The clonogenic assay has been used in numerous studies to quantify clonogenic growth and its abrogation by cytotoxic stimuli, including radiation, chemotherapeutic drugs, and/or molecularly targeted agents, in vitro. The current standard procedure to determine survival fractions is based on the assumption that clonogenic growth in treated cell cultures can be normalized to the untreated controls via dividing by a cell line-specific, constant PE.
Here we show, however, that this is not universally applicable. In contrast, our data clearly indicate that the correlation between the number of cells seeded in a culture dish and the number of colonies obtained is far from always being linear. For cell lines with cooperative behavior, the PE-based analysis of clonogenic survival data yielded results with large to enormous assay-intrinsic errors. Even if only culture dishes with reasonable numbers of colonies (C = 5 to 100) were used for analysis, clonogenic survival fractions at a given dose differed by far more than one order of magnitude for cell lines with high degrees of cellular cooperation. Of note, virtually any survival curve (steep or flat, moderately or strongly curved, linear, quadratic, or irregular) can be derived from this range of results calculated from the given dataset – an observation which might be of particular importance for radiation biologists.
Taken together, our data show that conventional PE-based analysis of clonogenic survival data performs inappropriately as soon as cellular cooperation occurs under one or more conditions within an experiment, and extracted survival results will vary within an unsatisfyingly large range. Specifically, the results will be heavily skewed if only one or few similar cell densities are plated. This practice generates assay-intrinsic errors which are a direct consequence of the chosen cell densities and therefore not amenable to statistical error analyses. For cooperatively growing cell lines, our observations may partly explain reported inter-assay, inter-researcher, and inter-laboratory incongruences of treatment response data . A meta-analysis of A549 colony formation assay data further supports this hypothesis: Within a panel of 156 different studies, Nuryadi et al. reported on SF4 values for this specific cell line ranging from 5–90% with an SF4 interquartile range of more than 25% . Although diverse other parameters may certainly influence treatment response data, we conclude from our data that cellular cooperation is a major factor explaining inter-study variability. Since even small differences in clonogenic survival fractions may encourage researchers to postulate and study new scientific hypotheses that might eventually be based on false precision, we developed a novel analysis approach which is less susceptible to the impact of cell density – especially but not only for cooperatively growing cell lines. This method accounts for non-linear relationships between cell numbers seeded and colony numbers obtained by scoring culture dishes with a wide range of cell numbers seeded for all treatment conditions.
Mathematically, our approach utilizes power regression and interpolation of matched numbers of colonies at different irradiation doses. Applied to the very same dataset that was used for PE-based calculations it provided clearly more stable, cell density-independent results. Attentive readers may have noticed that the survival fraction calculations performed according to the method presented here, rely solely on the coefficients a and b as extracted by non-weighted power regression. Although this obviously compensates for the effects of cellular cooperation, it bears another quality of error which derives from the inaccuracy of regression and which cannot be quantitatively compared to the similar quality of error in PE-based survival fraction calculations. Accordingly, this error should be minimized by ensuring careful experimental design with a sufficient number of independent replicates. Moreover, survival fraction calculations should only be performed with power regression results of proper performance as indicated by the regression coefficient R.
Our mathematical approach basically replaces PE-based clonogenic survival calculations by the question:
How many times more cells need to be seeded into a treated culture dish to yield the identical number of colonies as in a control dish?
The exponent b is of particular importance in this regard. It indicates whether the correlation between the number of seeded cells and the number of counted colonies is linear (b ≈ 1) or not. High b-values, as obtained for BT20 and SKLU1 cells, indicate that cell growth in vitro is decelerated (or entirely abrogated) if the volume of culture medium per cell is increased – either by use of large assay volumes or reduction of the number of cells seeded. It should be emphasized that b-values are by no means specific for a certain cell line but rather a consequence of the chosen cell culture medium, several assay incubation parameters, and the experimental procedure. For instance, use of conditioned media from near-confluent BT20 cells strongly attenuated the cooperative behavior of BT20 single cells, whereas this procedure had no impact on the clonogenic growth of non-cooperatively growing MDA-MB231 cells. Furthermore, the doubling time of cooperative BT20 cells was dependent on both assay incubation time and cell density in the well, thus giving a self-evident biological explanation for imprecise clonogenic survival fractions obtained by PE-based calculations: A proliferating cell cluster’s growth rate may simply be too slow to reach the threshold of 50 cells per colony within the assay incubation time. Hence, the apparent "non-clonality" of a cluster of e.g. 35 slowly proliferating cells at the stopping time point is merely an inevitable consequence of the assay incubation time which is – at least to a certain extent – chosen arbitrarily. In this context, we additionally analyzed the impact of the incubation time on clonogenic survival fractions obtained and observed that it is insufficient to determine the stopping time point by inspection of the control dishes alone as suggested by others : Premature termination of the incubation period may lead to exceedingly low survival fractions on plates with more aggressive treatment where damage repair before continuation of cell growth requires additional time.
Importantly, our data are fully in line with seminal findings of pioneering cell culture researchers in the 1940s and 1950s and simply reflect a phenomenon which was under extensive investigation at that time. Puck and colleagues were the first to publish the first survival curve of irradiated single cells in 1956. However, the biggest scientific challenge to this fundamental achievement was an at that time unresolved problem of mammalian cell culture: Cell lines stopped growing in vitro as soon as the cells were plated at low density. An attempt to overcome this problem was made in 1948 by Sanford et al., who succeeded at growing single-cell-derived fibroblast colonies in small capillaries where diffusion of cell-derived factors into the medium was strongly reduced, thus allowing sufficient autocrine growth stimulation . They identified the importance of pre-conditioning the culture medium by cultivated cells and concluded that a cell culture medium sufficient to allow infinite growth of high-density cell culture is in fact "far from optimal for the growth of a single cell". In line with this, Earle et al. described that plating the respective cell type at very low density resulted in cell death , and this work formed the basis for the first publication on clonogenic growth of mammalian cells in vitro by Puck and Marcus in 1955 . Inspired by the need of conditioned culture medium to facilitate single-cell growth, they used a co-culture system of HeLa single cells and a layer of heavily irradiated feeder cells of the same type. In agreement with the preceding studies, they concluded that the inhibition of single-cell growth in large assay volumes was due to the "loss of a short-lived, diffusible factor" . In later publications, such as the one with the first survival curve of irradiated mammalian cells, Puck and colleagues frequently omitted the use of feeder layers, since they had developed advanced culture techniques allowing single-cell growth with 100% PE without growth factor supplementation by feeder cells [2, 12]. They stated that careful washing and trypsinization protocols were essential in this regard  and coined the term "cooperative action" to describe that cells in a culture dish may differ with regard to genotype as well as physiological state . Our findings recapitulate these observations: Within a 50 cancer cell line panel, we observed that suboptimal growth of single cells in modern, standardized culture media supplemented with FCS is still a very common phenomenon as can be deduced from the finding that more than half of the cell lines displayed cooperative growth behavior. Hence, if suboptimal PEs are found for a certain cell line, the clonogenic assay is likely to simultaneously detect both the influence of the treatment of interest and the impact of cellular cooperation. We therefore integrated this well-described phenomenon into a computational method for clonogenic survival data analysis. Obviously, this approach using power regression and interpolation was beyond the technical capacities of the 1950s when survival data were fitted by eye . However, somehow the relevance of cellular cooperation moved out of focus during the following decades. Although a few reports on non-linearity in colony formation assays were reported over time, the limited performance of PE-based analyses was not addressed [20–23].
Interestingly, these studies reported on a less-than-linear increase in colony numbers with increasing numbers of seeded cells for certain cell types under specific conditions. In accordance with this, for a few cell lines in our panel we also obtained b-values slightly below 1.0. Three different scenarios may explain this observation, of which two are due to methodological artifacts: Firstly, b-values slightly below 1.0 may result from counting wells with a large number of overgrown colonies where small colonies are overlooked by the researcher (see wells marked with "nd" in Fig. 1a). Secondly, cell growth of dishes with high cell numbers may be inhibited in rather early stages due to a rapid decline in nutrient concentration thus resulting in abortive colonies. A third – and biologically less intuitive – option is competitive behavior of cell growth, for instance due to secretion of growth inhibitory factors. Importantly, any of these phenomena is accounted for by the regression and interpolation approach, because it considers any deviation from linearity as reflected by the b-value.
Moreover, it is remarkable that the b-values of various cell lines for untreated compared to irradiated cell lines are not identical. In the majority of these cases, b-values of irradiated cells tend to be higher than the respective b-values of untreated controls, indicating that cellular cooperation increases upon irradiation. Consequently, the range of survival fraction values obtained for C = 5–100 colonies becomes wider than in case of nearly identical b-values (see cell lines HCC1806 and A549). This implies that it is technically not possible to extract more precise survival values by means of the clonogenic assay procedure – unless one fixed number of colonies (Ci) was selected for analysis. Furthermore, cell lines with exceedingly high b-values for treated cells may be of particular interest with regard to therapy resistance studies. For instance, radiation-induced survival factor(s) secreted by a certain cell type might be identified due to a correspondingly high b-value.
In summary, our data show the need to carefully analyze data from colony formation experiments and to consider the underestimated impact of cellular cooperation on survival fraction calculations. This may greatly increase the reliability of the clonogenic assay – and the resilience of any hypothesis based on it.