The identification of similarities between biological networks: application to the metabolome and interactome

The increasing interest in systems biology has resulted in extensive experimental data describing networks of interactions (or associations) between molecules in metabolism, protein-protein interactions and gene regulation. Comparative analysis of these networks is central to understanding biological systems. We report a novel method (PHUNKEE: Pairing subgrapHs Using NetworK Environment Equivalence) by which similar subgraphs in a pair of networks can be identified. Like other methods, PHUNKEE explicitly considers the graphical form of the data and allows for gaps. However, it is novel in that it includes information about the context of the subgraph within the adjacent network. We also explore a new approach to quantifying the statistical significance of matching subgraphs. We report similar subgraphs in metabolic pathways and in protein-protein interaction networks. The most similar metabolic subgraphs were generally found to occur in processes central to all life, such as purine, pyrimidine and amino acid metabolism. The most similar pairs of subgraphs found in the protein-protein interaction networks of Drosophila melanogaster and Saccharomyces cerevisiae also include central processes such as cell division but, interestingly, also include protein sub-networks involved in pre-mRNA processing. The inclusion of network context information in the comparison of protein interaction networks increased the number of similar subgraphs found consisting of proteins involved in the same functional process. This could have implications for the prediction of protein function.     

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.     

Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs

SUMMARY: Biological and engineered networks have recently been shown to display network motifs: a small set of characteristic patterns that occur much more frequently than in randomized networks with the same degree sequence. Network motifs were demonstrated to play key information processing roles in biological regulation networks. Existing algorithms for detecting network motifs act by exhaustively enumerating all subgraphs with a given number of nodes in the network. The runtime of such algorithms increases strongly with network size. Here, we present a novel algorithm that allows estimation of subgraph concentrations and detection of network motifs at a runtime that is asymptotically independent of the network size. This algorithm is based on random sampling of subgraphs. Network motifs are detected with a surprisingly small number of samples in a wide variety of networks. Our method can be applied to estimate the concentrations of larger subgraphs in larger networks than was previously possible with exhaustive enumeration algorithms. We present results for high-order motifs in several biological networks and discuss their possible functions. AVAILABILITY: A software tool for estimating subgraph concentrations and detecting network motifs (mfinder 1.1) and further information is available at http://www.weizmann.ac.il/mcb/UriAlon/     

A Novel Core‐Attachment–Based Method to Identify Dynamic Protein Complexes Based on Gene Expression Profiles and PPI Networks

Cellular functions are always performed by protein complexes. At present, many approaches have been proposed to identify protein complexes from protein–protein interaction (PPI) networks. Some approaches focus on detecting local dense subgraphs in PPI networks which are regarded as protein‐complex cores, then identify protein complexes by including local neighbors. However, from gene expression profiles at different time points or tissues it is known that proteins are dynamic. Therefore, identifying dynamic protein complexes should become very important and meaningful. In this study, a novel core‐attachment–based method named CO‐DPC to detect dynamic protein complexes is presented. First, CO‐DPC selects active proteins according to gene expression profiles and the 3‐sigma principle, and constructs dynamic PPI networks based on the co‐expression principle and PPI networks. Second, CO‐DPC detects local dense subgraphs as the cores of protein complexes and then attach close neighbors of these cores to form protein complexes. In order to evaluate the method, the method and the existing algorithms are applied to yeast PPI networks. The experimental results show that CO‐DPC performs much better than the existing methods. In addition, the identified dynamic protein complexes can match very well and thus become more meaningful for future biological study.     

The Index-Based Subgraph Matching Algorithm with General Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph Enumeration

Subgraph matching algorithms are used to find and enumerate specific interconnection structures in networks. By enumerating these specific structures/subgraphs, the fundamental properties of the network can be derived. More specifically in biological networks, subgraph matching algorithms are used to discover network motifs, specific patterns occurring more often than expected by chance. Finding these network motifs yields information on the underlying biological relations modelled by the network. In this work, we present the Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS), an improved version of the Index-based Subgraph Matching Algorithm (ISMA). ISMA quickly finds all instances of a predefined motif in a network by intelligently exploring the search space and taking into account easily identifiable symmetric structures. However, more complex symmetries (possibly involving switching multiple nodes) are not taken into account, resulting in superfluous output. ISMAGS overcomes this problem by using a customised symmetry analysis phase to detect all symmetric structures in the network motif subgraphs. These structures are then converted to symmetry-breaking constraints used to prune the search space and speed up calculations. The performance of the algorithm was tested on several types of networks (biological, social and computer networks) for various subgraphs with a varying degree of symmetry. For subgraphs with complex (multi-node) symmetric structures, high speed-up factors are obtained as the search space is pruned by the symmetry-breaking constraints. For subgraphs with no or simple symmetric structures, ISMAGS still reduces computation times by optimising set operations. Moreover, the calculated list of subgraph instances is minimal as it contains no instances that differ by only a subgraph symmetry. An implementation of the algorithm is freely available at https://github.com/mhoubraken/ISMAGS.     

Identification of core-attachment complexes based on maximal frequent patterns in protein-protein interaction networks

In this paper, we present a method for core-attachment complexes identification based on maximal frequent patterns (CCiMFP) in yeast protein-protein interaction (PPI) networks. First, we detect subgraphs with high degree as candidate protein cores by mining maximal frequent patterns. Then using topological and functional similarities, we combine highly similar protein cores and filter insignificant ones. Finally, the core-attachment complexes are formed by adding attachment proteins to each significant core. We experimentally evaluate the performance of our method CCiMFP on yeast PPI networks. Using gold standard sets of protein complexes, Gene Ontology (GO), and localization annotations, we show that our method gains an improvement over the previous algorithms in terms of precision, recall, and biological significance of the predicted complexes. The colocalization scores of our predicted complex sets are higher than those of two known complex sets. Moreover, our method can detect GO-enriched complexes with disconnected cores compared with other methods based on the subgraph connectivity.     

eXPatGen: generating dynamic expression patterns for the systematic evaluation of analytical methods

MOTIVATION: Experimental gene expression data sets, such as those generated by microarray or gene chip experiments, typically have significant noise and complicated interconnectivities that make understanding even simple regulatory patterns difficult. Given these complications, characterizing the effectiveness of different analysis techniques to uncover network groups and structures remains a challenge. Generating simulated expression patterns with known biological features of expression complexity, diversity and interconnectivities provides a more controlled means of investigating the appropriateness of different analysis methods. A simulation-based approach can systematically evaluate different gene expression analysis techniques and provide a basis for improved methods in dynamic metabolic network reconstruction. RESULTS: We have developed an on-line simulator, called eXPatGen, to generate dynamic gene expression patterns typical of microarray experiments. eXPatGen provides a quantitative network structure to represent key biological features, including the induction, repression, and cascade regulation of messenger RNA (mRNA). The simulation is modular such that the expression model can be replaced with other representations, depending on the level of biological detail required by the user. Two example gene networks, of 25 and 100 genes respectively, were simulated. Two standard analysis techniques, clustering and PCA analysis, were performed on the resulting expression patterns in order to demonstrate how the simulator might be used to evaluate different analysis methods and provide experimental guidance for biological studies of gene expression. AVAILABILITY: http://www.che.udel.edu/eXPatGen/     

Dynamical systems for discovering protein complexes and functional modules from biological networks

Recent advances in high throughput experiments and annotations via published literature have provided a wealth of interaction maps of several biomolecular networks, including metabolic, protein-protein, and protein-DNA interaction networks. The architecture of these molecular networks reveals important principles of cellular organization and molecular functions. Analyzing such networks, i.e., discovering dense regions in the network, is an important way to identify protein complexes and functional modules. This task has been formulated as the problem of finding heavy subgraphs, the heaviest k-subgraph problem (k-HSP), which itself is NP-hard. However, any method based on the k-HSP requires the parameter k and an exact solution of k-HSP may still end up as a "spurious" heavy subgraph, thus reducing its practicability in analyzing large scale biological networks. We proposed a new formulation, called the rank-HSP, and two dynamical systems to approximate its results. In addition, a novel metric, called the standard deviation and mean ratio (SMR), is proposed for use in "spurious" heavy subgraphs to automate the discovery by setting a fixed threshold. Empirical results on both the simulated graphs and biological networks have demonstrated the efficiency and effectiveness of our proposal     

An iterative network partition algorithm for accurate identification of dense network modules

A key step in network analysis is to partition a complex network into dense modules. Currently, modularity is one of the most popular benefit functions used to partition network modules. However, recent studies suggested that it has an inherent limitation in detecting dense network modules. In this study, we observed that despite the limitation, modularity has the advantage of preserving the primary network structure of the undetected modules. Thus, we have developed a simple iterative Network Partition (iNP) algorithm to partition a network. The iNP algorithm provides a general framework in which any modularity-based algorithm can be implemented in the network partition step. Here, we tested iNP with three modularity-based algorithms: multi-step greedy (MSG), spectral clustering and Qcut. Compared with the original three methods, iNP achieved a significant improvement in the quality of network partition in a benchmark study with simulated networks, identified more modules with significantly better enrichment of functionally related genes in both yeast protein complex network and breast cancer gene co-expression network, and discovered more cancer-specific modules in the cancer gene co-expression network. As such, iNP should have a broad application as a general method to assist in the analysis of biological networks.     

Mining Dense Overlapping Subgraphs in weighted protein-protein interaction networks

Many methods have been proposed for mining protein complexes from a protein-protein interaction network; however, most of them focus on unweighted networks and cannot find overlapping protein complexes. Since one protein may serve different roles within different functional groups, mining overlapping protein complexes in a weighted protein-protein interaction network has attracted more and more attention recently. In this paper, we propose an effective method, called MDOS (Mining Dense Overlapping Subgraphs), for mining dense overlapping protein complexes (subgraphs) in a weighted protein-protein interaction network. The proposed method can integrate the information about known complexes into a weighted protein-protein interaction network to improve the mining results. The experiment results show that our method mines more known complexes and has higher sensitivity and accuracy than the CODENSE and MCL methods.     

Modelling the evolution of genetic regulatory networks

An evolutionary model of genetic regulatory networks is developed, based on a model of network encoding and dynamics called the Artificial Genome (AG). This model derives a number of specific genes and their interactions from a string of (initially random) bases in an idealized manner analogous to that employed by natural DNA. The gene expression dynamics are determined by updating the gene network as if it were a simple Boolean network. The generic behaviour of the AG model is investigated in detail. In particular, we explore the characteristic network topologies generated by the model, their dynamical behaviours, and the typical variance of network connectivities and network structures. These properties are demonstrated to agree with a probabilistic analysis of the model, and the typical network structures generated by the model are shown to lie between those of random networks and scale-free networks in terms of their degree distribution. Evolutionary processes are simulated using a genetic algorithm, with selection acting on a range of properties from gene number and degree of connectivity through periodic behaviour to specific patterns of gene expression. The evolvability of increasingly complex patterns of gene expression is examined in detail. When a degree of redundancy is introduced, the average number of generations required to evolve given targets is reduced, but limits on evolution of complex gene expression patterns remain. In addition, cyclic gene expression patterns with periods that are multiples of shorter expression patterns are shown to be inherently easier to evolve than others. Constraints imposed by the template-matching nature of the AG model generate similar biases towards such expression patterns in networks in initial populations, in addition to the somewhat scale-free nature of these networks. The significance of these results on current understanding of biological evolution is discussed.     

CPredictor3.0: detecting protein complexes from PPI networks with expression data and functional annotations

Background

Effectively predicting protein complexes not only helps to understand the structures and functions of proteins and their complexes, but also is useful for diagnosing disease and developing new drugs. Up to now, many methods have been developed to detect complexes by mining dense subgraphs from static protein-protein interaction (PPI) networks, while ignoring the value of other biological information and the dynamic properties of cellular systems.

Results

In this paper, based on our previous works CPredictor and CPredictor2.0, we present a new method for predicting complexes from PPI networks with both gene expression data and protein functional annotations, which is called CPredictor3.0. This new method follows the viewpoint that proteins in the same complex should roughly have similar functions and are active at the same time and place in cellular systems. We first detect active proteins by using gene express data of different time points and cluster proteins by using gene ontology (GO) functional annotations, respectively. Then, for each time point, we do set intersections with one set corresponding to active proteins generated from expression data and the other set corresponding to a protein cluster generated from functional annotations. Each resulting unique set indicates a cluster of proteins that have similar function(s) and are active at that time point. Following that, we map each cluster of active proteins of similar function onto a static PPI network, and get a series of induced connected subgraphs. We treat these subgraphs as candidate complexes. Finally, by expanding and merging these candidate complexes, the predicted complexes are obtained.We evaluate CPredictor3.0 and compare it with a number of existing methods on several PPI networks and benchmarking complex datasets. The experimental results show that CPredictor3.0 achieves the highest F1-measure, which indicates that CPredictor3.0 outperforms these existing method in overall.

Conclusion

CPredictor3.0 can serve as a promising tool of protein complex prediction.

     

Cytoscape ESP: simple search of complex biological networks

SUMMARY: Cytoscape enhanced search plugin (ESP) enables searching complex biological networks on multiple attribute fields using logical operators and wildcards. Queries use an intuitive syntax and simple search line interface. ESP is implemented as a Cytoscape plugin and complements existing search functions in the Cytoscape network visualization and analysis software, allowing users to easily identify nodes, edges and subgraphs of interest, even for very large networks. Availabiity: http://chianti.ucsd.edu/cyto_web/plugins/ CONTACT: ashkenaz@agri.huji.ac.il.     

Efficient detection of network motifs

Motifs in a given network are small connected subnetworks that occur in significantly higher frequencies than would be expected in random networks. They have recently gathered much attention as a concept to uncover structural design principles of complex networks. Kashtan et al. [Bioinformatics, 2004] proposed a sampling algorithm for performing the computationally challenging task of detecting network motifs. However, among other drawbacks, this algorithm suffers from a sampling bias and scales poorly with increasing subgraph size. Based on a detailed analysis of the previous algorithm, we present a new algorithm for network motif detection which overcomes these drawbacks. Furthermore, we present an efficient new approach for estimating the frequency of subgraphs in random networks that, in contrast to previous approaches, does not require the explicit generation of random networks. Experiments on a testbed of biological networks show our new algorithms to be orders of magnitude faster than previous approaches, allowing for the detection of larger motifs in bigger networks than previously possible and thus facilitating deeper insight into the field