Abstract
AbstractThe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Modeling and Simulation
Reference27 articles.
1. Ahrens J, Geveci B, Law C (2005) Paraview: an end-user tool for large data visualization. Vis Handb 717:50038–1
2. Alnæs M, Blechta J, Hake J, Johansson A, Kehlet B, Logg A, Richardson C, Ring J, Rognes ME, Wells GN (2015) The fenics project version 1.5. Arch Numer Softw 3
3. Ayachit U (2015) The paraview guide: a parallel visualization application. Kitware Inc, New York
4. Bandle C, Kabeya Y, Ninomiya H (2019) Bifurcating solutions of a nonlinear elliptic Neumann problem on large spherical caps. Funkcialaj Ekvacioj 62:285–317
5. Borgqvist J, Malik A, Lundholm C, Logg A, Gerlee P, Cvijovic M (2021) Cell polarisation in a bulk-surface model can be driven by both classic and non-classic turing instability. NPJ Syst Biol Appl 7:1–10