Reaction–Diffusion Finite Element Model of Lateral Line Primordium Migration to Explore Cell Leadership

Abstract

Collective cell migration plays a fundamental role in many biological phenomena such as immune response, embryogenesis and tumorigenesis. In the present work, we propose a reaction–diffusion finite element model of the lateral line primordium migration in zebrafish. The population is modelled as a continuum with embedded discrete motile cells, which are assumed to be viscoelastic and able to undergo large deformations. The Wnt/ß-catenin–FGF and cxcr4b–cxcr7b signalling pathways inside the cohort regulating the migration are described through coupled reaction–diffusion equations. The coupling between mechanics and the molecular scenario occurs in two ways. Firstly, the intensity of the protrusion–contraction movement of the cells depends on the cxcr4b concentration. Secondly, the intra-synchronization between the active deformations and the adhesion forces inside each cell is triggered by the cxcr4b–cxcr7b polarity. This influences the inter-synchronization between the cells and results in two main modes of migration: uncoordinated and coordinated. The main objectives of the work were (i) to validate our assumptions with respect to the experimental observations and (ii) to decipher the mechanical conditions leading to efficient migration of the primordium. To achieve the second goal, we will specifically focus on the role of the leader cells and their position inside the population.