Turing Patterning in Stratified Domains
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00343771" target="_blank" >RIV/68407700:21340/20:00343771 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11538-020-00809-9" target="_blank" >https://doi.org/10.1007/s11538-020-00809-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11538-020-00809-9" target="_blank" >10.1007/s11538-020-00809-9</a>
Alternative languages
Result language
angličtina
Original language name
Turing Patterning in Stratified Domains
Original language description
Reaction-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. We derive conditions for diffusion-driven instability of a spatially homogeneous equilibrium analogous to the classical conditions for a Turing instability in the simplest nontrivial setting where one domain has a standard reaction-diffusion system, and the other permits only diffusion. Due to the transverse coupling between these two regions, standard techniques for computing eigenfunctions of the Laplacian cannot be applied, and so we propose an alternative method to compute the dispersion relation directly. We compare instability conditions with full numerical simulations to demonstrate impacts of the geometry and coupling parameters on patterning, and explore various experimentally relevant asymptotic regimes. In the regime where the first domain is suitably thin, we recover a simple modulation of the standard Turing conditions, and find that often the broad impact of the diffusion-only domain is to reduce the ability of the system to form patterns. We also demonstrate complex impacts of this coupling on pattern formation. For instance, we exhibit non-monotonicity of pattern-forming instabilities with respect to geometric and coupling parameters, and highlight an instability from a nontrivial interaction between kinetics in one domain and diffusion in the other. These results are valuable for informing design choices in applications such as synthetic engineering of Turing patterns, but also for understanding the role of stratified media in modulating pattern-forming processes in developmental biology and beyond.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
BULLETIN OF MATHEMATICAL BIOLOGY
ISSN
0092-8240
e-ISSN
1522-9602
Volume of the periodical
82
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
37
Pages from-to
—
UT code for WoS article
000581737600001
EID of the result in the Scopus database
2-s2.0-85092608131