Catalytic Buffering for Optimal Scheduling of Self-Replication

Abstract

We study the scheduling problem of a self-replicating factory. We show that by maintaining a sufficiently large inventory of intermediate metabolites and catalysts required for self-replication, optimal replication times can be achieved by a family of random scheduling algorithms that are biochemically feasible, for which catalysts never idle if they can perform de-novo bio-synthesis. Optimally scheduled self-replication is facilitated by allowing several production lines to run in parallel. The excess inventory of catalysts and substrates decouples these lines, while dynamical balancing tunes average and variance completion, resulting in an overall universal distribution for the replication times belonging to the generalized extreme value family. We discuss biological implications and postulate that bacteria that are tuned by evolution for fast replication employ this natural scheduling strategy to achieve optimal asymptotic growth rates by stoichiometrically balancing the amount of work in progress thus globally controlling the number of parallel basic self-replicating units within them. Analysis of recently measured data of E. coli growth in rich media shows data-collapse on a single universal curve consistent with our prediction, suggesting wild type E. coli optimally schedule its replication.