Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth “Dialogue for Reverse Engineering Assessments and Methods” (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on “Systems Genetics” proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics

Analysis of precision/recall of the meta-analysis approach for DREAM5 Challenge 3A with individuals/Network1 data.

<p>Predicted gene regulations are classified into four groups depending on the label of the regulator and the target gene. A gene is labelled ‘<i>cis</i>’ if its marker has a <i>cis</i>-regulated effect on its expression level. Otherwise, gene is labelled ‘<i>trans</i>’. An edge between two ‘<i>cis</i>’ labelled genes is classified ‘<i>cis </i><i>cis</i>’, between two ‘<i>trans</i>’ labelled genes: ‘<i>trans </i><i>trans</i>’ and so on.</p

In-degree distribution of Network1-A999.

<p>The distribution is plotted on the log scale on the -axis since the in-degree distribution was assumed to be exponential in the true network (black crosses). Coloured symbols stand for the first (light green diamond shape), (middle green triangles) and (dark green circles) edges inferred by the meta-analysis.</p

Accuracy results for the GRN inference methods: ROC curves (upper panel) and PR curves (lower panel) for Network1-A999.

<p>Meta-analysis: green, BN: dashed red, Lasso: purple and Dantzig: blue. Points for inferred networks of , and edges are indicated.</p

AUC of the DREAM5 Challenge 3A for the meta-analysis of the SAaB team (source: [18]).

<p>^aAUC official values issued by the DREAM organisers.</p><p>^bAUC after minor corrections in our implementations.</p

Network1-A999 visualisation.

<p>(A) to (C) are networks inferred by the meta-analysis using the first (A), (B) and (C) edges. (D) to (F) represent the same predicted networks showing only correctly inferred edges. (G) is the true network. For clarity, vertices have been removed.</p

Size of the largest connected component inferred by the meta-analysis for the DREAM5 Challenge 3A networks vs. number of edges.

<p>Colours encode sample sizes: blue for individuals, red for and green for . Line style and symbols on curves represent networks: solid line squares for Networks ‘1’, short dashed line with circles for Networks ‘2’, dotted line with triangles for Networks ‘3’, alternate dashed and dotted line with plus for Networks ‘4’ and long dashed line with crosses for Networks ‘5’.</p

Out-degree distribution of Network1-A999.

<p>The distribution is plotted on a log-log scale since it was expected to be a power-law distribution in the true network (black crosses). Coloured symbols stand for the first (light green diamond shape), (middle green triangles) and (dark green circles) edges inferred by the meta-analysis. Points having ‘’ out-degree were transformed to .</p

Venn diagram between the three sets made up of the first edges inferred from one of the three approaches: BN (red circle), Lasso (blue circle) and Dantzig (green circle).

<p>Within each region of the diagram, the number of correctly inferred edges (over the bar) and the total number of edges (under the bar) are given. (top right) is the number of missing edges for the union of the three approaches.</p