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Beta Barrels

Complete and distorted barrels

Based on secondary structure information, barrel structures can be classified into two types: "complete barrels" and "distorted barrels". "Complete barrels" can be identified simply based on a complete ring of hydrogen bonds in the derived secondary structure information. Here, hydrogen bonds are calculated using SSTRUC, a local implementation (Smith, unpublished data) of DSSP (Kabsch & Sander, 1983). In contrast, it is very difficult to detect "distorted barrels", because hydrogen bonds are not formed between some barrel strands, or some strands are not detected at all by the algorithm. At present, only "complete barrels" are analysed here.

Exterior and interior residues on the barrel strands

The direction of side chains of residues on the strands are calculated based on the direction of the vector from the Ca atom to the Cb atom. For glycine, a dummy Cb atom is generated. The barrel axis is calculated so that it goes through the centre of the barrel, which is the average position of Ca atoms for the middle residue on each barrel strand, and the centre of the barrel bottom, which is the average position of Ca atoms for the N-terminal residue on each barrel strand. The angle made between the vector perpendicular to the barrel axis through the axis and the Ca atom and the vector from the Ca atom to the Cb atom is calculated. Where the angle is between 0 and 90 degrees, the residue is defined to be an "interior residue". Where the angle is between 90 and 180 degrees, the residue is defined to be an "exterior residue". The "exterior residues" and "interior residues" are represented by ovals and rectangles, respectively in HERA-plots (Fig. 1).

Fig. 1

Barrel strand number, n, and the shear number, S

There are two numbers used to describe the geometry of barrel structures. One is the number of strands making up the barrel structures, n, and the other is the shear number, S, proposed by McLachlan in 1979. The latter is a measure of the extent to which the beta-sheet is staggered. By rolling out the barrel, the hydrogen bonding pattern can be drawn (see Fig. 1). In the case of the upper barrel of Fig.1, nine strands are shown, as the first strand is drawn on both edges of the sheet. The residues can be thought of as lying at the grid points of a virtual lattice. Starting from the first residue (Phe 6) in strand 1, it is possible to move around the barrel until strand 1 is reached again. Here, the position of the first residue in the strand 1' (Phe 6) is now shifted by eight residues from its original position on strand 1 of the virtual lattice. The shear number for this barrel is eight. Since consecutive residues along a strand alternate between the two sides of the sheet, and corresponding residues on adjacent strands are on the same side of the sheet, the shear number should theoretically be an even integer.

Once calculated, the n and S values can be used to determine other geometrical parameters, such as strand tilt relative to the barrel axis and barrel radius. (McLachlan, 1979; Lesk et al., 1989; Murzin et al., 1994).

Bifurcation of barrel beta-sheets

Any beta-strand can be classified according to the number of other strands to which it is hydrogen bonded. "Usual strands" are hydrogen bonded to two adjacent strands, whilst "edge strands" are hydrogen bonded to only one adjacent strand, and "bifurcated strands" have more than two adjacent strands. Although typical complete barrel structures are composed of only "usual strands", some barrel structures have at least one "bifurcated strand" and correspondingly an "edge strand" (see Fig. 2). The numbers of bifurcated strands and edge strands are listed in the table.

Fig. 2

Removal of bulge residues

Sometimes, beta-bulge residues occur in the middle of a beta-strands, which can affect S values. Therefore, the S values without bulge residues are listed. The procedure of the bulge removal follows the algorithm developed by Chan et al. (1993).

An extended definition of layer structure
If S is equal to n or 2n, particular sets of residues on the barrel lie in planes, perpendicular to the barrel axis, and form stacked "layers" (Lesk et al., 1989; Murzin et al., 1994) (see Fig. 1). However, in the case of n<S<2n, such sets perpendicular to the barrel axis cannot be identified. Previously (Lesk et al., 1989), only interior residues involved in barrel packing were defined as "layers" of TIM barrel structures. However, exterior as well as interior residues lie in planes. Where S=n, a layer includes alternating interior and exterior residues. Where S=2n, layers include only all interior or all exterior residues, and adjacent layers alternate. Here, "semi-complete layers", in which the direction of glycine is allowed to be flipped from interior to exterior or vice-versa, are also detected.

References

Chan AWE, Hutchinson EG, Harris D and Thornton JM (1993). Identification, classification and analysis of beta-bulges in proteins. Protein Science, 2, 1574-1590.
Kabsch W and Sander C (1983). Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers, 22, 2577-2637.
Lesk AM, Branden C-I and Chothia C (1989). Structural principles of alpha/beta barrel proteins: the packing of the interior of the sheet. Proteins: Struct Funct Genet, 5, 139-148.
McLachlan AD (1979). Gene duplications in the structural evolution of chymotrypsin. J. Mol. Biol., 128, 49-79.
Murzin AG, Lesk AM and Chothia C (1994). Principles determining the structure of beta-sheet barrels in proteins. I. A theoretical analysis. J. Mol. Biol., 236, 1369-1381.
Murzin AG, Lesk AM and Chothia C (1994). Principles determining the structure of beta-sheet barrels in proteins. II. The observed structures. J. Mol. Biol., 236, 1382-1400.
Nagano N, Hutchinson EG and Thornton, JM (1999). Barrel structures in proteins: automatic identification and classification including a sequence analysis of TIM barrels. Protein Sci. 8, 2072-2084.

 

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