Aggregation and collapse in a mechanical model of fungal tip growth

Interconnected hyphal tubes form the mycelia of a fungal colony. The growth of the colony results from the elongation and branching of these single hyphae. The material being incorporated into the extending hyphal wall is supplied by vesicles which are formed further back in the hyphal tip. Such wall-destined vesicles appear conspicuously concentrated in the interior of the hypha, just before the hyphal apex, in the form of an apical body or Spitzenkörper. The cytoskeleton of the hyphal tube has been implicated in the organisation of the Spitzenkörper and the transport of vesicles, but as yet there is no postulated mechanism for this. We propose a mechanism by which forces generated by the cytoskeleton are responsible for biasing the movement of vesicles. A mathematical model is derived where the cytoskeleton is described as a viscoelastic fluid. Viscoelastic forces are coupled to the conservation equation governing the vesicle dynamics, by weighting the diffusion of vesicles via the strain tensor. The model displays collapse and aggregation patterns in one and two dimensions. These are interpreted in terms of the formation of the Spitzenkörper and the initiation of apical branching.