Synergistic Drug Combinations Promote the Development of Resistance in Acute Myeloid Leukemia

Combination therapy is a mainstay of cancer treatment, with many patients receiving multidrug regimens. Historically, combination therapy has shown great benefits over monotherapy in hematologic malignancies (1), and is becoming common for the treatment of solid tumors as well. Combination therapy was initially developed with the intention of reducing the emergence of drug-resistant tumor cells as combining therapies with different mechanisms of action decreases drug resistance and kills a higher proportion of tumor cells (1, 2). More recent preclinical studies focus on mechanistically explicit rationales for combination therapy, including overcoming or preventing acquired drug resistance and enhancing activity through synergistic drug interactions (3–5). With many approved anticancer agents and a plethora of investigational drugs, methods are needed to prioritize combinations that will produce meaningful clinical outcomes based on preclinical data. There are many examples of large preclinical screening efforts aimed at identifying novel drug combinations, often using drug synergy as a metric to identify combinations of interest (3–5); however, there are limitations to the utility of synergy.

Synergy can be defined using several different models, including Loewe, Chou–Talalay, or Bliss models. In each model, synergy is defined as greater activity than would be expected from the drugs’ monotherapy effects, with the calculation of the expected activity differing between the models (6). When drug synergy allows for higher efficacy than would be achievable with an additive or antagonistic combination, such as when one or both agents in a combination lack considerable monotherapy activity, there is inherent benefit to drug synergy (7). However, recent evidence demonstrates that clinical success of combination therapy in oncology does not require drug synergy, and in fact many clinically successful combination therapies show no evidence of synergy (8, 9). With a disconnect between preclinical combination screening strategies and studies investigating properties of clinically successful drug combinations, there is ongoing debate about what role drug synergy should play in identifying and prioritizing drug combinations in preclinical studies of cancer therapy (2, 4, 5, 8–10).

An extensive body of research on antibiotic combinations has found that synergistic drug interactions can accelerate the development of drug resistance in bacteria (11–14). Experiments and theory have shown that this arises because resistance to one or both drugs in a synergistic combination also diminishes the synergistic interaction, resulting in a particularly large loss of activity (11) as shown in Fig. 1A. Consequently, the fitness benefit of resistance can be higher when cells are exposed to a synergistic combination, resulting in faster evolution of resistance (7, 11). Recent mathematical modeling has predicted that the same phenomenon could also apply to anticancer combination therapy (7). These models demonstrate that when equal initial efficacy was achieved through either synergistic or nonsynergistic combinations, synergistic combinations accelerated resistance development. Synergistic interactions may involve complex trade-offs, with short-term improvements in efficacy at the cost of durability.

In this study, we aim to experimentally investigate whether drug synergy promotes the development of resistance to combination therapy in cancer cells, and how the fitness benefit of resistance differs between synergistic and additive combinations. Understanding the role synergy plays in driving the evolution of drug resistance has important implications for how combinations are prioritized in the preclinical space, advancing the goal of identifying therapeutic regimens that are likely to translate into not only highly active, and but also durable treatments.

To study the relationship between synergy and drug resistance in cancer cells, we adapted an experimental framework previously applied in bacteria (11). Duplicate plates of cancer cells were exposed to two-dimensional concentration gradients. One plate was used to measure inhibitory activity and drug–drug interactions at 72 hours, whereas the second plate was monitored for changes in growth rate and the emergence of drug resistance (Fig. 1B). We characterized the activity and drug–drug interactions for six different drug pairs in two acute myeloid leukemia (AML) cell lines, MOLM-13 and OCI-AML2 (Fig. 1C and D; Supplementary Fig. S1A–S1G). Given the importance of monotherapy activity in clinically effective combinations (9, 15), all combinations were composed of agents with cytotoxic monotherapy activity including two agents approved for the treatment of AML, venetoclax and cytarabine, and two investigational agents, AZD5991 and AZD1775, which inhibit MCL-1 and WEE1, respectively. Monotherapy and combination activity were highly concordant between biological replicates [Supplementary Fig. S1B; synergy was measured by calculating the excess activity over the Bliss or Loewe models of additivity (6), henceforth referred to as excess Bliss or excess Loewe], with large excess Bliss or excess Loewe indicating drug synergy (Fig. 1D; Supplementary Fig. S1D, S1E, and S1G). Synergy was highly concordant across both models (Supplementary Fig. S1H). Synergy was demonstrated by three combinations: venetoclax + AZD5991, venetoclax + cytarabine, and cytarabine + AZD1775; the remaining three combinations demonstrate additive effects (Fig. 1E; Supplementary Fig. S1D, S1E, and S1G). Across the six tested combinations, a wide range of both activity and degrees of synergy were captured (Supplementary Fig. S1I and S1J).

Resistance development was measured by calculating changes in growth rate over 21 days of drug exposure (Fig. 1B). In a subset of combination-treated conditions, we observed initial inhibition of growth rate followed by an increase in growth rate late in the experimental time course that we interpret to indicate the development of resistance. Figure 2A and B and Supplementary Fig. S2A show representative curves and images of an untreated well (DMSO only), a well treated with a low-activity combination dose, and a well treated with a highly cytotoxic combination dose in which resistance developed. Cells in the untreated and low activity wells reached peak growth rate during the first 72 hours of growth before reaching the carrying capacity of the wells. Cells in the high activity well have a delayed peak in growth rate. Given that the compounds are still active after exposure to 37°C media for 21 days (Supplementary Fig. S2B), similarly to previous studies (11), we interpret this delayed peak in growth rate to indicate that the cells have adapted to growing conditions and become resistant to the treatment. We measured the growth rate over time for cells treated across the combination dosing matrix with each combination in our study (Fig. 2C). In some drug combinations (venetoclax + AZD5991, cytarabine + venetoclax, cytarabine + AZD5991, and venetoclax + AZD1775) there was a subset of conditions where cells grew out after significant delay, indicating the acquisition of drug resistance (Fig. 2C).

To understand the role drug synergy plays on the development of resistance, the growth rate curves for all combinations shown in Fig. 2C were binned on the basis of excess Bliss and activity scores (Fig. 3A). We identified resistance as the presence of a delayed peak in growth rate, such as those demonstrated in Figs. 1B and 2A. Because previous work has shown that synergy accelerates resistance compared with equally active nonsynergistic combinations (7), we focused on the likelihood of resistance at fixed bands of activity. We focused on a medium activity band that represents treatment effects where the combination has measurable initial activity but is unable to fully eliminate cells, corresponding to a partial response in the clinical setting. Within the medium activity band, the proportion of wells that developed resistance increased as the excess Bliss score increased, from 3 of 14 (21%) conditions when excess Bliss scores were low (<10), to 3 of 8 (38%) conditions when excess Bliss scores were high (>50). We observed that there were nonsynergistic conditions where resistance developed, but when synergy was present the proportion of conditions where resistance developed increased (Fisher exact P = 0.0091).

To determine whether synergy was a predictor of resistance development when controlling for activity, we used a logistic regression to model the relationship between synergy, activity, and likelihood of resistance (Fig. 3B). Across biological replicates, using activity and excess Bliss as predictive variables, an increase in excess Bliss score was consistently predictive of increased likelihood of developing resistance (n = 150/replicate, Wald test replicate 1: P = 0.0011, replicate 2: P = 0.0023).

Observations over 3 weeks of cell culture may be confounded by depletion of nutrients or drugs, and we therefore repeated our experiments with fresh media and drug added every 7 days (Supplementary Fig. S3A and S3B). Logistic regression showed that synergy was still predictive of the development of resistance, confirming that late peaks in growth are a result of drug resistance, rather than the depletion of drug concentrations (Supplementary Fig. S3C, Wald test P = 8.46e-5). We confirmed the significant relationship between synergy and the development of resistance is not a unique feature of MOLM-13 cells by repeating in a second cell line, OCI-AML2 (Fig. 3C; Supplementary Fig. S3D and S3E, Wald test P = 0.0066). Thus, these experiments show that synergistic drug interactions are associated with an increased likelihood of developing resistance within 3 weeks of initial inhibitory effect.

To measure the magnitudes of fitness benefit exhibited by emerging drug-resistant cells, we calculated the difference between the maximum and initial growth rates (first 48 hours). This growth rate difference represents the difference between the activity of the combination on naïve cells and the activity of the combination after cells developed resistance (or a preexisting subpopulation has emerged; Fig. 3D; Supplementary Fig. S3F). Across all conditions in which cells were able to grow during drug exposure, the fitness benefit of resistance was significantly correlated with drug synergy (Fig. 3E; Pearson R = 0.71, P = 1.6 × 10⁻⁶, n = 35). Because there is stochasticity in the development of resistance, magnitudes of fitness benefit varied between biological replicates, but the correlation between excess Bliss and fitness benefit was maintained across independent replicates (Supplementary Fig. S3G and S3H). Furthermore, the relationship between fitness benefit and synergy was also maintained when synergy was quantified using the Loewe method (Supplementary Fig. S3I; Pearson R = 0.65, P = 2.7 × 10⁻⁵, n = 35). In experiments with MOLM-13 and OCI-AML2 where drug and media were replenished every 7 days there was a similar trend toward a relationship between fitness benefit and excess Bliss score, although it did not reach significance (Supplementary Fig. S3J and S3K), likely due to the noise in growth rate measurements introduced by media changes.

To confirm drug resistance developed in the conditions exhibiting a delayed peak in growth rate (Fig. 3A), cells were isolated at the end of the experiment and expanded to measure response to monotherapies and combination therapies. Each of the resistant cell lines developed combination resistance differently, with some becoming primarily resistant to one drug, and some becoming partially resistant to both drugs (Supplementary Fig. S4A and S4B). For each surviving culture we calculated the relative drug sensitivity to either monotherapy or combination therapy (Supplementary Fig. S4C). Cultures isolated from conditions with delayed growth peaks exhibited a significant decrease in relative drug sensitivity (Supplementary Fig. S4C and S4D), confirming the development of resistance.

To understand the relationship between synergy and the fitness benefit of drug resistance, we developed a mathematical model of synergy and resistance in a population undergoing exponential growth. We analyzed growth rates without a carrying capacity, to isolate the influence of drug synergy on fitness without the confounding effects of resource limitation. Carrying capacities do influence growth in reality, but saturation of growth halts dynamics and interferes with measurements of relative fitness across scenarios. A population of cancer cells was modeled with the majority of cells being sensitive to drug and a minority subpopulation that is partially resistant to one drug. The fitness benefit of drug resistance was calculated as the difference between final and initial growth rates (Fig. 4A), similar to our experimental analyses. The growth rates of each population depended on the strength of synergy and the drug doses (Eqs. (A)–(C) in the model). Using this model, we tested whether the fitness benefit of resistance increases as the degree of synergy between drugs increases. In simulated isobolograms, the fitness benefit of having partial resistance to one drug in a combination increases as synergy increases (Supplementary Fig. S5A) supporting the hypothesis that synergistic combinations create a stronger evolutionary advantage for cells with drug resistance. We used this model to simulate changes in fitness benefit across ranges of drug concentrations and found that increasing synergy increases fitness benefit within a single simulated dosing matrix with moderate synergistic interaction (Fig. 4B). We next calculated the median fitness benefit of resistance across a dosing matrix, and observed that median fitness benefit also increases with the strength of the synergistic interaction (Fig. 4C). The fitness of drug-resistant mutants can also be affected by drug cross-resistance or collateral sensitivity, where resistance to one drug increases or decreases resistance to a second drug, respectively. Modeling such effects showed that cross-resistance and synergistic interaction have similar consequences for the evolution of drug resistance, because in either case, gaining resistance to one drug allows a cell to substantially evade the effect of a drug combination (Supplementary Fig. S5B and S5C). This echoes the recent findings of Gjini and Wood (16) who showed that both drug interactions and collateral resistance effects determine the trajectory of resistance evolution. Together, this simple model of cell growth and drug resistance demonstrates an inherent relationship between drug synergy and fitness benefit of drug resistance, agnostic of specific drug mechanisms.

Data from both patient-derived tumor xenografts (PDX) and human clinical trials demonstrate that strong initial responses, which may arise from synergistic drug combinations, are not necessarily related to durability of response. In a database of thousands of drug-treated PDXs, containing more than 250 unique tumors exposed to 62 different treatments (17), among tumors with a drug response the initial rate of tumor shrinkage was not positively correlated with durability of response (Fig. 4D). This demonstrates that short-term efficacy and durability of response are distinct features of tumors’ drug responses in vivo. We next analyzed a phase III clinical trial in high-risk AML that compared the standard cytarabine and daunorubicin regimen (“7+3”) to a liposomal formulation of the same drugs (CPX-351) that uses a concentration ratio shown to act synergistically in vitro, whereas at their usual concentration ratio these drugs act additively (18). This trial offered a compelling test of our hypothesis because the same drugs were present in both treatment arms, removing many variables except for whether the concentration ratio of two drugs elicits an additive or synergistic effect. To understand how the risk of disease progression changes over time, we analyzed the ratio of cumulative hazards for event-free survival (EFS), which is a time-dependent metric, whereas HR assumes a constant benefit at all times. The ratio of cumulative hazards showed that the benefit of CPX-351 over 7+3 is strongest immediately after commencing therapy, and begins to fade as early as 3 months thereafter, reaching near-identical EFS as 7+3 by 12 months (Fig. 4E). This trial demonstrated a significant benefit of CPX-351 over 7+3, and shows that if all other variables are constant—including monotherapy activities—synergy provides benefits, though they may not be robust to the emergence of drug resistance. Consistent with cell culture and PDX studies, this trial provides clinical evidence that initial efficacy and durability are distinct features of tumor drug response.

In this study, we investigated whether synergistic drug combinations promote resistance in cancer cells, as previously shown in bacteria and predicted by computational models (7, 11, 12). Our experiments show a significant relationship between drug synergy and the likelihood of developing resistance and magnitude of fitness benefit associated with resistance. These results have important implications for the preclinical prioritization of drug combinations and the interpretation of synergy as a metric.

Combination therapy continues to be a valuable element of cancer treatment in the era of targeted therapies (1, 19, 20). Currently, preclinical strategies to identify new drug combinations often prioritize synergy (3–5); however, this approach may have drawbacks. First, synergy metrics do not assess absolute efficacy, therefore, synergy scores can prioritize combinations of drugs with little or no monotherapy activity, resulting in technically synergistic but weak treatments. This is a significant concern because synergy is most often observed among weak drugs (10). Second, synergy metrics are generally based on short-term assays and do not reveal response durability. Therefore, including other metrics, such as overall efficacy and durability of response may enhance the translational relevance of preclinical data.

The current data, supported by prior experiments and models (7, 11, 21, 22), suggest that combination strategies depending solely on synergy may compromise durability of response. In a synergistic combination, drugs depend on each other's activity to maximize effect; small losses in sensitivity to either component drug therefore produce a larger loss in sensitivity to the combination (Fig. 1A). This means that modest resistance to a single drug produces a large fitness benefit (Fig. 3D; Supplementary Fig. S5A), speeding the emergence of drug resistance. We emphasize that our study investigated the fitness advantage of drug resistant cells, which affects their emergence from a minority subpopulation, and did not study mutation rates or initial creation of drug resistant states. Drug resistance may be created by genetic or epigenetic changes, and may be preexisting or develop under therapy. Whether or how the initial creation of drug resistance is affected by combination therapy is a yet underexplored question, although the form of treatment logically cannot change the generation of preexisting heterogeneity. Because our findings are based on the phenotypic result of drug resistance and drug interactions, we anticipate that the core findings could apply to either preexisting or de novo drug resistance. Controlling for activity and synergy scores demonstrates a tradeoff between durability, synergy, and initial combination activity. When prioritizing potential combination partners based on synergy alone, high synergy combination must produce very high initial activity to overcome the increased likelihood of resistance (Fig. 3B).

These findings do not suggest there is no role for synergy. Instead, they support a proposal by Saputra and Tucker-Kellogg to sequentially use synergistic and nonsynergistic combinations as offensive and defensive strategies (8, 22). That is, high-activity synergistic combinations could be used to initially shrink tumor burden, followed by combinations of independently effective agents to eradicate remaining disease while decreasing the likelihood that resistance could develop against all distinct therapies in the combination. This strategy could enjoy the initial benefits of synergy while avoiding its possible disadvantages in durability. There are additional nuances to be explored in the clinical setting. In a clinical scenario where resistance develops after commencing therapy, initially strong response could confer the advantage of reducing cell divisions, thereby lowering the probability of resistance emergence. Conversely, in scenarios where drug resistance is preexisting, then it may be more desirable for a drug combination to minimize the fitness of preexisting drug-resistant cells.

This study does not measure absolute probabilities of resistance to these treatments but measures the likelihoods of observing resistance in this experimental design. These experiments cannot detect resistance developing later than the experimental duration, nor resistance developing to conditions with little initial efficacy (clinically this scenario would be considered intrinsic not acquired resistance). Our findings are supported by a simple computational model that removes the impact of carrying capacity. Carrying capacity may influence competitive dynamics, as shown by studies on adaptive therapy for solid tumors. We did not elect to investigate these phenomena for the purpose of simplicity, and because blood cancers in vivo are commonly fatal before approaching carrying capacity. However, experiments with a carrying capacity, and computational models without, both show the relationship between synergy and evolution of resistance.

While analysis of a database of thousands of PDXs demonstrated that strong initial responses are not predictive of durable responses (Fig. 4D), future work should explore the specific linkage of synergy and resistance in vivo, ideally in low-passage PDX models, which retain clinically relevant heterogeneity. It has previously been shown that AML cell proliferation in animal models corresponds well to in vitro doubling times, suggesting that our observations are not an artifact of rapid cell division in vitro (23). However, PDX studies could more comprehensively explore the roles of clonal heterogeneity, microenvironment, and nonconstant drug exposures. We anticipate that the general principles described in Fig. 1A can qualitatively apply to either in vitro or in vivo models.

While the relation between drug synergy and resistance is broadly relevant, we focused on AML using agents which all exhibit monotherapy activity and are of current clinical interest in AML (20, 24, 25). This includes targeted agents and chemotherapy, synergistic combinations acting in the same pathway (venetoclax and AZD5991), and synergistic combinations acting in different pathways (cytarabine combined with venetoclax or AZD1775). In future studies, it would be interesting to expand this approach to other indications and drug combinations. Given that the experimental dataset includes a variety of combinations, and the computational models are agnostic of disease biology, we also anticipate that the relationship between synergy and resistance observed in AML may be present in other treatment contexts.

Together, these data have important implications for how to prioritize combinations in oncology. We have shown that synergistic drug combinations, while potentially useful to achieve high efficacy, contribute to the evolutionary pressure to develop drug resistance. Therefore, to identify regimens that produce durable clinical response, preclinical assessments of drug combinations should consider metrics beyond synergy, such as monotherapy activity, overall combination activity, and durability of response.

MOLM-13 cells (male) were acquired from DSMZ, OCI-AML2 cells (male) were acquired from ATCC. Cells were validated by short tandem repeat fingerprinting and monitored for Mycoplasma contamination by RT-PCR. MOLM-13 cells were cultured in RPMI1640 medium containing 15% FBS, and 1× GlutaMAX supplement. OCI-AML2 cells were cultured in α-minimum essential medium containing nucleosides, 10% FBS, and 1× GlutaMAX supplement. All media were supplemented with penicillin/streptomycin for long-term growth assays. Cells were maintained at 37°C, 5% CO₂. Cells were kept in culture for 1 to 3 months.

White-walled/white bottom 384-well plates were dosed with given concentrations of compounds or vehicle (DMSO). Sixty microliters of cell suspension was added to each well, with cell concentrations being previously optimized. MOLM-13 cells were seeded 2,400 cells/well, OCI-AML2 were seeded 4,500 cells/well. Cells were seeded in a separate plate and analyzed immediately using Cell Titer Glo after seeding to use as a day 0 control.

CellTiter Glo reagent was reconstituted according to manufacturer's recommendations. Thirty microliters of CellTiter Glo reagent was added to each well, and allowed to incubate at room temperature in the dark for 10–15 minutes. Luminescence was measured using BioTek Synergy Neo2.

After 3-day incubation, 30 μL of CellTiter Glo reagent was added to each well of the treated plates. Plates were incubated at room temperature in the dark for 10 to 15 minutes, and then luminescence was measured using BioTek Synergy Neo2.

Drug activity was assessed with readouts at day 0 and day 3 to differentiate between cytostatic and cytotoxic effects. Data normalization, curve fitting, and synergy calculations were done using GeneData Screener software. Briefly, luminescence measurements were normalized following the NCI-60 methodology (26), rescaling to a 0 to 200 scale, with activity of 0 equaling no activity (DMSO control), activity of 100 being equaling stasis (day 0 controls), and activity of 200 equaling full cell killing. Expected activity scores were calculated using either the Loewe model or Bliss model (6, 27). Excess synergy scores were calculated by measuring the difference between the expected additive values (derived from either Loewe or Bliss models) and the observed activity values.

Black walled/clear bottom 384-well plates were dosed with given concentrations of compounds. Sixty microliters of cell suspension was added to each well, with cell concentrations being previously optimized. MOLM-13 cells were seeded 2,400 cells/well, OCI-AML2 were seeded 4,500 cells/well. Plates were placed in Incucyte S3 and set to image the full well every 6 hours. For redosing experiments, every 7 days plate was spun down for 3 minutes, 30 μL of media was removed through aspiration and replaced with 30 μL of fresh dosed media containing penicillin/streptomycin. After dosing, plates were placed back in Incucyte S3 to continue imaging. Confluence mapping was done on the phase images through the Incucyte Basic Analyser. Raw data was exported from Incucyte software and analyzed in Rstudio.

Confluence data from the Incucyte phase images was analyzed using Rstudio. Confluence values were log-transformed. Initial growth rate was calculated by performing a linear regression of log-transformed confluence curves from 24 to 72 hours (8 data points). Growth rate over time was calculated by taking a rolling linear regression of the log-transformed confluence values for the duration of the experiment. Rolling linear regression analysis used a 48-hour window (8 data points) for each linear regression calculation. In experiments where cells were redosed every 7 days, we excluded growth rate analysis in the 18-hour interval after each redosing event to minimize the introduction of noise into the growth rate curves caused by nutrient introduction and cell loss. Resistance was identified by the presence of a delayed peak in growth rate, defined by the presence of an increase in growth rate that occurs after 125 hours.

Maximum growth rate was calculated by identifying the maximum values from the growth rate over time curves derived from the rolling linear regression. Initial growth rate was calculated from the linear regression of log-transformed growth curves during the first 48 hours. In some cases, there was a growth rate nadir observed outside of the first 72 hours of the assay, likely due to delayed kinetics of the combination activity (Supplementary Fig. S3F). In these cases, fitness benefit was measured by calculating the difference between the maximum growth and the local nadir observed in the growth rate, as we interpreted this nadir to be a result of the initial activity of the combination (Supplementary Fig. S3F).

Resistant cell lines were isolated from long-term growth assay plates. Wells with evidence of resistance development were identified and cells were moved from 384-well plate into 24-well plate to expand in drug free media until there were sufficient cells to perform viability assay. Parental cells that had been in long term culture (>3 weeks, MOLM-13-long) were assayed in viability assays at the same time as the resistant cell lines to control for the effects of long-term cell culture. The difference in drug sensitivity between untreated (MOLM-13-long) and treated cultures was quantified by rescaling the measured dose–response of the treated culture (translation along an axis of log(concentration)) to find the shift in potency that minimizes the sum of square errors between the dose–response functions of the untreated and treated cultures.

In the mathematical model 0.08% of an initial population of 2,400 cells are modeled to be resistant to drug A, and 0.08% are modeled to be resistant to drug B. The remainder of the cells are sensitive to both drugs. Effective combination drug doses for each of the three populations are calculated using the following equations where x_A is the effective dose of drug A, x_B is the effective dose of drug B, and s is the strength of synergy.

Cells resistant to drug A have an effective combination drug dose of x_aB and cells resistant to drug B have an effective drug dose of x_Ab. In both cases, resistant cells are modeled as having a 50% decrease in drug potency (see Supplementary Fig. S5A). Drug effective doses are scaled such that a potency of 0 is equivalent to uninhibited growth, a potency of 100 is equivalent to growth arrest, and a potency of 200 is equivalent to less than one of the initial 2400 cells surviving.

In simulations, the fitness benefit is calculated as the difference between the final and initial slopes of the growth curve on a log scale. The initial slope is the growth rate of the sensitive cells, and the final slope is the growth rate of the most drug-resistant cells.

Checkerboards were simulated by taking a grid of 25 effective doses from 0 (uninhibited growth) to 100 (growth arrest) of drug A and 25 effective doses from 0 to 100 of drug B and calculating the combination effective dose for sensitive cells, drug A–resistant cells, and drug B–resistant cells at each point on the checkerboard. Exponential growth (or death for effective doses higher than 100) was then simulated for each population.

Where t is time in arbitrary units, N_AB is the number of sensitive cells and |${N}_{A{B}_0}$| is the initial number of sensitive cells (2396) and |${r}_{AB} = {r}_0 - \frac{{{r}_0}}{{100}}{x}_{AB}$| [Eq. (G)] such that the growth rate is the uninhibited growth rate r₀ when x_AB is zero and −r₀ when x_AB is 200. A value of r₀ = 1 is used in the model.

Excess Bliss is calculated in the model as x_AB minus the expected x_AB if s is equal to zero (no synergy).

In Supplementary Fig. S5, collateral effects are modeled as a range from cross resistance (collateral effect = −1), where a decrease in sensitivity to one drug results in the same magnitude of decreases in sensitivity to the other drug, to collateral sensitivity (collateral effect = 1), where a decrease in sensitivity to one drug results in the same magnitude of increase in sensitivity to the other drug.

Kinetics of approximately 4,500 in vivo tumor drug responses were obtained from Supplementary Table S1 of Gao and colleagues (17). To smooth day-to-day experimental error, each tumor's trajectory of volume v over time t was fitted to the regression–growth equation of Stein and colleagues (28): v(t) = exp(d⋅t) + exp(g⋅t) - 1. For all tumors that “responded” to treatment, defined by ≥30% reduction in volume, we used fitted kinetics v(t) to calculate time to tumor volume doubling, and the fastest rate of shrinkage exhibited at any time, quantified as change in log₁₀(v) per day (for example, 0.3 corresponds to halving volume in one day).

EFS distributions of 7+3 (n = 156 patients) and CPX-351 (n = 153 patients) were digitized from Fig. 2B of Lancet and colleagues (18), using DigitizeIt. EFS curves were fitted to a 100-degree spline; using a high degree closely tracks the curve (within 0.5%) but smooths individual patient events, which is needed to differentiate EFS(t). For both experimental and control EFS curves, hazard function h(t) was calculated as |$ - \frac{{d\,{\rm{EFS}}(t)}}{{dt}}$|/EFS(t), and cumulative hazard function H(t) was |$\int_{0}^{t}{{h(\tau )d\tau }}$|⁠. Ratio of cumulative hazards was H_experimental(t)/H_control(t).

All code used for this simulation and to make Fig. 4 and Supplementary Fig. S5 is available at https://github.com/palmerlabunc/synergy-resistance and https://codeocean.com/capsule/4719393/tree.

E. Mason-Osann reports other support from AstraZeneca outside the submitted work. A.E. Pomeroy reports grants from NIH during the conduct of the study and personal fees from Repiratorius AB outside the submitted work. A.C. Palmer reports grants from Prelude Therapeutics, personal fees from Merck, Sanofi, and Novartis, and personal fees from AstraZeneca outside the submitted work. J.T. Mettetal reports other support from AstraZeneca during the conduct of the study. No other disclosures were reported.

E. Mason-Osann: Conceptualization, formal analysis, validation, investigation, visualization, methodology, writing–original draft, writing–review and editing. A.E. Pomeroy: Software, formal analysis, investigation, methodology, writing–original draft, writing–review and editing. A.C. Palmer: Conceptualization, supervision, methodology, writing–review and editing. J.T. Mettetal: Conceptualization, supervision, funding acquisition, writing–review and editing.

We would like to thank the AstraZeneca Postdoc Programme, especially Alison Darke, for administrative support. We thank Lisa Drew and Steve Fawell for departmental support and encouraging broader discussion on the use of combinations in cancer. We would like to thank Mark O'Connor and Michael White for support with compounds and pharmacology. We thank Alan Rosen for technical support with combination dosing studies. We also thank Ultan McDermott, Art Schaffer, Alwin Schuller, Andrew Bloecher, Courtney Andersen, and the Palmer lab for scientific discussion and guidance throughout the project. This work was supported by AstraZeneca, the V Foundation for Cancer Research (V2020–010, to A.C. Palmer), and National Institute of General Medical Sciences grant K12-GM000678 (to A.E. Pomeroy).

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