Self-similar tip growth links exocytosis profile with cell wall shape

Exocytosis plays a crucial role in regulating the growth and migration of filamentous tip-growing cells. We present a mathematical framework that infers the spatial profile of exocytosis from the cell morphology in self-similar growing cells that elongate while preserving their apical domain shapes. By applying the framework to cell wall outline data from experiments across walled cell species, we find that while tapered cells have their exocytosis concentrated at the apex, cells with flatter tip shape beyond a threshold require exocytosis to peak in an annulus region away from the apex.