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PubMed2004

Automatic domain decomposition of proteins by a Gaussian Network Model.

Proteins are often comprised of domains of apparently independent folding units. These domains can be defined in various ways, but one useful definition divides the protein into substructures that seem to move more or less independently. The same methods that allow fairly accurate calculation of motion can be used to help classify these substructures. We show how the Gaussian Network Model (GNM), commonly used for determining motion, can also be adapted to automatically classify domains in proteins. Parallels between this physical network model and graph theory implementation are apparent. The method is applied to a nonredundant set of 55 proteins, and the results are compared to the visual assignments by crystallographers. Apart from decomposing proteins into structural domains, the algorithm can generally be applied to any large macromolecular system to decompose it into motionally decoupled sub-systems.

Algorithms↗
PubMed2006

Discrete time piecewise affine models of genetic regulatory networks.

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their asymptotic dynamics approaches that of a differential equation in another limiting case of this parameter. For intermediate values, the model present an original phenomenology which is argued to be due to delay effects. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle - with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.

Algorithms↗
PubMed1986

The uses of spatial analysis in medical geography: a review.

This paper is a review of how geographers and others have used spatial analysis to study disease and health care delivery patterns. Point, line, area and surface patterns, as well as map comparisons and relative spaces are discussed. Problems encountered in applying spatial analytic techniques in medical geography are pointed out. The paper is intended to stimulate discussion about where medical geography can and should go in this area of study. Point pattern techniques include standard distance, standard deviational ellipses, gradient analysis and space and space-time clustering. Line methods include random walks, vectors and graph theory or network analysis. Under areas, location quotients, standardized mortality ratios, Poisson probabilities, space and space-time clustering, autocorrelation measures and hierarchical clustering are discussed. Surface techniques mentioned are isolines and trend surfaces. For map comparisons, Lorenz curves, coefficients of areal correspondence and correlation coefficients have been used. Case-control matching, acquaintance networks, multidimensional scaling and cluster analysis are examples of methods that are based on relative or non-metric spaces. The review gives rise to the discussion of several general points: problems encountered in spatial analysis, theory building and verification, the appropriate role of technique and computer use. Some suggestions are made for further use of spatial analytic techniques in medical geography: Monte Carlo simulation of point patterns, network analysis to study referral systems and health care for pastoralists, geographic information systems to assess environmental risk, difference mapping for disease and risk factor map comparisons and multidimensional scaling to measure social distance.

Cross-Sectional Studies↗
PubMed2005

Biological master games: using biologists' reasoning to guide algorithm development for integrated functional genomics.

We review some powerful new algorithms that build on the intuitive biological interpretation techniques for statistical analysis of functional genomics experiments. Although they were originally designed for transcriptomics, we argue that these algorithms are applicable to any type of -omics study (transcriptomics, proteomics, metabolomics). Rank Products (RP), a strictly non-parametric test statistic to detect differentially regulated elements (genes, proteins, metabolites) in genome-wide screens. RP is particularly powerful for noisy data and low numbers of replicates and makes full use of the availability of a large number of parallel measurements that is typical of modern large-scale experiments. Iterative Group Analysis (iGA), a statistical method that makes the transition from regulated single elements to significant classes of elements, and thus provides an automatic functional annotation of an experiment. Graph-based iGA (GiGA), an extension of iGA that combines experimental data with a broad variety of biological annotations to highlight physiologically relevant regions in a given "evidence graph" (e.g., metabolic networks, signaling pathway diagrams, protein interaction maps). The sequential application of these techniques yields an increasingly abstract interpretation of experimental data that is at the same time quantitative, statistically rigorous, and biologically significant. The results can be used either as helpful tools to guide data visualization and exploration, or as the input for downstream computational applications in a systems biology framework.

Algorithms↗
PubMed2001

Development of a breast self-examination program for the Internet: health information for Korean women.

Internet-based health information will enable us to interact with many people despite distance and time constraints. Informational media by computer is expected to become an important factor that affects health behavior. This study was done to develop an accessible multimedia program about breast self-examination on the Internet. This study was designed by using the two steps of need assessment and program development. For the need assessment step, a survey was carried out. The sample consisted of the 82 women of Yonsei University selected by convenient random sampling. At the program development step, screen design took into account perspectives of computer engineering. A storyboard for every screen was made via screen design and then ported to computer using the Netscape Navigator program. A breast self-examination program was developed using Netscape 4.0 on the Windows 98 platform. The multimedia program, including text, graphics, animation, and sound, was constructed with HTML language using Memo Sheet in Netscape Navigator. The contents of health information posted on the Internet included general information about breast cancer, the importance of breast self-examination, self-risk appraisal of breast cancer, the diverse methods about breast self-examination, the monthly check list graph, and social network for consultation. It is possible to interact with clients through the Question and Answer function on screen. This Internet-based health information program provides enough information, which can be accessed using search systems on the Internet.

Adult↗
PubMed1992

Dynamics for communications data.

To create a complex dynamical model for a complex system, it is normally necessary to have a directed graph of the network, a dynamical model for each node, and a coupling function for each directed edge. But in many applications, the only observable data consists of communications from one node to another. In this situation, the modeler may infer a complex dynamical model for the network without any explicit knowledge of the independent dynamical behavior of the component systems (nodes). Here we present one procedure for this type of modeling problem, inspired by the attractor reconstruction procedure of chaos theory. Part of this proposal consists of a strategy for computer graphic presentation of the interactive dynamics of the complex system (or social network of dynamical schemes) called a netscope. We can imagine applications to diverse situations, such as decision groups, management, forecasting, international relations, classroom monitoring, therapy (personal, family, group, etc.) and distributed processors, to name a few.

Communication↗
PubMed2005

Integrating data from biological experiments into metabolic networks with the DBE information system.

Modern 'omics'-technologies result in huge amounts of data about life processes. For analysis and data mining purposes this data has to be considered in the context of the underlying biological networks. This work presents an approach for integrating data from biological experiments into metabolic networks by mapping the data onto network elements and visualising the data enriched networks automatically. This methodology is implemented in DBE, an information system that supports the analysis and visualisation of experimental data in the context of metabolic networks. It consists of five parts: (1) the DBE-Database for consistent data storage, (2) the Excel-Importer application for the data import, (3) the DBE-Website as the interface for the system, (4) the DBE-Pictures application for the up- and download of binary (e. g. image) files, and (5) DBE-Gravisto, a network analysis and graph visualisation system. The usability of this approach is demonstrated in two examples.

Computational Biology↗
PubMed2005

Adaptive walk on complex networks.

We investigate the properties of adaptive walks on an uncorrelated fitness landscape which is established in sequence spaces of complex structure. In particular, we perform numerical simulations of adaptive walks on random graphs and scale-free networks. For the former, we also derive some analytical approximations for the density of local optima of the fitness landscape and the mean length walk. We compare our results with those obtained for regular lattices. We obtain that the density of local optima decreases as 1/z, where z is the mean connectivity, for all networks we have investigated. In random graphs, the mean length walk L reaches the asymptotic value e - 1 for large z, which corresponds to the result for regular networks. Although we could not find an exact estimate, we derive an underestimated value for L. Unlike random graphs, scale-free networks show an upper asymptotic value of L.

Adaptation, Physiological↗
PubMed2006

An improved neural network model for the two-page crossing number problem.

The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as half-circles either above or below the line. Such drawings are called two-page book drawings. The smallest number of crossings over all two-page drawings of a graph G is called the two-page crossing number of G. Cimikowski and Shope have solved the two-page crossing number problem for an n-vertex and m-edge graph by using a Hopfield network with 2 m neurons. We present here an improved Hopfield model with m neurons. The new model achieves much better performance in the quality of solutions and is more efficient than the model of Cimikowski and Shope for all graphs tested. The parallel time complexity of the algorithm, without considering the crossing number calculations, is O(m) for the new Hopfield model with m processors clearly outperforming the previous algorithm.

Algorithms↗
PubMed2006

Ring structures and mean first passage time in networks.

In this paper we address the problem of the calculation of the mean first passage time on generic graphs. We focus in particular on the mean first passage time on a node for a random walker starting from a generic, unknown, node x. We introduce an approximate scheme of calculation which maps the original process in a Markov process in the space of the so-called rings, described by a transition matrix of size O(ln N/ln (k) x ln N/ln (k)), where is the size of the graph and (k) the average degree in the graph. In this way one has a drastic reduction of degrees of freedom with respect to the size of the transition matrix of the original process, corresponding to an extremely low computational cost. We first apply the method to the Erdös-Renyi random graphs for which the method allows for almost perfect agreement with numerical simulations. Then we extend the approach to the Barabási-Albert graph, as an example of scale-free graph, for which one obtains excellent results. Finally we test the method with two real-world graphs, Internet and a network of the brain, for which we obtain accurate results.

Cell Physiological Phenomena↗
PubMed2006

Genetic and functional analyses of the lgtH gene, a member of the beta-1,4-galactosyltransferase gene family in the genus Neisseria.

Lipooligosaccharide (LOS) is a major virulence factor of the pathogenic Neisseria. Three galactosyltransferase genes, lgtB, lgtE and lgtH, responsible for the biosynthesis of LOS oligosaccharide chains, were analysed in five Neisseria species. The function of lgtH in Neisseria meningitidis 6,275 was determined by mutagenesis and chemical characterization of the parent and mutant LOS chains. The chemical characterization included SDS-PAGE, immunoblot, hexose and mass spectrometry analyses. Compared with the parent LOS, the mutant LOS lacked galactose, and its oligosaccharide decreased by three or four sugar units in matrix-assisted laser desorption ionization (MALDI)-MS analysis. The results show that lgtH encodes a beta-1,4-galactosyltransferase, and that the glucose moiety linked to heptose (Hep) in the alpha chain is the acceptor site in the biosynthesis of Neisseria LOS. To understand the sequence diversity and relationships of lgtB, lgtE and lgtH, the entire lgt-1 locus was further sequenced in three N. meningitidis strains and three commensal Neisseria strains, and compared with the previously reported lgt genes from Neisseria species. Comparison of the protein sequences of the three enzymes LgtB, LgtE and LgtH showed a conserved N-terminal region, and a highly variable C-terminal region, suggesting functional constraint for substrate and acceptor specificity, respectively. The analyses of allelic variation and evolution of 23 lgtB, 12 lgtE and 14 lgtH sequences revealed a distinct evolutionary history of these genes in Neisseria. For example, the splits graph of lgtE displayed a network evolution, indicating frequent DNA recombination, whereas splits graphs of lgtB and lgtH displayed star-tree-like evolution, indicating the accumulation of point mutations. The data presented here represent examples of the evolution and variation of prokaryotic glycosyltransferase gene families. These imply the existence of multiple enzyme isoforms for biosynthesis of a great diversity of oligosaccharides in nature.

Alleles↗
PubMed2003

Some asymptotic properties of duplication graphs.

Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this "duplication-dominated" regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a nonzero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied.

Models, Statistical↗
PubMed2001

The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes.

In this paper, the structure and evolution of the protein interaction network of the yeast Saccharomyces cerevisiae is analyzed. The network is viewed as a graph whose nodes correspond to proteins. Two proteins are connected by an edge if they interact. The network resembles a random graph in that it consists of many small subnets (groups of proteins that interact with each other but do not interact with any other protein) and one large connected subnet comprising more than half of all interacting proteins. The number of interactions per protein appears to follow a power law distribution. Within approximately 200 Myr after a duplication, the products of duplicate genes become almost equally likely to (1) have common protein interaction partners and (2) be part of the same subnetwork as two proteins chosen at random from within the network. This indicates that the persistence of redundant interaction partners is the exception rather than the rule. After gene duplication, the likelihood that an interaction gets lost exceeds 2.2 x 10(-3)/Myr. New interactions are estimated to evolve at a rate that is approximately three orders of magnitude smaller. Every 300 Myr, as many as half of all interactions may be replaced by new interactions.

Evolution, Molecular↗
PubMed2002

A bi-recursive neural network architecture for the prediction of protein coarse contact maps.

Prediction of contact maps may be seen as a strategic step towards the solution of fundamental open problems in structural genomics. In this paper we focus on coarse grained maps that describe the spatial neighborhood relation between secondary structure elements (helices, strands, and coils) of a protein. We introduce a new machine learning approach for scoring candidate contact maps. The method combines a specialized noncausal recursive connectionist architecture and a heuristic graph search algorithm. The network is trained using candidate graphs generated during search. We show how the process of selecting and generating training examples is important for tuning the precision of the predictor.

Algorithms↗
PubMed2001

How to reconstruct a large genetic network from n gene perturbations in fewer than n(2) easy steps.

MOTIVATION: The reconstruction of genetic networks is the holy grail of functional genomics. Its core task is to identify the causal structure of a gene network, that is, to distinguish direct from indirect regulatory interactions among gene products. In other words, to reconstruct a genetic network is to identify, for each network gene, which other genes and their activity the gene influences directly. Crucial to this task are perturbations of gene activity. Genomic technology permits large-scale experiments perturbing the activity of many genes and assessing the effect of each perturbation on all other genes in a genome. However, such experiments cannot distinguish between direct and indirect effects of a genetic perturbation. RESULTS: I present an algorithm to reconstruct direct regulatory interactions in gene networks from the results of gene perturbation experiments. The algorithm is based on a graph representation of genetic networks and applies to networks of arbitrary size and complexity. Algorithmic complexity in both storage and time is low, less than O(n(2)). In practice, the algorithm can reconstruct networks of several thousand genes in mere CPU seconds on a desktop workstation. AVAILABILITY: A perl implementation of the algorithm is given in the Appendix. CONTACT: wagnera@unm.edu

Algorithms↗
PubMed2023

Inferring Metabolic States from Single Cell Transcriptomic Data via Geometric Deep Learning.

The ability to measure gene expression at single-cell resolution has elevated our understanding of how biological features emerge from complex and interdependent networks at molecular, cellular, and tissue scales. As technologies have evolved that complement scRNAseq measurements with things like single-cell proteomic, epigenomic, and genomic information, it becomes increasingly apparent how much biology exists as a product of multimodal regulation. Biological processes such as transcription, translation, and post-translational or epigenetic modification impose both energetic and specific molecular demands on a cell and are therefore implicitly constrained by the metabolic state of the cell. While metabolomics is crucial for defining a holistic model of any biological process, the chemical heterogeneity of the metabolome makes it particularly difficult to measure, and technologies capable of doing this at single-cell resolution are far behind other multiomics modalities. To address these challenges, we present GEFMAP (Gene Expression-based Flux Mapping and Metabolic Pathway Prediction), a method based on geometric deep learning for predicting flux through reactions in a global metabolic network using transcriptomics data, which we ultimately apply to scRNAseq. GEFMAP leverages the natural graph structure of metabolic networks to learn both a biological objective for each cell and estimate a mass-balanced relative flux rate for each reaction in each cell using novel deep learning models.

Preprint↗
PubMed2006

Hierarchical modularity of nested bow-ties in metabolic networks.

BACKGROUND: The exploration of the structural topology and the organizing principles of genome-based large-scale metabolic networks is essential for studying possible relations between structure and functionality of metabolic networks. Topological analysis of graph models has often been applied to study the structural characteristics of complex metabolic networks. RESULTS: In this work, metabolic networks of 75 organisms were investigated from a topological point of view. Network decomposition of three microbes (Escherichia coli, Aeropyrum pernix and Saccharomyces cerevisiae) shows that almost all of the sub-networks exhibit a highly modularized bow-tie topological pattern similar to that of the global metabolic networks. Moreover, these small bow-ties are hierarchically nested into larger ones and collectively integrated into a large metabolic network, and important features of this modularity are not observed in the random shuffled network. In addition, such a bow-tie pattern appears to be present in certain chemically isolated functional modules and spatially separated modules including carbohydrate metabolism, cytosol and mitochondrion respectively. CONCLUSION: The highly modularized bow-tie pattern is present at different levels and scales, and in different chemical and spatial modules of metabolic networks, which is likely the result of the evolutionary process rather than a random accident. Identification and analysis of such a pattern is helpful for understanding the design principles and facilitate the modelling of metabolic networks.

Algorithms↗
PubMed1997

Adaptive sampling in behavioral surveys.

Studies of populations such as drug users encounter difficulties because the members of the populations are rare, hidden, or hard to reach. Conventionally designed large-scale surveys detect relatively few members of the populations so that estimates of population characteristics have high uncertainty. Ethnographic studies, on the other hand, reach suitable numbers of individuals only through the use of link-tracing, chain referral, or snowball sampling procedures that often leave the investigators unable to make inferences from their sample to the hidden population as a whole. In adaptive sampling, the procedure for selecting people or other units to be in the sample depends on variables of interest observed during the survey, so the design adapts to the population as encountered. For example, when self-reported drug use is found among members of the sample, sampling effort may be increased in nearby areas. Types of adaptive sampling designs include ordinary sequential sampling, adaptive allocation in stratified sampling, adaptive cluster sampling, and optimal model-based designs. Graph sampling refers to situations with nodes (for example, people) connected by edges (such as social links or geographic proximity). An initial sample of nodes or edges is selected and edges are subsequently followed to bring other nodes into the sample. Graph sampling designs include network sampling, snowball sampling, link-tracing, chain referral, and adaptive cluster sampling. A graph sampling design is adaptive if the decision to include linked nodes depends on variables of interest observed on nodes already in the sample. Adjustment methods for nonsampling errors such as imperfect detection of drug users in the sample apply to adaptive as well as conventional designs.

Behavior↗