Figure 6.

(A) Predicted average value of f as a function of the rate k₀ of switching into the less favourable state 0. These results were obtained by numerical solution of Eq. (26), for an environment that switches stochastically as a Poisson process (with average rate 1), or periodically (once per time unit). When the environment switches, we set f → 1 − f in the simulation, keeping all other parameters fixed. When the rate k₁ of switching into the faster growth state is very small, the function 〈f(k₀)〉 is peaked at a non-zero value of k₀, implying that it is favourable for cells to switch into the slower growth state at some non-zero rate, whether the environment is stochastic or periodic. However for the larger value of k₁ simulated here, switching into the slower growth state is favourable only in the periodic environment. For even larger values of k₁, switching becomes unfavourable even in the periodic environment [140]. (B-D) Experiments with a stochastically switching strain of yeast cells, performed by Acar et al. [146] (images reproduced from Ref. [146]). (B) Schematic illustration of the experimental setup. Yeast cells can be in either of two states, labelled ON and OFF. Cells randomly switch between the states at rates r_ON and r_OFF which can be tuned by the experimenter. The environment is maintained in state E₁ for time T₁ before being switched to state E₂, which is maintained for time T₂. The proliferation rates γ of the two cell types depend on the environment; the ON cell type proliferates faster in E₁ while the OFF cell type proliferates faster in E₂. (C-D) Growth rates measured as a function of time during such an experiment, for cells that switch fast (red; r_ON ~ 0.047h⁻¹, r_OFF ~ 0.035h⁻¹) or slow (blue; r_ON ~ 0.004h⁻¹, r_OFF ~ 0.007h⁻¹). Panel C shows results for an experiment with T₁ = 20h, T₂ = 37h; here the fast-switching cells have on average a higher growth rate. Panel D shows results for T₁ = 96h, T₂ = 96h; here the slow-switching cells have a higher growth rate on average.