Fig 1.
Examples of protein globular domains with internal symmetry.
Protein domains are labeled with SCOP domain identifier [26, 27]. a) N-terminal domain of aldehyde ferredoxin oxidoreductase with 2-fold rotational symmetry (C2) of an alpha+beta motif; b) 5-bladed beta propeller with a helical insertion between second and third blades with 5-fold rotational symmetry (C5) of a 4-stranded beta-sheet motif; c) Beta-barrel with 8 beta strands in a 4-fold dihedral symmetry (D4) of single stranded motifs; d) 4-helical bundle with dihedral symmetry connectivity (D2) of single helical motifs; e) Beta-helix with single stranded right-handed helical symmetry (H3); f) Leucine rich repeats with open rotational symmetry (R) of 16 up and down alpha-beta motifs; g) Designed Ankyrin repeat protein with 4 translational repeats (R) of double helical motifs; h) Alpha-alpha right-handed superhelix (SH) of double helical motifs. Repeats are colored from blue, N-terminal, to red, C-terminal. Non-repeating parts of the structure are colored in grey.
Fig 2.
Flowchart of one iteration of the CE-Symm algorithm.
Algorithm steps are grey rectangles, inputs and outputs are blue rounded rectangles, decision rules are green rhomboid boxes and final classifications are orange hexagonal rectangles. Additional iterations on the resulting repeats may be performed to detect further symmetry axes or hierarchical symmetry. The images on the right represent, from top to bottom: a) initial structure, colored by secondary structure elements; b) self-alignment dot-plot matrix, where similarity score is a range from blue (high similarity) to magenta (low similarity), the identity alignment is blacked out and the optimal self-alignment path is in white; c) superposition of the structure against itself based on the optimal self-alignment, where the original structure is in blue and cyan and a copy of the structure is in yellow and orange (orange and cyan correspond to the regions of the alignment involving a circular permutation); d) subset of the alignment graph with seven connected components of six aligned residues each; e) superposition of the six internally symmetric repeats according to the symmetry axis (yellow bar) and their residue equivalencies; and f) structure inside the six-fold cyclic symmetry (C6) box, with repeats colored differently.
Fig 3.
Internal symmetry in crystallin proteins.
A) An archaean βγ-crystallin with two repeats per chain (3HZ2). The full chain is displayed along its 2-fold axis, followed by a superposition of the repeats. The conserved calcium binding motif N/D-N/D-#-I-S/T-S is highlighted in yellow throughout. B) Human γ-D crystallin structure with four repeats per chain (1HK0). Two levels of symmetry exist: a C2 symmetry within each globular domain, and an additional C2 axis relating the two domains. The calcium binding motif has been lost (red bar below sequence), but other conserved positions (blue and magenta in the sequence) show the homology between the repeats.
Fig 4.
A) Internal C2 symmetry in one chain of a MaoC domain protein dehydratase from Chloroflexus aurantiacus (4E3E) displaying a “double hot dog” fold. B) Full trimeric assembly, with the six individual hot dog domains colored. The quaternary structure has a threefold cyclic symmetry that combines with the twofold internal symmetry into a dihedral D3 symmetry equivalent to the quaternary structure of homologs without the internal domain duplication. C) Sequence alignment showing that the catalytic R/N-####-H motif (yellow) is lost in the first domain but retained in the second. Amino acid identity is shown in blue and similarity in magenta.
Fig 5.
Uneven stoichiometry as a consequence of internal symmetry.
The Bowman-Birk inhibitor from snail medic seeds (yellow) forms a complex with two bovine trypsin subunits (blue) in an uneven (A2B) stoichiometry and asymmetric assembly (2ILN). However, a 2-fold symmetry axis (red) can be identified in the complex when the internal symmetry of the inhibitor is taken into account, showing that the complex is equivalent to one with even (A2B2) stoichiometry.