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Turing pattern design principles and their robustness. [PDF]
Philos Trans A Math Phys Eng Sci, 2021 Turing patterns have morphed from mathematical curiosities into highly desirable targets for synthetic biology. For a long time, their biological significance was sometimes disputed but there is now ample evidence for their involvement in processes ranging from skin pigmentation to digit and limb formation.
Vittadello ST +3 more
europepmc +5 more sources
Turing pattern with proportion preservation [PDF]
Journal of Theoretical Biology, 2006 Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the proportionality of the pattern, i.e., the ratio of the wavelength to the size, that is often required in biological ...
Kunihiko Kaneko, Shuji Ishihara
exaly +5 more sources
Turing pattern outside of the Turing domain
Applied Mathematics Letters, 2007 There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter mu gives rise to a 'space-invariant' solution, and mu versus the ratio of the diffusion coefficients gives rise to a 'time-invariant' solution.
Santiago Schnell
exaly +5 more sources
A non-linear analysis of Turing pattern formation. [PDF]
PLoS ONE, 2019 Reaction-diffusion schemes are widely used to model and interpret phenomena in various fields. In that context, phenomena driven by Turing instabilities are particularly relevant to describe patterning in a number of biological processes.
Yanyan Chen, Javier Buceta
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Turing patterns inside cells. [PDF]
PLoS ONE, 2007 Concentration gradients inside cells are involved in key processes such as cell division and morphogenesis. Here we show that a model of the enzymatic step catalized by phosphofructokinase (PFK), a step which is responsible for the appearance of ...
Damián E Strier, Silvina Ponce Dawson
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Studies of Turing pattern formation in zebrafish skin [PDF]
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2021 Seita Miyazawa +2 more
exaly +2 more sources
PLoS ONE, 2021 Many cephalopods such as octopi and squid can purposefully and rapidly change their skin color. Furthermore, it is widely known that some octopi have the ability to rapidly change the color and unevenness of their skin to mimic their surroundings ...
Takeshi Ishida
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Nonlinear Analysis, 2022 It is well known that integer-order neural networks with diffusion have rich spatial and temporal dynamical behaviors, including Turing pattern and Hopf bifurcation.
Jiazhe Lin, Jiapeng Li, Rui Xu
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Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
Scientific Reports, 2021 The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation.
Shan Guo, Ming-zhu Sun, Xin Zhao
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Turing Patterning in Stratified Domains [PDF]
Bulletin of Mathematical Biology, 2020 AbstractReaction–diffusion processes across layered media arise in several scientific domains such as pattern-formingE. colion agar substrates, epidermal–mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction–diffusion systems and relate it to a range of existing models.
Andrew L. Krause +6 more
openaire +4 more sources