Text S 1 : supplementary information for Combinatorial gene regulation using autoregulation

As many as 59% of the transcription factors in Escherichia coli regulate the transcription rate of their own genes. This suggests that auto-regulation has one or more important functions. Here, one possible function is studied. Often the transcription rate of an auto-regulator is also controlled by additional transcription factors. In these cases, the way the expression of the auto-regulator responds to changes in the concentrations of the “input” regulators (the response function) is obviously affected by the auto-regulation. We suggest that, conversely, auto-regulation may be used to optimize this response function. To test this hypothesis, we use an evolutionary algorithm and a chemical–physical model of transcription regulation to design model cis-regulatory constructs with predefined response functions. In these simulations, auto-regulation can evolve if this provides a functional benefit. When selecting for a series of elementary response functions—Boolean logic gates and linear responses—the cis-regulatory regions resulting from the simulations indeed often exploit auto-regulation. Surprisingly, the resulting constructs use auto-activation rather than auto-repression. Several design principles show up repeatedly in the simulation results. They demonstrate how auto-activation can be used to generate sharp, switch-like activation and repression circuits and how linearly decreasing response functions can be obtained. Auto-repression, on the other hand, resulted only when a high response speed or a suppression of intrinsic noise was also selected for. The results suggest that, while auto-repression may primarily be valuable to improve the dynamical properties of regulatory circuits, auto-activation is likely to evolve even when selection acts on the shape of response function only.