Radioresistance mechanisms of mammary tumor initiating cells: unreliable biological conclusions based on limiting dilution assays.

The recent study of tumor initiating cells (TICs) in a p53 null mammary tumor model by Zhang et al. (1) emphasizes that the selective activation of the Akt and canonical Wnt/β-catenin signaling pathways within the tumorigenic TICs plays a critical role in radiation resistance of TICs. Limiting dilution experiments are used to estimate and to compare TIC frequencies in their protocols. As such, limiting dilution transplantation assays (LDTAs) compose a substantial part of their work, and the authors claim that the related results provided strong support to their biological conclusions. Specifically, the results of LDTAs support the hypothesis of a very high frequency (≈1/27) of TICs among the LinCD29CD24 subpopulation as compared with other subpopulations, LinCD29CD24, LinCD29CD24, or LinCD29CD24 and unfractionated (Lin) populations; next, by using a lentivirus containing a TOP-eGFP pathway reporter to evaluate the importance of canonical Wnt signaling in the TIC subpopulation, eGFP-positive cells show a 70-fold enrichment in TIC frequency, compared with eGFP-negative cells; and finally, the use of an Akt inhibitor, perifosine, sensitizes TICs to radiation treatment as demonstrated by a significant reduction of TIC frequency among eGFP-positive cells after combination in vivo of irradiation (IR) treatment and perifosine, in comparison with IR treatment alone. In all these LDTAs, calculations of TIC frequencies are based on the single-hit Poisson model (SHPM). However, the authors fail to check the adequacy of the SHPM to the data. We point out here that missing this important step may have a significant bearing on their conclusions. In two papers (2, 3) we advise a statistical test aimed at estimating the fit of the SHPM to the data and based on a generalized linear regression model termed GLMlog-log with slope β. This statistical data modeling is currently considered as the best method to evaluate the fit of the SHPM to limiting dilution data (4). In brief, rejecting the null hypothesis β 1⁄4 1 leads to the rejection of the SHPM hypothesis and invalidates the related TIC frequency estimate. The results of our statistical modeling study aimed at reanalyzing the 17 LDTAs of Zhang et al. (1) are presented in Table 1. In 9 LDTAs, the SHPM hypothesis cannot be assessed, because the GLMlog-log does not hold or as a consequence of GLMlog-log overfitting attributed to data sparseness. In the remaining 8 LDTAs, the SHPM is rejected or doubtful in 4 LDTAs. Overall, the SHPM hypothesis cannot be rejected only for 4 of the 17 LDTAs. This situation casts doubt on the accuracy of the TIC frequency estimates in most of the LDTAs and therefore profoundly impacts the validity of the above conclusions the authors make (1). In particular, the high TIC frequency among LinCD29CD24 subpopulations is doubtful, with Pðχ2Þ 1⁄4 0:059. Moreover, most of the LDTAs evaluating the impact of the activation of the Akt and canonical Wnt/β-catenin signaling pathways, or the effect of IR and perifosine, on TIC frequencies are untractable regarding the SHPM hypothesis. TIC frequencies remain to be accurately estimated in properly designed, and statistically checked, LDTAs.