A hybrid model of cell migration in zebrafish embryogenesis

¹ Istituto per le Applicazioni del Calcolo “M. Picone” – Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, 00131 Naples, Italy
² Istituto per le Applicazioni del Calcolo “M. Picone” – Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Rome, Italy
³ Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy

^a e-mail: e.dicostanzo@na.iac.cnr.it
^b e-mail: roberto.natalini@cnr.it
^c e-mail: luigi.preziosi@polito.it

Abstract

Starting from the results of recent biological experiments, we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our hybrid description is discrete on the cellular level and continuous on the molecular level. We prove the existence of steady solutions corresponding to the formation of particular biological structures, the neuromasts. Numerical simulations are performed to show the dynamics of the model and its accuracy to describe the evolution of the cell aggregate by a qualitative and quantitative point of view. Some related models, applied to the collective motion of cells, and to the behaviour of cardiac stem cells, are indicated.