Integrating data from heterogeneous sources is often modeled as merging graphs. Given two or more 'compatible', but not-isomorphic graphs, the first step is to identify a graph alignment, where a potentially partial mapping of vertices between two graphs is computed. A significant portion of the literature on this problem only takes the global structure of the input graphs into account. Only more recent ones additionally use vertex and edge attributes to achieve a more accurate alignment. However, these methods are not designed to scale to map large graphs arising in many modern applications. We propose a new iterative graph aligner, gsaNA, that uses the global structure of the graphs to significantly reduce the problem size and align large graphs with a minimal loss of information. Concretely, we show that our proposed technique is highly flexible, can be used to achieve higher recall, and it is orders of magnitudes faster than the current state of the art techniques.
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@cite_22: Background: In addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes computationally more challenging, as most meaningful assumptions instantly lead to NPhard problems. Most previous algorithmic work on network alignments is heuristic in nature. Results: We introduce the graph-based maximum structural matching formulation for pairwise global network alignment. We relate the formulation to previous work and prove NP-hardness of the problem. Based on the new formulation we build upon recent results in computational structural biology and present a novel Lagrangian relaxation approach that, in combination with a branch-and-bound method, computes provably optimal network alignments. The Lagrangian algorithm alone is a powerful heuristic method, which produces solutions that are often near-optimal and – unlike those computed by pure heuristics – come with a quality guarantee. Conclusion: Computational experiments on the alignment of protein-protein interaction networks and on the classification of metabolic subnetworks demonstrate that the new method is reasonably fast and has advantages over pure heuristics. Our software tool is freely available as part of the LISA library.
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@cite_36: Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology and disease. Comparison and alignment of biological networks will probably have a similar impact. Existing network alignments use information external to the networks, such as sequence, because no good algorithm for purely topological alignment has yet been devised. In this paper, we present a novel algorithm based solely on network topology, that can be used to align any two networks. We apply it to biological networks to produce by far the most complete topological alignments of biological networks to date. We demonstrate that both species phylogeny and detailed biological function of individual proteins can be extracted from our alignments. Topology-based alignments have the potential to provide a completely new, independent source of phylogenetic information. Our alignment of the protein–protein interaction networks of two very different species—yeast and human—indicate that even distant species share a surprising amount of network topology, suggesting broad similarities in internal cellular wiring across all life on Earth.
@cite_10: In this paper, a new memetic algorithm (MA) for multiobjective (MO) optimization is proposed, which combines the global search ability of particle swarm optimization with a synchronous local search heuristic for directed local fine-tuning. A new particle updating strategy is proposed based upon the concept of fuzzy global-best to deal with the problem of premature convergence and diversity maintenance within the swarm. The proposed features are examined to show their individual and combined effects in MO optimization. The comparative study shows the effectiveness of the proposed MA, which produces solution sets that are highly competitive in terms of convergence, diversity, and distribution
@cite_9: Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. In this paper we present a method for global network alignment that is fast and robust, and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. It is based on an integer linear programming formulation, generalizing the well-studied quadratic assignment problem. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the software tool natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative state-of-the-art methods with respect to quality and running time.
@cite_1: In this paper, we survey algorithms that perform global alignment of networks or graphs. Global network alignment aligns two or more given networks to find the best mapping from nodes in one network to nodes in other networks. Since graphs are a common method of data representation, graph alignment has become important with many significant applications. Protein-protein interactions can be modeled as networks and aligning these networks of protein interactions has many applications in biological research. In this survey, we review algorithms for global pairwise alignment highlighting various proposed approaches, and classify them based on their methodology. Evaluation metrics that are used to measure the quality of the resulting alignments are also surveyed. We discuss and present a comparison between selected aligners on the same datasets and evaluate using the same evaluation metrics. Finally, a quick overview of the most popular databases of protein interaction networks is presented focusing on datasets that have been used recently.
@cite_32: Important biological information is encoded in the topology of biological networks. Comparative analyses of biological networks are proving to be valuable, as they can lead to transfer of knowledge between species and give deeper insights into biological function, disease, and evolution. We introduce a new method that uses the Hungarian algorithm to produce optimal global alignment between two networks using any cost function. We design a cost function based solely on network topology and use it in our network alignment. Our method can be applied to any two networks, not just biological ones, since it is based only on network topology. We use our new method to align protein-protein interaction networks of two eukaryotic species and demonstrate that our alignment exposes large and topologically complex regions of network similarity. At the same time, our alignment is biologically valid, since many of the aligned protein pairs perform the same biological function. From the alignment, we predict function of yet unannotated proteins, many of which we validate in the literature. Also, we apply our method to find topological similarities between metabolic networks of different species and build phylogenetic trees based on our network alignment score. The phylogenetic trees obtained in this way bear a striking resemblance to the ones obtained by sequence alignments. Our method detects topologically similar regions in large networks that are statistically significant. It does this independent of protein sequence or any other information external to network topology.
@cite_34: Motivation: The global alignment of protein interaction networks is a widely studied problem. It is an important first step in understanding the relationship between the proteins in different species and identifying functional orthologs. Furthermore, it can provide useful insights into the species’ evolution. Results: We propose a novel algorithm, PISwap, for optimizing global pairwise alignments of protein interaction networks, based on a local optimization heuristic that has previously demonstrated its effectiveness for a variety of other intractable problems. PISwap can begin with different types of network alignment approaches and then iteratively adjust the initial alignments by incorporating network topology information, trading it off for sequence information. In practice, our algorithm efficiently refines other well-studied alignment techniques with almost no additional time cost. We also show the robustness of the algorithm to noise in protein interaction data. In addition, the flexible nature of this algorithm makes it suitable for different applications of network alignment. This algorithm can yield interesting insights into the evolutionary dynamics of related species. Availability: Our software is freely available for non-commercial purposes from our Web site, http: piswap.csail.mit.edu .
@cite_3: In this paper, we investigate heuristics for Approximate Graph Matching (AGM), in particular when it can be formulated as a Maximum Common Edge Subgraph (MCES) problem. First, we observe empirically that initializing a local search with a tiny subset of a known optimal solution always results in much better solutions than starting with an empty solution. The main challenge could then be to retrieve such small subsets for any problem instance. For this purpose, we propose several local similarity measures and evaluate their ability to predict node matches which could be used to start a local search. The resulting algorithm (SIM-T) is a classic tabu algorithm that is initialized by a greedy procedure relying mainly, in its earliest steps, on similarity measures. We conducted experiments on a large collection of random graphs of various orders (from 50 to 3000 nodes) and densities. Results obtained are mostly excellent, especially on similar pairs of labeled graphs. Comparisons made with two recent state-of-the-art algorithms-''BP'' and ''PATH''-indicate a superiority of our approach, in terms of both scores and computation times.
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@cite_27: Motivation: Protein interaction networks provide an important system-level view of biological processes. One of the fundamental problems in biological network analysis is the global alignment of a pair of networks, which puts the proteins of one network into correspondence with the proteins of another network in a manner that conserves their interactions while respecting other evidence of their homology. By providing a mapping between the networks of different species, alignments can be used to inform hypotheses about the functions of unannotated proteins, the existence of unobserved interactions, the evolutionary divergence between the two species and the evolution of complexes and pathways. Results: We introduce GHOST, a global pairwise network aligner that uses a novel spectral signature to measure topological similarity between subnetworks. It combines a seed-and-extend global alignment phase with a local search procedure and exceeds state-of-the-art performance on several network alignment tasks. We show that the spectral signature used by GHOST is highly discriminative, whereas the alignments it produces are also robust to experimental noise. When compared with other recent approaches, we find that GHOST is able to recover larger and more biologically significant, shared subnetworks between species. Availability: An efficient and parallelized implementation of GHOST, released under the Apache 2.0 license, is available at http: cbcb.umd.edu kingsford_group ghost Contact: rob@cs.umd.edu
@cite_31: We propose a new distributed algorithm for sparse variants of the network alignment problem, which occurs in a variety of data mining areas including systems biology, database matching, and computer vision. Our algorithm uses a belief propagation heuristic and provides near optimal solutions for this NP-hard combinatorial optimization problem. We show that our algorithm is faster and outperforms or ties existing algorithms on synthetic problems, a problem in bioinformatics, and a problem in ontology matching. We also provide a unified framework for studying and comparing all network alignment solvers.
@cite_16: We describe an algorithm, IsoRank, for global alignment of two protein-protein interaction (PPI) networks. IsoRank aims to maximize the overall match between the two networks; in contrast, much of previous work has focused on the local alignment problem-- identifying many possible alignments, each corresponding to a local region of similarity. IsoRank is guided by the intuition that a protein should be matched with a protein in the other network if and only if the neighbors of the two proteins can also be well matched. We encode this intuition as an eigenvalue problem, in a manner analogous to Google's PageRank method. We use IsoRank to compute the first known global alignment between the S. cerevisiae and D. melanogaster PPI networks. The common subgraph has 1420 edges and describes conserved functional components between the two species. Comparisons of our results with those of a well-known algorithm for local network alignment indicate that the globally optimized alignment resolves ambiguity introduced by multiple local alignments. Finally, we interpret the results of global alignment to identify functional orthologs between yeast and fly; our functional ortholog prediction method is much simpler than a recently proposed approach and yet provides results that are more comprehensive.
@cite_13: Motivation: Discovering and understanding patterns in networks of protein–protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. Results: We introduce a novel global network alignment tool, Lagrangian GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and Lagrangian relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. Availability and implementation: L-GRAAL is coded in C++. Software is available at: http: bio-nets.doc.ic.ac.uk L-GRAAL . Contact: ku.ca.lairepmi@ningod-dolam.n Supplementary information: Supplementary data are available at Bioinformatics online.
@cite_20: Motivation: Given protein–protein interaction (PPI) networks of a pair of species, a pairwise global alignment corresponds to a one-to-one mapping between their proteins. Based on the presupposition that such a mapping provides pairs of functionally orthologous proteins accurately, the results of the alignment may then be used in comparative systems biology problems such as function prediction verification or construction of evolutionary relationships. Results: We show that the problem is NP-hard even for the case where the pair of networks are simply paths. We next provide a polynomial time heuristic algorithm, SPINAL, which consists of two main phases. In the first coarse-grained alignment phase, we construct all pairwise initial similarity scores based on pairwise local neighborhood matchings. Using the produced similarity scores, the fine-grained alignment phase produces the final one-to-one mapping by iteratively growing a locally improved solution subset. Both phases make use of the construction of neighborhood bipartite graphs and the contributors as a common primitive. We assess the performance of our algorithm on the PPI networks of yeast, fly, human and worm. We show that based on the accuracy measures used in relevant work, our method outperforms the state-of-the-art algorithms. Furthermore, our algorithm does not suffer from scalability issues, as such accurate results are achieved in reasonable running times as compared with the benchmark algorithms. Availability: Supplementary Document, open source codes, useful scripts, all the experimental data and the results are freely available at http: code.google.com p spinal . Contact: cesim@khas.edu.tr Supplementary information: Supplementary data are available at Bioinformatics online.
@cite_17: Motivation: With the increasing availability of large protein–protein interaction networks, the question of protein network alignment is becoming central to systems biology. Network alignment is further delineated into two sub-problems: local alignment, to find small conserved motifs across networks, and global alignment, which attempts to find a best mapping between all nodes of the two networks. In this article, our aim is to improve upon existing global alignment results. Better network alignment will enable, among other things, more accurate identification of functional orthologs across species. Results: We introduce IsoRankN (IsoRank-Nibble) a global multiplenetwork alignment tool based on spectral clustering on the induced graph of pairwise alignment scores. IsoRankN outperforms existing algorithms for global network alignment in coverage and consistency on multiple alignments of the five available eukaryotic networks. Being based on spectral methods, IsoRankN is both error tolerant and computationally efficient. Availability: Our software is available freely for non-commercial purposes on request from: http: isorank.csail.mit.edu
Solution methods proposed in the literature for graph alignment can be roughly classified into four basic categories @cite_4 @cite_1 : spectral methods @cite_16 @cite_17 @cite_27 @cite_7 , graph structure similarity methods @cite_36 @cite_32 @cite_19 @cite_13 @cite_20 , tree search or tabu search methods @cite_34 @cite_14 @cite_10 @cite_3 , and integer linear programming (ILP) methods @cite_22 @cite_9 @cite_31 . All of these works have scalability issues. Our algorithms leverage global graph structure and reduces the problem space and augment that with semantic information to alleviate most of the scalability issues.