Buckling without bending morphogenesis: nonlinearities, spatial confinement, and branching hierarchies
Buckling without bending morphogenesis: nonlinearities, spatial confinement, and branching hierarchies
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DOI：
10.1088/1367-2630/ac03ce
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发表时间：
2021-02
影响因子：
3.3
通讯作者：
M. Gandikota;J. Schwarz
中科院分区：
文献类型：
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作者：
M. Gandikota;J. Schwarz
在形态发生过程中，一个无特征的凸状小脑形成褶皱。当它这样做时，皮质厚度在褶皱的顶部（脑回）最薄，在褶皱的谷部（脑沟）最厚。这种现象不能简单地用弹性屈曲理论来解释。最近的一个最小模型通过将发育中的皮质建模为在径向跨越弹性纤维、皱襞膜和非生长的子皮质的约束下生长的流体来解释这一现象（Engstrom et al 2019 Phys. Rev. X 8 041053）。在这个无弯曲形态发生的最小屈曲（BWBM）模型中，假设弹性纤维与应变呈线性关系。在这里，我们探讨如何非线性弹性影响BWBM内的形状发展。非线性弹性在控制系统形状的微分方程中产生二次非线性，并导致更尖锐的波谷和更宽的波峰，这是小脑褶皱在发育后期的识别特征。由于发育中的器官通常不是孤立的，我们还探索了空间限制的影响，并观察到波峰变平。最后，作为一个典型的例子，我们提出了一个层次版本的BWBM的一种新的机制，分支形态发生自然出现定性预测后期阶段的发展小脑的形态。
During morphogenesis, a featureless convex cerebellum develops folds. As it does so, the cortex thickness is thinnest at the crest (gyri) and thickest at the trough (sulci) of the folds. This observation cannot be simply explained by elastic theories of buckling. A recent minimal model explained this phenomenon by modeling the developing cortex as a growing fluid under the constraints of radially spanning elastic fibers, a plia membrane and a nongrowing sub-cortex (Engstrom et al 2019 Phys. Rev. X 8 041053). In this minimal buckling without bending morphogenesis (BWBM) model, the elastic fibers were assumed to act linearly with strain. Here, we explore how nonlinear elasticity influences shape development within BWBM. The nonlinear elasticity generates a quadratic nonlinearity in the differential equation governing the system’s shape and leads to sharper troughs and wider crests, which is an identifying characteristic of cerebellar folds at later stages in development. As developing organs are typically not in isolation, we also explore the effects of steric confinement, and observe flattening of the crests. Finally, as a paradigmatic example, we propose a hierarchical version of BWBM from which a novel mechanism of branching morphogenesis naturally emerges to qualitatively predict later stages of the morphology of the developing cerebellum.