Turing Pattern Formation Under Heterogeneous Distributions of Parameters for an Activator-Depleted Reaction Model

Hernandez-Aristizabal, David; Garzón‐Alvarado, Diego Alexander; Madzvamuse, Anotida

doi:10.1007/s00332-021-09685-6

Cited by 2 publications

(2 citation statements)

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“…Initial conditions are known to play a crucial role in mode competition and, therefore, the final pattern [3, 36]. When initial conditions are similar to one of the admissible modes, this mode typically dominates in the final pattern.…”

Section: Discussionmentioning

confidence: 99%

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Turing pattern prediction in three-dimensional domains: the role of initial conditions and growth

Tahar

Muñoz

Shefelbine

et al. 2023

Preprint

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Reaction-diffusion systems have been widely used to model pattern formation in biological systems. However, the emergence of Turing patterns in three-dimensional (3D) domains remains relatively unexplored. A few studies on this topic have shown that extending pattern formation from 2D to 3D is not straightforward. Linear stability analysis, which is commonly used to associate admissible wave modes with predicted patterns in 1D and 2D, has yet to be applied in 3D. We have used this approach, together with finite element modeling of a Turing system with Schnakenberg kinetics, to investigate the effects of initial conditions and growing domains on the competition between admissible modes in 3D Turing pattern emergence. Our results reveal that non-random initial conditions on the activator play a stronger role than those on the substrate. We also observe a path dependency of the evolving pattern within a growing domain. Our findings shed new light on the mechanisms ensuring reliable pattern formation in 3D domains and have important implications for the development of more robust models of morphogen patterning in developmental processes.

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Section: Discussionmentioning

confidence: 99%

“…Admissible modes for a specific set of model parameters are obtained from the linear analysis of the governing equations. The combination of the admissible modes leading to the final pattern is influenced by initial conditions [13,21,29,30,[34][35][36].…”

Section: Introductionmentioning

confidence: 99%