The best cancer dose may be the one that gives persisters less room to hide

In this model, a tumor’s best treatment can change abruptly when the dose sensitivity of cell killing and the dose sensitivity of drug tolerance stop matching. A drug that blocks tolerant cells from returning to sensitivity at doses too low to kill sensitive cells favors intermittent high-dose treatment. If both effects rise together—or if tolerance is induced at higher doses—the preferred strategy can instead be continuous low-dose therapy. That is a striking complication to the simple intuition that more drug should mean more tumor control.

The study’s practical suggestion is not that patients should change their treatment schedules. It is that maximum tolerated dose (MTD)—the highest dose a patient can receive without severe toxicity—may not be the best long-term strategy in every biological setting. A model of virtual patients suggests that a carefully chosen compromise schedule can outperform MTD for many kinds of underlying tumor dynamics, even when those dynamics are not known precisely. These are mathematical predictions, not clinical evidence, but they point toward a more useful question for experiments: how does the drug reshape the tumor’s cell states, as well as kill cells?

The Science

Cancer cells do not all respond to treatment in the same way. Some may enter a reversible drug-tolerant persister state: a low-growth mode that helps them survive a drug that kills more sensitive cells. Persisters are not necessarily permanently resistant. But they can provide a refuge from which a tumor may regrow and, over time, acquire more durable genetic or epigenetic resistance.

The paper, by Einar Bjarki Gunnarsson of the University of Iceland’s Division of Applied Mathematics, builds a model around two cell states: drug-sensitive and drug-tolerant. Sensitive cells divide, die, and can switch into tolerance. Tolerant cells divide more slowly, die at their own rate, and may revert to sensitivity. The model gives the drug two distinct possible effects: it can encourage the switch into tolerance, slow the return from tolerance, or do both.

That distinction matters because the dose needed to affect cell switching may not be the dose needed to kill sensitive cells. The model represents each dose response with a saturating curve: a half-maximal effective dose, often written as EC50, is the dose at which an effect reaches half its maximum. Gunnarsson allows the EC50 for cell death to differ from the EC50 for tolerance adoption or reversion. Their ratios describe which process responds at lower doses.

The analysis compares cyclic treatment schedules: a chosen dose is administered for a fraction of the time and withheld for the rest. It evaluates schedules by their long-run exponential tumor growth rate. This is a deliberately simplified view of therapy: the model assumes very short cycles and focuses on two cell states rather than the full complexity of a human tumor, immune system, drug pharmacology, or treatment toxicity. The authors motivate the short-cycle approximation with earlier modeling that found shorter cycles can do at least as well as longer ones under similar assumptions.

The key move is to treat a drug not only as a weapon against cells, but also as an influence on cell identity. A dose can kill sensitive cells while simultaneously changing the odds that survivors spend time in a tolerant state.

What They Found

When the drug only increases the rate at which sensitive cells adopt tolerance, continuous treatment is optimal across the parameter range the paper studies. The preferred dose, however, changes. If tolerance adoption is triggered at much lower doses than cell killing, increasing the dose adds little extra tolerance induction, so the model favors the maximum dose. If tolerance induction takes higher doses to ramp up than cell killing does, a lower dose can kill sensitive cells while limiting the drug’s push toward persistence.

The shift between those dose regimes is relatively sharp when the drug’s effect on tolerance is strong. But the long-run growth rates under the optimal low dose and maximum dose can be similar. The difference becomes more visible in the model’s recurrence time—the time for the tumor to return to its starting size—because a high dose kills sensitive cells quickly but can also send more cells into tolerance early. The low-dose schedule removes sensitive cells more gradually, while inducing fewer tolerant cells at once. In the illustrated scenario, the paper compares continuous doses of five and one hundred times the cell-killing EC50; those are model examples, not clinical recommendations.

A different pattern appears when the drug only inhibits reversion from tolerance back to sensitivity. Here the model finds a sharp switch around a ratio of one between the reversion-inhibition EC50 and the cell-killing EC50. Below that threshold, the optimal schedule is intermittent maximum-dose therapy. Drug-free intervals matter because tolerant cells can revert more readily when the drug is absent. Above the threshold, the optimum is continuous low-dose treatment: increasing the dose suppresses reversion, and a tolerant cell that reverts while treatment continues may soon be killed. In this setting, slowing reversion can effectively protect the tolerant population.

At the threshold itself, the model finds not one unique best schedule but a continuum: multiple dose-and-frequency combinations produce the same modeled long-run growth rate. This offers a useful conceptual result. If several schedules are equally effective in the model, practical considerations—such as toxicity, convenience, or drug supply—might help distinguish them, although those factors were not fully modeled here.

When the drug affects both switching directions, the best schedule depends on the combined effects. The paper’s figures show that the earlier low-dose and intermittent regimes persist across much of the parameter space, rather than collapsing into a single universal rule. But the model’s clean transitions are conditional: when the drug’s effect on switching is weak, MTD can again become optimal. The dose response is not a general argument against maximum dosing; it is an argument that the biological mechanism should determine the schedule.

The paper also asks what happens when those mechanisms are not known. Individualized optimization would require estimates of a patient’s tumor growth and switching rates—measurements that generally need longitudinal data across doses and can be hard to obtain clinically. To explore an alternative, the researchers simulated heterogeneous “virtual patients,” then selected a best-on-average strategy rather than optimizing separately for every modeled person.

In the baseline simulated group, this strategy improved the modeled long-run growth rate relative to MTD therapy for 70.4% of patients. The average modeled benefit was 5.8%; the paper also reports an average detriment of 2.0%, with a maximum detriment of 8.6%. Under one parameter constraint, the share helped rose to 99.9%, and the average benefit to 25.9%, while the maximum detriment was 5.4%. These numbers describe outcomes inside the model, not people treated in a clinical study. They show how assumptions about plausible drug effects can change the performance of a robust compromise.

Share of virtual patients helped by a best-on-average schedule

Label	Value
Baseline	70.4 %
Reversion effect at least half baseline rate	96.3 %
Tolerance effect capped at 10× baseline	100 %
Both dose sensitivities above 1	86.7 %
Both above 1; reversion effect at least half baseline	99.9 %

• Baseline 70.4 %
• Reversion effect at least half baseline rate 96.3 %
• Tolerance effect capped at 10× baseline 100 %
• Both dose sensitivities above 1 86.7 %
• Both above 1; reversion effect at least half baseline 99.9 %

Model-generated virtual-patient results; not observed clinical outcomes.

Average modeled benefit of the robust schedule

Label	Value
Baseline	5.8 %
Reversion effect at least half baseline rate	16.7 %
Tolerance effect capped at 10× baseline	18.6 %
Both dose sensitivities above 1	9.2 %
Both above 1; reversion effect at least half baseline	25.9 %

• Baseline 5.8 %
• Reversion effect at least half baseline rate 16.7 %
• Tolerance effect capped at 10× baseline 18.6 %
• Both dose sensitivities above 1 9.2 %
• Both above 1; reversion effect at least half baseline 25.9 %

Values are reported by the paper; outcomes are simulated, not clinical.

Why This Changes Things

The study helps explain why different dosing strategies can each look sensible in different cancers—or even in different tumors exposed to the same drug. If a treatment induces tolerance at relatively low doses, a large dose increase may bring little additional harm through that pathway. If tolerance rises with dose in the same range as cell killing, then pushing the dose can trade faster killing for more persister formation. The same logic applies in reverse to reversion: a drug-free interval may help if it lets tolerant cells become sensitive again, but can be less useful if the crucial reversion effect happens at low drug exposure.

That is a more mechanistic framework than the simple contest between “high dose” and “low dose.” It asks which dose-response curve moves first. Measuring the relationship between cell death and state switching could reveal whether an intermittent schedule or a lower continuous dose is worth testing. Recent experimental work cited by Gunnarsson found that targeted drugs can induce persister states in colorectal cancer cells, and that this effect varies between cell lines (Russo et al., 2024 as cited in the paper). The model’s premise is therefore tied to an active experimental question, not a claim that all tumors behave alike.

The robust-strategy result matters because precision medicine often asks for more data than a clinic can readily collect. A patient-specific “digital twin” needs reliable estimates of that person’s tumor dynamics. If a simple compromise performs reasonably well across a broad range of plausible parameters, researchers might have a way to prioritize candidate schedules before a full individualized model is possible. But “best on average” is not the same as safest or best for each patient. The baseline simulation itself leaves a minority worse off, making the size and distribution of detriment clinically important alongside the average gain.

The analysis also has implications beyond cancer. The authors note that drug-induced persistence can occur in bacteria, fungi, and other microbes. In those settings, a treatment can also alter the composition or state of a population while selecting which cells survive. The specific biological mechanisms and acceptable schedules differ, but the general lesson travels: treatment can change the future responsiveness of survivors, not merely their number today.

What the model does not show is that a lower dose or a drug holiday will improve outcomes in patients. It does not incorporate the full effects of drug concentrations over time, toxicity, immune responses, tumor evolution across many cell types, or the practical realities of treatment. Its long-run growth rate is a useful comparison metric, but real outcomes include tumor shrinkage, relapse, survival, quality of life, and adverse effects. Those are not interchangeable.

What’s Next

The next step is experimental measurement. Researchers need to estimate, at multiple doses, how quickly sensitive cells die, enter a tolerant state, and return from it. Longitudinal experiments can test whether those rates follow the different dose-response shapes the model assumes—and whether an apparent low-dose advantage persists when treatment cycles have realistic lengths. The study’s sharp transition near a sensitivity ratio of one gives experiments a specific prediction to challenge.

Patient-derived tumor organoids and other individualized cell models could eventually make this kind of dosing analysis more practical. Such systems can expose a patient’s tumor cells to a range of doses and schedules, helping estimate whether tolerance adoption or blocked reversion is the more important effect. But organoids do not reproduce a whole patient, and any proposed schedule would still need careful testing for safety and clinical benefit.

The most useful conclusion is therefore modest, but consequential: the dose that kills the most sensitive cells immediately may not always be the dose that best controls the population over time. By distinguishing cell killing from the drug’s effects on reversible persistence, Gunnarsson’s model gives researchers a map of which schedules to investigate—and a reason to measure how tumors adapt before assuming that maximum exposure is always optimal.