Multiple Network Alignment via MultiMAGNA+

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.

New GO-based measures in multiple network alignment

MOTIVATION

Protein-protein interaction (PPI) networks provide valuable insights into the function of biological systems. Aligning multiple PPI networks may expose relationships beyond those observable by pairwise comparisons. However, assessing the biological quality of multiple network alignments is a challenging problem.

RESULTS

We propose two new measures to evaluate the quality of multiple network alignments using functional information from Gene Ontology (GO) terms. When aligning multiple real PPI networks across species, we observe that both measures are highly correlated with objective quality indicators, such as common orthologs. Additionally, our measures strongly correlate with an alignment's ability to predict novel GO annotations, which is a unique advantage over existing GO-based measures.

AVAILABILITY AND IMPLEMENTATION

The scripts and the links to the raw and alignment data can be accessed at https://github.com/kimiayazdani/GO_Measures.git.

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.

Challenges and Limitations of Biological Network Analysis

High-Throughput technologies are producing an increasing volume of data that needs large amounts of data storage, effective data models and efficient, possibly parallel analysis algorithms. Pathway and interactomics data are represented as graphs and add a new dimension of analysis, allowing, among other features, graph-based comparison of organisms' properties. For instance, in biological pathway representation, the nodes can represent proteins, RNA and fat molecules, while the edges represent the interaction between molecules. Otherwise, biological networks such as Protein-Protein Interaction (PPI) Networks, represent the biochemical interactions among proteins by using nodes that model the proteins from a given organism, and edges that model the protein-protein interactions, whereas pathway networks enable the representation of biochemical-reaction cascades that happen within the cells or tissues. In this paper, we discuss the main models for standard representation of pathways and PPI networks, the data models for the representation and exchange of pathway and protein interaction data, the main databases in which they are stored and the alignment algorithms for the comparison of pathways and PPI networks of different organisms. Finally, we discuss the challenges and the limitations of pathways and PPI network representation and analysis. We have identified that network alignment presents a lot of open problems worthy of further investigation, especially concerning pathway alignment.

An Extensive Assessment of Network Embedding in PPI Network Alignment

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

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.

Comparative Analyses of Gene Co-expression Networks: Implementations and Applications in the Study of Evolution

Similarities and differences in the associations of biological entities among species can provide us with a better understanding of evolutionary relationships. Often the evolution of new phenotypes results from changes to interactions in pre-existing biological networks and comparing networks across species can identify evidence of conservation or adaptation. Gene co-expression networks (GCNs), constructed from high-throughput gene expression data, can be used to understand evolution and the rise of new phenotypes. The increasing abundance of gene expression data makes GCNs a valuable tool for the study of evolution in non-model organisms. In this paper, we cover motivations for why comparing these networks across species can be valuable for the study of evolution. We also review techniques for comparing GCNs in the context of evolution, including local and global methods of graph alignment. While some protein-protein interaction (PPI) bioinformatic methods can be used to compare co-expression networks, they often disregard highly relevant properties, including the existence of continuous and negative values for edge weights. Also, the lack of comparative datasets in non-model organisms has hindered the study of evolution using PPI networks. We also discuss limitations and challenges associated with cross-species comparison using GCNs, and provide suggestions for utilizing co-expression network alignments as an indispensable tool for evolutionary studies going forward.

Sparse self-attention aggregation networks for neural sequence slice interpolation

Background

Microscopic imaging is a crucial technology for visualizing neural and tissue structures. Large-area defects inevitably occur during the imaging process of electron microscope (EM) serial slices, which lead to reduced registration and semantic segmentation, and affect the accuracy of 3D reconstruction. The continuity of biological tissue among serial EM images makes it possible to recover missing tissues utilizing inter-slice interpolation. However, large deformation, noise, and blur among EM images remain the task challenging. Existing flow-based and kernel-based methods have to perform frame interpolation on images with little noise and low blur. They also cannot effectively deal with large deformations on EM images.

Results

In this paper, we propose a sparse self-attention aggregation network to synthesize pixels following the continuity of biological tissue. First, we develop an attention-aware layer for consecutive EM images interpolation that implicitly adopts global perceptual deformation. Second, we present an adaptive style-balance loss taking the style differences of serial EM images such as blur and noise into consideration. Guided by the attention-aware module, adaptively synthesizing each pixel aggregated from the global domain further improves the performance of pixel synthesis. Quantitative and qualitative experiments show that the proposed method is superior to the state-of-the-art approaches.

Conclusions

The proposed method can be considered as an effective strategy to model the relationship between each pixel and other pixels from the global domain. This approach improves the algorithm’s robustness to noise and large deformation, and can accurately predict the effective information of the missing region, which will greatly promote the data analysis of neurobiological research.

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.

MPGM: Scalable and Accurate Multiple Network Alignment

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 networks, the problem of MNA is gaining more attention in the systems-biology studies. In this paper, we introduce a new scalable and accurate algorithm, called MPGM, for aligning multiple networks. The MPGM algorithm has two main steps: (i) SeedGeneration and (ii) MultiplePercolation. In the first step, to generate an initial set of seed tuples, the SeedGeneration algorithm uses only protein sequence similarities. In the second step, to align remaining unmatched nodes, the MultiplePercolation algorithm uses network structures and the seed tuples generated from the first step. We show that, with respect to different evaluation criteria, MPGM outperforms the other state-of-the-art algorithms. In addition, we guarantee the performance of MPGM under certain classes of network models. We introduce a sampling-based stochastic model for generating k correlated networks. We prove that for this model if a sufficient number of seed tuples are available, the MultiplePercolation algorithm correctly aligns almost all the nodes. Our theoretical results are supported by experimental evaluations over synthetic networks.

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

BACKGROUND

Network alignment is an efficient computational framework in the prediction of protein function and phylogenetic relationships in systems biology. However, most of existing alignment methods focus on aligning PPIs based on static network model, which are actually dynamic in real-world systems. The dynamic characteristic of PPI networks is essential for understanding the evolution and regulation mechanism at the molecular level and there is still much room to improve the alignment quality in dynamic networks.

RESULTS

In this paper, we proposed a novel alignment algorithm, Twadn, to align dynamic PPI networks based on a strategy of time warping. We compare Twadn with the existing dynamic network alignment algorithm DynaMAGNA++ and DynaWAVE and use area under the receiver operating characteristic curve and area under the precision-recall curve as evaluation indicators. The experimental results show that Twadn is superior to DynaMAGNA++ and DynaWAVE. In addition, we use protein interaction network of Drosophila to compare Twadn and the static network alignment algorithm NetCoffee2 and experimental results show that Twadn is able to capture timing information compared to NetCoffee2.

CONCLUSIONS

Twadn is a versatile and efficient alignment tool that can be applied to dynamic network. Hopefully, its application can benefit the research community in the fields of molecular function and evolution.

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/.

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 Novel Computational Approach for Global Alignment for Multiple Biological Networks

Due to the rapid progress of biological networks for modeling biological systems, a lot of biomolecular networks have been producing more and more protein-protein interaction (PPI) data. Analyzing protein-protein interaction networks aims to find regions of topological and functional (dis)similarities between molecular networks of different species. The study of PPI networks has the potential to teach us as much about life process and diseases at the molecular level. Although few methods have been developed for multiple PPI network alignment and thus, new network alignment methods are of a compelling need. In this paper, we propose a novel algorithm for a global alignment of multiple protein-protein interaction networks called MAPPIN. The latter relies on information available for the proteins in the networks, such as sequence, function, and network topology. Our algorithm is perfectly designed to exploit current multi-core CPU architectures, and has been extensively tested on a real data (eight species). Our experimental results show that MAPPIN significantly outperforms NetCoffee in terms of coverage. Nevertheless, MAPPIN is handicapped by the time required to load the gene annotation file. An extensive comparison versus the pioneering PPI methods also show that MAPPIN is often efficient in terms of coverage, mean entropy, or mean normalized.

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/.