Mathematical Modelling of Collective Cell Migration

该项目属于EPSRC数学生物学研究领域。细胞集体迁移是一个完整的生物学过程，对许多生物体在其整个生命周期中的功能至关重要。例如，它在胚胎生长和组织发育，以及伤口愈合和癌症转移中起着至关重要的作用。在Ruth Baker教授和Sarah Waters教授指导的博士项目中，我们将开发新的细胞集体迁移的数学框架，重点关注细胞和细胞外基质（ECM，一种为单个细胞提供生化和结构支持的蛋白质和分子网络）之间的相互作用。在这种情况下，一个关键的悬而未决的问题是，细胞外基质的特性是如何增强或降低细胞入侵特定组织的能力的。我们将采用多尺度建模方法（见下面的方法论）来探讨这个问题。我们将与Paul Riley教授团队合作，将我们的模型应用于心脏伤口愈合。通过将我们的数学框架与实验相结合，我们的项目将提供一种新的跨学科方法来理解驱动心脏纤维化的机制。ObjectivesOb1)。建立各种复杂的细胞模型，以纳入细胞运动的不同机制。建立多尺度模型，将细胞运动与ECM动力学结合起来。使用定量实验数据估计模型参数。验证和完善模型，以提供新的生物学见解。我们将应用基于主体的建模技术来开发细胞运动的硅模型。根据不同的假设和细胞运动机制，硅模型可以从晶格上的，如细胞自动机，到晶格外的，如重叠的球体。将开发数值方法来模拟模型，必要时利用技术来提高效率，如方差减少和多网格方法，以确保有可能进行广泛的参数敏感性分析（见下面的M3）。通过将ECM动力学与M1中的仅细胞模型耦合，我们将构建多尺度模型，其中细胞被视为单个实体，ECM动力学使用偏微分方程系统建模。将考虑细胞和ECM之间的双向联系（例如通过接触引导和矩阵重塑）。此外，通过粗粒度方法，将开发简化的、基于微分方程的模型，这些模型适用于使用线性稳定性和行波分析等方法进行分析探索。m3)。基于Riley教授小组的实验数据，我们将使用贝叶斯框架来估计模型参数并量化它们的不确定性。例如，我们将首先使用轮廓似然分析，在使用Metropolis-Hastings马尔可夫链蒙特卡罗算法从后验参数分布中抽样之前，提供实际可识别性的初步评估。然后，我们将使用留一交叉验证和可识别性分析等方法进行模型校准、选择和细化。利用Riley教授团队的数据，我们将开发第一个完全验证的细胞通过ECM迁移的模型。该模型将用于探索细胞运动和ECM动力学之间的双向耦合。在生物学背景下，该模型将使我们能够更好地理解驱动心脏伤口愈合的机制，以及如何调节最佳心脏修复与过度炎症和纤维化之间的临界点。

This project falls within the EPSRC Mathematical Biology research area.BackgroundCollective cell migration is an integrated biological process, essential for the function of numerous organisms throughout their life span. For example, it plays a vital role in embryonic growth and tissue development, as well as in wound healing and cancer metastasis. In my doctoral project supervised by Prof. Ruth Baker and Prof. Sarah Waters, we will develop new mathematical frameworks of collective cell migration, focusing on the interplay between cells and the extracellular matrix (ECM, a network of proteins and molecules which provide biochemical and structural support for individual cells). In this context, a key unanswered question ishow do properties of the extracellular matrix enhance or decrease the ability of cells to invade a particular tissue.We will adopt a multiscale modelling approach (see Methodology below) to probe this question. We will collaborate with the group of Prof. Paul Riley to apply our models to cardiac wound healing. By integrating our mathematical framework with experiments, our project will provide a novel interdisciplinary approach to understanding mechanisms driving cardiac fibrosis. ObjectivesOb1). Build cell-only models of various complexities to incorporate different mechanisms of cell movements.Ob2). Develop multiscale models that couple cell motility with ECM dynamics.Ob3). Estimate model parameters using quantitative experimental data. Validate and refine the models to provide new biological insights.MethodologyM1). We will apply agent-based modelling techniques to develop in-silico models of cell motility. Depending on different hypotheses and cell movement mechanisms, the in-silico models can range from on-lattice ones, such as cellular automata, to off-lattice ones, such as overlapping spheres. Numerical methods will be developed to simulate the model, where necessary harnessing techniques to improve efficiency, such as variance reduction and multigrid methods, to ensure it is possible to conduct widespread parameter sensitivity analysis (see M3 below).M2). By coupling the ECM dynamics to the cell-only models in M1, we will construct multiscale models where cells are treated as individual entities and the ECM dynamics are modelled using systems of partial differential equations. The bi-directional linkages between cells and ECM (such as through contact guidance and matrix remodelling) will be considered. In addition, via coarse-graining methods, simplified, differential-equation-based models that are amenable to analytic exploration using approaches such as linear stability and travelling wave analysis will be developed.M3). Based on experimental data from Prof. Riley's group, we will use a Bayesian framework to estimate model parameters and quantify their uncertainties. For instance, we will first use profile likelihood analysis to provide a preliminary assessment of practical identifiability before sampling from the posterior parameter distribution using a Metropolis-Hastings Markov Chain Monte Carlo algorithm. We will then perform model calibration, selection, and refinement using methods such as leave-one-out cross validation and identifiability analysis.ImpactEquipped with data from Prof. Riley's group, we will develop the first fully validated model of cell migration through the ECM. This model will be used to explore the two-way coupling between cell movements and ECM dynamics. In a biological context, this model will enable us to better understand the mechanisms driving cardiac wound healing, and how to modulate the tipping point between optimal cardiac repair and excess inflammation and fibrosis.