Math Biology Seminar: Cole Zmurchok & Hildur Knutsdottir

Using a 3D deformable cell-based simulation, coupled to reaction-diffusion PDEs for chemical concentrations, we model and simulate the polarization, migration, and neuromast deposition in the zebrafish posterior lateral line primordium (PLLP). This primordium migrates from head to tail of the fish embryo, and deposits sensory neuromasts at regular intervals in its wake. The model combines realistic cell-cell adhesion, chemotaxis and interaction forces to describe the emergence of tissue polarity, as well as the cell-cluster shape and speed of collective cell migration. We base the chemical signalling model on receptor-ligand kinetics and mutually inhibitory FGF-Wnt signalling. Our signalling submodel allows predictions to be made for the position of the front-rear boundary in the PLLP, as a function of aggregate parameters such as steady-state receptor expression levels and IC50 parameters for the mutually-inhibitory effect. Our 3D model allows an investigation of the role of cell division, chemotaxis, adhesion and other parameters on the shape of the PLLP and demonstrates reasonable behaviour of control as well as mutant phenotypes.