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

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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.