A novel statistical approach identifies feedback interactions for the construction of robust stochastic transcriptional oscillators

Synthetic biology can be defined as applying engineering approaches, such as part standardisation, abstraction and mathematical modelling, to the design and engineering of novel biological systems. Engineering transcriptional networks presents many challenges including inherent uncertainty in the system structure, changing cellular context and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we define a measure of robustness that coincides with the Bayesian model evidence, which allows us to exploit Bayesian model selection to calculate the relative structural robustness of gene network models governed by stochastic dynamics. We then use this framework to examine the robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of auto-regulation, and degradation of mRNA and protein affects the frequency, amplitude and robustness of transcriptional oscillators. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modelling approaches to systems and synthetic biology.