标题： 魔幻尺寸能够实现编程壳的最小复杂度和高保真组装。 显示英文标题

标题： Magic sizes enable minimal-complexity, high-fidelity assembly of programmable shells

摘要： 合成方法的最新进展使得设计能够自组装成具有精确、有限尺寸和明确定义的结构的亚基成为可能，但产量常常因脱靶亚稳态结构的形成而受到抑制。增加复杂性（不同亚基类型的数量）可以抑制脱靶结构，但会导致动力学速度变慢和合成成本增加。本文，我们以可编程三角形亚基形成的二十面体壳层为模型系统，并确定了以最低复杂度获得最高目标产量的设计原则。我们采用基于对称性的构建方法，创建了一系列设计复杂性，从最大对称性的Caspar-Klug组装到完全可寻址的零对称组装。动力学蒙特卡罗模拟表明，导致脱靶组装的最主要缺陷是旋转对称位点的向错。我们推导出基于对称性的规则，用于识别能够抑制这些向错的最优（最低复杂度、最高对称性）设计，从而实现对任意大小且精确有限尺寸的靶标进行稳健、高保真组装。最优复杂度随靶标尺寸非单调变化，在对称轴不与三角网顶点相交的高对称性设计中，会出现“魔法”尺寸。魔法尺寸下的最优设计所需的不等价相互作用类型比（最小对称性）完全可寻址构造少12倍，这大大缩短了实现大靶标高保真组装所需的时间和实验成本。这种基于对称性的脱靶组装修剪原则可推广至具有不同拓扑结构的多种架构。 显示英文摘要

摘要： Recent advances in synthetic methods enable designing subunits that self-assemble into structures with precise, finite sizes and well-defined architectures, but yields are frequently suppressed by the formation of off-target metastable structures. Increasing the complexity (the number of distinct subunit types) can inhibit off-target structures, but leads to slower kinetics and higher synthesis costs. Here, we study icosahedral shells formed of programmable triangular subunits as a model system, and identify design principles that produce the highest target yield at the lowest complexity. We use a symmetry-based construction to create a range of design complexities, starting from the maximal symmetry Caspar-Klug assembly up to the fully addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal that the most prominent defects leading to off-target assemblies are disclinations at sites of rotational symmetry. We derive symmetry-based rules for identifying the optimal (lowest-complexity, highest-symmetry) design that inhibits these disclinations, leading to robust, high-fidelity assembly of targets with arbitrarily large, yet precise, finite sizes. The optimal complexity varies non-monotonically with target size, with `magic' sizes appearing for high-symmetry designs in which symmetry axes do not intersect vertices of the triangular net. The optimal designs at magic sizes require 12 times fewer inequivalent interaction-types than the (minimal symmetry) fully addressable construction, which greatly reduces the timescale and experimental cost required to achieve high fidelity assembly of large targets. This symmetry-based principle for pruning off-target assembly generalizes to diverse architectures with different topologies.