Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.
The emergence of the information age in the last few decades brought with it an explosion of biomedical data. But with great power comes great responsibility: there is now a pressing need for new data analysis algorithms to be developed to make sense of the data and transform this information into knowledge which can be directly translated into the clinic. Topological data analysis (TDA) provides a promising path forward: using tools from the mathematical field of algebraic topology, TDA provides a framework to extract insights into the often high-dimensional, incomplete, and noisy nature of biomedical data. Nowhere is this more evident than in the field of oncology, where patient-specific data is routinely presented to clinicians in a variety of forms, from imaging to single cell genomic sequencing. In this review, we focus on applications involving persistent homology, one of the main tools of TDA. We describe some recent successes of TDA in oncology, specifically in predicting treatment responses and prognosis, tumor segmentation and computer-aided diagnosis, disease classification, and cellular architecture determination. We also provide suggestions on avenues for future research including utilizing TDA to analyze cancer time-series data such as gene expression changes during pathogenesis, investigation of the relation between angiogenic vessel structure and treatment efficacy from imaging data, and experimental confirmation that geometric and topological connectivity implies functional connectivity in the context of cancer.
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.
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.
Intratumoral molecular cancer cell heterogeneity is conventionally ascribed to the accumulation of random mutations that occasionally generate fitter phenotypes. This model is built upon the “mutation-selection” paradigm in which mutations drive ever-fitter cancer cells independent of environmental circumstances. An alternative model posits spatio-temporal variation (e.g., blood flow heterogeneity) drives speciation by selecting for cancer cells adapted to each different environment. Here, spatial genetic variation is the consequence rather than the cause of intratumoral evolution. In nature, spatially heterogenous environments are frequently coupled through migration. Drawing from ecological models, we investigate adjacent well-perfused and poorly-perfused tumor regions as “source” and “sink” habitats, respectively. The source habitat has a high carrying capacity resulting in more emigration than immigration. Sink habitats may support a small (“soft-sink”) or no (“hard-sink”) local population. Ecologically, sink habitats can reduce the population size of the source habitat so that, for example, the density of cancer cells directly around blood vessels may be lower than expected. Evolutionarily, sink habitats can exert a selective pressure favoring traits different from those in the source habitat so that, for example, cancer cells adjacent to blood vessels may be suboptimally adapted for that habitat. Soft sinks favor a generalist cancer cell type that moves between the environment but can, under some circumstances, produce speciation events forming source and sink habitat specialists resulting in significant molecular variation in cancer cells separated by small distances. Finally, sink habitats, with limited blood supply, may receive reduced concentrations of systemic drug treatments; and local hypoxia and acidosis may further decrease drug efficacy allowing cells to survive treatment and evolve resistance. In such cases, the sink transforms into the source habitat for resistant cancer cells, leading to treatment failure and tumor progression. We note these dynamics will result in spatial variations in molecular properties as an alternative to the conventional branched evolution model and will result in cellular migration as well as variation in cancer cell phenotype and proliferation currently described by the stem cell paradigm.
The tragedy of the commons occurs when competition among individual members of a group leads to overexploitation of a shared resource to the detriment of the overall population. We hypothesize that cancer cells may engage in a tragedy of the commons when competing for a shared resource such as glucose. To formalize this notion, we create a game theoretic model of glucose uptake based on a cell’s investment in transporters relative to that of its neighboring cells. We show that production of transporters per cell increases as the number of competing cells in a microenvironment increases and nutrient uptake per cell decreases. Furthermore, the greater the resource availability, the more intense the tragedy of the commons at the ESS. Based on our simulations, cancer cells produce 2.2–2.7 times more glucose transporters than would produce optimal fitness for all group members. A tragedy of the commons affords novel therapeutic strategies. By simulating GLUT1 inhibitor and glucose deprivation treatments, we demonstrate a synergistic combination with standard-of-care therapies, while also displaying the existence of a trade-off between competition among cancer cells and depression of their gain function. Assuming cancer cell transporter production is heritable, we then show the potential for a sucker’s gambit therapy by exploiting this trade-off. By strategically changing environmental conditions, we can take advantage of cellular competition and gain function depression.
All biological systems depend on signals for coordination: signals which pass information among agents that run the gamut from cells to organisms. However, their very importance makes signals vulnerable to subversion. How can a receiver know whether a signal is honest or deceptive? In other words, are signals necessarily a reliable indicator of agent quality or need? By drawing parallels to ecological phenomena ranging from begging by nestlings to social insects, we investigate the role of signal degradation in cancer. We thus think of cancer as a form of corruption, in which cells command huge resource investment through relatively cheap signals, just as relatively small bribes can leverage large profits. We discuss various mechanisms which prevent deceptive signaling in the natural world and within tissues. We show how cancers evolve ways to escape these controls and relate these back to evasion mechanisms in ecology. We next introduce two related concepts, co-option and collusion, and show how they play critical roles in ecology and cancer. Drawing on public policy, we propose new approaches to view treatment based on taxation, changing the incentive structure, and the recognition of corrupted signaling networks.
The author constructs a mathematical model capturing tumor-immune dynamics, incorporating the evolution of drug resistance, pharmacokinetics and pharmacodynamics of administered drugs, and immunotherapy possibilities. Numerical simulations are performed to analyze the model under a variety of treatment possibilities. A sensitivity analysis is performed to determine the parameters contributing the most to the variance in effector cell, resistant, and sensitive tumor cell populations. Then, a detailed optimal control analysis is performed, along with a numerical simulation of optimal treatment profiles for a hypothetical patient.
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