Zebrafish Airineme Target Search and Optimal Curvature

Abstract

In addition to diffusive morphogens, cells in developing tissues also communicate via recently discovered cellular protrusions, such as airinemes, which mediate long distance signaling between pigment cells in zebrafish. Diffusive morphogens are characterized by a diffusion coefficient. In contrast, cellular protrusions are characterized by a velocity and an angular diffusion coefficient (or equivalently a directional persistence length) that determine the airinemes' curvature. What determines these parameters? Before establishing communication, an airineme must find its target cell. Here we present a simple mathematical model of airineme target cell search. We find that the probability of contacting the target cell is maximized for a balance between ballistic search (straight airinemes) and diffusive (highly curved, random) search. Further, we extract the curvature of airinemes in zebrafish from high-resolution microscopy and use maximum likelihood estimation to extract the angular diffusion coefficient. Surprisingly, we find that it is approximately the same value as the one found in the simple mathematical model for optimal search. We are extending the model to incorporate more realistic features, including obstacles and multiple target cells.