Stochastic Models and Numerical Algorithms for a Class of Regulatory Gene Networks
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- Fournier, T., Gabriel, JP., Mazza, C. et al. Bull. Math. Biol. (2009) 71: 1394. doi:10.1007/s11538-009-9407-9
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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.