Repository: Freie Universit├Ąt Berlin, Math Department

The Design Principles of Discrete Turing Patterning Systems

Leyshon, Thomas and Tonello, Elisa and Schnoerr, David and Siebert, Heike and Stumpf, Michael P.H. (2021) The Design Principles of Discrete Turing Patterning Systems. Journal of Theoretical Biology, 531 .

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The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.

Item Type:Article
Uncontrolled Keywords:Pattern formation Cellular automaton Developmental model Robustness
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2817
Deposited By: Ulrike Eickers
Deposited On:08 Apr 2022 09:33
Last Modified:08 Apr 2022 09:33

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