  Bacteria are able to maintain a narrow distribution of cell sizes by
regulating the timing of cell divisions. In rich nutrient conditions, cells
divide much faster than their chromosomes replicate. This implies that cells
maintain multiple rounds of chromosome replication per cell division by
regulating the timing of chromosome replications. Here, we show that both cell
size and chromosome replication may be simultaneously regulated by the
long-standing initiator accumulation strategy. The strategy proposes that
initiators are produced in proportion to the volume increase and is accumulated
at each origin of replication, and chromosome replication is initiated when a
critical amount per origin has accumulated. We show that this model maps to the
incremental model of size control, which was previously shown to reproduce
experimentally observed correlations between various events in the cell cycle
and explains the exponential dependence of cell size on the growth rate of the
cell. Furthermore, we show that this model also leads to the efficient
regulation of the timing of initiation and the number of origins consistent
with existing experimental results.
