Modelling Collective Cell Migration

集体细胞迁移是指单个细胞以连贯的方式移动，在生物学和医学的许多领域都可以观察到，例如发育生物学、伤口愈合、癌症生长。这个项目的目标是开始开发一个统一的数学建模框架来研究这种现象。这个数学框架应该考虑到多细胞、多种群的相互作用，同时拥有尽可能多的与这些系统动力学相关的关键生物学特征，同时保持数学/计算的可追溯性。具体的例子包括：(1)神经嵴细胞迁移，这是胚胎发生过程中发生的一种现象，对胚胎的正常发育至关重要；(2)血管生成，这是新的血管系统形成的过程，要么是对损伤的反应，要么是对需要更多营养的癌细胞释放的信号的反应。选择这两个示例是因为它们跨越了广泛的应用程序领域，同时共享许多公共流程。例如：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环境线索而改变；关键的“领导”细胞执行一个有偏见的随机漫步响应在化学引诱剂的梯度；线索（机械的和化学的）是由领导细胞产生的，它影响和排列“追随者”细胞。迄今为止，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（和修改）由偏微分方程（PDEs）表示的组织水平线索的离散实体，通过完整的连续描述，其中非局部相互作用通过积分核建模。在这个项目中，我们的目标是开发一个单一的数学框架，可以将这两个生物例子（以及其他）作为特殊情况纳入其中。我们将研究生态学中动物群集行为的大量文献，并利用动物集体迁移和细胞集体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（细胞水平）特性如何扩展到群体，组织水平的宏观尺度。这个统一的数学框架将允许我们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特征。例如，我们将使用该模型来深入了解导致成功细胞入侵所需的非局部信号的范围，以及哪些不同的环境线索确保细胞采用正确的表型行为。然后，我们将通过查阅文献和与实验合作者的讨论来了解这些行为是如何在生物学上实现的。该项目属于EPSRC数学生物学研究领域，因为它将推进生物科学的数学建模和跨学科研究。

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.