[论文解读] A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis

Chiara Villa, Alf Gerisch+1 more|arXiv (Cornell University)|May 24, 2021

Mathematical Biology Tumor Growth参考文献 120被引用 8

一句话总结

本文提出了一种新颖的非局部偏微分方程模型，用于模拟早期血管生成过程中内皮祖细胞（EPC）簇的形成，整合了内源性趋化性、基质降解、增殖以及非局部细胞黏附。模型揭示，趋化性驱动簇的拓扑结构，而基质降解则加速簇形成速度；仅靠非局部黏附无法长期稳定簇结构，表明需要改进黏附建模。

ABSTRACT

Neovascularisation is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo. This process is characterised by the formation of EPC clusters during its early stages and, while much progress has been made in identifying various mechanisms underlying cluster formation, we are still far from a comprehensive description of such spatio-temporal dynamics. In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a linear stability analysis on the system, solve the equations numerically, conduct a parametric analysis of the numerical solutions of the 1D problem to investigate the role of underlying dynamics on the speed of cluster formation and the size of clusters, and verify the key results of the parametric analysis with simulations of the 2D problem. Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, and they indicate that previous approaches to the nonlocal modelling of cell-to-cell adhesion, while they capture the aggregating effect of cell-to-cell adhesion, are not sufficient to capture its stabilising effect on clusters, and new continuum cell-adhesion modelling strategies are required.

研究动机与目标

• 开发一个早期阶段基于簇的血管生成的综合性数学模型，这是一种新近识别的新生血管形成机制。
• 研究缺氧条件下内皮祖细胞（EPC）簇形成的时空动力学。
• 确定内源性趋化性、基质降解、增殖以及非局部细胞黏附对簇形成贡献的相对重要性。
• 通过参数分析确定影响簇速度、宽度和紧凑性的关键参数。
• 通过识别当前黏附机制的局限性并提出新策略，为未来实验和建模工作提供指导。

提出的方法

• 构建一组非局部偏微分方程（PDE），描述EPC密度、基质密度、MMP浓度以及趋化因子（VEGF）的动力学。
• 引入非局部项以模拟细胞间及细胞-基质黏附，反映组织尺度上的长程相互作用。
• 整合关键生物过程：对VEGF的内源性趋化性、MMP介导的基质降解、EPC增殖以及基质重塑。
• 进行线性稳定性分析，评估均匀状态下空间模式的出现。
• 在1D系统中进行数值求解，并对簇的宽度和紧凑性指标进行参数分析。
• 在2D模拟中验证关键1D发现，以确认其鲁棒性和生物学相关性。

实验结果

研究问题

• RQ1 内源性趋化性与基质降解如何共同影响EPC簇形成的速率和拓扑结构？
• RQ2 非局部细胞黏附在多大程度上促进簇在长时间内的稳定性？
• RQ3 改变增殖率和降解率对簇大小和紧凑性有何定量影响？
• RQ4 该模型的预测与体外EPC簇形成实验数据相比如何？
• RQ5 当前非局部黏附项在维持长期簇完整性方面存在哪些局限性？

主要发现

• 内源性趋化性主要决定EPC簇的空间拓扑结构，引导细胞聚集形成明显分离的簇。
• 由MMP驱动的基质降解是加速簇形成速度的主要因素，降解越快，簇越早出现。
• 非局部细胞间黏附项促进初始聚集，但不足以在长时间内稳定簇结构，表明需要改进黏附建模。
• 1D中的参数分析显示，增殖率提高会导致簇更宽且更紧凑，而更高的降解率则减少簇宽度并提高形成速度。
• 2D模拟证实1D的参数结果具有鲁棒性，簇以空间上一致的模式形成，与体外观察结果一致。
• 模型预测与实验数据定性吻合，包括72小时后簇直径为100–400 μm，网络长度可达500 μm。