Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI, 02912, USA.
Mathematical Biosciences Institute, Ohio State University, 1735 Neil Avenue, Columbus, OH, 43210, USA.
Nat Commun. 2018 Aug 13;9(1):3231. doi: 10.1038/s41467-018-05629-z.
Zebrafish (Danio rerio) feature black and yellow stripes, while related Danios display different patterns. All these patterns form due to the interactions of pigment cells, which self-organize on the fish skin. Until recently, research focused on two cell types (melanophores and xanthophores), but newer work has uncovered the leading role of a third type, iridophores: by carefully orchestrated transitions in form, iridophores instruct the other cells, but little is known about what drives their form changes. Here we address this question from a mathematical perspective: we develop a model (based on known interactions between the original two cell types) that allows us to assess potential iridophore behavior. We identify a set of mechanisms governing iridophore form that is consistent across a range of empirical data. Our model also suggests that the complex cues iridophores receive may act as a key source of redundancy, enabling both robust patterning and variability within Danio.
斑马鱼(Danio rerio)具有黑色和黄色条纹,而相关的 Danio 则呈现出不同的图案。所有这些图案都是由于色素细胞的相互作用而形成的,这些色素细胞在鱼皮上自我组织。直到最近,研究才集中在两种细胞类型(黑色素细胞和黄色素细胞)上,但新的研究揭示了第三种细胞类型——虹彩细胞的主导作用:虹彩细胞通过精心协调的形态转变,指导其他细胞,但对于驱动它们形态变化的原因知之甚少。在这里,我们从数学角度来研究这个问题:我们开发了一个模型(基于已知的前两种细胞类型之间的相互作用),使我们能够评估虹彩细胞的潜在行为。我们确定了一组控制虹彩细胞形态的机制,这些机制在一系列经验数据中是一致的。我们的模型还表明,虹彩细胞接收到的复杂信号可能是冗余的一个关键来源,使 Danio 中既具有强大的模式化能力,又具有可变性。