Temporal constraints of a gene regulatory network: Refining a qualitative simulation

The modelling of gene regulatory networks (GRNs) has classically been addressed through very different approaches. Among others, extensions of Thomas’s asynchronous Boolean approach have been proposed, to better fit the dynamics of biological systems: genes may 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.