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. 2020 Mar 24;9:e52813. doi: 10.7554/eLife.52813

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© 2020, Hallinen et al

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Figure 2. — Top: bifurcation diagram showing stable (filled circles) and unstable (red dashed curves) fixed points for different values of drug influx ( $F$ ) and the total number of cells ( $N_{s} + N_{r}$ ). $F_{c} \approx μ K$ is the critical value of drug influx above which the zero solution (extinction) becomes stable; μ is the rate at which cells and drugs are removed from the system (and is measure in units of $g_{m a x}$ , the maximum per capita growth rate of cells in drug-free media, and $K_{r}$ is the factor increase in drug MIC of the resistant strain relative to the wild-type strain. Vertical black dashed lines correspond to $F = F_{1} > F_{c}$ (small drug influx, just above threshold) and $F_{2} ≫ F_{c}$ (large drug influx). Bottom panels: regions of survival (white) and extinction (grey) in the space of sensitive ( $N_{s}$ ) and resistant ( $N_{r}$ ) cells for flow rate $F = F_{1}$ (left) and $F = F_{2}$ (right). Dashed lines show separatrix, the contour separating survival from extinction. Multicolor lines represent constant resistant fractions (1/5, left; 3/4, right) at different total population sizes (ranging from 0 (blue) to a maximum density of 1 (red)). Cell numbers are measured in units of carrying capacity. Specific numerical plots were calculated with $h = 1.4$ , $g_{m i n} = 1 / 3$ , $g_{m a x} = 1$ , $ϵ_{1} = 1.1$ , $ϵ_{2} = 1.5$ , $γ = 0.1$ , $K_{r} = 14$ , $F_{1} = 1.4$ , and $F_{2} = 2.2$ .

Figure 2—figure supplement 1. — Top: bifurcation diagram showing stable (filled circles) and unstable (red dashed curves) fixed points for different values of drug influx ( $F$ ) and the total number of cells ( $N_{s} + N_{r}$ ). $F_{c} \approx μ K$ is the critical value of drug influx above which the zero solution (extinction) becomes stable; μ is the rate at which cells and drugs are removed from the system (and is measure in units of $g_{m a x}$ , the maximum per capita growth rate of cells in drug-free media, and $K_{r}$ is the factor increase in drug MIC of the resistant strain relative to the wild-type strain. Vertical black dashed lines correspond to $F = F_{1} > F_{c}$ (small drug influx, just above threshold) and $F_{2} ≫ F_{c}$ (large drug influx). Bottom panels: regions of survival (white) and extinction (grey) in the space of sensitive ( $N_{s}$ ) and resistant ( $N_{r}$ ) cells for flow rate $F = F_{1}$ (left) and $F = F_{2}$ (right). Dashed lines show separatrix, the contour separating survival from extinction. Multicolor lines represent constant resistant fractions (1/5, left; 3/4, right) at different total population sizes (ranging from 0 (blue) to a maximum density of 1 (red)). Cell numbers are measured in units of carrying capacity. Specific numerical plots were calculated with $h = 1.4$ , $g_{m i n} = 1 / 3$ , $g_{m a x} = 1$ , $ϵ_{1} = 1.1$ , $ϵ_{2} = 1.5$ , $γ = 0.1$ , $K_{r} = 14$ , $F_{1} = 1.4$ , and $F_{2} = 2.2$ .