In this work we showed using a simple mathematical model that reduction of signal intensity in the micro-environment is sufficient for immortalization of a homeostatic normal tissue. By performing in vitro experiments in breast carcinoma cells, we provided experimental support for the underlying theory. Despite its simplicity, our model yields extremely powerful tissue homeostasis, returning to almost stationary end cell production even after severe SC depletion (see analytical proof in ). This cooperative behavior primarily depends on the sensitivity of individual SCs to neighboring SC density, denoted QS.
Assuming that this model is a faithful portrayal of developing tissues, we have asked how such tight control on the integrity of normal tissues can succumb to cancer. Our results suggest that SCs are sensitive to the environmental context. Environmental changes that alter intercellular communication may cause SCs either to fully differentiate and disappear in a relatively short while, or to proliferate perpetually, suggesting that inexhaustible cell proliferation can be induced in the absence of carcinogenic mutations. In such cases mutations leading to tissue invasion and metastasis can be an outcome of extensive SC proliferation, rather than reflecting a replication infidelity of a primordial mutated SC, as suggested elsewhere [14, 25] (but see further discussion below).
Based on our results, showing that SC proliferation capacity is attenuated under increased signal intensity and augmented under diminished signal intensity, and on evidence for inflammatory cytokines-mediated tumor growth regulation , we hypothesize that chronic inflammation, such as that caused by H. pylori in the gastric mucosa, reduces signal intensity in the inflammation site and drives BMDCs to excessively proliferate. Moreover, our simulation results pinpoint the propensity of larger founding SC populations to become immortalized. This implies that significantly more extensive BMDC recruitment contributes to the uncontrollable SC proliferation in chronic, rather than acute, H. pylori infection . These hypotheses should be tested experimentally, possibly by tracking the correlations between proliferation and genetic mutations in BMDC residing in inflamed environments.
Our experimental data support the QS theory by demonstrating that, as the theory suggests, a fixed proportion of SCs in a cell population reaches steady state conditions, independently of their initial fraction. The experimental evidence was gathered from cell sorting of a breast cancer cell line using the expression of cell surface markers to enrich for SCs and the mammosphere culture technique to assay SC number. Our experimental results suggest that despite different initial fractions of SCs marked by either CD44+ or CD44+/24lo/ESA+, the same steady state is always achieved at, or before, population confluence.
It has been suggested that cell expression of CD44/24 is not fixed and that cancer is organized stochastically, rather than hierarchically, as the SC model suggests. Quintana et al  have recently proposed this is the case for melanoma and this has been considered mathematically in . Our experimental results in MCF7 cells, showing that different initial SC proportions yield fixed SC proportions at confluence, cannot be accounted for by the stochastic model, but are readily accounted for by the QS model.
A much debated aspect of SC replication is the diverse fate of the two daughter cells that result from each division. In principle, such divisions are considered to be symmetric if the two daughter cells are identical to each other, retaining SC properties, or become committed cells. Divisions are considered to be asymmetric if one daughter cell retains the SC properties of the parent, while the other cell commits to a more differentiated stage . We generalized the different types of SC division into one by assuming independence between the two daughter cell formation. This generalization simplifies our model without compromising its quality, since it allows to examine the forces affecting SC decision to yield either a SC offspring or a DC offspring. A model to evaluate the impact of symmetric and asymmetric SC replication on the expansion of mutant SCs has been recently provided by .
The choice between self-renewal and the initiation of differentiation has been suggested to be controlled by specific anatomic structures, termed stem cell niche . This niche is mainly composed of the extracellular matrix adhesion molecules, local cell populations and the secreted and cell-surface-bound molecules that these cells generate. In contrast to this theory, the QS theory argues that SC fate regulation does not require an externally imposed structure, but, rather, results from spontaneous organization of SCs, and the inter-cell communication in their immediate micro-environment. Nevertheless, it is plausible that micro-environmental maintenance of appropriate signal intensity, e.g., by other selected molecules, or by other factors, such as oxygen tension , is enabled by specialized niche structures. Further support for the existence of QS in human tissues should encourage the search for the specific molecules that regulate SC replication via this mechanism. Possible candidates are cytokines or cytokine-like molecules, small molecules which diffuse through gap-junction, or small regulatory RNA molecules that are known to be linked to cancer cell proliferation [5, 33, 34]. Interestingly, the latter molecules were found to be essential regulators of the QS mechanism of several bacteria species . The identification of the QS molecules may prove valuable for the manipulation of cancer SCs. These could be therapeutically applied to the tumor micro-environment as decoy SC neighbors, artificially driving cancer SCs to differentiation. This idea underlined our search for the QS molecule(s) in breast cancer SCs (BCSCs) . In this work a mathematical model for the major signaling pathways governing mammary BCSC fate-decision was developed. The model suggested that the Wnt pathway inhibitor, Dickhopf1 (Dkk1), was the QS molecule in breast cancer, and that high levels of this protein will drive BCSCs into differentiation, leading to tumor elimination. To verify model's predictions, Dkk1's effects on BCSCs were measured, showing that treatment by high Dkk1 concentrations, significantly decreases BCSC counts, both in BC cell line and in cells from primary tumor of a BC patient. We postulated that Dkk1 is a QS molecule governing SC fate decision in breast cancer.
Our results further show that replication infidelity, leading to mutations that alter cell kinetic parameters, may also affect the QS activity. From Table 1 we learn that shorter life span of DCs, e.g., due to large local death rates, provides a relative advantage to SC proliferation. This implies that drugs that are targeted at DCs, such as those attached to monoclonal antibodies that bind surface molecules expressed on DCs only, will be less effective than anti-proliferative agents. It seems plausible that, in some cases, such drugs may even aggravate cancer SC proliferation, rather than alleviate it. However, appropriately sequenced combinations of these drugs with anti-proliferatives should be tested as well.