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The study of self regulated gene expression networks must be modelled using chemical master equations. However, its solution is not available in the most cases. In this work, we derive a partial integral differential model as the continuous counterpart of one master equation with jump process. This model allows us to reproduce numerically the dynamic behaviour of the protein distribution whose steady state admits an analytical solution. To study the convergence to the equilibrium, we test the applicability of entropy methods. Using these techniques we find numerical evidences of exponential stability. The derivation and methods presented can be of the help to extend the applicability of this model to more complex gene regulatory networks including more than one protein.

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Stability of stochastic gene regulatory networks using entropy methods**This work has been partially supported by Ministerio de Economia y Competitividad AGL2012-39951-C02-01. M. Pajaro acknowledge support from grants BES-2013-063112 and EEBB-I-16-10540.