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Stochastic models and numerical algorithms for a class of regulatory gene networks. (English) Zbl 1171.92020

Summary: Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions [N. Guido et al., 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 D. Gillespie algorithm [J. Chem. Phys. 115, 1716–1733 (2001); ibid. 81, 2340–2361 (1977)] 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.

MSC:

92C40 Biochemistry, molecular biology
92D10 Genetics and epigenetics
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92-08 Computational methods for problems pertaining to biology
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