Fig. 3: Effect of switching between motility phenotypes stochastically.

a Model description. Phenotypes of motility ν_1,2 are added as an extra dimension to the staircase model, with individual cells allowed to switch between these phenotypes at rate s. b Adaptation rate heatmap on the (ν₁, ν₂) plane for different switching rates s. The (ν₁, ν₂) plane can be partitioned into different combinations of adaptation regimes and its diagonal corresponds to a population of a single motility. In this model, bacteria adapt as if all cells had the same effective motility, which corresponds to the intersection of the level sets (white dashed lines) with the diagonal. At low switching rate (s = 0/h), the effective motility matches the slower motility present in the population \(\min ({\nu }_{1},{\nu }_{2})\). At high switching rate (s = 5/h), the effective motility matches the average motility (ν₁ + ν₂)/2. When the environment is sink-like, a deadly motility regime (grey) exists in the high motility combination, and also appears in the mixed motility combination when the switching rate is high. c Wild-type profiles for different switching rates s. At low switching rate (s = 10⁻³/h), the wild-type profile is dominated by the slower phenotype. At high switching rate (s = 5/h), the wild-type profile coincides with the profile of a single average-motility phenotype. Therefore, the adaptation in low (resp. high) motility combinations follows the low (resp. high) motility regime irrespective of switching rate s, but a change of s in the mixed motility combination can change the adaptation regime. In short, stochastic motility switching shapes the evolution of antibiotic resistance by determining the effective motility of bacterial populations. Parameters: L = 8, K = 10⁵, r = 1/h, δ = 0.3/h, μ_b = 10⁻⁴/h, μ_f = 10⁻⁷/h.