The morphogenesis of zebrafish posterior lateral line (PLL) is a good predictive model largely used in biology to study cell coordinated reorganization and collective migration regulating pathologies and human embryonic processes. PLL development involves the formation of a placode formed by epithelial cells with mesenchymal characteristics which migrates within the animal myoseptum while cyclically assembling and depositing rosette-like clusters (progenitors of neuromast structures). The overall process mainly relies on the activity of specific diffusive chemicals, which trigger collective directional migration and patterning. Cell proliferation and cascade of phenotypic transitions play a fundamental role as well. The investigation on the mechanisms regulating such a complex morphogenesis has become a research topic, in the last decades, also for the mathematical community. In this respect, we present a multiscale hybrid model integrating a discrete approach for the cellular level and a continuous description for the molecular scale. The resulting numerical simulations are then able to reproduce both the evolution of wild-type (i.e. normal) embryos and the pathological behaviour resulting form experimental manipulations involving laser ablation. A qualitative analysis of the dependence of these model outcomes from cell-cell mutual interactions, cell chemical sensitivity and internalization rates is included. The aim is first to validate the model, as well as the estimated parameter values, and then to predict what happens in situations not tested yet experimentally.

This article is part of the theme issue ‘Multi-scale analysis and modelling of collective migration in biological systems'.

斑马鱼后侧线 (PLL) 的形态发生是一个很好的预测模型，主要用于生物学研究细胞协调重组和集体迁移调节病理和人类胚胎过程。PLL 发展涉及由具有间充质特征的上皮细胞形成的基板的形成，基板在动物肌隔内迁移，同时循环组装和沉积玫瑰花状簇（神经瘤结构的祖细胞）。整个过程主要依赖于特定扩散化学物质的活动，从而触发集体定向迁移和模式化。细胞增殖和表型转变的级联也起着重要作用。在过去的几十年中，对调节这种复杂形态发生的机制的研究已成为一个研究课题，也适用于数学界。在这方面，我们提出了一个多尺度混合模型，它集成了细胞水平的离散方法和分子尺度的连续描述。由此产生的数值模拟然后能够重现两者的演变野生型（即正常）胚胎和病理行为产生的形式涉及激光消融的实验操作。包括对这些模型结果对细胞间相互作用、细胞化学敏感性和内化率的依赖性的定性分析。目的是首先验证模型以及估计的参数值，然后预测在尚未经过实验测试的情况下会发生什么。

本文是主题问题“生物系统中集体迁移的多尺度分析和建模”的一部分。