ArticleBulletin of mathematical biology2021
Bespoke Turing Systems.
Article in Bulletin of mathematical biology, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 24 papers.
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Who cites it
24 citing papers in PubMed.
- Fundamental limits on symmetry breaking by Turing-like activator-inhibitor mechanisms.Development (Cambridge, England) · 2026Article
- How nature discovers rare Turing islands: Exploration by common limit cycles.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Article
- Persistent Homology Classifies Parameter Dependence of Patterns in Turing Systems.Bulletin of mathematical biology · 2025Article
- Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation.Bulletin of mathematical biology · 2025Article
- Designing reaction-cross-diffusion systems with Turing and wave instabilities.Journal of mathematical biology · 2025Article
- Article
- Widespread biochemical reaction networks enable Turing patterns without imposed feedback.Nature communications · 2024Article
- Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns.iScience · 2024Article
- Learning spatio-temporal patterns with Neural Cellular Automata.PLoS computational biology · 2024Article
- Minimal reaction schemes for pattern formation.Journal of the Royal Society, Interface · 2024Article
- Turing Instabilities are Not Enough to Ensure Pattern Formation.Bulletin of mathematical biology · 2024Article
- Self-organized BMP signaling dynamics underlie the development and evolution of digit segmentation patterns in birds and mammals.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Development shapes the evolutionary diversification of rodent stripe patterns.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- VisualPDE: Rapid Interactive Simulations of Partial Differential Equations.Bulletin of mathematical biology · 2023Article
- The reaction-diffusion basis of animated patterns in eukaryotic flagella.Nature communications · 2023Article
- Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems.Bulletin of mathematical biology · 2023Article
- Learning system parameters from turing patterns.Machine learning · 2023Article
- Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems.Bulletin of mathematical biology · 2022Article
- Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems.Bulletin of mathematical biology · 2022Article
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3 authors.
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Abstract
Reaction-diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned states from homogeneous symmetry breaking via the Turing instability. Although there are many prototypical "Turing systems" available, determining their parameters, functional forms, and general appropriateness for a given application is often difficult. Here, we consider the reverse problem. Namely, suppose we know the parameter region associated with the reaction kinetics in which patterning is required-we present a constructive framework for identifying systems that will exhibit the Turing instability within this region, whilst in addition often allowing selection of desired patterning features, such as spots, or stripes. In particular, we show how to build a system of two populations governed by polynomial morphogen kinetics such that the: patterning parameter domain (in any spatial dimension), morphogen phases (in any spatial dimension), and even type of resulting pattern (in up to two spatial dimensions) can all be determined. Finally, by employing spatial and temporal heterogeneity, we demonstrate that mixed mode patterns (spots, stripes, and complex prepatterns) are also possible, allowing one to build arbitrarily complicated patterning landscapes. Such a framework can be employed pedagogically, or in a variety of contemporary applications in designing synthetic chemical and biological patterning systems. We also discuss the implications that this freedom of design has on using reaction-diffusion systems in biological modelling and suggest that stronger constraints are needed when linking theory and experiment, as many simple patterns can be easily generated given freedom to choose reaction kinetics.
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