Network Alignment Algorithms Research Articles

Approximate IsoRank for Scalable and Functionally Meaningful Cross-Species Alignments of Protein Interaction Networks.

The IsoRank algorithm of Singh, Xu, and Berger was a pioneering algorithmic advance that applied spectral methods to the problem of cross-species global alignment of biological networks. We develop a new IsoRank approximation that exploits the mathematical properties of IsoRank's linear system to solve the problem in quadratic time with respect to the maximum size of the two protein-protein interaction (PPI) networks. We further propose a refinement to this initial approximation so that the updated result is even closer to the original IsoRank formulation while remaining computationally inexpensive. In experiments on synthetic and real PPI networks with various proposed metrics to measure alignment quality, we find the results of our approximate IsoRank are nearly as accurate as the original IsoRank. In fact, for functional enrichment-based measures of global network alignment quality, our approximation performs better than the exact IsoRank, which is doubtless because it is more robust to the noise of missing or incorrect edges. It also performs competitively against two more recent global network alignment algorithms. We also present an analogous approximation to IsoRankN, which extends the network alignment to more than two species.

Exact p-values for global network alignments via combinatorial analysis of shared GO terms

Network alignment aims to uncover topologically similar regions in the protein–protein interaction (PPI) networks of two or more species under the assumption that topologically similar regions tend to perform similar functions. Although there exist a plethora of both network alignment algorithms and measures of topological similarity, currently no “gold standard” exists for evaluating how well either is able to uncover functionally similar regions. Here we propose a formal, mathematically and statistically rigorous method for evaluating the statistical significance of shared GO terms in a global, 1-to-1 alignment between two PPI networks. Given an alignment in which k aligned protein pairs share a particular GO term g, we use a combinatorial argument to precisely quantify the p-value of that alignment with respect to g compared to a random alignment. The p-value of the alignment with respect to all GO terms, including their inter-relationships, is approximated using the Empirical Brown’s Method. We note that, just as with BLAST’s p-values, this method is not designed to guide an alignment algorithm towards a solution; instead, just as with BLAST, an alignment is guided by a scoring matrix or function; the p-values herein are computed after the fact, providing independent feedback to the user on the biological quality of the alignment that was generated by optimizing the scoring function. Importantly, we demonstrate that among all GO-based measures of network alignments, ours is the only one that correlates with the precision of GO annotation predictions, paving the way for network alignment-based protein function prediction.

A novel local alignment algorithm for Multilayer networks

Multilayer Network (MN) is a complex network comprising a set of graphs (also referred to as layers) interconnected by edges or interlayer edges (or inter-edges) linking the nodes of different layers. In biology, a MN may model interactions among diseases, genes, and drugs, only using its structure. Recently, there has been a growing interest in comparing two MNs by revealing local regions of similarity as a counterpart of Network Alignment algorithms (NA) for simple networks. However, classical algorithms for NA such as Local NA (LNA) cannot be applied on multilayer networks, since they are not able to deal with interlayer edges. Therefore, there is a need for the introduction of novel algorithms. In this paper, we present MuLan, an algorithm for the local alignment of multilayer networks. MuLan is based on the building of a multilayer alignment graph starting from a set of seed nodes. Then it analyses such a graph by revealing conserved regions. We first show as proof of concept the performances of MuLaN on a set of synthetic multilayer networks. Then, we used as a case study a real multilayer network in the biomedical domain. Our results show that MuLaN can build high-quality alignments and can extract knowledge about the aligned multilayer networks. MuLaN is available at https://github.com/pietrocinaglia/mulan.

SAMNA: accurate alignment of multiple biological networks based on simulated annealing.

Proteins are important parts of the biological structures and encode a lot of biological information. Protein-protein interaction network alignment is a model for analyzing proteins that helps discover conserved functions between organisms and predict unknown functions. In particular, multi-network alignment aims at finding the mapping relationship among multiple network nodes, so as to transfer the knowledge across species. However, with the increasing complexity of PPI networks, how to perform network alignment more accurately and efficiently is a new challenge. This paper proposes a new global network alignment algorithm called Simulated Annealing Multiple Network Alignment (SAMNA), using both network topology and sequence homology information. To generate the alignment, SAMNA first generates cross-network candidate clusters by a clustering algorithm on a k-partite similarity graph constructed with sequence similarity information, and then selects candidate cluster nodes as alignment results and optimizes them using an improved simulated annealing algorithm. Finally, the SAMNA algorithm was experimented on synthetic and real-world network datasets, and the results showed that SAMNA outperformed the state-of-the-art algorithm in biological performance.

GCNA-Cluster: A Gene Co-Expression Network Alignment to Cluster Cancer Patients Algorithm for Identifying Subtypes of Pancreatic Ductal Adenocarcinoma.

Cancer heterogeneity makes it necessary to use different treatment strategies for patients with the same pathological features. Accurate identification of cancer subtypes is a crucial step in this approach. The current studies of pancreatic ductal adenocarcinoma (PDAC) subtypes mainly focus on single genes and ignore the synergistic effects of genes. Here we proposed a network alignment algorithm GCNA-cluster to cluster patients based on gene co-expression networks. We constructed weighted gene co-expression networks for patients and aligned the networks of two patients to estimate the similarity of patients and their cancer subtypes. A scoring function is defined to measure the network alignment result and the score can indicate the similarity between patients. Then, the patients are clustered based on their similarities. We validated the accuracy of the algorithm on the GEO-PDAC dataset with real labels, and the experimental results show that the GCNA-cluster algorithm has better results than classical cancer subtyping algorithms. In addition, the GCNA-cluster algorithm applied to the TCGA-PDAC dataset identified two subtypes based on the Silhouette Coefficient. Biomarkers identified for the PDAC subtypes hint to cell growth, cell cycle or apoptosis as targets for new therapeutic strategies.

Graph-Theoretical Analysis of Biological Networks: A Survey

Biological networks such as protein interaction networks, gene regulation networks, and metabolic pathways are examples of complex networks that are large graphs with small-world and scale-free properties. An analysis of these networks has a profound effect on our understanding the origins of life, health, and the disease states of organisms, and it allows for the diagnosis of diseases to aid in the search for remedial processes. In this review, we describe the main analysis methods of biological networks using graph theory, by first defining the main parameters, such as clustering coefficient, modularity, and centrality. We then survey fundamental graph clustering methods and algorithms, followed by the network motif search algorithms, with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function that is carried out by that small network, and discovering such a function provides an insight into the overall function of the organism. Lastly, we review network alignment algorithms that find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor, and finding such a relationship may help researchers to derive ancestral relationships and to predict the future evolution of organisms to enable the design of new drugs. We provide a review of the research studies in all of these methods, and conclude using the current challenging areas of biological network analysis, and by using graph theory and parallel processing for high performance analysis.

HE-SNA: an efficient cross-platform network alignment scheme from privacy-aware perspective

User alignment across online social network platforms (OSNPs) is a growing concern with the rapid development of internet technology. In reality, users tend to register different accounts on multiple OSNPs, and the network platforms are reluctant to share network structure and user’s information due to business interest and privacy protection, which brings great obstacles to cross-platform user alignment. In view of this, we propose a homomorphic encryption-based social network alignment (HE-SNA) algorithm from the perspective of privacy leakage. Specifically, we first consider the OSNPs as a system containing multiple social networks, that each participant of OSNPs owns part of the network, i.e., a separate private sub-network. Then, encryption, fusion and decryption operations of the alignment information are performed by two third-party servers using HE scheme, which can protect the privacy information of sub-networks effectively. Finally, each sub-network uses the fused alignment information sent back from the third-party server for user alignment. Experimental results show that the HE-SNA method can provide a sum of locally trained models to third-party servers without leaking the privacy of any single sub-network. Moreover, the HE-SNA achieves a promising network alignment performance than only using the structural information and alignment data of single private sub-network while protecting its topology structure information.

Multi-SANA: Comparing Measures of Topological Similarity for Multiple Network Alignment

All life on Earth is related, so that some molecular interactions are common across almost all living cells, with the number of common interactions increasing as we look at more closely related species. In particular, we expect the protein–protein interaction (PPI) networks of closely related species to share high levels of similarity. This similarity may facilitate the transfer of functional knowledge between model species and human. Multiple network alignment is the process of uncovering the connection similarity between three or more networks simultaneously. Existing algorithms for multiple network alignment rely on sequence similarities to help drive the alignments, and no comprehensive study has been done to determine the most effective ways to utilize network connectivity—network topology—to drive multiple network alignment. Here, we devise and empirically test the efficacy of several measures of topological similarity between three or more networks. To evolve the alignments toward optimal, we use simulated annealing as the search algorithm since it is agnostic to the objective being optimized. We test the measures both on the partially synthetic and highly similar PPI networks from the integrated interaction database, as well as on real PPI networks from a recent BioGRID release.

SANA: cross-species prediction of Gene Ontology GO annotations via topological network alignment

Topological network alignment aims to align two networks node-wise in order to maximize the observed common connection (edge) topology between them. The topological alignment of two protein–protein interaction (PPI) networks should thus expose protein pairs with similar interaction partners allowing, for example, the prediction of common Gene Ontology (GO) terms. Unfortunately, no network alignment algorithm based on topology alone has been able to achieve this aim, though those that include sequence similarity have seen some success. We argue that this failure of topology alone is due to the sparsity and incompleteness of the PPI network data of almost all species, which provides the network topology with a small signal-to-noise ratio that is effectively swamped when sequence information is added to the mix. Here we show that the weak signal can be detected using multiple stochastic samples of “good” topological network alignments, which allows us to observe regions of the two networks that are robustly aligned across multiple samples. The resulting network alignment frequency (NAF) strongly correlates with GO-based Resnik semantic similarity and enables the first successful cross-species predictions of GO terms based on topology-only network alignments. Our best predictions have an AUPR of about 0.4, which is competitive with state-of-the-art algorithms, even when there is no observable sequence similarity and no known homology relationship. While our results provide only a “proof of concept” on existing network data, we hypothesize that predicting GO terms from topology-only network alignments will become increasingly practical as the volume and quality of PPI network data increase.

A Novel Algorithm for Local Network Alignment Based on Network Embedding

Networks are widely used in bioinformatics and biomedicine to represent associations across a large class of biological entities. Network alignment refers to the set of approaches that aim to reveal similarities among networks. Local Network Alignment (LNA) algorithms find (relatively small) local regions of similarity between two or more networks. Such algorithms are in general based on a set of seed nodes that are used to build the alignment incrementally. A large fraction of LNA algorithms uses a set of vertices based on context information as seed nodes, even if this may cause a bias or a data-circularity problem. Moreover, using topology information to choose seed nodes improves overall alignment. Finally, similarities among nodes can be identified by network embedding methods (or representation learning). Given there are two networks, we propose to use network embedding to capture structural similarity among nodes, which can also be used to improve LNA effectiveness. We present an algorithm and experimental tests on real and syntactic graph data to find LNAs.

An Extensive Assessment of Network Embedding in PPI Network Alignment.

Network alignment is a fundamental task in network analysis. In the biological field, where the protein–protein interaction (PPI) is represented as a graph, network alignment allowed the discovery of underlying biological knowledge such as conserved evolutionary pathways and functionally conserved proteins throughout different species. A recent trend in network science concerns network embedding, i.e., the modelling of nodes in a network as a low-dimensional feature vector. In this survey, we present an overview of current PPI network embedding alignment methods, a comparison among them, and a comparison to classical PPI network alignment algorithms. The results of this comparison highlight that: (i) only five network embeddings for network alignment algorithms have been applied in the biological context, whereas the literature presents several classical network alignment algorithms; (ii) there is a need for developing an evaluation framework that may enable a unified comparison between different algorithms; (iii) the majority of the proposed algorithms perform network embedding through matrix factorization-based techniques; (iv) three out of five algorithms leverage external biological resources, while the remaining two are designed for domain agnostic network alignment and tested on PPI networks; (v) two algorithms out of three are stated to perform multi-network alignment, while the remaining perform pairwise network alignment.

BioAlign: An Accurate Global PPI Network Alignment Algorithm.

Motivation:The advancement of high-throughput PPI profiling techniques results in generating a large amount of PPI data. The alignment of the PPI networks uncovers the relationship between the species that can help understand the biological systems. The comparative study reveals the conserved biological interactions of the proteins across the species. It can also help study the biological pathways and signal networks of the cells. Although several network alignment algorithms are developed to study and compare the PPI data, the development of the aligner that aligns the PPI networks with high biological similarity and coverage is still challenging.Results:This paper presents a novel global network alignment algorithm, BioAlign, that incorporates a significant amount of biological information. Existing studies use global sequence and/or 3D-structure similarity to align the PPI networks. In contrast, BioAlign uses the local sequence similarity, predicted secondary structure motifs, and remote homology in addition to global sequence and 3D-structure similarity. The extra sources of biological information help BioAlign to align the proteins with high biological similarity. BioAlign produces significantly better results in terms of AFS and Coverage (6-32 and 7-34 with respect to MF and BP, respectively) than the existing algorithms. BioAlign aligns a much larger number of proteins that have high biological similarities as compared to the existing aligners. BioAlign helps in studying the functionally similar protein pairs across the species.

On the current failure-but bright future-of topology-driven biological network alignment.

Since the function of a protein is defined by its interaction partners, and since we expect similar interaction patterns across species, the alignment of protein-protein interaction (PPI) networks between species, based on network topology alone, should uncover functionally related proteins across species. Surprisingly, despite the publication of more than fifty algorithms aimed at performing PPI network alignment, few have demonstrated a statistically significant link between network topology and functional similarity, and none have demonstrated that orthologs can be recovered using network topology alone. We find that the major contributing factors to this surprising failure are: (i) edge densities in most currently available experimental PPI networks are demonstrably too low to expect topological network alignment to succeed; (ii) in the few cases where the edge densities are high enough, some measures of topological similarity easily uncover functionally similar proteins while others do not; and (iii) most network alignment algorithms to date perform poorly at optimizing even their own topological objective functions, hampering their ability to use topology effectively. We demonstrate that SANA-the Simulated Annealing Network Aligner-significantly outperforms existing aligners at optimizing their own objective functions, even achieving near-optimal solutions when the optimal solution is known. We offer the first demonstration of global network alignments based on topology alone that align functionally similar proteins with p-values in some cases below 10-300. We predict that topological network alignment has a bright future as edge densities increase toward the value where good alignments become possible. We demonstrate that when enough common topology is present at high enough edge densities-for example in the recent, partly synthetic networks of the Integrated Interaction Database-topological network alignment easily recovers most orthologs, paving the way toward high-throughput functional prediction based on topology-driven network alignment.

ELRUNA

Networks model a variety of complex phenomena across different domains. In many applications, one of the most essential tasks is to align two or more networks to infer the similarities between cross-network vertices and to discover potential node-level correspondence. In this article, we propose ELRUNA ( el imination ru le-based n etwork a lignment), a novel network alignment algorithm that relies exclusively on the underlying graph structure. Under the guidance of the elimination rules that we defined, ELRUNA computes the similarity between a pair of cross-network vertices iteratively by accumulating the similarities between their selected neighbors. The resulting cross-network similarity matrix is then used to infer a permutation matrix that encodes the final alignment of cross-network vertices. In addition to the novel alignment algorithm, we improve the performance of local search , a commonly used postprocessing step for solving the network alignment problem, by introducing a novel selection method RAWSEM ( ra ndom- w alk-based se lection m ethod) based on the propagation of vertices’ mismatching across the networks. The key idea is to pass on the initial levels of mismatching of vertices throughout the entire network in a random-walk fashion. Through extensive numerical experiments on real networks, we demonstrate that ELRUNA significantly outperforms the state-of-the-art alignment methods in terms of alignment accuracy under lower or comparable running time. Moreover, ELRUNA is robust to network perturbations such that it can maintain a close-to-optimal objective value under a high level of noise added to the original networks. Finally, the proposed RAWSEM can further improve the alignment quality with a smaller number of iterations compared with the naive local search method. Reproducibility : The source code and data are available at https://tinyurl.com/uwn35an.

Scalable Algorithms for Multiple Network Alignment

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 17 June 2020Accepted: 19 April 2021Published online: 05 August 2021Keywordsmultiple network alignment, network alignment, low-rank tensor, $k$-partite matching, $k$-dimensional matchingAMS Subject Headings05C85, 90B10, 68R10Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3

A novel network aligner for the analysis of multiple protein-protein interaction networks

The analysis of protein-protein interaction networks can transfer the knowledge of well-studied biological functions to functions that are not yet adequately investigated by constructing networks and extracting similar network structures in different species. Multiple network alignment can be used to find similar regions among multiple networks. In this paper, we introduce Accurate Combined Clustering Multiple Network Alignment (ACCMNA), which is a new and accurate multiple network alignment algorithm. It uses both topology and sequence similarity information. First, the importance of all the nodes is calculated according to the network structures. Second, the seed-and-extend framework is used to conduct an iterative search. In each iteration, a clustering method is combined to generate the alignment. Extensive experimental results show that ACCMNA outperformed the state-of-the-art algorithms in producing functionally consistent and topological conservation alignments within an acceptable running time.

MONACO: accurate biological network alignment through optimal neighborhood matching between focal nodes.

Alignment of protein-protein interaction networks can be used for the unsupervised prediction of functional modules, such as protein complexes and signaling pathways, that are conserved across different species. To date, various algorithms have been proposed for biological network alignment, many of which attempt to incorporate topological similarity between the networks into the alignment process with the goal of constructing accurate and biologically meaningful alignments. Especially, random walk models have been shown to be effective for quantifying the global topological relatedness between nodes that belong to different networks by diffusing node-level similarity along the interaction edges. However, these schemes are not ideal for capturing the local topological similarity between nodes. In this article, we propose MONACO, a novel and versatile network alignment algorithm that finds highly accurate pairwise and multiple network alignments through the iterative optimal matching of 'local' neighborhoods around focal nodes. Extensive performance assessment based on real networks as well as synthetic networks, for which the ground truth is known, demonstrates that MONACO clearly and consistently outperforms all other state-of-the-art network alignment algorithms that we have tested, in terms of accuracy, coherence and topological quality of the aligned network regions. Furthermore, despite the sharply enhanced alignment accuracy, MONACO remains computationally efficient and it scales well with increasing size and number of networks. Matlab implementation is freely available at https://github.com/bjyoontamu/MONACO. Supplementary data are available at Bioinformatics online.

SAlign\u2013a structure aware method for global PPI network alignment

BackgroundHigh throughput experiments have generated a significantly large amount of protein interaction data, which is being used to study protein networks. Studying complete protein networks can reveal more insight about healthy/disease states than studying proteins in isolation. Similarly, a comparative study of protein–protein interaction (PPI) networks of different species reveals important insights which may help in disease analysis and drug design. The study of PPI network alignment can also helps in understanding the different biological systems of different species. It can also be used in transfer of knowledge across different species. Different aligners have been introduced in the last decade but developing an accurate and scalable global alignment algorithm that can ensures the biological significance alignment is still challenging.ResultsThis paper presents a novel global pairwise network alignment algorithm, SAlign, which uses topological and biological information in the alignment process. The proposed algorithm incorporates sequence and structural information for computing biological scores, whereas previous algorithms only use sequence information. The alignment based on the proposed technique shows that the combined effect of structure and sequence results in significantly better pairwise alignments. We have compared SAlign with state-of-art algorithms on the basis of semantic similarity of alignment and the number of aligned nodes on multiple PPI network pairs. The results of SAlign on the network pairs which have high percentage of proteins with available structure are 3–63% semantically better than all existing techniques. Furthermore, it also aligns 5–14% more nodes of these network pairs as compared to existing aligners. The results of SAlign on other PPI network pairs are comparable or better than all existing techniques. We also introduce hbox {SAlign}^{mathrm{mc}}, a Monte Carlo based alignment algorithm, that produces multiple network alignments with similar semantic similarity. This helps the user to pick biologically meaningful alignments.ConclusionThe proposed algorithm has the ability to find the alignments that are more biologically significant/relevant as compared to the alignments of existing aligners. Furthermore, the proposed method is able to generate alternate alignments that help in studying different genes/proteins of the specie.

Twadn: an efficient alignment algorithm based on time warping for pairwise dynamic networks

BackgroundNetwork alignment is an efficient computational framework in the prediction of protein function and phylogenetic relationships in systems biology. However, most of existing alignment methods focus on aligning PPIs based on static network model, which are actually dynamic in real-world systems. The dynamic characteristic of PPI networks is essential for understanding the evolution and regulation mechanism at the molecular level and there is still much room to improve the alignment quality in dynamic networks.ResultsIn this paper, we proposed a novel alignment algorithm, Twadn, to align dynamic PPI networks based on a strategy of time warping. We compare Twadn with the existing dynamic network alignment algorithm DynaMAGNA++ and DynaWAVE and use area under the receiver operating characteristic curve and area under the precision-recall curve as evaluation indicators. The experimental results show that Twadn is superior to DynaMAGNA++ and DynaWAVE. In addition, we use protein interaction network of Drosophila to compare Twadn and the static network alignment algorithm NetCoffee2 and experimental results show that Twadn is able to capture timing information compared to NetCoffee2.ConclusionsTwadn is a versatile and efficient alignment tool that can be applied to dynamic network. Hopefully, its application can benefit the research community in the fields of molecular function and evolution.

Multi-Neighborhood Learning for Global Alignment in Biological Networks.

The global alignment of biological networks (GABN) aims to find an optimal alignment between proteins across species, such that both the biological structures and the topological structures of the proteins are maximally conserved. The research on GABN has attracted great attention due to its applications on species evolution, orthology detection and genetic analyses. Most of the existing methods for GABN are difficult to obtain a good tradeoff between the conservation of the biological structures and topological structures. In this paper, we propose a multi-neighborhood learning method for solving GABN (called as CLMNA). CLMNA first models GABN as an optimization of a weighted similarity which evaluates the conserved biological and topological similarities of an alignment, and then it combines a first-proximity, second-proximity and individual-aware proximity learning algorithm to solve the modeled problem. Finally, systematic experiments on 10 pairs of biological networks across 5 species show the superiority of CLMNA over the state-of-the-art network alignment algorithms. They also validate the effectiveness of CLMNA as a refinement method on improving the performance of the compared algorithms.