Figure 1

Schematic of the model. (A) The continuous processes of growth, damage accumulation and repair. Substrate (S) is taken up and converted into active protein (P _act ). The substrate concentration may be either constant or dynamic, depending on the environment. This autocatalytic growth process is catalysed by the ‘growth machinery’, a fraction (1 − β) of active protein, producing more active protein. Active protein is converted at damage accumulation rate a into damaged protein (P _dam ), which may inhibit the growth process if it is toxic. Damaged protein may also be repaired according to Equation 1 by the ‘repair machinery’, the other fraction of active protein (β). Protein represents the entire biomass. (B) The discontinuous process of cell division. Both daughter cells inherit the same amounts of total biomass on average, specified by the variable θ that is chosen from a truncated normal distribution with mean 0.5, standard deviation 0.025. They may acquire the same proportions of active and damaged protein (symmetric division) or the old-pole cell may take on all (or as much as possible) of the damaged protein (asymmetric division). These are the two extreme cases of a continuum denoted by the variable α. (C) In a constant environment, a cell is randomly replaced by a new cell formed upon cell division; this models external mortality. Substrate is taken up by the cells but its concentration does not change. (D) In a dynamic environment, substrate at concentration S_in is fed into the system, and cells and substrate at concentration S leave the system, all in proportion to the dilution rate D. Removal of cells is a form of extrinsic mortality. See Additional files 1,3 for more details.