Ultrasensitive response in bacterial replication initiation

In bacteria, the time at which genome replication initiates is carefully regulated, as precision in this timing is crucial for cell cycle stability. Theoretical and experimental studies have shown that the probability of replication initiation sharply depends on cell volume as the cell grows. Such sharp response is usually termed "ultrasensitive" in biology, and has been subject of extensive theoretical study. Nevertheless, the source of ultrasensitivity in this system remains unclear. In this work, we show how ultrasensitivity in replication initiation emerges from the dynamics of DnaA, the central protein regulating initiation in all bacterial species. To do so, we propose a mechanistic, thermodynamically consistent model of the dynamics of DnaA, and study the conditions under which an ultrasensitive response arises. We find that ultrasensitivity results from a combination of regulatory processes, that varies with growth conditions. In slow growth, we find an interplay between sequestration of DnaA on chromosomal binding sites and DnaA binding at the origin of replication. This mechanism requires a "sweet spot" of origin binding affinities, whose values are consistent with available experimental measurements. In fast growth, ultrasensitivity instead arises from rapid transition between an inactive and an active form of DnaA, and requires cooperative binding at the origin of replication to be effective. Our results point to ultrasensitivity as the organizing principle underlying regulation of bacterial replication initiation.