Computational Network Inference for Bacterial Interactomics

ABSTRACT Since the large-scale experimental characterization of protein–protein interactions (PPIs) is not possible for all species, several computational PPI prediction methods have been developed that harness existing data from other species. While PPI network prediction has been extensively used in eukaryotes, microbial network inference has lagged behind. However, bacterial interactomes can be built using the same principles and techniques; in fact, several methods are better suited to bacterial genomes. These predicted networks allow systems-level analyses in species that lack experimental interaction data. This review describes the current network inference and analysis techniques and summarizes the use of computationally-predicted microbial interactomes to date.

transcription from an operon in one species indicates functional relation and often interaction in another (Fig. 1F) (79,81).

EVOLUTIONARY
Interacting protein pairs tend to evolve at the same rate (46, 87), and so the distribution of protein pairs will therefore be co-conserved if they interact (78,(88)(89)(90)(91). The phylogenetic profile method (Fig. 1G) infers interactions when two genes have a similar pattern of conservation (presence/absence) in multiple genomes (92,93). MirrorTree and ContextMirror algorithms extend this method beyond binary similarity to globally assess the phylogenies (94,95). Finally, in silico two-hybrid (i2H) method identifies interacting pairs from correlated mutations in multiple sequence alignments, since mutation in interacting proteins coevolve (96). Several other extensions to these methods have been proposed (97)(98)(99).

NETWORK VALIDATION
Once a predicted interactome has been built, it is essential to evaluate how accurately it represents real cellular biology and assess the level of false interactions that may be present. Evaluation of the quality of a predicted network is difficult due to the level of noise in the underlying data: often several validation methods are required. Small-scale experimental validation can be used on a subset of PPIs to give a level of confidence in the predicted network (20,64,122,127,128). However, experimental validation is only possible for a small number of interactions. Expression data sets can be used to assess PPIs since interacting proteins are likely to have correlated expression (64,119,(128)(129)(130)(131), and evidence of support for predicted PPIs can be found in other experimental data sets or from text-mined small-scale studies (122,(132)(133)(134).
Domain data can be used to assess networks predicted using other input data types (133). Similarly, interaction predictions from other methodologies can be assessed using phylogenetics (119,122,129,131). Hub proteins in predicted networks often correspond to hubs in other species (135). Clustering the network can be used to assess how well the network represents known protein complexes (136). Comparison of the predicted network with random networks can also be used to assess its biological relevance (64,137).
Protein functional annotations provide useful validation tools as interacting proteins tend to have shared function (64,119,128,131,132,138,139), shared cellular localization (128,132,138), and related phenotype (119,131,133). Protein functional prediction can provide an objective method of network evaluation by testing its ability to predict the known annotations, for example by a leave-one-out or partitioned crossvalidation (140)(141)(142)(143). Data partitioning can also be used in the training/testing phase of machine learning to provide a measure of network accuracy (134).

NETWORK ANALYSIS
Several network parameters can be used to reveal aspects of network topology and identify key proteins (144). The degree of a protein is its number of interactions; proteins with a high degree are considered hubs and tend to be essential and conserved (46,145,146), and are often targets for pathogens (147,148). Identification of hubs in predicted networks can highlight important proteins for further study (129). The degree distribution of a network, p(k), is the probability a selected protein has k links (149). This distribution reflects the organization of cellular processes (150), with many low degree proteins and a small number of hubs giving a scale-free distribution (4,149,151). This topology makes networks resistant to random perturbation (5,151) and has been found in several biological networks in a number of model species (17,(152)(153)(154), although some do not have this topology (27,155).
Biological networks are considered small world since they have small diameters (longest shortest path between two proteins) and small characteristic path lengths (average shortest path) relative to equivalently-sized random networks (156)(157)(158). The proteins of these networks are arranged in locally-dense regions interconnected by a small number of interactions, and, like scale-free networks, this topology is resistant to perturbation (5).
Several network measures assess the importance of proteins and interactions in networks' information flow to identify bottlenecks. For instance, betweenness centrality (159) measures the proportion of shortest paths passing through a protein/interaction. Proteins with high betweenness centrality and low degree often link network modules (160). Betweenness centrality can aid the identification of key proteins within a predicted network (116,147).
Biological networks tend to have a hierarchical structure of modules within modules (4,161). Dense network regions are believed to relate to the functional units of the cell (151,(162)(163)(164)(165). Partitioning or clustering large networks can reveal the underlying mechanisms of cellular biology and assign protein function (137,166,167). Module detection can use additional data, for instance gene expression data (168), functional annotations (169), or domain profiles (170).
Predicted networks can be used to directly annotate proteins with function (171). Network-based annotation transfers known annotations between pairs of directly connected proteins (172,173), between proteins with shared interaction partners (174), or more globally using network topology (175). Interaction confidence weights, such as those produced by machine learning algorithms, are particularly useful for annotation transfer (173). Annotation and other data can also be used to create process/condition-specific subnetworks (176,177).
available in a few species, and small-scale studies require considerable curation to analyze as a whole (195,196). However, several studies have produced a number of predicted interactomes (Table 1), providing insights into several aspects of microbial biology. Additionally, the STRING database and server contains functional interaction data, including co-citation, co-expression and gene neighborhood, for multiple microbial species (197). STRING data have been used as the initial data source for network studies in several species (115,178,(198)(199)(200)(201)(202)(203)(204).

CELLULAR BIOLOGY AND PROTEIN FUNCTION
In E. coli, an interactome study combined experimental data with genome context predictions to assign functions to proteins, including several involved in cell envelope biogenesis (20). A phylogenetic profile-based network was later produced, which contained previously uncharacterized components of several complexes, including the ribosome (205). Comparison of these networks (20,205) using edge propagation, demonstrated that both identify complexes overlapping functional modules (206). A support vector machine-derived E. coli network was shown to be scale-free and had good overlap with experimental data (134). The EcID database incorporated genome context and phylogenetic evidence into a Bayesian classifier to predict protein function, in particular linking yeaG and yeaH to nitrogen metabolism (121). EcoliNet is a probabilistic functional integrated network for E. coli comprising ;99% of the genome and has successfully predicted knockout phenotypes (124). The interacting domain profile pair method, IDPP, was evaluated on E. coli before producing a network for C. jejuni from H. pylori interaction data (207,208). IDPP was shown to successfully predict interactions in the target species that were not found in the source species.
Incorporating expression data, interologs and DDIs, Bacillus licheniformis proteins were assigned to complexes and putative functions (139). A probabilistic network for Klebsiella pneumoniae, derived from multiple data types, was used to identify antibiotic resistance genes (125). Wuchty and colleagues expanded experimental networks of Streptococcus pneumoniae and H. pylori using interolog data to improve their functional predictive power (30, 209). Interologs and DDIs were combined with experimental data to study the metabolic modules of Pseudomonas putida (210). In the related species P. aeruginosa, probabilistic functional network integration identified novel virulence and antibiotic resistance genes (126).
SynechoNET is a predicted interactome for Synechocystis, focused on membrane biology (204), while InteroPORC predicted an interactome for this species comprising 28% of the genome (51). Later Naïve Bayesian network classification was applied to protein functional prediction and modular analysis in Synechocystis (122). Interactome prediction has also been widely used to study Mycobacterium tuberculosis due to unavailability of accurate in vitro methods in this bacterium (211,212). Several predicted interactomes have been created to study network properties (119), evolution (205), protein function (115), virulence (213), and drug resistance (198) in this species. Finally, interolog networks for 22 bacterial species (the largest of which are included in Table 1) were produced by McDermott and colleagues and used to predict functions for a large number of unannotated bacterial proteins (142) demonstrating the potential of large-scale network studies to enhance our understanding of bacterial cellular physiology.
Computational prediction has also been used to understand the interplay between bacteriophages and bacteria (214). Phylogenetic profiles using genomic/metagenomic data have identified host-virus and virus-virus relationships (215)(216)(217)(218). Leite and colleagues used interactions, DDIs, and sequence properties to compare machine learning frameworks, concluding that predictive power will improve as input data increases (114). More recently, a Markov random field framework of virus-host and virus-virus similarity measures has been developed (219).

INTERACTOME EVOLUTION
Comparison of networks for different species can reveal insights into interactome evolution. Zitnik and colleagues used STRING data to create networks for 1,539 bacteria (178); comparison with those of eukaryotes revealed that interactomes have evolved to become more robust, and that bacterial interactome robustness is associated with more complex environments. Using a binary interaction data set for Treponema pallidum, interolog networks were created for 372 other genomes, ;28% of which were estimated to be true interactions (31). This study also revealed that bacterial proteins have higher degrees than eukaryotic proteins. These networks also revealed a central role for cell motility proteins in bacterial interactomes.
By comparing a Methanobrevibacter ruminantium network with those of Methanosarcina acetivorans, Methanosarcina barkeri and Methanococcus maripaludis biosynthetic subsystems involved in survival in the rumen were identified (202). By comparing the Methanothermobacter thermautotrophicus metabolic interactome with those of metalloving bacteria, separate evolution of niche-specific cellular functions was revealed (201). A comparison of 10 strains of Salmonella enterica identified distinct transcription factor targets conferring adaptation to gastrointestinal and extra-intestinal environments (220). Similarly, comparison of host-pathogen interactomes between two strains of Burkholderia pseudomallei revealed several interactions unique to the virulent strain and highlighted the potential roles of chaperon and drug/carbohydrate binding proteins during infection (221).

PATHOGEN-HOST INTERACTIONS
Interactome prediction can identify cross talk between pathogen and host (222,223). A DDI-based network suggested that human-M. tuberculosis PPIs tend to have more domains than intraspecies interactions (138), and this trend was later observed in an interolog-based mapping study, which also revealed that hub proteins of intraspecies networks tend to be involved in host-pathogen PPI (148). Using a random forest framework, the cancer pathway was involved in M. tuberculosis infection (117), while a DDI network implicated several PPIs involving heat shock, redox proteins (224). Finally, a combination of interolog and DDI mapping associated several genes of the host immune responses to M. tuberculosis infection (65).
In Fusobacterium nucleatum, a host-pathogen network implicated the Fap2 adhesin as a virulence protein (225). Comparison of machine learning classifiers for Bacillus anthracishumans PPI prediction, suggested neural networks outperform SVMs (120); the resulting interactions revealed involvement of apoptosis and immune regulation pathways in infection. The predicted networks between humans and B. anthracis, Francisella tularensis, and Yersinia pestis indicated that hubs and bottlenecks of the intraspecies networks tend to interact (147,226). Thirteen membrane proteins of Leptospira interrogans were predicted to be involved in cellular disruption during infection, four of which were common between strains (203). Coelho and colleagues produced a human-microbial PPI network of the oral cavity using a Bayeisan classifier, which revealed Rothia mucilaginosa, Leptotrichia buccalis, and Actinomyces odontolyticus as having the most interactions with human proteins (123).
In the plant pathogen Ralstonia solanacearum, interolog network analysis identified interactions between its transportation proteins and core proteins of the A. thaliana interactome (227). The response to metal ions was linked to the host defense response during Pseudomonas syringae infection of A. thaliana (228). Defense response proteins were also found to be enriched in random forest-derived networks between A. thaliana and the pathogens P. syringae, Hpaloperonospora arabidopsis, and Golovinomyces orontii (113). Interolog and DDI mapping has also been used to study plant-bacterial symbiosis, suggesting a role of host 14-3-3 and heat shock proteins in the relationship between Bradyrhizobium diazoefficiens and Glycine max (229).

VIRUSES
Computational prediction has been applied to viral species including HIV (230-232), hepatitis C virus (233), human papillomaviruses (234), and Ebola (235). In particular, the recent pandemic has highlighted the importance of understanding viral-host interaction, and having resources available to rapidly respond to new viral threats. Two studies have compared PPI prediction to emerging data from Sars-CoV-2: the first used interolog mapping, DDIs, and machine learning to link ACE2 and DPP4 to spike protein binding (236); the second used an ensemble machine learning algorithm based on experimental data and sequence features to predict .1,000 potential human protein targets (237).

DRUG TARGETS
Interactome networks can aid in the identification of potential drug targets by revealing essential pathogen interactions (238). A M. tuberculosis-human interactome was shown to be enriched in predicted drug targets (239), and several studies have used computational prediction to identify putative drug targets (199,213) and to understand the mechanisms of drug resistance in this important pathogen (198,240). In P. aeroginisa a random forest predicted network was used to prioritize drug targets based on their essentiality and topological importance (116). Using interolog mapping, 12 putative drug targets were identified in methicillin-resistant Staphylococcus aureus, including a histone deacetylase (241). A predicted Corynebacterium pseudotuberculosis interactome was used to identify 41 essential proteins as candidates for infection diagnosis in livestock, highlighting the tryptophan biosynthesis pathway as a potential drug target (200). The network also revealed that this species may use multiple iron acquisition strategies in low iron environments. In the swine pathogen Actinobacillus pleuropneumoniae, nine drug target candidates were identified using interolog mapping (242). Interolog analysis has also been applied to the gut microbiome to identify target species driving metabolic change during disease (243).

CONCLUSIONS AND FUTURE PERSPECTIVES
Although PPI network prediction has been extensively used in eukaryotes, microbial network inference can be achieved using the same principles and analysis techniques. Bacterial interactomes share common hierarchical properties, such as modularity and robustness (244). Many of the caveats to interactome prediction in eukaryotes, such as evolutionary distance, unequal conservation, and physiological context (245)(246)(247)(248)(249) are mitigated in prokaryotes due to their smaller genomes and single-celled nature. Several prediction methods, in particular gene neighborhood and gene cluster, are more suited to microbial than eukaryotic use (79,83), and phylogenetic profiles are powerful predictors, particularly when including inputs from the three domains of life (250).
Interolog and DDI mapping can only detect interactions within conserved areas of the genome (48), and these methods rely on the quality of the underlying interaction data; stochastic activation of reporters can give false positives and low sensitivity leads to false negatives (251,252), and different methods have their own strengths (253)(254)(255)(256). In eukaryotes, poor overlap has been observed between data sets of different types, and between those of the same type (10,189). Comparison of experimental data of C. jejuni, H. pylori, and E. coli suggests that these data sets have significant levels of overlap and similar rates of false results (27). Meta-interactome analysis can be used to identify broadly-conserved biological systems, although levels of conservation remain low due to lack of experimental interactome coverage in many species (257).
Current experimental interactome data are incomplete and biased toward well-studied proteins and species (178). Using a combination of computational methods (51,119,139,201,210), and experimental data if available (20,124,220), gives a more complete predicted interactome, reduces some biases, and strengthens the evidence of true interactions. Integration of diverse data types is particularly effective when using a probabilistic (124)(125)(126) or machine learning (115,116,121,134) framework, allowing thresholding of interaction confidence scores and therefore reduction of noise.
Filling in the gaps in bacterial interactomes is vital to our understanding of their biology, and computational prediction can help to pin down these areas and target further analyses by identifying areas of interest and providing putative protein functions. Microbial comparative interactomics is now possible on a large scale; for instance, the .1,500 predicted networks produced by Zitnik and colleagues revealed the evolutionary rewiring of interactomes through time (178). While there are parts of some interactomes that cannot currently be predicted due to the complexity of the protein locations and the lack of the accurate annotations in the genome of new bacterial isolates, interactome accuracy will improve as coverage of diverse species increases, providing insights in several areas of biology, in particular the identification of PPIs for antibacterial discovery (258), understanding of pathogenicity through host cell rewiring (256), and in engineering of synthetic cellular systems (259).

ACKNOWLEDGMENTS
This work received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Graphic produced by Patrick Lane, ScEYEnce Studios.