Remus Stana, Uri Ben-David, Daniel B Weissman, Yoav Ram

Evolutionary rescue happens when a population survives a sudden environmental change that initially causes the population to decline toward extinction. A prime example of evolutionary rescue is the ability of cancer to survive exposure to treatment. One evolutionary mechanism by which a population of cancer cells can adapt to chemotherapy is aneuploidy. Aneuploid cancer cells can be fitter in an environment altered by anti-cancer drugs, e.g., because aneuploidy disrupts the pathways usually targeted by the drugs. Indeed, aneuploidy is highly prevalent in tumors, and some anti-cancer drugs fight cancer by increasing chromosomal instability. Here, we model the impact of aneuploidy on the fate of a population of cancer cells. We use multi-type branching processes to approximate the probability that a tumor survives drug treatment as a function of the initial tumor size, the rates at which aneuploidy and other beneficial mutations occur, and the growth rates of the drug-sensitive and drug-resistant cells. Additionally, we investigate the effect of the pre-existent aneuploid cells on the probability of evolutionary rescue. Finally, we estimate the tumor’s mean recurrence time to revert to its initial size following treatment and evolutionary rescue. We propose that aneuploidy can play an essential role in the relapse of smaller secondary tumors.