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PubMed2001

Topology of technology graphs: small world patterns in electronic circuits.

Recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological, social, and technological networks: the presence of small world patterns. Here we analyze this problem by using several graphs obtained from one of the most common technological systems: electronic circuits. It is shown that both analogic and digital circuits exhibit small world behavior. We conjecture that the small world pattern arises from the compact design in which many elements share a small, close physical neighborhood plus the fact that the system must define a single connected component (which requires shortcuts connecting different integrated clusters). The degree distributions displayed are consistent with a conjecture concerning the sharp cutoffs associated to the presence of costly connections [Amaral et al., Proc. Natl. Acad. Sci. USA 97, 11 149 (2000)], thus providing a limit case for the classes of universality of small world patterns from real, artificial networks. The consequences for circuit design are outlined.

Journal Article↗
PubMed2001

Protein flexibility predictions using graph theory.

Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase.

Adenylate Kinase↗
PubMed2004

Modeling correlated main-chain motions in proteins for flexible molecular recognition.

We describe a new method for modeling protein and ligand main-chain flexibility, and show its ability to model flexible molecular recognition. The goal is to sample the full conformational space, including large-scale motions that typically cannot be reached in molecular dynamics simulations due to the computational intensity, as well as conformations that have not been observed yet by crystallography or NMR. A secondary goal is to assess the degree of flexibility consistent with protein-ligand recognition. Flexibility analysis of the target protein is performed using the graph-theoretic algorithm FIRST, which also identifies coupled networks of covalent and noncovalent bonds within the protein. The available conformations of the flexible regions are then explored with ROCK by random-walk sampling of the rotatable bonds. ROCK explores correlated motions by only sampling dihedral angles that preserve the coupled bond networks in the protein and generates conformers with good stereochemistry, without using a computationally expensive potential function. A representative set of the conformational ensemble generated this way can be used as targets for docking with SLIDE, which handles the flexibility of protein and ligand side-chains. The realism of this protein main-chain conformational sampling is assessed by comparison with time-resolved NMR studies of cyclophilin A motions. ROCK is also effective for modeling the flexibility of large cyclic and polycyclic ligands, as demonstrated for cyclosporin and zearalenol. The use of this combined approach to perform docking with main-chain flexibility is illustrated for the cyclophilin A-cyclosporin complex and the estrogen receptor in complex with zearalenol, while addressing the question of how much flexibility is allowed without hindering molecular recognition.

Biochemical Phenomena↗
PubMed1997

Osmotic behavior and transport properties of human islets in a dimethyl sulfoxide solution.

The osmotic responses of isolated human islets were evaluated using a perfusion cryomicroscope device. Individual islet volumes were measured following equilibration with a series of solutions of graded solute concentration. The osmotically inactive volume for human islets was determined to be 25% from a Boyle-van't Hoff plot of these data. A network thermodynamic model was developed via the bond graph method to describe the transport of water and cryoprotective agent in pancreatic islets. The model was curve fit to transient volumetric data for the response of islets to a stepwise exposure to 1 Me2SO at temperatures of 24.0, 3.0, or -3.5 degrees C. Standard membrane transport parameters (Lp, omega, sigma) and interstitial diffusion transport properties (kappa w, kappa p) were calculated from the fitting procedure. The temperature coefficients for membrane transport properties were expressed in terms of activation energies for water (ELp) and Me2SO (E omega). Osmotic challenge experiments conducted with fresh and cryopreserved human islets indicate that frozen/thawed islets exhibit a a slight increase in transport properties.

Biological Transport, Active↗
PubMed2006

Schizophrenic speech as a disordered trajectory in a collapsed cognitive "Small-World".

New theoretical instruments, as goal-directed neural networks models and geometric representations based on semantic graphs, open new approaches for our understanding of the schizophrenic speech. The neuropathologic disorders of the schizophrenia can be simulated using neural models, and these models can eventually explain the origin of goal confusion and incoherence in the schizophrenic discourse trajectory. Moreover, these models are useful to evaluate the different hypothesis about the pathogenic mechanisms of the disease. At the same time, a geometric representation of the trajectory of the speech can be obtained from real data. Our conjecture is that a context-dependent graph can be constructed in order to explore if, when the disease became more severe, a transition from a quasi ordered graph to a nearly completely random graph occurs. Plausibly, there exists a wide region where the graph has the properties of a "small-world". This kind of analyses could be potentially carried out using data coming from the spontaneous speech of schizophrenic patients, and can help to evaluate the progress of the disease. At the same time, these geometrical representations could help to evaluate the effect of treatments.

Attitude↗
PubMed2005

Learning protein secondary structure from sequential and relational data.

We propose a method for sequential supervised learning that exploits explicit knowledge of short- and long-range dependencies. The architecture consists of a recursive and bi-directional neural network that takes as input a sequence along with an associated interaction graph. The interaction graph models (partial) knowledge about long-range dependency relations. We tested the method on the prediction of protein secondary structure, a task in which relations due to beta-strand pairings and other spatial proximities are known to have a significant effect on the prediction accuracy. In this particular task, interactions can be derived from knowledge of protein contact maps at the residue level. Our results show that prediction accuracy can be significantly boosted by the integration of interaction graphs.

Animals↗
PubMed2001

Protein flexibility and dynamics using constraint theory.

A new approach is presented for determining the rigid regions in proteins and the flexible joints between them. The short-range forces in proteins are modeled as constraints and we use a recently developed formalism from graph theory to analyze flexibility in the bond network. Forces included in the analysis are the covalent bond-stretching and bond-bending forces, salt bridges, and hydrogen bonds. We use a local function to associate an energy with individual hydrogen bonds, which then can be included or excluded depending on the bond strength. Colored maps of the rigid and flexible regions provide a direct visualization of where the motion of the protein can take place, consistent with these distance constraints. We also define a flexibility index that quantifies the local density of flexible or floppy modes, in terms of the dihedral angles that remain free to rotate in each flexible region. A negative flexibility index provides a measure of the density of redundant bonds in rigid regions. A new application of this approach is to simulate the maximal range of possible motions of the flexible regions by introducing Monte Carlo changes in the free dihedral angles, subject to the distance constraints. This is done using a method that maintains closure of the rings formed by covalent and hydrogen bonds in the flexible parts of the protein, and van der Waals overlaps between atoms are avoided. We use the locus of the possible motions of HIV protease as an example: movies of its motion can be seen at http://www.pa.msu.edu/~lei.

Computer Simulation↗
PubMed2025

MPAC: a computational framework for inferring pathway activities from multi-omic data.

MOTIVATION: Fully capturing cellular state requires examining genomic, epigenomic, transcriptomic, proteomic, and other assays for a biological sample and comprehensive computational modeling to reason with the complex and sometimes conflicting measurements. Modeling these so-called multi-omic data is especially beneficial in disease analysis, where observations across omic data types may reveal unexpected patient groupings and inform clinical outcomes and treatments. RESULTS: We present Multi-omic Pathway Analysis of Cells (MPAC), a computational framework that interprets multi-omic data through prior knowledge from biological pathways. MPAC leverages network relationships encoded in pathways through a factor graph to infer consensus activity levels for proteins and associated pathway entities from multi-omic data, runs permutation testing to eliminate spurious activity predictions, and groups biological samples by pathway activities to allow identifying and prioritizing proteins with potential clinical relevance, e.g. associated with patient prognosis. Using DNA copy number alteration and RNA-seq data from head and neck squamous cell carcinoma patients from The Cancer Genome Atlas as an example, we demonstrate that MPAC predicts a patient subgroup related to immune responses not identified by analysis with either input omic data type alone. Key proteins identified via this subgroup have pathway activities related to clinical outcome as well as immune cell composition. Our MPAC R package enables similar multi-omic analyses on new datasets. AVAILABILITY AND IMPLEMENTATION: The MPAC package is available at Bioconductor https://bioconductor.org/packages/MPAC.

Humans↗
PubMed2004

Modeling interactome: scale-free or geometric?

MOTIVATION: Networks have been used to model many real-world phenomena to better understand the phenomena and to guide experiments in order to predict their behavior. Since incorrect models lead to incorrect predictions, it is vital to have as accurate a model as possible. As a result, new techniques and models for analyzing and modeling real-world networks have recently been introduced. RESULTS: One example of large and complex networks involves protein-protein interaction (PPI) networks. We analyze PPI networks of yeast Saccharomyces cerevisiae and fruitfly Drosophila melanogaster using a newly introduced measure of local network structure as well as the standardly used measures of global network structure. We examine the fit of four different network models, including Erdos-Renyi, scale-free and geometric random network models, to these PPI networks with respect to the measures of local and global network structure. We demonstrate that the currently accepted scale-free model of PPI networks fails to fit the data in several respects and show that a random geometric model provides a much more accurate model of the PPI data. We hypothesize that only the noise in these networks is scale-free. CONCLUSIONS: We systematically evaluate how well-different network models fit the PPI networks. We show that the structure of PPI networks is better modeled by a geometric random graph than by a scale-free model. SUPPLEMENTARY INFORMATION: Supplementary information is available at http://www.cs.utoronto.ca/~juris/data/data/ppiGRG04/

Algorithms↗
PubMed2025

MPAC: a computational framework for inferring pathway activities from multi-omic data.

Fully capturing cellular state requires examining genomic, epigenomic, transcriptomic, proteomic, and other assays for a biological sample and comprehensive computational modeling to reason with the complex and sometimes conflicting measurements. Modeling these so-called multi-omic data is especially beneficial in disease analysis, where observations across omic data types may reveal unexpected patient groupings and inform clinical outcomes and treatments. We present Multi-omic Pathway Analysis of Cells (MPAC), a computational framework that interprets multi-omic data through prior knowledge from biological pathways. MPAC leverages network relationships encoded in pathways through a factor graph to infer consensus activity levels for proteins and associated pathway entities from multi-omic data, runs permutation testing to eliminate spurious activity predictions, and groups biological samples by pathway activities to allow identifying and prioritizing proteins with potential clinical relevance, e.g., associated with patient prognosis. Using DNA copy number alteration and RNA-seq data from head and neck squamous cell carcinoma patients from The Cancer Genome Atlas as an example, we demonstrate that MPAC predicts a patient subgroup related to immune responses not identified by analysis with either input omic data type alone. Key proteins identified via this subgroup have pathway activities related to clinical outcome as well as immune cell compositions. Our MPAC R package, available at https://bioconductor.org/packages/MPAC, enables similar multi-omic analyses on new datasets.

Journal Article↗
PubMedDate not supplied

Visualizing Internet routing changes.

Today's Internet provides a global data delivery service to millions of end users and routing protocols play a critical role in this service. It is important to be able to identify and diagnose any problems occurring in Internet routing. However, the Internet's sheer size makes this task difficult. One cannot easily extract out the most important or relevant routing information from the large amounts of data collected from multiple routers. To tackle this problem, we have developed Link-Rank, a tool to visualize Internet routing changes at the global scale. Link-Rank weighs links in a topological graph by the number of routes carried over each link and visually captures changes in link weights in the form of a topological graph with adjustable size. Using Link-Rank, network operators can easily observe important routing changes from massive amounts of routing data, discover otherwise unnoticed routing problems, understand the impact of topological events, and infer root causes of observed routing changes.

Algorithms↗
PubMed2001

Using graphical models and genomic expression data to statistically validate models of genetic regulatory networks.

We propose a model-driven approach for analyzing genomic expression data that permits genetic regulatory networks to be represented in a biologically interpretable computational form. Our models permit latent variables capturing unobserved factors, describe arbitrarily complex (more than pair-wise) relationships at varying levels of refinement, and can be scored rigorously against observational data. The models that we use are based on Bayesian networks and their extensions. As a demonstration of this approach, we utilize 52 genomes worth of Affymetrix GeneChip expression data to correctly differentiate between alternative hypotheses of the galactose regulatory network in S. cerevisiae. When we extend the graph semantics to permit annotated edges, we are able to score models describing relationships at a finer degree of specification.

Bayes Theorem↗
PubMed2005

A new dynamical layout algorithm for complex biochemical reaction networks.

BACKGROUND: To study complex biochemical reaction networks in living cells researchers more and more rely on databases and computational methods. In order to facilitate computational approaches, visualisation techniques are highly important. Biochemical reaction networks, e.g. metabolic pathways are often depicted as graphs and these graphs should be drawn dynamically to provide flexibility in the context of different data. Conventional layout algorithms are not sufficient for every kind of pathway in biochemical research. This is mainly due to certain conventions to which biochemists/biologists are used to and which are not in accordance to conventional layout algorithms. A number of approaches has been developed to improve this situation. Some of these are used in the context of biochemical databases and make more or less use of the information in these databases to aid the layout process. However, visualisation becomes also more and more important in modelling and simulation tools which mostly do not offer additional connections to databases. Therefore, layout algorithms used in these tools have to work independently of any databases. In addition, all of the existing algorithms face some limitations with respect to the number of edge crossings when it comes to larger biochemical systems due to the interconnectivity of these. Last but not least, in some cases, biochemical conventions are not met properly. RESULTS: Out of these reasons we have developed a new algorithm which tackles these problems by reducing the number of edge crossings in complex systems, taking further biological conventions into account to identify and visualise cycles. Furthermore the algorithm is independent from database information in order to be easily adopted in any application. It can also be tested as part of the SimWiz package (free to download for academic users at 1). CONCLUSION: The new algorithm reduces the complexity of pathways, as well as edge crossings and edge length in the resulting graphical representation. It also considers existing and further biological conventions to create a drawing most biochemists are familiar with. A lot of examples can be found on 2.

Algorithms↗
PubMed1995

Uniqueness and multiplicity of steady states in monocyclic enzyme cascades: a graph-theoretic analysis.

Monocyclic enzyme cascades are important regulators of biochemical reactions in living cells. The reaction network may have either one steady state or many, depending on its structure. The occurrence of multiple steady states has important biological implications. A simple graph-theoretic method has been applied to five reaction mechanisms--which together cover many common monocyclic cascades--to determine which mechanisms generate just one steady state and which ones allow more than one state. It is shown that an unstable steady state in a multiplicity region can be usefully exploited and that in some cases transitions may occur between uniqueness and multiplicity regions. The possible effects of such transitions are discussed.

Animals↗
PubMed2005

Core-periphery organization of complex networks.

Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. Among other things we conclude that geographically embedded transportation networks have a strong core-periphery structure. We proceed to study radial statistics of the core, i.e., properties of the neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n neighborhoods at a certain distance from the core suggesting an effective radius for nontrivial network processes.

Journal Article↗
PubMed2005

Oligomeric protein structure networks: insights into protein-protein interactions.

BACKGROUND: Protein-protein association is essential for a variety of cellular processes and hence a large number of investigations are being carried out to understand the principles of protein-protein interactions. In this study, oligomeric protein structures are viewed from a network perspective to obtain new insights into protein association. Structure graphs of proteins have been constructed from a non-redundant set of protein oligomer crystal structures by considering amino acid residues as nodes and the edges are based on the strength of the non-covalent interactions between the residues. The analysis of such networks has been carried out in terms of amino acid clusters and hubs (highly connected residues) with special emphasis to protein interfaces. RESULTS: A variety of interactions such as hydrogen bond, salt bridges, aromatic and hydrophobic interactions, which occur at the interfaces are identified in a consolidated manner as amino acid clusters at the interface, from this study. Moreover, the characterization of the highly connected hub-forming residues at the interfaces and their comparison with the hubs from the non-interface regions and the non-hubs in the interface regions show that there is a predominance of charged interactions at the interfaces. Further, strong and weak interfaces are identified on the basis of the interaction strength between amino acid residues and the sizes of the interface clusters, which also show that many protein interfaces are stronger than their monomeric protein cores. The interface strengths evaluated based on the interface clusters and hubs also correlate well with experimentally determined dissociation constants for known complexes. Finally, the interface hubs identified using the present method correlate very well with experimentally determined hotspots in the interfaces of protein complexes obtained from the Alanine Scanning Energetics database (ASEdb). A few predictions of interface hot spots have also been made based on the results obtained from this analysis, which await experimental verification. CONCLUSION: The construction and analysis of oligomeric protein structure networks and their comparison with monomeric protein structure networks provide insights into protein association. Further, the interface hubs identified using the present method can be effective targets for interface de-stabilizing mutations. We believe this analysis will significantly enhance our knowledge of the principles behind protein association and also aid in protein design.

Animals↗
PubMed2004

WebInterViewer: visualizing and analyzing molecular interaction networks.

Molecular interaction networks, such as those involving protein-protein and protein-DNA interactions, often consist of thousands of nodes or even more, which severely limits the usefulness of many graph drawing tools because they become too slow for interactive analysis of the networks and because they produce cluttered drawings with many edge crossings. We present a new, fast-layout algorithm and its implementation called WebInterViewer for visualizing large-scale molecular interaction networks. WebInterViewer (i) finds a layout of the connected components of an entire network, (ii) finds a global layout of nodes with respect to pivot nodes within the connected components and (iii) refines the local layout of each connected component by first relocating midnodes with respect to their cutvertices and the direct neighbors of the cutvertices, and then relocating all nodes with respect to their neighbors within distance 2. The advantages of WebInterViewer over classical graph drawing methods include the facts that (i) it is an order of magnitude faster, (ii) it can visualize data directly from protein interaction databases and (iii) it provides several abstraction and comparison operations for analyzing large-scale biological networks effectively. WebInterViewer is accessible at http://interviewer.inha.ac.kr/.

Computer Graphics↗
PubMed2006

Identification of functional modules in a PPI network by clique percolation clustering.

Large-scale experiments and data integration have provided the opportunity to systematically analyze and comprehensively understand the topology of biological networks and biochemical processes in cells. Modular architecture which encompasses groups of genes/proteins involved in elementary biological functional units is a basic form of the organization of interacting proteins. Here we apply a graph clustering algorithm based on clique percolation clustering to detect overlapping network modules of a protein-protein interaction (PPI) network. Our analysis of the yeast Sacchromyces cerevisiae suggests that most of the detected modules correspond to one or more experimentally functional modules and half of these annotated modules match well with experimentally determined protein complexes. Our method of analysis can of course be applied to protein-protein interaction data for any species and even other biological networks.

Algorithms↗