Protein Quaternary Structure: Symmetry Patterns

Ronald E Stenkamp, University of Washington, Seattle, Washington, USA

Published online: December 2009

DOI: 10.1002/9780470015902.a0003121.pub2

Full Article on Wiley Online Library

Protein molecules can assemble into larger, multisubunit oligomers that possess unique quaternary structures and biological properties. The properties of the oligomeric protein can be quite different from those of the individual subunits. The noncovalent protein–protein interactions giving rise to oligomers often result in symmetric complexes containing identical monomers in identical environments. The symmetry properties of these complexes are described, in particular with respect to the types of subunit–subunit interactions giving rise to the oligomers. Because the symmetry of the macromolecular assemblies is based on the symmetric interactions between the subunits, understanding the symmetry provides further insight into the functioning of the oligomers. Specific examples discussed include: aspartate carbamoyltransferase (where symmetry concepts are tied to allosteric control), multienzyme complexes (built along the lines of the Platonic polyhedra) and virus capsids (large macromolecular complexes formed making use of symmetry and quasi-symmetry).

Keywords: quaternary structure; symmetry; viruses; multienzyme complexes; protein–protein interactions; protein oligomers

	Figure 1. (a) A schematic representation showing a dimeric protein with subunits interacting isologously. The region A_I on protomer I interacts with B_II on protomer II. Likewise, A_II on protomer II interacts with B_I on protomer I. Each subunit is represented by the kidney-shaped object. The 2-fold rotation axis relating the two subunits is perpendicular to the plane of the figure at the position labelled X. (b) Heterologous interactions between two protein subunits. The B_I region of protomer I binds to A_II of protomer II, but B_II of protomer II and A_I of protomer I do not interact. The two subunits (kidney-shaped objects) are related by a 2-fold screw operation along the direction of the arrow. (c) Heterologous interactions in a cyclic trimer. Each subunit uses its A region to bind to one of the other subunits and its B region to bind to the other. The 3-fold rotation axis relating the three subunits is perpendicular to the plane of the figure at position X.
	Figure 2. Objects possessing 222 symmetry. (a) A rectangular object can be related to itself by each of three mutually perpendicular 2-fold rotation axes (denoted by arrows). (b) The rectangle can be twisted along the directions shown by the arrows at its corners. (c) After twisting (green lines), the object still possesses 222 symmetry.
	Figure 3. Streptavidin, a tetrameric protein showing 222 symmetry. (a) View of the tetramer in a random orientation. Subunits are shown in yellow, red, blue and green. (b) View along one of the 2-fold axes showing the relationship between the yellow and blue subunits and between the red and green subunits. (c) View along another 2-fold rotation axis, the one relating the red and blue subunits and the green and yellow subunits. (d) View along the third 2-fold rotation axis showing the relationship between the blue and green subunits and between the red and yellow subunits. Figure drawn with XtalView and Raster3d.
	Figure 4. The Platonic solids. (a) The tetrahedron, (b) the cube, (c) the octahedron, (d) the dodecahedron and (e) the icosahedron. Figure drawn with XtalView and Raster3d.
	Figure 5. Rotational symmetry elements of the Platonic solids. (a) The tetrahedron possesses 3-fold axes passing through each vertex and its opposite face. There are also 2-fold rotation axes perpendicular to each pair of opposite edges. Each tetrahedron contains four 3-fold axes and three 2-fold axes. Only one example of each is shown for simplicity in each of the figures. (b) The cube possesses 4-fold axes perpendicular to the square faces, 3-fold axes along each body diagonal and 2-fold axes perpendicular to each set of opposite edges. (c) The octahedron contains the same symmetry elements, but with the 4-fold axes passing through opposite vertices, the 3-fold axes perpendicular to each pair of triangular faces and 2-fold axes perpendicular to pairs of opposite edges. (d). The dodecahedron possesses 5-fold axes perpendicular to each pentagonal face, 3-fold axes passing through opposite vertices and 2-fold axes perpendicular to pairs of opposite edges. (e) The icosahedron possesses 5-fold axes through opposite vertices, 3-fold axes perpendicular to the triangular faces and 2-fold axes perpendicular to opposite edges. Figure drawn with XtalView and Raster3d.
	Figure 6. The core structure of pyruvate dehydrogenase. (a) General view of the 60 subunits making up the core with dodecahedral symmetry. (b) Looking down the 5-fold axis. Five subunits coloured in yellow to show how they are related by the 5-fold rotation axis. (c) Looking down a 3-fold rotation axis. The blue subunits are related by the 3-fold, as are the purple subunits. The 3-fold axis applies to the entire particle, not just the coloured ones used to demonstrate the rotational symmetry. (d) Looking down a 2-fold axis. Figure drawn with XtalView and Raster3d.

Further Reading
	Anderson DH, Kickhoefer VA, Sievers SA, Rome LH and Eisenberg D (2007) Draft crystal structure of the vault shell at 9-Å resolution. PLoS Biology 5: 2661–2670.
	Caspar DLD and Klug A (1962) Physical principles in the construction of regular viruses. Cold Spring Harbor Symposia on Quantitative Biology 27: 1–24.
	book Cotton FA (1990) Chemical Applications of Group Theory. New York: Wiley.
	Goodsell DS and Olson AJ (2000) Structural symmetry and protein function. Annual Review of Biophysics and Biomolecular Structure 29: 105–153.
	book Hargittai I and Hargittai M (1994) Symmetry: A Unifying Concept. Bolinas, CA: Shelter Publications.
	Izard T, Ævarsson A, Allen MD et al. (1999) Principles of quasi-equivalence and Euclidean geometry govern the assembly of cubic and dodecahedral cores of pyruvate dehydrogenase complexes. Proceedings of the National Academy of Sciences of the USA 96: 1240–1245.
	Leibundgut M, Maier T, Jenni S and Ban N (2008) The multienzyme architecture of eukaryotic fatty acid synthases. Current Opinion in Structural Biology 18: 714–725.
	Tanaka H, Kato K, Yamashita E et al. (2009) The structure of rat liver vault at 3.5 Angstrom resolution. Science 323: 384–388.

Article Title:	Protein Quaternary Structure: Symmetry Patterns
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Protein Quaternary Structure: Symmetry Patterns

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