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Reversibility of state transitions is intensively studied topic in manyscientific disciplines over many years. In cell biology, it plays an importantrole in epigenetic variation of phenotypes, known as phenotypic plasticity.More interestingly, the cell state reversibility is probably crucial in theadaptation of population phenotypic heterogeneity to environmental fluctuationsby evolving bet-hedging strategy, which might confer to cancer cells resistanceto therapy. In this article, we propose a formalization of the evolution ofhighly reversible states in the environments of periodic variability. Twointerrelated models of heterogeneous cell populations are proposed and theirbehavior is studied. The first model captures selection dynamics of the cellclones for the respective levels of phenotypic reversibility. The second modelfocuses on the interplay between reversibility and drug resistance in theparticular case of cancer. Overall, our results show that the thresholddependencies are emergent features of the investigated model with eventualtherapeutic relevance. Presented examples demonstrate importance of taking intoaccount cell to cell heterogeneity within a system of clones with differentreversibility quantified by appropriately chosen genetic and epigenetic entropymeasures.

Toward understanding of the role of reversibility of phenotypic switching in the evolution of resistance to therapy