Population dynamics of cancer cells with cell state conversions.

Cancer stem cell (CSC) theory suggests a cell-lineage structure in tumor cells in which CSCs are capable of giving rise to the other non-stem cancer cells (NSCCs) but not vice versa. However, an alternative scenario of bidirectional interconversions between CSCs and NSCCs was proposed very recently. Here we present a general population model of cancer cells by integrating conventional cell divisions with direct conversions between different cell states, namely, not only can CSCs differentiate into NSCCs by asymmetric cell division, NSCCs can also dedifferentiate into CSCs by cell state conversion. Our theoretical model is validated when applying the model to recent experimental data. It is also found that the transient increase in CSCs proportion initiated from the purified NSCCs subpopulation cannot be well predicted by the conventional CSC model where the conversion from NSCCs to CSCs is forbidden, implying that the cell state conversion is required especially for the transient dynamics. The theoretical analysis also gives the condition such that our general model can be equivalently reduced into a simple Markov chain with only cell state transitions keeping the same cell proportion dynamics.