Optimization of sequential therapies to maximize extinction of resistant bacteria through collateral sensitivity

TL;DR

This work investigates how collateral sensitivity can be harnessed with sequential antibiotic switching to eradicate bacterial populations and suppress resistance evolution. Using a minimal four‑genotype stochastic model with two antibiotics, the authors quantify extinction probabilities under periodic switching and subinhibitory doses, revealing a nonmonotonic dependence on the switching period and a critical role for CS strength. They develop predictive frameworks—a hierarchical geometric model and a sigmoid‑based pre‑switch predictor—that capture extinction dynamics across multiple switches and reveal a Pareto trade‑off between maximizing extinction and minimizing double resistance, with an optimal switching window near $ au\approx 42$. The findings provide quantitative design principles for CS‑guided regimens and highlight the potential for extending to more complex collateral‑sensitivity networks and adaptive treatment strategies in clinical settings.

Abstract

Antimicrobial resistance (AMR) threatens global health. A promising and underexplored strategy to tackle this problem are sequential therapies exploiting collateral sensitivity (CS), whereby resistance to one drug increases sensitivity to another. Here, we develop a four-genotype stochastic birth-death model with two bacteriostatic antibiotics to identify switching periods that maximize bacterial extinction under subinhibitory concentrations. We show that extinction probability depends nonlinearly on switching period, with stepwise increases aligned to discrete switch events: fast sequential therapies are suboptimal as they do not allow for the evolution of resistance, a key ingredient in these therapies. A geometric distribution framework accurately predicts cumulative extinction probabilities, where the per-switch extinction probability rises with switching period. We further derive a heuristic approximation for the extinction probability based on times to fixation of single-resistant mutants. Sensitivity analyses reveal that strong reciprocal CS is required for this strategy to work, and we explore how increasing antibiotic doses and higher mutation rates modulate extinction in a nonmonotonic manner. Finally, we discuss how longer therapies maximize extinction but also cause higher resistance, leading to a Pareto front of optimal switching periods. Our results provide quantitative design principles for in vitro and clinical sequential antibiotic therapies, underscoring the potential of CS-guided regimens to suppress resistance evolution and eradicate infections.

Figures (15)

• Figure 1: Four-genotype model. (a) We consider four genotypes: $x_0$ (blue), susceptible to both antibiotics, $x_1$ (green), resistant to antibiotic $A$ but susceptible to $B$, $x_2$ (orange) resistant to $B$ and susceptible to $A$, and $x_3$ (red), resistant to both antibiotics. Mutation rates between the genotypes are indicated next to the corresponding arrows. (b) Illustrative trajectory. We start our simulations with antibiotic $A$ and, after some time $\tau$, we switch to antibiotic $B$, and repeat the process.
• Figure 2: Sequential therapies with subinhibitory antibiotic concentrations cause extinction for a wide range of switching periods. (a) Probability of extinction at the end of the treatment as switching periods vary. The intervals between two vertical lines share the same number of treatment cycles. $10,000$ trajectories were used to estimate the probability as a function of $\tau$. (b) Distribution of extinction times as a function of switching periods. Each point corresponds to the time a simulation went extinct. The colors represent the density of these events. The same background color represents the same antibiotic used. The red line represents the end of the time we allow for switching antibiotics. (c) One thousand individual trajectories switching treatment every 20 time units. Blue, red, green, purple and orange represent the mean of trajectories that go extinct upon switching antibiotics at different switching events. Black represents the mean of those trajectories that do not go extinct. Dashed lines indicate the antibiotic switch. (d) Cumulative extinction probability over 10 treatment switches with different switching periods $\tau$. Points represent extinction probabilities estimated through simulation, while the solid line reflects a fit to a hierarchical geometric distribution. (e) Extinction probability for populations undergoing one antibiotic switch, blue points represent the simulation and the red points are the fitted extinction probabilities for the corresponding $\tau$ using the hierarchical geometric model (the red line is a guide to the eye). (f) Predicted extinction probabilities for populations undergoing one to four antibiotic switches using the hierarchical geometric model. Simulations were performed with final times $\tau \cdot$(number of switches)$+ 50$. Parameter values in Appendix \ref{['app:table1']}, Table \ref{['tab:parameters']}.
• Figure 3: Heuristic approximation for the extinction probability. (a) Sigmoid fit for the extinction probability at the end of the treatment, using the population composition before the switch. Blue circles represent the simulation; gray circles are the prediction of the sigmoid function fitted with the population before the switches; and red circles are the prediction of the sigmoid function fitted with the population before the switches for switching periods greater than $30$. (b) Heuristic fit for the same probability as in (a) using fixed final time treatments, and considering several switching periods $\tau$. (c) Heuristic fit for the extinction probability under different number of antibiotic switches. Circles are the values of extinction probabilities measured in simulations; each color represents a different number of antibiotic changes, as indicated in the legend. The solid lines indicate the estimated value of the probability of extinction for each $\tau$, using the heuristic to estimate $p$. Parameter values in Appendix \ref{['app:table1']}, Table \ref{['tab:parameters']}.
• Figure 4: Distributions for key transition times in the model. Simulated distributions (blue histograms) and fitted lognormal probability density functions (dashed curves) for two temporal processes underlying the heuristic extinction estimate. (a) Time until the system transitions between stable states following an antibiotic change. Starting from $x_2(0)=80$ and $x_i(0)=0$ for $i=0,1,3$ under antibiotic $A$ until $x_1(t)>80$. (b) Time to extinction under a new antibiotic, measured only for simulations where extinction occurs. (c) Time dependent probability of having $x_0+x_2+x_3 \geq 2$ starting from the initial conditions indicated by colors in the legend. $10000$ trajectories were simulated for estimating these distributions.
• Figure 5: Extinction probability sensitivity to model parameters. (a) Collateral sensitivity (CS) is necessary for extinction. Extinction probabilities decrease as the parameter $k_{CS}$ increases, across a range of switching periods ($\tau$, shown in color). (b) Increasing antibiotic concentration (lowering $k$) robustly leads to extinction, depending on the number of treatment cycles. We observe a threshold near the MIC, beyond which most populations go extinct regardless of the switching period. (c) Extinction probability as a function of antibiotic concentration for $\tau = 50$. Close to the MIC, every trajectory becomes extinct. For subinhibitory doses, there is an intermediate dose that maximizes extinction.