Universal folding pathways of polyhedron nets
Universal folding pathways of polyhedron nets
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DOI：
10.1073/pnas.1722681115
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发表时间：
2018-07-17
影响因子：
11.1
通讯作者：
Glotzer, Sharon C.
中科院分区：
文献类型：
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作者：
Dodd, Paul M.;Damasceno, Pablo F.;Glotzer, Sharon C.
低维物体，如分子链，梯子和片材具有影响其折叠成3D物体的倾向的内在特征。理解这种关系仍然是从头设计功能结构的一个挑战。使用分子动力学模拟，我们调查的重折叠的24个可能的二维展开（“网”）的三个最简单的柏拉图的形状，并证明了属性的网络的拓扑网络的紧凑性和叶子上的切割图与热力学折叠倾向。为了解释这些相关性，我们详尽地列举了折叠过程中的网络路径，并确定了一个交叉温度Tx，低于该温度时，网络通过非原生接触折叠（在网络完全折叠之前，键必须断裂），高于该温度时，网络通过原生接触折叠（新形成的键也存在于折叠结构中）。Tx上方的折叠显示了通过消除形成键时的内部自由度来减少熵与通过局部合作边缘结合来获得势能之间的普遍平衡。利用这种普遍性，我们设计了一种数值方法来有效地计算任何网络的所有高温折叠路径，使我们能够预测剩余柏拉图固体的86，760个网络中具有最高折叠倾向的网络。我们的研究结果提供了一个一般的启发式设计的2D物体随机折叠成目标3D几何形状，并建议一种机制，几何形状和折叠倾向相关的Tx以上，其中本地债券占主导地位的折叠。
Low-dimensional objects such as molecular strands, ladders, and sheets have intrinsic features that affect their propensity to fold into 3D objects. Understanding this relationship remains a challenge for de novo design of functional structures. Using molecular dynamics simulations, we investigate the refolding of the 24 possible 2D unfoldings ("nets") of the three simplest Platonic shapes and demonstrate that attributes of a net's topology-net compactness and leaves on the cutting graph-correlate with thermodynamic folding propensity. To explain these correlations we exhaustively enumerate the pathways followed by nets during folding and identify a crossover temperature Tx below which nets fold via nonnative contacts (bonds must break before the net can fold completely) and above which nets fold via native contacts (newly formed bonds are also present in the folded structure). Folding above Tx shows a universal balance between reduction of entropy via the elimination of internal degrees of freedom when bonds are formed and gain in potential energy via local, cooperative edge binding. Exploiting this universality, we devised a numerical method to efficiently compute all high-temperature folding pathways for any net, allowing us to predict, among the combined 86,760 nets for the remaining Platonic solids, those with highest folding propensity. Our results provide a general heuristic for the design of 2D objects to stochastically fold into target 3D geometries and suggest a mechanism by which geometry and folding propensity are related above Tx, where native bonds dominate folding.