Modelling Collective Cell Migration

细胞集体运动是一个广泛观察到的现象，在生物学的许多领域，特别是在发育生物学和医学。已经开发了许多建模方法来研究集体细胞迁移的不同模式，从偏微分方程模型到基于个体的模型。然而，尽管越来越多的证据表明它们与驱动集体细胞运动相关，但这些模型通常没有考虑到诸如群体异质性和细胞信号传导作用等生物学细节。因此，该项目的目的是扩展现有的数学框架，以包括多种不同信号信号的存在，以及细胞异质性和表型转换。这项研究将首先考虑大量已经可用的文献，以借鉴用于研究集体运动的技术（不仅在生物学和医学上，而且在生态学上）。现有的大部分工作都是关于紧密聚集的个体（被认为是点粒子）的运动，重点是了解短程相互作用如何影响集体运动。这项研究的新颖之处在于，既要了解更松散的人口如何作为一个连贯的单位移动，又要扩展高密度情况的模型，以考虑排除的体积效应。具体应用将是颅神经嵴细胞迁移。神经嵴的适当迁移对正常发育至关重要，但该系统也可作为更普遍的细胞迁移范例（例如，肿瘤细胞侵袭）。实验已经观察到（由牛津小组先前的建模研究驱动），神经嵴中的细胞对多种信号信号做出反应，也会改变表型。然而，还没有一个系统的方法来模拟这些现象。为了在这个具有挑战性的问题上取得进展，我将首先建立一个混合细胞自动机模型，在这个模型中，我将编码表型转换和多种信号信号（特别是趋化性和趋化性）。然后，我将系统地对这个模型进行粗化，以生成一个新的偏微分方程（PDE）模型。这不仅使我们能够确定微观（单个细胞）和宏观（组织或群体）水平之间的参数如何缩放，而且还将明确用于推导现象学PDE模型的模型假设。在颅神经嵴的背景下，我们将使用混合细胞自动机框架来确定细胞迁移的领导者/追随者描述的适当实施，其中“领导者”细胞对细胞诱导的化学引诱剂梯度作出反应，并通过触致性影响“追随者”的运动。然后，我们将对该系统进行粗粒度处理，以推导出一个PDE模型，我们将其设想为一个完全非线性耦合系统，具有新颖的非线性输运（扩散和平流）和反应项，可以解释细胞-环境反馈。对该模型的分析（分析和数值）将使我们能够确定模型的行为对参数值变化的鲁棒性，进而为我们的合作者提出验证模型的实验建议。该项目属于EPSRC数学生物学研究领域，作为一个跨学科项目，旨在通过使用数学建模来提高对生物状况的理解，包括拥挤、肿瘤生长和发育生物学。

Collective cell motility is a widely observed phenomenon in many areas of biology, particularly in developmental biology and medicine. There have been a number of modelling approaches developed for studying the different modes of collective cell migration, ranging from partial differential equation models to individual-based models. However, such models generally do not take into account biological details such as population heterogeneity and the role of cell signalling, despite increasing evidence for their relevance in driving collective cell motility. As such, the aim of this project is to extend existing mathematical frameworks to include the presence of multiple different signalling cues, as well as cell heterogeneity and phenotypic switching. This research will begin by considering the vast range of literature already available to draw upon the techniques used to study collective motion (not only in biology and medicine, but also in ecology). Much of this existing work concerns the movement of closely packed individuals (considered as point particles), with a focus on understanding how short-range interactions impact collective motility. The novel aspect of this research will be both to develop an understanding of how more loosely packed populations can move as a coherent unit, and to extend the models of high-density situations to take account of excluded volume effects. The specific application will be to cranial neural crest cell migration. Proper migration of the neural crest is vital for normal development, but this system also serves as a paradigm for cell migration more generally (for example, tumour cell invasion). It has already been observed experimentally (driven by previous modelling studies by the Oxford group) that cells in the neural crest respond to multiple signalling cues and also switch phenotype. However, a systematic approach to modelling these phenomena has yet to be developed. To make progress on this challenging problem, I will first build a hybrid cellular automaton model in which I will encode phenotypic switching and multiple signalling cues (specifically chemotaxis and haptotaxis). I will then systematically coarse-grain this model to generate a new partial differential equation (PDE) model. Not only will this allow us to determine how parameters scale between microscopic (individual cell) and macroscopic (tissue or population) levels, it will also make explicit the model assumptions that are used to derive phenomenological PDE models. We will use the hybrid cellular automaton framework to determine, in the context of the cranial neural crest, the appropriate implementation of a leader/follower description of cell migration, where 'leader' cells respond to a cell-induced gradient of chemoattractant, and influence the movement of 'followers' via haptotaxis. We will then coarse-grain this system to derive a PDE model which we envisage as being a fully nonlinear coupled system with novel nonlinear transport (diffusion and advection) and reaction terms that account for cell-environment feedback. Analysis of this model (analytical and numerical) will then allow us to determine how robust the behaviour of the model is to changes in parameter values and this, in turn, will suggest experiments for our collaborators to perform to validate the model.This project falls within the EPSRC Mathematical Biology research area, as an interdisciplinary project aiming to improve the understanding of biological situations, including crowding, tumour growth and developmental biology through the use of mathematical modelling.