Collective cell migration guided by dynamically maintained gradients.

How cell collectives move and deposit subunits within a developing embryo is a question of outstanding interest. In many cases, a chemotactic mechanism is employed, where cells move up or down a previously generated attractive or repulsive gradient of signalling molecules. Recent studies revealed the existence of systems with isotropic chemoattractant expression in the lateral line primordium of zebrafish. Here we propose a mechanism for a cell collective, which actively modulates an isotropically expressed ligand and encodes an initial symmetry breaking in its velocity. We derive a closed solution for the velocity and identify an optimal length that maximizes the tissues' velocity. A length dependent polar gradient is identified, its use for pro-neuromast deposition is shown by simulations and a critical time for cell deposition is derived. Experiments to verify this model are suggested.