Graduation Year

2024

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Molecular Biosciences

Major Professor

Joel S. Brown, Ph.D.

Committee Member

Frederick R. Adler, Ph.D.

Committee Member

Sarah R. Amend, Ph.D.

Committee Member

Alexander R. A. Anderson, Ph.D.

Committee Member

Andriy Marusyk, Ph.D.

Committee Member

Kateřina Staňková, Ph.D.

Keywords

Cancer Evolution, Evolutionary Demography, Evolutionary Game Theory, Life History Theory, Mathematical Modeling

Abstract

In this dissertation, I develop and apply eco-evolutionary modeling techniques to understand how the polyaneuploid cancer cell (PACC) state, entered when aneuploid cells exit the cell cycle after S phase and undergo a whole genome duplication, contributes to therapeutic resistance. Since resistance remains one of the primary causes of treatment failure in cancer patients, it is critical to understand how such demographic state transitions allow for acclimatization of cancer cells to therapeutic stressors and how they interact with evolutionary processes to promote irreversible resistance.

In Chapters Two and Three, I lay the foundation for this work. In Chapter Two, I describe how mathematical modeling, and evolutionary game theory (sensu G functions) in particular, is well-suited for understanding cancer’s dynamics, from basic growth to cellular competition, to resistance. Included in this didactic chapter is a basic web tool that allows users to explore basic G function models without needing to fully understand the underlying mathematics. I have found this to be a pedagogically useful tool in helping explain the power of mathematical modeling to those less inclined towards using or understanding mathematics. In Chapter Three, I provide a background of polyploidization in cancer and explain how the PACC state fits into the broader landscape of cellular enlargement reprogramming. As this is a rather new and rapidly changing field, much of the biology remains to be discovered and several research groups have been investigating the same (or closely related) phenomena using different terminology. This not only makes it daunting and off-putting for newcomers to the field, but it also hampers collaborations (akin to the ongoing divide between G functions and adaptive dynamics). To help remedy this problem, Chapter Three provides a brief classification system for some of the main concepts in the field and hopefully prompts further efforts towards clarification.

Chapters Four, Five, and Six are the primary modeling chapters in this dissertation. They show how qualitative modeling and (observational) experimental work can be a two-way street. Based on initial observations of the PACC state, these chapters explore how evolutionary triage (ET) and the PACC state provides a refuge for cells from therapy and confers greater heritable variation to progeny, increasing their evolvability. In Chapter Four, I used a strong inference approach to create mathematical models of the ET and a couple other hypotheses (a single state model wherein the PACC state was entirely ignored and a non-proliferation hypothesis wherein the PACC state solely provides cells a refuge from therapy) to show how the PACC state may contribute to the ecological and evolutionary dynamics of cancer resistance. Additionally, I showed how life history enlightened measures, which use drug to block transitions among cell states in conjunction with standard chemotherapy, may be effective for cancer eradication.

Colleagues at Johns Hopkins University tested my simulation predictions with in vitro experiments and found discrepancies: They noticed that cells exiting the PACC state immediately displayed high levels of resistance to therapy. Unlike as would be expected under classical Darwinian evolution with Mendelian inheritance, there was no observable death of mutant clones. This challenge prompted the investigations in Chapter Five. In this chapter, I model a self (epi) genetic modification (SGM) process whereby cells in the PACC state (PACCs) find a viable solution to the stressor and only then depolyploidize, generating heritably resistant progeny. I created and used a Gillespie eco-evolutionary-demographic simulation algorithm to model and compare SGM to ET. Qualitative results from our SGM simulations indeed matched those found in the lab. Namely, we were able to qualitatively capture the observation that under extreme stress, cells transition into the PACC state and, after a delay, depolyploidization immediately produces resistant progeny (without any creative destruction). Furthermore, we showed that although such an SGM process may be favored in highly stressful environments in which only survival matters, ET may be favored in mildly stressful environments in which density-dependent competition becomes more important.

Chapter Six was inspired by observations from my Johns Hopkins collaborators, which suggested that PACC progeny exhibit lower death rates upon repeated exposure to (the same or different) therapy. Using my simulation algorithm from Chapter Five, I showed that transgenerational plasticity, wherein PACC progeny are more likely to re-enter the PACC state under stressful conditions, could account for this observation, as could a stress-agnostic mechanism of increased innate resistance.

In Chapter Seven, I provide the mathematical grounding for the modeling techniques I developed to model the eco-evolutionary dynamics of cancer populations with 2N+ and PACC states in Chapter Four. This technique combines aspects of matrix population modeling and evolutionary game theory to model eco-evolutionary dynamics of structured populations in discrete and continuous time. We define key equilibrium concepts and assess stability properties of these equilibria. Additionally, we briefly touch upon multi-state structured populations and introduce a technique for their analysis. We illustrate our method using a toy model of baboon life history. The methodology is general to diverse life-history phenomena well beyond important applications in cancer.

Overall, this work provides a modeling and conceptual framework for the PACC state. It explores ways by which the PACC state contributes to resistance, hypothesizes novel mechanisms of resistance acquisition, and presents mathematical tools to model non-traditional forms of inheritance and eco-evolutionary dynamics in structured populations.

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