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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.

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Related in: MedlinePlus

Models.(A) In the CSC model, CSCs (red) can divide symmetrically yielding two CSCs with probability  or asymmetrically yielding a CSC and a CC with probability . CCs divide symmetricaly for M generation after which they turn senescent. (B) Phenotipic switching is modeled by introducing a probability p that a CC transform back to the CSC state instead of duplicating. (C) In the imperfect marker model, the switching concerns marker expression not the CSC state. Both CSCs and CCs can be positive to the marker and upon division the expression of the marker can change randomly with respect to the originating cell according to the probabilities q for CSCs and q± for positive and negative CCs.
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f3: Models.(A) In the CSC model, CSCs (red) can divide symmetrically yielding two CSCs with probability or asymmetrically yielding a CSC and a CC with probability . CCs divide symmetricaly for M generation after which they turn senescent. (B) Phenotipic switching is modeled by introducing a probability p that a CC transform back to the CSC state instead of duplicating. (C) In the imperfect marker model, the switching concerns marker expression not the CSC state. Both CSCs and CCs can be positive to the marker and upon division the expression of the marker can change randomly with respect to the originating cell according to the probabilities q for CSCs and q± for positive and negative CCs.

Mentions: We consider a stochastic model for the proliferation of hierarchically organized cancer cells introduced in Ref. [11] and illustrated in Fig. 3A. According to the CSC hypothesis, cells are organized hierarchically, with CSCs at the top of the structure. CSCs can divide symmetrically giving rise to two new CSCs with probability or asymmetrically with probability giving rise to a CSC and a CC. While CSCs can duplicate for an indefinite amount of time, CCs become senescent and stop duplicating after a finite number of generations M. This is the minimal ingredient needed to model the CSC hierarchy. It is possible that CSCs differ in other biological aspects from CCs, but this is irrelevant from the point of view of population dynamics. This model was successfully used to describe the growth of melanoma cells, where the best fit to the data yields and M = 3811.


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

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

Models.(A) In the CSC model, CSCs (red) can divide symmetrically yielding two CSCs with probability  or asymmetrically yielding a CSC and a CC with probability . CCs divide symmetricaly for M generation after which they turn senescent. (B) Phenotipic switching is modeled by introducing a probability p that a CC transform back to the CSC state instead of duplicating. (C) In the imperfect marker model, the switching concerns marker expression not the CSC state. Both CSCs and CCs can be positive to the marker and upon division the expression of the marker can change randomly with respect to the originating cell according to the probabilities q for CSCs and q± for positive and negative CCs.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Models.(A) In the CSC model, CSCs (red) can divide symmetrically yielding two CSCs with probability or asymmetrically yielding a CSC and a CC with probability . CCs divide symmetricaly for M generation after which they turn senescent. (B) Phenotipic switching is modeled by introducing a probability p that a CC transform back to the CSC state instead of duplicating. (C) In the imperfect marker model, the switching concerns marker expression not the CSC state. Both CSCs and CCs can be positive to the marker and upon division the expression of the marker can change randomly with respect to the originating cell according to the probabilities q for CSCs and q± for positive and negative CCs.
Mentions: We consider a stochastic model for the proliferation of hierarchically organized cancer cells introduced in Ref. [11] and illustrated in Fig. 3A. According to the CSC hypothesis, cells are organized hierarchically, with CSCs at the top of the structure. CSCs can divide symmetrically giving rise to two new CSCs with probability or asymmetrically with probability giving rise to a CSC and a CC. While CSCs can duplicate for an indefinite amount of time, CCs become senescent and stop duplicating after a finite number of generations M. This is the minimal ingredient needed to model the CSC hierarchy. It is possible that CSCs differ in other biological aspects from CCs, but this is irrelevant from the point of view of population dynamics. This model was successfully used to describe the growth of melanoma cells, where the best fit to the data yields and M = 3811.

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