IntNetDB v1.0: an integrated protein-protein interaction network database generated by a probabilistic model

Background  

Although protein-protein interaction (PPI) networks have been explored by various experimental methods, the maps so built are still limited in coverage and accuracy. To further expand the PPI network and to extract more accurate information from existing maps, studies have been carried out to integrate various types of functional relationship data. A frequently updated database of computationally analyzed potential PPIs to provide biological researchers with rapid and easy access to analyze original data as a biological network is still lacking.     

QuateXelero: An Accelerated Exact Network Motif Detection Algorithm

Finding motifs in biological, social, technological, and other types of networks has become a widespread method to gain more knowledge about these networks’ structure and function. However, this task is very computationally demanding, because it is highly associated with the graph isomorphism which is an NP problem (not known to belong to P or NP-complete subsets yet). Accordingly, this research is endeavoring to decrease the need to call NAUTY isomorphism detection method, which is the most time-consuming step in many existing algorithms. The work provides an extremely fast motif detection algorithm called QuateXelero, which has a Quaternary Tree data structure in the heart. The proposed algorithm is based on the well-known ESU (FANMOD) motif detection algorithm. The results of experiments on some standard model networks approve the overal superiority of the proposed algorithm, namely QuateXelero, compared with two of the fastest existing algorithms, G-Tries and Kavosh. QuateXelero is especially fastest in constructing the central data structure of the algorithm from scratch based on the input network.     

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.     

Protein side-chain packing problem: a maximum edge-weight clique algorithmic approach

"Protein Side-chain Packing" has an ever-increasing application in the field of bio-informatics, dating from the early methods of homology modeling to protein design and to the protein docking. However, this problem is computationally known to be NP-hard. In this regard, we have developed a novel approach to solve this problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain packing problem to a graph and then solving the reduced graph to find the maximum clique by applying an efficient clique finding algorithm developed by our co-authors. Since our approach is based on deterministic algorithms in contrast to the various existing algorithms based on heuristic approaches, our algorithm guarantees of finding an optimal solution. We have tested this approach to predict the side-chain conformations of a set of proteins and have compared the results with other existing methods. We have found that our results are favorably comparable or better than the results produced by the existing methods. As our test set contains a protein of 494 residues, we have obtained considerable improvement in terms of size of the proteins and in terms of the efficiency and the accuracy of prediction.     

Fully automated protein complex prediction based on topological similarity and community structure

To understand the function of protein complexes and their association with biological processes, a lot of studies have been done towards analyzing the protein-protein interaction (PPI) networks. However, the advancement in high-throughput technology has resulted in a humongous amount of data for analysis. Moreover, high level of noise, sparseness, and skewness in degree distribution of PPI networks limits the performance of many clustering algorithms and further analysis of their interactions.In addressing and solving these problems we present a novel random walk based algorithm that converts the incomplete and binary PPI network into a protein-protein topological similarity matrix (PP-TS matrix). We believe that if two proteins share some high-order topological similarities they are likely to be interacting with each other. Using the obtained PP-TS matrix, we constructed and used weighted networks to further study and analyze the interaction among proteins. Specifically, we applied a fully automated community structure finding algorithm (Auto-HQcut) on the obtained weighted network to cluster protein complexes. We then analyzed the protein complexes for significance in biological processes. To help visualize and analyze these protein complexes we also developed an interface that displays the resulting complexes as well as the characteristics associated with each complex.Applying our approach to a yeast protein-protein interaction network, we found that the predicted protein-protein interaction pairs with high topological similarities have more significant biological relevance than the original protein-protein interactions pairs. When we compared our PPI network reconstruction algorithm with other existing algorithms using gene ontology and gene co-expression, our algorithm produced the highest similarity scores. Also, our predicted protein complexes showed higher accuracy measure compared to the other protein complex predictions.     

Basic networks: Definition and applications

We define basic networks as the undirected subgraphs with minimal number of units in which the distances (geodesics, minimal path lengths) among a set of selected nodes, which we call seeds, in the original graph are conserved. The additional nodes required to draw the basic network are called connectors. We describe a heuristic strategy to find the basic networks of complex graphs. We also show how the characterization of these networks may help to obtain relevant biological information from highly complex protein-protein interaction data.     

Functional annotation from predicted protein interaction networks

MOTIVATION: Progress in large-scale experimental determination of protein-protein interaction networks for several organisms has resulted in innovative methods of functional inference based on network connectivity. However, the amount of effort and resources required for the elucidation of experimental protein interaction networks is prohibitive. Previously we, and others, have developed techniques to predict protein interactions for novel genomes using computational methods and data generated from other genomes. RESULTS: We evaluated the performance of a network-based functional annotation method that makes use of our predicted protein interaction networks. We show that this approach performs equally well on experimentally derived and predicted interaction networks, for both manually and computationally assigned annotations. We applied the method to predicted protein interaction networks for over 50 organisms from all domains of life, providing annotations for many previously unannotated proteins and verifying existing low-confidence annotations. AVAILABILITY: Functional predictions for over 50 organisms are available at http://bioverse.compbio.washington.edu and datasets used for analysis at http://data.compbio.washington.edu/misc/downloads/nannotation_data/. SUPPLEMENTARY INFORMATION: A supplemental appendix gives additional details not in the main text. (http://data.compbio.washington.edu/misc/downloads/nannotation_data/supplement.pdf).     

Path matching and graph matching in biological networks.

We develop algorithms for the following path matching and graph matching problems: (i) given a query path p and a graph G, find a path p' that is most similar to p in G; (ii) given a query graph G (0) and a graph G, find a graph G (0)' that is most similar to G (0) in G. In these problems, p and G (0) represent a given substructure of interest to a biologist, and G represents a large network in which the biologist desires to find a related substructure. These algorithms allow the study of common substructures in biological networks in order to understand how these networks evolve both within and between organisms. We reduce the path matching problem to finding a longest weighted path in a directed acyclic graph and show that the problem of finding top k suboptimal paths can be solved in polynomial time. This is in contrast with most previous approaches that used exponential time algorithms to find simple paths which are practical only when the paths are short. We reduce the graph matching problem to finding highest scoring subgraphs in a graph and give an exact algorithm to solve the problem when the query graph G (0) is of moderate size. This eliminates the need for less accurate heuristic or randomized algorithms.We show that our algorithms are able to extract biologically meaningful pathways from protein interaction networks in the DIP database and metabolic networks in the KEGG database. Software programs implementing these techniques (PathMatch and GraphMatch) are available at http://faculty.cs.tamu.edu/shsze/pathmatch and http://faculty.cs.tamu.edu/shsze/graphmatch.     

Predicting protein functions from PPI networks using functional aggregation

Predicting protein functions computationally from massive protein-protein interaction (PPI) data generated by high-throughput technology is one of the challenges and fundamental problems in the post-genomic era. Although there have been many approaches developed for computationally predicting protein functions, the mutual correlations among proteins in terms of protein functions have not been thoroughly investigated and incorporated into existing prediction methods, especially in voting based prediction methods. In this paper, we propose an innovative method to predict protein functions from PPI data by aggregating the functional correlations among relevant proteins using the Choquet-Integral in fuzzy theory. This functional aggregation measures the real impact of each relevant protein function on the final prediction results, and reduces the impact of repeated functional information on the prediction. Accordingly, a new protein similarity and a new iterative prediction algorithm are proposed in this paper. The experimental evaluations on real PPI datasets demonstrate the effectiveness of our method.     

Growing Bayesian network models of gene networks from seed genes

MOTIVATION: For the last few years, Bayesian networks (BNs) have received increasing attention from the computational biology community as models of gene networks, though learning them from gene-expression data is problematic. Most gene-expression databases contain measurements for thousands of genes, but the existing algorithms for learning BNs from data do not scale to such high-dimensional databases. This means that the user has to decide in advance which genes are included in the learning process, typically no more than a few hundreds, and which genes are excluded from it. This is not a trivial decision. We propose an alternative approach to overcome this problem. RESULTS: We propose a new algorithm for learning BN models of gene networks from gene-expression data. Our algorithm receives a seed gene S and a positive integer R from the user, and returns a BN for the genes that depend on S such that less than R other genes mediate the dependency. Our algorithm grows the BN, which initially only contains S, by repeating the following step R + 1 times and, then, pruning some genes; find the parents and children of all the genes in the BN and add them to it. Intuitively, our algorithm provides the user with a window of radius R around S to look at the BN model of a gene network without having to exclude any gene in advance. We prove that our algorithm is correct under the faithfulness assumption. We evaluate our algorithm on simulated and biological data (Rosetta compendium) with satisfactory results.     

MTMO: an efficient network-centric algorithm for subtree counting and enumeration

Background: The frequency of small subtrees in biological, social, and other types of networks could shed light into the structure, function, and evolution of such networks. However, counting all possible subtrees of a prescribed size can be computationally expensive because of their potentially large number even in small, sparse networks. Moreover, most of the existing algorithms for subtree counting belong to the subtree-centric approaches, which search for a specific single subtree type at a time, potentially taking more time by searching again on the same network. Methods: In this paper, we propose a network-centric algorithm (MTMO) to efficiently count k-size subtrees. Our algorithm is based on the enumeration of all connected sets of k–1 edges, incorporates a labeled rooted tree data structure in the enumeration process to reduce the number of isomorphism tests required, and uses an array-based indexing scheme to simplify the subtree counting method. Results: The experiments on three representative undirected complex networks show that our algorithm is roughly an order of magnitude faster than existing subtree-centric approaches and base network-centric algorithm which does not use rooted tree, allowing for counting larger subtrees in larger networks than previously possible. We also show major differences between unicellular and multicellular organisms. In addition, our algorithm is applied to find network motifs based on pattern growth approach. Conclusions: A network-centric algorithm which allows for a faster counting of non-induced subtrees is proposed. This enables us to count larger motif in larger networks than previously.     

Assessing significance of connectivity and conservation in protein interaction networks.

Comparative analyses of cellular interaction networks enable understanding of the cell's modular organization through identification of functional modules and complexes. These techniques often rely on topological features such as connectedness and density, based on the premise that functionally related proteins are likely to interact densely and that these interactions follow similar evolutionary trajectories. Significant recent work has focused on efficient algorithms for identification of such functional modules and their conservation. In spite of algorithmic advances, development of a comprehensive infrastructure for interaction databases is in relative infancy compared to corresponding sequence analysis tools. One critical, and as yet unresolved aspect of this infrastructure is a measure of the statistical significance of a match, or a dense subcomponent. In the absence of analytical measures, conventional methods rely on computationally expensive simulations based on ad-hoc models for quantifying significance. In this paper, we present techniques for analytically quantifying statistical significance of dense components in reference model graphs. We consider two reference models--a G(n, p) model in which each pair of nodes in a graph has an identical likelihood, p, of sharing an edge, and a two-level G(n, p) model, which accounts for high-degree hub nodes generally observed in interaction networks. Experiments performed on a rich collection of protein interaction (PPI) networks show that the proposed model provides a reliable means of evaluating statistical significance of dense patterns in these networks. We also adapt existing state-of-the-art network clustering algorithms by using our statistical significance measure as an optimization criterion. Comparison of the resulting module identification algorithm, SIDES, with existing methods shows that SIDES outperforms existing algorithms in terms of sensitivity and specificity of identified clusters with respect to available GO annotations.     

Efficient algorithms for detecting signaling pathways in protein interaction networks.

The interpretation of large-scale protein network data depends on our ability to identify significant substructures in the data, a computationally intensive task. Here we adapt and extend efficient techniques for finding paths and trees in graphs to the problem of identifying pathways in protein interaction networks. We present linear-time algorithms for finding paths and trees in networks under several biologically motivated constraints. We apply our methodology to search for protein pathways in the yeast protein-protein interaction network. We demonstrate that our algorithm is capable of reconstructing known signaling pathways and identifying functionally enriched paths and trees in an unsupervised manner. The algorithm is very efficient, computing optimal paths of length 8 within minutes and paths of length 10 in about three hours.     

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.     

Extended graphical lasso for multiple interaction networks for high dimensional omics data

There has been a spate of interest in association networks in biological and medical research, for example, genetic interaction networks. In this paper, we propose a novel method, the extended joint hub graphical lasso (EDOHA), to estimate multiple related interaction networks for high dimensional omics data across multiple distinct classes. To be specific, we construct a convex penalized log likelihood optimization problem and solve it with an alternating direction method of multipliers (ADMM) algorithm. The proposed method can also be adapted to estimate interaction networks for high dimensional compositional data such as microbial interaction networks. The performance of the proposed method in the simulated studies shows that EDOHA has remarkable advantages in recognizing class-specific hubs than the existing comparable methods. We also present three applications of real datasets. Biological interpretations of our results confirm those of previous studies and offer a more comprehensive understanding of the underlying mechanism in disease.     

Network Reconstruction Based on Proteomic Data and Prior Knowledge of Protein Connectivity Using Graph Theory

Modeling of signal transduction pathways is instrumental for understanding cells’ function. People have been tackling modeling of signaling pathways in order to accurately represent the signaling events inside cells’ biochemical microenvironment in a way meaningful for scientists in a biological field. In this article, we propose a method to interrogate such pathways in order to produce cell-specific signaling models. We integrate available prior knowledge of protein connectivity, in a form of a Prior Knowledge Network (PKN) with phosphoproteomic data to construct predictive models of the protein connectivity of the interrogated cell type. Several computational methodologies focusing on pathways’ logic modeling using optimization formulations or machine learning algorithms have been published on this front over the past few years. Here, we introduce a light and fast approach that uses a breadth-first traversal of the graph to identify the shortest pathways and score proteins in the PKN, fitting the dependencies extracted from the experimental design. The pathways are then combined through a heuristic formulation to produce a final topology handling inconsistencies between the PKN and the experimental scenarios. Our results show that the algorithm we developed is efficient and accurate for the construction of medium and large scale signaling networks. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGF/TNFA stimulation against made up experimental data. To avoid the possibility of erroneous predictions, we performed a cross-validation analysis. Finally, we validate that the introduced approach generates predictive topologies, comparable to the ILP formulation. Overall, an efficient approach based on graph theory is presented herein to interrogate protein–protein interaction networks and to provide meaningful biological insights.     

A Graph Algorithmic Approach to Separate Direct from Indirect Neural Interactions

Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between multiple neural sources. Interactions are often reconstructed using pairwise bivariate analyses, overlooking the multivariate nature of interactions: it is neglected that investigating the effect of one source on a target necessitates to take all other sources as potential nuisance variables into account; also combinations of sources may act jointly on a given target. Bivariate analyses produce networks that may contain spurious interactions, which reduce the interpretability of the network and its graph metrics. A truly multivariate reconstruction, however, is computationally intractable because of the combinatorial explosion in the number of potential interactions. Thus, we have to resort to approximative methods to handle the intractability of multivariate interaction reconstruction, and thereby enable the use of networks in neuroscience. Here, we suggest such an approximative approach in the form of an algorithm that extends fast bivariate interaction reconstruction by identifying potentially spurious interactions post-hoc: the algorithm uses interaction delays reconstructed for directed bivariate interactions to tag potentially spurious edges on the basis of their timing signatures in the context of the surrounding network. Such tagged interactions may then be pruned, which produces a statistically conservative network approximation that is guaranteed to contain non-spurious interactions only. We describe the algorithm and present a reference implementation in MATLAB to test the algorithm’s performance on simulated networks as well as networks derived from magnetoencephalographic data. We discuss the algorithm in relation to other approximative multivariate methods and highlight suitable application scenarios. Our approach is a tractable and data-efficient way of reconstructing approximative networks of multivariate interactions. It is preferable if available data are limited or if fully multivariate approaches are computationally infeasible.     

Counting motifs in dynamic networks

Background

A network motif is a sub-network that occurs frequently in a given network. Detection of such motifs is important since they uncover functions and local properties of the given biological network. Finding motifs is however a computationally challenging task as it requires solving the costly subgraph isomorphism problem. Moreover, the topology of biological networks change over time. These changing networks are called dynamic biological networks. As the network evolves, frequency of each motif in the network also changes. Computing the frequency of a given motif from scratch in a dynamic network as the network topology evolves is infeasible, particularly for large and fast evolving networks.

Results

In this article, we design and develop a scalable method for counting the number of motifs in a dynamic biological network. Our method incrementally updates the frequency of each motif as the underlying network’s topology evolves. Our experiments demonstrate that our method can update the frequency of each motif in orders of magnitude faster than counting the motif embeddings every time the network changes. If the network evolves more frequently, the margin with which our method outperforms the existing static methods, increases.

Conclusions

We evaluated our method extensively using synthetic and real datasets, and show that our method is highly accurate(≥?96%) and that it can be scaled to large dense networks. The results on real data demonstrate the utility of our method in revealing interesting insights on the evolution of biological processes.