Protein assembles into Archimedean geometry

A combination of ideas from geometry, computer science and molecular biology is ushering in a golden age for the design of nanometre-scale materials made from protein building blocks1. Naturally occurring cellular and viral structures highlight the diverse architectures that can be formed from protein molecules, and also hint at possible technological applications for designer proteins with predetermined shapes2. Writing in Nature, Malay et al.3 report the production of a surprising and extraordinary protein structure: a cage-like architecture composed of 264 protein subunits held together at their edges by gold ions.

Efforts to make geometric protein architectures have generally focused on symmetrical 3D shapes. In particular, the Platonic solids4 — which include the tetrahedron, cube and icosahedron — have provided strategic design targets owing to their geometric simplicity5. These architectures can be realized by arrangements in which multiple protein subunits occupy identical spatial environments in the protein assembly.

Cubes, for example, have been constructed68 from protein trimers (complexes of three identical protein subunits). Each trimer occupies a corner of a cube, so that eight of them are needed to form the complete shape (Fig. 1a). Each subunit in a trimer can contact a subunit from another trimer along one of the edges of the cube. Those contacts are all identical, and hold the assembly together.

Figure 1 | The assembly of proteins into Platonic and Archimedean geometries.a, Platonic solids are a family of symmetrical 3D shapes that includes the cube. To assemble proteins into these shapes, protein multimers (such as trimers, for a cube) can be placed at the vertices. Interactions between multimers along a shape’s edges hold the assembly together. Dual shapes form if the vertices are replaced by faces, and vice versa; the dual of a cube is an octahedron. b, A snub cube is an Archimedean solid — a polyhedron that has identical vertices but different types of edge and face. Malay et al.3 found that an undecameric protein complex (an assembly formed of 11 identical protein subunits) can be engineered to assemble at the 24 vertices of a snub cube. The connections between subunits are mediated by metal ions along the edges. The resulting protein assembly has the shape of a pentagonal icositetrahedron, which is the dual of the snub cube.

All three types of symmetry embodied by the Platonic solids — tetrahedral, octahedral and icosahedral — have been assembled using protein building blocks69. But the family of Platonic solids consists of just five shapes, which limits the architectures that can be made, and also constrains the geometries of the protein building blocks that can be used to construct them. This raises the question of what other shapes could be constructed using building blocks whose geometries make them unsuitable for making Platonic solids. A membrane-protein assembly described in 2014 showed evidence of unusual possibilities10.

Enter Malay et al., who started with a naturally occurring protein that forms a ring-shaped assembly containing 11 identical copies of the protein molecule (an undecamer). They engineered the protein’s sequence to incorporate a cysteine amino-acid residue, which has a thiol group (SH) in its side chain. The resulting undecamer ring therefore presents 11 thiol groups around its perimeter. Thiol groups can bind to metal atoms, so the perimeter thiol groups allow multiple undecamers to assemble into larger structures through thiol–metal interactions.

Malay and colleagues observed that the undecamers assembled into cage-like structures when mixed with a source of either gold or mercury ions. The authors knew that the 11-fold symmetry of the undecamers was incompatible with the construction of a Platonic solid, but the flexibility and reversibility of metal-mediated interactions could allow a diverse range of other architectures to form11. Characterizing the structure was challenging, but the researchers ultimately succeeded in visualizing it in atomic detail using cryo-electron microscopy.

The structure is of a type not seen before in molecular systems: 24 copies of the 11-membered ring are held together by specific interactions between the rings. Malay et al. identified the arrangement as a snub cube, which belongs to a group of polyhedra known as Archimedean solids4. The vertices in Archimedean solids are all equivalent, but the faces and edges can be of distinct types.

Each vertex in the snub cube is connected by the edges to five other vertices, but — in contrast to the case for Platonic solids — the angles between the connections at a given vertex are not all the same. Instead, one of the angles is larger than the other four (Fig. 1b). Fortuitously for Malay et al., the edges of the snub cube very nearly match up with the alternating ‘spokes’ that radiate from the centre of an undecagon to its edges. This means that one of the authors’ undecamers can be placed at each of the 24 vertices of a snub cube to make contacts with the other undecamers, thus forming 60 edges.

Only 10 of the 11 thiol groups in any given undecamer participate in metal-mediated connections. This feature arises as a result of using metal ions for assembly: the strategy tolerates the presence of potential sites of attachment that do not actually form interactions through metal ions. This contrasts with design approaches that are based only on direct interactions between protein subunits6 — the ‘sticky’ hydrophobic surfaces on proteins that mediate such interactions can lead to random aggregation if they do not interact successfully with other protein subunits.

In the reported snub cube, the 11 subunits in a given undecamer ring occupy different spatial environments and connect differently to neighbouring rings, breaking the symmetry of the system. Symmetry-breaking is also a feature of the architectures of many viral capsids (protein shells). A diverse array of viral capsids can be understood as systems in which a simple icosahedron is elaborated into something more complex, for example by subdividing its triangular faces into smaller triangles12. In such systems, large numbers of protein subunits can be tiled onto capsid faces so that there are only modest differences in the angles between them and in the environments they occupy. This ‘quasi-equivalence’12 allows unbroken interactions between subunits to be maintained throughout the capsid, so that an essentially solid shell can be formed.

Malay and colleagues’ structure shows that molecular Archimedean architectures break symmetry differently: by not using a subset of potential lateral interactions. The resulting architectures therefore contain sizeable holes (Fig. 1b), which renders them more cage-like than shell-like. Interestingly, holes have previously been observed in other large, artificial protein shells that deviate from quasi-equivalence13.

The authors’ findings suggest an explanation for why (as far as we know) Archimedean protein architectures haven’t evolved in nature, for use in cells, for example. The apparently unavoidable openings in such structures might have made them less suitable as enclosures, compared with their quasi-equivalent icosahedral (Platonic) counterparts, which evolved many times in viruses.

The current result was a serendipitous finding, but further studies should address whether similar outcomes can be obtained predictably using other protein building blocks. With this in mind, Malay et al. have produced computer models of architectures based on other Archimedean solids (such as the cuboctahedron), which might be constructed using other ring sizes, including 7-, 10- and 16-sided polygons. Success in building those architectures would be another exciting development in the field of designed protein assemblies.

Nature 569, 340-342 (2019)

Updates & Corrections

  • Correction 13 May 2019: An earlier version of this article said that only 5 of the 11 thiol groups of an undecameric protein participate in metal-mediated connections to assemble into a pentagonal icositetrahedron. The correct number is 10 of the 11. The main text, figure and caption have been corrected accordingly.


  1. 1.

    Yeates, T. O. Annu. Rev. Biophys. 46, 23–42 (2017)

    PubMed  Article  Google Scholar 

  2. 2.

    Aumiller, W. M., Uchida, M. & Douglas, T. Chem. Soc. Rev. 47, 3433–3469 (2018).

    PubMed  Article  Google Scholar 

  3. 3.

    Malay, A. D. et al. Nature 569, 439–443 (2019).

    Article  Google Scholar 

  4. 4.

    Holden, A. Shapes, Space, and Symmetry (Columbia Univ. Press, 1971).

    Google Scholar 

  5. 5.

    Padilla, J. E., Colovos, C. & Yeates, T. O. Proc. Natl Acad. Sci. USA 98, 2217–2221 (2001).

    PubMed  Article  Google Scholar 

  6. 6.

    King, N. P. et al. Science 336, 1171–1174 (2012).

    PubMed  Article  Google Scholar 

  7. 7.

    Lai, Y.-T. et al. Nature Chem. 6, 1065–1071 (2014).

    Article  Google Scholar 

  8. 8.

    Sciore, A. et al. Proc. Natl Acad. Sci. USA 113, 8681–8686 (2016).

    PubMed  Article  Google Scholar 

  9. 9.

    Bale, J. B. et al. Science 353, 389–394 (2016).

    PubMed  Article  Google Scholar 

  10. 10.

    Basta, T. et al. Proc. Natl Acad. Sci. USA 111, 670–674 (2014).

    PubMed  Article  Google Scholar 

  11. 11.

    Salgado, E. N., Radford, R. J. & Tezcan, F. A. Acc. Chem. Res. 43, 661–672 (2010).

    PubMed  Article  Google Scholar 

  12. 12.

    Caspar, D. L. & Klug, A. Cold Spring Harb. Symp. Quant. Biol. 27, 1–24 (1962).

    PubMed  Article  Google Scholar 

  13. 13.

    Sasaki, E. et al. Nature Commun. 8, 14663 (2017).

    PubMed  Article  Google Scholar 

Download references

Nature Briefing

An essential round-up of science news, opinion and analysis, delivered to your inbox every weekday.

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing