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.

‘Generic’ physical mechanisms of morphogenesis and pattern formation

Development ◽  
1990 ◽  
Vol 110 (1) ◽  
pp. 1-18 ◽  
Author(s):  
S.A. Newman ◽  
W.D. Comper
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Physical Mechanisms ◽  
Extracellular Matrix Components ◽  
Genetic Mechanisms ◽  
Chemical Waves ◽  
Phylogenetic Lineages ◽  
Living Tissues ◽  
Highly Evolved

The role of ‘generic’ physical mechanisms in morphogenesis and pattern formation of tissues is considered. Generic mechanisms are defined as those physical processes that are broadly applicable to living and non-living systems, such as adhesion, surface tension and gravitational effects, viscosity, phase separation, convection and reaction-diffusion coupling. They are contrasted with ‘genetic’ mechanisms, a term reserved for highly evolved, machine-like, biomolecular processes. Generic mechanisms acting upon living tissues are capable of giving rise to morphogenetic rearrangements of cytoplasmic, tissue and extracellular matrix components, sometimes leading to ‘microfingers’, and to chemical waves or stripes. We suggest that many morphogenetic and patterning effects are the inevitable outcome of recognized physical properties of tissues, and that generic physical mechanisms that act on these properties are complementary to, and interdependent with genetic mechanisms. We also suggest that major morphological reorganizations in phylogenetic lineages may arise by the action of generic physical mechanisms on developing embryos. Subsequent evolution of genetic mechanisms could stabilize and refine developmental outcomes originally guided by generic effects.

scholarly journals Reaction-Diffusion Systems: Self-Balancing Diffusion and the Use of the Extent of Reaction as a Descriptor of Reaction Kinetics

2019 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Reaction Kinetics ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
And Diffusion ◽  
Reaction And Diffusion

Self-balancing diffusion is a concept which restricts the introduction of extents of reactions. This concept is analyzed in detail for mass- and molar-based balances of reaction-diffusion mixtures, in relation to non-self-balancing cases, and with respect to its practical consequences. A note on a recent generalization of the concept of reaction and diffusion extents is also included.<br>

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.

scholarly journals It takes two transducins to activate the cGMP-phosphodiesterase 6 in retinal rods

Open Biology ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 180075 ◽  
Author(s):  
Bilal M. Qureshi ◽  
Elmar Behrmann ◽  
Johannes Schöneberg ◽  
Justus Loerke ◽  
Jörg Bürger ◽  
...  
Keyword(s):  
Signal Transduction ◽  
G Protein ◽  
Reaction Diffusion ◽  
Structural Data ◽  
Functional Asymmetry ◽  
Activation Mechanism ◽  
Visual Signal ◽  
Local Concentration ◽  
Retinal Rods ◽  
Membrane Bound

Among cyclic nucleotide phosphodiesterases (PDEs), PDE6 is unique in serving as an effector enzyme in G protein-coupled signal transduction. In retinal rods and cones, PDE6 is membrane-bound and activated to hydrolyse its substrate, cGMP, by binding of two active G protein α-subunits (Gα*). To investigate the activation mechanism of mammalian rod PDE6, we have collected functional and structural data, and analysed them by reaction–diffusion simulations. Gα* titration of membrane-bound PDE6 reveals a strong functional asymmetry of the enzyme with respect to the affinity of Gα* for its two binding sites on membrane-bound PDE6 and the enzymatic activity of the intermediary 1 : 1 Gα* · PDE6 complex. Employing cGMP and its 8-bromo analogue as substrates, we find that Gα* · PDE6 forms with high affinity but has virtually no cGMP hydrolytic activity. To fully activate PDE6, it takes a second copy of Gα* which binds with lower affinity, forming Gα* · PDE6 · Gα*. Reaction–diffusion simulations show that the functional asymmetry of membrane-bound PDE6 constitutes a coincidence switch and explains the lack of G protein-related noise in visual signal transduction. The high local concentration of Gα* generated by a light-activated rhodopsin molecule efficiently activates PDE6, whereas the low density of spontaneously activated Gα* fails to activate the effector enzyme.

Spiral Wave Solutions of Practical Reaction-Diffusion Systems

1980 ◽  
Vol 39 (1) ◽  
pp. 8-13 ◽  
Author(s):  
M. R. Duffy ◽  
N. F. Britton ◽  
J. D. Murray
Keyword(s):  
Spiral Wave ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Wave Solutions ◽  
Diffusion Systems
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