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

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1 Growt rate inibition metrics correct for confounders in measuring sensitivity to cancer drugs Marc Hafner,, Mario Niepel,, Mirra Cung & Peter K Sorger 6 Nature America, Inc. All rigts reserved. Drug sensitivity and resistance are conventionally quantified by IC 5 or values, but tese metrics are igly sensitive to te number of divisions taking place over te course of a response assay. Te dependency of IC 5 and on division rate creates artefactual correlations between genotype and drug sensitivity, wile obscuring valuable biological insigts and interfering wit biomarker discovery. We derive alternative small molecule drug-response metrics tat are insensitive to division number. Tese are based on estimation of te magnitude of drug-induced growt rate inibition () using endpoint or time-course assays. We sow tat 5 and max are superior to conventional metrics for assessing te effects of small molecule drugs in dividing cells. Moreover, adopting metrics requires only modest canges in experimental protocols. We expect metrics to improve te study of cell signaling and growt using small molecules and biologics and to facilitate te discovery of drug-response biomarkers and te identification of drugs effective against specific patient-derived tumor cells. Te quantification of drug response is fundamental to te discovery of terapeutic molecules, te investigation of teir mecanisms of action, and te study of signal transduction, cell division, and oter biological processes using cemical biology approaces 4,5. In te case of anticancer drugs, cells are typically exposed to drugs over a range of concentrations, and te number of viable cells (or surrogates, suc as ATP level assayed using CellTiter-Glo, CTG) is measured several days later. Data comprising cell counts in te presence of drug divided by counts for untreated controls are fitted to a sigmoidal curve to compute (i) te concentration of drug at wic te cell count is alf te control (IC 5 ), (ii) te fraction of viable cells at te igest drug concentration ( ), and (iii) te area under te dose response curve (AUC) 6,7. Dose response and genomic datasets are often combined to discover drug-response biomarkers,8,9, but it as recently been found tat large-scale drug-response data vary from one study to te next for reasons tat remain poorly understood. We sow ere tat, for dividing cells, traditional drugresponse metrics suc as IC 5 suffer from a fundamental flaw wen tey are estimated from cell counts made at te end of te experiment (te standard approac): if control cells undergo different numbers of divisions during te course of an assay because of natural differences in proliferation rate, variation in growt conditions, or canges in te duration of an experiment, IC 5,, and AUC values will vary dramatically, independently of any canges in te underlying biology. Tus, biomarkers tat predict sensitivity under one (potentially arbitrary) set of assay conditions may not predict sensitivity under sligtly different conditions. We terefore propose a new metod for parameterizing drug response, te normalized growt rate inibition (), wic is based on te comparison of growt rates in te presence and absence of drug. Parameterization of data yields 5, max, AOC, and (Hill slope), values tat are largely independent of cell division rate and assay duration (we use area over te curve, AOC, rater tan AUC for reasons discussed in Online Metods). metrics can be determined wit modest canges in experimental procedures, and we propose tat tese metrics replace IC 5 and values in assessing cellular response to drugs, RNAi, and oter perturbations in wic control cells divide over te course of te assay. RESULTS Definition of normalized growt rate inibition () We used computer simulation to model te drug response of tree idealized cell lines wit identical sensitivity to a cytostatic drug (i.e., a drug tat arrests but does not kill cells) and different division times (T d =.8,.4, or.9 d). Tese division times correspond to te lower quartile, median, and upper quartile for breast cancer cell lines and are similar to te division times of NCI-6 cells 4. In te slowly dividing cell line (T d =.9 d), te total number of cells did not double in an assay typically run over days, and tus was.5, and IC 5 was undefined. In te case of te two faster-growing cell lines, IC 5 and values fell as division rate increased (Fig. a) because cell number (or CTG value) was normalized to a drug-naïve control in wic cell number increased as division time fell (compare curves across panels of Fig. a). We can compensate for te confounding effects of division rate on drug-response measurements by computing te value at time t in te presence of drug at concentration c: k( c, t)/ k( ) ( c, t) = HMS LINCS Center Laboratory of Systems Parmacology, Department of Systems Biology, Harvard Medical Scool, Boston, Massacusetts, USA. Tese autors contributed equally to tis work. Correspondence sould be addressed to P.K.S. (peter_sorger@ms.arvard.edu). Received October 5; accepted April 6; publised online May 6; doi:.8/nmet.85 nature metods ADVANCE ONLINE PUBLICATION

2 6 Nature America, Inc. All rigts reserved. Figure Modeling drug response and te dependence of drug-response metrics on division time (T d, values given in days). (a) Simulation of a simple drug-response model yields relative cell counts across a concentration range for a cytostatic drug for a slow- (left), medium- (middle), and fast-growing cell line (rigt). Black lines correspond to untreated control samples and red lines denote 5% growt inibition. Black marks sow were IC 5 and are evaluated. n/a, not applicable. a.u., arbitrary units. (b d) Metods for evaluating value: (b) conceptual approac based on growt rates (k and k(c)), (c) fixedinterval approac based eiter on cell number at te start (x ) and end of te experiment (x ctrl and x(c)) and (d) time-dependent value based on cell count before and after a time interval t (x(c,t ± t)). (e) Simulated data sowing relative cell count (green lines) and value (purple lines) for a cytostatic drug assayed over d. Te darker te line, te longer te division time (given in days; see key below); note tat all curves overlap. IC 5 and 5 are projected onto te x-axis; and max are projected onto te y-axis. (f) IC 5 or (green) and 5 or max (purple) computed from a teoretical -day assay for cells wit division time ranging from to 4 d; vertical line sows T d =.4 d (AUC and AOC values in Supplementary Fig. c). Cell count normalized to t = count were k(c,t) is te growt rate of drug-treated cells and k() is te growt rate of untreated control cells (Fig. b). Te value is simply te ratio between growt rates under treated and untreated conditions normalized to a single cell division. Te sign of te value relates directly to response penotype: it lies between and in te case of partial growt inibition, it equals in te case of complete cytostasis, and it lies between and in te case of cell deat. Given values for a range of drug concentrations, 5 is te concentration at wic (c) =.5, max is te maximal measured value, and is te slope of te sigmoidal fit; AOC is calculated by integrating te curve over a range of concentrations (Online Metods). In practice, values can be estimated from endpoint measurement of cell number in treated and untreated samples, given te initial cell number (Fig. c; tis is related to te procedure for GI 5 determination, see Supplementary Note). Alternatively, te doubling time for untreated cells can be measured under te same conditions in parallel experiments and used in place of te initial cell number (Online Metods). A time-dependent value can be evaluated given cell count measurements at two or more time points. Time-dependent values capture adaptive responses, varying kinetics of drug target interaction, drug efflux, etc. (Fig. d). Introducing time as a variable makes it possible to relate drug-induced canges in cell states to dynamic measures of drug response at a molecular level (equations for all calculations are provided in Online Metods wit links to scripts). To compare dose response curves to conventional curves, we created syntetic data for cells tat ad T d ranging from to 4 d and tat were exposed to a drug tat was partially cytostatic, fully cytostasic, or cytotoxic (models are described in Online a Cell count normalized to t = count Relative cell count.5. IC 5..5 IC 5 = n/a.5.5 = Slow (T d =.9) Untreated Treated 7 (c) = k(c)/k() IC Cytostatic response... Concentration (a.u.) Untreated Treated 7 log (c) = (x(c)/x )/log (x ctrl /x ) 5 max... Concentration (a.u.) IC x ctrl x(c) x Untreated Treated Metods). For all tree drugs, IC 5 and values were strongly correlated wit division time and assay duration, but tis was not true of corresponding metrics (Fig. e,f; Supplementary Fig. a,b; and Online Metods). In te case of drugs tat kill cells rapidly and independently of cell cycle state, max still varies wit growt rate, and time-dependent values are preferable (Supplementary Fig. and Online Metods). AUC combines IC 5 or data and is less sensitive to experimental noise,6,, but it suffers from te same dependence on cell division time; AOC corrects for tis (Supplementary Fig. c). metrics are robust to experimental variability To study ow canging cell division affects IC 5 values, we expressed BRAF V6E in TERT-immortalized retinal pigment epitelial (RPE) cells and ten exposed tem to etoposide, a topoisomerase II inibitor tat as a cytostatic effect in RPE cells (and wose mecanism of action is independent of BRAF). Oncogene overexpression is known to slow te growt of nontransformed cells 5,6, and expression of BRAF V6E in RPE cells under te control of a doxycycline-inducible promoter was observed to increase division time tree-fold as te doxycycline concentration increased from to 6 nm. Under tese conditions te estimated IC 5 value for etoposide increased -fold and increased from.5 to.6 (Fig. a and Supplementary Fig. a). In contrast, 5 and max values varied only sligtly under tese conditions because te effects of etoposide per cell division were uncanged. In a second experiment, we measured etoposide sensitivity in MCF A cells grown in serum-free medium supplemented wit different concentrations of epidermal growt factor (EGF)...75 IC 5.5 t 7 x(,t + t) x(,t t) x(c,t + t) x(c,t t) log (x(c,t + t)/x(c,t t)) (c,t) = log (x(,t + t)/x(,t t)) t Cell count relative to endpoint From growt rates From cell numbers Time-dependent value exp(t k()) Medium (T d =.4) IC 5 =. = at drug concentration c b c d e T d exp(t k(c)) f IC 5 and 5 (a.u.) Fast (T d =.8) IC 5 =.4 = Cytostatic response IC 5, and max , max. Concentration (a.u.). 4 4 T d T d ADVANCE ONLINE PUBLICATION nature metods

3 6 Nature America, Inc. All rigts reserved. Figure values are independent of bot te lengt of te assay and te division time. (a) Effect of altering T d of TERT RPE- cells on metrics of etoposide sensitivity. Relationsip between T d and doxycycline (DOX) concentration (left) to cells expressing BRAF V6E under te control of a DOX-regulated promoter. Values for IC 5 and 5 (middle) and and max (rigt) were evaluated at 48 at different concentrations of DOX. Large and undefined values for IC 5 were set at µm for purposes of illustration. (b) Effect of altering T d of MCF A cells on metrics of etoposide sensitivity. Relationsip between T d and concentration of EGF in serum-free medium (left). Values for IC 5 and 5 (middle) and and max (rigt) were evaluated at 59 at different concentrations of EGF in serum-free medium. Large and undefined values for IC 5 were set at µm for purposes of illustration. (c) Evaluation of relative cell count (top) and values (bottom) for a drug concentration close to te 5 value (left) and computed response metrics at different time points (middle and rigt), as estimated from live-cell imaging of MCF A cells exposed to one of five drugs wit different mecanisms of action. (d) Time-dependent values estimated over 8- intervals for MCF A cells grown as speroids treated wit omipalisib (left) and corresponding time-dependent 5 values (rigt). Dased line sows te 5 value evaluated at 9. In all panels, te data sown derive from one of tree biological replicates. Te division time of MCF A cells varied from > d at. ng ml EGF to < d at ng ml EGF (Fig. c). Across tis range, IC 5 and for etoposide were substantially more variable tan 5 or max values (Fig. b and Supplementary Fig. b). Tus, potentially arbitrary and unintended differences in cell culture conditions can lead to large variation in IC 5 and values tat is unlikely to ave a biological basis. To test te approac in a typical small-scale drug sensitivity screen, we exposed MCF A and BT- cells (expressing HBmCerry to facilitate automated cell counting) to five different drugs cosen for diverse mecanisms of action. We measured cell number approximately every 8 over d using an automated microscope. Estimated IC 5 and values converged only after tree divisions (~6 ), wereas metrics stabilized by te first division (< for MCF A and ~6 for BT-; Fig. c and Supplementary Fig. c). Tis confirms tat metrics are substantially less dependent on assay duration tan are IC 5 and. In te case of very slow and uneven growt (by primary uman tumor cells, for example), te stabilization of values witin one cell division is likely to be a real advantage in obtaining reliable estimates of drug sensitivity. Wen grown in D culture, MCF A cells are known to adapt to inibitors of PIK and mtor (suc as omipalisib), becoming less sensitive over time 7. Endpoint measures of drug sensitivity a b c Relative cell count No. of divisions T d T d RPE- cells 6 6 DOX (nm) MCF A cells.... EGF (ng/ml) Time of assay () Tanespimycin - HSP9 (. µm) d Time-dependent IC 5 and 5 (µm) IC 5 and 5 (µm)... Fold cange from 7 Fold cange from 7 >.... >. Etoposide sensitivity... IC 5 5 Etoposide - topiosomerase (. µm) Omipalisib over time Omipalisib (µm) DOX (nm) Etoposide sensitivity IC EGF (ng/ml) No. of divisions 4 Cange in IC Cange in Time of assay () Omipalisib - panpik (. µm) Time-dependent 5 (nm) interval No. of divisions do not report on suc adaptive responses. However, wen we monitored speroids by live-cell imaging, we observed tat te time-dependent and 5 values were lowest ~ after omipalisib addition, and tey increased ~-fold by day 4 (Fig. d); endpoint 5 values lay midway in tis range (Fig. d). Tus, time-dependent data directly capture te decreasing effectiveness of omipalisib in MCF A speroids, enabling detection and furter analysis of adaptive mecanisms. Analysis of ig-trougput data using metrics Te majority of large-scale drug-response datasets publised to date neiter report cell division rates nor allow one to estimate tem. An exception is a study by Heiser et al., wic recorded cell numbers for breast cancer cell lines before and after exposure to a panel of anticancer drugs for days. For many drugs in tis dataset, IC 5 correlates wit division rate 6 (e.g., for cell cycle inibitors, regression coefficient of.54, Spearman s P-value < 66, N =,956; difference from 7 max difference from Linsitinib - IGFR ( µm) Omipalisib 5 over time 9 endpoint Etoposide sensitivity max DOX (nm) Etoposide sensitivity.... EGF (ng/ml).5 max Cange in 4 Cange in max Time of assay () PLX47 - BRAF ( µm) max max nature metods ADVANCE ONLINE PUBLICATION

4 6 Nature America, Inc. All rigts reserved. Figure Evaluation of metrics in a ig-trougput dataset. (a,b) Fitted dose response curves for (a) relative cell count and (b) values for paclitaxel in breast cancer cell lines (-day assay data from Heiser et al. ). Red denotes cytotoxic response and blue denotes cytostatic response; darker curves denote cell lines wit fewer divisions. Marginal distributions (below and to te rigt of te dose response plots) sow te relation between estimated IC 5 or 5 and or max values and number of divisions for tat line over d; ρ-values are Spearman s correlation coefficients. (c) Number of divisions over d for cell lines in te dataset grouped by subtype: HER-amplified (HER amp ), triplenegative breast cancer (TNBC), ormone receptor positive (HR + ), and nonmalignant (NM). (d,e) Distribution of IC 5 (green) and 5 (purple) for all drugs in Heiser et al. (d) or for ErbB inibitors only (e) grouped by clinical subtype. P-values were derived from a rank-sum test for IC 5 or 5 values for NM cell (d) or for HER amp cell lines (e) versus all oter subtypes. Supplementary Fig. 4a). However, we could reproduce tis correlation by using an idealized model tat does not assume any biological connection between drug sensitivity and division rate and by repeatedly simulating drug responses using random parameters (Supplementary Fig. 4b and Online Metods). Tis finding suggests tat te correlation between drug sensitivity and division rate found in experimental data is spurious; also, te correlation was absent wen drug response was measured using 5 (Spearman s P-value =., Supplementary Data ), suggesting tat it is an artifact of te way IC 5 is calculated. Paclitaxel, a taxane microtubule inibitor widely used in cemoterapy, is one drug tat exibits a strong negative correlation between sensitivity and division rate as well as substantial variation (-fold) in IC 5 across cell lines (Fig. a). Tis relationsip as previously been described and is tougt to arise because paclitaxel acts primarily on mitotic cells, and te faster a cell line divides, te more likely it is to be in mitosis 8,9. However, reanalysis of data in Heiser et al. sows tat 5 values for paclitaxel actually span a narrow range centered around nm (Fig. b and Supplementary Fig. 4c), close to te estimated affinity of paclitaxel for assembled microtubules in vitro. In contrast, max values for paclitaxel vary considerably across cell lines and subtypes. In HER-amplified (HER amp ) and triple-negative breast cancer (TNBC) lines max values are negative, wic is indicative of a cytotoxic response, wereas ormone receptorpositive (HR + ) and nonmalignant lines generally exibit cytostatic responses (Supplementary Fig. 4c). Tis is consistent wit data sowing tat HER amp and TNBC (basal-like) uman tumors are more taxane-sensitive tan tumors in oter types of breast cancer. We propose tat future attempts to find biomarkers Relative cell count No. of divisions in d No. of divisions c a No. of Paclitaxel relative cell count divisions IC 5 (µm) Division rate by subtype HER amp TNBC HR + NM =.66 d IC 5 and 5 (µm) =.6 >.. HER amp TNBC HR + predictive of paclitaxel response focus on variation in max rater tan variation in IC 5,. Te average division rate of breast cancer cell lines in culture differs wit clinical subtype: among cells studied by Heiser et al., HR + and HER amp subtypes divided most slowly (median T d =. d), TNBC cells divided faster (median T d =. d), and nonmalignant cells divided still faster (median T d =.8 d, Fig. c). As measured by IC 5 values, nonmalignant cells were, on average, more sensitive to anticancer drugs tan tumor cells, wereas 5 values sowed tat te mean and range of drug sensitivity was similar (Fig. d). Focusing on HER amp lines, IC 5 values for inibitors of EGFR and ErbB were similar across breast cancer subtypes, even toug HER amp uman tumors are preferentially sensitive to suc drugs and ErbB inibitors are frontline terapy for tis disease 4,5. 5 data for HER amp cell lines in Heiser et al. sow tat tis subtype of breast cancer is ~-fold more sensitive tan oter subtypes to EGFR/ErbB inibitors in vitro (Fig. e; P =. 4 ). Te failure of IC 5 values to sow te preferential sensitivity of HER amp cell lines to EGFR/ErbB inibitors arises because teir relatively slow growt rate is a idden confounder in IC 5 calculation. From tese data we conclude tat artefactual dependency of IC 5 on cell division rate creates associations were none exist and also obscures meaningful associations between genotype and drug sensitivity. b No. of divisions P =.69 Potency for all drugs P =.4 NM Paclitaxel =.... e IC 5 and 5 (µm) IC 5 5 (µm) >.. HER amp P =.7 No. of divisions =.4 max ErbB inibitor potency 5 P =.9 4 TNBC HR + NM a MCFA HS578T MDAMB MCF7 SKBR BT MCFA HS578T MDAMB MCF7 SKBR BT Spearman's correlation wit seeding number IC 5 *.4.4 Correlation 5 * *.4.4 Correlation MCFA ** HS578T MDAMB MCF7 SKBR BT.4.4 MCFA HS578T MDAMB MCF7 SKBR BT Correlation max *.4.4 Correlation b No. of divisions in d ,5,5 5, Seeding number BT MCFA MDAMB HS578T MCF7 SKBR Figure 4 Plating density affects division rate and drug sensitivity. (a) Spearman s correlation between estimated values for IC 5,, 5, and max and seeding number for te six breast cancer cell lines sown. Data derive from an experiment in wic cells were plated at a range of six densities and treated wit drugs aving diverse mecanisms of action (Online Metods and Supplementary Data ). Significance: *P <.5, **P <., P <.. (b) Relationsip between seeding number and te number of divisions in d. Error bars are te s.e.m. of five to nine biological replicates. 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5 6 Nature America, Inc. All rigts reserved. Figure 5 Time-dependent metrics reveal diverse mecanisms of drug sensitivity and resistance. Evaluation of tree selected drugs for wic seeding density ad a significant effect on values in MCF A cells based on data summarized in Figure 4. (a) Influence of ratio of cell number to medium volume for two drugs related to metabolism. Timedependent values for MCF A cells at different seeding numbers following exposure to. µm metotrexate (left). Time-dependent 5 values for MCF A cells for metotrexate or oligomycin (middle); values are capped at µm for illustration purposes. dose response curves at d for MCF A treated wit metotrexate wit a constant number of seeded cells but in different volumes of medium (rigt). Data sown derive from one of two biological replicates. (b) Medium conditioning and adaptive resistance to linsitinib, an IGFR inibitor. dose response curves at d for MCF A treated wit linsitinib at different cell densities (left). Error bars are te s.e.m. of tree biological replicates. Time-dependent values for MCF A at different seeding numbers following exposure to µm linsitinib in te absence (middle) or presence (rigt) of µm batimastat, a matrix metalloproteinase inibitor. Data sown are from one of tree biological replicates. (c) Paclitaxel-induced cytostasis at low cell density and apoptosis at ig cell density. values for MCF A cells seeded at different densities and treated wit paclitaxel for d (left). Error bars are te s.e.m. of tree biological replicates. Fraction of MCF Linsitinib (µm) Effects of cell density on drug sensitivity metrics allow us to quantify ow drug sensitivity canges in te face of variables tat affect division rate. One suc variable is seeding density: increasing density as widely been reported to promote drug resistance 6 9. To investigate tis, we cultured six breast cell lines representative of different subtypes at six seeding densities over a -fold range. 4 after plating, cells were exposed to drugs wit diverse mecanisms of action. Growt rates, IC 5,, and metrics were estimated by imaging and counting fixed cells at te time of drug addition and 7 after treatment (Supplementary Data ). Overall, IC 5 and correlated positively wit seeding number for MCF A, MDA-MB-, and Hs 578T cells, and tey correlated negatively for BT- and SK-BR- cells (P <., Fig. 4a). In te first tree cell lines, division rate decreased wit density, presumably because of contact inibition, depletion of essential medium components, and oter effects (Fig. 4b). In BT- and SK-BR- cells, division rate increased wit density, presumably because of conditioning of te growt medium,. Correlations between density and IC 5 and were weakest for MCF7 cells, wic grew equally well across all densities. Tus, te effect of density on number of divisions, and consequently on IC 5 and, varied dramatically among cell lines (Supplementary Fig. 5a). However, only a small number of cell line drug pairs exibited a statistically significant association a b c Time-dependent Metotrexate,. µm 4 6 Linsitinib dose response 56 65,5,5 5, 56 Seeding number 65,5... Paclitaxel dose response Paclitaxel (µm) 56 65,5,5 5, Time-dependent 5 (µm) Time-dependent Fraction of ccasp- positive cells Metabolic inibitor 5 over time Metotrexate Oligomycin µm linsitinib, no batimastat Seeding number 56 65, Paclitaxel,. µm ,5 Seeding density,5 5, between plating density and 5 or max values. We wondered weter tese were situations in wic te biology of drug response was altered by density. In MCF A cells, six drugs were associated wit significant variation in 5 or max (or bot) across seeding densities; RNA-seq revealed tat gene expression in tese cells also varied wit cell density, wit significant enricment for genes involved in catabolic processes, cellular respiration, and wounding responses,4 (Supplementary Fig. 6a). Wen te data was analyzed by principal-component analysis, te first principal component (wic captured % of variance) was strongly correlated wit te number of cells at te time of collection (Spearman s ρ =.98) and less so wit time in culture (ρ =.57), suggesting tat te cell density at te time of assay and not te istory of te culture was te primary determinant of transcriptional state (Supplementary Fig. 6b). Follow-up studies wit metotrexate sowed tat te ratio between cell number and medium volume, and not cell density per se, was te key variable for sensitivity to tis drug (tis was also true of oligomycin, an inibitor of ATP syntase; Fig. 5a and Supplementary Fig. 7); since cells grew in a constant volume of medium, 5 was terefore time dependent. Density- (and time-) dependent variation in 5 were also observed for linsitinib, an IGFR inibitor currently in Pase II clinical trials (Fig. 5b). Variation in 5 wit time and density was reduced by cotreatment wit te metalloprotease inibitor Time-dependent Time-dependent max Metotrexate dose response Metotrexate (µm) µm linsitinib, µm batimastat.4. Seeding number 56 65,5 56 µl 4 µl 6 µl 8 µl µl µl Paclitaxel max over time 65,5 Seeding number A cells positive for cleaved caspase- at different time points and cell densities following exposure to. µm paclitaxel (middle). Time-dependent max values for paclitaxel in MCF A cells seeded at different densities (rigt). Data sown are from one of two biological replicates. nature metods ADVANCE ONLINE PUBLICATION 5

6 6 Nature America, Inc. All rigts reserved. batimastat, suggesting a role for autocrine conditioning of te microenvironment in drug response. In te case of paclitaxel, 5 values remained at ~5 nm across plating densities, but max was strongly density dependent, varying from ~ (cytostatic) at low cell densities to negative values (cytotoxic) at iger densities (Fig. 5c, left). Time-dependent max reaced its greatest negative value at 4, concomitant wit an increase in te fraction of taxol-treated cells tat contain cleaved caspase-, confirming tat negative max values corresponded to elevated apoptosis (Fig. 5c, middle and rigt). Toug its molecular basis is unknown, tis effect may be one reason for te discrepancy between cell-killing dynamics in low-density culture and in ig-density xenograft tumors 5. DISCUSSION Accurate measurement of drug sensitivity and resistance is te cornerstone of cancer biology, parmacology, and of many fundamental studies on cell signaling and cell division. In tis paper we demonstrate teoretically and experimentally tat variation in division rate seriously confounds existing drug-response metrics. We also sow tat division rate varies wit cell type, medium composition, and seeding density, often in unpredictable ways. Cell division rate slows down in some cell lines as density increases, wile it speeds up in oters. Suc variation can cange apparent IC 5 -fold or more and terefore introduce artificial correlations in data, obscure te true effects of drug action, and introduce unknown complications into biomarker discovery. As an alternative, we propose metrics tat are computed by comparing growt rates in te presence and absence of drug. 5 and max are robust to variation in cell division rate and sould replace IC 5 and in studies in wic control cells divide (including te study of drugs, gene depletion or overexpression, and variation in te extracellular environment). 5 quantifies te potency of a drug on a per-division basis, ensuring tat fastand slow-growing cells wit similar biocemical responses to drug are scored equivalently. max captures te maximal drug effect on growt rate and differs from in tat it falls between and, were negative values denote cell deat, denotes cytostasis, and positive values denote partial inibition. AOC and values can also be calculated from curves; te former is often te most robust metric in te face of experimental noise, and te latter quantifies an important relationsip between dose and response tat is often neglected 6. In te simplest version of our metod, metrics are computed after measuring cell number or a surrogate (e.g., CTG value) before and after exposure of a culture to varying concentrations of drug or oter perturbation for a fixed time (Fig. c). Wen cell division rates under similar culture conditions are known from previous data, only te final cell number is needed (altoug we believe tat before and after data on cell number are a valuable control to ensure data quality). Time-course data make it possible to compute time-dependent values and to quantify penomena suc as delayed response, drug adaptation, or variation in te kinetics of drug target interaction (Fig. d). To facilitate te use of metrics by oters we provide MATLAB and pyton routines and an online calculator (ttp://www. grcalculator.org/). Moreover, te data in tis paper, including te 5 and max values for te Heiser et al. dataset, are available online (ttp://lincs.ms.arvard.edu/). Large-scale drug-response studies based on existing response metrics,,8,9 are discrepant for poorly understood reasons 5,,, raising concerns about te value of drug-response biomarkers. We speculate tat comparison of datasets across centers (or even witin a center) migt be confounded by differences in plating density, growt medium, and oter factors tat affect cell division rate. It migt be possible to correct for tis in existing data by computing values post facto, but tis will require recreating te original assay conditions and ten measuring division rates. Based on te results in tis paper, we believe tat use of metrics in lieu of traditional IC 5,, or AUC values will improve our ability to identify genes and biological processes responsible for drug sensitivity and resistance. metrics decouple any effect tat genotype or microenvironment ave on division rate from teir effect on drug sensitivity. Cell biology studies involving te modification of genes or te microenvironment often result in canges in cell division rate, leading to potentially spurious correlations wit drug sensitivity (as illustrated ere by oncogene overexpression and canges in EGF levels), and sould also benefit from te use of metrics. By analogy wit antimicrobial susceptibility testing for bacterial infections, it as recently been suggested tat cancer terapy migt be personalized by screening primary uman tumor cells against panels of drugs 6,7. Suc cells grow slowly and unevenly in culture, making division number a poorly controlled variable. Accounting for suc differences using metrics sould create drug-response data tat are more reproducible and useful for optimizing patient terapy. Metods Metods and any associated references are available in te online version of te paper. Accession codes. Data are deposited in te Gene Expression Omnibus (GEO) database wit accession number GSE897. Note: Any Supplementary Information and Source Data files are available in te online version of te paper. Acknowledgments Tis work was funded by grants U54-HL765 and P5-GM768 to P.K.S. and by a fellowsip from te Swiss National Science Foundation (PP_47876) to M.H. We tank M. Soumillon for expression profiling, J. Cen (Department of Systems Biology, Harvard Medical Scool, Boston, Massacusetts, USA) for te modified RPE- cells and A. Palmer, M. Eisenstein, and G. Berriz for elp wit te manuscript. AUTHOR CONTRIBUTIONS M.H., M.N., and P.K.S. conceived tis study and wrote te paper. M.N., M.C., and M.H. performed te experiments; M.H. conceived metrics and performed te computational analyses. COMPETING FINANCIAL INTERESTS Te autors declare no competing financial interests. Reprints and permissions information is available online at ttp:// com/reprints/index.tml.. Barretina, J. et al. Te Cancer Cell Line Encyclopedia enables predictive modelling of anticancer drug sensitivity. 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8 ONLINE METHODS Metrics of drug response. Determining relative cell counts. Cell counts in te presence of drug are normalized to DMSO-treated controls grown on te same plate under te same conditions. In te current study, relevant conditions include seeding density, te concentration of exogenous growt factors (e.g., EGF in te case of MCF A cells), and te concentration of a second drug suc as doxycycline or batimastat. For eac cell line, drug, and drug concentration, we define te relative cell count as x(c)/x ctrl, were x(c) is te count in te presence of drug at concentration c and x ctrl is te 5%-trimmed mean of te count for control cells. Tecnical replicates are averaged to yield an average relative cell count. We typically collect data from tree tecnical replicates (on tree separate plates). : te Hill coefficient of te fitted curve, wic reflects ow steep te dose response curve is. In practice, we typically constrain to a value between. and 5. GEC 5 : te concentration at alf-maximal effect. To avoid artefacts in curve fitting we constrain GEC 5 to be two orders of magnitude iger and lower tan te experimentally tested concentration range (in practice, tis is usually about 5 to µm). If te fit of te curve is not significantly better tan tat of a flat curve (i.e., (c) inf ) based on an F-test wit cutoff of P =.5, te response is considered flat and te parameter GEC 5 is set to (Supplementary Fig. 8d). 6 Nature America, Inc. All rigts reserved. Calculating values using endpoint drug-response data. Normalized growt rate inibition is calculated according to te formula: log ( x( c)/ x) log ( xctrl / x) ( c) = (Fig. c), were x(c) and x ctrl are as described above, and x is te 5%-trimmed mean of te cell count from a sample grown in parallel and measured just prior to drug exposure. Alternatively, te untreated division time T d = ln()/k() can be measured in independent experiments and used in place of te initial cell number (x = x ctrl T/T d): log ( x( c) xctrl ) + / T / T ( c) = d, were T is te duration of te assay. Calculating time-dependent values. values can be evaluated over a time interval ( t) around any time point t based on te equation: ( ) log x( c, t+ t)/ x( c, t t) log x(, t + t)/ x(, t t) ( c, t) ( = ) (Fig. d). Inferred drug-response metrics. Te 5 value is te concentration of drug at wic (c = 5 ) =.5. If te value for inf is above.5, te 5 value is not defined and is terefore set to + (Supplementary Fig. 8c). By extension, oter tresolds can be defined in a similar manner. For example, corresponds to te concentration at wic a drug is fully cytostatic: (c = ) =. Te max is te maximum effect of te drug at te igest tested concentration, and it lies between and ; a value of corresponds to a fully cytostatic response, and a negative value corresponds to a cytotoxic response. max can be estimated from te fitted curve or obtained directly from experimental data; we often do te latter. For time course data, all metrics are evaluated at eac time point individually. Area under te curve and over te curve ( AOC ). Anoter common metric for quantifying dose response data is te area under te response curve (AUC), wic is based on integrating te dose response curve over te range of tested concentrations. In te case of curves, wic can ave negative values, it is more intuitive to use te area over te curve: AOC = ( ) ( ) c dc ci, c i Te time-dependent values in te current paper were computed wit t = to 8, wic corresponds to about alf a cell division time. Curve fitting and estimating drug-response metrics. data are fitted to a sigmoidal curve as follows (Supplementary Fig. 8b): ( c) = inf inf + + ( c/ GEC ) 5 were te fitted parameters are: inf : te effect of te drug at infinite concentration ( inf (c )). inf lies between and ; negative values correspond to cytotoxic responses (i.e., induction of cell deat, Supplementary Fig. 8a), a value of corresponds to a fully cytostatic response (Supplementary Fig. 8b), and a positive value corresponds to partial growt inibition (Supplementary Fig. 8c). were (c i ) are measured values at discrete concentrations c i. AOC as te benefit tat, in te case of no response, it as a value of. Te AOC can be normalized to te range of concentrations as, for example, AOC /log (c max /c min ), were c max and c min are te igest and lowest tested concentrations. It is important to note tat AOC values (like conventional AUC) sould only be used to compare responses evaluated across te same drug concentration range. Te AOC value captures variation in potency and efficacy at te same time. Te calculation of AOC at discrete (experimentally determined) concentrations as te advantage tat it does not require curve fitting and is terefore free of fitting artifacts. Tis is especially useful for assays were fewer tan five concentrations are measured, and curve fitting is unreliable. AOC values are also more robust to experimental noise tan metrics derived from curve fitting; max values are particularly sensitive to outlier values wen directly obtained from data. nature metods doi:.8/nmet.85

9 6 Nature America, Inc. All rigts reserved. Drug concentration range. Te drug concentrations used for fitting drug-response curves need to span a sufficiently wide range and ave sufficiently intermediate values in order to obtain reliable estimates for GEC 5,, and inf. Denser sampling provides more precise estimates, especially in te case of steep dose response curves. Optimal design of dose response curves as been discussed elsewere 7. In practice, we suggest using nine doses spanning four orders of magnitude from nm to µm. Tis range can be sifted to lower concentrations for more potent drugs or to iger concentrations for less potent drugs wit te caveat tat AOC values for different drugs sould be compared only if evaluated over te same concentration range. We suggest discarding any 5 value tat is more tan an order of magnitude above te igest tested concentration because values extrapolated from te fitted curves are more subject to fitting artefacts tan interpolated values. Similarly, inf value is not properly constrained if te (c) dose response curve does not reac a plateau at te igest measured concentration. In suc cases, AOC is te most reliable metric. Computing metrics. Source code for computing metrics is provided (Supplementary Software). To facilitate te computation of metrics we provide updated source code available under an open source software license and MATLAB and pyton scripts at ttps://gitub.com/sorgerlab/gr5_tools. We also provide an online calculator at ttp:// Tis website contains a user guide, various tutorials and explanatory materials, and example datasets, including all of te data in te current manuscript. Teoretical model of drug response. To simulate te effect of division time on and conventional drug-response metrics under different assumptions about te degree of cytostasis or cell killing, we developed a teoretical model of drug response. To te first approximation, cell growt can be considered exponential, wit drugs eiter decreasing te division rate or killing cells in a cell-cycle-dependent manner: Integrating tese equations for an assay of t days yields te cell count at concentration c: S c k c M L x( c, t) = x exp t k t SC5 + c LC5 + c, were x x(t = ) is te cell number at te time of treatment. Tus, te relative cell count is: M IC c t x c t xctrl exp t k S c kl c (, ) = (, )/ = t, SC5 + c LC5 + c were xctrl x (, t ), and te normalized growt rate inibition ( value) is: SM c log x( c, t)/ x k L c x SC log c t ctrl / x (, ) ( ) = 5 = + c k LC + c 5. Tis equation for (c) is independent of te lengt of te assay t and, tus, te metrics 5, max, AUC, and are also independent of t. For cases were drug action is mainly related to te cell cycle (k L = ), values are also independent of te untreated growt rate k. As sown in Supplementary Figures and a,b, te impact of k L > is minimal on 5 and relatively small on max. Tis is also illustrated by te analytical formula for inf : inf = ^( S M k L /k). Note tat te metrics derived from growt inibition (GI) values used in Heiser et al., suc as GI 5, are more robust tan traditional metrics, but tey still depend on bot division time and assay lengt (see Supplementary Note). Parameters for simulations in figure panels. Model parameters used in te numerical simulations sown in te main and supplemental figures (Fig. b; Supplementary Figs.,, and 7) were as follows: S c M x = x k, SC5 + c were x is te cell count, k is te untreated growt rate (per day), c is te drug concentration, S M is te maximal inibitory effect, SC 5 is te concentration at alf-maximal effect of drug, and is te Hill coefficient. Te growt rate k corresponds to te division rate k as k = ln() k = ln()/t d, were T d is te division time. S M can be larger tan to account for drugs inducing cell deat at a specific pase of te cell cycle. Te model can also be generalized to account for drugs tat induce cell deat independent of te cell cycle: S c k c M L x = x k x, SC5 + c LC5 + c were k L is te maximal killing rate (per day) and LC 5 is te concentration of drug tat produces alf-maximal cell killing. Cytostatic: S M =, S 5 =.5, T M =, =.6 Partial response: S M =.65, S 5 =., T M =, =.6 Cytotoxic: S M =.6, S 5 =, T M =, =.6 Partial toxic response: S M =.45, S 5 =., T M =.5, T 5 = 5, =.6 Mixed response: S M =.65, S 5 =., T M =., T 5 =, =.6 Complete cytotoxic: S M =.6, S 5 =., T M =, T 5 =, =.6 For Supplementary Figure b, te parameters were randomly sampled witin te following distribution: Division rate k: normal distribution around.9 divisions per day wit s.d. of.46 and a lower bound of.4 Hill coefficient : uniform distribution between.5 and.5 Maximum inibition S M : uniform distribution between and Half inibition concentration S 5 : log-uniform distribution ranging from. to doi:.8/nmet.85 nature metods

10 6 Nature America, Inc. All rigts reserved. Maximum toxic effect T M : for 5% of values, uniform distribution between and.5 for te oter 5% of values Half inibition concentration T 5 : log-uniform distribution ranging from.56 to 5.6 Experimental metods and data processing. Cell lines and tissue culture. MCF A, Hs 578T, MDA-MB-, MCF7, SK-BR-, and BT- were obtained from te ATCC and grown according to ATCC recommendations. For time-lapse experiments, MCF A and BT- cells were modified by inserting an HBmCerry expression cassette (gift of R. Benezra, Addgene plasmid # 97) 8 tat comprised AAVS omology arms, te PGK promotor, and SV4 polya terminator (gift from R. Jaenisc, Addgene plasmid # 7) 9 into te AAVS safe arbor genomic locus using CRISPR/Cas9. MCF A-HB-mCerry cells were grown in te same manner as te parental strain, wit te exception tat traditional DMEM was replaced wit FluoroBrite DMEM (Termo Fiser Scientific) for imaging. Te modified TERT RPE- cells (gift from J. Cen) were created by inserting te full-lengt BRAF V6E expression cassette (Addgene plasmid # 569) 4 driven by a tet-inducible promotor (Addgene plasmid # 494). Cell identity was confirmed by sort tandem repeat (STR) profiling at te Dana-Farber Cancer Institute, and all cells were tested wit te MycoAlert PLUS mycoplasma detection kit (Lonza) and found to be free of mycoplasma prior to analysis. Drugs and dyes. Drugs were obtained from commercial vendors and tested for purity inouse as described in detail in te HMS LINCS drug collection database (ttp://lincs.ms.arvard.edu/db/sm/). Drugs and reporter dyes were dispensed directly into multiwell plates using a D Digital Dispenser (Hewlett-Packard). To stain cells, YOYO- and TOTO- (Termo Fiser Scientific) were used at 5 nm and nm, respectively; NucView 488 caspase- substrate (Biotium) was used at nm. Manipulating cell growt rate to determine effects on drug sensitivity. RPE- or MCF A-HB-mCerry cells were plated in 84-well plates using te Multidrop Combi Reagent Dispenser (Termo Scientific) at 5 and 5 cells per well, respectively. To modulate te growt rate in RPE- cells, we induced expression of te BRAF V6E oncogene by treating cells wit indicated doses of doxycycline using a D Digital Dispenser (Hewlett-Packard). To modulate te growt rate in MCF A-HB-mCerry we serum-starved cells twice wit DMEM/F medium supplemented wit.% bovine serum albumin and % penicillin streptomycin. Medium canges and cell wasing were performed using an EL46 Microplate Waser Dispenser (BioTek). Cells were treated wit indicated doses of uman epidermal growt factor (EGF, Peprotec) using a D Digital Dispenser. After 4 te cells were treated wit a dilution series of etoposide using a D Digital Dispenser. RPE- cells were stained and fixed for analysis at te time of drug treatment and after 7. MCF A- HB-mCerry cells were imaged in an IncuCyte ZOOM live-cell imager (Essen Bioscience) starting at te time of EGF treatment, and drug sensitivity was evaluated 7 after drug addition. Evaluating drug-response metrics in MCF A and BT- over time. MCF A-HB-mCerry and BT--HB-mCerry cells were plated at,5 and,5 cells per well, respectively, in 84-well plates using te Multidrop Combi Reagent Dispenser (Termo Scientific) and grown for 4. Cells were treated wit a dilution series of te indicated drugs using a D Digital Dispenser (Hewlett-Packard) and imaged after drug addition in an Operetta Hig-Content Imaging System (PerkinElmer) equipped wit a live-cell camber over a period of 96. For tese experiments, we used te following drugs: Etoposide, topoisomerase inibitor Linsitinib, IGFR inibitor Omipalisib/GSK6458, panpik/mtor inibitor PLX47, B-RAF inibitor Tanespimycin/7-AAG, HSP9 inibitor Evaluating drug sensitivity in MCF A speroids over time. MCF A-HB-mCerry cells were plated at cells per well into ultralow attacment-coated, flat-bottom, 84-well plates (Corning) wit te addition of.5% growt factor reduced basement membrane matrix Matrigel (Corning) to te growt medium. After 48, cells were treated wit a dilution series of omipalisib using a D Digital Dispenser (Hewlett-Packard) and imaged in an IncuCyte ZOOM live-cell imager (Essen Bioscience) for an additional 96. Drug sensitivity was evaluated by computing values every 5 over a 9 time frame. Evaluating drug sensitivity in breast cancer cells plated at different seeding densities. MCF A, Hs 578T, MDA-MB-, MCF7, SK-BR-, and BT- were plated at densities ranging from 56 to 5, cells per well in 84-well plates using te Multidrop Combi Reagent Dispenser (Termo Scientific) and grown for 4. Cells were treated wit a dilution series of te indicated drugs using a D Digital Dispenser (Hewlett-Packard). Cells were stained and fixed for analysis at te time of drug treatment and after 7 of incubation wit drug. For tese experiments, we used te following drugs: Erlotinib, EGFR inibitor Etoposide, topoisomerase inibitor Lapatinib, EGFR/ErbB inibitor Linsitinib, IGFR inibitor Metotrexate, diydrofolate reductase inibitor Omipalisib/GSK6458, panpik/mtor inibitor Paclitaxel, target microtubules Palbociclib, CDK4/6 inibitor PLX47, B-RAF inibitor TAE684, ALK inibitor Tanespimycin/7-AAG, HSP9 inibitor Investigating density-dependent drug effects. MCF A-HBmCerry cells were plated at densities tat ranged from 56 to 5, cells per well in 84-well plates using te Multidrop Combi Reagent Dispenser (Termo Scientific) and grown for 4. Cells were treated wit a dilution series of drugs using a D Digital Dispenser (Hewlett-Packard) and imaged after drug addition in an Operetta Hig-Content Imaging System (PerkinElmer) equipped wit a live-cell camber over a period of 7. In te case of metotrexate and oligomycin,,5 cells were plated in µl of medium per well, treated wit a dilution series of drug, and imaged for 7. nature metods doi:.8/nmet.85