  Reversibility of state transitions is intensively studied topic in many
scientific disciplines over many years. In cell biology, it plays an important
role in epigenetic variation of phenotypes, known as phenotypic plasticity.
More interestingly, the cell state reversibility is probably crucial in the
adaptation of population phenotypic heterogeneity to environmental fluctuations
by evolving bet-hedging strategy, which might confer to cancer cells resistance
to therapy. In this article, we propose a formalization of the evolution of
highly reversible states in the environments of periodic variability. Two
interrelated models of heterogeneous cell populations are proposed and their
behavior is studied. The first model captures selection dynamics of the cell
clones for the respective levels of phenotypic reversibility. The second model
focuses on the interplay between reversibility and drug resistance in the
particular case of cancer. Overall, our results show that the threshold
dependencies are emergent features of the investigated model with eventual
therapeutic relevance. Presented examples demonstrate importance of taking into
account cell to cell heterogeneity within a system of clones with different
reversibility quantified by appropriately chosen genetic and epigenetic entropy
measures.
