title: Stochastic models and numerical algorithms for a class of regulatory gene networks.
abstract: Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.
authors.affiliation: Department of Mathematics, University of Fribourg, Chemin du Musée 23, 1700 Fribourg, Switzerland.
authors.forename: Thomas
authors.initials: T
authors.lastname: Fournier
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Gabriel
authors.forename: Jerôme
authors.initials: J
authors.lastname: Pasquier
authors.forename: Christian
authors.initials: C
authors.lastname: Mazza
authors.forename: José
authors.initials: J
authors.lastname: Galbete
authors.forename: Nicolas
authors.initials: N
authors.lastname: Mermod
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D004318:Doxycycline / Q000378:metabolism; D025461:Feedback, Physiological / Q000235:genetics; D005786:Gene Expression Regulation / Q000502:physiology; D053263:Gene Regulatory Networks / Q000502:physiology*; D015316:Genetic Therapy; D049452:Green Fluorescent Proteins / Q000235:genetics; D006801:Humans; D007700:Kinetics; D016014:Linear Models; D008390:Markov Chains; D008957:Models, Genetic; D055503:Protein Multimerization / Q000502:physiology; D012097:Repressor Proteins / Q000378:metabolism; D013269:Stochastic Processes; D015534:Trans-Activators / Q000378:metabolism; D019076:Transgenes / Q000235:genetics
chemical_list: D012097:Repressor Proteins; D015534:Trans-Activators; C485184:enhanced green fluorescent protein; C034811:tetracycline resistance-encoding transposon repressor protein; D049452:Green Fluorescent Proteins; D004318:Doxycycline