Frequency domain analysis of small non-coding RNAs shows summing junction-like behaviour

Small non-coding RNAs (sRNA) are a key bacterial regulatory mechanism that has yet to be fully exploited in synthetic gene regulatory networks. In this paper a linear design methodology for gene regulatory networks presented previously is extended for application to sRNAs. Standard models of both sRNA inhibition and activation are presented, linearised and transformed into the frequency domain. We demonstrate how these mechanisms can emulate subtraction and minimum comparator functions in specific parameter regimes. Finally, the design of a genetic feedback circuit is included, illustrating that sRNAs can be used to improve the performance of a range of synthetic biological systems.