Principles of stem cell biology and cancer: future applications and therapeutics. Edited by T. Regad, T. J. Sayers and R. C. Rees. John Wiley & Sons (2015)
Part II. Cancer stem cells
A critical discussion of the recent literature on CSC biomarkers highlights a large amount of controversial information and conflicting results. This may lead to the conclusion that CSCs do not exist in some tumours (Quintana et al., 2008, 2010) or else to the hypothesis that their phenotype is dynamic and stochastically reversible (Gupta et al., 2011). If the CSC phenotype is stochastic and reversible, it becomes complicated to define a precise hierarchy between the cells. In a heterogenous cell population, in which phenotypes can switch stochastically to and from the CSC state, defining CSCs might be difficult. A similar scenario is much like the traditional stochastic model of cancer, in which each cell has the potential to seed a tumour.
We believe that before the CSC hypothesis can be abandoned, we should critically analyse the existing data and assess whether it is possible to reconcile the apparent contradictions. In this respect, an interdisciplinary approach combining traditional cell biology with tools and models from applied mathematics and statistical physics could be of great help. Quantitative methods could contribute to overcome the limitations posed by a purely biological approach, as we discuss in this section, reconsidering some of the evidence usually interpreted against the presence of CSCs.
In analogy with stem cells, it is sometimes argued that CSCs should be very uncommon. Hence, the presence of many putative CSCs is difficult to understand. We have recently studied a mathematical model that can be used to quantitatively reproduce the growth curves for both stem cells and CSCs by varying just one parameter related to stem cell homeostatic conditions (La Porta et al., 2012). In one case, we expect homeostasis, so that stem cells do not proliferate and their fraction in a cell population is vanishingly small. In tumours, however, homeostasis is broken and CSCs proliferate exponentially. Yet, in most cases, the fraction of CSCs in the population is small, since non-CSCs proliferate as well, although for a limited number of divisions. Under some experimental conditions favouring the growth of CSCs (e.g. the use of matrigel, mice permissive conditions; Quintana et al., 2008, 2010), the number of CSCs does not need to be small. There is no reason to believe that the growth rates of CSCs and non-CSCs are independent of the environment, leading to the observed dependence of CSC numbers on assay conditions.
When a cell population has been purified from the CSC phenotype by a suitable marker, we would expect the marker not to be expressed again in the population as time goes on. Evidence of the reversible expression of a marker from purified tumour cell populations has led to the concept of phenotypic switching (Gupta et al., 2011). The same data, however, could be quantitatively explained by assuming that there is no one-to-one correspondence between a given marker expression and CSCs. For instance, some CSCs might prevalently express a marker, but not all CSCs. Conversely, most cancer cell would not express the marker, but some would. The net outcome is that the positive cell subpopulation would be CSC-enriched and therefore much more likely to seed a tumour. On the other hand, the negative subpopulation would still express the marker, and eventually the few CSCs would restore the original phenotypic proportion. The validity of this imperfect-marker scenario can be tested quantitatively by comparing mathematical models with experiments (Zapperi et al., 2012). This has been successfully done for ABCG2 in melanoma: thanks to the model, one can estimate that the ABCG2+ population contains 16% CSCs, and the ABCG2one only 0.6% (La Porta et al., 2012). This explains the enhanced ability of ABCG2+ cells to seed tumours in xenografts (La Porta et al., 2012).
Additional factors that can lead to reversible marker expression are the inevitable errors of the sorting process. These should also be quantified and analysed in terms of mathematical models.
Figure 15.1. Population dynamics models for cancer progression. (A) The stochastic model postulates that cancer cells are heterogeneous but can all potentially seed a tumour. (B) According to the CSC model, cancer cells are organized hierarchically and only CSCs can seed a tumour. (C) If phenotypic switching occurs, non-CSCs can switch back to the CSC state and seed a tumour. (D) The imperfect-marker model recognizes that sorting by a biological marker is not an exact process and that some CSCs can be present in the negative subpopulation.