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

Spatial simulation of autologous cell defection for cancer treatment

Cancer cells are highly cooperative in a nepotistic way and evolutionarily dynamic. Present cancer treatments often overlook these aspects, inducing the selection of resistant cancer cells and the corresponding relapse. As an alternative method of cancer elimination, autologous cell defection (ACD) was suggested by which modified cancer cells parasitically reliant on other cancer cells are implemented to the cancer cluster. Specifically, modified cancer cells should not produce costly growth factors that promote the growth of other cancer cells while receiving the benefit of exposure to such growth factors. Analytical models and rudimentary experiments up to date provide the medical feasibility of this method. In this study, I built comprehensive spatial simulation models by embracing the effects of the multiple growth factors, the Warburg effect, mutations and immunity. The simulation results based on planar spatial structures indicate that implementation of the defective modified tumours may replace the existing cancer cluster and defective cells would later collapse by themselves. Furthermore, I built a mathematical model that compares the fitness of the cells adjacent to the hypertumour-cancer interface. I also calculated whether anticancer drugs that reduce the effects of the growth factors promote or demote the utility of ACD under diverse fitness functions. The computational examination implies that anticancer drugs may impede the therapeutic effect of ACD when there is a strong concavity in the fitness function. The analysis results could work as a general guidance for effective ACD that may expand the paradigm of cancer treatment.

The paradox of cooperation among selfish cancer cells

It is traditionally assumed that during cancer development, tumor cells abort their initially cooperative behavior (i.e., cheat) in favor of evolutionary strategies designed solely to enhance their own fitness (i.e., a "selfish" life style) at the expense of that of the multicellular organism. However, the growth and progress of solid tumors can also involve cooperation among these presumed selfish cells (which, by definition, should be noncooperative) and with stromal cells. The ultimate and proximate reasons behind this paradox are not fully understood. Here, in the light of current theories on the evolution of cooperation, we discuss the possible evolutionary mechanisms that could explain the apparent cooperative behaviors among selfish malignant cells. In addition to the most classical explanations for cooperation in cancer and in general (by-product mutualism, kin selection, direct reciprocity, indirect reciprocity, network reciprocity, group selection), we propose the idea that "greenbeard" effects are relevant to explaining some cooperative behaviors in cancer. Also, we discuss the possibility that malignant cooperative cells express or co-opt cooperative traits normally expressed by healthy cells. We provide examples where considerations of these processes could help understand tumorigenesis and metastasis and argue that this framework provides novel insights into cancer biology and potential strategies for cancer prevention and treatment.

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.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

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.