Frequent Pattern Discovery in Multiple Biological Networks: Patterns and Algorithms

The rapid accumulation of biological network data is creating an urgent need for computational methods capable of integrative network analysis. This paper discusses a suite of algorithms that we have developed to discover biologically significant patterns that appear frequently in multiple biological networks: coherent dense subgraphs, frequent dense vertex-sets, generic frequent subgraphs, differential subgraphs, and recurrent heavy subgraphs. We demonstrate these methods on gene co-expression networks, using the identified patterns to systematically annotate gene functions, map genome to phenome, and perform high-order cooperativity analysis.     

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.     

Identifying protein complexes from interaction networks based on clique percolation and distance restriction

Background

Identification of protein complexes in large interaction networks is crucial to understand principles of cellular organization and predict protein functions, which is one of the most important issues in the post-genomic era. Each protein might be subordinate multiple protein complexes in the real protein-protein interaction networks. Identifying overlapping protein complexes from protein-protein interaction networks is a considerable research topic.

Result

As an effective algorithm in identifying overlapping module structures, clique percolation method (CPM) has a wide range of application in social networks and biological networks. However, the recognition accuracy of algorithm CPM is lowly. Furthermore, algorithm CPM is unfit to identifying protein complexes with meso-scale when it applied in protein-protein interaction networks. In this paper, we propose a new topological model by extending the definition of k-clique community of algorithm CPM and introduced distance restriction, and develop a novel algorithm called CP-DR based on the new topological model for identifying protein complexes. In this new algorithm, the protein complex size is restricted by distance constraint to conquer the shortcomings of algorithm CPM. The algorithm CP-DR is applied to the protein interaction network of Sacchromyces cerevisiae and identifies many well known complexes.

Conclusion

The proposed algorithm CP-DR based on clique percolation and distance restriction makes it possible to identify dense subgraphs in protein interaction networks, a large number of which correspond to known protein complexes. Compared to algorithm CPM, algorithm CP-DR has more outstanding performance.

     

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.     

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.     

NetMODE: Network Motif Detection without Nauty

A motif in a network is a connected graph that occurs significantly more frequently as an induced subgraph than would be expected in a similar randomized network. By virtue of being atypical, it is thought that motifs might play a more important role than arbitrary subgraphs. Recently, a flurry of advances in the study of network motifs has created demand for faster computational means for identifying motifs in increasingly larger networks. Motif detection is typically performed by enumerating subgraphs in an input network and in an ensemble of comparison networks; this poses a significant computational problem. Classifying the subgraphs encountered, for instance, is typically performed using a graph canonical labeling package, such as Nauty, and will typically be called billions of times. In this article, we describe an implementation of a network motif detection package, which we call NetMODE. NetMODE can only perform motif detection for -node subgraphs when , but does so without the use of Nauty. To avoid using Nauty, NetMODE has an initial pretreatment phase, where -node graph data is stored in memory (). For we take a novel approach, which relates to the Reconstruction Conjecture for directed graphs. We find that NetMODE can perform up to around times faster than its predecessors when and up to around times faster when (the exact improvement varies considerably). NetMODE also (a) includes a method for generating comparison graphs uniformly at random, (b) can interface with external packages (e.g. R), and (c) can utilize multi-core architectures. NetMODE is available from netmode.sf.net.     

A lock-and-key model for protein-protein interactions

MOTIVATION: Protein-protein interaction networks are one of the major post-genomic data sources available to molecular biologists. They provide a comprehensive view of the global interaction structure of an organism's proteome, as well as detailed information on specific interactions. Here we suggest a physical model of protein interactions that can be used to extract additional information at an intermediate level: It enables us to identify proteins which share biological interaction motifs, and also to identify potentially missing or spurious interactions. RESULTS: Our new graph model explains observed interactions between proteins by an underlying interaction of complementary binding domains (lock-and-key model). This leads to a novel graph-theoretical algorithm to identify bipartite subgraphs within protein-protein interaction networks where the underlying data are taken from yeast two-hybrid experimental results. By testing on synthetic data, we demonstrate that under certain modelling assumptions, the algorithm will return correct domain information about each protein in the network. Tests on data from various model organisms show that the local and global patterns predicted by the model are indeed found in experimental data. Using functional and protein structure annotations, we show that bipartite subnetworks can be identified that correspond to biologically relevant interaction motifs. Some of these are novel and we discuss an example involving SH3 domains from the Saccharomyces cerevisiae interactome. AVAILABILITY: The algorithm (in Matlab format) is available (see http://www.maths.strath.ac.uk/~aas96106/lock_key.html).     

The Problem of Colliding Networks and its Relation to Cell Fusion and?Cancer

Cell fusion, a process that merges two or more cells into one, is required for normal development and has been explored as a tool for stem cell therapy. It has also been proposed that cell fusion causes cancer and contributes to its progression. These functions rely on a poorly understood ability of cell fusion to create new cell types. We suggest that this ability can be understood by considering cells as attractor networks whose basic property is to adopt a set of distinct, stable, self-maintaining states called attractors. According to this view, fusion of two cell types is a collision of two networks that have adopted distinct attractors. To learn how these networks reach a consensus, we model cell fusion computationally. To do so, we simulate patterns of gene activities using a formalism developed to simulate patterns of memory in neural networks. We find that the hybrid networks can assume attractors that are unrelated to parental attractors, implying that cell fusion can create new cell types by nearly instantaneously moving cells between attractors. We also show that hybrid networks are prone to assume spurious attractors, which are emergent and sporadic network states. This finding means that cell fusion can produce abnormal cell types, including cancerous types, by placing cells into normally inaccessible spurious states. Finally, we suggest that the problem of colliding networks has general significance in many processes represented by attractor networks, including biological, social, and political phenomena.     

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.     

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.

     

Discovering protein complexes in protein interaction networks via exploring the weak ties effect

Background

Studying protein complexes is very important in biological processes since it helps reveal the structure-functionality relationships in biological networks and much attention has been paid to accurately predict protein complexes from the increasing amount of protein-protein interaction (PPI) data. Most of the available algorithms are based on the assumption that dense subgraphs correspond to complexes, failing to take into account the inherence organization within protein complex and the roles of edges. Thus, there is a critical need to investigate the possibility of discovering protein complexes using the topological information hidden in edges.

Results

To provide an investigation of the roles of edges in PPI networks, we show that the edges connecting less similar vertices in topology are more significant in maintaining the global connectivity, indicating the weak ties phenomenon in PPI networks. We further demonstrate that there is a negative relation between the weak tie strength and the topological similarity. By using the bridges, a reliable virtual network is constructed, in which each maximal clique corresponds to the core of a complex. By this notion, the detection of the protein complexes is transformed into a classic all-clique problem. A novel core-attachment based method is developed, which detects the cores and attachments, respectively. A comprehensive comparison among the existing algorithms and our algorithm has been made by comparing the predicted complexes against benchmark complexes.

Conclusions

We proved that the weak tie effect exists in the PPI network and demonstrated that the density is insufficient to characterize the topological structure of protein complexes. Furthermore, the experimental results on the yeast PPI network show that the proposed method outperforms the state-of-the-art algorithms. The analysis of detected modules by the present algorithm suggests that most of these modules have well biological significance in context of complexes, suggesting that the roles of edges are critical in discovering protein complexes.

     

Asymmetric comparison and querying of biological networks

Comparing and querying the protein-protein interaction (PPI) networks of different organisms is important to infer knowledge about conservation across species. Known methods that perform these tasks operate symmetrically, i.e., they do not assign a distinct role to the input PPI networks. However, in most cases, the input networks are indeed distinguishable on the basis of how the corresponding organism is biologically well characterized. In this paper a new idea is developed, that is, to exploit differences in the characterization of organisms at hand in order to devise methods for comparing their PPI networks. We use the PPI network (called Master) of the best characterized organism as a fingerprint to guide the alignment process to the second input network (called Slave), so that generated results preferably retain the structural characteristics of the Master network. Technically, this is obtained by generating from the Master a finite automaton, called alignment model, which is then fed with (a linearization of) the Slave for the purpose of extracting, via the Viterbi algorithm, matching subgraphs. We propose an approach able to perform global alignment and network querying, and we apply it on PPI networks. We tested our method showing that the results it returns are biologically relevant.     

Discovering large conserved functional components in global network alignment by graph matching

Background

Aligning protein-protein interaction (PPI) networks is very important to discover the functionally conserved sub-structures between different species. In recent years, the global PPI network alignment problem has been extensively studied aiming at finding the one-to-one alignment with the maximum matching score. However, finding large conserved components remains challenging due to its NP-hardness.

Results

We propose a new graph matching method GMAlign for global PPI network alignment. It first selects some pairs of important proteins as seeds, followed by a gradual expansion to obtain an initial matching, and then it refines the current result to obtain an optimal alignment result iteratively based on the vertex cover. We compare GMAlign with the state-of-the-art methods on the PPI network pairs obtained from the largest BioGRID dataset and validate its performance. The results show that our algorithm can produce larger size of alignment, and can find bigger and denser common connected subgraphs as well for the first time. Meanwhile, GMAlign can achieve high quality biological results, as measured by functional consistency and semantic similarity of the Gene Ontology terms. Moreover, we also show that GMAlign can achieve better results which are structurally and biologically meaningful in the detection of large conserved biological pathways between species.

Conclusions

GMAlign is a novel global network alignment tool to discover large conserved functional components between PPI networks. It also has many potential biological applications such as conserved pathway and protein complex discovery across species. The GMAlign software and datasets are avaialbile at https://github.com/yzlwhu/GMAlign.

     

Protein complex detection with semi-supervised learning in protein interaction networks

Background

Protein-protein interactions (PPIs) play fundamental roles in nearly all biological processes. The systematic analysis of PPI networks can enable a great understanding of cellular organization, processes and function. In this paper, we investigate the problem of protein complex detection from noisy protein interaction data, i.e., finding the subsets of proteins that are closely coupled via protein interactions. However, protein complexes are likely to overlap and the interaction data are very noisy. It is a great challenge to effectively analyze the massive data for biologically meaningful protein complex detection.

Results

Many people try to solve the problem by using the traditional unsupervised graph clustering methods. Here, we stand from a different point of view, redefining the properties and features for protein complexes and designing a “semi-supervised” method to analyze the problem. In this paper, we utilize the neural network with the “semi-supervised” mechanism to detect the protein complexes. By retraining the neural network model recursively, we could find the optimized parameters for the model, in such a way we can successfully detect the protein complexes. The comparison results show that our algorithm could identify protein complexes that are missed by other methods. We also have shown that our method achieve better precision and recall rates for the identified protein complexes than other existing methods. In addition, the framework we proposed is easy to be extended in the future.

Conclusions

Using a weighted network to represent the protein interaction network is more appropriate than using a traditional unweighted network. In addition, integrating biological features and topological features to represent protein complexes is more meaningful than using dense subgraphs. Last, the “semi-supervised” learning model is a promising model to detect protein complexes with more biological and topological features available.

     

NWE: Node-weighted expansion for protein complex prediction using random walk distances

Background

Protein complexes are important entities to organize various biological processes in the cell, like signal transduction, gene expression, and molecular transmission. In most cases, proteins perform their intrinsic tasks in association with their specific interacting partners, forming protein complexes. Therefore, an enriched catalog of protein complexes in a cell could accelerate further research to elucidate the mechanisms underlying many biological processes. However, known complexes are still limited. Thus, it is a challenging problem to computationally predict protein complexes from protein-protein interaction networks, and other genome-wide data sets.

Methods

Macropol et al. proposed a protein complex prediction algorithm, called RRW, which repeatedly expands a current cluster of proteins according to the stationary vector of a random walk with restarts with the cluster whose proteins are equally weighted. In the cluster expansion, all the proteins within the cluster have equal influences on determination of newly added protein to the cluster. In this paper, we extend the RRW algorithm by introducing a random walk with restarts with a cluster of proteins, each of which is weighted by the sum of the strengths of supporting evidence for the direct physical interactions involving the protein. The resulting algorithm is called NWE (Node-Weighted Expansion of clusters of proteins). Those interaction data are obtained from the WI-PHI database.

Results

We have validated the biological significance of the results using curated complexes in the CYC2008 database, and compared our method to RRW and MCL (Markov Clustering), a popular clustering-based method, and found that our algorithm outperforms the other algorithms.

Conclusions

It turned out that it is an effective approach in protein complex prediction to expand a cluster of proteins, each of which is weighted by the sum of the strengths of supporting evidence for the direct physical interactions involving the protein.

     

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.     

Protein-protein interaction network-based detection of functionally similar proteins within species

Although functionally similar proteins across species have been widely studied, functionally similar proteins within species showing low sequence similarity have not been examined in detail. Identification of these proteins is of significant importance for understanding biological functions, evolution of protein families, progression of co-evolution, and convergent evolution and others which cannot be obtained by detection of functionally similar proteins across species. Here, we explored a method of detecting functionally similar proteins within species based on graph theory. After denoting protein-protein interaction networks using graphs, we split the graphs into subgraphs using the 1-hop method. Proteins with functional similarities in a species were detected using a method of modified shortest path to compare these subgraphs and to find the eligible optimal results. Using seven protein-protein interaction networks and this method, some functionally similar proteins with low sequence similarity that cannot detected by sequence alignment were identified. By analyzing the results, we found that, sometimes, it is difficult to separate homologous from convergent evolution. Evaluation of the performance of our method by gene ontology term overlap showed that the precision of our method was excellent.     

Inferring gene-phenotype associations via global protein complex network propagation

Background

Phenotypically similar diseases have been found to be caused by functionally related genes, suggesting a modular organization of the genetic landscape of human diseases that mirrors the modularity observed in biological interaction networks. Protein complexes, as molecular machines that integrate multiple gene products to perform biological functions, express the underlying modular organization of protein-protein interaction networks. As such, protein complexes can be useful for interrogating the networks of phenome and interactome to elucidate gene-phenotype associations of diseases.

Methodology/Principal Findings

We proposed a technique called RWPCN (Random Walker on Protein Complex Network) for predicting and prioritizing disease genes. The basis of RWPCN is a protein complex network constructed using existing human protein complexes and protein interaction network. To prioritize candidate disease genes for the query disease phenotypes, we compute the associations between the protein complexes and the query phenotypes in their respective protein complex and phenotype networks. We tested RWPCN on predicting gene-phenotype associations using leave-one-out cross-validation; our method was observed to outperform existing approaches. We also applied RWPCN to predict novel disease genes for two representative diseases, namely, Breast Cancer and Diabetes.

Conclusions/Significance

Guilt-by-association prediction and prioritization of disease genes can be enhanced by fully exploiting the underlying modular organizations of both the disease phenome and the protein interactome. Our RWPCN uses a novel protein complex network as a basis for interrogating the human phenome-interactome network. As the protein complex network can capture the underlying modularity in the biological interaction networks better than simple protein interaction networks, RWPCN was found to be able to detect and prioritize disease genes better than traditional approaches that used only protein-phenotype associations.