Proportional-Integral Feedback Controllers for Robust and Tight Mitigation of Mammalian Gene Expression Burden

The modular engineering of complex genetic circuits is often complicated by unexpected interactions between individual circuit components. Recently, the competition for finite pools of shared resources in gene expression has been identified as a major source of such interactions. Here, we introduce a mammalian implementation of antithetic integral and proportional-integral feedback to robustly control gene expression in various contexts. To realize integral feedback, we exploit the sequestration of the mRNA of a synthetic transcription factor by its antisense complement and use it to compute the mathematical integral of the error between a reference and the transcription factor expression level. The resulting integral feedback control robustly and precisely matches the expression level of the transcription factor to the reference. By introducing additional negative feedback from the mRNA of the synthetic transcription factor on its translation through a bicistornically encoded RNA-binding protein, the integral feedback is extended to realize proportional-integral feedback. We show that the integral controller rejects disturbances that result from increasing the degradation rate of the controlled transcription factor while providing adaptation to changes in the structure of the controlled network. We then show that the proportional-integral controller, in addition, reduces cell-to-cell variability of the controlled species. Finally, we introduce supplementary expression of a constitutive fluorescent protein as a disturbance to the availability of gene expression resources and show that both the integral and proportional-integral controllers manage to maintain the expression of the synthetic transcription factor. Again, the proportional-integral controller also demonstrably reduces the variability of the expression of the synthetic transcription factor in comparison to the integral controller alone. We expect that integral and proportional-integral controllers are going to be important additions to the synthetic biologist's toolkit, adding robustness and precision to cellular function through more sophisticated negative feedback control.