Dynamic Network-Based Epistasis Analysis: Boolean Examples

In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches

Finding missing interactions of the Arabidopsis thaliana root stem cell niche gene regulatory network

AbstractOver the last few decades, the Arabidopsis thaliana root stem cell niche has become a model system for the study of plant development and the stem cell niche. Currently, many of the molecular mechanisms involved in root stem cell niche maintenance and development have been described. A few years ago, we published a gene regulatory network model integrating this information. This model suggested that there were missing components or interactions. Upon updating the model, the observed stable gene configurations of the root stem cell niche could not be recovered, indicating that there are additional missing components or interactions in the model. In fact, due to the lack of experimental data, gene regulatory networks inferred from published data are usually incomplete. However, predicting the location and nature of the missing data is a not trivial task. Here, we propose a set of procedures for detecting and predicting missing interactions in Boolean networks. We used these procedures to predict putative missing interactions in the A. thaliana root stem cell niche network model. Using our approach, we identified three necessary interactions to recover the reported gene activation configurations that have been experimentally uncovered for the different cell types within the root stem cell niche: 1) a regulation of PHABULOSA to restrict its expression domain to the vascular cells, 2) a self-regulation of WOX5, possibly by an indirect mechanism through the auxin signalling pathway and 3) a positive regulation of JACKDAW by MAGPIE. The procedures proposed here greatly reduce the number of possible Boolean functions that are biologically meaningful and experimentally testable and that do not contradict previous data. We believe that these procedures can be used on any Boolean network. However, because the procedures were designed for the specific case of the root stem cell niche, formal demonstrations of the procedures should be shown in future efforts