# Functional Networks¶

In order to leverage the vast collections of raw, noisy genomic data, they must be integrated, summarized, and presented in a biologically informative manner. We provide a means of mining tens of thousands of whole-genome experiments by way of functional interaction networks. Each interaction network represents a body of data, probabilistically weighted and integrated, focused on a particular biological question. These questions can include, for example, the function of a gene, the relationship between two pathways, or the processes disrupted in a genetic disorder. (Huttenhower, et. al 2008)

## Method¶

Briefly, functional integration relies on the construction of process-specific functional relationship networks. These are interaction networks in which each node represents a gene, each edge a functional relationship, and an edge between two genes is probabilistically weighted based on experimental evidence relating to those genes. We integrate evidence from many data sets, with each data set weighted in a process-specific manner.

One naïve Bayesian classifier is trained per biological area of interest (e.g. a tissue, or a specific biological process), using the appropriate gold standard for the biological context in addition to one global process-unaware classifier trained using the complete gold standard. Each classifier f consisted of a class node predicting the binary presence or absence of a functional relationship (FR) between two genes and n nodes conditioned on FR, each representing the value of a data set Dk.

Parameter regularization is performed as described in Steck and Jaakkola (2002) using mutual information between data sets to estimate a strength of prior belief for each data set. While a large amount of shared information does not guarantee a redundant data set, since the same subset of information could be shared many times, it provides a valuable quantitative estimate of data set uniqueness.

## Genomics data types¶

We collected and integrated 987 genome-scale data sets encompassing approximately 38,000 conditions from an estimated 14,000 publications including both expression and interaction measurements.

• Gene co-expression: All gene expression data sets are from NCBI’s Gene Expression Omnibus (GEO). Genes with more than 30% of values missing were removed, and remaining missing values were imputed using ten nearest neighbors. Non-log-transformed data sets were log transformed. Expression measurements were summarized to Entrez identifiers, and duplicate identifiers were merged. The Pearson correlation was calculated for each gene pair, normalized with Fisher’s z transform, mean subtracted and divided by the standard deviation.
• Protein-interaction: Interaction data are collected from BioGRID, IntAct, MINT, and MIPS.
• TF regulation: To estimate shared transcription factor regulation between genes, we collected binding motifs from JASPAR. Genes were scored for the presence of transcription factor binding sites using the MEME software suite. Motif matches were treated as binary scores (present if P < 0.001). The final score for each gene pair was obtained by calculating the Pearson correlation between the motif association vectors for the genes.
• MSigDB purturbations and miRNA: Chemical and genetic perturbation (c2:CGP) and microRNA target (c3:MIR) profiles were downloaded from the Molecular Signatures Database (MSigDB). Each gene pair’s score was the sum of shared profiles weighted by the specificity of each profile

## Evidence¶

The “evidence” for an edge is measured as the contribution or “influence” of each dataset on the posterior classification probability. Each dataset contribution is calculated as the posterior probability of a functional relationship given only that dataset, minus the prior probablility.

Contribution of dataset D to an edge functional relationship prediction (FR):

contribution(D) = P(FR | D) - P(FR)


Note that the contributions will not sum to 1.0, as each contribution is measured separately. Generally, individual gene expression datasets will not contribute much to the posterior probability but cumulatively can make a significant contribution.