Duque Carlos M, Hall Douglas M, Tyukodi Botond, Hagan Michael F, Santangelo Christian D, Grason Gregory M
Max Planck Institute of Molecular Cell Biology and Genetics, Dresden 01307, Germany.
Center for Systems Biology Dresden, Dresden 01307, Germany.
Proc Natl Acad Sci U S A. 2024 Apr 30;121(18):e2315648121. doi: 10.1073/pnas.2315648121. Epub 2024 Apr 26.
We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.
我们提出并研究了将病毒衣壳组装的卡斯帕 - 克卢格对称原理扩展到尺寸可控的三重周期多面体的可编程组装，这些多面体是原始、钻石和螺旋面立方最小表面的离散变体。受近期一类可编程DNA折纸胶体的启发，我们证明，在这些晶体组装中，就随着尺寸尺度（例如周期性）增加所需的不同粒子种类数量的增长而言，设计的经济性与病毒外壳相当。我们通过动态组装模拟进一步测试了几何特异性在这些组装中的作用，结果表明，同时实现高效和高保真组装的条件要求在可编程组装中局部角度和长度具有中等程度的灵活性。偏离目标的错误组装是通过引入一种位错缺陷变体发生的，这种变体推广到了双曲晶体的情况。这些拓扑缺陷的可能性是构成经济设计基础的相同对称原理的直接结果，揭示了可编程、尺寸可控组装的设计经济性与保真度之间的基本权衡。
