Limits...
Do cancer cells undergo phenotypic switching? The case for imperfect cancer stem cell markers.

Zapperi S, La Porta CA - Sci Rep (2012)

Bottom Line: Here we explore an alternative explanation based on the hypothesis that markers are not perfect and are thus unable to identify all cancer stem cells.Our analysis is based on a mathematical model for cancer cell proliferation that takes into account phenotypic switching, imperfect markers and error in the sorting process.Our conclusion is that the observation of reversible expression of surface markers after sorting does not provide sufficient evidence in support of phenotypic switching.

View Article: PubMed Central - PubMed

Affiliation: CNR-IENI, Via R. Cozzi 53, 20125 Milano, Italy. stefano.zapperi@cnr.it

ABSTRACT
The identification of cancer stem cells in vivo and in vitro relies on specific surface markers that should allow to sort cancer cells in phenotypically distinct subpopulations. Experiments report that sorted cancer cell populations after some time tend to express again all the original markers, leading to the hypothesis of phenotypic switching, according to which cancer cells can transform stochastically into cancer stem cells. Here we explore an alternative explanation based on the hypothesis that markers are not perfect and are thus unable to identify all cancer stem cells. Our analysis is based on a mathematical model for cancer cell proliferation that takes into account phenotypic switching, imperfect markers and error in the sorting process. Our conclusion is that the observation of reversible expression of surface markers after sorting does not provide sufficient evidence in support of phenotypic switching.

Show MeSH

Related in: MedlinePlus

Evolution of the concentration of positive cells after an imperfect sorting.(A) The evolution of the concentration of positive cells after sorting for positive (+) and negative (−) subpopulations as a function of the number of generations N for different values of the sorting efficiency η. The dynamics is obtained solving the CSC model with M = 30 and . (B) The same plot as panel (A) for η = 10−4 and different values of M.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3369193&req=5

f6: Evolution of the concentration of positive cells after an imperfect sorting.(A) The evolution of the concentration of positive cells after sorting for positive (+) and negative (−) subpopulations as a function of the number of generations N for different values of the sorting efficiency η. The dynamics is obtained solving the CSC model with M = 30 and . (B) The same plot as panel (A) for η = 10−4 and different values of M.

Mentions: To quantify the effect of an imperfect sorting, we consider the evolution of the concentration of positive cells as a function of the sorting efficiency η. Using the CSC model, we start from steady-state concentrations of CSCs and CCs and sort them into two subpopulations according to Eq. 11. Next, we integrate Eqs. 5 and at each generation we compute the fraction of positive cells. The result also in this case is that after some time the system returns to the steady state. As illustrated in Fig. 6A for M = 30 and , the evolution depends on η only for the negative subpopulation and is independent on η for the positive subpopulation. In both cases, the number of generations needed to reach the steady state is controlled by M, as shown in Fig. 6B. Hence, we can estimate the typical equilibration time to be around for the positive subpopulation and slightly larger for the negative one. The main difference between imperfect sorting and imperfect marker or phenotipic switching is that in the first case there is a net asymmetry between positive and negative subpopulations: the negative subpopulation remains roughly constant for the first M generations, while the positive subpopulation decreases from the beginning.


Do cancer cells undergo phenotypic switching? The case for imperfect cancer stem cell markers.

Zapperi S, La Porta CA - Sci Rep (2012)

Evolution of the concentration of positive cells after an imperfect sorting.(A) The evolution of the concentration of positive cells after sorting for positive (+) and negative (−) subpopulations as a function of the number of generations N for different values of the sorting efficiency η. The dynamics is obtained solving the CSC model with M = 30 and . (B) The same plot as panel (A) for η = 10−4 and different values of M.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3369193&req=5

f6: Evolution of the concentration of positive cells after an imperfect sorting.(A) The evolution of the concentration of positive cells after sorting for positive (+) and negative (−) subpopulations as a function of the number of generations N for different values of the sorting efficiency η. The dynamics is obtained solving the CSC model with M = 30 and . (B) The same plot as panel (A) for η = 10−4 and different values of M.
Mentions: To quantify the effect of an imperfect sorting, we consider the evolution of the concentration of positive cells as a function of the sorting efficiency η. Using the CSC model, we start from steady-state concentrations of CSCs and CCs and sort them into two subpopulations according to Eq. 11. Next, we integrate Eqs. 5 and at each generation we compute the fraction of positive cells. The result also in this case is that after some time the system returns to the steady state. As illustrated in Fig. 6A for M = 30 and , the evolution depends on η only for the negative subpopulation and is independent on η for the positive subpopulation. In both cases, the number of generations needed to reach the steady state is controlled by M, as shown in Fig. 6B. Hence, we can estimate the typical equilibration time to be around for the positive subpopulation and slightly larger for the negative one. The main difference between imperfect sorting and imperfect marker or phenotipic switching is that in the first case there is a net asymmetry between positive and negative subpopulations: the negative subpopulation remains roughly constant for the first M generations, while the positive subpopulation decreases from the beginning.

Bottom Line: Here we explore an alternative explanation based on the hypothesis that markers are not perfect and are thus unable to identify all cancer stem cells.Our analysis is based on a mathematical model for cancer cell proliferation that takes into account phenotypic switching, imperfect markers and error in the sorting process.Our conclusion is that the observation of reversible expression of surface markers after sorting does not provide sufficient evidence in support of phenotypic switching.

View Article: PubMed Central - PubMed

Affiliation: CNR-IENI, Via R. Cozzi 53, 20125 Milano, Italy. stefano.zapperi@cnr.it

ABSTRACT
The identification of cancer stem cells in vivo and in vitro relies on specific surface markers that should allow to sort cancer cells in phenotypically distinct subpopulations. Experiments report that sorted cancer cell populations after some time tend to express again all the original markers, leading to the hypothesis of phenotypic switching, according to which cancer cells can transform stochastically into cancer stem cells. Here we explore an alternative explanation based on the hypothesis that markers are not perfect and are thus unable to identify all cancer stem cells. Our analysis is based on a mathematical model for cancer cell proliferation that takes into account phenotypic switching, imperfect markers and error in the sorting process. Our conclusion is that the observation of reversible expression of surface markers after sorting does not provide sufficient evidence in support of phenotypic switching.

Show MeSH
Related in: MedlinePlus