Stochastic models of Mendelian and reverse transcriptional inheritance in state-structured cancer populations

Abstract

Recent evidence suggests that a polyaneuploid cancer cell (PACC) state may play a key role in the adaptation of cancer cells to stressful environments and in promoting therapeutic resistance. The PACC state allows cancer cells to pause cell division and to avoid DNA damage and programmed cell death. Transition to the PACC state may also lead to an increase in the cancer cell's ability to generate heritable variation (evolvability). One way this can occur is through evolutionary triage. Under this framework, cells gradually gain resistance by scaling hills on a fitness landscape through a process of mutation and selection. Another way this can happen is through self-genetic modification whereby cells in the PACC state find a viable solution to the stressor and then undergo depolyploidization, passing it on to their heritably resistant progeny. Here, we develop a stochastic model to simulate both of these evolutionary frameworks. We examine the impact of treatment dosage and extent of self-genetic modification on eco-evolutionary dynamics of cancer cells with aneuploid and PACC states. We find that under low doses of therapy, evolutionary triage performs better whereas under high doses of therapy, self-genetic modification is favored. This study generates predictions for teasing apart these biological hypotheses, examines the implications of each in the context of cancer, and provides a modeling framework to compare Mendelian and non-traditional forms of inheritance.

Figure 1

Flowcharts depicting the probabilistic and hence stochastic steps for the simulations of evolutionary triage (a) and self-genetic modification (b). The green text indicates where in the simulation process SGM differs from ET. See the Supplemental Material for a thorough explanation for how Eq. (1) translates into the stochastic birth–death switching process.

Figure 2

When evolutionary triage and self-genetic modification occurs. The curves depicted here are sample, schematic adaptive landscapes. They are not representative of any underlying biological phenomenon, but are rather provided as an illustration of what happens when species are at, close to, or far from an evolutionary peak. When cells are at a fitness peak (a), technically, due to a lack of selection pressure, no evolution occurs. When cells are bobbing near the sea level (b), only evolutionary triage occurs. When cells are drowning (c), primarily self-genetic modification occurs, though evolutionary triage can still occur via the 2N+ state.

Figure 3

No therapy (a), continuous therapy (b), and intermittent therapy (c) under evolutionary triage and self-genetic modification. Under SGM, the stable PACC state allows cells to persist under therapy and buys them enough time to evolve adequate levels of resistance and avoid extinction. Under ET, in most cases, the cells are able to evolve resistance quickly enough to avoid extinction; however, extinction still occurs in a minority of cases.

Figure 4

Low dose (a) and high dose (b) continuous therapy under evolutionary triage and self-genetic modification. The higher the dose of therapy, the longer cells remain in the stable PACC state under SGM. Under ET, all populations avoid extinction under low dose therapy, but the vast majority go extinct when exposed to a high dose of therapy.

Figure 5

Population and strategy dynamics for self-genetic modification under continuous therapy. The degree of self-genetic modification influences when the cancer cell population shifts from self-genetic modification to evolutionary triage: the greater the degree of self-genetic modification, the longer the cells will remain in a stable PACC state.

Figure 6

Competitive dynamics of cancer populations with self-genetic modification and evolutionary triage under continuous therapy. Under low dose therapy (a), cell population under ET outcompete those under SGM in the majority of cases. Conversely, under high dose therapy (b), cell populations under SGM outcompete those under ET.

Figure 7

Extinction rates for evolutionary triage and self-genetic modification for various drug doses. ET is favored under low selection regimes and SGM is favored under high selection regimes. When external selection pressures are very low, SGM and ET mechanistically act in an identical fashion.