领导者-追随者行为连续模型中的孤子近似
Soliton approximation in continuum models of leader-follower behavior
AI总结：
本研究通过粗粒化混合随机智能体模型得到连续偏微分方程，在趋化主导时发现前导阶解可用孤子波描述，揭示了离散与连续方法的共性及集体动力学机制。
摘要：
复杂的生物过程涉及实体（细菌、细胞、动物）在多个长度和时间尺度上的集体行为，可以通过追踪个体的离散模型或涉及密度和场的连续模型来描述。我们考虑了分支形态发生和血管生成（从现有脉管系统中创建新血管）的混合随机基于智能体的模型，这些模型将细胞视为受潜在连续化学和/或机械场引导的个体。在这些描述中，领导者（尖端）细胞从现有分支中出现，追随者（茎）细胞在其后构建新芽。血管分支和融合（吻合）是尖端和茎细胞动力学的结果。在适当极限下对这些混合模型进行粗粒化，产生用于内皮细胞密度的连续偏微分方程（PDE），这些方程在分析上更易处理。虽然这些模型在非线性方面有所不同，但在趋化性占主导时，它们在前导阶产生相似的方程。我们在简单的准一维几何中分析该前导阶系统，并表明前导阶PDE的数值解很好地由从血管到源演化的孤子波描述。该波在中间时间是一个吸引子，直到它到达释放生长因子的缺氧区域。因此，这里使用的数学技术识别了离散和连续方法的共同特征，并为控制其集体动力学的普遍生物机制提供了见解。
英文摘要：
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from pre-existing vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse-graining these hybrid models in appropriate limits produces continuum partial differential equations (PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equations at leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
