Numerical Method to Compute Hypha Tip Growth for Data Driven Validation

Abstract

Hyphae are fungal filaments that can occur in both pathogenic and symbiotic fungi. Consequently, it is important to understand what drives the growth of hyphae. A single hypha cell grows by localized cell extension at their tips. This type of growth is referred to as tip growth. The interconnection between different biological components driving the tip growth is not fully understood. Consequently, many theoretical models have been formulated. It is important to develop methods, such that these theoretical models can be validated using experimentally obtained data. In this paper, we consider the Ballistic Ageing Thin viscous Sheet (BATS) model by Prokert, Hulshof, and de Jong (2019). The governing equations of the BATS model are given by ordinary differential equations that depend on a function called the viscosity function. We present a numerical method for computing solutions of the governing equations that resemble the tip growth. These solutions can be compared to experimental data to validate the BATS model. Since the authors are unaware of the existence of the required data to validate this model, a variety of theoretical scenarios were considered. Our numerical results suggest that if there exists a solution that corresponds to the tip growth, then there exists a one-parameter family of solutions corresponding to the tip growth.

Keywords

• Bifurcation
• biomechanics
• cells (biology)
• differential equations
• morphogenesis
• Newton method