Abstract
Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data.
Highlights
A central focus in genomic research is to infer how genes are related to each other
We developed a full Bayesian Inference approach for a Boolean Network (BIBN), which is based on maximizing the joint posterior probability over the whole network
We model the relations among the n genes under study as a directed acyclic graph denoted by a set of components fG, T, Fg, where G represents the set of nodes fg1, Á Á Á,gi, Á Á Á,gng, F denotes a set of Boolean functions ff1, Á Á Á,fi, Á Á Á,fng, and T represents the topology of the network, i.e., the input-output connectivity information
Summary
A central focus in genomic research is to infer how genes are related to each other. Due to the complexity of real biological systems, it is essential to learn genetic networks in a holistic rather than an atomistic manner [1]. Various network models have been proposed to describe gene regulatory mechanisms, such as deterministic Boolean networks, random Boolean networks [2], probabilistic Boolean networks [3], probabilistic gene regulatory networks [4], Bayesian networks [5, 6], etc. For a review of methods for reconstructing genetic networks, see [7]. Each model has its own advantages and drawbacks.
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