Before revision:  Finally, it is shown that one obtains the classical rate equations form the corresponding stochastic versions as the equations satisfied by the mean values of the random variables .
After revision:  Finally, it is shown that one obtains the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables. It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a notion of coupled random dynamical system. Finally, we illustrate our framework with three simple examples of "single-gene dynamics", which are the build blocks of our networks .