and verification of pedigrees within large genealogies. A frequent problem in medical genetics is to connect distant relatives with a pedigree. PedHunter uses methods from graph theory to solve two versions of the pedigree connection problem for genealogies as well as other pedigree analysis problems. The pedigrees are produced by PedHunter as files in LINKAGE format ready for linkage analysis. PedHunter uses a relational database of genealogy data, with tables in specified format, for all calculations. The functionality and utility of PedHunter are illustrated by examples using the Amish Genealogy Database (AGDB), which was created for the Old Order Amish community of Lancaster County, Pennsylvania.

Christianity↗
PubMed2001

World Wide Web scaling exponent from Simon's 1955 model.

The statistical properties of the World Wide Web have attracted considerable attention recently since self-similar regimes were first observed in the scaling of its link structure. One characteristic quantity is the number of (in-)links k that point to a particular web page. Its probability distribution P(k) shows a pronounced power-law scaling P(k) approximately k(-gamma) that is not readily explained by standard random graph theory. Here, we recall a simple and elegant model for scaling phenomena in general copy- and growth-processes as proposed by Simon in 1955. When combined with an experimental measurement of network growth in the World Wide Web, this classical model is able to model the in-link dynamics and predicts the scaling exponent gamma=2.1 in accordance with observation.

Journal Article↗
PubMed2005

Spectral measures of bipartivity in complex networks.

We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.

Journal Article↗
PubMed2001

Exactly solvable model with two conductor-insulator transitions driven by impurities.

We present an exact analysis of two conductor-insulator transitions in the random graph model where low connectivity means high impurity concentration. The adjacency matrix of the random graph is used as a hopping Hamiltonian. We compute the height of the delta peak at zero energy in its spectrum exactly and describe analytically the structure and contribution of localized eigenvectors. The system is a conductor for average connectivities between 1.421 529ellipsis and 3.154 985ellipsis but an insulator in the other regimes. We explain the spectral singularity at average connectivity e = 2.718 281ellipsis and relate it to other enumerative problems in random graph theory.

Journal Article↗
PubMed1990

Graph-set analysis of hydrogen-bond patterns in organic crystals.

A method is presented based on graph theory for categorizing hydrogen-bond motifs in such a way that complex hydrogen-bond patterns can be disentangled, or decoded, systematically and consistently. This method is based on viewing hydrogen-bond patterns topologically as if they were intertwined nets with molecules as the nodes and hydrogen bonds as the lines. Surprisingly, very few parameters are needed to define the hydrogen-bond motifs comprising these networks. The methods for making these assignments, and examples of their chemical utility are given.

Chemical Phenomena↗
PubMed2001

A rate distortion optimal ECG coding algorithm.

Signal compression is an important problem encountered in many applications. Various techniques have been proposed over the years for addressing the problem. In this paper, we present a time domain algorithm based on the coding of line segments which are used to approximate the signal. These segments are fit in a way that is optimal in the rate distortion sense. Although the approach is applicable to any type of signal, we focus, in this paper, on the compression of electrocardiogram (ECG) signals. ECG signal compression has traditionally been tackled by heuristic approaches. However, it has been demonstrated [1] that exact optimization algorithms outperform these heuristic approaches by a wide margin with respect to reconstruction error. By formulating the compression problem as a graph theory problem, known optimization theory can be applied in order to yield optimal compression. In this paper, we present an algorithm that will guarantee the smallest possible distortion among all methods applying linear interpolation given an upper bound on the available number of bits. Using a varied signal test set, extensive coding experiments are presented. We compare the results from our coding method to traditional time domain ECG compression methods, as well as, to more recently developed frequency domain methods. Evaluation is based both on percentage root-mean-square difference (PRD) performance measure and visual inspection of the reconstructed signals. The results demonstrate that the exact optimization methods have superior performance compared to both traditional ECG compression methods and the frequency domain methods.

Algorithms↗