Abstract
Systems like the prototypical lac operon can reliably hold repression of transcription upon DNA replication across cell cycles with just 10 repressor molecules per cell and behave as if they were at equilibrium. The origin of this phenomenology is still an unresolved question. 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 linking actual with predicted equilibrium transcription via a single kinetic parameter. We show that even the lac operon functions beyond the physical limits of naive regulation through compensatory mechanisms that suppress non-equilibrium effects. Synthetic systems without adjuvant activators, such as the cAMP receptor protein (CRP), lack 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.
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