Bard J B, French V
J Embryol Exp Morphol. 1984 Dec;84:255-74.
The formation of the wing pigmentation patterns of three species of butterflies has been modelled using a mechanism based on a tripod of assumptions. First, that there may be morphogen sources in the foci of eyespots and morphogen sinks at some parts of the wing margin, all other cells being passive. Second, that the morphogen has a finite half life and diffuses simply and freely away from the sources throughout a wing of hexagonally packed cells. Third, that the overt pattern derives from cells interpreting the local morphogen concentration with respect to thresholds which determine scale colours. The final pattern thus follows lines of constant morphogen concentration and may, depending on the distribution of sources, comprise rings, curves or bands. With such a model, we have been able to compute stable patterns having the essential topology of the compound spots of Tenaris domitilla, the large rings of Diaethria marchalii and the pattern of eyespots, rings and asymmetric bands of Ragadia minoa. Quantitative analysis of the pattern-forming process shows that, with a biologically realistic diffusion constant (approximately 5.10(-7) cm2 sec-1) and a morphogen half life less than 6h, the patterns form within approximately 12h over a wing of approximately 1000 cells in length. The limitations of the model are that the exact morphology of the eyespots and bands do not match precisely those of the original wings, that there are edge distortions and that optimal patterns may be critically dependent on the exact positions of sources and sinks. An explanation for part of the discrepancy is that we have assumed an adult wing shape and foci coordinates in modelling a process that took place earlier in development. Nevertheless, the limitations of the model argue against a mechanism based on a single morphogen operating in vivo. However, as the model can generate many features of butterfly wing patterns, it may be considered as a degenerate case of that mechanism.
已使用基于三个假设的机制对三种蝴蝶翅膀色素沉着模式的形成进行了建模。首先，在眼斑的焦点处可能存在形态发生源，而在翅膀边缘的某些部位存在形态发生汇，所有其他细胞都是被动的。其次，形态发生素具有有限的半衰期，并在由六边形排列的细胞组成的整个翅膀中简单且自由地从源扩散开来。第三，明显的模式源自细胞根据决定鳞片颜色的阈值来解释局部形态发生素浓度。最终的模式因此遵循形态发生素浓度恒定的线条，并且根据源的分布情况，可能包括环、曲线或带。通过这样一个模型，我们能够计算出具有以下基本拓扑结构的稳定模式：多尾凤蝶（Tenaris domitilla）复合斑点的拓扑结构、马氏黛眼蝶（Diaethria marchalii）的大环以及米诺娜黛眼蝶（Ragadia minoa）的眼斑、环和不对称带的模式。对模式形成过程的定量分析表明，在生物学上现实的扩散常数（约5×10⁻⁷平方厘米每秒）和形态发生素半衰期小于6小时的情况下，模式在长度约为1000个细胞的翅膀上大约12小时内形成。该模型的局限性在于，眼斑和带的确切形态与原始翅膀的形态并不完全匹配存在边缘扭曲，并且最佳模式可能严重依赖于源和汇的确切位置。部分差异的一个解释是，我们在对一个在发育早期发生的过程进行建模时假设了成虫翅膀的形状和焦点坐标。然而，该模型存在的局限性表明，体内不存在基于单一形态发生素的机制。不过，由于该模型能够生成蝴蝶翅膀模式的许多特征，它可以被视为该机制的一种退化情况。
