Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’

Krause, Andrew L.; Gaffney, Eamonn A.; Maini, Philip K.; Klika, Václav

doi:10.1098/rsta.2020.0280

Cited by 13 publications

(11 citation statements)

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“…The recent issue of Philosophical Transactions (Krause et al. 2021 ) highlights the state of the art in how the patterns that emerge from a Turing instability have been used to explain many phenomena in biology. There is also a parallel literature in the wider theory of pattern formation across many different length scales of physics from micromechanics to spatial ecology; see also the other recent volumes (Yochelis et al.…”

Section: Introductionmentioning

confidence: 99%

General conditions for Turing and wave instabilities in reaction -diffusion systems

Villar-Sepúlveda

Champneys

2023

J. Math. Biol.

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Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction–diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to $$\infty $$ ∞ , gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh–Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.

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Section: Introductionmentioning

confidence: 99%

General conditions for Turing and wave instabilities in reaction -diffusion systems

Villar-Sepúlveda

Champneys

2023

J. Math. Biol.

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“…These universal RPApermissive design principles now represent a launching-point for future explorations of more complex phenotypes -including some classes of embryonic patterning problems, for instance, where integral control is known to play a role in promoting adaptation of segmentation boundaries to variations in organism size 14,15 . The identification of universal design principles for many other complex phenotypes, such as Turing patterns 37,40,41 and multistability/ switching-responses 42,43 , is likely to prove more challenging -due, in part, to the central role of equilibrium stabilities, or instabilities, in generating these responses. These grand challenges remain open, and we hope that our study will inspire bold new mathematical thinking in these vitally important directions.…”

Section: Discussionmentioning

confidence: 99%

Universal structures for adaptation in biochemical reaction networks

Araujo

Liotta

2023

Nat Commun

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At the molecular level, the evolution of life is driven by the generation and diversification of adaptation mechanisms. A universal description of adaptation-capable chemical reaction network (CRN) structures has remained elusive until now, since currently-known criteria for adaptation apply only to a tiny subset of possible CRNs. Here we identify the definitive structural requirements that characterize all adaptation-capable collections of interacting molecules, however large or complex. We show that these network structures implement a form of integral control in which multiple independent integrals can collaborate to confer the capacity for adaptation on specific molecules. Using an algebraic algorithm informed by these findings, we demonstrate the existence of embedded integrals in a variety of biologically important CRNs that have eluded previous methods, and for which adaptation has been observed experimentally. This definitive picture of biological adaptation at the level of intermolecular interactions represents a blueprint for adaptation-capable signaling networks across all domains of life, and for the design of synthetic biosystems.

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“…There have been many extensions to the basic DDI model proposed in order to obtain a richer, and more robust, range of patterning behaviours, reflecting those observed in biology [6]. One such extension is domain growth.…”

Section: 1])mentioning

confidence: 99%