Box 2 | Promotion of inherited (acquired) resistance

Using this version of the model, which includes mutation as a stochastic process, we first consider the antibiotic treatment protocol used to generate the simulations outlined in Fig. 2, and assume a mutation rate of 10^-8 per cell per division, a total of 10⁷ bacteria in the unprotected compartment, and no exchange with a protected population (that is, only susceptible bacteria). Under these conditions, resistance arose in only 2 out of 100 runs (see Figure). On first consideration, it might seem that if there was a protected compartment increasing the total number of bacteria and extending the duration of the infection, genetically resistant mutants would arise more frequently than if there was no protected compartment. Although this would be true if the treatment continued indefinitely and the bacteria were not cleared, the presence of a protected compartment for short periods of treatment would only have a modest effect on the likelihood of resistance arising in the unprotected compartment. For example, if it is assumed that there are 10⁶ bacteria in both the unprotected and protected sites, the frequency of simulations where resistance arises in the unprotected compartment would be 11% (compared with 2% in the absence of a protected compartment; see Figure). Increasing the number of bacteria in the protected site (to 10⁷ bacteria) or increasing the rate of turnover and the intensity of selection in the protected compartment (pink bars) considerably augments the likelihood of resistance evolving during the two weeks of treatment. Increasing the maximum rate of replication in the protected site increases the number of generations of bacterial growth, and increasing the maximum kill rate in the protected site increases the intensity of selection. As such, there is an escalation in the likelihood that resistant mutants will make their way to the unprotected site. The figure illustrates the frequency of runs in which resistant mutants arise during 2 weeks of treatment. In all runs, the mutation rate to generate resistance was 10^-8 per cell per division. One hundred independent simulation runs were made for each set of parameters. In the simulation results shown in green, the pharmacodynamic, pharmacokinetic and other parameters are identical to those detailed in Fig. 2. In the simulation results shown in pink, the maximum replication rate and maximum kill rate of sensitive bacteria in the protected site were 10-fold higher (0.1 hr^-1 rather than 0.01 hr^-1). All other parameters are the same as those used in Fig. 2.