Turing Pattern Formation with Two Kinds of Cells and a Diffusive Chemical
Turing Pattern Formation with Two Kinds of Cells and a Diffusive Chemical
复制标题
DOI：
10.1007/s11538-007-9230-0
复制
发表时间：
2007-06
影响因子：
3.5
通讯作者：
Koichiro Uriu;Y. Iwasa
中科院分区：
文献类型：
--
作者：
Koichiro Uriu;Y. Iwasa
我们研究了具有两种细胞和扩散化学物质的三变量图灵系统，考虑了具有多个色素细胞的鱼皮图案的形成和维持。这两种细胞是由未分化的细胞产生的。它们抑制其他细胞类型的供应率，形成相同细胞类型的局部集群。此外，一种类型的细胞只能在另一种细胞类型产生的扩散性化学物质的存在下维持，导致两种细胞类型在异质空间模式中共存。我们假设细胞和化学物质之间的线性相互作用，并且细胞供应速率被约束为正或零。我们推导出扩散驱动不稳定性的条件。在一维模型中，我们研究了周期图案的波长如何依赖于参数。在二维模型中，我们研究了斑点、条纹或反向斑点图案出现的条件（图案选择）。我们讨论了启发式标准的模式选择。
We study a three-variable Turing system with two kinds of cells and a diffusive chemical, considering the formation and maintenance of fish skin patterns with multiple pigment cells. The two types of cells are produced from undifferentiated cells. They inhibit the supply rate of the other cell type, forming local clusters of the same cell type. In addition, the cells of one type can be maintained only in the presence of a diffusive chemical produced by the other cell type, resulting in the coexistence of two cell types in heterogeneous spatial patterns. We assume linear interaction among cells and the chemical, and cell supply rates constrained to be positive or zero. We derive the condition for diffusion-driven instability. In one-dimensional model, we examine how the wavelength of the periodic pattern depends on parameters. In the two-dimensional model, we study the condition for spot, stripe or reversed spot pattern to emerge (pattern selection). We discuss heuristic criteria for the pattern selection.