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arxiv: 2510.01808 · v4 · submitted 2025-10-02 · 🧬 q-bio.PE · physics.bio-ph

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

Javier Molina-Hern\'andez , Jos\'e A. Cuesta , Beatriz Pascual-Escudero , Sa\'ul Ares , Pablo Catal\'an This is my paper

Pith reviewed 2026-05-18 11:05 UTC · model grok-4.3

classification 🧬 q-bio.PE physics.bio-ph
keywords collateral sensitivitysequential antibiotic therapybacterial extinctionstochastic birth-death modelswitching periodantimicrobial resistancepopulation dynamics
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0 comments X

The pith

Switching between two antibiotics at tuned intervals drives resistant bacteria to extinction by exploiting collateral sensitivity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper builds a stochastic model of bacterial populations exposed to two antibiotics that exhibit reciprocal collateral sensitivity, where resistance to one drug heightens vulnerability to the other. It shows that the probability of total bacterial extinction changes nonlinearly as the time between drug switches varies, rising in discrete steps tied to particular switch moments rather than gradually. Fast switching performs poorly because it skips the window in which resistant mutants arise and then become targets for the alternate drug. A geometric distribution describes the cumulative extinction chance from the success rate at each individual switch, and this rate itself grows with longer intervals. The analysis also uncovers a trade-off in which extended treatment periods raise extinction odds yet leave higher residual resistance, defining a set of balanced switching schedules.

Core claim

In a four-genotype stochastic birth-death model with two bacteriostatic antibiotics exhibiting strong reciprocal collateral sensitivity, the extinction probability of the bacterial population under subinhibitory concentrations varies nonlinearly with the switching period. This dependence manifests as stepwise increases in extinction probability that align with discrete switch events. Fast sequential therapies prove suboptimal because they fail to allow for the evolution of resistance, which serves as a crucial component in achieving eradication through collateral sensitivity. A geometric distribution framework provides accurate predictions for cumulative extinction probabilities, with the 0

What carries the argument

Four-genotype stochastic birth-death model that tracks wild-type, single-resistant, and double-resistant bacteria under alternating subinhibitory antibiotic concentrations linked by reciprocal collateral sensitivity.

Load-bearing premise

The two antibiotics exhibit strong reciprocal collateral sensitivity so that resistance to one substantially increases sensitivity to the other.

What would settle it

Laboratory experiments that measure extinction rates for bacterial populations with documented collateral sensitivity would falsify the claim if lengthening the switching period to match single-resistant mutant fixation times produced no stepwise rise in extinction probability.

Figures

Figures reproduced from arXiv: 2510.01808 by Beatriz Pascual-Escudero, Javier Molina-Hern\'andez, Jos\'e A. Cuesta, Pablo Catal\'an, Sa\'ul Ares.

Figure 1
Figure 1. Figure 1: FIG. 1. Four-genotype model. (a) We consider four geno [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Sequential therapies with subinhibitory antibiotic concentrations cause extinction for a wide range of switching periods. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Heuristic approximation for the extinction probability. (a) Sigmoid fit for the extinction probability at the end of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Distributions for key transition times in the model. Simulated distributions (blue histograms) and fitted lognormal [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Extinction probability sensitivity to model parameters. (a) Collateral sensitivity (CS) is necessary for extinction. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Optimal therapy. (a) Extinction probability as a function of the switching period. (b) Probability of double resistant [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Optimal window. Simulated therapy trajectories were generated with different switching periods ( [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Extinction histograms for the hybrid method: Tau-leaping and Gillespie’s algorithm. The top row (blue) shows [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Changing the extinction threshold does not change [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Cumulative extinction probability over 10 treatment switches with different switching periods [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Mean population trajectories. Mean values of the [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Effect of changes in antibiotic concentration. Mean [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Collateral sensitivity is irrelevant when high doses [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Effect of changes in mutation rates. The extinction [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Effect of changes in mutation rates. Mean population composition prior to the switch for trajectories that do not [PITH_FULL_IMAGE:figures/full_fig_p013_15.png] view at source ↗
read the original abstract

Antimicrobial resistance (AMR) threatens global health. A promising and underexplored strategy to tackle this problem is 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript develops a four-genotype stochastic birth-death model for bacterial populations under sequential therapies with two bacteriostatic antibiotics exhibiting collateral sensitivity. It claims that extinction probability depends nonlinearly on switching period, with stepwise increases aligned to discrete switch events; fast sequential therapies are suboptimal because they do not allow resistance evolution. A geometric distribution framework predicts cumulative extinction probabilities (with per-switch extinction rising with period), and a heuristic approximation is derived from times to fixation of single-resistant mutants. Sensitivity analyses show that strong reciprocal collateral sensitivity is required for high extinction probabilities, while increasing doses and mutation rates modulate extinction nonmonotonically; longer therapies maximize extinction but increase resistance, yielding a Pareto front of optimal periods.

Significance. If the central claims hold, the work supplies quantitative design principles for collateral-sensitivity-guided sequential therapies that could inform in vitro and clinical protocols. The largely parameter-free qualitative structure, the geometric and heuristic approximations, and the explicit Pareto-front trade-off between extinction and resistance are strengths. The stochastic modeling and sensitivity analyses add rigor, though the dependence on strong reciprocal CS narrows the immediate translational scope.

major comments (1)
  1. [Sensitivity analyses] Sensitivity analyses section: the headline result (nonlinear rise in extinction probability with switching period and suboptimality of fast switching) is shown to collapse when reciprocal collateral sensitivity is weakened. Because this assumption is load-bearing for the design principle and the manuscript provides no discussion or citations on the empirical prevalence of strong reciprocal CS in clinical or environmental isolates, the applicability of the proposed switching-period optima remains uncertain.
minor comments (2)
  1. [Abstract] The abstract states that the geometric framework 'accurately predicts' cumulative extinction probabilities; a brief quantitative comparison (e.g., mean absolute error or R^{2} against simulations) in the main text would strengthen this claim.
  2. [Methods] Notation for the four genotypes and the fitness parameters under each drug could be introduced with a single table or diagram early in the Methods to improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and insightful review of our manuscript. We address the major comment below in a point-by-point manner.

read point-by-point responses

  1. Referee: [Sensitivity analyses] Sensitivity analyses section: the headline result (nonlinear rise in extinction probability with switching period and suboptimality of fast switching) is shown to collapse when reciprocal collateral sensitivity is weakened. Because this assumption is load-bearing for the design principle and the manuscript provides no discussion or citations on the empirical prevalence of strong reciprocal CS in clinical or environmental isolates, the applicability of the proposed switching-period optima remains uncertain.

    Authors: We appreciate the referee drawing attention to this aspect of our sensitivity analyses. The manuscript already states that strong reciprocal collateral sensitivity is required for the strategy to produce high extinction probabilities and that the headline nonlinear dependence on switching period collapses under weaker CS. This is presented as a central result rather than an afterthought. We agree that the current version lacks explicit discussion of how commonly strong reciprocal CS occurs in clinical or environmental isolates, which limits immediate claims about applicability. In the revised manuscript we will add a dedicated paragraph in the Discussion that reviews published empirical examples of strong reciprocal CS (e.g., in Pseudomonas aeruginosa and other opportunistic pathogens under beta-lactam/aminoglycoside or fluoroquinolone pairings), cites the relevant experimental literature, and explicitly qualifies the translational scope of the predicted switching-period optima pending further strain-specific validation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from model dynamics

full rationale

The paper constructs a four-genotype stochastic birth-death process with explicit fitness parameters encoding collateral sensitivity, then computes extinction probabilities via direct simulation and standard approximations (geometric distribution over per-switch events, heuristic based on fixation times of single-resistant mutants). These steps follow from solving or approximating the underlying Markov process rather than redefining inputs as outputs. No load-bearing self-citations, no parameters fitted to the target extinction probability and then relabeled as predictions, and no ansatz or uniqueness claim imported from prior author work. Sensitivity analyses independently vary the CS strength, confirming the result depends on an explicit modeling assumption rather than embedding it tautologically. The chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of strong reciprocal collateral sensitivity and on the validity of the four-genotype stochastic birth-death process under subinhibitory concentrations; no explicit free parameters or invented entities are named in the abstract.

axioms (2)
  • domain assumption Strong reciprocal collateral sensitivity exists between the two bacteriostatic antibiotics.
    Sensitivity analyses in the abstract state that this condition is required for the strategy to produce high extinction probabilities.
  • domain assumption Bacterial population dynamics can be captured by a four-genotype stochastic birth-death process.
    The model structure is introduced as the basis for all extinction-probability calculations.

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Reference graph

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