A new parameter of growth inhibition for cell proliferation assays

2.1 Cell cultures

Lung adenocarcinoma A549 and prostate adenocarcinoma PC3 cell lines were obtained from cell bank of the IRCCS University Hospital San Martino—IST National Institute for Cancer Research (Genova, Italy). Cells were cultured in DMEM supplemented with L-Glutamine and 10% FBS (Lifetech) at 37°C, 5% CO₂ humidified air.

2.2 Kinetics of cell proliferation

500 A549 cells suspended in 20 μl of complete culture medium without phenol red were plated in 384 well flat, clear bottom black microplate (Corning #3764). After 18–24 hr, 10 μl of fresh supplemented culture medium, containing Etoposide (Sigma–AldrichMerck Group, Darmstadt, Germany, #E2600000), SiR-Hoechst (Spirochrome #SC007) (Lukinavičius et al., 2015), and CellTox™ Green Dye (Promega, Madison, WI, #G873A), were added to each well of the cell plate, to a final concentration of SiR-Hoechst 0.5 μM in vehicle (DMSO) 0.8%. A549 cells were treated with eleven 1:2 serial dilutions of Etoposide in technical triplicate, ranging from 40 to 40 nM. Plating of cells, preparation of Etoposide serial dilutions and addition of compound solutions to the cells were performed using an automated liquid handling platform (Gilson Pipetmax®, Middleton, WI). Multiple live-cell imaging in far-red fluorescence (led cube 625 nm, filter cube excitation 650 ± 30 nm, emission 800 ± 90 nm), green fluorescence (led cube 465 nm, filter cube excitation 469 ± 25 nm, emission 525 ± 25 nm) and phase contrast was performed at 37°C, 5% CO₂ using a gas controller associated to the microscope, after 1, 24, 48, and 72 hr of treatment with a 4× objective, using an automated digital widefield microscope (BioTek Cytation 5, Winooski, VT). For each sample, four images were taken to cover the entire area of the well. Image merging, processing, and cell count were performed using BioTek Gen5 software. Briefly, the number of cells was calculated as count of far-red fluorescence stained nuclei and the number of dead cells was calculated as count of green fluorescence stained cells. Threshold of fluorescence background and range of nuclei size settings were manually adjusted in each experiment by overlapping images of far-red and green fluorescence with images in phase contrast as reference. Count of live cells was calculated by subtracting count of dead cells to the count of total cells. For what concerns cytotoxicity assays in PC3 cells, 2,000 cells suspended in 80 μl of complete culture medium without phenol red were plated in 96 well flat, clear bottom black microplate (Corning #3603). After 18–24 hr, 20 μl of fresh supplemented culture medium, prepared as previously described for A549 cells, was added to each well of the cell plate. PC3 cells were treated with nine 1:2 serial dilutions ranging from 10 to 40 nM in technical duplicate. Live-cell imaging and analysis were performed as previously described.

2.3 Statistical analysis

Regression analysis and T-tests were performed with microsoft excel.

3.1 The relative cell number is function of cell proliferation

R is a widely used parameter to determine drug efficacy in cell proliferation assays, and it is also used to calculate the IC₅₀ and compare drug efficacy between distinct cell models. R can be described as:

(1)

where T is number of cells at the measuring point in the compound-treated sample and U is number of cells in the untreated control sample. R has a value from “0,” which means maximum drug efficacy, to “100,” which means absence of any effect by the treatment on cell proliferation. However, cell populations that grow “faster” in culture, referring to cells that duplicate more times in the same amount of time than “slower” ones, tend to show lower R. This logical deduction can be assumed if we imagine to treat two distinct cell lines (A and B) with a drug that induces total arrest of cell growth, termed cytostasis, in both cell lines (Figure 1a). Despite the same phenotype is induced in both cell lines, R_A of the “faster” cell line A will be lower than R_B of the “slower” cell line B, and therefore A will be inferred more sensitive than B when comparing drug efficacy between the two cell lines. For the same reason, R is function of the period of treatment before estimation of cell number: if we treat a cell line with cytostatic doses of a drug and estimate the number of cells at distinct time points, R logically tends to show lower values at longer period of treatment because of the increased cell number in untreated sample, independently by additive drug effects due to longer exposition (Figure 1b). To experimentally evaluate these assumptions, we treated a representative cell line, A549, with serial dilutions of a well-characterized representative chemotherapy agent, etoposide, and live cell number was monitored every 24 hr for 3 days (Figure 2). A preliminary normalization of cell number among wells at each time point was carried out taking advantage of the multiple readings with live-cell imaging:

Subsequently, R and IC₅₀ were calculated using normalized data at each time point (Supplemental Data S1 and Table 1, respectively). A much higher coefficient of variation was observed in the IC₅₀ at 24 hr compared to 48 and 72 hr of treatment (Table 1). Since a concomitant higher coefficient of variation in the proliferation of untreated cells was not observed (Table 1), we concluded that tiny differences in drug concentration and timing of data collection among the biological replicates would strongly affect drug efficacy at a short time of treatment, as 24 hr. Therefore, we compared R and IC₅₀ values between 48 and 72 hr of treatment. As shown in Figure 1c, R values after 72 hr of treatment were lower than those obtained at 48 hr. Consistently, IC₅₀ after 72 hr of treatment was significantly lower than IC₅₀ at 48 hr (Table 1, p < 0.01, two-tail heteroscedastic t-test). Similar results were obtained using a different set of data originated by treatment of PC3 cells with serial dilutions of etoposide (Table 2, Figure 1d and Supplemental Data S2). Despite it could be argued that lower R at 72 hr of treatment could be partially or totally due to the longer exposure of cells to the drug, we showed that R is function of cell proliferation rate, suggesting that R would not be a proper parameter to determine drug efficacy in cell proliferation assays, if the aim is to compare drug sensitivity between cell lines with distinct proliferation rates.

3.2 The percentage of growth inhibition is function of cell proliferation

Researchers at the NCI's Drug Discovery Program developed, more than 20 years ago, a parameter to compare efficacy of small molecules with potential anticancer activity in a panel of 60 tumor cell lines, which is still used in their program (Boyd et al., 1992). Cell number is estimated at the time of compound addition and after 48 or 72 hr of treatment, and efficacy is determined as percentage of growth (PG). PG is differently calculated based on the type of effect: percentage of cell death (PG_T) if a cytotoxic effect occurs, or percentage of growth inhibition (PG_S) if a decrement of cell proliferation or cytostasis occurs. PG_T and PG_S are described as:

(2)

(3)

where I is the number of cells measured at the time of drug addition to cells. PG has a value from +100 to −100 and it is used to determine three response parameters: 50% growth inhibition (GI₅₀, PG = 50), total growth inhibition (TGI, PG = 0), and lethal concentration 50% (LC₅₀, PG = −50) (Boyd & Paull, 1995). First, PG is a more informative parameter than R to evaluate in vitro drug efficacy since it distinguishes among growth inhibition and cytotoxic effects. PG_T describes the percentage of cells that die as a consequence of the treatment, and therefore it does not take into account the proliferation rate in untreated cells. In the same manner, if cytostasis occurs, PG_S is “0” regardless of cell proliferation properties. In contrast, if a partial growth inhibition occurs, PG_S is calculated as the percentage of linear increase in the number of treated cells to the linear increase in the number of untreated cells. As a consequence, PG_S will be function of cell proliferation if cell proliferation shows a non-linear progression (Figure 3a). To experimentally evaluate PG dependency to cell proliferation rate, we calculated PG, GI₅₀ and TGI of previously used data of etoposide-treated A549 and PC3 cells. PG values in A549 cells after 72 hr of treatment were lower than PG values obtained after 48 hr for drug doses that induced growth inhibition (Figure 3b, right top quadrant). Consistently, GI₅₀ after 72 hr of etoposide treatment in A549 cells was lower than GI₅₀ after 48 hr, despite with lesser extent than IC₅₀ values (Table 1, P < 0.05, two-tail heteroscedastic t-test). We did not observe any difference in PG values for drug doses that induced a cytostatic (PG ∼ 0) or a cytotoxic (PG < 0) effect (Figure 3b, in proximity of 0 values and left bottom quadrant, respectively). Consistently, the TGI concentration did not significantly differ between 48 and 72 hr of treatment in A549 cells (Table 1). This latter fact supports our hypothesis that both R and PG_S decrements at 72 hr of treatment are consequence of the increased cell number in untreated sample, and not of the longer drug exposure, otherwise a PG decrement would be observed also for drug doses that induced a cytostatic or cytotoxic effect (Figure 3b). For what concerns PC3 cells, GI₅₀, and PG_s at 72 hr of treatment showed a slighter, not significant change between 48 and 72 hr of treatment (Table 2, Figure 3c and Supplemental Data S2).

3.3 Untreated cell populations cultivated under standard conditions grow in an exponential manner

We hypothesized that the occurrence of an exponential, and not linear, growth of untreated A549 cells would contribute to the gradual PG_S decrement over the time of treatment in this cell line. This hypothesis was based on the logical assumption that each mother cell duplicates into two daughter cells, which will duplicate into two new cells and so on. To evaluate which mode of growth, linear, or exponential, best fits cells maintained under standard culture conditions, we performed both linear and exponential regression analyses to the previously used data of untreated A549 and PC3 cells and calculated their coefficients of determination (R²) (Figure 4a and Supplemental Data S3). The exponential regression of the growth curves of untreated A549 samples showed a R² > 0.99 in all the three biological replicates performed, whereas the linear regression showed a R² < 0.95. In PC3 cells, both the exponential and the linear regression analyses showed a R² > 0.95, with a slight higher R² in the exponential one. It was likely that the slighter, not significant difference of GI₅₀ in PC3 cells between the two time-points was due to the growth properties of this cell line, whose fit both a linear and an exponential regression analysis in standard culture conditions. In contrast, our results confirmed that A549 cells grew in an exponential manner, and the PG_S decrement observed between 48 and 72 hr of etoposide treatment could be explained by the non-linear proliferation of untreated samples in this cell line.

We next asked if a model of exponential growth would better fit also growth curves of etoposide-treated samples (Supplemental Data S4). We arbitrary partitioned data into milder and stronger growth inhibition effects, using PG_S 35 as cut-off value, to evaluate more in detail the effects of growth inhibition on the proliferation property of the cells. Samples treated with doses of drug that induced a milder growth inhibition (PG > 35) showed similar R² values of untreated cells in both cell lines, and therefore we concluded that a mild growth inhibition does not affect the growth properties of the cells (Figures 4b and 4c). In contrast, both regression analyses showed low R² values in samples that induced a stronger growth inhibition (0 < PG < 35), and no difference between linear and exponential R² values were observed (Figures 4b and 4c). Therefore, we concluded that a strong growth inhibition negatively affect the exponential growth of the cells. Overall, we confirmed that proliferation in untreated samples, in particular A549 cells, better fit a model of exponential growth and that this growth property is negatively affected by drug treatment, in particular for drug doses that induce a strong growth inhibition. We therefore speculated that PG_S decrement between 48 and 72 hr of etoposide treatment, shown in Figure 3b, was consequence of the exponential growth property of the cells.

3.4 The relative doubling parameter determines growth inhibition of exponential growing cell populations

Based on our previous observations and conclusions, we defined a parameter of drug efficacy representative of the residual exponential growth in treated cell populations. Taking into account that each cell duplicates into two daughter cells, number of cells in an untreated population at any time point can be described as:

(4)

where P is the number of population doublings that an asynchronous cell population accomplished in a defined period of time. Therefore, population doublings can be described as:

(5)

Based on the hypothesis that growth inhibition is consequence of the impaired cell population doubling performance induced by the treatment, and therefore capacity of cell duplication, number of cells in a treated population (T) can be described as:

(6)

where D, the doubling capacity, is between +1 and 0 and can consequently be described as:

(7)

To calculate the efficacy of treatment to impair the doubling capacity of the cell population, the number of population doublings accomplished by untreated cells was applied to treated sample. RD can be described as:

(8)

Whereas PG_S is the relative linear growth of treated sample to the linear growth of untreated sample, RD can be described as the doubling capacity of treated sample to the doubling capacity of untreated sample. As for R and PG_S, RD has a value from 0 to 100 and can be used as well to determine two response parameters: 50% doubling capacity inhibition (RD₅₀, RD = 50) and total doubling capacity inhibition, which corresponds to cytostasis as for TGI (RD₀, RD = 0). We calculated RD, RD₅₀, and RD₀ of etoposide-treated A549 and PC3 cells using previously used data of etoposide treatment. In Figures 5a and 5c we show RD at 48 and 72 hr of treatment, in addition to PG_S values as previously shown in Figures 3b and 3c, and in Figures 5c and 5d we provide a more detailed analysis by reporting the decrements of RD and PGs between 48 and 72 hr of treatment. In both cell lines, the decrement at 72 hr compared to 48 hr of treatment observed in PG_S values was strikingly reduced in RD values. Consistently, the decrement of RD₅₀ at 72 hr, compared to 48 hr, was significantly less pronounced than GI₅₀ decrement in both cell lines (Tables 1 and 2, p < 0.01 and p < 0.05 in A549 and PC3 cells, respectively. One-tail paired t-test). As expected, we did not observe significant differences between TGI and RD₀ in A549 cells, since the value is “0” in both parameters regardless of cell proliferation (Table 1). These results confirmed that a parameter that measures the ability to negatively affect the doubling capacity of cell populations is more accurate than PG_S to represent in vitro growth inhibition, since it is not affected by the exponential growth property of cells in culture.