Bespoke Turing patterns with specific nonlinear properties

Woolley, Thomas ORCID: https://orcid.org/0000-0001-6225-5365 Bespoke Turing patterns with specific nonlinear properties. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Preview

PDF - Accepted Post-Print Version Available under License Creative Commons Attribution. Download (3MB) | Preview

Abstract

Turing patterns offer a mechanism for understanding self-organisation in biological systems. However, due to their flexibility, it is a mechanism that can often be abused. Here, we construct a minimal Turing system defined by just four parameters controlling the: diffusion rate, steady state, linear dynamics, and nonlinear dynamics. Using just these four parameters we can construct a set of kinetics with a number of desirable properties. Firstly, we can turn any homogeneous steady state into a Turing unstable steady state. Secondly, we can ensure that the Turing instability appears within any chosen parameter region. Thirdly, this formulation provides an unbounded patterning parameter space with guaranteed positive solutions. Finally, using weakly nonlinear analysis, we demonstrate that if we have freedom in any two of the parameters then we can define any required pattern transition (i.e. spots-to-stripes, or stripes-to-spots) under any given changes of one of the parameters. Thus, if a Turing system is going to be applied to understand a specific biological system and, moreover, if it is going to be used to extrapolate predictions for experimental perturbations, then our findings underscore the necessity of heavily restricting the modelling components and parameter values, since any freedom could be exploited to generate potentially contradictory predictions.

Item Type:	Article
Status:	In Press
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	The Royal Society
ISSN:	1364-5021
Date of First Compliant Deposit:	21 March 2025
Date of Acceptance:	14 March 2025
Last Modified:	21 Mar 2025 10:45
URI:	https://orca.cardiff.ac.uk/id/eprint/177056

Actions (repository staff only)

Edit Item