Fungal tip growth arising through a codimension-1 global bifurcation

TL;DR

This paper analyzes a simplified toy model derived from the BATS model to demonstrate a codimension-1 global bifurcation responsible for fungal tip growth, using topological methods to identify bifurcation points.

Contribution

It introduces a toy model that captures the bifurcation behavior of the BATS model and provides a proof of the bifurcation, advancing understanding of fungal tip growth mechanisms.

Findings

Toy model exhibits an analogue of the bifurcation.

Topological method identifies bifurcation points.

Proof suggests possible generalization to the BATS model.

Abstract

Tip growth is a growth stage which occurs in fungal cells. During tip growth, the cell exhibits continuous extreme lengthwise growth while its shape remains qualitatively the same. A model for single celled fungal tip growth is given by the Ballistic Ageing Thin viscous Sheet (BATS) model, which consists of a 5-dimensional system of first order differential equations. The solutions of the BATS model that correspond to fungal tip growth arise through a codimension-1 global bifurcation in a 2-parameter family of solutions. In this paper we derive a toy model from the BATS model. The toy model is given by 2-dimensional system of first order differential equations which depend on a single parameter. The main achievement of this paper is a proof that the toy model exhibits an analogue of the codimension-1 global bifurcation in the BATS model. An important ingredient of the proof is a topological method which enables the identification of the bifurcation points. Finally, we discuss how the proof may be generalized to the BATS model.