Figure 4.

Dynamical predictions for the population density of E. coli bacteria growing on glucose, with parameters r_max = 1hr⁻¹, d = 0.5hr⁻¹, K_s = 1μM and Γ = 1.8 × 10¹⁰ glucose molecules per bacterium. The nutrient inflow rate b is varied, such that we have β = 0.1, χ = 0 (corresponding to b = 0.1μMh⁻¹ and R=0; such that s* = 1μM and n* ≈ 10⁷ bacteria per litre) and β = 0.01, χ = 0 (corresponding to b = 0.01μMh⁻¹ and R=0; such that s* = 1μM and n* ≈ 10⁶ bacteria per litre). Panel A shows results for the deterministic model, Eqs. (18-19). Panel B shows results for the stochastic model, Eq. (22), for a system volume of 1ml; i.e. for approximate absolute bacterial numbers of 10⁴ (red) and 10³ (blue). Note the different time axes in the two panels. In these simulations, the bacterial densities are much lower than in a typical microbiology lab experiment, and are 1-2 orders of magnitude lower than the bacterial density in seawater, but they are similar to the bacterial density that might be found in drinking water.