Stochasticity in bacterial division control: Preliminary consequences for protein concentration

The stochastic nature of protein concentration inside cells can have important consequences in their physiology and population fitness. Classical models of gene expression consider these processes as first-order reactions with little dependence with the cell size. However, the concentrations of the relevant molecules depend directly on the cellular volume. Here we model the cell size dynamics as exponential growth followed by division with occurrence rate proportional to the size. This framework, together with known models of chromosome replication and both protein and mRNA synthesis, lets us predict relationships between cell size and both protein number and concentration. As a main result, we find that protein production strategies (constant rate or rate proportional to either chromosome number, cell size or chromosome number times cell size) can be experimentally distinguished from the correlation between protein concentration and cell size.