Greedy scheduling of cellular self-replication leads to optimal doubling times with a log-Frechet distribution

Bacterial self-replication is a complex process composed of many de novo synthesis steps catalyzed by a myriad of molecular processing units, e.g., the transcription-translation machinery, metabolic enzymes, and the replisome. Successful completion of all production tasks requires a schedule-a temporal assignment of each of the production tasks to its respective processing units that respects ordering and resource constraints. Most intracellular growth processes are well characterized. However, the manner in which they are coordinated under the control of a scheduling policy is not well understood. When fast replication is favored, a schedule that minimizes the completion time is desirable. However, if resources are scarce, it is typically computationally hard to find such a schedule, in the worst case. Here, we show that optimal scheduling naturally emerges in cellular self-replication. Optimal doubling time is obtained by maintaining a sufficiently large inventory of intermediate metabolites and processing units required for self-replication and additionally requiring that these processing units be "greedy," i.e., not idle if they can perform a production task. We calculate the distribution of doubling times of such optimally scheduled self-replicating factories, and find it has a universal form-log-Frechet, not sensitive to many microscopic details. Analyzing two recent datasets of Escherichia coli growing in a stationary medium, we find excellent agreement between the observed doubling-time distribution and the predicted universal distribution, suggesting E. coli is optimally scheduling its replication. Greedy scheduling appears as a simple generic route to optimal scheduling when speed is the optimization criterion. Other criteria such as efficiency require more elaborate scheduling policies and tighter regulation.