Modelling Collective Cell Migration

集体细胞迁移，其中单个细胞以连贯的方式移动，通常在生物学和医学的许多领域中观察到，例如，发育生物学，伤口愈合，癌症生长。该项目的目标是开始开发一个统一的数学建模框架，以研究这一现象。这个数学框架应该考虑多细胞，多种群的相互作用，同时拥有尽可能多的关键相关的生物学特性，伴随着这些系统的动态，同时保持数学/计算的易处理性。具体的例子将包括（i）神经嵴细胞迁移，这是胚胎发生期间发生的现象，这是胚胎正常发育所必需的，和（ii）血管生成，新的脉管系统形成的过程，无论是响应于创伤，还是响应于需要更多营养的癌细胞释放的线索。之所以选择这两个示例，是因为它们跨越了广泛的应用领域，同时共享许多通用流程。举例来说：在这两种情况下，都存在细胞表型异质性，并且细胞表型可以响应于环境线索而改变;关键“领导”细胞响应于化学引诱物的梯度而执行有偏随机游走;线索（机械的和化学的）由影响和排列“跟随”细胞的领导细胞产生。到目前为止，这两个过程已经通过一系列方法建模-例如，基于代理的模型，其中细胞被认为是响应于（和修改）由偏微分方程（PDE）表示的组织水平线索，直到完全连续描述，其中非局部相互作用通过积分内核建模。在这个项目中，我们将致力于开发一个单一的数学框架，可以将这两个生物学例子（和其他例子）作为特例。我们将研究大量的文献，已经开发的生态学中的动物群集行为，并利用集体动物迁移和集体细胞迁移之间存在的许多相似之处，但也解释了一些非常重要的差异。我们将比较和对比一些不同的方法（例如，现象学PDE描述，动力学理论和流体动力学模型方法），以研究不同的微观尺度（细胞级）属性如何扩展到人口，组织级宏观尺度。这个统一的数学框架将使我们能够以系统的方式比较和对比这些模型，并开始识别和阐明集体细胞迁移的标志。例如，我们将使用该模型来深入了解稳健地导致成功的细胞入侵所需的非局部信号传导的范围，以及不同的环境线索确保细胞采取正确的表型行为。然后，我们将看到这些行为是如何实现生物学通过查阅文献，并在与我们的实验合作者讨论。这个项目属于EPSRC数学生物学研究领域的福尔斯，因为它将推进数学建模和生物科学的跨学科研究。

Collective cell migration, in which individual cells move in a coherent manner, is commonly observed in many areas of biology and medicine, for example, developmental biology, wound healing, cancer growth. The goal of this project is to begin to develop a unified mathematical modelling framework in which to study this phenomenon. This mathematical framework should account for multicellular, multi-population interactions whilst possessing as many of the key relevant biological characteristics that accompany the dynamics of such systems as possible, while maintaining mathematical/computational tractability. Specific examples will include (i) neural crest cell migration, a phenomenon that occurs during embryogenesis, which is essential for the normal development of the embryo, and (ii) angiogenesis, the process by which new vasculature forms, either in response to wounding, or to cues released by cancer cells requiring more nutrient. These two examples are chosen because they span a broad range of application areas, while sharing many common processes. For example: in both cases there is cell phenotype heterogeneity, and cell phenotype can change in response to environment cues; key "leader" cells perform a biased random walk in response to a gradient in chemoattractant; cues (mechanical and chemical) are created by leader cells that influence and align "follower" cells. To date, these two processes have been modelled via a range of approaches - for example, agent-based models in which cells are considered as discrete entities responding to (and modifying) tissue-level cues represented by partial differential equations (PDEs), through to fully continuum descriptions in which non-local interactions are modelled via an integral kernel.In this project, we will aim to develop a single mathematical framework that can incorporate these two biological examples (and others) as special cases. We will investigate the vast literature that has been developed for flocking behaviour of animals in ecology, and exploit many of the similarities that exist between collective animal migration and collective cell migration, but also account for some of the very important differences. We will compare and contrast a number of different methodologies (for example, phenomenological PDE descriptions, kinetic theory and hydrodynamical model approaches) to investigate how different microscale (cell-level) properties scale up to the population, tissue-level macroscale. This unified mathematical framework would then allow us to compare and contrast these models in a systematic fashion and begin to identify and elucidate the hallmarks of collective cell migration. For example, we will use the model to develop insights on what is the range of non-local signalling required for robustly leading to successful cell invasion, and what different environmental cues ensure that cells adopt the correct phenotypic behaviours. We will then see how such behaviours are realised biologically through consulting the literature and in discussions with our experimental collaborators.This project falls within the EPSRC Mathematical Biology research area as it will advance mathematical modelling and interdisciplinary research in the biological sciences.