Morphodynamics of tip growing cells

Abstract

Pollen tubes, root hairs and fungal hyphae elongate by adding material at their tips. The region in the immediate vicinity of the tip is dynamically pliable and allows for the addition of new wall material even as it flows in response to the turgor that drives it. Any imbalance between the rate of material addition and its consequent flow will cause a tip growing cell to either burst because its wall thins or stop growing because its wall thickens. We use an experimentally-inspired feedback law that couples vesicle exocytosis to wall mechanics via the local strain rate to construct a minimal theory for the dynamics of tip growing cells. Our theory characterizes the parameter regime where stable steady tip growth is possible in terms of two dimensionless parameters: a scaled turgor pressure, and a ratio of length scales describing gradients of wall extensibility and vesicle composition near the tip. Our analysis also explains the experimentally observed shape response of tip growing cells observed when external turgor is dynamically varied. All together our formalism provides a general framework for the coupled dynamics of internal vesicular transport and wall mechanics in tip-growing cells.