  Regulatory genes called small RNAs (sRNAs) are known to play critical roles
in cellular responses to changing environments. For several sRNAs, regulation
is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs).
The nonlinearity inherent in this regulatory scheme indicates that exact
analytical solutions for the corresponding stochastic models are intractable.
Here, we present a variational approach to analyze a well-studied stochastic
model for regulation by sRNAs via coupled degradation. The proposed approach is
efficient and provides accurate estimates of mean mRNA levels as well as higher
order terms. Results from the variational ansatz are in excellent agreement
with data from stochastic simulations for a wide range of parameters, including
regions of parameter space where mean-field approaches break down. The proposed
approach can be applied to quantitatively model stochastic gene expression in
complex regulatory networks.
