Network Motif Discovery Research Articles

MOSER: Scalable Network Motif Discovery Using Serial Test

Given a graph G , a motif (e.g., 3-node clique) is a fundamental building block for G. Recently, motif-based graph analysis has attracted much attention due to its efficacy in tasks such as clustering, ranking, and link prediction. These tasks require Network Motif Discovery (NMD) at the early stage to identify the motifs of G. However, existing NMD solutions have two drawbacks: (1) Lack of theoretical guarantees on the quality of the samples generated using the existing methods, and (2) inefficient algorithms, which are not scalable for large graphs. These limitations hinder the exploration of motifs for analyzing large graphs. To address the above issues, we propose a novel solution named MOSER ( MO tif Discovery using SER ial Test). This novel NMD framework leverages a significance testing method known as the serial test, which differs from the existing solutions. We further propose two fast incremental subgraph counting algorithms, allowing MOSER to scale to larger graphs than ever possible before. Extensive experimental results show that using MOSER can improve the state-of-the-art up to 5 orders of magnitude in efficiency and that the motifs found by MOSER facilitate downstream tasks such as link prediction.

Network alignment and motif discovery in dynamic networks

Network alignment and motif discovery in dynamic networks

Discovery of network motifs based on induced subgraphs using a dynamic expansion tree

Biological networks are powerful representations of topological features in biological systems. Finding network motifs in biological networks is a computationally hard problem due to their huge size and abrupt increase of search space with the increase of motif size. Motivated by the computational challenges of network motif discovery and considering the importance of this topic, an efficient and scalable network motif discovery algorithm based on induced subgraphs in a dynamic expansion tree is proposed. This algorithm uses a pruning strategy to overcome the space limitation of the static expansion tree. The proposed algorithm can identify large network motifs up to size 15 by significantly reducing the computationally expensive subgraph isomorphism checks. Further, the present work avoids the unnecessary growth of patterns that do not have any statistical significance. The runtime performance of the proposed algorithm outperforms most of the existing algorithms for large network motifs.

Exploiting Reuse for GPU Subgraph Enumeration

Subgraph enumeration is important for many applications such as network motif discovery, community detection, and frequent subgraph mining. To accelerate the execution, recent works utilize graphics processing units (GPUs) to parallelize subgraph enumeration. The performances of these parallel schemes are dominated by the set intersection operations which account for up to 95 percent of the total processing time. (Un)surprisingly, a significant portion (as high as 99 percent) of these operations is actually redundant, i.e., the same set of vertices is repeatedly encountered and evaluated. Therefore, in this article, we seek to salvage and recycle the results of such operations to avoid repeated computation. Our solution consists of two phases. In the first phase, we generate a reusable plan that determines the opportunity for reuse. The plan is based on a novel reuse discovery mechanism that can identify available results to prevent redundant computation. In the second phase, the plan is executed to produce the subgraph enumeration results. This processing is based on a newly designed reusable parallel search strategy that can efficiently maintain and retrieve the results of set intersection operations. Our implementation on GPUs shows that our approach can achieve up to 5 times speedups compared with the state-of-the-art GPU solutions.

Parallelization of network motif discovery using star contraction

Network motifs are widely used to uncover structural design principles of complex networks. Current sequential network motif discovery algorithms become inefficient as motif size grows, thus parallelization methods have been proposed in the literature. In this study, we use star contraction algorithm to partition complex networks efficiently for parallel discovery of network motifs. We propose two new heuristics to make star contraction more suitable for partitioning of complex networks. The effectiveness of our partitioning strategies is verified using the ESU algorithm for subgraph counting. We also propose a ghost vertices detection algorithm to ensure that all the motifs located in multiple parts are exactly found. We implement our method using MPI libraries and tested on real-life complex networks of different domains. We compared speedups of star contraction algorithm with speedups of other graph partitioning algorithms. Our algorithm obtained better speedups than those of other partitioning algorithms for most cases. Our algorithm provides significant speedups when compared to sequential ESU algorithm allowing discovery of larger network motifs.

Review of tools and algorithms for network motif discovery in biological networks.

Network motifs are recurrent and over‐represented patterns having biological relevance. This is one of the important local properties of biological networks. Network motif discovery finds important applications in many areas such as functional analysis of biological components, the validity of network composition, classification of networks, disease discovery, identification of unique subunits etc. The discovery of network motifs is a computationally challenging task due to the large size of real networks, and the exponential increase of search space with respect to network size and motif size. This problem also includes the subgraph isomorphism check, which is Nondeterministic Polynomial (NP)‐complete. Several tools and algorithms have been designed in the last few years to address this problem with encouraging results. These tools and algorithms can be classified into various categories based on exact census, mapping, pattern growth, and so on. In this study, critical aspects of network motif discovery, design principles of background algorithms, and their functionality have been reviewed with their strengths and limitations. The performances of state‐of‐art algorithms are discussed in terms of runtime efficiency, scalability, and space requirement. The future scope, research direction, and challenges of the existing algorithms are presented at the end of the study.

Intrinsic limitations in mainstream methods of identifying network motifs in biology

BackgroundNetwork motifs are connectivity structures that occur with significantly higher frequency than chance, and are thought to play important roles in complex biological networks, for example in gene regulation, interactomes, and metabolomes. Network motifs may also become pivotal in the rational design and engineering of complex biological systems underpinning the field of synthetic biology. Distinguishing true motifs from arbitrary substructures, however, remains a challenge.ResultsHere we demonstrate both theoretically and empirically that implicit assumptions present in mainstream methods for motif identification do not necessarily hold, with the ramification that motif studies using these mainstream methods are less able to effectively differentiate between spurious results and events of true statistical significance than is often presented. We show that these difficulties cannot be overcome without revising the methods of statistical analysis used to identify motifs.ConclusionsPresent-day methods for the discovery of network motifs, and, indeed, even the methods for defining what they are, are critically reliant on a set of incorrect assumptions, casting a doubt on the scientific validity of motif-driven discoveries. The implications of these findings are therefore far-reaching across diverse areas of biology.

FSM: Fast and scalable network motif discovery for exploring higher-order network organizations.

Networks exhibit rich and diverse higher-order organizational structures. Network motifs, which are recurring significant patterns of inter-connections, are recognized as fundamental units to study the higher-order organizations of networks. However, the principle of selecting representative network motifs for local motif based clustering remains largely unexplored. We present a scalable algorithm called FSM for network motif discovery. FSM is advantageous in twofold. First, it accelerates the motif discovery process by effectively reducing the number of times for subgraph isomorphism labeling. Second, FSM adopts multiple heuristic optimizations for subgraph enumeration and classification to further improve its performance. Experimental results on biological networks show that, comparing with the existing network motif discovery algorithm, FSM is more efficient on computational efficiency and memory usage. Furthermore, with the large, frequent, and sparse network motifs discovered by FSM, the higher-order organizational structures of biological networks were successfully revealed, indicating that FSM is suitable to select network representative network motifs for exploring high-order network organizations.

Disjoint motif discovery in biological network using pattern join method.

The biological network plays a key role in protein function annotation, protein superfamily classification, disease diagnosis, etc. These networks exhibit global properties like small‐world property, power‐law degree distribution, hierarchical modularity, robustness, etc. Along with these, the biological network also possesses some local properties like clustering and network motif. Network motifs are recurrent and statistically over‐represented subgraphs in a target network. Operation of a biological network is controlled by these motifs, and they are responsible for many biological applications. Discovery of network motifs is a computationally hard problem and involves a subgraph isomorphism check which is NP‐complete. In recent years, researchers have developed various tools and algorithms to detect network motifs efficiently. However, it is still a challenging task to discover the network motif within a practical time bound for the large motif. In this study, an efficient pattern‐join based algorithm is proposed to discover network motif in biological networks. The performance of the proposed algorithm is evaluated on the transcription regulatory network of Escherichia coli and the protein interaction network of Saccharomyces cerevisiae. The running time of the proposed algorithm outperforms most of the existing algorithms to discover large motifs.

Motif discovery in biological network using expansion tree.

Networks are powerful representation of topological features in biological systems like protein interaction and gene regulation. In order to understand the design principles of such complex networks, the concept of network motifs emerged. Network motifs are recurrent patterns with statistical significance that can be seen as basic building blocks of complex networks. Identification of network motifs leads to many important applications, such as understanding the modularity and the large-scale structure of biological networks, classification of networks into super-families, protein function annotation, etc. However, identification of network motifs is challenging as it involves graph isomorphism which is computationally hard. Though this problem has been studied extensively in the literature using different computational approaches, we are far from satisfactory results. Motivated by the challenges involved in this field, an efficient and scalable network Motif Discovery algorithm based on Expansion Tree (MODET) is proposed. Pattern growth approach is used in this proposed motif-centric algorithm. Each node of the expansion tree represents a non-isomorphic pattern. The embeddings corresponding to a child node of the expansion tree are obtained from the embeddings of the parent node through vertex addition and edge addition. Further, the proposed algorithm does not involve any graph isomorphism check and the time complexities of these processes are and , respectively. The proposed algorithm has been tested on Protein-Protein Interaction (PPI) network obtained from the MINT database. The computational efficiency of the proposed algorithm outperforms most of the existing network motif discovery algorithms.

IndeCut evaluates performance of network motif discovery algorithms.

Genomic networks represent a complex map of molecular interactions which are descriptive of the biological processes occurring in living cells. Identifying the small over-represented circuitry patterns in these networks helps generate hypotheses about the functional basis of such complex processes. Network motif discovery is a systematic way of achieving this goal. However, a reliable network motif discovery outcome requires generating random background networks which are the result of a uniform and independent graph sampling method. To date, there has been no method to numerically evaluate whether any network motif discovery algorithm performs as intended on realistically sized datasets-thus it was not possible to assess the validity of resulting network motifs. In this work, we present IndeCut, the first method to date that characterizes network motif finding algorithm performance in terms of uniform sampling on realistically sized networks. We demonstrate that it is critical to use IndeCut prior to running any network motif finder for two reasons. First, IndeCut indicates the number of samples needed for a tool to produce an outcome that is both reproducible and accurate. Second, IndeCut allows users to choose the tool that generates samples in the most independent fashion for their network of interest among many available options. The open source software package is available at https://github.com/megrawlab/IndeCut. megrawm@science.oregonstate.edu or david.koslicki@math.oregonstate.edu. Supplementary data are available at Bioinformatics online.

Fast analytical methods for finding significant labeled graph motifs

Network motif discovery is the problem of finding subgraphs of a network that occur more frequently than expected, according to some reasonable null hypothesis. Such subgraphs may indicate small sc...

Network Motif Discovery: A GPU Approach

The identification of network motifs has important applications in numerous domains, such as pattern detection in biological networks and graph analysis in digital circuits. However, mining network motifs is computationally challenging, as it requires enumerating subgraphs from a real-life graph, and computing the frequency of each subgraph in a large number of random graphs. In particular, existing solutions often require days to derive network motifs from biological networks with only a few thousand vertices. To address this problem, this paper presents a novel study on network motif discovery using Graphical Processing Units (GPUs). The basic idea is to employ GPUs to parallelize a large number of subgraph matching tasks in computing subgraph frequencies from random graphs, so as to reduce the overall computation time of network motif discovery. We explore the design space of GPU-based subgraph matching algorithms, with careful analysis of several crucial factors (such as branch divergences and memory coalescing) that affect the performance of GPU programs. Based on our analysis, we develop a GPU-based solution that (i) considerably differs from existing CPU-based methods in how it enumerates subgraphs, and (ii) exploits the strengths of GPUs in terms of parallelism while mitigating their limitations in terms of the computation power per GPU core. With extensive experiments on a variety of biological networks, we show that our solution is up to two orders of magnitude faster than the best CPU-based approach, and is around $20$ times more cost-effective than the latter, when taking into account the monetary costs of the CPU and GPUs used.

A comparative study on network motif discovery algorithms

Subgraphs that occur in complex networks with significantly higher frequency than those in randomised networks are called network motifs. Such subgraphs often play important roles in the functioning of those networks. Finding network motifs is a computationally challenging problem. The main difficulties arise from the fact that real networks are large and the size of the search space grows exponentially with increasing network and motif size. Numerous methods have been developed to overcome these challenges. This paper provides a comparative study of the key network motif discovery algorithms in the literature and presents their algorithmic details on an example network.

The Index-Based Subgraph Matching Algorithm (ISMA): Fast Subgraph Enumeration in Large Networks Using Optimized Search Trees

Subgraph matching algorithms are designed to find all instances of predefined subgraphs in a large graph or network and play an important role in the discovery and analysis of so-called network motifs, subgraph patterns which occur more often than expected by chance. We present the index-based subgraph matching algorithm (ISMA), a novel tree-based algorithm. ISMA realizes a speedup compared to existing algorithms by carefully selecting the order in which the nodes of a query subgraph are investigated. In order to achieve this, we developed a number of data structures and maximally exploited symmetry characteristics of the subgraph. We compared ISMA to a naive recursive tree-based algorithm and to a number of well-known subgraph matching algorithms. Our algorithm outperforms the other algorithms, especially on large networks and with large query subgraphs. An implementation of ISMA in Java is freely available at http://sourceforge.net/projects/isma/.

Sustained-input switches for transcription factors and microRNAs are central building blocks of eukaryotic gene circuits

WaRSwap is a randomization algorithm that for the first time provides a practical network motif discovery method for large multi-layer networks, for example those that include transcription factors, microRNAs, and non-regulatory protein coding genes. The algorithm is applicable to systems with tens of thousands of genes, while accounting for critical aspects of biological networks, including self-loops, large hubs, and target rearrangements. We validate WaRSwap on a newly inferred regulatory network from Arabidopsis thaliana, and compare outcomes on published Drosophila and human networks. Specifically, sustained input switches are among the few over-represented circuits across this diverse set of eukaryotes.

Building blocks of biological networks: a review on major network motif discovery algorithms

In recent years, there has been a great interest in studying different aspects of complex networks in a range of fields. One important local property of networks is network motifs, recurrent and statistically significant sub-graphs or patterns, which assists researchers in the identification of functional units in the networks. Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challenging. Therefore several algorithms have been introduced to resolve this computationally hard problem. These algorithms can be classified under various paradigms such as exact counting methods, sampling methods, pattern growth methods and so on. Here, the authors will give a review on computational aspects of major algorithms and enumerate their related benefits and drawbacks from an algorithmic perspective.

Mesoscopic Models of Neurotransmission as Intermediates between Disease Simulators and Tools for Discovering Design Principles

Two grand challenges have been declared as premier goals of computational systems biology. The first is the discovery of network motifs and design principles that help us understand and rationalize why biological systems are organized in the manner we encounter them rather than in a different fashion. The second goal is the development of computational models supporting the investigation of complex systems, in particular, as simulation platforms in personalized medicine and predictive health. Interestingly, most published systems models in biology contain between a handful and a few dozen variables. They are usually too complicated for systemic analyses of organizing principles, but they are at the same time too coarse to allow reliable simulations of diseases. While it may thus appear that the modeling efforts of the past have missed the declared targets of systems biology, we argue in this article that midsized mesoscopic models are excellent starting points for pursuing both goals in computational systems biology.

An algorithm for network motif discovery in biological networks

Network motif discovery is a key problem in analysis of biological networks. In this paper, we present an efficient algorithm for detecting consensus motifs. First, we extend subgraph searching algorithm Enumerate Subgraphs (ESU) to efficiently search non-treelike subgraphs of which the probability of occurrence in random networks is small. Then, we classify isomorphic subgraphs into different groups. Finally, we use hierarchical clustering method to cluster subgraphs, and derive a consensus motif from the clusters. Our algorithm is applied to the Protein-Protein Interaction (PPI) networks and the transcriptional regulatory networks of E. coli and S. cerevisiae. The experiment results show that the algorithm can efficiently discover motifs, which are consistent with current biology knowledge. And, it can also detect several consensus motifs with a given size, which may help biologists go further into cellular process.

Parallel discovery of network motifs

Many natural structures can be naturally represented by complex networks. Discovering network motifs, which are overrepresented patterns of inter-connections, is a computationally hard task related to graph isomorphism. Sequential methods are hindered by an exponential execution time growth when we increase the size of motifs and networks. In this article we study the opportunities for parallelism in existing methods and propose new parallel strategies that adapt and extend one of the most efficient serial methods known from the Fanmod tool. We propose both a master–worker strategy and one with distributed control, in which we employ a randomized receiver initiated methodology capable of providing dynamic load balancing during the whole computation process. Our strategies are capable of dealing both with exact and approximate network motif discovery. We implement and apply our algorithms to a set of representative networks and examine their scalability up to 128 processing cores. We obtain almost linear speedups, showcasing the efficiency of our proposed approach and are able to reach motif sizes that were not previously achievable using conventional serial algorithms.