Fig. 9: The enforcement of modularity by our integral controller.

a Our integral controller mitigates the effect of competing synthetic genes and changes of the culture medium on the performance of an inducible genetic module, which consists of a transcription activation factor ta and the output gene x regulated by it. b, c The module of interest’s induction curve (steady-state output protein concentrations plotted against inducer levels in the medium) in open- and closed-loop setups with and without different disturbances. d, e Open- and closed-loop steady-state concentrations of the output protein px relative to their values for a given inducer concentration f in the default culture medium and without disturbing gene expression. Unless specified otherwise, simulation parameters for all panels are given in Supplementary Table 9, and the ODEs used to simulate the controller are Supplementary Eqs. (121)–(134) in Supplementary Note S4.4.1. Source data are provided as a Source Data file.