Painter Kevin J, Ho William, Headon Denis J
Department of Mathematics & Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, UK; Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy.
Roslin Institute & Royal (Dick) School of Veterinary Studies, University of Edinburgh, UK.
J Theor Biol. 2018 Jan 21;437:225-238. doi: 10.1016/j.jtbi.2017.10.026. Epub 2017 Oct 31.
The orderly formation of the avian feather array is a classic example of periodic pattern formation during embryonic development. Various mathematical models have been developed to describe this process, including Turing/activator-inhibitor type reaction-diffusion systems and chemotaxis/mechanical-based models based on cell movement and tissue interactions. In this paper we formulate a mathematical model founded on experimental findings, a set of interactions between the key cellular (dermal and epidermal cell populations) and molecular (fibroblast growth factor, FGF, and bone morphogenetic protein, BMP) players and a medially progressing priming wave that acts as the trigger to initiate patterning. Linear stability analysis is used to show that FGF-mediated chemotaxis of dermal cells is the crucial driver of pattern formation, while perturbations in the form of ubiquitous high BMP expression suppress patterning, consistent with experiments. Numerical simulations demonstrate the capacity of the model to pattern the skin in a spatial-temporal manner analogous to avian feather development. Further, experimental perturbations in the form of bead-displacement experiments are recapitulated and predictions are proposed in the form of blocking mesenchymal cell proliferation.
禽类羽毛阵列的有序形成是胚胎发育过程中周期性模式形成的经典例子。已经开发了各种数学模型来描述这一过程，包括图灵/激活剂-抑制剂型反应扩散系统以及基于细胞运动和组织相互作用的趋化性/机械模型。在本文中，我们基于实验结果构建了一个数学模型，该模型涉及关键细胞（真皮和表皮细胞群体）和分子（成纤维细胞生长因子，FGF，以及骨形态发生蛋白，BMP）之间的一组相互作用，以及作为启动模式形成触发因素的向内侧推进的引发波。线性稳定性分析表明，FGF介导的真皮细胞趋化性是模式形成的关键驱动因素，而普遍高表达BMP形式的扰动会抑制模式形成，这与实验结果一致。数值模拟证明了该模型以类似于禽类羽毛发育的时空方式对皮肤进行模式化的能力。此外，概括了珠子位移实验形式的实验扰动，并以阻断间充质细胞增殖的形式提出了预测。
