Like the cerebralcortex, the surface of the cerebellum is repeatedly folded. Unlike the cerebralcortex, however, cerebellar folds are much thinner and more numerous; repeatthemselves largely along a single direction, forming accordion‐like folds transverseto the mid‐sagittal plane; and occur in all but the smallest cerebella. We haveshown previously that while the location of folds in mammalian cerebral cortex isclade‐specific, the overall degree of folding strictly follows a universalpower law relating cortical thickness and the exposed and total surface areas predictedfrom the minimization of the effective free energy of an expanding, self‐avoidingsurface of a certain thickness. Here we show that this scaling law extends tothe folding of the mid‐sagittal sections of the cerebellum of 53 speciesbelonging to six mammalian clades. Simultaneously, we show that each clade hasa previously unsuspected distinctive spatial pattern of folding evident at themid‐sagittal surface of the cerebellum. We note, however, that the mammaliancerebellum folds as a multi‐fractal object, because of the difference betweenthe outside‐in development of the cerebellar cortex around a preexisting coreof already connected white matter, compared to the inside‐out development ofthe cerebral cortex with a white matter volume that develops as the cerebralcortex itself gains neurons. We conclude that repeated folding, one of the mostrecognizable features of biology, can arise simply from the interplay betweenthe universal applicability of the physics of self‐organization and biological,phylogenetical clade‐specific contingency, without the need for invokingselective pressures in evolution.

中文翻译：

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小脑皮质的折叠在形式上具有进化枝特异性，但在程度上具有普遍性

与大脑皮层一样，小脑的表面也反复折叠。然而，与大脑皮层不同的是，小脑皱襞更薄、数量更多。大部分沿单一方向重复，形成横向于中矢状面的手风琴状褶皱；并且发生在除了最小的小脑之外的所有部位。我们之前已经表明，虽然哺乳动物大脑皮层中的褶皱位置是进化枝特异性的，但折叠的总体程度严格遵循与皮质厚度相关的普遍幂律，以及根据扩展的有效自由能的最小化预测的暴露面积和总表面积。 ‐避免一定厚度的表面。在这里，我们展示了这种缩放定律延伸到属于 6 个哺乳动物进化枝的 53 个物种的小脑中矢状部分的折叠。同时，我们表明，每个分支都有一个以前未曾怀疑过的独特的折叠空间模式，在小脑的中矢状表面很明显。然而，我们注意到，哺乳动物的小脑折叠成一个多重分形物体，因为小脑皮层围绕已存在的白质核心的由外向内的发育与具有特定结构的大脑皮层的由内而外的发育之间存在差异。随着大脑皮层本身获得神经元而形成的白质体积。我们得出的结论是，重复折叠是生物学中最容易识别的特征之一，它可以简单地源于自组织物理学的普遍适用性与生物、系统发育分支特定偶然性之间的相互作用，而无需在进化中引入选择压力。