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

Regulation by small RNAs via coupled degradation: mean-field and variational approaches