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Register a new userStudying the emergence of invasiveness in tumours using game theory
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Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative mathematical model based on game theory and computer simulations using cellular automata. With this model we study the circumstances under which mutations that confer increased motility to cells can spread through a tumour made of rapidly proliferating cells. The analysis suggests therapies that could help prevent the progression towards malignancy and invasiveness of benign tumours.
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Tumour progression has been described as a sequence of traits or phenotypes that cells have to acquire if the neoplasm is to become an invasive and malignant cancer. Although the genetic mutations that lead to these phenotypes are random, the process by which some of these mutations become successful and spread is influenced by the tumour microenvironment and the presence of other phenotypes. It is thus likely that some phenotypes that are essential in tumour progression will emerge in the tumour population only with the prior presence of other different phenotypes. In this paper we use evolutionary game theory to analyse the interactions between three different tumour cell phenotypes defined by autonomous growth, anaerobic glycolysis, and cancer cell invasion. The model allows to understand certain specific aspects of glioma progression such as the emergence of diffuse tumour cell invasion in low-grade tumours. We find that the invasive phenotype is more likely to evolve after the appearance of the glycolytic phenotype which would explain the ubiquitous presence of invasive growth in malignant tumours. The result suggests that therapies which increase the fitness cost of switching to anaerobic glycolysis might decrease the probability of the emergence of more invasive phenotypes
We present a mathematical study of the emergence of phenotypic heterogeneity in vascularised tumours. Our study is based on formal asymptotic analysis and numerical simulations of a system of non-local parabolic equations that describes the phenotypic evolution of tumour cells and their nonlinear dynamic interactions with the oxygen, which is released from the intratumoural vascular network. Numerical simulations are carried out both in the case of arbitrary distributions of intratumour blood vessels and in the case where the intratumoural vascular network is reconstructed from clinical images obtained using dynamic optical coherence tomography. The results obtained support a more in-depth theoretical understanding of the eco-evolutionary process which underpins the emergence of phenotypic heterogeneity in vascularised tumours. In particular, our results offer a theoretical basis for empirical evidence indicating that the phenotypic properties of cancer cells in vascularised tumours vary with the distance from the blood vessels, and establish a relation between the degree of tumour tissue vascularisation and the level of intratumour phenotypic heterogeneity.
Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the evolution of cells in a tumour towards more malignant and aggressive phenotypes that tend to have a fitness advantage over the older populations. Although the evolutionary nature of cancer has been recognised for more than three decades (ever since the seminal work of Nowell) it has been only recently that tools traditionally used by ecological and evolutionary researchers have been adopted to study the evolution of cancer phenotypes in populations of individuals capable of co-operation and competition. In this chapter we will describe game theory as an important tool to study the emergence of cell phenotypes in a tumour and will critically review some of its applications in cancer research. These applications demonstrate that game theory can be used to understand the dynamics of somatic cancer evolution and suggest new therapies in which this knowledge could be applied to gain some control over the evolution of the tumour.
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of tumour cells, the concentration of oxygen and the concentration of a chemotherapeutic agent. In order to disentangle the impact of different evolutionary parameters on the emergence of intra-tumour phenotypic heterogeneity and the development of resistance to chemotherapy, we construct explicit solutions to the equation for the phenotypic distribution of tumour cells and provide a detailed quantitative characterisation of the long-time asymptotic behaviour of such solutions. Analytical results are integrated with numerical simulations of a calibrated version of the model based on biologically consistent parameter values. The results obtained provide a theoretical explanation for the observation that the phenotypic properties of tumour cells in vascularised tumours vary with the distance from the blood vessels. Moreover, we demonstrate that lower oxygen levels may correlate with higher levels of phenotypic variability, which suggests that the presence of hypoxic regions supports intra-tumour phenotypic heterogeneity. Finally, the results of our analysis put on a rigorous mathematical basis the idea, previously suggested by formal asymptotic results and numerical simulations, that hypoxia favours the selection for chemoresistant phenotypic variants prior to treatment. Consequently, this facilitates the development of resistance following chemotherapy.
Background: Analysing tumour architecture for metastatic potential usually focuses on phenotypic differences due to cellular morphology or specific genetic mutations, but often ignore the cells position within the heterogeneous substructure. Similar disregard for local neighborhood structure is common in mathematical models. Methods: We view the dynamics of disease progression as an evolutionary game between cellular phenotypes. A typical assumption in this modeling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard local heterogeneities. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go vs. grow game. Results: We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane -- we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (EMT positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Interpretation: Pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. We expect our approach to extend to other evolutionary game models where interaction neighborhoods change at fixed system boundaries.
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