Selective advantage of trisomic human cells cultured in non-standard conditions

An abnormal chromosome number, a condition known as aneuploidy, is a ubiquitous feature of cancer cells. A number of studies have shown that aneuploidy impairs cellular fitness. However, there is also evidence that aneuploidy can arise in response to specific challenges and can confer a selective advantage under certain environmental stresses. Cancer cells are likely exposed to a number of challenging conditions arising within the tumor microenvironment. To investigate whether aneuploidy may confer a selective advantage to cancer cells, we employed a controlled experimental system. We used the diploid, colorectal cancer cell line DLD1 and two DLD1-derived cell lines carrying single-chromosome aneuploidies to assess a number of cancer cell properties. Such properties, which included rates of proliferation and apoptosis, anchorage-independent growth, and invasiveness, were assessed both under standard culture conditions and under conditions of stress (i.e., serum starvation, drug treatment, hypoxia). Similar experiments were performed in diploid vs. aneuploid non-transformed human primary cells. Overall, our data show that aneuploidy can confer selective advantage to human cells cultured under non-standard conditions. These findings indicate that aneuploidy can increase the adaptability of cells, even those, such as cancer cells, that are already characterized by increased proliferative capacity and aggressive tumorigenic phenotypes.


Mathematical model, parameters, and assumptions.
To determine whether the experimentally observed mitotic indices and rates of apoptosis (Figures 2B, F) could explain the growth trends ( Figure 1) of the three DLD1 CRC cell lines cultured under different conditions, we used a deterministic mathematical model, in which we assumed the growth to be exponential and be described by the following equation: In this model, N represents the number of cells, t is time, is the rate of cell division, and is the rate of apoptotic cell death. The solution to this differential equation is the exponential growth equation, shown below: The use of such a deterministic model is justified because we can assume that (i) our cells are not approaching carrying capacity; (ii) culture conditions are maintained constant; (iii) there is no competition from other cell types (as could be the case in vivo).
In order to determine the rates of cell division and apoptotic death, we needed to estimate the times needed for cell division and apoptotic death (TUNEL-positive state) to occur. Cell division times were experimentally measured for each of the three cell lines (DLD1, DLD1+7 and DLD1+13) using phase contrast live-cell microscopy and measuring the elapsed time from cell round-up to anaphase (Table S1). As for the time required for apoptotic cell death, although we knew the frequencies of TUNELpositive cells in the population ( Figure 2F), it is not known how long cells persist in a TUNELpositive state. Therefore, we needed to estimate this time. We tested a range of times, but found that TUNEL-positivity times above 60 minutes did not significantly affect the theoretical results, whereas times significantly below 45 minutes resulted in very low rates of theoretical growth (i.e., very high rates of cell death), which is inconsistent with our experimental data. Moreover, given that the overall apoptotic process is known to take hours to be completed 1 , it is reasonable to believe that the stage during which cells persist as TUNEL-positive is unlikely to be shorter than 45-60 minutes. Thus, the data presented here consist of two sets, in which TUNEL-positivity time was either 45 or 60 minutes.
From the cell division and TUNEL-positivity values, we calculated the following as rates of cell division and apoptotic cell death: The values for mitotic indices and fraction of TUNEL-positive cells for each CRC cell line under different culture conditions were obtained from the data reported in Figure 2 and are summarized in Table S2. Table S2. Initial population size (from data reported in Figure 1), mitotic indices, and fractions of TUNEL-positive cells for each CRC cell line under different culture conditions.

Comparison of theoretical and experimental data.
Using the exponential growth equation (2) and the parameters and assumptions described in the previous section, we calculated theoretical growth curves ( Figures S1 and S2). Figure S1. Plots show theoretical and experimental growth curves. Points with error bars are experimental results obtained by cell counts (as in Figure 1). Solid black lines show theoretical growth curves given experimentally defined mitotic indices (Table S2), mitotic timing (Table S1), and TUNEL-positivity values (Table S2) Figure 1). Solid black lines show theoretical growth curves given experimentally defined mitotic indices (Table S2), mitotic timing (Table S1), and TUNEL-positivity values (Table S2) and with a set TUNEL-positivity duration of 60 minutes. Grey regions show variance in theoretical values based on variance in mitotic indices and mitotic duration.
The theoretical data did not closely match the experimental data, generally showing faster growth compared to the experimental curves. Thus, we set out to estimate the difference between the two data sets. The experimental growth curve can be represented as: where k represents the change in the population, including birth of new cells due to mitosis and death due to any cause. We can rewrite our theoretical growth curve as: In this curve, all values are the same as in equation (1), but the term is added to account for contributing factors that were not accounted for by the growth rate or the death rate in equation (1). By curve fitting to the experimental data, we can extrapolate k, and then find as the difference between the experimental growth curve and the theoretical growth curve. Thus, we first obtained k values for different CRC cell lines under different culture conditions by fitting the curve described by equation (3) to the experimental data set. The k values obtained in such way are reported in Table S3. Next, by subtracting ( − ) from these k values, we determined values for different CRC cell lines under different culture conditions. These values are reported in Table S4. All the γ values were negative, indicating that in all cases the experimental growth was lower than the theoretically predicted growth, as also evident in Figures S1 and S2. All the parameters used for the simulations were experimentally measured, except the TUNEL-positivity time. If the TUNELpositivity time parameters were the only contributing factor to the differences between theoretical and experimental growth curves, we would expect the see uniformity in the γ values. The fact that the γ values were different under different culture conditions, suggests that in our experiments either cell proliferation occurred at lower rates than calculated based on mitotic indices and mitotic duration or that cells were dying more than what the TUNEL assay data indicated. Lower cell proliferation could be caused by cell cycle delays. However, this would be reflected in the rates of mitosis, given that arrest/delay in a cell cycle stage other than mitosis would result in fewer cells entering mitosis. Therefore, the mitotic parameters used for the model already account for such possible cell cycle delay(s). Instead, our only measure of cell death was based on the TUNEL assay, which may allow for detection of some forms of cell death, but not others 2 . Thus, we suggest that the differences