Cell division time (T_{d}) | ||
Potency of the drug (SC_{50}) | ||
Maximal effect of the drug | ||
on cell division (S_{M}) | ||
Hill slope (h) |
Drug sensitivity and resistance are quantified using IC_{50} or E_{max} values, but these metrics suffer from a fundamental flaw when applied to growing cells: they are highly sensitive to the number of divisions that take place over the course of a response assay (see the exploration tool below). Division rate varies across cell lines and experimental conditions. The dependency of IC_{50} and E_{max} on division rate creates artefactual correlations between genotype and drug sensitivity while obscuring important biological insights and interfering with biomarker discovery. To address this, we derived alternative drug response metrics that are insensitive to division number. These metrics are based on estimating growth rate inhibition (GR) in the presence of a drug (relative to an untreated control) using endpoint or time-course assays. The latter provides a direct measure of phenomena such as adaptive drug resistance. Theory and experiments published in Hafner et al. (2016) show that GR_{50} and GR_{max} are superior to IC_{50} and E_{max} for assessing the effects of drugs on dividing cells. Moreover, adopting GR metrics requires only modest changes in experimental protocols. GR metrics should improve the use of drugs to identify response biomarkers, study mechanisms of cell signaling and growth and identify drugs effective on specific patient-derived tumor cells. Through this website we provide an online tool to calculate GR metrics from user-provided data. Scripts are also available on GitHub.
On this website you will find:
Additional information about measuring dose-response curves and calculating GR metrics can be found in the slides from the: ICSB 2017 Workshop on Drug Response Measurement and Analysis. Applications of GR metrics are further discussed in Hafner et al. (2016) and Hafner et al. (2107). Please cite these paper for all applications of GR metrics.
The GR metrics model and the associated computational scripts were developed by members of the Sorger lab at the Harvard Medical School (HMS) LINCS Center, which is funded by NIH grant U54 HL127365. The online GR tools were developed by the LINCS-BD2K Data Coordination and Integration Center, which is funded by NIH grant U54HL127624, in collaboration with the HMS LINCS Center.
Commonly, relative cell count at the end of treatment is used to assess drug response. Across a range of concentrations, the measured cell count or a surrogate of it (e.g. measurement of ATP using CellTiter-Glo®) is normalized to the cell count of DMSO-treated controls grown on the same plate under the same conditions. For each condition (combination of cell line, drug, and drug concentration), we define the relative cell count as x(c)/x_{ctrl}, where x(c) is the count in the presence of drug and x_{ctrl} is the 50%-trimmed mean of the count for control cells. Based on a sigmoidal curve fitted to the relative cell count across different concentrations, one can define:
More details on dose-response assays and traditional metrics can be found in Sebaugh (2010).
As an alternative to traditional metrics, we propose to use GR metrics, which are based on inhibition of the growth rate over the course of the assay and are independent of the division rate of the assayed cell lines.
Growth can be estimated at different concentrations based on the cell count at the time of treatment (x_{0}), the cell count in the untreated control (xctrl), and the cell count after treatment at concentration c (x(c)):
This equation assumes exponential growth and constant growth inhibition by the drug. Many phenomena such as drug efflux, homeostasis and adaptation can result in non-exponential growth. In such cases, time course assays and time-dependent GR values are better suited to evaluating drug response. Given measurements of cell count at different time points, time-dependent GR values are defined as:
GR(c) values (or time-dependent GR(c,t) values at a given time t) across a range of concentrations are fitted to a sigmoidal curve:
where the fitted parameters are:
If time-dependent GR(c,t) values are used, GR metrics can be estimated at a different time points to study how sensitivity evolves over time.
The GR_{50} value is the concentration of drug at which GR(c = GR_{50}) = 0.5. If the value for GR_{inf} is above 0.5, the GR_{50} value is not defined and is therefore set to +∞. By extension, other thresholds can be defined in a similar manner. For example, GR_{100} corresponds to the concentration at which a drug is fully cytostatic: GR(c = GR_{100}) = 0.
GR_{max} is the maximum effect of the drug at the highest tested concentration. It lies between -1 and 1. A value of 0 corresponds to a fully cytostatic response, and negative values correspond to a cytotoxic response. GR_{max} can be estimated from the fitted curve or obtained directly from experimental data. (We often do the later.)
For time course data, all metrics are evaluated at each time point individually.
Another common metric for quantifying dose response is the area under the response curve (AUC), which is based on integrating the dose-response curve over the range of tested concentrations. In the case of GR curves, which can have negative values, it is more intuitive to use the area over the curve:
where GR(c_{i}) are measured GR values at discrete concentrations c_{i}. GR_{AOC} has the benefit that, in the case of no response, it has a value of 0. It is important to note that GR_{AOC} values (like conventional AUC) can only be used to compare responses evaluated across the same drug concentration range.
The GR_{AOC} value captures variation in potency and efficacy at the same time. The calculation of GR_{AOC} at discrete (experimentally determined) concentrations has the advantage that it does not require curve fitting and is therefore free of fitting artifacts. This is especially useful for assays where fewer than five concentrations are measured and curve fitting is unreliable. GR_{AOC} values are also more robust to experimental noise than metrics derived from curve fitting; e.g. GR_{max} is particularly sensitive to outlier values when directly obtained from data.
We used computer simulation (see below) to model drug response by three idealized cell lines having identical sensitivity to a partial, or complete cytostatic drug (i.e., a drug that arrests but does not kill cells), or a cytotoxic drug (i.e., a drug that kills cells) and different division times (T_{d}). For example, the lower quartile, median, and upper quartile of the division times for breast cancer cell lines has been reported as 1.8, 2.4, or 3.9 days, respectively (Heiser et al. (2012)). These values are similar to those of NCI-60 cells. In a slow-dividing cell line (T_{d} > 3.9 d), the total number of cells does not double in a typical three-day assay; thus E_{max} ≥ 0.5 and IC_{50} are undefined. In the case of the two faster-growing cell lines, IC_{50} and E_{max} values fall as division rate increases simply because cell number (or CTG value) is normalized to a drug-naïve control in which cell number increases as division time falls.
Cell division time (T_{d}) | ||
Potency of the drug (SC_{50}) | ||
Maximal effect of the drug | ||
on cell division (S_{M}) | ||
Hill slope (h) |
To simulate the effect of division time on GR and conventional drug-response metrics under different assumptions about the degree of cytostasis or cell killing, we developed a theoretical model of drug response. To the first approximation, cell growth can be considered exponential, with drugs either decreasing the division rate or killing cells in a cell cycle-dependent manner:
where x is the cell count, k is the untreated growth rate (per day), c is the drug concentration, S_{M} is the maximal inhibitory effect, SC_{50} is the concentration at half-maximal effect of drug, and h is the Hill coefficient. The growth rate k corresponds to the division rate k_{0} as k = ln(2)⋅k_{0} = ln(2)/T_{d}, where T_{d} is the division time. S_{M} can be larger than 1 to account for drugs inducing cell death at a specific phase of the cell cycle.
Integrating these equations for an assay of t days yields the cell count at concentration c:
where x_{0} = x(t = 0) is the cell number at the time of treatment. Thus, the relative cell count is:
where x_{ctrl} ≡ x(0), and the normalized growth rate inhibition (GR value) is:
This equation for GR(c) is independent of the length of the assay t and the untreated growth rate k, and, thus, the metrics GR_{50}, GR_{max}, GR_{AOC}, and h_{GR} are also independent of t and k.
Through the accompanying webpages we provide online tools that allow users to upload their own endpoint data, calculate the corresponding GR values and GR metrics, and compare their results across the variables in the assay, such as cell line, agent (drug), time and replicate. Through the above Online GR Calculator webpage, we provide online tools that allow users to upload their own endpoint data, calculate the corresponding GR values and GR metrics, and compare their results across the variables in the assay, such as cell line, agent (drug), time and replicate. Python, R and MATLAB code for calculating GR value and GR metrics is also available in the gr_metrics repository on GitHub. Our R code is also available in the Bioconductor package GRmetrics.
The GRcalculator takes in either comma-separated (.csv) or tab-separated (.tsv) files with specified column names. See the step-by-step example. For more explicit instructions, go to the GRcalculator and click "Import Data File" and select a "GR Calculation Method" and "Input File Format" to see the exact columns needed for a particular input style.
The following GR metrics are calculated:
In addition, the online calculator reports the r-squared of the fit and evaluates the significance of the sigmoidal fit based on an F-test. Further information about these calculations is available through our GR tutorial. Traditional metrics based on relative cell count (e.g. IC_{50}, E_{max}, etc.) are computed as well for comparison.
The results of analysis of existing LINCS dose-response datasets using the GR model are available in the LINCS GR Data Browser webpage.
The following tabs allow users to analyze and visualize their data and the calculated GR metrics:
We welcome your feedback on all of these tools and resources. Please visit our support page for additional resources and to provide feedback.
This website was designed and built by the following members of the LINCS-BD2K Data Coordination and Integration Center and the Harvard Medical School (HMS) LINCS Center based on analytical tools described in Hafner et al. (2016):
^{1}LINCS-BD2K Data Coordination and Integration Center; ^{2}HMS LINCS Center, Harvard Medical School