The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

Predicting resistance and pseudoprogression: are minimalistic immunoediting mathematical models capable of forecasting checkpoint inhibitor treatment outcomes in lung cancer?

BACKGROUND

The increased application of immune checkpoint inhibitors (ICIs) targeting PD-1/PD-L1 in lung cancer treatment generates clinical need to reliably predict individual patients' treatment outcomes.

METHODS

To bridge the prediction gap, we examine four different mathematical models in the form of ordinary differential equations, including a novel delayed response model. We rigorously evaluate their individual and combined predictive capabilities with regard to the patients' progressive disease (PD) status through equal weighting of model-derived outcome probabilities.

RESULTS

Fitting the complete treatment course, the novel delayed response model (R2=0.938) outperformed the simplest model (R2=0.865). The model combination was able to reliably predict patient PD outcome with an overall accuracy of 77% (sensitivity = 70%, specificity = 81%), solely through calibration with primary tumor longest diameter measurements. It autonomously identified a subset of 51% of patients where predictions with an overall accuracy of 81% (sensitivity = 81%, specificity = 81%) can be achieved. All models significantly outperformed a fully data-driven machine learning-based approach.

IMPLICATIONS

These modeling approaches provide a dynamic baseline framework to support clinicians in treatment decisions by identifying different treatment outcome trajectories with already clinically available measurement data.

LIMITATIONS AND FUTURE DIRECTIONS

Conjoint application of the presented approach with other predictive tools and biomarkers, as well as further disease information (e.g. metastatic stage), could further enhance treatment outcome prediction. We believe the simple model formulations allow widespread adoption of the developed models to other cancer types. Similar models can easily be formulated for other treatment modalities.

The effect of tumor composition on the success of adaptive therapy: The case of metastatic Castrate-Resistant Prostate Cancer

Prostate-specific antigen (PSA) is the most commonly used serum marker for prostate cancer. It plays a role in cancer detection, treatment monitoring, and more recently, in guiding adaptive therapy protocols, where treatment is alternated based on PSA levels. However, the relationship between PSA levels and tumor volume remains poorly understood. Empirical evidence suggests that different cancer cell types produce varying amounts of PSA. Despite this, current mathematical cancer models often assume either that all cell types contribute equally to PSA levels or that only certain subpopulations produce PSA at fixed rates. In this study, we compare Zhang et al.'s classical adaptive therapy protocol with the standard of care, which involves continuous maximum tolerable dose treatment, under different assumptions regarding PSA production. Specifically, we explore the possibility that testosterone-dependent, testosterone-producing, and testosterone-independent cells contribute to PSA production to varying degrees. We use the time to competitive release as a proxy for the time to disease progression. Our findings indicate that adaptive therapy consistently results in a longer time to competitive release compared to the standard of care, regardless of the assumptions about PSA production. However, when testosterone-independent cells are the sole PSA producers, Zhang et al.'s adaptive therapy protocol becomes inapplicable, as PSA levels never fall to half of their initial value, preventing therapy discontinuation. Additionally, we observe that the number and duration of treatment cycles in adaptive therapy are highly sensitive to assumptions about how much each cell type contributes to PSA production. Overall, our results emphasize the need for a deeper understanding of patient-specific PSA dynamics, which could enhance the effectiveness of adaptive therapy in prostate cancer treatment.

A novel combination therapy for ER+ breast cancer suppresses drug resistance via an evolutionary double-bind

Chemotherapy remains a commonly used and important treatment option for metastatic breast cancer. A majority of ER+ metastatic breast cancer patients ultimately develop resistance to chemotherapy, resulting in disease progression. We hypothesized that an "evolutionary double-bind", where treatment with one drug improves the response to a different agent, would improve the effectiveness and durability of responses to chemotherapy. This approach exploits vulnerabilities in acquired resistance mechanisms. Evolutionary models can be used in refractory cancer to identify alternative treatment strategies that capitalize on acquired vulnerabilities and resistance traits for improved outcomes. To develop and test these models, ER+ breast cancer cell lineages sensitive and resistant to chemotherapy are grown in spheroids with varied initial population frequencies to measure cross-sensitivity and efficacy of chemotherapy and add-on treatments such as disulfiram combination treatment. Different treatment schedules then assessed the best strategy for reducing the selection of resistant populations. We developed and parameterized a game-theoretic mathematical model from this in vitro experimental data, and used it to predict the existence of a double-bind where selection for resistance to chemotherapy induces sensitivity to disulfiram. The model predicts a dose-dependent re-sensitization (a double-bind) to chemotherapy for monotherapy disulfiram.

An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer

This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signalling pathways in oesophageal cancer. The framework is based on a novel dynamical model that takes into account the dynamic progression of signalling pathways, resistance mechanisms and monoclonal antibody therapies. This game involves a scenario in which signalling pathways and monoclonal antibodies are the players competing against each other, where monoclonal antibodies use Brentuximab and Pembrolizumab dosages as strategies to counter the evolutionary resistance strategy implemented by the signalling pathways. Their interactions are described by the dynamical model, which serves as the game's playground. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash equilibria, are conducted within this framework to ascertain the most favourable outcome for the patient. By comparing Stackelberg equilibria with Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signalling pathways and are critical for the success of monoclonal antibodies in improving oesophageal cancer patient outcomes.

Phenotypic noise and plasticity in cancer evolution

Non-genetic alterations can produce changes in a cell's phenotype. In cancer, these phenomena can influence a cell's fitness by conferring access to heritable, beneficial phenotypes. Herein, we argue that current discussions of 'phenotypic plasticity' in cancer evolution ignore a salient feature of the original definition: namely, that it occurs in response to an environmental change. We suggest 'phenotypic noise' be used to distinguish non-genetic changes in phenotype that occur independently from the environment. We discuss the conceptual and methodological techniques used to identify these phenomena during cancer evolution. We propose that the distinction will guide efforts to define mechanisms of phenotype change, accelerate translational work to manipulate phenotypes through treatment, and, ultimately, improve patient outcomes.

A war on many fronts: cross disciplinary approaches for novel cancer treatment strategies

Cancer is a disease characterized by uncontrolled cellular growth where cancer cells take advantage of surrounding cellular populations to obtain resources and promote invasion. Carcinomas are the most common type of cancer accounting for almost 90% of cancer cases. One of the major subtypes of carcinomas are adenocarcinomas, which originate from glandular cells that line certain internal organs. Cancers such as breast, prostate, lung, pancreas, colon, esophageal, kidney are often adenocarcinomas. Current treatment strategies include surgery, chemotherapy, radiation, targeted therapy, and more recently immunotherapy. However, patients with adenocarcinomas often develop resistance or recur after the first line of treatment. Understanding how networks of tumor cells interact with each other and the tumor microenvironment is crucial to avoid recurrence, resistance, and high-dose therapy toxicities. In this review, we explore how mathematical modeling tools from different disciplines can aid in the development of effective and personalized cancer treatment strategies. Here, we describe how concepts from the disciplines of ecology and evolution, economics, and control engineering have been applied to mathematically model cancer dynamics and enhance treatment strategies.

N-of-1 medicine

ABSTRACT

The fields of precision and personalised medicine have led to promising advances in tailoring treatment to individual patients. Examples include genome/molecular alteration-guided drug selection, single-patient gene therapy design and synergy-based drug combination development, and these approaches can yield substantially diverse recommendations. Therefore, it is important to define each domain and delineate their commonalities and differences in an effort to develop novel clinical trial designs, streamline workflow development, rethink regulatory considerations, create value in healthcare and economics assessments, and other factors. These and other segments are essential to recognise the diversity within these domains to accelerate their respective workflows towards practice-changing healthcare. To emphasise these points, this article elaborates on the concept of digital health and digital medicine-enabled N-of-1 medicine, which individualises combination regimen and dosing using a patient's own data. We will conclude with recommendations for consideration when developing novel workflows based on emerging digital-based platforms.

A landscape of patient-derived cancer-associated fibroblast signals in endometrial cancers

In conversation with endometrial tumor cells, the endometrial cancer-associated fibroblasts (CAFs) are the "partners in crime" of uterine neoplasm's highly heterogeneous tumor microenvironment (TME). We designed a laboratory-friendly method to culture endometrial CAFs on a patient-to-patient basis for studying the CAF-TME and CAF-tumor cell interaction(s). Here, we present a comprehensive characterization of endometrial CAFs derived from patients' tumor tissues (T) and tumor-adjacent normal tissues (N). We used more than 80 T and N from 53 consecutive consented patients with endometrial cancers at the Avera Cancer Institute. We derived TCAF and NCAF in a non-enzymatic feeder-layer culture and characterized their expression of markers by qRT-PCR, flow cytometry, immunocytochemistry, immunofluorescence, and Western blot. Although similar in the expression pattern of EpCAM-/CK18-/vimentin+ as in ovarian CAFs, endometrial NCAFs, and TCAFs characteristically presented dual morphology in culture. Endometrial CAFs were EpCAM-/CK18-/CD45-/CD31-/SMA+/TE-7+/PDGFRA+/CXCL12+/Meflin+/CD155+/CD90+ with patient-specific positivity for S100A4/FAP/PD-L1/CD44. Endometrial CAFs expressed mRNAs for signaling proteins of several pathways and receptor-ligands, including (1) cell cycle pathway, (2) TGF pathway, (3) FGF pathway, (4) Wnt-beta-catenin pathway, (5) HER pathway, (6) tyrosine kinase receptor ligands, and (7) steroid receptors. We tested the hypoxic response of CAFs to show that endometrial CAFs upregulate MMP1 in a HIF-1a-independent manner. In trying to delineate the relationship between expressions of CAF markers and T-cells in the tumor tissue, we observed that FAP-positive CAFs that are derived from CD4/CD8 positive tumor tissue expressed CXCL12 mRNA. The data indicate the role of the CXCL12-CXCR4 pathway of the CAF-rich stroma in the lymphocytic infiltration of the tumor. We demonstrate that endometrial CAFs can be cultured in an enzymatic-digestion-independent manner, and their signaling landscape can be mapped toward understanding CAF-TME dialogue. Our data will help unearth the functional relevance of endometrial CAFs in the context of clinical outcomes and designing CAF-inclusive therapy in the future.

Cancer Evolution: A Multifaceted Affair

Cancer cells adapt and survive through the acquisition and selection of molecular modifications. This process defines cancer evolution. Building on a theoretical framework based on heritable genetic changes has provided insights into the mechanisms supporting cancer evolution. However, cancer hallmarks also emerge via heritable nongenetic mechanisms, including epigenetic and chromatin topological changes, and interactions between tumor cells and the tumor microenvironment. Recent findings on tumor evolutionary mechanisms draw a multifaceted picture where heterogeneous forces interact and influence each other while shaping tumor progression. A comprehensive characterization of the cancer evolutionary toolkit is required to improve personalized medicine and biomarker discovery.

SIGNIFICANCE

Tumor evolution is fueled by multiple enabling mechanisms. Importantly, genetic instability, epigenetic reprogramming, and interactions with the tumor microenvironment are neither alternative nor independent evolutionary mechanisms. As demonstrated by findings highlighted in this perspective, experimental and theoretical approaches must account for multiple evolutionary mechanisms and their interactions to ultimately understand, predict, and steer tumor evolution.

Tumor-TME Bipartite Landscape of PD-1/PD-L1 in Endometrial Cancers

The bipartite landscape of tumor cells and stromal cells determines a tumor's response to treatment during disease management. In endometrial cancers (ECs), the mechanistic contribution of PD-L1/L2 and PD-1 signaling of the host's tumor microenvironment (TME) (CAF and immune cells) in the context of the tumor cells is elusive. To understand the tumor-stroma-immune crosstalk, we studied the compartmental pattern of PD-L1/L2 and PD-1 expression in EC tissues and their matched CAFs. Over 116 surgically resected tumors (T) and the tumor-adjacent normal tissues (N) were obtained from consented unselected consecutive patients. IHC was performed in T, N-epi-thelium, and the stromal mesenchymal environment (SME; mesenchyme) in the T and N tissues. The staining intensity and distribution patterns of PD-L1/L2 and PD-1 in the FFPE sections of T and N were evaluated by a pathologist using a standard scoring system of TPS and CPS. We tested the PD-L1/L2 and PD-1 immune landscape of tumor-TME pair and normal epithelial-stromal mesenchyme pairs from patients with different grades of disease vis-à-vis their CAF PD-L1 levels. We used qRT-PCR to determine the expressions of mRNAs, while the flow cytometry and ICC determined the level of expression of proteins. We observed higher levels of PD-L1 mRNA and protein expression in primary CAFs from the resected tumor tissue compared to the tumor-adjacent normal tissues. We also determined the expression of patients' soluble PD-L1/L2 as peripheral readouts of PD-L1/L2 and PD-1. As we evaluated the results in the context of their pathological parameters, such as grades, stages, lymphovascular invasion, percentage of myometrial invasion, and dMMR in patients, the dominance of PD-L1 expression in TME was positively correlated to the higher pathological grades of tumors, and its relationship with the dMMR. Since the neutralization of CD8-positive cytotoxic T-cells is PD-L1-dependent, our data indicate that irrespective of the PD-L1 positivity of tumor cells, the PD-L1-positive CAFs can play a critical role in bringing out an additional load of PD-L1 for an effective engagement of PD-1 within a tumor mass.

Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks

Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the local strategy-dependent feedbacks. However, the impacts of these two types of environmental changes have only been studied separately, a complete picture of the environmental effects exerted by the combination of these two aspects remains unclear. Here we develop a theoretical framework that integrates group strategic behaviors with their general dynamic environments, where the global environmental fluctuations are associated with a nonlinear factor in public goods game and the local environmental feedbacks are described by the 'eco-evolutionary game'. We show how the coupled dynamics of local game-environment evolution differ in static and dynamic global environments. In particular, we find the emergence of cyclic evolution of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Further, we observe that this cyclic evolution disappears and transforms into an interior stable equilibrium when the global environment is frequency-dependent. Our results provide important insights into how diverse evolutionary outcomes could emerge from the nonlinear interactions between strategies and the changing environments.

Effects of Heterogeneity on Cancer: A Game Theory Perspective

In this study, we explore interactions between cancer cells by using the hawk-dove game. We analyze the heterogeneity of tumors by considering games with populations composed of 2 or 3 types of cell. We determine what strategies are evolutionarily stable in the 2-type and 3-type population games and what the corresponding expected payoffs are. Our results show that the payoff of the best-off cell in the 2-type population game is higher than that of the best-off cell in the 3-type population game. When these mathematical findings are transferred to the field of oncology they suggest that a tumor with low intratumor heterogeneity pursues a more aggressive course than one with high intratumor heterogeneity. Some histological and genomic data on clear cell renal cell carcinomas is consistent with these results. We underline the importance of identifying intratumor heterogeneity in routine practice and suggest that therapeutic strategies that preserve heterogeneity may be promising as they may slow down cancer growth.

Biomarkers or biotargets? Using competition to lure cancer cells into evolutionary traps

Background and Objectives

Cancer biomarkers provide information on the characteristics and extent of cancer progression and help inform clinical decision-making. However, they can also play functional roles in oncogenesis, from enabling metastases and inducing angiogenesis to promoting resistance to chemotherapy. The resulting evolution could bias estimates of cancer progression and lead to suboptimal treatment decisions.

Methodology

We create an evolutionary game theoretic model of cell-cell competition among cancer cells with different levels of biomarker production. We design and simulate therapies on top of this pre-existing game and examine population and biomarker dynamics.

Results

Using total biomarker as a proxy for population size generally underestimates chemotherapy efficacy and overestimates targeted therapy efficacy. If biomarker production promotes resistance and a targeted therapy against the biomarker exists, this dynamic can be used to set an evolutionary trap. After chemotherapy selects for a high biomarker-producing cancer cell population, targeted therapy could be highly effective for cancer extinction. Rather than using the most effective therapy given the cancer's current biomarker level and population size, it is more effective to 'overshoot' and utilize an evolutionary trap when the aim is extinction. Increasing cell-cell competition, as influenced by biomarker levels, can help prime and set these traps.

Conclusion and Implications

Evolution of functional biomarkers amplify the limitations of using total biomarker levels as a measure of tumor size when designing therapeutic protocols. Evolutionarily enlightened therapeutic strategies may be highly effective, assuming a targeted therapy against the biomarker is available.

Stackelberg evolutionary game theory: how to manage evolving systems

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader's most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. We show how our results have the potential to help in fields where humans try to bring an evolutionary system into the desired outcome, such as, among others, fisheries management, pest management and cancer treatment. Finally, we discuss limitations and opportunities for applying SEGs to improve the management of evolving biological systems. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

A CAF-Based Two-Cell Hybrid Co-Culture Model to Test Drug Resistance in Endometrial Cancers

The management of advanced or recurrent endometrial cancers presents a challenge due to the development of resistance to treatments. The knowledge regarding the role of the tumor microenvironment (TME) in determining the disease's progression and treatment outcome has evolved in recent years. As a TME component, cancer-associated fibroblasts (CAFs) are essential in developing drug-induced resistance in various solid tumors, including endometrial cancers. Hence, an unmet need exists to test the role of endometrial CAF in overcoming the roadblock of resistance in endometrial cancers. We present a novel tumor-TME two-cell ex vivo model to test CAF's role in resisting the anti-tumor drug, paclitaxel. Endometrial CAFs, both NCAFs (tumor-adjacent normal-tissue-derived CAFs) and TCAFs (tumor-tissue-derived CAFs) were validated by their expression markers. Both TCAFs and NCAFs expressed positive markers of CAF, including SMA, FAP, and S100A4, in varying degrees depending on the patients, while they consistently lacked the negative marker of CAF, EpCAM, as tested via flow cytometry and ICC. CAFs expressed TE-7 and immune marker, PD-L1, via ICC. CAFs better resisted the growth inhibitory effect of paclitaxel on endometrial tumor cells in 2D and 3D formats compared to the resistance of the tumoricidal effect of paclitaxel in the absence of CAFs. TCAF resisted the growth inhibitory effect of paclitaxel on endometrial AN3CA and RL-95-2 cells in an HyCC 3D format. Since NCAF similarly resisted the growth inhibitor action of paclitaxel, we tested NCAF and TCAF from the same patient to demonstrate the protective action of NCAF and TCAF in resisting the tumoricidal effect of paclitaxel in AN3CA in both 2D and 3D matrigel formats. Using this hybrid co-culture CAF and tumor cells, we established a patient-specific, laboratory-friendly, cost-effective, and time-sensitive model system to test drug resistance. The model will help test the role of CAFs in developing drug resistance and contribute to understanding tumor cell-CAF dialogue in gynecological cancers and beyond.

Clonal interactions in cancer: integrating quantitative models with experimental and clinical data

Tumors consist of different genotypically distinct subpopulations-or subclones-of cells. These subclones can influence neighboring clones in a process called "clonal interaction." Conventionally, research on driver mutations in cancer has focused on their cell-autonomous effects that lead to an increase in fitness of the cells containing the driver. Recently, with the advent of improved experimental and computational technologies for investigating tumor heterogeneity and clonal dynamics, new studies have shown the importance of clonal interactions in cancer initiation, progression, and metastasis. In this review we provide an overview of clonal interactions in cancer, discussing key discoveries from a diverse range of approaches to cancer biology research. We discuss common types of clonal interactions, such as cooperation and competition, its mechanisms, and the overall effect on tumorigenesis, with important implications for tumor heterogeneity, resistance to treatment, and tumor suppression. Quantitative models-in coordination with cell culture and animal model experiments-have played a vital role in investigating the nature of clonal interactions and the complex clonal dynamics they generate. We present mathematical and computational models that can be used to represent clonal interactions and provide examples of the roles they have played in identifying and quantifying the strength of clonal interactions in experimental systems. Clonal interactions have proved difficult to observe in clinical data; however, several very recent quantitative approaches enable their detection. We conclude by discussing ways in which researchers can further integrate quantitative methods with experimental and clinical data to elucidate the critical-and often surprising-roles of clonal interactions in human cancers.

A policy-making model for evolutionary SME behavior during a pandemic recession supported on game theory approach

The global economy has experienced a tremendous shock caused by the Covid-19 pandemic and its effects on the normal activities of SMEs, which provide essential driving economic force. Considering that there is currently no precise prediction about the end of this pandemic, many SMEs must make critical decisions about whether to remain in the market during the pandemic or to leave it, investing their assets in a more secure sector of the economy. However, in order to convince SMEs to remain in the market, thus maintaining the damaged economy, governments may variously apply punitive or supportive measures. In this regard, the interaction between SMEs strategies and government measures can be considered as an evolutionary game, in which the governments impose various policies after observing the evolutionary behaviors of SMEs. An evolutionary stable strategy (ESS) is derived through a replicator dynamic system, and the available payoff of each player is calculated by Nash equilibrium (NA). Finally, a numerical example is presented, and related managerial insights are proposed at the end of the current study. For instance, contrary to general belief, it can be inferred from investigating possible scenarios that punitive policies are more effective than supportive measures in convincing SMEs to remain in the market.

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

Evolutionary analysis of replicator dynamics about anti-cancer combination therapy

The emergence and growth of drug-resistant cancer cell subpopulations during anti-cancer treatment is a major challenge for cancer therapies. Combination therapies are usually applied for overcoming drug resistance. In the present paper, we explored the evolution outcome of tumor cell populations under different combination schedules of chemotherapy and p53 vaccine, by construction of replicator dynamical model for sensitive cells, chemotherapy-resistant cells and p53 vaccine-resistant cells. The local asymptotic stability analysis of the evolutionary stable points revealed that cancer population could evolve to the population with single subpopulation, or coexistence of sensitive cells and p53 vaccine-resistant cells, or coexistence of chemotherapy-resistant cells and p53 vaccine-resistant cells under different monotherapy or combination schedules. The design of adaptive therapy schedules that maintain the subpopulations under control is also demonstrated by sequential and periodic application of combination treatment strategies based on the evolutionary velocity and evolutionary absorbing regions. Applying a new replicator dynamical model, we further explored the supportive effects of sensitive cancer cells on targeted therapy-resistant cells revealed in mice experiments. It was shown that the supportive effects of sensitive cells could drive the evolution of cell population from sensitive cells to coexistence of sensitive cells and one type of targeted therapy-resistant cells.

Abiraterone-Docetaxel scheduling for metastatic castration-resistant prostate cancer based on evolutionary dynamics

Patients with metastatic castration-resistant prostate cancer (mCRPC) are divided into three groups based on their response to Abiraterone treatment: best responder, responder, and non-responder. In the latter two groups, successful outcomes may not be achieved due to the development of drug-resistant cells in the tumor environment during treatment. To overcome this challenge, a secondary drug can be used to control the population of drug-resistant cells, potentially leading to a longer period of disease inhibition. This paper proposes using a combination of Docetaxel and Abiraterone in some polytherapy methods to control both the overall cancer cell population and the drug-resistant subpopulation. To investigate the competition and evolution of mCRPC cancer phenotypes, as in previous studies, the Evolutionary Game Theory (EGT) has been used as a mathematical modeling of evolutionary biology concepts.

The conditional defector strategies can violate the most crucial supporting mechanisms of cooperation

Cooperation is essential for all domains of life. Yet, ironically, it is intrinsically vulnerable to exploitation by cheats. Hence, an explanatory necessity spurs many evolutionary biologists to search for mechanisms that could support cooperation. In general, cooperation can emerge and be maintained when cooperators are sufficiently interacting with themselves. This communication provides a kind of assortment and reciprocity. The most crucial and common mechanisms to achieve that task are kin selection, spatial structure, and enforcement (punishment). Here, we used agent-based simulation models to investigate these pivotal mechanisms against conditional defector strategies. We concluded that the latter could easily violate the former and take over the population. This surprising outcome may urge us to rethink the evolution of cooperation, as it illustrates that maintaining cooperation may be more difficult than previously thought. Moreover, empirical applications may support these theoretical findings, such as invading the cooperator population of pathogens by genetically engineered conditional defectors, which could be a potential therapy for many incurable diseases.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

Measuring competitive exclusion in non-small cell lung cancer

In this study, we experimentally measure the frequency-dependent interactions between a gefitinib-resistant non-small cell lung cancer population and its sensitive ancestor via the evolutionary game assay. We show that cost of resistance is insufficient to accurately predict competitive exclusion and that frequency-dependent growth rate measurements are required. Using frequency-dependent growth rate data, we then show that gefitinib treatment results in competitive exclusion of the ancestor, while the absence of treatment results in a likely, but not guaranteed, exclusion of the resistant strain. Then, using simulations, we demonstrate that incorporating ecological growth effects can influence the predicted extinction time. In addition, we show that higher drug concentrations may not lead to the optimal reduction in tumor burden. Together, these results highlight the potential importance of frequency-dependent growth rate data for understanding competing populations, both in the laboratory and as we translate adaptive therapy regimens to the clinic.

What do cellular responses to acidity tell us about cancer?

The notion that invasive cancer is a product of somatic evolution is a well-established theory that can be modelled mathematically and demonstrated empirically from therapeutic responses. Somatic evolution is by no means deterministic, and ample opportunities exist to steer its trajectory towards cancer cell extinction. One such strategy is to alter the chemical microenvironment shared between host and cancer cells in a way that no longer favours the latter. Ever since the first description of the Warburg effect, acidosis has been recognised as a key chemical signature of the tumour microenvironment. Recent findings have suggested that responses to acidosis, arising through a process of selection and adaptation, give cancer cells a competitive advantage over the host. A surge of research efforts has attempted to understand the basis of this advantage and seek ways of exploiting it therapeutically. Here, we review key findings and place these in the context of a mathematical framework. Looking ahead, we highlight areas relating to cellular adaptation, selection, and heterogeneity that merit more research efforts in order to close in on the goal of exploiting tumour acidity in future therapies.

Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

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.