Mathematical investigation into the role of cell-cell communication pathways on collective cell migration

发育和各种疾病(如肿瘤的生长和侵袭、伤口愈合、形态发生)中的大量基本过程都是细胞协调运动的结果。与细胞类型无关，集体运动通常涉及三个因素：细胞与细胞和细胞与基质的相互作用，细胞极化为“领导者”和“追随者”，以及允许细胞相互交流的化学和物理信号。细胞运动有多种方式，从单个细胞运动到集体运动(细胞在运动时保持连接)。在过去的几十年里，人们对单个细胞的运动进行了非常详细的研究，并且已经确定了单个细胞运动的关键方面(例如，细胞突起的分子控制、细胞与其底物之间的相互作用)。然而，人们对细胞的集体运动知之甚少，而且关于这种类型的运动所涉及的机制还有许多悬而未决的问题。例如，人们对细胞运动和细胞间通讯如何相互作用以创造新的组织或允许细胞在特定区域定居的了解较少。另一个鲜为人知的方面是，细胞如何解释和整合来自环境和其他细胞的信号，以产生特定类型的细胞聚集和集体运动。最后，目前尚不清楚是所有细胞都感知引导信号，还是只有领先细胞感知这些信号，然后指示其他细胞跟随它们。为了阐明有助于解决这些问题的假设，我们将推导出一类描述细胞运动和通过不同通信机制进行细胞间相互作用的机械性数学模型。利用不同的数学技术(如行波分析、分叉分析)，我们将研究不同的细胞间通讯机制对细胞聚集运动和结构的作用。我们还将研究参数对不同类型细胞运动行为之间转换的影响。

A large number of fundamental processes in development and various diseases (e.g., cancer growth and invasion, wound healing, morphogenesis) are the result of the coordinated movement of cells. Independent of cell types, collective movement usually involves three factors: cell-cell and cell-matrix interactions, polarization of cells into "leaders" and "followers", and chemical and physical signals that allow cells to communicate with each other. There are multiple ways of cell movement, ranging from single cell movement to collective movement (where cells stay connected as they move).The movement of single cells has been investigated quite in detail over the past decades, and the key aspects of single cell movement (e.g., molecular control of cell protrusions, interactions between cells and their substrate) have been already identified. However, the collective movement of cells is less understood, and there are many open questions regarding the mechanisms involved in this type of movement. For example, it is less understood how cell movement and cell-cell communication interact to create new tissues, or to allow cells to colonise specific areas. Another aspect less understood is how cells interpret and integrate signals from the environment and from other cells to produce specific types of cell aggregations and collective movement. Finally, it is still unknown whether all cells sense guidance signals, or only the leader cells sense these signals and then instruct other cells to follow them.To formulate hypotheses that could help address these questions, we will derive a class of mechanistic mathematical models that describe cell movement and cell-cell interactions via different communication mechanisms. Using various mathematical techniques (e.g. travelling wave analysis, bifurcation analysis), we will investigate the role of different cell-cell communication mechanisms on the movement and structure of cell aggregations. We will also investigate the effect of parameters on the transitions between different types of cell movement behaviours.