Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits

Mathematical modeling of regulatory networks of intracellular processes – Aims and selected methods

“…Following rapid developments in new experimental techniques, mathematical modeling of regulatory pathways that control intracellular biological and chemical processes has almost become a separate scientific discipline, offering large number of methods, tailored to specific purposes (see, e.g., [20] , [28] , [38] , [68] , [124] and references therein). Analysis of biological data has led to much better understanding of the nature of intracellular processes.…”

Weak synchronization and convergence in coupled genetic regulatory networks: Applications to damped oscillators and multistable circuits

“…In our recent work, 12 as well as in References 14,15, coupled genetic networks are studied using piecewise affine (PWA) models, which approximate continuous sigmoidal-like activity functions by step functions and facilitate an algorithmic analysis of the dynamics. This is an interesting framework since various tools are available for analysis of PWA systems 16 and a practical method for finding Lyapunov functions for PWA systems was also recently proposed in Reference 17. In this article, our goal is to improve the current understanding of the emergent behaviors that may appear through coupling, while determining which properties of the individual systems are preserved. We thus propose to focus on the behavior of a class of smoothly coupled monostable genetic regulatory networks where the smoothness hypothesis is made to enable the use of smooth functions and apply the classical Lyapunov theory.…”

“…In our recent work, 12 as well as in References 14,15, coupled genetic networks are studied using piecewise affine (PWA) models, which approximate continuous sigmoidal‐like activity functions by step functions and facilitate an algorithmic analysis of the dynamics. This is an interesting framework since various tools are available for analysis of PWA systems 16 and a practical method for finding Lyapunov functions for PWA systems was also recently proposed in Reference 17.…”

“…The variables and represent the concentrations of two interacting proteins such that 1 inhibits 2 while 2 promotes the production of 1. Note that the diagonal terms of A which correspond to self‐inhibitions of the nodes are usually taken equal to zero in the standard model (see, for instance Reference 16), and it is a known fact that such system converges towards a steady state both in the smooth and PWA case, which corresponds to the limit case (see, for instance Reference 4). Notice that a system driven by Equation (2) and associated coupled systems can be put under the general form studied in Reference 21(theorem 1).…”

Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

“…They are useful for the analysis of large regulatory networks when mechanistic details underlying are scarce, insufficiently defined, or even controversial, as it has been discussed that, in such models, the interaction type (inhibition or activation) and network topology are enough for capturing dynamics of gene networks [11,12], without the need of estimating parameters, thereby reducing model complexity. For example, they are being used extensively to represent interactions revealed by high throughput sequencing technologies in the context of systems biology [13,14]. Although some of these assumptions make them less applicable for certain biological processes, they have proved very valuable for predicting the behavior of genes during bacterial metabolism [15] or in the context of interspecies interactions [16].…”