Before revision:  Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
After revision:  Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system .