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Mathematical approaches to differentiation and gene regulation
- Source :
- Comptes Rendus Biologies. 329:13-20
- Publication Year :
- 2006
- Publisher :
- Elsevier BV, 2006.
-
Abstract
- We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. Once such a graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. In this paper we discuss a rule proposed by R.Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential or boolean type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models and the corresponding discrete models. We discuss open problems as well.<br />Comment: To appear in Notes Comptes-Rendus Acad. Sc. Paris, Biologie
- Subjects :
- Regulation of gene expression
Discrete mathematics
Models, Genetic
General Immunology and Microbiology
Computer science
Molecular Networks (q-bio.MN)
Gene regulatory network
Reproducibility of Results
Cell Differentiation
General Medicine
General Biochemistry, Genetics and Molecular Biology
Boolean network
Gene Expression Regulation
Differential inclusion
FOS: Biological sciences
Arrow
Quantitative Biology - Molecular Networks
Preprint
General Agricultural and Biological Sciences
Mathematics
Multistability
Stationary state
Subjects
Details
- ISSN :
- 16310691
- Volume :
- 329
- Database :
- OpenAIRE
- Journal :
- Comptes Rendus Biologies
- Accession number :
- edsair.doi.dedup.....c1046af0f8ca80f94256fc322a71047d