Elucidating and leveraging design principles towards realistic Boolean models of gene regulatory networks [HBNI Th246]

Abstract

Cells make decisions based on underlying gene regulatory networks (GRNs). GRNs may be modeled as a Boolean network (BN) in which nodes and directed edges represent genes or proteins and their interactions respectively. In BNs, a gene assumes a binary state and its temporal dynamics is governed by the state of its regulators via a regulatory logic rule (or logical update rule or Boolean function (BF)). The dynamics of BNs under synchronous update (in which all nodes are updated simultaneously) lead to fixed point attractors (which correspond to cellular phenotypes) or cyclic attractors. Stuart Kauffman conceived BNs in 1969, and modeled GRNs as random Bns due to paucity of experimental data. Advances in experimental techniques including omics approaches have fostered the reconstruction of real Boolean GRNs for several cellular processes in a wide range of species. It is now imperative to understand whether the regulatory logic rules in such models, which have remained largely unexplored, are just random or possess distinct features. In this thesis, we systematically investigate the nature of real regulatory logic rules by first compiling a dataset of 2687 logic rules from 88 reconstructed discrete models, and then examining in that dataset, the preponderance of various known types of biologically meaningful BFs. Two types that are particularly preponderant in our dataset are read-once functions (RoFs) and nested canalyzing functions (NCFs). We explain this by showing that RoFs and NCFs have the minimum complexity at a given number of inputs (k) and given bias (P) in terms the Boolean complexity and the average sensitivity respectively. Furthermore, we also explore the abundance and biological plausibility of more recently published types of logic rules, namely, link operator functions (LOFs) and composition structures respectively. The voluminous biological data generated over the past three decades has driven both manual reconstruction of Boolean GRNs and advancement of automated methods to reconstruct Boolean GRNs. Even if the network structure of a GRN is kept fixed, there is generally a very large number of combinations of BFs (across all nodes) that can recover the same set of biological fixed points (or cellular phenotypes), and it is usually unclear how a certain model or subset of models are chosen as the biologically relevant ones during reconstruction. In this thesis, we leverage the relative stability of cell states derived from its developmental landscape to develop a framework that performs model selection on an ensemble of models that are otherwise equally plausible in the cell states they recover and in the type of logic rules (based on the minimum complexity criteria) they employ. We demonstrate our model selection framework on the latest root development Boolean GRN of Arabidopis thaliana and provide several improved models over the original one. In sum, we elucidate design principles of regulatory logic in GRNs and leverage those principles to develop methods for realistic reconstruction of Boolean models of biological systems in this thesis