The unreasonable effectiveness of equilibrium gene regulation through the cell cycle

Systems like the prototypical lac operon can reliably hold the repression of transcription upon DNA replication across cell cycles with just ten repressor molecules per cell and, in addition, behave as if they were at equilibrium. The origin of this type of phenomena is still an unresolved question of major implications. Here, we develop a general theory to analyze strong perturbations in quasi-equilibrium systems and use it to quantify the effects of DNA replication in gene regulation. We find a scaling law that connects actual transcription with its predicted equilibrium values in terms of a single kinetic parameter. We show that even the simplest, exceptionally reliable natural system functions beyond the physical limits of naïve regulation through compensatory mechanisms that suppress nonequilibrium effects. We validate the approach with both in vivo cell-population and single-cell characterization of the lac operon. Analyses of synthetic systems without adjuvant activators, such as the cAMP receptor protein (CRP), do not show this reliability. Our results provide a rationale for the function of CRP, beyond just being a tunable activator, as a mitigator of cell cycle perturbations.