Leveraging Developmental Landscapes for Model Selection in Boolean Gene Regulatory Networks

Boolean models are a well-established framework to model developmental gene regulatory networks (DGRN) for acquisition of cellular identity. During the reconstruction of Boolean DGRNs, even if the network structure is given, there is generally a very large number of combinations of Boolean functions (BFs) that will reproduce the different cell fates (biological attractors). Here we leverage the developmental landscape to enable model selection on such ensembles using the relative stability of the attractors. First we show that 5 previously proposed measures of relative stability are strongly correlated and we stress the usefulness of the one that captures best the cell state transitions via the mean first passage time (MFPT) as it also allows the construction of a cellular lineage tree. A property of great computational convenience is the relative insensitivity of the different measures to changes in noise intensities. That allows us to use stochastic approaches to estimate the MFPT and thus to scale up the computations to large networks. Given this methodology, we study the landscape of 3 Boolean models of Arabidopsis thaliana root development and find that the latest one (a 2020 model) does not respect the biologically expected hierarchy of cell states based on their relative stabilities. Therefore we developed an iterative greedy algorithm that searches for models which satisfy the expected hierarchy of cell states. By applying our algorithm to the 2020 model, we find many Boolean models that do satisfy the expected hierarchy. Our methodology thus provides new tools that can enable reconstruction of more realistic and accurate Boolean models of DGRNs.