Mathematical model for the cancer stem cell hypothesis - PubMed (original) (raw)

Mathematical model for the cancer stem cell hypothesis

R Ganguly et al. Cell Prolif. 2006 Feb.

Abstract

Recent research on the origin of brain cancer has implicated a subpopulation of self-renewing brain cancer stem cells for malignant tumour growth. Various genes that regulate self-renewal in normal stem cells are also found in cancer stem cells. This implies that cancers can occur because of mutations in normal stem cells and early progenitor cells. A predictive mathematical model based on the cell compartment method is presented here to pose and validate non-intuitive scenarios proposed through the neural cancer stem cell hypothesis. The growths of abnormal (stem and early progenitor) cells from their normal counterparts are ascribed with separate mutation probabilities. Stem cell mutations are found to be more significant for the development of cancer than a similar mutation in the early progenitor cells. The model also predicts that, as previously hypothesized, repeated insult to mature cells increases the formation of abnormal progeny, and hence the risk of cancer.

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Figures

Figure 1

Figure 1

Schematic representation of the model. SC, stem cells; EP, early progenitor cells; LP, late progenitor cells; SCA, abnormal stem cells; EPA, abnormal early progenitor cells; AP, abnormal progeny (tumour); P, self‐renewal probability.

Figure 2

Figure 2

Transient response of the model beginning with _N_SC = 1.0 and with all other cell populations set to zero. (a) The SC, EP, LP and MC populations and (b) the internal signalling described by the model in terms of the transient values of αSC, αEP and P SC.

Figure 3

Figure 3

Growth rate of populations of abnormal stem cells, EP cells and abnormal progeny for a specific mutation probability in the SC or EP cell compartments. Model response for (a) M SC = 10−3, M EP = 0, and (b) M SC = 0, M EP = 10−3.

Figure 4

Figure 4

(a) Transient response of the SC, EP, LP and MC populations to periodic insult that depletes 50% of the MC population every 200 h. The corresponding response in the SCA, EPA and AP populations is shown for (b) M SC = 10−3, M EP = 0, and (c) M SC = 0, M EP = 10−3.

Figure 5

Figure 5

Response of the in SCA, EPA and AP populations when 50% of the MC population is depleted every 100 h.

Figure 6

Figure 6

AP cell growth as a function of the time between consecutive insults. The AP cell population (after 700 h) increases with increasing frequency of insult. The plots correspond to the conditions: M EP = 0 (solid symbols) with M SC = 0.002 (▪) and 0.001 (▴); and M SC = 0 (empty symbols) with M EP = 0.002 (□) and 0.001 (▵).

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