Noise propagation in chemical reaction networks: Analysis of a molecular subtractor module

The realization of embedded molecular control systems is a challenging aim in Synthetic Biology, where a major goal is to design synthetic biological circuits performing specific tasks. In this field, the novel emergent approach is to assemble the circuit in a modular fashion, possibly restraining reciprocal interactions from interconnected modules (zero-retroactivity). Within this framework, recent results have been proposed, dealing with the realization of an embedded subtractor module, with the idea of exploiting it in a more general chemical reaction network that resembles a classical control scheme. So far, this research has been carried out according to the deterministic approach. More sophisticated analysis requires the use of stochastic models, which play a paramount role in investigating noise propagation in chemical reaction networks, especially when the species copy number is low and the intrinsic stochasticity of the phenomena under investigation cannot be neglected. This note deals with a first analysis of the subtractor module, according to the stochastic approach. To this end, Chemical Master Equations are exploited to model one of the possible molecular circuits implementing the subtractor, and moment equations are written in order to evaluate how noise propagates with respect to different values of the inputs and different model parameter settings.