We propose a hybrid discrete–continuum model to study the ground state of protein shells. The model allows for shape transformation of the shell and buckling transitions as well as the competition between states with different symmetries that characterize discrete particle models with radial pair potentials. Our main results are as follows. For large Föppl–von Kármán (FvK) numbers the shells have stable isometric ground states. As the FvK number is reduced, shells undergo a buckling transition resembling that of thin-shell elasticity theory. When the width of the pair potential is reduced below a critical value, then buckling coincides with the onset of structural instability triggered by over-stretched pair potentials. Chiral shells are found to be more prone to structural instability than achiral shells. It is argued that the well-width appropriate for protein shells lies below the structural instability threshold. This means that the self-assembly of protein shells with a well-defined, stable structure is possible only if the bending energy of the shell is sufficiently low so that the FvK number of the assembled shell is above the buckling threshold.

中文翻译：

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蛋白质壳的基态不稳定性可通过屈曲消除

我们提出了一种混合离散连续谱模型来研究蛋白质壳的基态。该模型允许壳的形状转换和屈曲过渡，以及具有不同对称性的状态之间的竞争，这些状态具有径向对电势的离散粒子模型的特征。我们的主要结果如下。对于较大的Föppl–vonKármán（FvK）数，壳具有稳定的等距基态。随着FvK数的减少，壳会发生类似于薄壳弹性理论的屈曲过渡。当线对电位的宽度减小到临界值以下时，屈曲与过度拉伸的线对电位触发的结构不稳定性的发生相吻合。发现手性壳比非手性壳更倾向于结构不稳定。有人认为适合蛋白质壳的孔宽度低于结构不稳定性阈值。这意味着只有在壳的弯曲能量足够低以至于组装后的壳的FvK数高于屈曲阈值时，才可以进行具有明确定义的稳定结构的蛋白壳的自组装。