Reconstructing Causal Biological Networks through Active Learning

<div><p>Reverse-engineering of biological networks is a central problem in systems biology. The use of intervention data, such as gene knockouts or knockdowns, is typically used for teasing apart causal relationships among genes. Under time or resource constraints, one needs to carefully choose which intervention experiments to carry out. Previous approaches for selecting most informative interventions have largely been focused on discrete Bayesian networks. However, continuous Bayesian networks are of great practical interest, especially in the study of complex biological systems and their quantitative properties. In this work, we present an efficient, information-theoretic active learning algorithm for Gaussian Bayesian networks (GBNs), which serve as important models for gene regulatory networks. In addition to providing linear-algebraic insights unique to GBNs, leading to significant runtime improvements, we demonstrate the effectiveness of our method on data simulated with GBNs and the DREAM4 network inference challenge data sets. Our method generally leads to faster recovery of underlying network structure and faster convergence to final distribution of confidence scores over candidate graph structures using the full data, in comparison to random selection of intervention experiments.</p></div

Performance comparison with PC and GIES on DREAM4 data sets.

<p>We evaluated the final prediction accuracy of our active learning algorithm in identifying edges in the undirected skeleton of the ground truth network. The resulting precision-recall (PR) curves were compared to PC with different values of <i>α</i> (significance level) in {0.01, 0.05, 0.1, 0.2, 0.3} using only observational data and to GIES using both observational and intervention data. We used the implementations of PC and GIES provided in the pcalg package in R. The dashed lines are drawn at one standard deviation from the mean in each direction based on five random trials. Our performance generally dominates that of PC and GIES, suggesting the effectiveness of our Bayesian learning approach.</p

Comparative β-Helix Alignments

<p>Aligned portions of the eight SABmark domains in the set Group 144, consisting of the left-handed β-helix fold as aligned by Posa, Mustang, MultiProt, and Matt. Backbone atoms that participate in the common core of the alignment show up colored as red (PDB ID d1hm9a1), green (PDB ID d1kk6a), blue (PDB ID d1krra), magenta (PDB ID d1lxa), yellow (PDB Is that are not placed into the alignment by the tested algorithm are shown in gray. These pictureD d1ocxa), orange (PDB ID d1qrea), cyan (PDB ID d1xat), and pink (PDB ID d3tdt); residues in all three chains were generated by the Swiss PDB Viewer (DeepView) [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0040010#pcbi-0040010-b043" target="_blank">43</a>].</p

Additional file 3: of Finding RNA structure in the unstructured RBPome

Figure S3 There is no improvement in binding prediction from amino acid sequence by utilizing RNA structure with random structure probabilities. A) When we add RNA structural features to the sequence k-mer space of AffinityRegression, but assign structure probabilities randomly, we do no predict binding any better than using sequence features alone. B) When we add RNA structural features to the sequence k-mer space of AffinityRegression, but assign structure probabilities randomly, we do not predict the top-bound probes as compared to unbound probes any better than using sequence features alone. (PNG 68 kb

Reconstruction performance on DREAM4 benchmark data.

<p>The results are summarized over five trials. The dotted lines are drawn at one standard deviation from the mean in each direction. Active learner achieves higher accuracy and faster convergence than random learner.</p

Active learning framework for network reconstruction.

<p>We first estimate our belief over candidate graph structures based on the initial data set that contains observational and/or intervention samples. Then, we iteratively acquire new data instances by carrying out the optimal intervention experiment predicted to cause the largest change in our belief (in expectation) and updating the belief. The final belief is summarized into a predicted network via Bayesian model averaging.</p

Overview of the Matt Algorithm

<p>Overview of the Matt Algorithm</p

Two Sequential Block Pairs that Could Form Part of an Assembly

<p>Block pair <i>BC</i> precedes block pair <i>DE</i> because <i>B</i> precedes <i>D</i> and <i>C</i> precedes <i>E</i> in their respective protein sequences.</p

HapTree (solid lines) and HapCompass (dashed lines) on simulated triploid genomes: Likelihood of Perfect Solution and Vector Error Rates, 1000 Trials, Block lengths: 10, 20, and 40.

<p>HapTree (solid lines) and HapCompass (dashed lines) on simulated triploid genomes: Likelihood of Perfect Solution and Vector Error Rates, 1000 Trials, Block lengths: 10, 20, and 40.</p

Additional file 2: of Finding RNA structure in the unstructured RBPome

Figure S2 A) RNA structural binding preferences do not improve in vitro binding prediction when random structure probabilities are assigned. Correlation results over 488 paired experiments reveals that RNA structure does not improve binding prediction when structure probabilities are assigned randomly. B) RNA structural binding preferences do not improve in vivo binding prediction when random structure probabilities are assigned. AUC results of 96 paired eCLIP and RNAcompete experiments over 21 joint proteins demonstrate that RNA structural binding preferences learned from in vitro data do not correlate well with protein-RNA interactions measured in vivo when structure probabilities are assigned randomly. (PNG 85 kb