Modeling the Dynamics of Genetic Regulatory Networks:
Continuous and Discrete Approaches
Hidde de Jong and Ricardo Lima
We discuss methods for the modeling and simulation of one particular
type of molecular interaction network, called genetic regulatory network.
Today, a large part of the experimental data available, notably gene transcription data, concerns these networks of genes, proteins, and their mutual interactions. Many reviews of the modeling
and simulation of genetic
regulatory networks have been published in recent years, presenting the
wide variety of formalisms that have been proposed in the literature, such as oriented graphs, Bayesian networks, Boolean networks, differential equations, and stochastic master equations.
We restrict the discussion here to ordinary differential equations and to iterations of maps. These continuous-time and discrete-time models have been often used for the modeling of biological
systems and a large number of powerful techniques for their analysis are available. In section 2, we introduce some biological notions, fundamental for understanding the nature of genetic
regulation and genetic regulatory networks. Sections 3 and 4 discuss the analysis of a simple example network, a cross-inhibition network of two genes, by means of several continuoustime
differential equations and discrete-time dynamical systems. In addition, references are made to modeling studies of real genetic regulatory networks underlying the functioning and development of several prokaryote and eukaryote systems. The chapter ends with a brief discussion and conclusions.
The pdf version of this review is here
Gene networks, models for a dynamical collective self regulation.
A presentation at ZiF Bielefeld during the workshop on Complexity, Mathematics and Socio-Economic Problems, 1-11 september 2009.
The pdf version of this presentation is here
Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks
Claudine Chaouiya, Ouerdia Ourrad, Ricardo Lima
the pdf version of this article is here
We consider threshold Boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when
the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie
(when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast.
Moreover, several studies consider stochastic extensions to assess the robustness of such a model.
Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates.
We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants to the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing.
Abstract: We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is put on the interplay between the internal properties of the open systems and the different possible inputs on them to deduce new functionalities of the modules. We use discrete-time, piecewise-affine and piecewise-contracting models with interactions of a regulatory nature to perform our study
The pdf version of this article is here