Quaternary Structure - Symmetry
Index to Course Material
Index to Section 11
Symmetry is the concept of repetitive arrangements of similar objects
in space. In three dimensions, objects may be arranged in a large
number of ways - many of these are exhibited in crystal forms. Each
possible arrangement is achieved by a combination of simple, basic
operations. These include translation, rotation, screw-rotation,
mirror, inversion, inversion-rotation, and glide-reflection. The total
number of possible ways of arranging copies of the same object to form
a repeating lattice in 3D-space is 230. These are
the `Space Groups' familiar to crystallographers. They are enumerated
and detailed in The International Tables of Crystallography.
Proteins are chiral objects, and cannot be mirror-inverted whilst
remaining the same. Their mirror reflection is different. Thus, many of
these arrangements are actually precluded. In fact, proteins may only
adopt 65 of the 230 possible 3D space groups. Many of these are
observed when we crystallise proteins.
In the case of naturally occurring multimers of proteins, other
constraints occur which limit the possible arrangements. We are
speaking here of individual assemblies of monomer units, creating
(usually soluble) complexes which exhibit internal symmetry.
Thus, the monomers must associate with van der Waals contact interfaces
between the sub-units of the assembly. That is, the sub-units can touch
but not intersect. They may interpenetrate only in so far as there
exist corresponding `holes' into which `knobs' can be fit. Furthermore,
axes of rotational symmetry may not actually pass `through' a protein
This leads to the limited possibilities listed below.
Protein Multimer Symmetry
(Diagrams adapted from Voet and Voet, 1990; after Irving Geis)
A cyclic symmetry, designated CN
has N identical units related by a single N-fold rotational axis.
That is, successive rotations of a single unit through (360/N)°
result in the positions of the other units. Therefore, cyclic symmetries of
N = 2 to infinity are permitted. Examples presented below range from
C2 to C11.
VERY common - examples include horse-liver alcohol dehydrogenase ,
growth factors (e.g.
nerve growth factors, by Judith Murray-Rust)
Examples include chloramphenicol acetyltransferase (pdb file of trimer in PPS hypertree, 400Kb,
generated from structure 3cla,
glucagon 1gcn (25Kb)
(Exercise: Create the trimer)
serum amyloid P-component(GIF)
C-reactive protein from the horse-shoe crab (Limulus)
- eg Light harvesting complex
- eg TRAP Trp attenuation protein of Bacillus
Note: the biological unit of this protein is an undecamer (11-mer),
exhibiting C11 symmetry; however in this particular crystal
(1wap) the rings pack back-to-back, and there are two rings in the
asymmetric unit. Therefore the appearance is of D11 symmetry
(see below). Diagram courtesy of The Protein Structure Group,
Chemistry Department, University of York; if you would like to read more about
this protein, follow this link:
Trp attenuation protein of Bacillus subtilis.
A dihedral symmetry, designated DN
has 2xN identical units related by a single N-fold rotational axis and N
2-fold rotational axes.
Examples include lactate dehydrogenase
pdb file,790Kb, of complete biological unit at Brookhaven,
( 1gd1 (966Kb) [Bbk|BNL|ExP|Waw|Hal],
Fe or Mn superoxide dismutase (
Examples include hemerythrin (
pdb file of octamer in PPS hypertree, 549Kb, generated from structure 1hmo
- eg glutamine synthetase (
- eg GroEL
An octohedral symmetry, designated O
has 24 identical units related by three 4-, four 3- and six 2-fold rotational axes.
Tetrahedral (Tetramer of Trimers)
A tetrahedral symmetry, designated T
has 12 identical units related by four 3- and three 2-fold rotational axes.
An icosahedral symmetry, designated I/532
has 60 identical units related by six 5-, ten 3- and fifteen 2-fold rotational
yeast Ty retrotransposon particles
The units in a helical symmetry are related by a screw axis (a translation
and rotation operation).
Fibrous proteins exhibit helical symmetry, although in some cases there are
several entwined helical strands (e.g. 2 in the case of actin filaments, 3
in collagen). Single helical structures are the protein coats of rod-shaped
viruses, and microtubules. Click for a diagram of a
microtubule (from the page on larger
assemblies in this Section).
Birkbeck are distributing a
Symmetry Teaching programme
that runs under Microsoft Windows. Let us know if you find it useful.
- Voet, D. and Voet, J.G. (1990) Biochemistry, John Wiley and Sons, New York
- Klotz, L.M., Klippenstein, G.L., & Hendrickson, W.A. (1976) Science 192, 335-344
- Cooper, J., McIntyre, K., Badasso, M., Wood, S., Zhang, Y., Garbe, T. &
Young, D. (1995) J.Mol.Biol. 246, 531-544
Index to Course Material
Index to Section 11
Alan Mills, John Kenney, John Walshaw
Last updated 3rd Jul '96