Turing pattern formation on the sphere is robust to the removal of a hole
Journal article, 2024

The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit diffusion-driven pattern formation, thus providing a mechanism for bud formation. However, it is not known how the accumulation of bud scars on the cell membrane affect the ability of the Schnakenberg system to form patterns. We have approached this problem by modelling a bud scar on the cell membrane with a hole on the sphere. We have studied how the spectrum of the Laplace–Beltrami operator, which determines the resulting pattern, is affected by the size of the hole, and by numerically solving the Schnakenberg system on a sphere with a hole using the finite element method. Both theoretical predictions and numerical solutions show that pattern formation is robust to the introduction of a bud scar of considerable size, which lends credence to the hypothesis that bud formation is driven by diffusion-driven instability.

RD-models

Bud scars

Turing patterns

FEM

Author

Johannes Borgqvist

University of Oxford

Philip Gerlee

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Carl Lundholm

Umeå University

Journal of Mathematical Biology

0303-6812 (ISSN) 1432-1416 (eISSN)

Vol. 88 2 23

Subject Categories

Computational Mathematics

DOI

10.1007/s00285-023-02034-z

PubMed

38296874

More information

Latest update

2/19/2024