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At least 343 records · Page 19Linked to original sources
PubMed2005

Scale-free network hidden in a collapsing polymer.

We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent gamma=1/(2-c) up to a cutoff degree dc proportional to L(2-c), where is the loop exponent for dense polymers (c=11/8 in two dimensions) and is the length of the polymer. Our results exemplify how a scale-free network can emerge from standard criticality.

Journal Article↗
PubMedDate not supplied

TreePlus: interactive exploration of networks with enhanced tree layouts.

Despite extensive research, it is still difficult to produce effective interactive layouts for large graphs. Dense layout and occlusion make food webs, ontologies, and social networks difficult to understand and interact with. We propose a new interactive Visual Analytics component called TreePlus that is based on a tree-style layout. TreePlus reveals the missing graph structure with visualization and interaction while maintaining good readability. To support exploration of the local structure of the graph and gathering of information from the extensive reading of labels, we use a guiding metaphor of "Plant a seed and watch it grow." It allows users to start with a node and expand the graph as needed, which complements the classic overview techniques that can be effective at (but often limited to) revealing clusters. We describe our design goals, describe the interface, and report on a controlled user study with 28 participants comparing TreePlus with a traditional graph interface for six tasks. In general, the advantage of TreePlus over the traditional interface increased as the density of the displayed data increased. Participants also reported higher levels of confidence in their answers with TreePlus and most of them preferred TreePlus.

Algorithms↗
PubMed2005

Scaling of optimal-path-lengths distribution in complex networks.

We study the distribution of optimal path lengths in random graphs with random weights associated with each link ("disorder"). With each link i we associate a weight tau(i) = exp (a r(i)), where r(i) is a random number taken from a uniform distribution between 0 and 1, and the parameter a controls the strength of the disorder. We suggest, in an analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form that is controlled by the expression (1/p(c)) (l(infinity)/a), where l(infinity) is the optimal path length in strong disorder (a --> infinity) and p(c) is the percolation threshold. This relation is supported by numerical simulations for Erdos-Rényi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network.

Journal Article↗
PubMed2004

Physical network models.

We develop a new framework for inferring models of transcriptional regulation. The models, which we call physical network models, are annotated molecular interaction graphs. The attributes in the model correspond to verifiable properties of the underlying biological system such as the existence of protein-protein and protein-DNA interactions, the directionality of signal transduction in protein-protein interactions, as well as signs of the immediate effects of these interactions. Possible configurations of these variables are constrained by the available data sources. Some of the data sources, such as factor-binding data, involve measurements that are directly tied to the variables in the model. Other sources, such as gene knock-outs, are functional in nature and provide only indirect evidence about the variables. We associate each observed knock-out effect in the deletion mutant data with a set of causal paths (molecular cascades) that could in principle explain the effect, resulting in aggregate constraints about the physical variables in the model. The most likely settings of all the variables, specifying the most likely graph annotations, are found by a recursive application of the max-product algorithm. By testing our approach on datasets related to the pheromone response pathway in S. cerevisiae, we demonstrate that the resulting model is consistent with previous studies about the pathway. Moreover, we successfully predict gene knock-out effects with a high degree of accuracy in a cross-validation setting. When applying this approach genome-wide, we extract submodels consistent with previous studies. The approach can be readily extended to other data sources or to facilitate automated experimental design.

Computational Biology↗
PubMed2004

An efficient algorithm for detecting frequent subgraphs in biological networks.

MOTIVATION: With rapidly increasing amount of network and interaction data in molecular biology, the problem of effectively analyzing this data is an important one. Graph theoretic formalisms, commonly used for these analysis tasks, often lead to computationally hard problems due to their relation with subgraph isomorphism. RESULTS: This paper presents an innovative new algorithm for detecting frequently occurring patterns and modules in biological networks. Using an innovative graph simplification technique, which is ideally suited to biological networks, our algorithm renders these problems computationally tractable. Indeed, we show experimentally that our algorithm can extract frequently occurring patterns in metabolic pathways extracted from the KEGG database within seconds. The proposed model and algorithm are applicable to a variety of biological networks either directly or with minor modifications. AVAILABILITY: Implementation of the proposed algorithms in the C programming language is available as open source at http://www.cs.purdue.edu/homes/koyuturk/pathway/

Algorithms↗
PubMed2003

Naturally deducing estimate for the coefficient of CELSS closure.

The term Closed Ecological System (CES) is in wide use. However there is no generally accepted measure of the closure of ecological systems. In order to obtain reproducibility of experiments with natural and man-made CES (with respect to degree of closure) some universal estimate needs to be developed. Understanding ecological systems as a network and closure as the degree of matter recycling allows the use of matrix graphs. Graphs are very natural forms for the presentation of the network of matter flows in ecosystems. An estimate equal to the sum of products of weights of oriented edges that constitute contour is suggested as a measure of the degree of closure in ecosystems. It is shown that this estimate can be uniformly applied to ecosystems of arbitrary size and configuration of flows.

Biomass↗
PubMed2004

Statistical mechanics of networks.

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the same role in the study of networks as is played by the Boltzmann distribution in classical statistical mechanics; they offer the best prediction of network properties subject to the constraints imposed by a given set of observations. We give exact solutions of models within this class that incorporate arbitrary degree distributions and arbitrary but independent edge probabilities. We also discuss some more complex examples with correlated edges that can be solved approximately or exactly by adapting various familiar methods, including mean-field theory, perturbation theory, and saddle-point expansions.

Journal Article↗
PubMed2004

Weighted competition scale-free network.

While many scale-free (SF) networks have been introduced recently for complex systems, most of them are binary random graphs and the rate at which the node in the network increases its connectivity depends on the time it arrived. We propose a model of weighted scale-free networks incorporating a fit-gets-richer scheme which means the connectivity of the node depends on both the degree and fitness of the node. The topology and weights of links of the network evolve as time goes on. The combined numerical and analytical approach indicates that asymptotically the scaling behaviors of the total weight distribution and the connectivity distribution are identical. The asymptotical sameness has also been observed in real networks.

Journal Article↗
PubMed2003

Stoichiometric design of metabolic networks: multifunctionality, clusters, optimization, weak and strong robustness.

Starting from a limited set of reactions describing changes in the carbon skeleton of biochemical compounds complete sets of metabolic networks are constructed. The networks are characterized by the number and types of participating reactions. Elementary networks are defined by the condition that a specific chemical conversion can be performed by a set of given reactions and that this ability will be lost by elimination of any of these reactions. Groups of networks are identified with respect to their ability to perform a certain number of metabolic conversions in an elementary way which are called the network's functions. The number of the network functions defines the degree of multifunctionality. Transitions between networks and mutations of networks are defined by exchanges of single reactions. Different mutations exist such as gain or loss of function mutations and neutral mutations. Based on these mutations neighbourhood relations between networks are established which are described in a graph theoretical way. Basic properties of these graphs are determined such as diameter, connectedness, distance distribution of pairs of vertices. A concept is developed to quantify the robustness of networks against changes in their stoichiometry where we distinguish between strong and weak robustness. Evolutionary algorithms are applied to study the development of network populations under constant and time dependent environmental conditions. It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured. Under changing environmental conditions multifunctional networks prove to be optimal and will be selected.

Algorithms↗
PubMed2003

Spectra of complex networks.

We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local treelike structure), exact equations are derived. These equations are generalized to the case of networks with correlations between neighboring vertices. The tail of the density of eigenvalues rho(lambda) at large /lambda/ is related to the behavior of the vertex degree distribution P(k) at large k. In particular, as P(k) approximately k(-gamma), rho(lambda) approximately /lambda/(1-2 gamma). We propose a simple approximation, which enables us to calculate spectra of various graphs analytically. We analyze spectra of various complex networks and discuss the role of vertices of low degree. We show that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real-world networks, e.g., of the Internet.

Journal Article↗
PubMed1995

A conceptual graphs modeling of UMLS components.

The Unified Medical Language System (UMLS) of the U.S. National Library of Medicine is a complex collection of terms, concepts, and relationships derived from standard classifications. Potential applications would benefit from a high level representation of its components. This paper proposes a conceptual representation of both the Metathesaurus and the Semantic Network of the UMLS based on conceptual graphs. It shows that the addition of a dictionary of concepts to the UMLS knowledge base allows the capability to exploit it pertinently. This dictionary defines more precisely the core concepts and adds constraints on their use. Constraints are dedicated to guide an "intelligent" browsing of the UMLS knowledge sources.

Dictionaries as Topic↗
PubMed2004

Families and clustering in a natural numbers network.

We develop a network in which the natural numbers are the vertices. The decomposition of natural numbers by prime numbers is used to establish the connections. We perform data collapse and show that the degree distribution of these networks scales linearly with the number of vertices. We explore the families of vertices in connection with prime numbers decomposition. We compare the average distance of the network and the clustering coefficient with the distance and clustering coefficient of the corresponding random graph. In case we set connections among vertices each time the numbers share a common prime number the network has properties similar to a random graph. If the criterion for establishing links becomes more selective, only prime numbers greater than p(l) are used to establish links, where the network has high clustering coefficient.

Journal Article↗
PubMed2006

Edge-count probabilities for the identification of local protein communities and their organization.

We present a computational approach based on a local search strategy that discovers sets of proteins that preferentially interact with each other. Such sets are referred to as protein communities and are likely to represent functional modules. Preferential interaction between module members is quantified via an analytical framework based on a network null model known as the random graph with given expected degrees. Based on this framework, the concept of local protein community is generalized to that of community of communities. Protein communities and higher-level structures are extracted from two yeast protein interaction data sets and a network of published interactions between human proteins. The high level structures obtained with the human network correspond to broad biological concepts such as signal transduction, regulation of gene expression, and intercellular communication. Many of the obtained human communities are enriched, in a statistically significant way, for proteins having no clear orthologs in lower organisms. This indicates that the extracted modules are quite coherent in terms of function.

Cell Adhesion↗
PubMed1992

Neonatal physiological trend monitoring by computer.

A premature baby born up to four months early is a fragile patient dependent on intensive care. The body systems are physiologically immature and so tolerate stress badly. The tendency of these infants to rapidly deteriorate, has led us to use a cotside computer monitoring system which displays physiological trends. Information from standard neonatal monitors is accessed by individual cotside PC's linked to a central network server and Doctors terminal. Trend graphs can be easily manipulated, displaying from 7 minutes to 3 days of physiological information on a single screen. Pathology may be observed in real time as it occurs. The system has 3 main areas of use, (a) as a real time clinical aid to patient management, e.g. apnoea of the newborn; (b) as a research tool, demonstrating the effects of procedures on physiology; (c) for educating members of staff about how physiological events develop. Data is saved for the whole of each neonates intensive care stay. Assessment of staff and parent attitudes by questionnaire have been favourable.

Humans↗
PubMed2006

A comparative study of cells in inflammation, EAE and MS using biomedical literature data mining.

Biomedical literature and database annotations, available in electronic forms, contain a vast amount of knowledge resulting from global research. Users, attempting to utilize the current state-of-the-art research results are frequently overwhelmed by the volume of such information, making it difficult and time-consuming to locate the relevant knowledge. Literature mining, data mining, and domain specific knowledge integration techniques can be effectively used to provide a user-centric view of the information in a real-world biological problem setting. Bioinformatics tools that are based on real-world problems can provide varying levels of information content, bridging the gap between biomedical and bioinformatics research. We have developed a user-centric bioinformatics research tool, called BioMap, that can provide a customized, adaptive view of the information and knowledge space. BioMap was validated by using inflammatory diseases as a problem domain to identify and elucidate the associations among cells and cellular components involved in multiple sclerosis (MS) and its animal model, experimental allergic encephalomyelitis (EAE). The BioMap system was able to demonstrate the associations between cells directly excavated from biomedical literature for inflammation, EAE and MS. These association graphs followed the scale-free network behavior (average gamma = 2.1) that are commonly found in biological networks.

Animals↗
PubMed2004

BACUS: A Bayesian protocol for the identification of protein NOESY spectra via unassigned spin systems.

NMR frequency assignments are usually considered a prerequisite for the analysis of NOESY spectra, in turn required for the calculation of biomolecular structures. In contrast, as we propose here, relatively high numbers of unambiguous NOE identities can be consistently achieved in an automated manner by relying only on grouping resonances into connected spin systems. To achieve this goal, we have developed for proteins two protocols, SPI and BACUS, based on Bayesian inference. SPI (Grishaev and Llinás, 2002c) produces a list of the (1)H resonance frequencies from homo- and hetero-nuclear multidimensional spectra, grouped into effective spin systems. BACUS automatically establishes probabilistic identities of NOESY cross-peaks in terms of the chemical shifts provided by SPI. BACUS requires neither assignment of resonances nor an initial structural model. It successfully copes with chemical shift overlap and does so without cycling through 3D structure calculations. The method exploits the self-consistency of the NOESY graph by taking advantage of a network of J- as well as NOE-connected "reporter" protons sorted via SPI. BACUS was validated by tests on experimental NOESY data recorded for the col 2 and kringle 2 domains.

Bayes Theorem↗
PubMed2004

The metabolic world of Escherichia coli is not small.

To elucidate the organizational and evolutionary principles of the metabolism of living organisms, recent studies have addressed the graph-theoretic analysis of large biochemical networks responsible for the synthesis and degradation of cellular building blocks [Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N. & Barabási, A. L. (2000) Nature 407, 651-654; Wagner, A. & Fell, D. A. (2001) Proc. R. Soc. London Ser. B 268, 1803-1810; and Ma, H.-W. & Zeng, A.-P. (2003) Bioinformatics 19, 270-277]. In such studies, the global properties of the network are computed by considering enzymatic reactions as links between metabolites. However, the pathways computed in this manner do not conserve their structural moieties and therefore do not correspond to biochemical pathways on the traditional metabolic map. In this work, we reassessed earlier results by digitizing carbon atomic traces in metabolic reactions annotated for Escherichia coli. Our analysis revealed that the average path length of its metabolism is much longer than previously thought and that the metabolic world of this organism is not small in terms of biosynthesis and degradation.

Escherichia coli↗
PubMed2006

Modular organization of protein interaction networks.

MOTIVATION: Accumulating evidence suggests that biological systems are composed of interacting, separable, functional modules. Identifying these modules is essential to understand the organization of biological systems. RESULT: In this paper, we present a framework to identify modules within biological networks. In this approach, the concept of degree is extended from the single vertex to the sub-graph, and a formal definition of module in a network is used. A new agglomerative algorithm was developed to identify modules from the network by combining the new module definition with the relative edge order generated by the Girvan-Newman (G-N) algorithm. A JAVA program, MoNet, was developed to implement the algorithm. Applying MoNet to the yeast core protein interaction network from the database of interacting proteins (DIP) identified 86 simple modules with sizes larger than three proteins. The modules obtained are significantly enriched in proteins with related biological process Gene Ontology terms. A comparison between the MoNet modules and modules defined by Radicchi et al. (2004) indicates that MoNet modules show stronger co-clustering of related genes and are more robust to ties in betweenness values. Further, the MoNet output retains the adjacent relationships between modules and allows the construction of an interaction web of modules providing insight regarding the relationships between different functional modules. Thus, MoNet provides an objective approach to understand the organization and interactions of biological processes in cellular systems. AVAILABILITY: MoNet is available upon request from the authors.

Algorithms↗