Probabilistic protein function prediction from heterogeneous genome-wide data

Artificial intelligence for neurodegenerative experimental models

INTRODUCTION

Experimental models are essential tools in neurodegenerative disease research. However, the translation of insights and drugs discovered in model systems has proven immensely challenging, marred by high failure rates in human clinical trials.

METHODS

Here we review the application of artificial intelligence (AI) and machine learning (ML) in experimental medicine for dementia research.

RESULTS

Considering the specific challenges of reproducibility and translation between other species or model systems and human biology in preclinical dementia research, we highlight best practices and resources that can be leveraged to quantify and evaluate translatability. We then evaluate how AI and ML approaches could be applied to enhance both cross-model reproducibility and translation to human biology, while sustaining biological interpretability.

DISCUSSION

AI and ML approaches in experimental medicine remain in their infancy. However, they have great potential to strengthen preclinical research and translation if based upon adequate, robust, and reproducible experimental data.

HIGHLIGHTS

There are increasing applications of AI in experimental medicine. We identified issues in reproducibility, cross-species translation, and data curation in the field. Our review highlights data resources and AI approaches as solutions. Multi-omics analysis with AI offers exciting future possibilities in drug discovery.

PrismEXP: gene annotation prediction from stratified gene-gene co-expression matrices

Background

Gene-gene co-expression correlations measured by mRNA-sequencing (RNA-seq) can be used to predict gene annotations based on the co-variance structure within these data. In our prior work, we showed that uniformly aligned RNA-seq co-expression data from thousands of diverse studies is highly predictive of both gene annotations and protein-protein interactions. However, the performance of the predictions varies depending on whether the gene annotations and interactions are cell type and tissue specific or agnostic. Tissue and cell type-specific gene-gene co-expression data can be useful for making more accurate predictions because many genes perform their functions in unique ways in different cellular contexts. However, identifying the optimal tissues and cell types to partition the global gene-gene co-expression matrix is challenging.

Results

Here we introduce and validate an approach called PRediction of gene Insights from Stratified Mammalian gene co-EXPression (PrismEXP) for improved gene annotation predictions based on RNA-seq gene-gene co-expression data. Using uniformly aligned data from ARCHS4, we apply PrismEXP to predict a wide variety of gene annotations including pathway membership, Gene Ontology terms, as well as human and mouse phenotypes. Predictions made with PrismEXP outperform predictions made with the global cross-tissue co-expression correlation matrix approach on all tested domains, and training using one annotation domain can be used to predict annotations in other domains.

Conclusions

By demonstrating the utility of PrismEXP predictions in multiple use cases we show how PrismEXP can be used to enhance unsupervised machine learning methods to better understand the roles of understudied genes and proteins. To make PrismEXP accessible, it is provided via a user-friendly web interface, a Python package, and an Appyter. AVAILABILITY. The PrismEXP web-based application, with pre-computed PrismEXP predictions, is available from: https://maayanlab.cloud/prismexp; PrismEXP is also available as an Appyter: https://appyters.maayanlab.cloud/PrismEXP/; and as Python package: https://github.com/maayanlab/prismexp.

A Gated Recurrent Unit based architecture for recognizing ontology concepts from biological literature

Background

Annotating scientific literature with ontology concepts is a critical task in biology and several other domains for knowledge discovery. Ontology based annotations can power large-scale comparative analyses in a wide range of applications ranging from evolutionary phenotypes to rare human diseases to the study of protein functions. Computational methods that can tag scientific text with ontology terms have included lexical/syntactic methods, traditional machine learning, and most recently, deep learning.

Results

Here, we present state of the art deep learning architectures based on Gated Recurrent Units for annotating text with ontology concepts. We use the Colorado Richly Annotated Full Text Corpus (CRAFT) as a gold standard for training and testing. We explore a number of additional information sources including NCBI’s BioThesauraus and Unified Medical Language System (UMLS) to augment information from CRAFT for increasing prediction accuracy. Our best model results in a 0.84 F1 and semantic similarity.

Conclusion

The results shown here underscore the impact for using deep learning architectures for automatically recognizing ontology concepts from literature. The augmentation of the models with biological information beyond that present in the gold standard corpus shows a distinct improvement in prediction accuracy.

A review of deep learning applications in human genomics using next-generation sequencing data

Genomics is advancing towards data-driven science. Through the advent of high-throughput data generating technologies in human genomics, we are overwhelmed with the heap of genomic data. To extract knowledge and pattern out of this genomic data, artificial intelligence especially deep learning methods has been instrumental. In the current review, we address development and application of deep learning methods/models in different subarea of human genomics. We assessed over- and under-charted area of genomics by deep learning techniques. Deep learning algorithms underlying the genomic tools have been discussed briefly in later part of this review. Finally, we discussed briefly about the late application of deep learning tools in genomic. Conclusively, this review is timely for biotechnology or genomic scientists in order to guide them why, when and how to use deep learning methods to analyse human genomic data.

Comparing protein-protein interaction networks of SARS-CoV-2 and (H1N1) influenza using topological features

SARS-CoV-2 pandemic first emerged in late 2019 in China. It has since infected more than 298 million individuals and caused over 5 million deaths globally. The identification of essential proteins in a protein–protein interaction network (PPIN) is not only crucial in understanding the process of cellular life but also useful in drug discovery. There are many centrality measures to detect influential nodes in complex networks. Since SARS-CoV-2 and (H1N1) influenza PPINs pose 553 common human proteins. Analyzing influential proteins and comparing these networks together can be an effective step in helping biologists for drug-target prediction. We used 21 centrality measures on SARS-CoV-2 and (H1N1) influenza PPINs to identify essential proteins. We applied principal component analysis and unsupervised machine learning methods to reveal the most informative measures. Appealingly, some measures had a high level of contribution in comparison to others in both PPINs, namely Decay, Residual closeness, Markov, Degree, closeness (Latora), Barycenter, Closeness (Freeman), and Lin centralities. We also investigated some graph theory-based properties like the power law, exponential distribution, and robustness. Both PPINs tended to properties of scale-free networks that expose their nature of heterogeneity. Dimensionality reduction and unsupervised learning methods were so effective to uncover appropriate centrality measures.

Computational Network Inference for Bacterial Interactomics

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.

A New Family of Similarity Measures for Scoring Confidence of Protein Interactions Using Gene Ontology

The large-scale protein-protein interaction (PPI) data has the potential to play a significant role in the endeavor of understanding cellular processes. However, the presence of a considerable fraction of false positives is a bottleneck in realizing this potential. There have been continuous efforts to utilize complementary resources for scoring confidence of PPIs in a manner that false positive interactions get a low confidence score. Gene Ontology (GO), a taxonomy of biological terms to represent the properties of gene products and their relations, has been widely used for this purpose. We utilize GO to introduce a new set of specificity measures: Relative Depth Specificity (RDS), Relative Node-based Specificity (RNS), and Relative Edge-based Specificity (RES), leading to a new family of similarity measures. We use these similarity measures to obtain a confidence score for each PPI. We evaluate the new measures using four different benchmarks. We show that all the three measures are quite effective. Notably, RNS and RES more effectively distinguish true PPIs from false positives than the existing alternatives. RES also shows a robust set-discriminating power and can be useful for protein functional clustering as well.

Protein function prediction with gene ontology: from traditional to deep learning models

Protein function prediction is a crucial part of genome annotation. Prediction methods have recently witnessed rapid development, owing to the emergence of high-throughput sequencing technologies. Among the available databases for identifying protein function terms, Gene Ontology (GO) is an important resource that describes the functional properties of proteins. Researchers are employing various approaches to efficiently predict the GO terms. Meanwhile, deep learning, a fast-evolving discipline in data-driven approach, exhibits impressive potential with respect to assigning GO terms to amino acid sequences. Herein, we reviewed the currently available computational GO annotation methods for proteins, ranging from conventional to deep learning approach. Further, we selected some suitable predictors from among the reviewed tools and conducted a mini comparison of their performance using a worldwide challenge dataset. Finally, we discussed the remaining major challenges in the field, and emphasized the future directions for protein function prediction with GO.

Knowledge graphs and their applications in drug discovery

INTRODUCTION

Knowledge graphs have proven to be promising systems of information storage and retrieval. Due to the recent explosion of heterogeneous multimodal data sources generated in the biomedical domain, and an industry shift toward a systems biology approach, knowledge graphs have emerged as attractive methods of data storage and hypothesis generation.

AREAS COVERED

In this review, the author summarizes the applications of knowledge graphs in drug discovery. They evaluate their utility; differentiating between academic exercises in graph theory, and useful tools to derive novel insights, highlighting target identification and drug repurposing as two areas showing particular promise. They provide a case study on COVID-19, summarizing the research that used knowledge graphs to identify repurposable drug candidates. They describe the dangers of degree and literature bias, and discuss mitigation strategies.

EXPERT OPINION

Whilst knowledge graphs and graph-based machine learning have certainly shown promise, they remain relatively immature technologies. Many popular link prediction algorithms fail to address strong biases in biomedical data, and only highlight biological associations, failing to model causal relationships in complex dynamic biological systems. These problems need to be addressed before knowledge graphs reach their true potential in drug discovery.

Protein functional annotation of simultaneously improved stability, accuracy and false discovery rate achieved by a sequence-based deep learning

Functional annotation of protein sequence with high accuracy has become one of the most important issues in modern biomedical studies, and computational approaches of significantly accelerated analysis process and enhanced accuracy are greatly desired. Although a variety of methods have been developed to elevate protein annotation accuracy, their ability in controlling false annotation rates remains either limited or not systematically evaluated. In this study, a protein encoding strategy, together with a deep learning algorithm, was proposed to control the false discovery rate in protein function annotation, and its performances were systematically compared with that of the traditional similarity-based and de novo approaches. Based on a comprehensive assessment from multiple perspectives, the proposed strategy and algorithm were found to perform better in both prediction stability and annotation accuracy compared with other de novo methods. Moreover, an in-depth assessment revealed that it possessed an improved capacity of controlling the false discovery rate compared with traditional methods. All in all, this study not only provided a comprehensive analysis on the performances of the newly proposed strategy but also provided a tool for the researcher in the fields of protein function annotation.

A Method for the Annotation of Functional Similarities of Coding DNA Sequences: the Case of a Populated Cluster of Transmembrane Proteins

The analysis of a large number of human and mouse genes codifying for a populated cluster of transmembrane proteins revealed that some of the genes significantly vary in their primary nucleotide sequence inter-species and also intra-species. In spite of that divergence and of the fact that all these genes share a common parental function we asked the question of whether at DNA level they have some kind of common compositional structure, not evident from the analysis of their primary nucleotide sequence. To reveal the existence of gene clusters not based on primary sequence relationships we have analyzed 13574 human and 14047 mouse genes by the composon-clustering methodology. The data presented show that most of the genes from each one of the samples are distributed in 18 clusters sharing the common compositional features between the particular human and mouse clusters. It was observed, in addition, that between particular human and mouse clusters having similar composon-profiles large variations in gene population were detected as an indication that a significant amount of orthologs between both species differs in compositional features. A gene cluster containing exclusively genes codifying for transmembrane proteins, an important fraction of which belongs to the Rhodopsin G-protein coupled receptor superfamily, was also detected. This indicates that even though some of them display low sequence similarity, all of them, in both species, participate with similar compositional features in terms of composons. We conclude that in this family of transmembrane proteins in general and in the Rhodopsin G-protein coupled receptor in particular, the composon-clustering reveals the existence of a type of common compositional structure underlying the primary nucleotide sequence closely correlated to function.

SGFSC: speeding the gene functional similarity calculation based on hash tables

Background

In recent years, many measures of gene functional similarity have been proposed and widely used in all kinds of essential research. These methods are mainly divided into two categories: pairwise approaches and group-wise approaches. However, a common problem with these methods is their time consumption, especially when measuring the gene functional similarities of a large number of gene pairs. The problem of computational efficiency for pairwise approaches is even more prominent because they are dependent on the combination of semantic similarity. Therefore, the efficient measurement of gene functional similarity remains a challenging problem.

Results

To speed current gene functional similarity calculation methods, a novel two-step computing strategy is proposed: (1) establish a hash table for each method to store essential information obtained from the Gene Ontology (GO) graph and (2) measure gene functional similarity based on the corresponding hash table. There is no need to traverse the GO graph repeatedly for each method with the help of the hash table. The analysis of time complexity shows that the computational efficiency of these methods is significantly improved. We also implement a novel Speeding Gene Functional Similarity Calculation tool, namely SGFSC, which is bundled with seven typical measures using our proposed strategy. Further experiments show the great advantage of SGFSC in measuring gene functional similarity on the whole genomic scale.

Conclusions

The proposed strategy is successful in speeding current gene functional similarity calculation methods. SGFSC is an efficient tool that is freely available at http://nclab.hit.edu.cn/SGFSC. The source code of SGFSC can be downloaded from http://pan.baidu.com/s/1dFFmvpZ.

Methods for biological data integration: perspectives and challenges

Rapid technological advances have led to the production of different types of biological data and enabled construction of complex networks with various types of interactions between diverse biological entities. Standard network data analysis methods were shown to be limited in dealing with such heterogeneous networked data and consequently, new methods for integrative data analyses have been proposed. The integrative methods can collectively mine multiple types of biological data and produce more holistic, systems-level biological insights. We survey recent methods for collective mining (integration) of various types of networked biological data. We compare different state-of-the-art methods for data integration and highlight their advantages and disadvantages in addressing important biological problems. We identify the important computational challenges of these methods and provide a general guideline for which methods are suited for specific biological problems, or specific data types. Moreover, we propose that recent non-negative matrix factorization-based approaches may become the integration methodology of choice, as they are well suited and accurate in dealing with heterogeneous data and have many opportunities for further development.

The PFP and ESG protein function prediction methods in 2014: effect of database updates and ensemble approaches

Background

Functional annotation of novel proteins is one of the central problems in bioinformatics. With the ever-increasing development of genome sequencing technologies, more and more sequence information is becoming available to analyze and annotate. To achieve fast and automatic function annotation, many computational (automated) function prediction (AFP) methods have been developed. To objectively evaluate the performance of such methods on a large scale, community-wide assessment experiments have been conducted. The second round of the Critical Assessment of Function Annotation (CAFA) experiment was held in 2013–2014. Evaluation of participating groups was reported in a special interest group meeting at the Intelligent Systems in Molecular Biology (ISMB) conference in Boston in 2014. Our group participated in both CAFA1 and CAFA2 using multiple, in-house AFP methods. Here, we report benchmark results of our methods obtained in the course of preparation for CAFA2 prior to submitting function predictions for CAFA2 targets.

Results

For CAFA2, we updated the annotation databases used by our methods, protein function prediction (PFP) and extended similarity group (ESG), and benchmarked their function prediction performances using the original (older) and updated databases. Performance evaluation for PFP with different settings and ESG are discussed. We also developed two ensemble methods that combine function predictions from six independent, sequence-based AFP methods. We further analyzed the performances of our prediction methods by enriching the predictions with prior distribution of gene ontology (GO) terms. Examples of predictions by the ensemble methods are discussed.

Conclusions

Updating the annotation database was successful, improving the F_max prediction accuracy score for both PFP and ESG. Adding the prior distribution of GO terms did not make much improvement. Both of the ensemble methods we developed improved the average F_max score over all individual component methods except for ESG. Our benchmark results will not only complement the overall assessment that will be done by the CAFA organizers, but also help elucidate the predictive powers of sequence-based function prediction methods in general.

Electronic supplementary material

The online version of this article (doi:10.1186/s13742-015-0083-4) contains supplementary material, which is available to authorized users.

Computational characterization of moonlighting proteins

Moonlighting proteins perform multiple independent cellular functions within one polypeptide chain. Moonlighting proteins switch functions depending on various factors including the cell-type in which they are expressed, cellular location, oligomerization status and the binding of different ligands at different sites. Although an increasing number of moonlighting proteins have been experimentally identified in recent years, the quantity of known moonlighting proteins is insufficient to elucidate their overall landscape. Moreover, most moonlighting proteins have been identified as a serendipitous discovery. Hence, characterization of moonlighting proteins using bioinformatics approaches can have a significant impact on the overall understanding of protein function. In this work, we provide a short review of existing computational approaches for illuminating the functional diversity of moonlighting proteins.

Review of biological network data and its applications

Studying biological networks, such as protein-protein interactions, is key to understanding complex biological activities. Various types of large-scale biological datasets have been collected and analyzed with high-throughput technologies, including DNA microarray, next-generation sequencing, and the two-hybrid screening system, for this purpose. In this review, we focus on network-based approaches that help in understanding biological systems and identifying biological functions. Accordingly, this paper covers two major topics in network biology: reconstruction of gene regulatory networks and network-based applications, including protein function prediction, disease gene prioritization, and network-based genome-wide association study.

A combined approach for genome wide protein function annotation/prediction

Background

Today large scale genome sequencing technologies are uncovering an increasing amount of new genes and proteins, which remain uncharacterized. Experimental procedures for protein function prediction are low throughput by nature and thus can't be used to keep up with the rate at which new proteins are discovered. On the other hand, proteins are the prominent stakeholders in almost all biological processes, and therefore the need to precisely know their functions for a better understanding of the underlying biological mechanism is inevitable. The challenge of annotating uncharacterized proteins in functional genomics and biology in general motivates the use of computational techniques well orchestrated to accurately predict their functions.

Methods

We propose a computational flow for the functional annotation of a protein able to assign the most probable functions to a protein by aggregating heterogeneous information. Considered information include: protein motifs, protein sequence similarity, and protein homology data gathered from interacting proteins, combined with data from highly similar non-interacting proteins (hereinafter called Similactors). Moreover, to increase the predictive power of our model we also compute and integrate term specific relationships among functional terms based on Gene Ontology (GO).

Results

We tested our method on Saccharomyces Cerevisiae and Homo sapiens species proteins. The aggregation of different structural and functional evidence with GO relationships outperforms, in terms of precision and accuracy of prediction than the other methods reported in literature. The predicted precision and accuracy is 100% for more than half of the input set for both species; overall, we obtained 85.38% precision and 81.95% accuracy for Homo sapiens and 79.73% precision and 80.06% accuracy for Saccharomyces Cerevisiae species proteins.

Using PPI network autocorrelation in hierarchical multi-label classification trees for gene function prediction

BACKGROUND

Ontologies and catalogs of gene functions, such as the Gene Ontology (GO) and MIPS-FUN, assume that functional classes are organized hierarchically, that is, general functions include more specific ones. This has recently motivated the development of several machine learning algorithms for gene function prediction that leverages on this hierarchical organization where instances may belong to multiple classes. In addition, it is possible to exploit relationships among examples, since it is plausible that related genes tend to share functional annotations. Although these relationships have been identified and extensively studied in the area of protein-protein interaction (PPI) networks, they have not received much attention in hierarchical and multi-class gene function prediction. Relations between genes introduce autocorrelation in functional annotations and violate the assumption that instances are independently and identically distributed (i.i.d.), which underlines most machine learning algorithms. Although the explicit consideration of these relations brings additional complexity to the learning process, we expect substantial benefits in predictive accuracy of learned classifiers.

RESULTS

This article demonstrates the benefits (in terms of predictive accuracy) of considering autocorrelation in multi-class gene function prediction. We develop a tree-based algorithm for considering network autocorrelation in the setting of Hierarchical Multi-label Classification (HMC). We empirically evaluate the proposed algorithm, called NHMC (Network Hierarchical Multi-label Classification), on 12 yeast datasets using each of the MIPS-FUN and GO annotation schemes and exploiting 2 different PPI networks. The results clearly show that taking autocorrelation into account improves the predictive performance of the learned models for predicting gene function.

CONCLUSIONS

Our newly developed method for HMC takes into account network information in the learning phase: When used for gene function prediction in the context of PPI networks, the explicit consideration of network autocorrelation increases the predictive performance of the learned models. Overall, we found that this holds for different gene features/ descriptions, functional annotation schemes, and PPI networks: Best results are achieved when the PPI network is dense and contains a large proportion of function-relevant interactions.

In-depth performance evaluation of PFP and ESG sequence-based function prediction methods in CAFA 2011 experiment

BACKGROUND

Many Automatic Function Prediction (AFP) methods were developed to cope with an increasing growth of the number of gene sequences that are available from high throughput sequencing experiments. To support the development of AFP methods, it is essential to have community wide experiments for evaluating performance of existing AFP methods. Critical Assessment of Function Annotation (CAFA) is one such community experiment. The meeting of CAFA was held as a Special Interest Group (SIG) meeting at the Intelligent Systems in Molecular Biology (ISMB) conference in 2011. Here, we perform a detailed analysis of two sequence-based function prediction methods, PFP and ESG, which were developed in our lab, using the predictions submitted to CAFA.

RESULTS

We evaluate PFP and ESG using four different measures in comparison with BLAST, Prior, and GOtcha. In addition to the predictions submitted to CAFA, we further investigate performance of a different scoring function to rank order predictions by PFP as well as PFP/ESG predictions enriched with Priors that simply adds frequently occurring Gene Ontology terms as a part of predictions. Prediction accuracies of each method were also evaluated separately for different functional categories. Successful and unsuccessful predictions by PFP and ESG are also discussed in comparison with BLAST.

CONCLUSION

The in-depth analysis discussed here will complement the overall assessment by the CAFA organizers. Since PFP and ESG are based on sequence database search results, our analyses are not only useful for PFP and ESG users but will also shed light on the relationship of the sequence similarity space and functions that can be inferred from the sequences.

A domain-centric solution to functional genomics via dcGO Predictor

Background

Computational/manual annotations of protein functions are one of the first routes to making sense of a newly sequenced genome. Protein domain predictions form an essential part of this annotation process. This is due to the natural modularity of proteins with domains as structural, evolutionary and functional units. Sometimes two, three, or more adjacent domains (called supra-domains) are the operational unit responsible for a function, e.g. via a binding site at the interface. These supra-domains have contributed to functional diversification in higher organisms. Traditionally functional ontologies have been applied to individual proteins, rather than families of related domains and supra-domains. We expect, however, to some extent functional signals can be carried by protein domains and supra-domains, and consequently used in function prediction and functional genomics.

Results

Here we present a domain-centric Gene Ontology (dcGO) perspective. We generalize a framework for automatically inferring ontological terms associated with domains and supra-domains from full-length sequence annotations. This general framework has been applied specifically to primary protein-level annotations from UniProtKB-GOA, generating GO term associations with SCOP domains and supra-domains. The resulting 'dcGO Predictor', can be used to provide functional annotation to protein sequences. The functional annotation of sequences in the Critical Assessment of Function Annotation (CAFA) has been used as a valuable opportunity to validate our method and to be assessed by the community. The functional annotation of all completely sequenced genomes has demonstrated the potential for domain-centric GO enrichment analysis to yield functional insights into newly sequenced or yet-to-be-annotated genomes. This generalized framework we have presented has also been applied to other domain classifications such as InterPro and Pfam, and other ontologies such as mammalian phenotype and disease ontology. The dcGO and its predictor are available at http://supfam.org/SUPERFAMILY/dcGO including an enrichment analysis tool.

Conclusions

As functional units, domains offer a unique perspective on function prediction regardless of whether proteins are multi-domain or single-domain. The 'dcGO Predictor' holds great promise for contributing to a domain-centric functional understanding of genomes in the next generation sequencing era.

Evaluation of function predictions by PFP, ESG,and PSI-BLAST for moonlighting proteins

Background

Advancements in function prediction algorithms are enabling large scale computational annotation for newly sequenced genomes. With the increase in the number of functionally well characterized proteins it has been observed that there are many proteins involved in more than one function. These proteins characterized as moonlighting proteins show varied functional behavior depending on the cell type, localization in the cell, oligomerization, multiple binding sites, etc. The functional diversity shown by moonlighting proteins may have significant impact on the traditional sequence based function prediction methods. Here we investigate how well diverse functions of moonlighting proteins can be predicted by some existing function prediction methods.

Results

We have analyzed the performances of three major sequence based function prediction methods, PSI-BLAST, the Protein Function Prediction (PFP), and the Extended Similarity Group (ESG) on predicting diverse functions of moonlighting proteins. In predicting discrete functions of a set of 19 experimentally identified moonlighting proteins, PFP showed overall highest recall among the three methods. Although ESG showed the highest precision, its recall was lower than PSI-BLAST. Recall by PSI-BLAST greatly improved when BLOSUM45 was used instead of BLOSUM62.

Conclusion

We have analyzed the performances of PFP, ESG, and PSI-BLAST in predicting the functional diversity of moonlighting proteins. PFP shows overall better performance in predicting diverse moonlighting functions as compared with PSI-BLAST and ESG. Recall by PSI-BLAST greatly improved when BLOSUM45 was used. This analysis indicates that considering weakly similar sequences in prediction enhances the performance of sequence based AFP methods in predicting functional diversity of moonlighting proteins. The current study will also motivate development of novel computational frameworks for automatic identification of such proteins.

Identification of methylated proteins in the yeast small ribosomal subunit: a role for SPOUT methyltransferases in protein arginine methylation

We have characterized the posttranslational methylation of Rps2, Rps3, and Rps27a, three small ribosomal subunit proteins in the yeast Saccharomyces cerevisiae, using mass spectrometry and amino acid analysis. We found that Rps2 is substoichiometrically modified at arginine-10 by the Rmt1 methyltransferase. We demonstrated that Rps3 is stoichiometrically modified by ω-monomethylation at arginine-146 by mass spectrometric and site-directed mutagenic analyses. Substitution of alanine for arginine at position 146 is associated with slow cell growth, suggesting that the amino acid identity at this site may influence ribosomal function and/or biogenesis. Analysis of the three-dimensional structure of Rps3 in S. cerevisiae shows that arginine-146 makes contacts with the small subunit rRNA. Screening of deletion mutants encoding potential yeast methyltransferases revealed that the loss of the YOR021C gene results in the absence of methylation of Rps3. We demonstrated that recombinant Yor021c catalyzes ω-monomethylarginine formation when incubated with S-adenosylmethionine and hypomethylated ribosomes prepared from a YOR021C deletion strain. Interestingly, Yor021c belongs to the family of SPOUT methyltransferases that, to date, have only been shown to modify RNA substrates. Our findings suggest a wider role for SPOUT methyltransferases in nature. Finally, we have demonstrated the presence of a stoichiometrically methylated cysteine residue at position 39 of Rps27a in a zinc-cysteine cluster. The discovery of these three novel sites of protein modification within the small ribosomal subunit will now allow for an analysis of their functional roles in translation and possibly other cellular processes.

CombFunc: predicting protein function using heterogeneous data sources

Only a small fraction of known proteins have been functionally characterized, making protein function prediction essential to propose annotations for uncharacterized proteins. In recent years many function prediction methods have been developed using various sources of biological data from protein sequence and structure to gene expression data. Here we present the CombFunc web server, which makes Gene Ontology (GO)-based protein function predictions. CombFunc incorporates ConFunc, our existing function prediction method, with other approaches for function prediction that use protein sequence, gene expression and protein–protein interaction data. In benchmarking on a set of 1686 proteins CombFunc obtains precision and recall of 0.71 and 0.64 respectively for gene ontology molecular function terms. For biological process GO terms precision of 0.74 and recall of 0.41 is obtained. CombFunc is available at http://www.sbg.bio.ic.ac.uk/combfunc.

Network approaches to the functional analysis of microbial proteins

Large amounts of detailed biological data have been generated over the past few decades. Much of these data is freely available in over 1000 online databases; an enticing, but frustrating resource for microbiologists interested in a systems-level view of the structure and function of microbial cells. The frustration engendered by the need to trawl manually through hundreds of databases in order to accumulate information about a gene, protein, pathway, or organism of interest can be alleviated by the use of computational data integration to generated network views of the system of interest. Biological networks can be constructed from a single type of data, such as protein-protein binding information, or from data generated by multiple experimental approaches. In an integrated network, nodes usually represent genes or gene products, while edges represent some form of interaction between the nodes. Edges between nodes may be weighted to represent the probability that the edge exists in vivo. Networks may also be enriched with ontological annotations, facilitating both visual browsing and computational analysis via web service interfaces. In this review, we describe the construction, analysis of both single-data source and integrated networks, and their application to the inference of protein function in microbes.

Quantification of protein group coherence and pathway assignment using functional association

Background

Genomics and proteomics experiments produce a large amount of data that are awaiting functional elucidation. An important step in analyzing such data is to identify functional units, which consist of proteins that play coherent roles to carry out the function. Importantly, functional coherence is not identical with functional similarity. For example, proteins in the same pathway may not share the same Gene Ontology (GO) terms, but they work in a coordinated fashion so that the aimed function can be performed. Thus, simply applying existing functional similarity measures might not be the best solution to identify functional units in omics data.

Results

We have designed two scores for quantifying the functional coherence by considering association of GO terms observed in two biological contexts, co-occurrences in protein annotations and co-mentions in literature in the PubMed database. The counted co-occurrences of GO terms were normalized in a similar fashion as the statistical amino acid contact potential is computed in the protein structure prediction field. We demonstrate that the developed scores can identify functionally coherent protein sets, i.e. proteins in the same pathways, co-localized proteins, and protein complexes, with statistically significant score values showing a better accuracy than existing functional similarity scores. The scores are also capable of detecting protein pairs that interact with each other. It is further shown that the functional coherence scores can accurately assign proteins to their respective pathways.

Conclusion

We have developed two scores which quantify the functional coherence of sets of proteins. The scores reflect the actual associations of GO terms observed either in protein annotations or in literature. It has been shown that they have the ability to accurately distinguish biologically relevant groups of proteins from random ones as well as a good discriminative power for detecting interacting pairs of proteins. The scores were further successfully applied for assigning proteins to pathways.

Network-based prediction for sources of transcriptional dysregulation using latent pathway identification analysis

Understanding the systemic biological pathways and the key cellular mechanisms that dictate disease states, drug response, and altered cellular function poses a significant challenge. Although high-throughput measurement techniques, such as transcriptional profiling, give some insight into the altered state of a cell, they fall far short of providing by themselves a complete picture. Some improvement can be made by using enrichment-based methods to, for example, organize biological data of this sort into collections of dysregulated pathways. However, such methods arguably are still limited to primarily a transcriptional view of the cell. Augmenting these methods still further with networks and additional -omics data has been found to yield pathways that play more fundamental roles. We propose a previously undescribed method for identification of such pathways that takes a more direct approach to the problem than any published to date. Our method, called latent pathway identification analysis (LPIA), looks for statistically significant evidence of dysregulation in a network of pathways constructed in a manner that implicitly links pathways through their common function in the cell. We describe the LPIA methodology and illustrate its effectiveness through analysis of data on (i) metastatic cancer progression, (ii) drug treatment in human lung carcinoma cells, and (iii) diagnosis of type 2 diabetes. With these analyses, we show that LPIA can successfully identify pathways whose perturbations have latent influences on the transcriptionally altered genes.

Fusion methodologies for biomedical data

Data fusion methods are powerful tools for integrating the different views of an organism provided by various types of experimental data. We describe various methodologies for integrating and drawing inferences from a collection of biomedical data, primarily focusing on protein and gene expression data. Computational experiments performed using biomedical data, including known protein-protein interactions, hydropathy profiles, gene expression data and amino acid sequences, demonstrate the utility of this approach. Overall, studies agree in that methodologies using carefully selected data of various types to predict particular classes, groups and interactions, perform better than when applied to a single type of data.

Mapping the protein-protein interface between a toxin and its cognate antitoxin from the bacterial pathogen Streptococcus pyogenes

Protein--protein interactions are ubiquitous and essential for most biological processes. Although new proteomic technologies have generated large catalogs of interacting proteins, considerably less is known about these interactions at the molecular level, information that would aid in predicting protein interactions, designing therapeutics to alter these interactions, and understanding the effects of disease-producing mutations. Here we describe mapping the interacting surfaces of the bacterial toxin SPN (Streptococcus pyogenes NAD(+) hydrolase) in complex with its antitoxin IFS (immunity factor for SPN) by using hydrogen-deuterium amide exchange and electrospray ionization mass spectrometry. This approach affords data in a relatively short time for small amounts of protein, typically 5-7 pmol per analysis. The results show a good correspondence with a recently determined crystal structure of the IFS--SPN complex but additionally provide strong evidence for a folding transition of the IFS protein that accompanies its binding to SPN. The outcome shows that mass-based chemical footprinting of protein interaction surfaces can provide information about protein dynamics that is not easily obtained by other methods and can potentially be applied to large, multiprotein complexes that are out of range for most solution-based methods of biophysical analysis.

Protein annotation from protein interaction networks and Gene Ontology

We introduce a novel method for annotating protein function that combines Naïve Bayes and association rules, and takes advantage of the underlying topology in protein interaction networks and the structure of graphs in the Gene Ontology. We apply our method to proteins from the Human Protein Reference Database (HPRD) and show that, in comparison with other approaches, it predicts protein functions with significantly higher recall with no loss of precision. Specifically, it achieves 51% precision and 60% recall versus 45% and 26% for Majority and 24% and 61% for χ²-statistics, respectively.

Prediction of protein functions with gene ontology and interspecies protein homology data

Accurate computational prediction of protein functions increasingly relies on network-inspired models for the protein function transfer. This task can become challenging for proteins isolated in their own network or those with poor or uncharacterized neighborhoods. Here, we present a novel probabilistic chain-graph-based approach for predicting protein functions that builds on connecting networks of two (or more) different species by links of high interspecies sequence homology. In this way, proteins are able to "exchange" functional information with their neighbors-homologs from a different species. The knowledge of interspecies relationships, such as the sequence homology, can become crucial in cases of limited information from other sources of data, including the protein-protein interactions or cellular locations of proteins. We further enhance our model to account for the Gene Ontology dependencies by linking multiple but related functional ontology categories within and across multiple species. The resulting networks are of significantly higher complexity than most traditional protein network models. We comprehensively benchmark our method by applying it to two largest protein networks, the Yeast and the Fly. The joint Fly-Yeast network provides substantial improvements in precision, accuracy, and false positive rate over networks that consider either of the sources in isolation. At the same time, the new model retains the computational efficiency similar to that of the simpler networks.

Improving the prediction of yeast protein function using weighted protein-protein interactions

Background

Bioinformatics can be used to predict protein function, leading to an understanding of cellular activities, and equally-weighted protein-protein interactions (PPI) are normally used to predict such protein functions. The present study provides a weighting strategy for PPI to improve the prediction of protein functions. The weights are dependent on the local and global network topologies and the number of experimental verification methods. The proposed methods were applied to the yeast proteome and integrated with the neighbour counting method to predict the functions of unknown proteins.

Results

A new technique to weight interactions in the yeast proteome is presented. The weights are related to the network topology (local and global) and the number of identified methods, and the results revealed improvement in the sensitivity and specificity of prediction in terms of cellular role and cellular locations. This method (new weights) was compared with a method that utilises interactions with the same weight and it was shown to be superior.

Conclusions

A new method for weighting the interactions in protein-protein interaction networks is presented. Experimental results concerning yeast proteins demonstrated that weighting interactions integrated with the neighbor counting method improved the sensitivity and specificity of prediction in terms of two functional categories: cellular role and cell locations.

Accurate protein structure annotation through competitive diffusion of enzymatic functions over a network of local evolutionary similarities

High-throughput Structural Genomics yields many new protein structures without known molecular function. This study aims to uncover these missing annotations by globally comparing select functional residues across the structural proteome. First, Evolutionary Trace Annotation, or ETA, identifies which proteins have local evolutionary and structural features in common; next, these proteins are linked together into a proteomic network of ETA similarities; then, starting from proteins with known functions, competing functional labels diffuse link-by-link over the entire network. Every node is thus assigned a likelihood z-score for every function, and the most significant one at each node wins and defines its annotation. In high-throughput controls, this competitive diffusion process recovered enzyme activity annotations with 99% and 97% accuracy at half-coverage for the third and fourth Enzyme Commission (EC) levels, respectively. This corresponds to false positive rates 4-fold lower than nearest-neighbor and 5-fold lower than sequence-based annotations. In practice, experimental validation of the predicted carboxylesterase activity in a protein from Staphylococcus aureus illustrated the effectiveness of this approach in the context of an increasingly drug-resistant microbe. This study further links molecular function to a small number of evolutionarily important residues recognizable by Evolutionary Tracing and it points to the specificity and sensitivity of functional annotation by competitive global network diffusion. A web server is at http://mammoth.bcm.tmc.edu/networks.

Network-based auto-probit modeling for protein function prediction

Predicting the functional roles of proteins based on various genome-wide data, such as protein-protein association networks, has become a canonical problem in computational biology. Approaching this task as a binary classification problem, we develop a network-based extension of the spatial auto-probit model. In particular, we develop a hierarchical Bayesian probit-based framework for modeling binary network-indexed processes, with a latent multivariate conditional autoregressive Gaussian process. The latter allows for the easy incorporation of protein-protein association network topologies-either binary or weighted-in modeling protein functional similarity. We use this framework to predict protein functions, for functions defined as terms in the Gene Ontology (GO) database, a popular rigorous vocabulary for biological functionality. Furthermore, we show how a natural extension of this framework can be used to model and correct for the high percentage of false negative labels in training data derived from GO, a serious shortcoming endemic to biological databases of this type. Our method performance is evaluated and compared with standard algorithms on weighted yeast protein-protein association networks, extracted from a recently developed integrative database called Search Tool for the Retrieval of INteracting Genes/proteins (STRING). Results show that our basic method is competitive with these other methods, and that the extended method-incorporating the uncertainty in negative labels among the training data-can yield nontrivial improvements in predictive accuracy.

An improved method for scoring protein-protein interactions using semantic similarity within the gene ontology

Background

Semantic similarity measures are useful to assess the physiological relevance of protein-protein interactions (PPIs). They quantify similarity between proteins based on their function using annotation systems like the Gene Ontology (GO). Proteins that interact in the cell are likely to be in similar locations or involved in similar biological processes compared to proteins that do not interact. Thus the more semantically similar the gene function annotations are among the interacting proteins, more likely the interaction is physiologically relevant. However, most semantic similarity measures used for PPI confidence assessment do not consider the unequal depth of term hierarchies in different classes of cellular location, molecular function, and biological process ontologies of GO and thus may over-or under-estimate similarity.

Results

We describe an improved algorithm, Topological Clustering Semantic Similarity (TCSS), to compute semantic similarity between GO terms annotated to proteins in interaction datasets. Our algorithm, considers unequal depth of biological knowledge representation in different branches of the GO graph. The central idea is to divide the GO graph into sub-graphs and score PPIs higher if participating proteins belong to the same sub-graph as compared to if they belong to different sub-graphs.

Conclusions

The TCSS algorithm performs better than other semantic similarity measurement techniques that we evaluated in terms of their performance on distinguishing true from false protein interactions, and correlation with gene expression and protein families. We show an average improvement of 4.6 times the F₁ score over Resnik, the next best method, on our Saccharomyces cerevisiae PPI dataset and 2 times on our Homo sapiens PPI dataset using cellular component, biological process and molecular function GO annotations.

PoGO: Prediction of Gene Ontology terms for fungal proteins

Background

Automated protein function prediction methods are the only practical approach for assigning functions to genes obtained from model organisms. Many of the previously reported function annotation methods are of limited utility for fungal protein annotation. They are often trained only to one species, are not available for high-volume data processing, or require the use of data derived by experiments such as microarray analysis. To meet the increasing need for high throughput, automated annotation of fungal genomes, we have developed a tool for annotating fungal protein sequences with terms from the Gene Ontology.

Results

We describe a classifier called PoGO (Prediction of Gene Ontology terms) that uses statistical pattern recognition methods to assign Gene Ontology (GO) terms to proteins from filamentous fungi. PoGO is organized as a meta-classifier in which each evidence source (sequence similarity, protein domains, protein structure and biochemical properties) is used to train independent base-level classifiers. The outputs of the base classifiers are used to train a meta-classifier, which provides the final assignment of GO terms. An independent classifier is trained for each GO term, making the system amenable to updating, without having to re-train the whole system. The resulting system is robust. It provides better accuracy and can assign GO terms to a higher percentage of unannotated protein sequences than other methods that we tested.

Conclusions

Our annotation system overcomes many of the shortcomings that we found in other methods. We also provide a web server where users can submit protein sequences to be annotated.

Bayesian Markov Random Field analysis for protein function prediction based on network data

Inference of protein functions is one of the most important aims of modern biology. To fully exploit the large volumes of genomic data typically produced in modern-day genomic experiments, automated computational methods for protein function prediction are urgently needed. Established methods use sequence or structure similarity to infer functions but those types of data do not suffice to determine the biological context in which proteins act. Current high-throughput biological experiments produce large amounts of data on the interactions between proteins. Such data can be used to infer interaction networks and to predict the biological process that the protein is involved in. Here, we develop a probabilistic approach for protein function prediction using network data, such as protein-protein interaction measurements. We take a Bayesian approach to an existing Markov Random Field method by performing simultaneous estimation of the model parameters and prediction of protein functions. We use an adaptive Markov Chain Monte Carlo algorithm that leads to more accurate parameter estimates and consequently to improved prediction performance compared to the standard Markov Random Fields method. We tested our method using a high quality S.cereviciae validation network with 1622 proteins against 90 Gene Ontology terms of different levels of abstraction. Compared to three other protein function prediction methods, our approach shows very good prediction performance. Our method can be directly applied to protein-protein interaction or coexpression networks, but also can be extended to use multiple data sources. We apply our method to physical protein interaction data from S. cerevisiae and provide novel predictions, using 340 Gene Ontology terms, for 1170 unannotated proteins and we evaluate the predictions using the available literature.

Searching for functional gene modules with interaction component models

BACKGROUND

Functional gene modules and protein complexes are being sought from combinations of gene expression and protein-protein interaction data with various clustering-type methods. Central features missing from most of these methods are handling of uncertainty in both protein interaction and gene expression measurements, and in particular capability of modeling overlapping clusters. It would make sense to assume that proteins may play different roles in different functional modules, and the roles are evidenced in their interactions.

RESULTS

We formulate a generative probabilistic model for protein-protein interaction links and introduce two ways for including gene expression data into the model. The model finds interaction components, which can be interpreted as overlapping clusters or functional modules. We demonstrate the performance on two data sets of yeast Saccharomyces cerevisiae. Our methods outperform a representative set of earlier models in the task of finding biologically relevant modules having enriched functional classes.

CONCLUSIONS

Combining protein interaction and gene expression data with a probabilistic generative model improves discovery of modules compared to approaches based on either data source alone. With a fairly simple model we can find biologically relevant modules better than with alternative methods, and in addition the modules may be inherently overlapping in the sense that different interactions may belong to different modules.

On the importance of comprehensible classification models for protein function prediction

The literature on protein function prediction is currently dominated by works aimed at maximizing predictive accuracy, ignoring the important issues of validation and interpretation of discovered knowledge, which can lead to new insights and hypotheses that are biologically meaningful and advance the understanding of protein functions by biologists. The overall goal of this paper is to critically evaluate this approach, offering a refreshing new perspective on this issue, focusing not only on predictive accuracy but also on the comprehensibility of the induced protein function prediction models. More specifically, this paper aims to offer two main contributions to the area of protein function prediction. First, it presents the case for discovering comprehensible protein function prediction models from data, discussing in detail the advantages of such models, namely, increasing the confidence of the biologist in the system's predictions, leading to new insights about the data and the formulation of new biological hypotheses, and detecting errors in the data. Second, it presents a critical review of the pros and cons of several different knowledge representations that can be used in order to support the discovery of comprehensible protein function prediction models.

Integrative approaches to the prediction of protein functions based on the feature selection

Background

Protein function prediction has been one of the most important issues in functional genomics. With the current availability of various genomic data sets, many researchers have attempted to develop integration models that combine all available genomic data for protein function prediction. These efforts have resulted in the improvement of prediction quality and the extension of prediction coverage. However, it has also been observed that integrating more data sources does not always increase the prediction quality. Therefore, selecting data sources that highly contribute to the protein function prediction has become an important issue.

Results

We present systematic feature selection methods that assess the contribution of genome-wide data sets to predict protein functions and then investigate the relationship between genomic data sources and protein functions. In this study, we use ten different genomic data sources in Mus musculus, including: protein-domains, protein-protein interactions, gene expressions, phenotype ontology, phylogenetic profiles and disease data sources to predict protein functions that are labelled with Gene Ontology (GO) terms. We then apply two approaches to feature selection: exhaustive search feature selection using a kernel based logistic regression (KLR), and a kernel based L1-norm regularized logistic regression (KL1LR). In the first approach, we exhaustively measure the contribution of each data set for each function based on its prediction quality. In the second approach, we use the estimated coefficients of features as measures of contribution of data sources. Our results show that the proposed methods improve the prediction quality compared to the full integration of all data sources and other filter-based feature selection methods. We also show that contributing data sources can differ depending on the protein function. Furthermore, we observe that highly contributing data sets can be similar among a group of protein functions that have the same parent in the GO hierarchy.

Conclusions

In contrast to previous integration methods, our approaches not only increase the prediction quality but also gather information about highly contributing data sources for each protein function. This information can help researchers collect relevant data sources for annotating protein functions.

Integrating diverse information to gain more insight into microarray analysis

Microarray technology provides an opportunity to view transcriptions at genomic level under different conditions controlled by an experiment. From an array experiment using a human cancer cell line that is engineered to differ in expression of tumor antigen, integrin alpha6beta4, few hundreds of differentially expressed genes are selected and are clustered using one of several standard algorithms. The set of genes in a cluster is expected to have similar expression patterns and are most likely to be coregulated and thereby expected to have similar function. The highly expressed set of upregulated genes become candidates for further evaluation as potential biomarkers. Besides these benefits, microarray experiment by itself does not help us to understand or discover potential pathways or to identify important set of genes for potential drug targets. In this paper we discuss about integrating protein-to-protein interaction information, pathway information with array expression data set to identify a set of "important" genes, and potential signal transduction networks that help to target and reverse the oncogenic phenotype induced by tumor antigen such as integrin alpha6beta4. We will illustrate the proposed method with our recent microarray experiment conducted for identifying transcriptional targets of integrin alpha6beta4 for cancer progression.

Gene networks in Drosophila melanogaster: integrating experimental data to predict gene function

BACKGROUND

Discovering the functions of all genes is a central goal of contemporary biomedical research. Despite considerable effort, we are still far from achieving this goal in any metazoan organism. Collectively, the growing body of high-throughput functional genomics data provides evidence of gene function, but remains difficult to interpret.

RESULTS

We constructed the first network of functional relationships for Drosophila melanogaster by integrating most of the available, comprehensive sets of genetic interaction, protein-protein interaction, and microarray expression data. The complete integrated network covers 85% of the currently known genes, which we refined to a high confidence network that includes 20,000 functional relationships among 5,021 genes. An analysis of the network revealed a remarkable concordance with prior knowledge. Using the network, we were able to infer a set of high-confidence Gene Ontology biological process annotations on 483 of the roughly 5,000 previously unannotated genes. We also show that this approach is a means of inferring annotations on a class of genes that cannot be annotated based solely on sequence similarity. Lastly, we demonstrate the utility of the network through reanalyzing gene expression data to both discover clusters of coregulated genes and compile a list of candidate genes related to specific biological processes.

CONCLUSIONS

Here we present the the first genome-wide functional gene network in D. melanogaster. The network enables the exploration, mining, and reanalysis of experimental data, as well as the interpretation of new data. The inferred annotations provide testable hypotheses of previously uncharacterized genes.

Predicting eukaryotic transcriptional cooperativity by Bayesian network integration of genome-wide data

Transcriptional cooperativity among several transcription factors (TFs) is believed to be the main mechanism of complexity and precision in transcriptional regulatory programs. Here, we present a Bayesian network framework to reconstruct a high-confidence whole-genome map of transcriptional cooperativity in Saccharomyces cerevisiae by integrating a comprehensive list of 15 genomic features. We design a Bayesian network structure to capture the dominant correlations among features and TF cooperativity, and introduce a supervised learning framework with a well-constructed gold-standard dataset. This framework allows us to assess the predictive power of each genomic feature, validate the superior performance of our Bayesian network compared to alternative methods, and integrate genomic features for optimal TF cooperativity prediction. Data integration reveals 159 high-confidence predicted cooperative relationships among 105 TFs, most of which are subsequently validated by literature search. The existing and predicted transcriptional cooperativities can be grouped into three categories based on the combination patterns of the genomic features, providing further biological insights into the different types of TF cooperativity. Our methodology is the first supervised learning approach for predicting transcriptional cooperativity, compares favorably to alternative unsupervised methodologies, and can be applied to other genomic data integration tasks where high-quality gold-standard positive data are scarce.

Network inference with confidence from multivariate time series

Networks--collections of interacting elements or nodes--abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions, it is common to include edges between those nodes whose time series exhibit sufficient functional connectivity, typically defined as a measure of coupling exceeding a predetermined threshold. However, when uncertainty exists in the original network measurements, uncertainty in the inferred network is likely, and hence a statistical propagation of error is needed. In this manuscript, we describe a principled and systematic procedure for the inference of functional connectivity networks from multivariate time series data. Our procedure yields as output both the inferred network and a quantification of uncertainty of the most fundamental interest: uncertainty in the number of edges. To illustrate this approach, we apply a measure of linear coupling to simulated data and electrocorticogram data recorded from a human subject during an epileptic seizure. We demonstrate that the procedure is accurate and robust in both the determination of edges and the reporting of uncertainty associated with that determination.