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Growth Rate Inhibition Metrics Correct for Confounders in Measuring ARTICLES Growth rate inhibition metrics correct for confounders in measuring sensitivity to cancer drugs Marc Hafner1,2, Mario Niepel1,2, Mirra Chung1 & Peter K Sorger1 Drug sensitivity and resistance are conventionally quantified by different numbers of divisions during the course of an assay IC50 or Emax values, but these metrics are highly sensitive to the because of natural differences in proliferation rate, variation in number of divisions taking place over the course of a response growth conditions, or changes in the duration of an experiment, assay. The dependency of IC50 and Emax on division rate creates IC50, Emax, and AUC values will vary dramatically, independently artefactual correlations between genotype and drug sensitivity, of any changes in the underlying biology. Thus, biomarkers that while obscuring valuable biological insights and interfering predict sensitivity under one (potentially arbitrary) set of assay with biomarker discovery. We derive alternative small molecule conditions may not predict sensitivity under slightly different drug-response metrics that are insensitive to division number. conditions. We therefore propose a new method for param- These are based on estimation of the magnitude of drug-induced eterizing drug response, the normalized growth rate inhibition growth rate inhibition (GR) using endpoint or time-course (GR), which is based on the comparison of growth rates in the assays. We show that GR50 and GRmax are superior to presence and absence of drug. Parameterization of GR data yields conventional metrics for assessing the effects of small GR50, GRmax, GRAOC, and hGR (Hill slope), values that are largely molecule drugs in dividing cells. Moreover, adopting GR metrics independent of cell division rate and assay duration (we use ‘area requires only modest changes in experimental protocols. over the curve’, GRAOC, rather than AUC for reasons discussed We expect GR metrics to improve the study of cell signaling and in Online Methods). GR metrics can be determined with modest growth using small molecules and biologics and to facilitate the changes in experimental procedures, and we propose that these discovery of drug-response biomarkers and the identification of metrics replace IC50 and Emax values in assessing cellular response drugs effective against specific patient-derived tumor cells. to drugs, RNAi, and other perturbations in which control cells Nature America, Inc. All rights reserved. Inc. Nature America, divide over the course of the assay. 6 The quantification of drug response is fundamental to the discov- ery of therapeutic molecules, the investigation of their mechanisms RESULTS © 201 of action1–3, and the study of signal transduction, cell division, and Definition of normalized growth rate inhibition (GR) other biological processes using chemical biology approaches4,5. We used computer simulation to model the drug response of three In the case of anticancer drugs, cells are typically exposed to drugs idealized cell lines with identical sensitivity to a cytostatic drug over a range of concentrations, and the number of viable cells (or (i.e., a drug that arrests but does not kill cells) and different divi- surrogates, such as ATP level assayed using CellTiter-Glo, CTG) sion times (Td = 1.8, 2.4, or 3.9 d). These division times correspond is measured several days later. Data comprising cell counts in the to the lower quartile, median, and upper quartile for breast cancer presence of drug divided by counts for untreated controls are fit- cell lines3 and are similar to the division times of NCI-60 cells14. ted to a sigmoidal curve to compute (i) the concentration of drug In the slowly dividing cell line (Td = 3.9 d), the total number of at which the cell count is half the control (IC50), (ii) the fraction of cells did not double in an assay typically run over 3 days, and thus viable cells at the highest drug concentration (Emax), and (iii) the Emax was ≥0.5, and IC50 was undefined. In the case of the two 6,7 area under the dose–response curve (AUC) . Dose–response and faster-growing cell lines, IC50 and Emax values fell as division rate genomic datasets are often combined to discover drug-response increased (Fig. 1a) because cell number (or CTG value) was nor- biomarkers1–3,8,9, but it has recently been found that large-scale malized to a drug-naïve control in which cell number increased as drug-response data vary from one study to the next10 for reasons division time fell (compare curves across panels of Fig. 1a). that remain poorly understood11–13. We can compensate for the confounding effects of division rate We show here that, for dividing cells, traditional drug- on drug-response measurements by computing the GR value at response metrics such as IC50 suffer from a fundamental flaw time t in the presence of drug at concentration c: when they are estimated from cell counts made at the end of the experiment (the standard approach): if control cells undergo GR()c, t =2k(, c t)/ k()0 − 1 1HMS LINCS Center Laboratory of Systems Pharmacology, Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, USA. 2These authors contributed equally to this work. Correspondence should be addressed to P.K.S. ([email protected]). RECEIVED 2 OCToBEr 2015; ACCEPTED 1 APrIL 2016; PUBLISHED oNLINE 2 MAY 2016; DoI:10.1038/NmETH.3853 NaTURE METHODS | ADVANCE ONLINE PUBLICATION | ARTICLES Figure 1 | Modeling drug response and the a Slow (Td = 3.9) Medium (Td = 2.4) Fast (Td = 1.8) 1.5 1.00 1.00 1.00 ) dependence of drug-response metrics on d 20 2.0 3 division time (Td, values given in days). 0.75 0.75 0.75 (a) Simulation of a simple drug-response model 1.0 1.5 2 2 IC IC IC yields relative cell counts across a concentration 50 1.0 50 50 Cell count = 0 count t 0.5 range for a cytostatic drug for a slow- (left), 1 0.2 to 0.25 0.25 0.25 IC = n/a IC = 3.1 IC = 1.4 relative to endpoint 50 0.5 50 50 Concentration (a.u. medium- (middle), and fast-growing cell line E = 0.66 E = 0.43 E = 0.28 Cell count normalize max max max 0 0 0 0 0 0 (right). Black lines correspond to untreated 0 24 48 72 0 24 48 72 0 24 48 72 control samples and red lines denote 50% Time (h) Time (h) Time (h) growth inhibition. Black marks show where GR at drug concentration c IC50 and Emax are evaluated. n/a, not applicable. b From growth rates c From cell numbers d Time-dependent value a.u., arbitrary units. (b–d) Methods for x(0,t + t) 2 × ∆t ∆ d 3 exp(t × k(0)) 3 xctrl 3 evaluating GR value: (b) conceptual approach x(0,t – ∆t) based on growth rates (k and k(c)), (c) fixed- x(c) 0 2 2 2 x(c,t + ∆t) interval approach based either on cell number exp(t × k(c)) x0 = 0 count x(c,t – ∆t) at the start (x0) and end of the experiment t 1 1 1 (x and x(c)) and (d) time-dependent value to Untreated Untreated Untreated ctrl Treated Treated Treated t 0 0 0 based on cell count before and after a time Cell count normalize 0 72 0 72 0 72 interval 2 × ∆t (x(c,t ± ∆t)). (e) Simulated Time (h) Time (h) Time (h) data showing relative cell count (green lines) log2(x(c,t + ∆t)/x(c,t – ∆t)) log (x(c)/x )/log (x /x ) k(c)/k(0) 2 0 2 ctrl 0 log (x(0,t + ∆t)/x(0,t – ∆t)) and GR value (purple lines) for a cytostatic GR(c) = 2 – 1 GR(c) = 2 – 1 GR(c,t) = 2 2 – 1 drug assayed over 3 d. The darker the line, e Cytostatic response f Cytostatic response the longer the division time (given in days; 1.0 1.0 x 1.0 x x ma see key below); note that all GR curves overlap. ma 10 E 0.5 ma (a.u.) 0.5 0 5 IC and GR are projected onto the x-axis; GR 50 50 3.2 0.5 0 0 Emax and GRmax are projected onto the y-axis. GR and GR (f) IC or E (green) and GR or GR (purple) –0.5 1 x 50 max 50 max and GR –0.5 ma IC GR 0 5 50 50 E computed from a theoretical 3-day assay for Relative cell count 0 –1.0 IC 0.32 –1.0 cells with division time ranging from 1 to 4 d; 0.1 1.0 10.0 0.1 1.0 10.0 1 2 3 4 1 2 3 4 Concentration (a.u.) Concentration (a.u.) T T vertical line shows Td = 2.4 d (AUC and GRAOC d d values in Supplementary Fig. 1c). IC , E GR , GR Td 1.0 1.4 1.8 3.9 50 max 50 max where k(c,t) is the growth rate of drug-treated cells and k(0) is the Methods). For all three drugs, IC50 and Emax values were strongly growth rate of untreated control cells (Fig. 1b). The GR value is correlated with division time and assay duration, but this was simply the ratio between growth rates under treated and untreated not true of corresponding GR metrics (Fig. 1e,f; Supplementary conditions normalized to a single cell division. The sign of the GR Fig. 1a,b; and Online Methods). In the case of drugs that kill cells Nature America, Inc. All rights reserved.
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