Combinatorial explosion in model gene networks

Chaos
R Edwards, Leon Glass

Abstract

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresp...Continue Reading

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Citations

Mar 8, 2006·Journal of Mathematical Biology·R CoutinhoA Meyroneinc
Dec 31, 2005·Journal of Mathematical Biology·Etienne Farcot
May 26, 2009·Journal of Mathematical Biology·Linghong Lu, Roderick Edwards
Feb 12, 2004·Bulletin of Mathematical Biology·Hidde De JongJohannes Geiselmann
Jun 5, 2003·Journal of Theoretical Biology·Qingwu YangJeffrey J Morgan
Mar 26, 2002·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Hidde de Jong
Apr 25, 2008·Journal of the Royal Society, Interface·Madalena Chaves, Réka Albert
Jun 5, 2003·Chaos·R. EdwardsL. Glass
Sep 28, 2004·Chaos·Jonathan MasonLeon Glass
Oct 4, 2006·Chaos·Xiao-Song Yang, Yan Huang
Oct 11, 2008·Journal of Theoretical Biology·N IchinoseK Aihara
Jun 17, 2009·Birth Defects Research. Part C, Embryo Today : Reviews·Nicholas Geard, Kai Willadsen
Aug 11, 2004·Journal of Theoretical Biology·Theodore J PerkinsLeon Glass
Jun 29, 2004·Artificial Intelligence in Medicine·Changwon Yoo, Gregory F Cooper
Sep 29, 2006·Journal of Theoretical Biology·Jacques-A SepulchreWilliam Nasser
Dec 13, 2005·Journal of Theoretical Biology·Hideki NakayamaToshimitsu Ushio
Oct 31, 2009·Developmental Biology·Bartek Wilczynski, Eileen E M Furlong
Jun 8, 2002·Journal of Theoretical Biology·Christopher SewellPaul A Lindahl
Aug 26, 2016·PLoS Computational Biology·William Letsou, Long Cai
Sep 15, 2020·BMC Bioinformatics·Vitaly A LikhoshvaiTamara M Khlebodarova
Mar 26, 2013·Physical Review Letters·David P RosinEckehard Schöll

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