Glimm T, Bhat R, Newman S A
Department of Mathematics, Western Washington University, Bellingham, WA 98229, USA.
Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
J Theor Biol. 2014 Apr 7;346:86-108. doi: 10.1016/j.jtbi.2013.12.004. Epub 2013 Dec 16.
We present a mathematical model for the morphogenesis and patterning of the mesenchymal condensations that serve as primordia of the avian limb skeleton. The model is based on the experimentally established dynamics of a multiscale regulatory network consisting of two glycan-binding proteins expressed early in limb development: CG (chicken galectin)-1A, CG-8 and their counterreceptors that determine the formation, size, number and spacing of the "protocondensations" that give rise to the condensations and subsequently the cartilaginous elements that serve as the templates of the bones. The model, a system of partial differential and integro-differential equations containing a flux term to represent local adhesion gradients, is simulated in a "full" and a "reduced" form to confirm that the system has pattern-forming capabilities and to explore the nature of the patterning instability. The full model recapitulates qualitatively and quantitatively the experimental results of network perturbation and leads to new predictions, which are verified by further experimentation. The reduced model is used to demonstrate that the patterning process is inherently morphodynamic, with cell motility being intrinsic to it. Furthermore, subtle relationships between cell movement and the positive and negative interactions between the morphogens produce regular patterns without the requirement for activators and inhibitors with widely separated diffusion coefficients. The described mechanism thus represents an extension of the category of activator-inhibitor processes capable of generating biological patterns with repetitive elements beyond the morphostatic mechanisms of the Turing/Gierer-Meinhardt type.
我们提出了一个数学模型，用于研究作为鸟类肢体骨骼原基的间充质凝聚物的形态发生和模式形成。该模型基于一个多尺度调控网络的实验确定动力学，该网络由在肢体发育早期表达的两种聚糖结合蛋白组成：CG（鸡半乳糖凝集素）-1A、CG-8及其反受体，它们决定了产生凝聚物以及随后作为骨骼模板的软骨元件的“原凝聚物”的形成、大小、数量和间距。该模型是一个包含通量项以表示局部粘附梯度的偏微分和积分 - 微分方程组，以“完整”和“简化”形式进行模拟，以确认该系统具有模式形成能力，并探索模式形成不稳定性的本质。完整模型定性和定量地重现了网络扰动的实验结果，并得出了新的预测，这些预测通过进一步的实验得到了验证。简化模型用于证明模式形成过程本质上是形态动力学的，细胞运动性是其内在特征。此外，细胞运动与形态发生素之间的正负相互作用之间的微妙关系产生了规则模式，而无需具有广泛不同扩散系数的激活剂和抑制剂。因此，所描述的机制代表了激活剂 - 抑制剂过程类别的扩展，能够产生具有重复元素的生物模式，超越了图灵/吉勒尔 - 迈因哈特类型的形态静态机制。
