Many proteins remain functionally unannotated. Sequence alignment (SA) uncovers missing annotations by transferring functional knowledge between species' sequence-conserved regions. Because SA is imperfect, network alignment (NA) complements SA by transferring functional knowledge between conserved biological network, rather than just sequence, regions of different species. Existing NA assumes that it is topological similarity (isomorphic-like matching) between network regions that corresponds to the regions' functional relatedness. However, we recently found that functionally unrelated proteins are almost as topologically similar as functionally related proteins. So, we redefined NA as a data-driven framework, TARA, which learns from network and protein functional data what kind of topological relatedness (rather than similarity) between proteins corresponds to the proteins' functional relatedness. TARA used topological information (within each network) but not sequence information (between proteins across networks). Yet, its alignments yielded higher protein functional prediction accuracy than alignments of existing NA methods, even those that used both topological and sequence information. Here, we propose TARA++ that is also data-driven, like TARA and unlike other existing methods, but that uses across-network sequence information on top of within-network topological information, unlike TARA. To deal with the within-and-across-network analysis, we adapt social network embedding to the problem of biological NA. TARA++ outperforms protein functional prediction accuracy of existing methods.
Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely 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 …
The alignment of biological networks has the potential to teach us as much about biology and disease as has sequence alignment. Sequence alignment can be optimally solved in polynomial time. In contrast, network alignment is $NP$-hard, meaning optimal solutions are impossible to find, and the quality of found alignments depend strongly upon the algorithm used to create them. Every network alignment algorithm consists of two orthogonal components: first, an objective function or measure $M$ that is used to evaluate the quality of any proposed alignment, and second, a search algorithm used to ex…
Analogous to genomic sequence alignment, biological network alignment (NA) aims to find regions of similarities between molecular networks (rather than sequences) of different species. NA can be either local (LNA) or global (GNA). LNA aims to identify highly conserved common subnetworks, which are typically small, while GNA aims to identify large common subnetworks, which are typically suboptimally conserved. We recently showed that LNA and GNA yield complementary results: LNA has high functional but low topological alignment quality, while GNA has high topological but low functional alignment…
Biological network alignment is currently in a state of disarray, with more than two dozen network alignment tools having been introduced in the past decade, with no clear winner, and other new tools being published almost quarterly. Part of the problem is that almost every new tool proposes both a new objective function and a new search algorithm to optimize said objective. These two aspects of alignment are orthogonal, and confounding them makes it difficult to evaluate them separately. A more systematic approach is needed. To this end, we bring these two orthogonal issues into sharp focus i…
Network alignment (NA) aims to find regions of similarities between molecular networks of different species. There exist two NA categories: local (LNA) or global (GNA). LNA finds small highly conserved network regions and produces a many-to-many node mapping. GNA finds large conserved regions and produces a one-to-one node mapping. Given the different outputs of LNA and GNA, when a new NA method is proposed, it is compared against existing methods from the same category. However, both NA categories have the same goal: to allow for transferring functional knowledge from well- to poorly-studied …
Interaction networks are of central importance in post-genomic molecular biology, with increasing amounts of data becoming available by high-throughput methods. Examples are gene regulatory networks or protein interaction maps. The main challenge in the analysis of these data is to read off biological functions from the topology of the network. Topological motifs, i.e., patterns occurring repeatedly at different positions in the network have recently been identified as basic modules of molecular information processing. In this paper, we discuss motifs derived from families of mutually similar …
Our Microbiome Network Alignment Algorithm (MiNAA) aligns two microbial networks using a combination of the GRAph ALigner (GRAAL) algorithm and the Hungarian algorithm. Network alignment algorithms find pairs of nodes (one node from the first network and the other node from the second network) that have the highest similarity. Traditionally, similarity has been defined as topological similarity such that the neighborhoods around the two nodes are similar. Recent implementations of network alignment methods such as NETAL and L-GRAAL also include measures of biological similarity, yet these meth…
One of the most difficult problems difficult problem in systems biology is to discover protein-protein interactions as well as their associated functions. The analysis and alignment of protein-protein interaction networks (PPIN), which are the standard model to describe protein-protein interactions, has become a key ingredient to obtain functional orthologs as well as evolutionary conserved pathways and protein complexes. Several methods have been proposed to solve the PPIN alignment problem, aimed to match conserved subnetworks or functionally related proteins. However, the right balance betw…
Complex interactions between genes or proteins contribute a substantial part to phenotypic evolution. Here we develop an evolutionarily grounded method for the cross-species analysis of interaction networks by {\em alignment}, which maps bona fide functional relationships between genes in different organisms. Network alignment is based on a scoring function measuring mutual similarities between networks taking into account their interaction patterns as well as sequence similarities between their nodes. High-scoring alignments and optimal alignment parameters are inferred by a systematic Bayesi…
PPI network alignment aims to find topological and functional similarities between networks of different species. Several alignment approaches have been proposed. Each of these approaches relies on a different alignment method and uses different biological information during the alignment process such as the topological structure of the networks and the sequence similarities between the proteins, but less of them integrate the functional similarities between proteins. In this context, we present our algorithm PPINA (Protein-Protein Interaction Network Aligner), which is an extension of the NET…
The function of a protein is defined by its interaction partners. Thus, topology-driven network alignment of the protein-protein interaction (PPI) networks of two species should uncover similar interaction patterns and allow identification of functionally similar proteins. Howver, few of the fifty or more algorithms for PPI network alignment have demonstrated a significant link between network topology and functional similarity, and none have recovered orthologs using network topology alone. We find that the major contributing factors to this failure are: (i) edge densities in current PPI netw…
Sequence alignment has had an enormous impact on our understanding of biology, evolution, and disease. The alignment of biological {\em networks} holds similar promise. Biological networks generally model interactions between biomolecules such as proteins, genes, metabolites, or mRNAs. There is strong evidence that the network topology -- the "structure" of the network -- is correlated with the functions performed, so that network topology can be used to help predict or understand function. However, unlike sequence comparison and alignment -- which is an essentially solved problem -- network c…
Biological network alignment (NA) aims to identify similar regions between molecular networks of different species. NA can be local or global. Just as the recent trend in the NA field, we also focus on global NA, which can be pairwise (PNA) and multiple (MNA). PNA produces aligned node pairs between two networks. MNA produces aligned node clusters between more than two networks. Recently, the focus has shifted from PNA to MNA, because MNA captures conserved regions between more networks than PNA (and MNA is thus considered to be more insightful), though at higher computational complexity. The …
The discovery of nucleic acids and the structure of DNA have brought considerable advances in the understanding of life. The development of next-generation sequencing technologies has led to a large-scale generation of data, for which computational methods have become essential for analysis and knowledge discovery. In particular, RNAs have received much attention because of the diversity of their functionalities in the organism and the discoveries of different classes with different functions in many biological processes. Therefore, the correct identification of RNA sequences is increasingly i…
Proteins interact with other proteins within biological pathways, forming connected subgraphs in the protein-protein interactome (PPI). Proteins are often involved in multiple biological pathways which complicates interpretation of interactions between proteins. Gene expression data can assist our inference since genes within a particular pathway tend to have more correlated expression patterns than genes from distinct pathways. We provide an algorithm that uses gene expression information to remove inter-pathway protein-protein interactions, thereby simplifying the structure of the protein-pr…
Biological network alignment (NA) aims to find a node mapping between species' molecular networks that uncovers similar network regions, thus allowing for transfer of functional knowledge between the aligned nodes. However, current NA methods do not end up aligning functionally related nodes. A likely reason is that they assume it is topologically similar nodes that are functionally related. However, we show that this assumption does not hold well. So, a paradigm shift is needed with how the NA problem is approached. We redefine NA as a data-driven framework, TARA (daTA-dRiven network Alignmen…
Network alignment (NA) aims to find a node mapping between molecular networks of different species that identifies topologically or functionally similar network regions. Analogous to genomic sequence alignment, NA can be used to transfer biological knowledge from well- to poorly-studied species between aligned network regions. Pairwise NA (PNA) finds similar regions between two networks while multiple NA (MNA) can align more than two networks. We focus on MNA. Existing MNA methods aim to maximize total similarity over all aligned nodes (node conservation). Then, they evaluate alignment quality…
Biological databases can be analysed as a complex network which may reveal some its underlying biological mechanisms. Frequently, such databases are identified as scale-free networks or as hierarchical networks depending on connectivity distributions or clustering coefficients. Since these databases do grow over time, one would expect that their network topology may undergo some changes. Here, we analysed the historical versions of miRBase, a database of microRNAs where we performed an alignment of all mature and precursor miRNAs and calculated a pairwise similarity index. We found that the cl…
Protein-protein interaction (PPI) network alignment is a canonical operation to transfer biological knowledge among species. The alignment of PPI-networks has many applications, such as the prediction of protein function, detection of conserved network motifs, and the reconstruction of species' phylogenetic relationships. A good multiple-network alignment (MNA), by considering the data related to several species, provides a deep understanding of biological networks and system-level cellular processes. With the massive amounts of available PPI data and the increasing number of known PPI network…
Biological network alignment aims to identify similar regions between networks of different species. Existing methods compute node "similarities" to rapidly identify from possible alignments the "high-scoring" alignments with respect to the overall node similarity. However, the accuracy of the alignments is then evaluated with some other measure that is different than the node similarity used to construct the alignments. Typically, one measures the amount of conserved edges. Thus, the existing methods align similar nodes between networks hoping to conserve many edges (after the alignment is co…
Quantum Optimisation for Protein-Protein Interaction Network Alignment
University of Hamburg（汉堡大学）；Parity Quantum Computing Germany GmbH（帕里特量子计算德国有限公司）；Parity Quantum Computing GmbH（帕里特量子计算有限公司）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Department of Mathematics and Computer Science, University of Southern Denmark（南丹麦大学数学与计算机科学系）
Comparative analyses of protein-protein interaction networks play important roles in the understanding of biological processes. However, the growing enormity of available data on the networks becomes a computational challenge for the conventional alignment algorithms. Quantum algorithms generally provide greater efficiency over their classical counterparts in solving various problems. One of such algorithms is the quantum phase estimation algorithm which generates the principal eigenvector of a stochastic matrix with probability one. Using the quantum phase estimation algorithm, we introduce a…
Networks are ubiquitous in biology where they encode connectivity patterns at all scales of organization, from molecular to the biome. However, biological networks are noisy due to the limitations of measurement technology and inherent natural variation, which can hamper discovery of network patterns and dynamics. We propose Network Enhancement (NE), a method for improving the signal-to-noise ratio of undirected, weighted networks. NE uses a doubly stochastic matrix operator that induces sparsity and provides a closed-form solution that increases spectral eigengap of the input network. As a re…
