Growth rate inhibition metrics correct for confounders in measuring sensitivity to cancer drugs

Abstract

Drug sensitivity and resistance are conventionally quantified by IC50 or Emax values, but these metrics are highly sensitive to the number of divisions taking place over the course of a response assay. The dependency of IC50 and Emax on division rate creates artefactual correlations between genotype and drug sensitivity, while obscuring valuable biological insights and interfering with biomarker discovery. We derive alternative small molecule drug-response metrics that are insensitive to division number. These are based on estimation of the magnitude of drug-induced growth rate inhibition (GR) using endpoint or time-course assays. We show that GR50 and GRmax are superior to conventional metrics for assessing the effects of small molecule drugs in dividing cells. Moreover, adopting GR metrics requires only modest changes in experimental protocols. We expect GR metrics to improve the study of cell signaling and growth using small molecules and biologics and to facilitate the discovery of drug-response biomarkers and the identification of drugs effective against specific patient-derived tumor cells.

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Figure 1: Modeling drug response and the dependence of drug-response metrics on division time (Td, values given in days).
Figure 2: GR values are independent of both the length of the assay and the division time.
Figure 3: Evaluation of GR metrics in a high-throughput dataset.
Figure 4: Plating density affects division rate and drug sensitivity.
Figure 5: Time-dependent GR metrics reveal diverse mechanisms of drug sensitivity and resistance.

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Acknowledgements

This work was funded by grants U54-HL127365 and P50-GM107618 to P.K.S. and by a fellowship from the Swiss National Science Foundation (P300P3_147876) to M.H. We thank M. Soumillon for expression profiling, J. Chen (Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, USA) for the modified RPE-1 cells and A. Palmer, M. Eisenstein, and G. Berriz for help with the manuscript.

Author information

M.H., M.N., and P.K.S. conceived this study and wrote the paper. M.N., M.C., and M.H. performed the experiments; M.H. conceived GR metrics and performed the computational analyses.

Correspondence to Peter K Sorger.

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Competing interests

The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Modeling drug response and dependence of drug response metrics on division time.

(a-b) Simulated data showing relative cell count (green lines) and GR value (purple lines) for a partial cytostatic (a) or cytotoxic (b); see Online Methods for parameter values. The darker the line the longer the division time (Td, given in days, see legend); note that all GR curves overlap. IC50 and GR50 are projected onto the x-axis, Emax and GRmax onto the y-axis. The subsequent three columns show values of IC50 and GR50 (left), Emax and GRmax (middle), and AUC and GRAOC (right) computed from a theoretical three-day assay with cells dividing at different rates under the same drug response models. (c) Values of AUC and GRAOC for a 3 day assay over a range of division times, with drug response model corresponding to Fig. 1g.

Supplementary Figure 2 Modeling toxic drug response and dependence of drug response metrics on division time.

(a-c) Simulated data showing relative cell count (green lines) and GR value (purple lines) for partial toxic effect (a), mixed toxic and cytostatic effects (b), or a strong toxic effect (c); see Online Methods for parameter values. The darker the line the longer the division time (Td,, given in days, see legend); note that all GR curves overlap. IC50 and GR50 are projected onto the x-axis, Emax and GRmax onto the y-axis. The subsequent three columns show values of IC50 and GR50 (left), Emax and GRmax (middle), and AUC and GRAOC (right) computed from a theoretical three-day assay with cells dividing at different rates under the same drug response models..

Supplementary Figure 3 GR values are independent of the length of the assay and the division time.

(a) Relative cell count (left) and GR values (right) were evaluated for hTERT RPE-1 cells expressing BRAFV600E under the control of a DOX-regulated promoter 48 h after treatment with etoposide. Color intensity reflects the concentration of DOX used to stimulate BRAFV600E expression. (b) Relative cell count (left) and GR values (right) were evaluated for MCF 10A cells grown in serum-free media with different levels of EGF 59 h after treatment with etoposide. Color intensity reflects treatments with different concentrations of EGF. (c) Evaluation of relative cell count (top) and GR values (bottom) for a drug concentration close to the GR50 value (left) and computed response metrics at different time points (middle and right) as estimated from live-cell imaging of BT-20 cells exposed to one of five drugs with different mechanisms of action. Data shown are from one of two biological replicates.

Supplementary Figure 4 Evaluation of GR metrics in a high-throughput data set.

(a) Values of IC50 and GR50 (left) and Emax and GRmax (right) for cell cycle drugs evaluated by Heiser et al. Black lines show the median for a given number of divisions, color intensity reflects density of the data points. Undefined and large IC50 and GR50 values are capped at 100 μM for illustration purposes. (b) Values of IC50 and GR50 (left) and Emax and GRmax (right) for 20,000 models of drug response with randomized parameters and numbers of divisions. Black lines show the median for a given number of divisions, color intensity reflects density. Undefined and large IC50 and GR50 values are capped at 30 μM for illustration purposes. (c) Distribution of IC50 and GR50 (left) as well as Emax and GRmax (right) for paclitaxel response in cells grouped by subtype: HER2-amplified (HER2amp), triple-negative breast cancer (TNBC), hormone receptor-positive (HR+), and non-malignant (NM).

Supplementary Figure 5 Plating density affects division rate and drug sensitivity.

Spearman’s correlation between IC50 (top left), Emax (top right), GR50 (bottom left), or GRmax (bottom right) and number of divisions for six breast cancer cell lines. Data derive from an experiment in which cells were plated at a range of six densities and treated with eleven drugs having diverse mechanisms of action (see Online Methods and Supplementary Data 2). Significance: * for p<0.05, ** for p<0.01, and *** for p<0.001.

Supplementary Figure 6 Plating density affects cellular state.

(a) Enriched gene sets for genes on the first principal component of transcriptional data from MCF 10A cells collected at different densities, 2 and 3 days after plating. Only genes in the leading edge of sets enriched at high density and late time points with FDR<0.1 are shown. Yellow represents up-regulation and blue down-regulation. Conditions are ordered by interpolated cell number (left column). (b) PCA projection of transcriptional data from MCF 10A cells collected at different densities, 2 and 3 days after plating. Shapes, day of collection; size, seeding density; color, interpolated cell number at time of collection. Axis labels include the Spearman’s correlation value between the cell number and the PCA coordinate.

Supplementary Figure 7 Drug response is affected by cell number and culture volume.

GR value dose-response curves for MCF 10A cells seeded at different densities (indicated by color intensity) and treated with a dilution series of methotrexate for 3 days (left). Error bars are the SEM from three biological replicates. GR dose-response curves at 3 days for MCF 10A treated with oligomycin with a constant number of seeded cells in different volumes of media in each well (right). Data shown are from one of two biological replicates.

Supplementary Figure 8 Example of dose-response curves and corresponding metrics.

(a) Curve with negative GRmax value corresponds to a cytotoxic response (cell death). (b) Curve with GRmax value converging to 0 corresponds to a cytostatic response (no growth). (c) Curve with positive GRmax value corresponds to a partial growth inhibition; GR50 is not defined as GRinf is above 0.5. (d) Noisy, weak response for which the sigmoidal fit is not significantly better than a flat fit, and thus GEC50 is set to 0 and GR50 is not defined. Hill slope, hGR, is defined in all but the last case, whereas the area over the curve (GRAOC) can always be calculated.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–8 and Supplementary Note (PDF 1505 kb)

Supplementary Data 1

GR values and metrics computed from the drug-response data publishedin Heiser et al. (2012) (ZIP 2201 kb)

Supplementary Data 2

GR values and metrics for the drug-response data collected across different densities (ZIP 175 kb)

Supplementary Software

Source code for computing GR metrics. (ZIP 5 kb)

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Hafner, M., Niepel, M., Chung, M. et al. Growth rate inhibition metrics correct for confounders in measuring sensitivity to cancer drugs. Nat Methods 13, 521–527 (2016). https://doi.org/10.1038/nmeth.3853

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