Figure 4. Eliminating reverse inoculum effect eliminates inverted bistability.

(A) Numerical phase diagram in absence of reverse inoculum effect (${ϵ}_{\mathrm{1}}\mathrm{=}\mathrm{0}$) indicating regions of extinction (black), survival (white), and bistability (light gray; initially large population survives, small population dies). There are no regions of ‘inverted’ bistability (initially small population survives, large population dies). Red ’x’ marks fall along a line that previously traversed a region of inverted bistability in the presence of a reverse inoculum effect (Figure 3) but includes only surviving populations in its absence. $F_c$ is the critical influx rate above which the extinct solution (population size 0) first becomes stable; it depends on model parameters, including media refresh rate (µ), maximum kill rate of the antibiotic ($g_{m\mathrm{}i\mathrm{}n}$), the Hill coefficient of the dose-response curve ($h$), and the MIC of the drug-resistant population in the low-density limit where cooperation is negligible ($K$). Specific phase diagram was calculated with same parameters as in Figure 3 except ${ϵ}_{\mathrm{1}}$, which corresponds to the reverse inoculum effect, is set to 0. (B) Experimental time series for mixed populations starting at a total density of OD = 0.1 (blue) or OD = 0.6 (red) in regular media (left panels) or strongly buffered media (right panels). The initial populations are comprised of resistant cells at a total population fraction of 0.11 (top) and 0.15 (bottom) and for influx rate of $F_{\mathrm{1}}\mathrm{=}\mathrm{18}$ µg/mL. Light curves are individual experiments, dark curves are means across all experiments.