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At least 235 records · Page 13Linked to original sources
PubMed2002

Recursive domains in proteins.

The domain is a fundamental unit of protein structure. Numerous studies have analyzed folding patterns in protein domains of known structure to gain insight into the underlying protein folding process. Are such patterns a haphazard assortment or are they similar to sentences in a language, which can be generated by an underlying grammar? Specifically, can a small number of intuitively sensible rules generate a large class of folds, including feasible new folds? In this paper, we explore the extent to which four simple rules can generate the known all-beta folds, using tools from graph theory. As a control, an exhaustive set of beta-sandwiches was tested and found to be largely incompatible with such a grammar. The existence of a protein grammar has potential implications for both the mechanism of folding and the evolution of domains.

Dimerization↗
PubMed2005

A screening methodology for the identification and ranking of infrastructure vulnerabilities due to terrorism.

The extreme importance of critical infrastructures to modern society is widely recognized. These infrastructures are complex and interdependent. Protecting the critical infrastructures from terrorism presents an enormous challenge. Recognizing that society cannot afford the costs associated with absolute protection, it is necessary to identify and prioritize the vulnerabilities in these infrastructures. This article presents a methodology for the identification and prioritization of vulnerabilities in infrastructures. We model the infrastructures as interconnected digraphs and employ graph theory to identify the candidate vulnerable scenarios. These scenarios are screened for the susceptibility of their elements to a terrorist attack, and a prioritized list of vulnerabilities is produced. The prioritization methodology is based on multiattribute utility theory. The impact of losing infrastructure services is evaluated using a value tree that reflects the perceptions and values of the decisionmaker and the relevant stakeholders. These results, which are conditional on a specified threat, are provided to the decisionmaker for use in risk management. The methodology is illustrated through the presentation of a portion of the analysis conducted on the campus of the Massachusetts Institute of Technology.

Journal Article↗
PubMed2005

Formation of regulatory patterns during signal propagation in a Mammalian cellular network.

We developed a model of 545 components (nodes) and 1259 interactions representing signaling pathways and cellular machines in the hippocampal CA1 neuron. Using graph theory methods, we analyzed ligand-induced signal flow through the system. Specification of input and output nodes allowed us to identify functional modules. Networking resulted in the emergence of regulatory motifs, such as positive and negative feedback and feedforward loops, that process information. Key regulators of plasticity were highly connected nodes required for the formation of regulatory motifs, indicating the potential importance of such motifs in determining cellular choices between homeostasis and plasticity.

Algorithms↗
PubMed2005

Spectral properties of contact matrix: application to proteins.

A protein can be modelled by a set of points representing its amino acids. Topologically, this set of points is entirely defined by its contact matrix (adjacency matrix in graph theory). The contact matrix characterizing the relation between neighboring amino acids is deduced from Voronoi or Laguerre decomposition. This method allows contact matrices to be defined without any arbitrary cut-off that could induce arbitrary effects. Eigenvalues of these matrices are related with elementary excitations in proteins. We present some spectral properties of these matrices that reflect global properties of proteins. The eigenvectors indicate participation of each amino acids to the excitation modes of the proteins. It is interesting to compare the protein modelled as a close packing of amino acids, with a random close packing of spheres. The main features of the protein are those of a packing, a result that confirms the importance of the dense packing model for proteins. Nevertheless there are some properties, specific to the hierarchical organization of the protein: the primary chain order, the secondary structures and the domain structures.

Amino Acids↗
PubMed2000

Flexibility and critical hydrogen bonds in cytochrome c.

We show that protein flexibility can be characterized using graph theory, from a single protein conformation. Covalent and hydrogen bonds are modeled by distance and angular constraints, and a map is constructed of the regions in this network that are flexible or rigid, based on whether their dihedral bonds remain rotatable or are locked by other interactions in the network. This analysis takes only a second on a typical PC, and interatomic potentials; the most time-consuming aspect of molecular dynamics calculations, are not required. Our preliminary work has shown that this approach identifies the experimentally observed, biologically important flexible regions in HIV protease and lysine-arginine-ornithine binding protein. Here we analyze three evolutionarily distant cytochromes c, and find strong similarity between their flexible regions, despite having only 39% sequence identity. Furthermore, we show how the structural flexibility increases as the weaker hydrogen bonds are removed, as would happen under thermal denaturation of the protein. This approach identifies the critical hydrogen bonds that cross-link the tertiary structure.

Amino Acid Sequence↗
PubMed2005

Toward predictive models of mammalian cells.

Progress in experimental and theoretical biology is likely to provide us with the opportunity to assemble detailed predictive models of mammalian cells. Using a functional format to describe the organization of mammalian cells, we describe current approaches for developing qualitative and quantitative models using data from a variety of experimental sources. Recent developments and applications of graph theory to biological networks are reviewed. The use of these qualitative models to identify the topology of regulatory motifs and functional modules is discussed. Cellular homeostasis and plasticity are interpreted within the framework of balance between regulatory motifs and interactions between modules. From this analysis we identify the need for detailed quantitative models on the basis of the representation of the chemistry underlying the cellular process. The use of deterministic, stochastic, and hybrid models to represent cellular processes is reviewed, and an initial integrated approach for the development of large-scale predictive models of a mammalian cell is presented.

Amino Acid Motifs↗
PubMed1987

Solvent flow in osmosis and hydraulics: network thermodynamics and representation by bond graphs.

A tutorial introduction to network thermodynamics and bond graphs as a modeling technique for any physiochemical system is presented with a particular emphasis on reaction diffusion systems. It combines the generality of nonequilibrium thermodynamics with the advantages of a graph theory. It is applied to the representation of osmotic and hydraulic flows across a semipermeable membrane on the basis of the solvent diffusion theory of osmosis. This theory allows for an easy derivation of the van't Hoff law of osmotic pressure from the Fick law of diffusion. Molar flows and volume flows are transformed into one another by transducers, the modulus of which is the partial molar volume of water, in such a way that power is conserved by a reciprocal transformation between the chemical potential and the pressure. Osmotic and hydraulic resistances are calculated, and their dependence on pore size is estimated.

Diffusion↗
PubMed2000

New algorithms based on the Voronoi Diagram applied in a pilot study on normal mucosa and carcinomas.

An adequate reproducibility in the description of tissue architecture is still a challenge to diagnostic pathology, sometimes with unfortunate prognostic implications. To assess a possible diagnostic and prognostic value of quantitiative tissue architecture analysis, structural features based on the Voronoi Diagram (VD) and its subgraphs were developed and tested. A series of 27 structural features were developed and tested in a pilot study of 30 cases of prostate cancer, 10 cases of cervical carcinomas, 8 cases of tongue cancer and 8 cases of normal oral mucosa. Grey level images were acquired from hematoxyline-eosine (HE) stained sections by a charge coupled device (CCD) camera mounted on a microscope connected to a personal computer (PC) with an image array processor. From the grey level images obtained, cell nuclei were automatically segmented and the geometrical centres of cell nuclei were computed. The resulting 2-dimensional (2D) swarm of pointlike seeds distributed in a flat plane was the basis for construction of the VD and its subgraphs. From the polygons, triangulations and arborizations thus obtained, 27 structural features were computed as numerical values. Comparison of groups (normal vs. cancerous oral mucosa, cervical and prostate carcinomas with good and poor prognosis) with regard to distribution in the values of the structural features was performed with Student's t-test. We demonstrate that some of the structural features developed are able to distinguish structurally between normal and cancerous oral mucosa (P = 0.001), and between good and poor outcome groups in prostatic (P = 0.001) and cervical carcinomas (P = 0.001). We present results confirming previous findings that graph theory based algorithms are useful tools for describing tissue architecture (e.g., normal versus malignant). The present study also indicates that these methods have a potential for prognostication in malignant epithelial lesions.

Algorithms↗
PubMed1998

Classification of temporal patterns in dynamic biological networks.

A general method is presented to classify temporal patterns generated by rhythmic biological networks when synaptic connections and cellular properties are known. The method is discrete in nature and relies on algebraic properties of state transitions and graph theory. Elements of the set of rhythms generated by a network are compared using a metric that quantifies the functional differences among them. The rhythms are then classified according to their location in a metric space. Examples are given, and biological implications are discussed.

Models, Neurological↗
PubMed2006

Small-world brain networks.

Many complex networks have a small-world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any (distant) pair of nodes due to the existence of relatively few long-range connections. This is an attractive model for the organization of brain anatomical and functional networks because a small-world topology can support both segregated/specialized and distributed/integrated information processing. Moreover, small-world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity. The authors introduce some of the key mathematical concepts in graph theory required for small-world analysis and review how these methods have been applied to quantification of cortical connectivity matrices derived from anatomical tract-tracing studies in the macaque monkey and the cat. The evolution of small-world networks is discussed in terms of a selection pressure to deliver cost-effective information-processing systems. The authors illustrate how these techniques and concepts are increasingly being applied to the analysis of human brain functional networks derived from electroencephalography/magnetoencephalography and fMRI experiments. Finally, the authors consider the relevance of small-world models for understanding the emergence of complex behaviors and the resilience of brain systems to pathological attack by disease or aberrant development. They conclude that small-world models provide a powerful and versatile approach to understanding the structure and function of human brain systems.

Animals↗
PubMed2006

Ancient genomic architecture for mammalian olfactory receptor clusters.

BACKGROUND: Mammalian olfactory receptor (OR) genes reside in numerous genomic clusters of up to several dozen genes. Whole-genome sequence alignment nets of five mammals allow their comprehensive comparison, aimed at reconstructing the ancestral olfactory subgenome. RESULTS: We developed a new and general tool for genome-wide definition of genomic gene clusters conserved in multiple species. Syntenic orthologs, defined as gene pairs showing conservation of both genomic location and coding sequence, were subjected to a graph theory algorithm for discovering CLICs (clusters in conservation). When applied to ORs in five mammals, including the marsupial opossum, more than 90% of the OR genes were found within a framework of 48 multi-species CLICs, invoking a general conservation of gene order and composition. A detailed analysis of individual CLICs revealed multiple differences among species, interpretable through species-specific genomic rearrangements and reflecting complex mammalian evolutionary dynamics. One significant instance involves CLIC #1, which lacks a human member, implying the human-specific deletion of an OR cluster, whose mouse counterpart has been tentatively associated with isovaleric acid odorant detection. CONCLUSION: The identified multi-species CLICs demonstrate that most of the mammalian OR clusters have a common ancestry, preceding the split between marsupials and placental mammals. However, only two of these CLICs were capable of incorporating chicken OR genes, parsimoniously implying that all other CLICs emerged subsequent to the avian-mammalian divergence.

Animals↗
PubMed2006

Enhancing text categorization with semantic-enriched representation and training data augmentation.

OBJECTIVE: Acquiring and representing biomedical knowledge is an increasingly important component of contemporary bioinformatics. A critical step of the process is to identify and retrieve relevant documents among the vast volume of modern biomedical literature efficiently. In the real world, many information retrieval tasks are difficult because of high data dimensionality and the lack of annotated examples to train a retrieval algorithm. Under such a scenario, the performance of information retrieval algorithms is often unsatisfactory, therefore improvements are needed. DESIGN: We studied two approaches that enhance the text categorization performance on sparse and high data dimensionality: (1) semantic-preserving dimension reduction by representing text with semantic-enriched features; and (2) augmenting training data with semi-supervised learning. A probabilistic topic model was applied to extract major semantic topics from a corpus of text of interest. The representation of documents was projected from the high-dimensional vocabulary space onto a semantic topic space with reduced dimensionality. A semi-supervised learning algorithm based on graph theory was applied to identify potential positive training cases, which were further used to augment training data. The effects of data transformation and augmentation on text categorization by support vector machine (SVM) were evaluated. RESULTS AND CONCLUSION: Semantic-enriched data transformation and the pseudo-positive-cases augmented training data enhance the efficiency and performance of text categorization by SVM.

Algorithms↗
PubMed2005

In vitro RNA random pools are not structurally diverse: a computational analysis.

In vitro selection of functional RNAs from large random sequence pools has led to the identification of many ligand-binding and catalytic RNAs. However, the structural diversity in random pools is not well understood. Such an understanding is a prerequisite for designing sequence pools to increase the probability of finding complex functional RNA by in vitro selection techniques. Toward this goal, we have generated by computer five random pools of RNA sequences of length up to 100 nt to mimic experiments and characterized the distribution of associated secondary structural motifs using sets of possible RNA tree structures derived from graph theory techniques. Our results show that such random pools heavily favor simple topological structures: For example, linear stem-loop and low-branching motifs are favored rather than complex structures with high-order junctions, as confirmed by known aptamers. Moreover, we quantify the rise of structural complexity with sequence length and report the dominant class of tree motifs (characterized by vertex number) for each pool. These analyses show not only that random pools do not lead to a uniform distribution of possible RNA secondary topologies; they point to avenues for designing pools with specific simple and complex structures in equal abundance in the goal of broadening the range of functional RNAs discovered by in vitro selection. Specifically, the optimal RNA sequence pool length to identify a structure with x stems is 20x.

Computational Biology↗
PubMed2025

Exploring the transmission of cognitive task information through optimal brain pathways.

Understanding the large-scale information processing that underlies complex human cognition is the central goal of cognitive neuroscience. While emerging activity flow models demonstrate that cognitive task information is transferred by interregional functional or structural connectivity, graph-theory-based models typically assume that neural communication occurs via the shortest path of brain networks. However, whether the shortest path is the optimal route for empirical cognitive information transmission remains unclear. Based on a large-scale activity flow mapping framework, we found that the performance of activity flow prediction with the shortest path was significantly lower than that with the direct path. The shortest path routing was superior to other network communication strategies, including search information, path ensembles, and navigation. Intriguingly, the shortest path outperformed the direct path in activity flow prediction when the physical distance constraint and asymmetric routing contribution were simultaneously considered. This study not only challenges the shortest path assumption through empirical network models but also suggests that cognitive task information routing is constrained by the spatial and functional embedding of the brain network.

Humans↗
PubMed2002

Branching-pattern analysis of the dendritic arborization in the thalamic nuclei of the rat brain.

We investigated the dendritic patterns of rapid Golgi-impregnated, highly similar multipolar neurons from two functionally different thalamic regions of the rat brain: two dorsal nuclei (the nucleus laterodorsalis thalami, pars dorsomedialis and the nucleus laterodorsalis thalami, pars ventrolateralis), and two ventral nuclei (the nucleus ventrolateralis thalami and the nucleus ventromedialis thalami). The analysis involved conventional morphometric parameters (height and size) and a new parameter derived from graph theory, the relative imbalance (RI), derived from the branching patterns of the dendrites, which permits quantitative characterization of the dendritic arborization of a neuron. On this basis, neurons can be grouped into three fundamentally different types: type A, or highly-polarized (imbalanced) neurons (RI values close to 1); type B, or medium-polarized neurons (RI values around 0.5); and type C, or balanced neurons with low polarization (RI values close to 0). The orientations of the dendritic arbor, and thus the receptive fields, of the dorsal and ventral thalamic neurons, were mutually perpendicular. The H and S values indicated that the neurons in the dorsal and ventral thalamic nuclei differed significantly. However, their RI values demonstrated that they were similar neurons of type B. Our data reveal that 1 ) the dendritic arbor cannot be reliably characterized purely on the basis of height and size, and 2) RI is a valuable morphometric parameter that identifies the true nature of the dendritic arborization.

Animals↗
PubMed2006

Quantifying population substructure: extending the graph-theoretic approach.

Among the few universal themes in ecology is that resources, energy, and organisms themselves, are patchily distributed. This patchy distribution imposes a need for some level of dispersal or connectivity among spatially separate patches in order to allow organisms to acquire sufficient resources for survival. To date, general patterns of connectivity have not emerged. This is, in part, because different species respond to different scales of patchiness. I propose an extension of the graph-theoretic approach to control for such differences and reveal potential generalities about how natural populations are organized. Using statistical methods and simple applications of graph theory, continuum percolation, and metapopulation models, I demonstrate a pattern of hierarchical clustering among populations in both a plant-pathogen system at an extent of 1000 m and gene flow in a salamander species across a subcontinental range. Results suggest that some patches or populations have a disproportionately high importance to the maintenance of overall connectivity in the system within and across scales.

Animals↗
PubMed1991

Quantitative and methodological aspects of stimulus equivalence.

The number of different ways of linking stimuli in the training phase of a conditional discrimination procedure designed to teach equivalence relations has hitherto been underestimated. An algorithm from graph theory that produces the correct number of such different ways is given. The establishment of equivalence relations requires transitive stimulus control. A misconception in a previous analysis of the conditions necessary for demonstrating transitive stimulus control is indicated. This misconception concerns responding in an unreinforced test trial to a negative rather than a positive comparison stimulus. Such behavior cannot be attributed to discriminative control by degree of association with reinforcement if the negative comparison stimulus has been less associated with reinforcement than the positive comparison stimulus in an antecedent training phase.

Journal Article↗
PubMed2003

Modeling proteome networks with range-dependent graphs.

In this paper we consider the problem of characterizing and modeling large-scale protein-protein association networks using a class of range-dependent graphs which possess appropriate small world properties. These graphs may be employed in representing given association network using a maximum likelihood approach. This in turn annotates every observed association with its 'range', representing the tendency for such an association to be transitive. The application of a very rapidly developing field of graph theory to the emerging field of proetemics is novel and allows for a many-to-many relationship between individual proteins and groupings of proteins, which in turn may correspond to distinct functional behavior.

Models, Biological↗