Bridging spatial and evolutionary game theory: Implications in mathematical oncology

连接空间博弈论和进化博弈论：对数学肿瘤学的影响

• 批准号: EP/W003074/1
• 金额: $ 33.63万
• 依托单位: University of St Andrews
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW003074%2F1
• 关键词: Bridging; spatial; evolutionary; game; theory

In this research programme, we aim to develop new mathematical equations that are designed to find optimal anti-cancer treatment strategies in solid tumours. These equations will be formulated using game theory. Classical game theory provides a mathematical framework in which to study strategic interactions amongst rational agents (or players) that aim to maximise their utility (or payoff) by choosing the best strategies. In the context of mathematical oncology, game theory has been adapted to describe cell-cell interactions amongst cancer and tumour cells, where the cells are players that do not rationally choose their strategies, but rather act according to their genotypic and phenotypic makeup. The interactions are then abstractions of biological exchanges of signalling molecules, or competition for space or nutrients, and the payoffs describe any gain or loss in reproductive ability (or fitness) that cells acquire as a consequence of interacting with other cells. Upon identification the payoffs, the reproductive rates (and by extension the evolution) of various genotypic and phenotypic subpopulations that co-exist in a tumour can be mathematically modelled. Two branches of game theory that have been applied to model interactions amongst cancer cells are spatial game theory (SGT) and evolutionary game theory (EGT).In an SGT model, cells can be modelled as autonomous agents that evolve on a spatial grid and partake in interactions with other cells in their vicinity. Such agent-based models are naturally able to incorporate spatial heterogeneity. However, they do not lend themselves to rigorous mathematical analysis, and are often difficult to parameterise and computationally expensive. In EGT models, the temporal evolution of phenotypic subpopulations of cells can be described by a set of mathematically tractable equations, called the replicator equations, after imposing a set of simplifying modelling assumptions. According to a mean-field assumption, the replicator equations notably assume that the cells are well-mixed, so that each cell interacts with all other cells in the system with equal probability. The replicator equations allow for rigorous mathematical analysis and feasible clinical applications. Consequently, EGT is one of the mathematical approaches that is currently being used to inform pre-clinical and clinical treatment strategies in oncology, where the general premise is that by perturbing the cell-cell interactions elucidated by EGT, tumour evolution can be pushed into a state that is better manageable by treatments. The EGT replicator equations are, however, not spatially resolved and can therefore not faithfully capture the dynamics of heterogeneous solid tumours. In fact, previous work has shown that imposing spatial constraints on agent-agent interactions, via SGT models, often results in system dynamics that vastly contradicts that simulated by EGT!Due to the pre-clinical and clinical applications of EGT, there exists a need to bridge spatial and evolutionary game theory. In this research program, we aim to achieve this SGT-EGT bridging by formulating spatio-temporal EGT equations that capture the heterogeneity found in solid tumours, whilst being more mathematically tractable than SGT models. The novel equations developed in this research programme will enrich the mathematical research fields of game theory and mathematical oncology, and may also have applications in pre-clinical and clinical cancer research!This work will be led by Dr Sara Hamis (University of St Andrews, UK), who will be supported by an international and interdisciplinary team with mathematical, experimental and clinical expertise. Team members are Prof Mark A.J. Chaplain (University of St Andrews), Dr Alexander J. Stewart (University of St Andrews), Dr Tommaso Lorenzi (Politecnico di Torino, Italy), Dr Philip Gerlee (Chalmers University of Technology, Sweden) and Jacob G. Scott, MD (Cleveland Clinic, USA).

在该研究计划中，我们旨在开发新的数学方程，旨在在实体瘤中找到最佳的抗癌治疗策略。这些方程式将使用游戏理论制定。古典游戏理论提供了一个数学框架，在其中研究了旨在通过选择最佳策略来最大化其效用（或回报）的理性代理（或玩家）之间的战略互动。在数学肿瘤学的背景下，游戏理论已适应描述癌症和肿瘤细胞之间的细胞细胞相互作用，在癌症和肿瘤细胞中，这些细胞是没有合理选择其策略的参与者，而是根据其基因型和表型组成的作用。然后，相互作用是信号分子的生物交换或空间或养分竞争的抽象，而收益描述了细胞因与其他细胞相互作用而获得的生殖能力（或适应性）的任何增益或损失。通过鉴定回报，可以通过数学上建模在肿瘤中共存的各种基因型和表型亚群的生殖速率（并扩展）。游戏理论的两个分支已应用于癌细胞之间建模的相互作用，是空间游戏理论（SGT）和进化游戏理论（EGT）。在SGT模型中，可以将细胞建模为自主剂，它们在空间网格上演化并参与其遗传学中与其他细胞的相互作用。这种基于代理的模型自然能够结合空间异质性。但是，它们不适合严格的数学分析，并且通常很难参数化和计算昂贵。在EGT模型中，在强加了一组简化的建模假设之后，可以通过一组数学上可拖动的方程（称为复制器方程）来描述细胞表型亚群的时间演变。根据平均场假设，复制器方程特别假定细胞混合良好，因此每个细胞都以同样的概率与系统中的所有其他单元相互作用。复制器方程允许进行严格的数学分析和可行的临床应用。因此，EGT是目前正在使用的数学方法之一，用于为肿瘤学中的临床前和临床治疗策略提供信息，其中一般前提是通过扰动EGT阐明的细胞 - 细胞相互作用，可以将肿瘤进化推向一种可以通过治疗更好地管理的状态。但是，EGT复制器方程未在空间上解析，因此不能忠实地捕获异质实体瘤的动力学。实际上，先前的工作表明，通过SGT模型对代理代理相互作用施加空间限制通常会导致系统动态，这些动力与EGT的临床前和临床应用相矛盾，这与EGT模拟相矛盾，因此需要桥接空间和进化游戏理论。在该研究计划中，我们旨在通过制定捕获实体瘤中发现的异质性的时空EGT方程来实现这种SGT-EGT桥接，而在数学上比SGT模型更容易触及。该研究计划中开发的新颖方程式将丰富游戏理论和数学肿瘤学的数学研究领域，并且还可能在临床前和临床癌症研究中有应用！这项工作将由萨拉·哈米斯（Sara Hamis）（英国圣安德鲁斯大学）博士领导，后者将得到由国际和学科的数学和实验性，实验性，实验性和培训范围的国际和学科团队的支持。团队成员是Mark A.J.教授牧师（圣安德鲁斯大学），亚历山大·J·斯图尔特博士（圣安德鲁斯大学），托马索·洛伦兹（Tommaso Lorenzi）博士（意大利政治上的迪利诺明会），菲利普·格里（Philip Gerlee）博士（Chalmers技术大学）和雅各布·G·斯科特（Jacob G.Scott）