A life history model of the ecological and evolutionary dynamics of polyaneuploid cancer cells

Abstract

Therapeutic resistance is one of the main reasons for treatment failure in cancer patients. The polyaneuploid cancer cell (PACC) state has been shown to promote resistance by providing a refuge for cancer cells from the effects of therapy and by helping them adapt to a variety of environmental stressors. This state is the result of aneuploid cancer cells undergoing whole genome doubling and skipping mitosis, cytokinesis, or both. In this paper, we create a novel mathematical framework for modeling the eco-evolutionary dynamics of state-structured populations and use this framework to construct a model of cancer populations with an aneuploid and a PACC state. Using in silico simulations, we explore how the PACC state allows cancer cells to (1) survive extreme environmental conditions by exiting the cell cycle after S phase and protecting genomic material and (2) aid in adaptation to environmental stressors by increasing the cancer cell’s ability to generate heritable variation (evolvability) through the increase in genomic content that accompanies polyploidization. In doing so, we demonstrate the ability of the PACC state to allow cancer cells to persist under therapy and evolve therapeutic resistance. By eliminating cells in the PACC state through appropriately-timed PACC-targeted therapies, we show how we can prevent the emergence of resistance and promote cancer eradication.

Modeling cancer’s ecological and evolutionary dynamics

“…Although we have presented a simplified version of the evolution of drug resistance in cancer, there are many ways this model can be extended, depending on the question of interest. For example, one could consider the influence of other cell types such as immune cells and fibroblasts, spatiotemporal variation and heterogeneity in the microenvironment [ 27 , 61 , 85 ], side effects of drugs [ 86 ], drug scheduling [ 109 ], evolutionarily informed therapies [ 18 , 19 ], and the effects of plasticity and cell states [ 20 , 21 ].…”

“…At each time step, the trait changes based on the slope of the adaptive landscape ( ) and the “step size” ( k ), with local and favorable alternatives being preferred at each step. Although k may be variable [ 20 , 21 ], changing as a function of how stressed cells are in their environment (e.g., via stress-induced mutagenesis [ 41 ]), we choose to fix k to a constant value here for expositional purposes.…”

“…In recent years, however, there has been a growing appreciation among both theorists and empiricists for cancer as an ecological and evolutionary process [ 35 , 58 , 100 ]. This view has led to a better understanding of the initiation and spread of cancer [ 2 , 12 , 45 , 95 ], innovations in evolutionarily informed therapies [ 19 , 20 , 47 , 105 ], and a reframing of the way we think about cancer [ 5 , 17 , 51 , 76 , 83 , 91 ]. In this paper, we introduce an evolutionary game theoretic (EGT) approach called G functions that allow us to mathematically formalize notions of ecology and evolution in cancer.…”

Computational Biology Helps Understand How Polyploid Giant Cancer Cells Drive Tumor Success

“…Polyploid cells are vulnerable during meiosis due to chromosome pairing difficulties and genomic instability [ 30 ]; this can be solved by a transient reversion of polyploidy (depolyploidization) [ 32 ], multipolar division [ 33 ], chromosomal rearrangement, and DNA divergence. A high degree of polyploidy or aneuploidy are detrimental to the cell, but can increase cellular adaptability and plasticity, fueling intratumoral heterogeneity [ 34 , 35 ].…”

Integrating eco‐evolutionary dynamics into matrix population models for structured populations: Discrete and continuous frameworks

“…Evolutionary game theoretic techniques such as the G function framework are naturally suited to model and analyse eco‐evolutionary dynamics of populations. These methods have been developed over several decades and have been implemented in continuous (Cohen et al, 1999; Meszéna et al, 2005; Ripa et al, 2009) and discrete (Parvinen, 2006, 2007) time, in stochastic (Bukkuri et al, 2022b; Champagnat et al, 2006; Klebaner et al, 2011) and deterministic (Apaloo et al, 2009; Bukkuri & Brown, 2021; Bukkuri, Gatenby, et al, 2022; Bukkuri et al, 2022a; Orlando et al, 2012) fashion, and at population (Bukkuri et al, 2022b; Dieckmann et al, 1995) and agent‐based (Ackermann & Doebeli, 2004; Baptestini et al, 2009; Mágori et al, 2005) levels. And although much work has been done to examine how environmental feedback impact underlying eco‐evolutionary games (Hauert et al, 2019; Tilman et al, 2020; Wang & Fu, 2020; Weitz et al, 2016), these models very rarely include state‐structure within the population (see Bukkuri et al, 2022a; Cunningham et al, 2021; Knight et al, 2015 for notable exceptions).…”