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PubMed2004

Disulfide connectivity prediction using recursive neural networks and evolutionary information.

MOTIVATION: We focus on the prediction of disulfide bridges in proteins starting from their amino acid sequence and from the knowledge of the disulfide bonding state of each cysteine. The location of disulfide bridges is a structural feature that conveys important information about the protein main chain conformation and can therefore help towards the solution of the folding problem. Existing approaches based on weighted graph matching algorithms do not take advantage of evolutionary information. Recursive neural networks (RNN), on the other hand, can handle in a natural way complex data structures such as graphs whose vertices are labeled by real vectors, allowing us to incorporate multiple alignment profiles in the graphical representation of disulfide connectivity patterns. RESULTS: The core of the method is the use of machine learning tools to rank alternative disulfide connectivity patterns. We develop an ad-hoc RNN architecture for scoring labeled undirected graphs that represent connectivity patterns. In order to compare our algorithm with previous methods, we report experimental results on the SWISS-PROT 39 dataset. We find that using multiple alignment profiles allows us to obtain significant prediction accuracy improvements, clearly demonstrating the important role played by evolutionary information. AVAILABILITY: The Web interface of the predictor is available at http://neural.dsi.unifi.it/cysteines

Algorithms↗

PubMed1993

A conceptual model for information retrieval with UMLS.

Information retrieval in large information databases is a non-deterministic process which needs a sequence of search steps generally. One of the main problems to which the end-users are faced is to parse efficiently their questions into the query language that the computer systems allow. 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 the end-users querieson the basis of the thesaurus and the semantic network of the UMLS project.

Information Storage and Retrieval↗

PubMedDate not supplied

Knowledge-based approaches to the maintenance of a large controlled medical terminology.

OBJECTIVE: Develop a knowledge-based representation for a controlled terminology of clinical information to facilitate creation, maintenance, and use of the terminology. DESIGN: The Medical Entities Dictionary (MED) is a semantic network, based on the Unified Medical Language System (UMLS), with a directed acyclic graph to represent multiple hierarchies. Terms from four hospital systems (laboratory, electrocardiography, medical records coding, and pharmacy) were added as nodes in the network. Additional knowledge about terms, added as semantic links, was used to assist in integration, harmonization, and automated classification of disparate terminologies. RESULTS: The MED contains 32,767 terms and is in active clinical use. Automated classification was successfully applied to terms for laboratory specimens, laboratory tests, and medications. One benefit of the approach has been the automated inclusion of medications into multiple pharmacologic and allergenic classes that were not present in the pharmacy system. Another benefit has been the reduction of maintenance efforts by 90%. CONCLUSION: The MED is a hybrid of terminology and knowledge. It provides domain coverage, synonymy, consistency of views, explicit relationships, and multiple classification while preventing redundancy, ambiguity (homonymy) and misclassification.

Computer Simulation↗

PubMed2005

Complex trait analysis of gene expression uncovers polygenic and pleiotropic networks that modulate nervous system function.

Patterns of gene expression in the central nervous system are highly variable and heritable. This genetic variation among normal individuals leads to considerable structural, functional and behavioral differences. We devised a general approach to dissect genetic networks systematically across biological scale, from base pairs to behavior, using a reference population of recombinant inbred strains. We profiled gene expression using Affymetrix oligonucleotide arrays in the BXD recombinant inbred strains, for which we have extensive SNP and haplotype data. We integrated a complementary database comprising 25 years of legacy phenotypic data on these strains. Covariance among gene expression and pharmacological and behavioral traits is often highly significant, corroborates known functional relations and is often generated by common quantitative trait loci. We found that a small number of major-effect quantitative trait loci jointly modulated large sets of transcripts and classical neural phenotypes in patterns specific to each tissue. We developed new analytic and graph theoretical approaches to study shared genetic modulation of networks of traits using gene sets involved in neural synapse function as an example. We built these tools into an open web resource called WebQTL that can be used to test a broad array of hypotheses.

Animals↗

PubMed2004

Comment on "Families and clustering in a natural numbers network".

Corso [Phys. Rev. E 69, 036106 (2004)] constructs a family of graphs from subsets of the natural numbers, and numerically estimates diameter, degree and clustering. We give exact asymptotic formulas for these quantities, and thereby argue that number theory is a more appropriate tool than simulation.

Comment↗

PubMed2004

Analysis of weighted networks.

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum-flow-minimum-cut theorem.

Journal Article↗

PubMed2005

Uncovering the overlapping community structure of complex networks in nature and society.

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.

Community Networks↗

PubMed2004

A Boolean Hebb rule for binary associative memory design.

A binary associative memory design procedure that gives a Hopfield network with a symmetric binary weight matrix is introduced in this paper. The proposed method is based on introducing the memory vectors as maximal independent sets to an undirected graph, which is constructed by Boolean operations analogous to the conventional Hebb rule. The parameters of the resulting network is then determined via the adjacency matrix of this graph in order to find a maximal independent set whose characteristic vector is close to the given distorted vector. We show that the method provides attractiveness for each memory vector and avoids spurious memories whenever the set of given memory vectors satisfy certain compatibility conditions, which implicitly imply sparsity. The applicability of the design method is finally investigated by a quantitative analysis of the compatibility conditions.

Memory↗

PubMed1990

Graph-theoretic approach to metabolic pathways.

A graph-theoretic approach is shown to be applicable within the framework of the metabolic control analysis. Kinetic differential equations linearized near a steady state are presented as kinetic graphs (schemes), their structure being correlated with kinetic properties of corresponding metabolic networks. The global properties may be expressed in terms of the local properties for steady states of metabolic systems. Instability, bistability, and concentrational oscillations are shown to be induced by specific graph fragments. The approach is illustrated by an example of systems showing the oscillatory kinetic behaviour.

Biotransformation↗

PubMed2005

Supervised enzyme network inference from the integration of genomic data and chemical information.

MOTIVATION: The metabolic network is an important biological network which relates enzyme proteins and chemical compounds. A large number of metabolic pathways remain unknown nowadays, and many enzymes are missing even in known metabolic pathways. There is, therefore, an incentive to develop methods to reconstruct the unknown parts of the metabolic network and to identify genes coding for missing enzymes. RESULTS: This paper presents new methods to infer enzyme networks from the integration of multiple genomic data and chemical information, in the framework of supervised graph inference. The originality of the methods is the introduction of chemical compatibility as a constraint for refining the network predicted by the network inference engine. The chemical compatibility between two enzymes is obtained automatically from the information encoded by their Enzyme Commission (EC) numbers. The proposed methods are tested and compared on their ability to infer the enzyme network of the yeast Saccharomyces cerevisiae from four datasets for enzymes with assigned EC numbers: gene expression data, protein localization data, phylogenetic profiles and chemical compatibility information. It is shown that the prediction accuracy of the network reconstruction consistently improves owing to the introduction of chemical constraints, the use of a supervised approach and the weighted integration of multiple datasets. Finally, we conduct a comprehensive prediction of a global enzyme network consisting of all enzyme candidate proteins of the yeast to obtain new biological findings. AVAILABILITY: Softwares are available upon request.

Algorithms↗

PubMed2004

Explicit spectral formulas for scaling quantum graphs.

We present an exact analytical solution of the spectral problem of quasi-one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that despite their classical stochasticity all scaling quantum graphs are explicitly solvable in the form E(n) =f (n) , where n is the sequence number of the energy level of the quantum graph and f is a known function, which depends only on the physical and geometrical properties of the quantum graph. Our method of solution motivates a new classification scheme for quantum graphs: we show that each quantum graph can be uniquely assigned an integer m reflecting its level of complexity. We show that a network of taut strings with piecewise constant mass density provides an experimentally realizable analogue system of scaling quantum graphs.

Journal Article↗

PubMed2006

CFinder: locating cliques and overlapping modules in biological networks.

UNLABELLED: Most cellular tasks are performed not by individual proteins, but by groups of functionally associated proteins, often referred to as modules. In a protein association network modules appear as groups of densely interconnected nodes, also called communities or clusters. These modules often overlap with each other and form a network of their own, in which nodes (links) represent the modules (overlaps). We introduce CFinder, a fast program locating and visualizing overlapping, densely interconnected groups of nodes in undirected graphs, and allowing the user to easily navigate between the original graph and the web of these groups. We show that in gene (protein) association networks CFinder can be used to predict the function(s) of a single protein and to discover novel modules. CFinder is also very efficient for locating the cliques of large sparse graphs. AVAILABILITY: CFinder (for Windows, Linux and Macintosh) and its manual can be downloaded from http://angel.elte.hu/clustering. SUPPLEMENTARY INFORMATION: Supplementary data are available on Bioinformatics online.

Biology↗

PubMed2002

Epidemic threshold in structured scale-free networks.

We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the susceptible-infected-susceptible model of epidemics the prevalence undergoes a phase transition at a finite threshold of the transmission probability. Comparing with the absence of a finite threshold in networks with purely random wiring, our result suggests that high clustering (modularity) and degree correlations protect scale-free networks against the spreading of viruses. We introduce and verify a quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs.

Disease Outbreaks↗

PubMed2026

NExON-Bayes: a Bayesian approach to network estimation informed by ordinal covariates.

MOTIVATION: In heterogeneous disease settings, accounting for intrinsic sample variability is crucial for obtaining reliable and interpretable omic network estimates. However, most graphical model analyses of biomedical data assume homogeneous conditional dependence structures, potentially leading to misleading conclusions. To address this, we propose a joint Gaussian graphical model that leverages sample-level ordinal covariates (e.g. disease stage) to account for heterogeneity and improve the estimation of partial correlation structures. RESULTS: Our modelling framework, called NExON-Bayes, extends the graphical spike-and-slab framework to account for ordinal covariates, jointly estimating their relevance to the graph structure and leveraging them to improve the accuracy of network estimation. To scale to high-dimensional omic settings, we develop an efficient variational inference algorithm tailored to our model. Through simulations, we demonstrate that our method outperforms the vanilla graphical spike-and-slab (with no covariate information), as well as other state-of-the-art network approaches which exploit covariate information. Applying our method to reverse phase protein array data from patients diagnosed with stage I, II or III breast carcinoma, we estimate the behaviour of proteomic networks as cancer progresses. Our model provides insights not only through inspection of the estimated proteomic networks, but also of the estimated ordinal covariate dependencies of key groups of proteins within those networks, offering a comprehensive understanding of how biological pathways shift across disease stages. AVAILABILITY AND IMPLEMENTATION: A user-friendly R package for NExON-Bayes with tutorials is available on Github at github.com/jf687/NExON, and archived at https://doi.org/10.5281/zenodo.20312938. The source of the dataset used is cited in the relevant section.

Bayes Theorem↗

PubMed1991

Structural analysis of neural circuits using the theory of directed graphs.

A new approach to analysis of structural properties of biological neural circuits is proposed based on their representation in the form of abstract structures called directed graphs. To exemplify this methodology, structural properties of a biological neural network and randomly wired circuits (RC) were compared. The analyzed biological circuit (BC) represented a sample of 39 neural nuclei which are responsible for the control of the cardiovascular function in higher vertebrates. Initially, direct connections of both circuits were stored in a square matrix format. Then, standard algorithms derived from the theory of directed graphs were applied to analyze the pathways of the circuits according to their length (in number of synapses), degree of connectedness, and structural strength. Thus, the BC was characterized by the presence of short, reciprocal, and unidirectional pathways which presented a high degree of heterogeneity in their strengths. This heterogeneity was mainly due to the existence of a small cluster of reciprocally connected neural nuclei in the circuit that have access, through short pathways, to most of the network. On the other hand, RCs were characterized by the presence of long and mainly reciprocal pathways which showed lower and absolute homogeneous strengths. Through this study the proposed methodology was demonstrated to be a simple and efficient way to store, analyze, and compare basic neuroanatomical information.

Animals↗

PubMed2004

Modelling disease outbreaks in realistic urban social networks.

Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

Contact Tracing↗

PubMed2004

Mathematical methods for inferring regulatory networks interactions: application to genetic regulation.

This paper deals with the problem of reconstruction of the intergenic interaction graph from the raw data of genetic co-expression coming with new technologies of bio-arrays (DMA-arrays, protein-arrays, etc.). These new imaging devices in general only give information about the asymptotical part (fixed configurations of co-expression or limit cycles of such configurations) of the dynamical evolution of the regulatory networks (genetic and/or proteic) underlying the functioning of living systems. Extracting the casual structure and interaction coefficients of a gene interaction network from the observed configurations is a complex problem. But if all the fixed configurations are supposedly observed and if they are factorizable into two or more subsets of values, then the interaction graph possesses as many connected components as the number of factors and the solution is obtained in polynomial time. This new result allows us for example to partly solve the topology of the genetic regulatory network ruling the flowering in Arabidopsis thaliana .

Algorithms↗

PubMed2005

EXAMINE: a computational approach to reconstructing gene regulatory networks.

Reverse-engineering of gene networks using linear models often results in an underdetermined system because of excessive unknown parameters. In addition, the practical utility of linear models has remained unclear. We address these problems by developing an improved method, EXpression Array MINing Engine (EXAMINE), to infer gene regulatory networks from time-series gene expression data sets. EXAMINE takes advantage of sparse graph theory to overcome the excessive-parameter problem with an adaptive-connectivity model and fitting algorithm. EXAMINE also guarantees that the most parsimonious network structure will be found with its incremental adaptive fitting process. Compared to previous linear models, where a fully connected model is used, EXAMINE reduces the number of parameters by O(N), thereby increasing the chance of recovering the underlying regulatory network. The fitting algorithm increments the connectivity during the fitting process until a satisfactory fit is obtained. We performed a systematic study to explore the data mining ability of linear models. A guideline for using linear models is provided: If the system is small (3-20 elements), more than 90% of the regulation pathways can be determined correctly. For a large-scale system, either clustering is needed or it is necessary to integrate information in addition to expression profile. Coupled with the clustering method, we applied EXAMINE to rat central nervous system development (CNS) data with 112 genes. We were able to efficiently generate regulatory networks with statistically significant pathways that have been predicted previously.

Algorithms↗