A New Model for Fungal Hyphae Growth Using the Thin Viscous Sheet Equations

Abstract

In this paper, we model the growth of single nonbranching fungal hypha cell. The growth proceeds as an elongating expansion in a single direction. Modelling of hyphae growth consists out of two parts: transport of cell wall building material to the cell wall and growth of the cell wall as new cell wall building material arrives. In this paper we present a new model for hyphae growth using the work of Barnicki- Garcia et al. (1989), which assumes that cell wall building material is transported in straight lines by an isotropic point source, and the work of Campas and Mahadevan (2009), which assumes that the cell wall is a thin viscous sheet. Furthermore, we include a novel equation which models the hardening of the cell wall with age.We show numerically that these governing equations have solutions corresponding to hyphae growth.We also compute asymptotic expansions near the apex and the base of the cell.