Cancer quasispecies and stem-like adaptive aneuploidy

In this paper we develop a theoretical frame to understand self-regulation of aneuploidy rate in cancer and stem cells. This is accomplished building upon quasispecies theory, by leaving its formal mathematical structure intact, but by drastically changing the meaning of its objects. In particular, we propose a novel definition of chromosomal master sequence, as a sequence of physically distinct whole or fragmented chromosomes, whose length is taken to be the sum of the copy numbers of each whole or fragmented chromosome. This fundamental change in the functional objects of quasispecies theory allows us to show that previously measured aneuploidy rates in cancer populations are already close to a formally derived aneuploid error threshold, and that any value of aneuploidy rate larger than the aneuploid error threshold would lead to a loss of fitness of a tumor population. Finally, we make a phenomenological analysis of existing experimental evidence to argue that single clone cancer cells, derived from an aneuploid cancer subpopulation, are capable of self-regulating their aneuploidy rate and of adapting it to distinct environments, namely primary and metastatic microenvironments. We also discuss the potential origin of this self-regulatory ability in the wider context of developmental and comparative biology and we hypothesize the existence of a diversification factor, i.e. a cellular mechanism that regulates adaptation of aneuploidy rates, active in all embryo, adult and cancer stem cells.