Qualitative modelling and analysis of gene regulatory networks: application to the adaptation of Escherichia coli bacterium to carbon availability

Jamil Ahmad (1) , Jérémie Bourdon (2, 3) , Damien Eveillard (2) , Jonathan Fromentin (1) , Olivier Roux (4) , Christine Sinoquet (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 LINA - Laboratoire d'Informatique de Nantes Atlantique
3 SYMBIOSE - Biological systems and models, bioinformatics and sequences
4 MeForBio

Attempts to model Gene Regulatory Networks (GRNs) have yielded very different approaches. Among others, variants of Thomas's asynchronous boolean approach have been proposed, to better fit the dynamics of biological systems: notably, genes were allowed to reach different discrete expression levels, depending on the states of other genes, called the regulators: thus, activations and inhibitions are triggered conditionally on the proper expression levels of these regulators. In contrast, some fine-grained propositions have focused on the molecular level as modelling the evolution of biological compound concentrations through differential equation systems. Both approaches are limited. The first one leads to an oversimplification of the system, whereas the second is incapable to tackle large GRNs. In this context, hybrid paradigms, that mix discrete and continuous features underlying distinct biological properties, achieve significant advances for investigating biological properties. One of these hybrid formalisms proposes to focus, within a GRN abstraction, on the time delay to pass from a gene expression level to the next. Until now, no research work has been carried out, which attempts to benefit from the modelling of a GRN by differential equations, converting it into a multi-valued logical formalism of Thomas, with the aim of performing biological applications. The present research work fills this gap by describing a whole pipelined process which orchestrates the following stages: (i) model conversion from a Piece-wise Affine Differential Equation (PADE) modelization scheme into a discrete model with attractors, (ii) characterization of subgraphs through a graph simplification phase which is based on probabilistic criteria, (iii) conversion of the subgraphs into Parametric Linear Hybrid Automata, (iv) analysis of dynamical properties (e.g. cyclic behaviours) using hybrid model-checking techniques. The present work is the outcome of a methodological investigation launched to cope with the GRN responsible for the reaction of Escherichia coli bacterium to carbon starvation. As expected, we retrieve a remarkable cycle already exhibited by a previous analysis of the PADE model. Above all, hybrid model-checking enables us to discover additional insightful results, whose interpretations are in accordance with biological evidences.

Mots clés: gene regulatory network; differential equations; model conversion; delays; model-checking; parametric linear hybrid automaton; Escherichia coli carbon availability response

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Jamil Ahmad, Jérémie Bourdon, Damien Eveillard, Jonathan Fromentin, Olivier Roux, et al.. Qualitative modelling and analysis of gene regulatory networks: application to the adaptation of Escherichia coli bacterium to carbon availability. 2009. ⟨hal-00359530⟩