Why Turing mechanism is an obstacle to stationary periodic patterns in bounded reaction-diffusion media with advection

2010 ◽  
Vol 12 (16) ◽  
pp. 3957 ◽  
Author(s):  
Arik Yochelis ◽  
Moshe Sheintuch
Keyword(s):  
Reaction Diffusion ◽  
Periodic Patterns ◽  
Diffusion Media ◽  
Turing Mechanism

scholarly journals The periodic coloration in birds forms through a prepattern of somite origin

Science ◽  
2018 ◽  
Vol 361 (6408) ◽  
pp. eaar4777 ◽  
Author(s):  
Nicolas Haupaix ◽  
Camille Curantz ◽  
Richard Bailleul ◽  
Samantha Beck ◽  
Annie Robic ◽  
...  
Keyword(s):  
Expression Profile ◽  
Natural Variation ◽  
Reaction Diffusion ◽  
Positional Information ◽  
Pigment Production ◽  
Periodic Patterns ◽  
Local Dynamics ◽  
Step Process ◽  
Early Developmental ◽  
Dose Dependent

The periodic stripes and spots that often adorn animals’ coats have been largely viewed as self-organizing patterns, forming through dynamics such as Turing’s reaction-diffusion within the developing skin. Whether preexisting positional information also contributes to the periodicity and orientation of these patterns has, however, remained unclear. We used natural variation in colored stripes of juvenile galliform birds to show that stripes form in a two-step process. Autonomous signaling from the somite sets stripe position by forming a composite prepattern marked by the expression profile of agouti. Subsequently, agouti regulates stripe width through dose-dependent control of local pigment production. These results reveal that early developmental landmarks can shape periodic patterns upstream of late local dynamics, and thus constrain their evolution.

Information Processing by Chemical Reaction-Diffusion Media

2011 ◽  
pp. 455-483
Author(s):  
Nicholas G. Rambidi
Keyword(s):  
Cerebral Cortex ◽  
Information Processing ◽  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Neural Net ◽  
Optical Illusions ◽  
Diffusion Media

Biological roots and specific neural net architecture of reaction-diffusion media seem to enable simulating some phenomena inherent in the cerebral cortex, such as optical illusions.

scholarly journals Biomolecular nonlinear dynamic mechanisms as a foundation for human traits of information processing machine

2001 ◽  
Vol 6 (4) ◽  
pp. 263-279
Author(s):  
Nicholas G. Rambaidi
Keyword(s):  
Image Processing ◽  
Information Processing ◽  
Nonlinear Dynamic ◽  
Reaction Diffusion ◽  
Dynamic Mechanisms ◽  
Diffusion Media ◽  
Operational Information ◽  
Basic Features ◽  
Biological Entities ◽  
High Computational Complexity

A pseudo-biological paradigm in information processing launched by McCulloch and Pitts in the early 1940s has been advanced during the last decades. Different attempts were made based on these developments to design operational information processing devices capable of solving problems of high computational complexity.One of them was the use of nonlinear dynamic mechanisms inherent in information processing by biochemical, biomolecular, and simple biological entities. Chemical reaction–diffusion media proved to be effective tools for the implementation of these capabilities.Basic features of these information processing means and modeling of their information processing capabilities are discussed in this paper. Belousov–Zhabotinsky type reaction–diffusion media were used to simulate image processing operations and finding paths in a labyrinth.

scholarly journals Spatially periodic calcium profiles around single channels

2016 ◽  
Author(s):  
S. L. Mironov
Keyword(s):  
Calcium Binding ◽  
Linear Models ◽  
Single Channel ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Cell Physiology ◽  
Single Channels ◽  
Periodic Patterns ◽  
Calcium Diffusion ◽  
Spatially Periodic

AbstractThe concept of calcium nanodomains established around the sites of calcium entry into the cell is fundamental for mechanistic consideration of key physiological responses. It stems from linear models of calcium diffusion from single channel into the cytoplasm, but is only valid for calcium increases smaller than the concentration of calcium-binding species. Recent experiments indicate much higher calcium levels in the vicinity of channel exit that should cause buffer saturation. I here derive explicit solutions of respective non-linear reaction-diffusion problem and found dichotomous solution - for small fluxes the steady state calcium profiles have quasi-exponential form, whereas in the case of buffer saturation calcium distributions show spatial periodicity. These non-trivial and novel spatial calcium profiles are supported by Monte-Carlo simulations. Imaging of 1D- and radial distributions around single α-synuclein channels measured in cell-free conditions supports the theory. I suggest that periodic patterns may arise under different physiological conditions and play specific role in cell physiology.

scholarly journals The people behind the papers – Andrew Economou and Jeremy Green

Development ◽  
2020 ◽  
Vol 147 (20) ◽  
pp. dev197293
Keyword(s):  
Developmental Biology ◽  
Perturbation Analysis ◽  
Reaction Diffusion ◽  
Biological Complexity ◽  
Periodic Patterns ◽  
Alan Turing ◽  
King's College ◽  
The People

ABSTRACTInteracting morphogens produce periodic patterns in developing tissues. Such patterning can be modelled as reaction-diffusion (RD) processes (as originally formulated by Alan Turing), and although these models have been developed and refined over the years, they often tend to oversimplify biological complexity by restricting the number of interacting morphogens. A new paper in Development reports how perturbation analysis can guide multi-morphogen modelling of the striped patterning the roof of the mouse mouth. To hear more about the story, we caught up with first author Andrew Economou and his former supervisor Jeremy Green, Professor of Developmental Biology at King's College, London.

scholarly journals Study on the Formation of Complex Chemical Waveforms by Different Computational Methods

Processes ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 393
Author(s):  
Jiali Ai ◽  
Chi Zhai ◽  
Wei Sun
Keyword(s):  
Reaction Kinetics ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Local Concentration ◽  
Periodic Patterns ◽  
Concentration Difference ◽  
Complex Chemical ◽  
Mass Transfer Theory ◽  
Chemical Waves ◽  
Oregonator Model

Chemical wave is a special phenomenon that presents periodic patterns in space-time domain, and the Belousov–Zhabotinsky (B-Z) reaction is the first well-known reaction-diffusion system that exhibits organized patterns out of a homogeneous environment. In this paper, the B-Z reaction kinetics is described by the Oregonator model, and formation and evolution of chemical waves are simulated based on this model. Two different simulation methods, partial differential equations (PDEs) and cellular automata (CA) are implemented to simulate the formation of chemical waveform patterns, i.e., target wave and spiral wave on a two-dimensional plane. For the PDEs method, reaction caused changes of molecules at different location are considered, as well as diffusion driven by local concentration difference. Specifically, a PDE model of the B-Z reaction is first established based on the B-Z reaction kinetics and mass transfer theory, and it is solved by a nine-point finite difference (FD) method to simulate the formation of chemical waves. The CA method is based on system theory, and interaction relations with the cells nearest neighbors are mainly concerned. By comparing these two different simulation strategies, mechanisms that cause the formation of complex chemical waves are explored, which provides a reference for the subsequent research on complex systems.

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