Isolating Patterns in Open Reaction-Diffusion Systems.
Isolating Patterns in Open Reaction-Diffusion Systems.
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DOI：
10.1007/s11538-021-00913-4
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发表时间：
2021-06-04
影响因子：
3.5
通讯作者：
Gaffney EA
中科院分区：
文献类型：
--
作者：
Krause AL;Klika V;Maini PK;Headon D;Gaffney EA
控制空间和时空模式形成的反应扩散现象的现实例子很少是孤立的系统，无论是化学上还是化学上。然而，即使是“开放”的反应扩散系统的配方往往忽略了域边界的作用。封闭反应扩散系统的大多数理想化都采用无通量边界条件，并且经常会在这些边界上或沿着形成图案。受与胚胎发育中空间形式的出现有关的图案化领域的边界的启发，我们提出了一组混合边界条件，用于两种反应扩散系统，该系统形成远离各种不同反应动力学的域边界的非均匀解，在边界附近具有规定的均匀状态。我们表明，这些边界条件可以来自一个更大的异质领域，表明这些条件可以自然出现，如果细胞信号或介质的其他属性在空间中变化。我们解释了这种模式本地化背后的基本机制，并证明它可以捕获大范围的本地化模式在一个，两个和三个维度，这个框架可以应用于涉及两个以上的物种的系统。此外，提出的边界条件导致更对称的模式上的内部域和可扩展地捕捉更现实的边界发展系统。最后，我们表明，这些孤立的模式是更强大的初始条件的波动，他们允许有趣的可能性，通过几何图案选择，从已知的选择机制不同。
Realistic examples of reaction–diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of ‘open’ reaction–diffusion systems often neglect the role of domain boundaries. Most idealizations of closed reaction–diffusion systems employ no-flux boundary conditions, and often patterns will form up to, or along, these boundaries. Motivated by boundaries of patterning fields related to the emergence of spatial form in embryonic development, we propose a set of mixed boundary conditions for a two-species reaction–diffusion system which forms inhomogeneous solutions away from the boundary of the domain for a variety of different reaction kinetics, with a prescribed uniform state near the boundary. We show that these boundary conditions can be derived from a larger heterogeneous field, indicating that these conditions can arise naturally if cell signalling or other properties of the medium vary in space. We explain the basic mechanisms behind this pattern localization and demonstrate that it can capture a large range of localized patterning in one, two, and three dimensions and that this framework can be applied to systems involving more than two species. Furthermore, the boundary conditions proposed lead to more symmetrical patterns on the interior of the domain and plausibly capture more realistic boundaries in developmental systems. Finally, we show that these isolated patterns are more robust to fluctuations in initial conditions and that they allow intriguing possibilities of pattern selection via geometry, distinct from known selection mechanisms.
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影响因子：
5.9
作者：
Esposito, Massimiliano
通讯作者：
Esposito, Massimiliano
影响因子：
2.9
作者：
Bozzini, B.;Gambino, G.;Sgurad, I.
通讯作者：
Sgurad, I.
DOI：
10.1073/pnas.94.24.12765
发表时间：
1997-11-25
影响因子：
11.1
作者：
DeWit, A;Borckmans, P;Dewel, G
通讯作者：
Dewel, G
影响因子：
4
作者：
DEKEPPER, P;CASTETS, V;BOISSONADE, J
通讯作者：
BOISSONADE, J
影响因子：
3.5
作者：
Crampin, EJ;Hackborn, WW;Maini, PK
通讯作者：
Maini, PK