Mathematical modelling of the role of cell heterogeneity in promoting melanoma metastasis

黑色素瘤是最具侵袭性的皮肤癌。如果早期诊断，生存率很高。然而，如果肿瘤转移（或扩散），5年生存率会从99%下降到30%。了解转移是如何发生的，对于理解黑色素瘤如何发展和确定新的治疗方法可以预防它是至关重要的。患者活检分析显示黑色素瘤是高度异质性的，包含至少五种不同的转录细胞状态。其中最突出的是高度增殖和侵入性状态。虽然这两种细胞状态在几乎所有患者中都可见，但对这些不同状态的细胞如何相互作用以及这种相互作用对肿瘤进展的影响知之甚少。怀特实验室最近的实验表明，增殖性和侵袭性细胞的共同培养会自发地形成空间结构的簇，侵袭性细胞被增殖细胞的外缘包围。另外的体内实验表明，这些异质性集群的转移率明显高于仅由增殖或侵袭性细胞组成的集群。该项目的目的是了解增殖性和侵袭性细胞之间的相互作用如何增强异质细胞簇转移的能力，以及这些相互作用如何靶向抑制黑色素瘤的扩散。为了实现这一目标，我们将开发机械数学模型来描述转移性簇如何在原发肿瘤部位形成，它们在迁移阶段的行为，以及它们如何在继发组织中定植。在项目过程中，我们将开发和分析一系列日益复杂的数学模型，以更好地了解黑色素瘤转移的过程。首先，我们将开发一个基于凝固-破碎框架的混合良好的细胞群体的常微分方程模型，并将预测与相应细胞水平行为的随机模拟进行比较。我们将使用从White实验室进行的体外实验中收集的时间过程数据来验证我们的模型，其中包括每个集群中随时间推移的增殖和侵袭性细胞的数量。这将使我们能够确定控制大小依赖的凝聚和破碎速率的数学内核。然后，我们将使用全局参数敏感性分析来探索可能的行为范围。为了了解黑色素瘤簇在转移过程中增殖和侵袭细胞簇的空间结构，我们随后将开发一个基于agent的簇形成模型。然后，我们将扩展基于代理的模型，以包括额外的转录细胞状态，这些状态的数量和属性将通过分析White实验室收集的转录组学数据来确定。转移的过程还没有被很好地理解，而数据驱动的数学模型的发展将使我们能够在纯生物学实验室研究过程中不可能的水平上进行模拟和模拟实验。模拟结果将用于未来的实验设计，并提出可能的治疗方法。这在模型和实验之间建立了一种共生关系，从而得出数学上和生物学上相关的结论。这项研究的潜在影响远远超出了黑色素瘤，因为聚集和转移的过程也不是黑色素瘤所独有的。因此，发现的结果也可以适用于黑色素瘤和其他癌症，以改善可能的患者预后。该项目属于EPSRC数学生物学研究领域。它由牛津大学数学研究所和路德维希癌症研究所的教员共同监督。

Melanoma is the most aggressive skin cancer. Survival rates are excellent if it is diagnosed early. However if the tumour metastasises (or spreads), five-year survival rates drop from about 99% to 30%. Understanding how metastasis occurs is crucial for understanding how melanoma progresses and for identification of new treatments that could prevent it.Analysis of patient biopsies shows that melanomas are highly heterogeneous and contain at least five different transcriptional cell states. Amongst the most prominent are highly proliferative and invasive states. While both these cell states are seen in nearly all patients, little is known about how cells in these different states interact, and the impact such interactions have on tumour progression. Recent experiments in the White lab have shown that co-cultures of proliferative and invasive cells spontaneously form spatially structured clusters, with invasive cells surrounded by an outer rim of proliferating cells. Additional in vivo experiments show that these heterogeneous clusters metastasise at rates which are significantly higher than clusters comprising proliferative or invasive cells alone.The aim of this project will be to understand how interactions between proliferative and invasive cells enhance the ability of heterogeneous cell clusters to metastasise and how these interactions may be targeted to inhibit melanoma spread. To achieve this, we will develop mechanistic mathematical models that describe how metastatic clusters form at primary tumour locations, their behaviour during the migratory phase, and how they colonise secondary tissues.Over the course of the project, we will develop and analyse a series of increasingly complex mathematical models to better understand the process of melanoma metastasis. Initially we will develop an ordinary differential equation model for a well-mixed population of cells that is based upon the coagulation-fragmentation framework, and we will compare predictions with stochastic simulations of the corresponding cell-level behaviours. We will validate our models using time course data collected from in vitro experiments carried out in the White lab, which consists of the number of proliferative and invasive cells in each cluster over time. This will allow us to pin down the mathematical kernels governing the size-dependent rates of coagulation and fragmentation. We will then explore the range of possible behaviours using a global parameter sensitivity analysis.To understand the spatial architecture of the clusters of proliferative and invasive cells in melanoma clusters during metastasis we will subsequently develop an agent-based model of cluster formation. We will then extend the agent-based model to include additional transcriptional cell states, the number and properties of these states being determined through the analysis of transcriptomics data collected in the White lab.The process of metastasis is not well understood, and the development of a collection of data-driven mathematical models will allow us to run simulations and mock experiments on a level that is impossible in a purely biological lab-based research process. The simulation results will be used to inform future experimental design, and suggest possible treatments. This creates a symbiotic relationship between the models and experiments leading to both mathematically and biologically relevant conclusions.The potential impact of this research extends far beyond just melanoma as the process of clustering and metastasis is also not unique to melanoma. Therefore, results found could also be applicable to both melanoma and other cancers to improve possible patient outcomes.This project falls within the EPSRC Mathematical Biology research area. It is jointly supervised by faculty from the Mathematical Institute and Ludwig Institute for Cancer Research, University of Oxford.