Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability

NPJ Syst Biol Appl. 2021 Feb 26;7(1):13. doi: 10.1038/s41540-021-00173-x.

Abstract

The GTPase Cdc42 is the master regulator of eukaryotic cell polarisation. During this process, the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation-inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study, we developed, analysed and validated a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability by deriving necessary conditions for which this occurs and conclude that the non-classic case can be viewed as a limit case of the classic case of diffusion-driven instability. Using three-dimensional Spatio-temporal simulation we predicted pole size and time to polarisation, suggesting that cell polarisation is mainly driven by the reaction strength parameter and that the size of the pole is determined by the relative diffusion.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Biological Phenomena
  • Cell Polarity / physiology*
  • Computer Simulation
  • Diffusion
  • Linear Models
  • Models, Biological
  • Models, Theoretical
  • Spindle Poles / physiology*
  • cdc42 GTP-Binding Protein / metabolism*
  • cdc42 GTP-Binding Protein / physiology

Substances

  • cdc42 GTP-Binding Protein