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.

Current and future directions in network biology

Summary

Network biology is an interdisciplinary field bridging computational and biological sciences that has proved pivotal in advancing the understanding of cellular functions and diseases across biological systems and scales. Although the field has been around for two decades, it remains nascent. It has witnessed rapid evolution, accompanied by emerging challenges. These stem from various factors, notably the growing complexity and volume of data together with the increased diversity of data types describing different tiers of biological organization. We discuss prevailing research directions in network biology, focusing on molecular/cellular networks but also on other biological network types such as biomedical knowledge graphs, patient similarity networks, brain networks, and social/contact networks relevant to disease spread. In more detail, we highlight areas of inference and comparison of biological networks, multimodal data integration and heterogeneous networks, higher-order network analysis, machine learning on networks, and network-based personalized medicine. Following the overview of recent breakthroughs across these five areas, we offer a perspective on future directions of network biology. Additionally, we discuss scientific communities, educational initiatives, and the importance of fostering diversity within the field. This article establishes a roadmap for an immediate and long-term vision for network biology.

Availability and implementation

Not applicable.

Mechanism-based and data-driven modeling in cell-free synthetic biology

Cell-free systems have emerged as a versatile platform in synthetic biology, finding applications in various areas such as prototyping synthetic circuits, biosensor development, and biomanufacturing. To streamline the prototyping process, cell-free systems often incorporate a modeling step that predicts the outcomes of various experimental scenarios, providing a deeper insight into the underlying mechanisms and functions. There are two recognized approaches for modeling these systems: mechanism-based modeling, which models the underlying reaction mechanisms; and data-driven modeling, which makes predictions based on data without preconceived interactions between system components. In this highlight, we focus on the latest advancements in both modeling approaches for cell-free systems, exploring their potential for the design and optimization of synthetic genetic circuits.

A protein-protein interaction network aligner study in the multi-objective domain

BACKGROUND AND OBJECTIVE

The protein-protein interaction (PPI) network alignment has proven to be an efficient technique in the diagnosis and prevention of certain diseases. However, the difficulty in maximizing, at the same time, the two qualities that measure the goodness of alignments (topological and biological quality) has led aligners to produce very different alignments. Thus making a comparative study among alignments of such different qualities a big challenge. Multi-objective optimization is a computer method, which is very powerful in this kind of contexts because both conflicting qualities are considered together. Analysing the alignments of each PPI network aligner with multi-objective methodologies allows you to visualize a bigger picture of the alignments and their qualities, obtaining very interesting conclusions. This paper proposes a comprehensive PPI network aligner study in the multi-objective domain.

METHODS

Alignments from each aligner and all aligners together were studied and compared to each other via Pareto dominance methodologies. The best alignments produced by each aligner and all aligners together for five different alignment scenarios were displayed in Pareto front graphs. Later, the aligners were ranked according to the topological, biological, and combined quality of their alignments. Finally, the aligners were also ranked based on their average runtimes.

RESULTS

Regarding aligners constructing the best overall alignments, we found that SAlign, BEAMS, SANA, and HubAlign are the best options. Additionally, the alignments of best topological quality are produced by: SANA, SAlign, and HubAlign aligners. On the contrary, the aligners returning the alignments of best biological quality are: BEAMS, TAME, and WAVE. However, if there are time constraints, it is recommended to select SAlign to obtain high topological quality alignments and PISwap or SAlign aligners for high biological quality alignments.

CONCLUSIONS

The use of the SANA aligner is recommended for obtaining the best alignments of topological quality, BEAMS for alignments of the best biological quality, and SAlign for alignments of the best combined topological and biological quality. Simultaneously, SANA and BEAMS have above-average runtimes. Therefore, it is suggested, if necessary due to time restrictions, to choose other, faster aligners like SAlign or PISwap whose alignments are also of high quality.

Exact p-values for global network alignments via combinatorial analysis of shared GO terms : REFANGO: Rigorous Evaluation of Functional Alignments of Networks using Gene Ontology

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.

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.

Joint embedding of biological networks for cross-species functional alignment

MOTIVATION

Model organisms are widely used to better understand the molecular causes of human disease. While sequence similarity greatly aids this cross-species transfer, sequence similarity does not imply functional similarity, and thus, several current approaches incorporate protein-protein interactions to help map findings between species. Existing transfer methods either formulate the alignment problem as a matching problem which pits network features against known orthology, or more recently, as a joint embedding problem.

RESULTS

We propose a novel state-of-the-art joint embedding solution: Embeddings to Network Alignment (ETNA). ETNA generates individual network embeddings based on network topological structure and then uses a Natural Language Processing-inspired cross-training approach to align the two embeddings using sequence-based orthologs. The final embedding preserves both within and between species gene functional relationships, and we demonstrate that it captures both pairwise and group functional relevance. In addition, ETNA's embeddings can be used to transfer genetic interactions across species and identify phenotypic alignments, laying the groundwork for potential opportunities for drug repurposing and translational studies.

AVAILABILITY AND IMPLEMENTATION

https://github.com/ylaboratory/ETNA.

Supervised biological network alignment with graph neural networks

MOTIVATION

Despite the advances in sequencing technology, massive proteins with known sequences remain functionally unannotated. Biological network alignment (NA), which aims to find the node correspondence between species' protein-protein interaction (PPI) networks, has been a popular strategy to uncover missing annotations by transferring functional knowledge across species. Traditional NA methods assumed that topologically similar proteins in PPIs are functionally similar. However, it was recently reported that functionally unrelated proteins can be as topologically similar as functionally related pairs, and a new data-driven or supervised NA paradigm has been proposed, which uses protein function data to discern which topological features correspond to functional relatedness.

RESULTS

Here, we propose GraNA, a deep learning framework for the supervised NA paradigm for the pairwise NA problem. Employing graph neural networks, GraNA utilizes within-network interactions and across-network anchor links for learning protein representations and predicting functional correspondence between across-species proteins. A major strength of GraNA is its flexibility to integrate multi-faceted non-functional relationship data, such as sequence similarity and ortholog relationships, as anchor links to guide the mapping of functionally related proteins across species. Evaluating GraNA on a benchmark dataset composed of several NA tasks between different pairs of species, we observed that GraNA accurately predicted the functional relatedness of proteins and robustly transferred functional annotations across species, outperforming a number of existing NA methods. When applied to a case study on a humanized yeast network, GraNA also successfully discovered functionally replaceable human-yeast protein pairs that were documented in previous studies.

AVAILABILITY AND IMPLEMENTATION

The code of GraNA is available at https://github.com/luo-group/GraNA.

Network-Based Structural Alignment of RNA Sequences Using TOPAS

TOPAS (TOPological network-based Alignment of Structural RNAs) is a network-based alignment algorithm that predicts structurally sound pairwise alignment of RNAs. In order to take advantage of recent advances in comparative network analysis for efficient structurally sound RNA alignment, TOPAS constructs topological network representations for RNAs, which consist of sequential edges connecting nucleotide bases as well as structural edges reflecting the underlying folding structure. Structural edges are weighted by the estimated base-pairing probabilities. Next, the constructed networks are aligned using probabilistic network alignment techniques, which yield a structurally sound RNA alignment that considers both the sequence similarity and the structural similarity between the given RNAs. Compared to traditional Sankoff-style algorithms, this network-based alignment scheme leads to a significant reduction in the overall computational cost while yielding favorable alignment results. Another important benefit is its capability to handle arbitrary folding structures, which can potentially lead to more accurate alignment for RNAs with pseudoknots.

Short Linear Motifs in Colorectal Cancer Interactome and Tumorigenesis

Colorectal tumorigenesis is driven by alterations in genes and proteins responsible for cancer initiation, progression, and invasion. This multistage process is based on a dense network of protein-protein interactions (PPIs) that become dysregulated as a result of changes in various cell signaling effectors. PPIs in signaling and regulatory networks are known to be mediated by short linear motifs (SLiMs), which are conserved contiguous regions of 3-10 amino acids within interacting protein domains. SLiMs are the minimum sequences required for modulating cellular PPI networks. Thus, several in silico approaches have been developed to predict and analyze SLiM-mediated PPIs. In this review, we focus on emerging evidence supporting a crucial role for SLiMs in driver pathways that are disrupted in colorectal cancer (CRC) tumorigenesis and related PPI network alterations. As a result, SLiMs, along with short peptides, are attracting the interest of researchers to devise small molecules amenable to be used as novel anti-CRC targeted therapies. Overall, the characterization of SLiMs mediating crucial PPIs in CRC may foster the development of more specific combined pharmacological approaches.

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.

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.

Research on Chinese Audio and Text Alignment Algorithm Based on AIC-FCM and Doc2Vec

“Audiobook” is a multimedia-based reading technology that has emerged in recent years. Realizing the alignment of e-book text and book audio is the most important part of its processing. This article describes an audio and text alignment algorithm using deep learning and neural network technology to improve the efficiency and quality of audiobook production. The algorithm first uses dual-threshold endpoint detection technology to segment long audio into short audio with sentence dimensions and recognizes it as short text. The threshold is calculated by AIC-FCM optimized based on simulated annealing genetic algorithm. Then the algorithm uses Doc2vec optimized by the threshold prediction method based on the average length of the short text to calculate the text similarity. Finally, proofread and output the text sequence and audio segment aligned in the time dimension to meet the needs of audiobook production. Experiments show that compared to traditional audio and text alignment algorithms, the proposed algorithm is closer to the ideal segmentation result in long audio segmentation, and the alignment effect is basically the same as Doc2vec and the time complexity is reduced by about 35%.

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.

A Combinatorial Optimization Framework for Scoring Students in University Admissions

BACKGROUND AND OBJECTIVES

Selecting applications for college admission is critical for university operation and development. This paper leverages machine learning techniques to support enrollment management teams through data-informed decision-making in this otherwise laborious admissions processing.

RESEARCH DESIGN AND MEASURES

Two aspects of university admissions are considered. An ensemble learning approach, through the SuperLearner algorithm, is used to predict student show (yield) rate. The goal is to improve prediction accuracy to minimize over- or under-enrollment. A combinatorial optimization framework is proposed to weigh academic performance and experiential factors for ranking and selecting students for admission. This framework uses simulated annealing, and an efficacy study is presented to evaluate performance.

RESULTS

The proposed framework is illustrated for selecting an incoming class by optimizing predicted graduation rate and by developing an eligibility index. Each example presents a selection process under potential academic performance and experiential factor targets a university may place on an admitted class. R code is provided for higher education researchers and practitioners to apply the proposed methods in their own settings.

Pairwise Biological Network Alignment Based on Discrete Bat Algorithm

The development of high-throughput technology has provided a reliable technical guarantee for an increased amount of available data on biological networks. Network alignment is used to analyze these data to identify conserved functional network modules and understand evolutionary relationships across species. Thus, an efficient computational network aligner is needed for network alignment. In this paper, the classic bat algorithm is discretized and applied to the network alignment. The bat algorithm initializes the population randomly and then searches for the optimal solution iteratively. Based on the bat algorithm, the global pairwise alignment algorithm BatAlign is proposed. In BatAlign, the individual velocity and the position are represented by a discrete code. BatAlign uses a search algorithm based on objective function that uses the number of conserved edges as the objective function. The similarity between the networks is used to initialize the population. The experimental results showed that the algorithm was able to match proteins with high functional consistency and reach a relatively high topological quality.

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.

The protein-protein interaction network alignment using recurrent neural network

The main challenge of biological network alignment is that the problem of finding the alignments in two graphs is NP-hard. The discovery of protein-protein interaction (PPI) networks is of great importance in bioinformatics due to their utilization in identifying the cellular pathways, finding new medicines, and disease recognition. In this regard, we describe the network alignment method in the form of a classification problem for the very first time and introduce a deep network that finds the alignment of nodes present in the two networks. We call this method RENA, which means Network Alignment using REcurrent neural network. The proposed solution consists of three steps; in the first phase, we obtain the sequence and topological similarities from the networks' structure. For the second phase, the dataset needed for the transformation of the problem into a classification problem is created from obtained features. In the third phase, we predict the nodes' alignment between two networks using deep learning. We used Biogrid dataset for RENA evaluation. The RENA method is compared with three classification approaches of support vector machine, K-nearest neighbors, and linear discriminant analysis. The experimental results demonstrate the efficiency of the RENA method and 100% accuracy in PPI network alignment prediction.

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

MOTIVATION

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.

RESULTS

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.

AVAILABILITY AND IMPLEMENTATION

Matlab implementation is freely available at https://github.com/bjyoontamu/MONACO.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Data-driven biological network alignment that uses topological, sequence, and functional information

BACKGROUND

Network alignment (NA) can transfer functional knowledge between species' conserved biological network regions. Traditional 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 as topologically similar as functionally related proteins. So, we redefined NA as a data-driven method called TARA, which learns from network and protein functional data what kind of topological relatedness (rather than similarity) between proteins corresponds to their functional relatedness. TARA used topological information (within each network) but not sequence information (between proteins across networks). Yet, TARA yielded higher protein functional prediction accuracy than existing NA methods, even those that used both topological and sequence information.

RESULTS

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.

CONCLUSIONS

As such, combining research knowledge from different domains is promising. Overall, improvements in protein functional prediction have biomedical implications, for example allowing researchers to better understand how cancer progresses or how humans age.

Common Neighbors Extension of the Sticky Model for PPI Networks Evaluated by Global and Local Graphlet Similarity

The structure of protein-protein interaction (PPI) networks has been studied for over a decade. Many theoretical models have been proposed to model PPI network structure, but continuing noise and incompleteness in these networks make conclusions about their structure difficult. Using newer, larger networks from Sept. 2018 BioGRID and Jan. 2019 IID, we show the joint distribution of degree products and common neighbors has a greater impact on PPI edge connectivity than their individual distributions, and introduce two new models (CN and STICKY-CN) for PPI networks employing these features. Since graphlet-based measures are believed to be among the most discerning and sensitive network comparison tools available, we assess their overall global and local fits to PPI networks using Graphlet Kernel (GK). We fit 10 theoretical models to nine BioGRID networks and twelve Integrated Interactive Database (IID) networks and find: (1) STICKY and STICKY-CN are the overall globally best fitting models according to GK, (2) Hyperbolic Geometric Graph model is a better fit than any STICKY-based model on 4 species, (3) though STICKY-CN provides a better local fit than the STICKY model, the CN model provides the greatest local fit over most species. We conclude that the inclusion of CN into STICKY-CN makes it the best overall fit for PPI networks as it is a good fit locally and globally.

Protein2Vec: Aligning Multiple PPI Networks with Representation Learning

Research of Protein-Protein Interaction (PPI) Network Alignment is playing an important role in understanding the crucial underlying biological knowledge such as functionally homologous proteins and conserved evolutionary pathways across different species. Existing methods of PPI network alignment often try to improve the coverage ratio of the alignment result by aligning all proteins from different species. However, there is a fundamental biological premise that needs to be considered carefully: not every protein in a species can, nor should, find its homologous proteins in other species. In this work, we propose a novel alignment method to map only those proteins with the most similarity throughout the PPI networks of multiple species. For the similarity features of the protein in the networks, we integrate both topological features with biological characteristics to provide enhanced supports for the alignment procedures. For topological features, we apply a representation learning method on the networks and generate a low dimensional vector embedding with its surrounding structural features for each protein. The topological similarity of proteins from different PPI networks can thus be transferred as the similarity of their corresponding vector representations, which provides a new way to comprehensively quantify the topological similarities between proteins. We also propose a new measure for the topological evaluation of the alignment results which better uncover the structural quality of the alignment across multiple networks. Both biological and topological evaluations on the alignment results of real datasets demonstrate our approach is promising and preferable against previous multiple alignment methods.

A review of protein-protein interaction network alignment: From pathway comparison to global alignment

Network alignment provides a comprehensive way to discover the similar parts between molecular systems of different species based on topological and biological similarity. With such a strong basis, one can do comparative studies at a systems level in the field of computational biology. In this survey paper, we focus on protein-protein interaction networks and review some representative algorithms for network alignment in the past two decades as well as the state-of-the-art aligners. We also introduce the most popular evaluation measures in the literature to benchmark the performance of these approaches. Finally, we address several future challenges and the possible ways to conquer the existing problems of biological network alignment.

Data-driven network alignment

In this study, we deal with the problem of biological network alignment (NA), which aims to find a node mapping between species' molecular networks that uncovers similar network regions, thus allowing for the transfer of functional knowledge between the aligned nodes. We provide evidence that current NA methods, which assume that topologically similar nodes (i.e., nodes whose network neighborhoods are isomorphic-like) have high functional relatedness, do not actually end up aligning functionally related nodes. That is, we show that the current topological similarity assumption does not hold well. Consequently, we argue that a paradigm shift is needed with how the NA problem is approached. So, we redefine NA as a data-driven framework, called TARA (data-driven NA), which attempts to learn the relationship between topological relatedness and functional relatedness without assuming that topological relatedness corresponds to topological similarity. TARA makes no assumptions about what nodes should be aligned, distinguishing it from existing NA methods. Specifically, TARA trains a classifier to predict whether two nodes from different networks are functionally related based on their network topological patterns (features). We find that TARA is able to make accurate predictions. TARA then takes each pair of nodes that are predicted as related to be part of an alignment. Like traditional NA methods, TARA uses this alignment for the across-species transfer of functional knowledge. TARA as currently implemented uses topological but not protein sequence information for functional knowledge transfer. In this context, we find that TARA outperforms existing state-of-the-art NA methods that also use topological information, WAVE and SANA, and even outperforms or complements a state-of-the-art NA method that uses both topological and sequence information, PrimAlign. Hence, adding sequence information to TARA, which is our future work, is likely to further improve its performance. The software and data are available at http://www.nd.edu/~cone/TARA/.

NAIGO: An Improved Method to Align PPI Networks Based on Gene Ontology and Graphlets

With the development of high throughput technologies, there are more and more protein–protein interaction (PPI) networks available, which provide a need for efficient computational tools for network alignment. Network alignment is widely used to predict functions of certain proteins, identify conserved network modules, and study the evolutionary relationship across species or biological entities. However, network alignment is an NP-complete problem, and previous algorithms are usually slow or less accurate in aligning big networks like human vs. yeast. In this study, we proposed a fast yet accurate algorithm called Network Alignment by Integrating Biological Process (NAIGO). Specifically, we first divided the networks into subnets taking the advantage of known prior knowledge, such as gene ontology. For each subnet pair, we then developed a novel method to align them by considering both protein orthologous information and their local structural information. After that, we expanded the obtained local network alignments in a greedy manner. Taking the aligned pairs as seeds, we formulated the global network alignment problem as an assignment problem based on similarity matrix, which was solved by the Hungarian method. We applied NAIGO to align human and Saccharomyces cerevisiae S288c PPI network and compared the results with other popular methods like IsoRank, GRAAL, SANA, and NABEECO. As a result, our method outperformed the competitors by aligning more orthologous proteins or matched interactions. In addition, we found a few potential functional orthologous proteins such as RRM2B in human and DNA2 in S. cerevisiae S288c, which are related to DNA repair. We also identified a conserved subnet with six orthologous proteins EXO1, MSH3, MSH2, MLH1, MLH3, and MSH6, and six aligned interactions. All these proteins are associated with mismatch repair. Finally, we predicted a few proteins of S. cerevisiae S288c potentially involving in certain biological processes like autophagosome assembly.

L-HetNetAligner: A novel algorithm for Local Alignment of Heterogeneous Biological Networks

Networks are largely used for modelling and analysing a wide range of biological data. As a consequence, many different research efforts have resulted in the introduction of a large number of algorithms for analysis and comparison of networks. Many of these algorithms can deal with networks with a single class of nodes and edges, also referred to as homogeneous networks. Recently, many different approaches tried to integrate into a single model the interplay of different molecules. A possible formalism to model such a scenario comes from node/edge coloured networks (also known as heterogeneous networks) implemented as node/ edge-coloured graphs. Therefore, the need for the introduction of algorithms able to compare heterogeneous networks arises. We here focus on the local comparison of heterogeneous networks, and we formulate it as a network alignment problem. To the best of our knowledge, the local alignment of heterogeneous networks has not been explored in the past. We here propose L-HetNetAligner a novel algorithm that receives as input two heterogeneous networks (node-coloured graphs) and builds a local alignment of them. We also implemented and tested our algorithm. Our results confirm that our method builds high-quality alignments. The following website *contains Supplementary File 1 material and the code.

Pairwise Versus Multiple Global Network Alignment

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 hypothesized to yield higher-quality alignments), though at higher computational complexity. The issue is that, due to the different outputs of PNA and MNA, a PNA method is only compared to other PNA methods, and an MNA method is only compared to other MNA methods. Comparison of PNA against MNA must be done to evaluate whether MNA indeed yields higher-quality alignments, as only this would justify MNA's higher computational complexity. We introduce a framework that allows for this. We evaluate eight prominent PNA and MNA methods, on synthetic and real-world biological networks, using topological and functional alignment quality measures. We compare PNA against MNA in both a pairwise (native to PNA) and multiple (native to MNA) manner. PNA is expected to perform better under the pairwise evaluation framework. Indeed this is what we find. MNA is expected to perform better under the multiple evaluation framework. Shockingly, we find this not always to hold; PNA is often better than MNA in this framework, depending on the choice of evaluation test.

A Guide to Conquer the Biological Network Era Using Graph Theory

Networks are one of the most common ways to represent biological systems as complex sets of binary interactions or relations between different bioentities. In this article, we discuss the basic graph theory concepts and the various graph types, as well as the available data structures for storing and reading graphs. In addition, we describe several network properties and we highlight some of the widely used network topological features. We briefly mention the network patterns, motifs and models, and we further comment on the types of biological and biomedical networks along with their corresponding computer- and human-readable file formats. Finally, we discuss a variety of algorithms and metrics for network analyses regarding graph drawing, clustering, visualization, link prediction, perturbation, and network alignment as well as the current state-of-the-art tools. We expect this review to reach a very broad spectrum of readers varying from experts to beginners while encouraging them to enhance the field further.

An Introductory Guide to Aligning Networks Using SANA, the Simulated Annealing Network Aligner

Sequence alignment has had an enormous impact on our understanding of biology, evolution, and disease. The alignment of biological 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 comparison and alignment is an NP-complete problem for which heuristic algorithms must be used.Here we introduce SANA, the Simulated Annealing Network Aligner. SANA is one of many algorithms proposed for the arena of biological network alignment. In the context of global network alignment, SANA stands out for its speed, memory efficiency, ease-of-use, and flexibility in the arena of producing alignments between two or more networks. SANA produces better alignments in minutes on a laptop than most other algorithms can produce in hours or days of CPU time on large server-class machines. We walk the user through how to use SANA for several types of biomolecular networks.

LePrimAlign: local entropy-based alignment of PPI networks to predict conserved modules

Background

Cross-species analysis of protein-protein interaction (PPI) networks provides an effective means of detecting conserved interaction patterns. Identifying such conserved substructures between PPI networks of different species increases our understanding of the principles deriving evolution of cellular organizations and their functions in a system level. In recent years, network alignment techniques have been applied to genome-scale PPI networks to predict evolutionary conserved modules. Although a wide variety of network alignment algorithms have been introduced, developing a scalable local network alignment algorithm with high accuracy is still challenging.

Results

We present a novel pairwise local network alignment algorithm, called LePrimAlign, to predict conserved modules between PPI networks of three different species. The proposed algorithm exploits the results of a pairwise global alignment algorithm with many-to-many node mapping. It also applies the concept of graph entropy to detect initial cluster pairs from two networks. Finally, the initial clusters are expanded to increase the local alignment score that is formulated by a combination of intra-network and inter-network scores. The performance comparison with state-of-the-art approaches demonstrates that the proposed algorithm outperforms in terms of accuracy of identified protein complexes and quality of alignments.

Conclusion

The proposed method produces local network alignment of higher accuracy in predicting conserved modules even with large biological networks at a reduced computational cost.

PrimAlign: PageRank-inspired Markovian alignment for large biological networks

Motivation

Cross-species analysis of large-scale protein–protein interaction (PPI) networks has played a significant role in understanding the principles deriving evolution of cellular organizations and functions. Recently, network alignment algorithms have been proposed to predict conserved interactions and functions of proteins. These approaches are based on the notion that orthologous proteins across species are sequentially similar and that topology of PPIs between orthologs is often conserved. However, high accuracy and scalability of network alignment are still a challenge.

Results

We propose a novel pairwise global network alignment algorithm, called PrimAlign, which is modeled as a Markov chain and iteratively transited until convergence. The proposed algorithm also incorporates the principles of PageRank. This approach is evaluated on tasks with human, yeast and fruit fly PPI networks. The experimental results demonstrate that PrimAlign outperforms several prevalent methods with statistically significant differences in multiple evaluation measures. PrimAlign, which is multi-platform, achieves superior performance in runtime with its linear asymptotic time complexity. Further evaluation is done with synthetic networks and results suggest that popular topological measures do not reflect real precision of alignments.

Availability and implementation

The source code is available at http://web.ecs.baylor.edu/faculty/cho/PrimAlign.

Supplementary information

Supplementary data are available at Bioinformatics online.

Aligning dynamic networks with DynaWAVE

Motivation

Network alignment (NA) aims to find similar (conserved) regions between networks, such as cellular networks of different species. Until recently, existing methods were limited to aligning static networks. However, real-world systems, including cellular functioning, are dynamic. Hence, in our previous work, we introduced the first ever dynamic NA method, DynaMAGNA++, which improved upon the traditional static NA. However, DynaMAGNA++ does not necessarily scale well to larger networks in terms of alignment quality or runtime.

Results

To address this, we introduce a new dynamic NA approach, DynaWAVE. We show that DynaWAVE complements DynaMAGNA++: while DynaMAGNA++ is more accurate yet slower than DynaWAVE for smaller networks, DynaWAVE is both more accurate and faster than DynaMAGNA++ for larger networks. We provide a friendly user interface and source code for DynaWAVE.

Availability and implementation

https://www.nd.edu/∼cone/DynaWAVE/.

Contact

tmilenko@nd.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

SANA NetGO: a combinatorial approach to using Gene Ontology (GO) terms to score network alignments

Motivation

Gene Ontology (GO) terms are frequently used to score alignments between protein-protein interaction (PPI) networks. Methods exist to measure GO similarity between proteins in isolation, but proteins in a network alignment are not isolated: each pairing is dependent on every other via the alignment itself. Existing measures fail to take into account the frequency of GO terms across networks, instead imposing arbitrary rules on when to allow GO terms.

Results

Here we develop NetGO, a new measure that naturally weighs infrequent, informative GO terms more heavily than frequent, less informative GO terms, without arbitrary cutoffs, instead downweighting GO terms according to their frequency in the networks being aligned. This is a global measure applicable only to alignments, independent of pairwise GO measures, in the same sense that the edge-based EC or S3 scores are global measures of topological similarity independent of pairwise topological similarities. We demonstrate the superiority of NetGO in alignments of predetermined quality and show that NetGO correlates with alignment quality better than any existing GO-based alignment measures. We also demonstrate that NetGO provides a measure of taxonomic similarity between species, consistent with existing taxonomic measuresa feature not shared with existing GObased network alignment measures. Finally, we re-score alignments produced by almost a dozen aligners from a previous study and show that NetGO does a better job at separating good alignments from bad ones.

Availability and implementation

Available as part of SANA.

Contact

whayes@uci.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Multiple Network Alignment via MultiMAGNA+

Network alignment (NA) aims to find a node mapping that identifies topologically or functionally similar network regions between molecular networks of different species. 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 by measuring the amount of conserved edges, but only after the alignment is constructed. Directly optimizing edge conservation during alignment construction in addition to node conservation may result in superior alignments. Thus, we present a novel MNA method called multiMAGNA++ that can achieve this. Indeed, multiMAGNA++ outperforms or is on par with existing MNA methods, while often completing faster than existing methods. That is, multiMAGNA++ scales well to larger network data and can be parallelized effectively. During method evaluation, we also introduce new MNA quality measures to allow for more fair MNA method comparison compared to the existing alignment quality measures. The multiMAGNA++ code is available on the method's web page at http://nd.edu/~cone/multiMAGNA++/.

From homogeneous to heterogeneous network alignment via colored graphlets

Network alignment (NA) compares networks with the goal of finding a node mapping that uncovers highly similar (conserved) network regions. Existing NA methods are homogeneous, i.e., they can deal only with networks containing nodes and edges of one type. Due to increasing amounts of heterogeneous network data with nodes or edges of different types, we extend three recent state-of-the-art homogeneous NA methods, WAVE, MAGNA++, and SANA, to allow for heterogeneous NA for the first time. We introduce several algorithmic novelties. Namely, these existing methods compute homogeneous graphlet-based node similarities and then find high-scoring alignments with respect to these similarities, while simultaneously maximizing the amount of conserved edges. Instead, we extend homogeneous graphlets to their heterogeneous counterparts, which we then use to develop a new measure of heterogeneous node similarity. Also, we extend S3, a state-of-the-art measure of edge conservation for homogeneous NA, to its heterogeneous counterpart. Then, we find high-scoring alignments with respect to our heterogeneous node similarity and edge conservation measures. In evaluations on synthetic and real-world biological networks, our proposed heterogeneous NA methods lead to higher-quality alignments and better robustness to noise in the data than their homogeneous counterparts. The software and data from this work is available at https://nd.edu/~cone/colored_graphlets/.

GLAlign: A Novel Algorithm for Local Network Alignment

Networks are successfully used as a modelling framework in many application domains. For instance, Protein-Protein Interaction Networks (PPINs) model the set of interactions among proteins in a cell. A critical application of network analysis is the comparison among PPINs of different organisms to reveal similarities among the underlying biological processes. Algorithms for comparing networks (also referred to as network aligners) fall into two main classes: global aligners, which aim to compare two networks on a global scale, and local aligners that evidence single sub-regions of similarity among networks. The possibility to improve the performance of the aligners by mixing the two approaches is a growing research area. In our previous work, we started to explore the possibility to use global alignment to improve the local one. We here examine further this possibility by using topological information extracted from global alignment to guide the steps of the local alignment. Therefore, we present GLAlign (Global Local Aligner), a methodology that improves the performances of local network aligners by exploiting a preliminary global alignment. Furthermore, we provide an implementation of GLAlign. As a proof-of-principle, we evaluated the performance of the GLAlign prototype. Results show that GLAlign methodology outperforms the state-of-the-art local alignment algorithms. GLAlign is publicly available for academic use and can be downloaded here: https://sites.google.com/site/globallocalalignment/.

Graphettes: Constant-time determination of graphlet and orbit identity including (possibly disconnected) graphlets up to size 8

Graphlets are small connected induced subgraphs of a larger graph G. Graphlets are now commonly used to quantify local and global topology of networks in the field. Methods exist to exhaustively enumerate all graphlets (and their orbits) in large networks as efficiently as possible using orbit counting equations. However, the number of graphlets in G is exponential in both the number of nodes and edges in G. Enumerating them all is already unacceptably expensive on existing large networks, and the problem will only get worse as networks continue to grow in size and density. Here we introduce an efficient method designed to aid statistical sampling of graphlets up to size k = 8 from a large network. We define graphettes as the generalization of graphlets allowing for disconnected graphlets. Given a particular (undirected) graphette g, we introduce the idea of the canonical graphette [Formula: see text] as a representative member of the isomorphism group Iso(g) of g. We compute the mapping [Formula: see text], in the form of a lookup table, from all 2k(k - 1)/2 undirected graphettes g of size k ≤ 8 to their canonical representatives [Formula: see text], as well as the permutation that transforms g to [Formula: see text]. We also compute all automorphism orbits for each canonical graphette. Thus, given any k ≤ 8 nodes in a graph G, we can in constant time infer which graphette it is, as well as which orbit each of the k nodes belongs to. Sampling a large number N of such k-sets of nodes provides an approximation of both the distribution of graphlets and orbits across G, and the orbit degree vector at each node.

Alignment of dynamic networks

MOTIVATION

Network alignment (NA) aims to find a node mapping that conserves similar regions between compared networks. NA is applicable to many fields, including computational biology, where NA can guide the transfer of biological knowledge from well- to poorly-studied species across aligned network regions. Existing NA methods can only align static networks. However, most complex real-world systems evolve over time and should thus be modeled as dynamic networks. We hypothesize that aligning dynamic network representations of evolving systems will produce superior alignments compared to aligning the systems' static network representations, as is currently done.

RESULTS

For this purpose, we introduce the first ever dynamic NA method, DynaMAGNA ++. This proof-of-concept dynamic NA method is an extension of a state-of-the-art static NA method, MAGNA++. Even though both MAGNA++ and DynaMAGNA++ optimize edge as well as node conservation across the aligned networks, MAGNA++ conserves static edges and similarity between static node neighborhoods, while DynaMAGNA++ conserves dynamic edges (events) and similarity between evolving node neighborhoods. For this purpose, we introduce the first ever measure of dynamic edge conservation and rely on our recent measure of dynamic node conservation. Importantly, the two dynamic conservation measures can be optimized with any state-of-the-art NA method and not just MAGNA++. We confirm our hypothesis that dynamic NA is superior to static NA, on synthetic and real-world networks, in computational biology and social domains. DynaMAGNA++ is parallelized and has a user-friendly graphical interface.

AVAILABILITY AND IMPLEMENTATION

http://nd.edu/∼cone/DynaMAGNA++/ .

CONTACT

tmilenko@nd.edu.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.