Exact Likelihood Computation in Boolean Networks with probabilistic time delays, and its application in Signal Network reconstruction

Motivation: For biological pathways, it is common to measure a gene expression time series after various knockdowns of genes that are putatively involved in the process of interest. This interventional, time-resolved data is most suitable for the elucidation of dynamic, causal relationships in signaling networks. Even with this kind of data it is still a major and largely unsolved challenge to infer the topology and interaction logic of the underlying regulatory network. Results: In this work we present a novel, model-based approach involving Boolean networks to reconstruct small to medium-sized regulatory networks. In particular, we solve the problem of exact likeli-hood computation in Boolean networks with probabilistic exponential time delays. Simulations demonstrate the high accuracy of our ap-proach. We apply our method to data of Ivanova et al. (Ivanova et al., 2006), where RNAi knockdown experiments were used to build a network of the key regulatory genes governing mouse stem cell main-tenance and differentiation. In contrast to previous analyses of that data set, our method can identify feedback loops and provides new in-sights into the interplay of some master regulators in embryonic stem cell development. Availability: The algorithm is implemented in the statistical lan-guage R. Code and documentation are available at Bioinformatics online. Supplementary information: Supplementary Materials are avail-able at Bioinfomatics online