Abstract

A general framework for the generation of long wavelength patterns in multi-cellular (discrete) systems is proposed, which extends beyond conventional reaction-diffusion (continuum) paradigms. The standard partial differential equations of reaction-diffusion framework can be considered as a mean-field like ansatz which corresponds, in the biological setting, to sending to zero the size (or volume) of each individual cell. By relaxing this approximation and, provided a directionality in the flux is allowed for, we demonstrate here that instability leading to spatial pattern formation can always develop if the (discrete) system is large enough, namely, composed of sufficiently many cells, the units of spatial patchiness. The macroscopic patterns that follow the onset of the instability are robust and show oscillatory or steady state behavior.

Graphical abstract

中文翻译：

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在多细胞系统中形成图案的通用途径

摘要

提出了在多细胞（离散）系统中生成长波长模式的通用框架，该框架超越了常规的反应扩散（连续谱）范式。反应扩散框架的标准偏微分方程可以被视为平均场，如ansatz，在生物学环境中，其对应于将每个单个细胞的大小（或体积）发送至零。通过放宽该近似值，并在允许通量具有方向性的情况下，我们在此处证明，如果（离散）系统足够大（即由足够多的单元组成）的空间，总会形成导致空间模式形成的不稳定性。空间斑驳。跟随不稳定性开始的宏观模式是稳健的，并显示出振荡或稳态行为。

图形概要