Discrete time piecewise affine models of genetic regulatory networks

Journal of Mathematical Biology
R CoutinhoA Meyroneinc

Abstract

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their asymptotic dynamics approaches that of a differential equation in another limiting case of this parameter. For intermediate values, the model present an original phenomenology which is argued to be due to delay effects. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle - with a rotation number depending continuously a...Continue Reading

References

Dec 1, 1973·Journal of Theoretical Biology·R Thomas
Aug 19, 1997·Proceedings of the National Academy of Sciences of the United States of America·B Novak, J J Tyson
May 11, 1999·Bio Systems·D Thieffry, D Romero
Sep 17, 1999·Bioinformatics·L MendozaE R Alvarez-Buylla
Mar 26, 2002·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Hidde de Jong
May 17, 2002·Current Biology : CB·Eli MeirGarrett M Odell
Mar 22, 2003·Current Opinion in Cell Biology·John J TysonBela Novak
Jun 5, 2003·Chaos·R. Edwards, L. Glass
Jun 5, 2003·Chaos·R. EdwardsL. Glass
Feb 12, 2004·Bulletin of Mathematical Biology·Hidde De JongJohannes Geiselmann
Oct 1, 2005·Journal of Mathematical Biology·Richard CaseyJean-Luc Gouzé

❮ Previous
Next ❯

Citations

Oct 6, 2010·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·M di Bernardo, S J Hogan
Aug 8, 2013·PloS One·Claudine ChaouiyaRicardo Lima
Mar 24, 2007·Journal of Mathematical Biology·R EdwardsLin Wang
Jun 2, 2012·Mathematical Biosciences·Andong LiuBo Chen
Mar 12, 2010·Journal of Theoretical Biology·Beatriz Carely Luna OliveraAgustino Martínez-Antonio
Aug 12, 2009·Journal of Theoretical Biology·A PolynikisM di Bernardo
May 21, 2013·Molecular BioSystems·Beatriz LunaAgustino Martínez-Antonio
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bastien Fernandez, Lev S Tsimring

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.