Painter K J, Maini P K, Othmer H G
Centre for Mathematical Biology, Mathematical Institute Oxford, OX1 3LB, United Kingdom.
Proc Natl Acad Sci U S A. 1999 May 11;96(10):5549-54. doi: 10.1073/pnas.96.10.5549.
Current interest in pattern formation can be traced to a seminal paper by Turing, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce stable nonuniform concentration patterns in space. Recently, a Turing model has been suggested to explain the development of pigmentation patterns on species of growing angelfish such as Pomacanthus semicirculatus, which exhibit readily observed changes in the number, size, and orientation of colored stripes during development of juvenile and adult stages, but the model fails to predict key features of the observations on stripe formation. Here we develop a generalized Turing model incorporating cell growth and movement, we analyze the effects of these processes on patterning, and we demonstrate that the model can explain important features of pattern formation in a growing system such as Pomacanthus. The applicability of classical Turing models to biological pattern formation is limited by virtue of the sensitivity of patterns to model parameters, but here we show that the incorporation of growth results in robustly generated patterns without strict parameter control. In the model, chemotaxis in response to gradients in a morphogen distribution leads to aggregation of one type of pigment cell into a striped spatial pattern.
当前对图案形成的兴趣可追溯到图灵的一篇开创性论文，他证明了一种由称为形态发生素的反应性和扩散性化学物质组成的系统能够相互作用，从而在空间中产生稳定的非均匀浓度图案。最近，有人提出用图灵模型来解释像半环刺盖鱼等生长中的神仙鱼物种色素沉着图案的形成，这类神仙鱼在幼鱼和成鱼阶段发育过程中，其彩色条纹的数量、大小和方向变化易于观察，但该模型未能预测条纹形成观察结果的关键特征。在此，我们开发了一个纳入细胞生长和运动的广义图灵模型，分析了这些过程对图案形成的影响，并证明该模型能够解释像半环刺盖鱼这样的生长系统中图案形成的重要特征。经典图灵模型对生物图案形成的适用性因图案对模型参数的敏感性而受到限制，但我们在此表明，纳入生长因素会导致在无需严格参数控制的情况下稳健地生成图案。在该模型中，对形态发生素分布梯度作出响应的趋化作用会导致一种色素细胞聚集形成条纹状空间图案。
