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PubMed1999

Visualisation and modelling of renal capillaries from confocal images.

A computer aided design was developed to support three-dimensional visualisation and modelling of vascular networks. Volume data comprised a series of images obtained using a Zeiss confocal laser scanning microscope. The profiles of vessels were automatically segmented using two-dimensional morphological filters. Segmented contours of the vessels were used to form a spatial model of the network. The centre points of segmented contours were used to derive a three-dimensional graph representing the vascular network. The proposed method was applied to renal capillary networks of normal rats, and showed well the lobular structure of glomeruli. The average length of renal capillary networks was 6.09 mm. Three-dimensional models based on confocal data require much less effort than reconstructions based on serial sections, and can be adapted for any vascular patterns.

Animals↗
PubMed2002

The average distances in random graphs with given expected degrees.

Random graph theory is used to examine the "small-world phenomenon"; any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees the average distance is almost surely of order log nlog d, where d is the weighted average of the sum of squares of the expected degrees. Of particular interest are power law random graphs in which the number of vertices of degree k is proportional to 1kbeta for some fixed exponent beta. For the case of beta > 3, we prove that the average distance of the power law graphs is almost surely of order log nlog d. However, many Internet, social, and citation networks are power law graphs with exponents in the range 2 < beta < 3 for which the power law random graphs have average distance almost surely of order log log n, but have diameter of order log n (provided having some mild constraints for the average distance and maximum degree). In particular, these graphs contain a dense subgraph, which we call the core, having n(clog log n) vertices. Almost all vertices are within distance log log n of the core although there are vertices at distance log n from the core.

Journal Article↗
PubMed2006

Hawks and Doves on small-world networks.

We explore the Hawk-Dove game on networks with topologies ranging from regular lattices to random graphs with small-world networks in between. This is done by means of computer simulations using several update rules for the population evolutionary dynamics. We find the overall result that cooperation is sometimes inhibited and sometimes enhanced in those network structures, with respect to the mixing population case. The differences are due to different update rules and depend on the gain-to-cost ratio. We analyze and qualitatively explain this behavior by using local topological arguments.

Journal Article↗
PubMed2006

Width of percolation transition in complex networks.

It is known that the critical probability for the percolation transition is not a sharp threshold. Actually it is a region of nonzero width Deltap(c) for systems of finite size. Here we present evidence that for complex networks Deltap(c) approximately p(c)/l, where l approximately Nnu(opt), where is the average length of the percolation cluster, and N is the number of nodes in the network. For Erdos-Rényi graphs nu(opt)=1/3, while for scale-free networks with a degree distribution P(k) approximately k(-lambda) and 3<lambda<4, nu(opt)=(lambda-3)/(lambda-1) . We show analytically and numerically that the survivability S(p,l), which is the probability of a cluster to survive l chemical shells at probability p, behaves near criticality as S(p,l)=S(p(c),l)exp[(p-p(c))l/p(c)]. Thus for probabilities inside the region |p-p(c)|<p(c)/l the behavior of the system is indistinguishable from that of the critical point.

Journal Article↗
PubMedDate not supplied

Dose-response modeling in reproductive toxicology in the systems biology era.

Systems biology approaches for modeling cellular signaling networks affected by chemical exposures should soon produce integrated methodologies capable of predicting dose-response relationships for developmental toxicants and for other toxic responses. This paper outlines an emerging strategy for systems biology approaches in dose-response modeling. Genome-wide functional screens, bioinformatic tools, and network mapping technologies together can provide directed graph representations of the cellular signaling networks. The graphical representations can be converted into mathematical models that permit predicting the shapes of dose-response curves for altered cell signaling by test compounds during development. Systems biology approaches require interdisciplinary teams with expertise in reproduction, cell biology, signal transduction, mathematical/biomedical modeling, and risk assessment. In addition to outlining a systems approach for dose-response research, this paper discusses initial stages of application of this strategy to examine inhibition of steroidogenesis in testes by phthalate esters.

Animals↗
PubMed2026

Network-based integration of metabolomics data from large-scale repositories.

INTRODUCTION: Public metabolomics data repositories such as MetaboLights and Metabolomics Workbench host rapidly growing volumes of raw data, processed results, and metadata. As data deposition becomes a prerequisite for funding and publication, there is an increasing need for tools that enable integration and joint reanalysis of datasets across studies to maximise reuse and reproducibility. OBJECTIVES: This study aims to enable large-scale integrative meta-analysis of public metabolomics data, exploiting harmonised metabolite annotations to identify robust multi-study metabolite and pathway signatures and to provide global visual overviews of repository content. METHODS: We developed a network-based integration framework operating at both the study (dataset) level and the metabolite or pathway level. Metabolite-level meta-networks integrate studies with shared biological context using co-occurrences of differential metabolites represented as bipartite graphs. Study-level networks compare observed metabolites for overall repository exploration. Networks can be explored interactively using a dedicated Python Dash app available at https://github.com/EloisaRL/Metabolomic-data-analysis-app/tree/main . RESULTS: As an example, the approach was applied to six COVID-19 plasma datasets from MetaboLights generated using LC-MS and NMR. Ten metabolites were identified as differential in at least three studies, including consistently up-regulated pyroglutamic acid, in agreement with the literature. Pathway-level networks provided an overview of shared biological processes across studies. A global network of 1,181 studies in Metabolomics Workbench demonstrated clustering by assay coverage and associated metadata, as expected. CONCLUSION: Network-based integration of harmonised metabolomics data enables robust cross-study analyses and highlights the critical importance of standardised annotation pipelines. Such approaches enhance the reuse, reproducibility, and impact of public metabolomics datasets, accelerating biological discovery.

Metabolomics↗
PubMed1998

Finding Genetic Network from Experiments by Weighted Network Model.

We study the problem of finding a genetic network from data obtained by multiple gene disruptions and overexpressions. We define a genetic network as a weighted graph, and analyze the computational complexity of the problem. We show that if there exists a weighted network which is consistent with given data, we can find it in polynomial time. Moreover, we also consider the optimization problem, where we try to find an optimally consistent weighted network with given data. We show that the problem is NP-hard. On the other hand, we give a polynomial-time approximation algorithm to solve it with approximation ratio 2. We report some simulation results on experiments.

Journal Article↗
PubMed2001

Spectra of "real-world" graphs: beyond the semicircle law.

Many natural and social systems develop complex networks that are usually modeled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semicircle law is known to describe the spectral densities of uncorrelated random graphs, much less is known about the spectra of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations, or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more than a few thousand nodes is prohibitively time and memory consuming. Making use of recent advances in algorithms for spectral characterization, here we develop methods to determine the eigenvalues of networks comparable in size to real systems, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random matrices does not converge to the semicircle law. Furthermore, the spectra of real-world graphs have specific features, depending on the details of the corresponding models. In particular, scale-free graphs develop a trianglelike spectral density with a power-law tail, while small-world graphs have a complex spectral density consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.

Journal Article↗
PubMed2005

Being around and knowing the players: networks of influence in health policy.

The accumulation and use of power is crucial to the health policy process. This paper examines the power of the medical profession in the health policy arena, by analysing which actors are perceived as influential, and how influence is structured in health policy. It combines an analysis of policy networks and social networks, to examine positional and personal influence in health policy in the state of Victoria, Australia. In the sub-graph of the influence network examined here, those most widely regarded as influential are academics, medically qualified and male. Positional actors (the top politician, political advisor and bureaucrat in health and the top nursing official) form part of a core group within this network structure. A second central group consists of medical influentials working in academia, research institutes and health-related NGOs. In this network locale overall, medical academics appear to combine positional and personal influence, and play significant intermediary roles across the network. While many claim that the medical profession has lost power in health policy and politics, this analysis yields few signs that the power of medicine to shape the health policy process has been greatly diminished in Victoria. Medical expertise is a potent embedded resource connecting actors through ties of association, making it difficult for actors with other resources and different knowledge to be considered influential. The network concepts and analytical techniques used here provide a novel means for uncovering different types of influence in health policy.

Administrative Personnel↗
PubMed2003

Diffusion-limited friendship network: a model for six degrees of separation.

A dynamic model of a society is studied where each person is an uncorrelated and noninteracting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the pairs of mutual friendships. This network exhibits a different percolationlike phase transition in all dimensions. On introducing simultaneous death and birth rates in the population, we show that the friendship network shows the six degrees of separation for ever after where the precise value of the network diameter depends on the death/birth rate. A susceptible-infected-susceptible-type model of disease spreading shows that this society always remains healthy if the population density is less than certain threshold value.

Journal Article↗
PubMed2006

Detecting functional modules in the yeast protein-protein interaction network.

MOTIVATION: Identification of functional modules in protein interaction networks is a first step in understanding the organization and dynamics of cell functions. To ensure that the identified modules are biologically meaningful, network-partitioning algorithms should take into account not only topological features but also functional relationships, and identified modules should be rigorously validated. RESULTS: In this study we first integrate proteomics and microarray datasets and represent the yeast protein-protein interaction network as a weighted graph. We then extend a betweenness-based partition algorithm, and use it to identify 266 functional modules in the yeast proteome network. For validation we show that the functional modules are indeed densely connected subgraphs. In addition, genes in the same functional module confer a similar phenotype. Furthermore, known protein complexes are largely contained in the functional modules in their entirety. We also analyze an example of a functional module and show that functional modules can be useful for gene annotation. CONTACT: yuan.33@osu.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Algorithms↗
PubMed2006

A method for the generation of standardized qualitative dynamical systems of regulatory networks.

BACKGROUND: Modeling of molecular networks is necessary to understand their dynamical properties. While a wealth of information on molecular connectivity is available, there are still relatively few data regarding the precise stoichiometry and kinetics of the biochemical reactions underlying most molecular networks. This imbalance has limited the development of dynamical models of biological networks to a small number of well-characterized systems. To overcome this problem, we wanted to develop a methodology that would systematically create dynamical models of regulatory networks where the flow of information is known but the biochemical reactions are not. There are already diverse methodologies for modeling regulatory networks, but we aimed to create a method that could be completely standardized, i.e. independent of the network under study, so as to use it systematically. RESULTS: We developed a set of equations that can be used to translate the graph of any regulatory network into a continuous dynamical system. Furthermore, it is also possible to locate its stable steady states. The method is based on the construction of two dynamical systems for a given network, one discrete and one continuous. The stable steady states of the discrete system can be found analytically, so they are used to locate the stable steady states of the continuous system numerically. To provide an example of the applicability of the method, we used it to model the regulatory network controlling T helper cell differentiation. CONCLUSION: The proposed equations have a form that permit any regulatory network to be translated into a continuous dynamical system, and also find its steady stable states. We showed that by applying the method to the T helper regulatory network it is possible to find its known states of activation, which correspond the molecular profiles observed in the precursor and effector cell types.

Cell Differentiation↗
PubMed2006

Integrating multi-attribute similarity networks for robust representation of the protein space.

MOTIVATION: A global view of the protein space is essential for functional and evolutionary analysis of proteins. In order to achieve this, a similarity network can be built using pairwise relationships among proteins. However, existing similarity networks employ a single similarity measure and therefore their utility depends highly on the quality of the selected measure. A more robust representation of the protein space can be realized if multiple sources of information are used. RESULTS: We propose a novel approach for analyzing multi-attribute similarity networks by combining random walks on graphs with Bayesian theory. A multi-attribute network is created by combining sequence and structure based similarity measures. For each attribute of the similarity network, one can compute a measure of affinity from a given protein to every other protein in the network using random walks. This process makes use of the implicit clustering information of the similarity network, and we show that it is superior to naive, local ranking methods. We then combine the computed affinities using a Bayesian framework. In particular, when we train a Bayesian model for automated classification of a novel protein, we achieve high classification accuracy and outperform single attribute networks. In addition, we demonstrate the effectiveness of our technique by comparison with a competing kernel-based information integration approach.

Algorithms↗
PubMed2004

Estimating genomic coexpression networks using first-order conditional independence.

We describe a computationally efficient statistical framework for estimating networks of coexpressed genes. This framework exploits first-order conditional independence relationships among gene-expression measurements to estimate patterns of association. We use this approach to estimate a coexpression network from microarray gene-expression measurements from Saccharomyces cerevisiae. We demonstrate the biological utility of this approach by showing that a large number of metabolic pathways are coherently represented in the estimated network. We describe a complementary unsupervised graph search algorithm for discovering locally distinct subgraphs of a large weighted graph. We apply this algorithm to our coexpression network model and show that subgraphs found using this approach correspond to particular biological processes or contain representatives of distinct gene families.

Algorithms↗
PubMed1986

A stochastic description of evolutionary processes in underoccupied systems.

A stochastic description for underoccupied systems (large networks with small overall particle number) is given and represented by graphs. Evolutionary processes on this network are considered, especially the mutation process between components (hopping from one component to another) and the selection process.

Biological Evolution↗
PubMed2006

Efficient estimation of graphlet frequency distributions in protein-protein interaction networks.

MOTIVATION: Algorithmic and modeling advances in the area of protein-protein interaction (PPI) network analysis could contribute to the understanding of biological processes. Local structure of networks can be measured by the frequency distribution of graphlets, small connected non-isomorphic induced subgraphs. This measure of local structure has been used to show that high-confidence PPI networks have local structure of geometric random graphs. Finding graphlets exhaustively in a large network is computationally intensive. More complete PPI networks, as well as PPI networks of higher organisms, will thus require efficient heuristic approaches. RESULTS: We propose two efficient and scalable heuristics for finding graphlets in high-confidence PPI networks. We show that both PPI and their model geometric random networks, have defined boundaries that are sparser than the 'inner parts' of the networks. In addition, these networks exhibit 'uniformity' of local structure inside the networks. Our first heuristic exploits these two structural properties of PPI and geometric random networks to find good estimates of graphlet frequency distributions in these networks up to 690 times faster than the exhaustive searches. Our second heuristic is a variant of a more standard sampling technique and it produces accurate approximate results up to 377 times faster than the exhaustive searches. We indicate how the combination of these approaches may result in an even better heuristic. AVAILABILITY: Supplementary information is available at http://www.cs.toronto.edu/~natasha/BIOINF-2005-0946/Supplementary.pdf. Software implementing the algorithms is available at http://www.cs.toronto.edu/~natasha/BIOINF-2005-0946/estimate_grap-hlets.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Algorithms↗
PubMed2004

What makes biochemical networks tick?

In view of the increasing number of reported concentration oscillations in living cells, methods are needed that can identify the causes of these oscillations. These causes always derive from the influences that concentrations have on reaction rates. The influences reach over many molecular reaction steps and are defined by the detailed molecular topology of the network. So-called 'autoinfluence paths', which quantify the influence of one molecular species upon itself through a particular path through the network, can have positive or negative values. The former bring a tendency towards instability. In this molecular context a new graphical approach is presented that enables the classification of network topologies into oscillophoretic and nonoscillophoretic, i.e. into ones that can and ones that cannot induce concentration oscillations. The network topologies are formulated in terms of a set of uni-molecular and bi-molecular reactions, organized into branched cycles of directed reactions, and presented as graphs. Subgraphs of the network topologies are then classified as negative ones (which can) and positive ones (which cannot) give rise to oscillations. A subgraph is oscillophoretic (negative) when it contains more positive than negative autoinfluence paths. Whether the former generates oscillations depends on the values of the other subgraphs, which again depend on the kinetic parameters. An example shows how this can be established. By following the rules of our new approach, various oscillatory kinetic models can be constructed and analyzed, starting from the classified simplest topologies and then working towards desirable complications. Realistic biochemical examples are analyzed with the new method, illustrating two new main classes of oscillophore topologies.

Algorithms↗
PubMed2006

Modelling protein-protein interaction networks via a stickiness index.

What type of connectivity structure are we seeing in protein-protein interaction networks? A number of random graph models have been mooted. After fitting model parameters to real data, the models can be judged by their success in reproducing key network properties. Here, we propose a very simple random graph model that inserts a connection according to the degree, or 'stickiness', of the two proteins involved. This model can be regarded as a testable distillation of more sophisticated versions that attempt to account for the presence of interaction surfaces or binding domains. By computing a range of network similarity measures, including relative graphlet frequency distance, we find that our model outperforms other random graph classes. In particular, we show that given the underlying degree information, fitting a stickiness model produces better results than simply choosing a degree-matching graph uniformly at random. Therefore, the results lend support to the basic modelling methodology.

Adhesiveness↗