We investigate the mechanical origin of polymorphic structures in two-dimensional tubulin assemblies, of which microtubules are the best known example. These structures feature twisted ribbons, flat tubulin sheets, macrotubules, and hoops, and they spontaneously assemble depending on the chemical environment. Upon modelling tubulin aggregates as minimally anisotropic elastic shells and using a combination of numerical simulations and analytical work, we show that the mechanical strain in tubulin lattices, originating from asymmetries at the single dimer level, naturally gives rise to polymorphic assemblies, among which cylinders and other tubular structures are predominant for a wide range of values of spontaneous curvature. Furthermore, our model suggests that switching the sign of the sheets' spontaneous Gaussian curvature from positive (i.e. sphere-like) to negative (i.e. saddle-like), could provide a possible route to microtubules disassembly.

中文翻译：

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微管蛋白组件中的多态性：机械模型

我们研究了二维微管蛋白组件中多态结构的机械起源，其中微管是最著名的例子。这些结构具有扭曲的丝带、扁平的微管蛋白片、宏管和箍，它们根据化学环境自发组装。在将微管蛋白聚集体建模为最小各向异性弹性壳并结合数值模拟和分析工作后，我们表明微管蛋白晶格中的机械应变源自单个二聚体水平的不对称性，自然会产生多态组装，其中圆柱体和其他管状结构在自发曲率的广泛范围内占主导地位。此外，我们的模型表明，将片材的自发高斯曲率的符号从正数（即