Inferring Genetic Regulatory Networks from Microarray Experiments with Bayesian Networks

Abstract

Molecular pathways consisting of interacting proteins underlie the major functions of living cells, and a central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Several approaches to the reverse engineering of genetic regulatory networks from gene expression data have been explored. At the most refined level of detail is a mathematical description of the biophysical processes in terms of a system of coupled differential equations that describe, for instance, the processes of transcription factor binding, protein and RNA degradation, and diffusion. Besides facing inherent identifiability problems, this approach is usually restricted to very small systems. At the other extreme is the coarse-scale approach of clustering, which provides a computationally cheap way to extract useful information from large-scale expression data sets. However, while clustering indicates which genes are co-regulated and may therefore be involved in related biological processes, it does not lead to a fine resolution of the interaction processes that would indicate, for instance, whether an interaction between two genes is direct or mediated by other genes, or whether a gene is a regulator or regulatee. A promising compromise between these two extremes is the approach of Bayesian networks, which are interpretable and flexible models for representing conditional dependence relations between multiple interacting quantities, and whose probabilistic nature is capable of handling noise inherent in both the biological processes and the microarray experiments. This chapter will first briefly recapitulate the Bayesian network paradigm and the work of Friedman et al. [8], [23], who spearheaded the application of Bayesian networks to gene expression data. Next, the chapter will discuss the shortcomings of static Bayesian networks and show how these shortcomings can be overcome with dynamic Bayesian networks. Finally, the chapter will address the important question of the reliability of the inference procedure. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very sparse data sets, typically containing only a few dozen time points during a cell cycle. The results of a simulation study to test the viability of the Bayesian network paradigm are reported. In this study, gene expression data are simulated from a realistic molecular biological network involving DNAs, mRNAs and proteins, and then regulatory networks are inferred from these data in a reverse engineering approach, using dynamic Bayesian networks and Bayesian learning with Markov chain Monte Carlo. The simulation results are presented as receiver operator characteristics (ROC) curves. This allows an estimation of the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy, and the inclusion of further, sequence-based information.