Cells in tissue can communicate long-range via diffusive signals. In addition, another class of cell-cell communication is by long, thin cellular protrusions that are ~100 microns (many cell-lengths) in length and ~100 nanometers (below traditional microscope resolution) in width. These protrusions have been recently discovered in many organisms, including cytonemes in humans and insects, nanotubes in cancers, and airinemes in zebrafish. Before establishing communication, these protrusions must find their target cell. In this work, we use mathematical modeling to understand the effect of the morphology of airinemes in target cell search, finding a key role for curvature: The probability of contacting the target cell is maximized for a balance between straight and highly curved (random) search. We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We therefore demonstrate an example where a simple-to-state objective is optimized by a living system. Different performance objectives, e.g., maximizing traffic or providing directional information, have different optimal geometries, and therefore, it is intriguing to speculate what other cellular projections have geometries optimized for different performance objectives.

Jun Allard is an Associate Professor of Physics and Mathematics at the University of California Irvine, where he is affiliated with the Center for Complex Biological Systems and the NSF-Simons Center for Multiscale Cell Fate. His research uses mathematical modelling to understand cell mechanics. He serves as the Director of the Graduate Gateway Program in Mathematical, Computational and Systems Biology