Beta-Strand Shuffler
What is Beta-Strand Shuffler?
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The Beta-Strand Shuffler generates all N! * 2^(N-2) possible
beta-sheet topologies. For each topology the program then proceeds to
slide de strands relative to the others, this is called
registering. Then, for each valid strand configuration the program
evaluates the beta-sheet in a fashion similar to [3] (see MODEL
section). This program is usefull to generate plausible beta-sheet
topologies given a list of beta-strands. The list of strands can be
inferred from secondary structure prediction or CD or NMR.
The featured beta-sheet is from Baker's Top7 de novo protein (PDB code
1QYS) [12]. Step 4 is used to get the mean number of H-bonds per
generated sheet, here 28, and is used in Step 5 with the -H and -B
options. The minimum sheet energy should be -75.29 kcal/mol ("grep
Total baker.sheet.top | sort -g"), and corresponds to the native
topology in Top7. The O option specifies which residues should be on
opposite sides of the sheet, so as to force the alpha-helices to go on
top of the sheet. Residues 23 and 46, as well as 54 and 78, are forced
to be on opposite sides of the sheet. The extent of the strands are
those annotated by our program beta-Spider.
The energy model that is used to score the beta-sheets is as follow:
- Amino-acid composition in parallel and anti-parallel sheets differ [1].
- Amino-acid pairings are not "random" [2][3].
- Beta-sheets often have an hydrophobic face [4].
- Number of H-bonds given a topology (~2.8 kcal/mol/h-bond) [5].
Note: I have derived the optimal weights for each terms in
this equation and this is a subject to a paper. e-mail me for further
details.
Following the execution of:
"./bShuffle.exe -S -R 6 -O 23-46 -O 54-78 -H -B 28 ./baker.str"
The best topology for Top7 given by bShuffle is:
2 -> [ 15:K+][ 16:N ][ 17:F@][ 18:D-][ 19:Y@][ 20:T ][ 21:Y@][ 22:T ][ 23:V ]
1 <- [ 12:D-][ 11:D-][ 10:I ][ 9:N ][ 8:V ][ 7:Q ][ 6:V ][ 5:Q ][ 4:I ]
3 -> [ 46:K+][ 47:R+][ 48:V ][ 49:R+][ 50:I ][ 51:S ][ 52:I ][ 53:T ][ 54:A ]
5 <- [ 94:L ][ 93:Q ][ 92:G ][ 91:E-][ 90:V ][ 89:T ][ 88:V ][ 87:T ][ 86:D-]
4 -> [ 78:D-][ 79:I ][ 80:N ][ 81:V ][ 82:T ][ 83:F@][ 84:D-]
Pairing Energy: -25.50 kcal/mol
Hydrophobicity Energy: -26.17 kcal/mol
(Face 1 Hydrophobicity Score: +17.32)
(Face 2 Hydrophobicity Score: -21.56)
H-bonding Energy: -20.00 kcal/mol
(Alternative 1: 32 H-bonds [ 54 with 4] Energy: -10.00 kcal/mol)
(Alternative 2: 36 H-bonds [ 4 with 23] Energy: -20.00 kcal/mol)
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Total Sheet Energy: -75.29 kcal/mol
Which also happens to be the native topology, and the resulting
beta-sheet is in a pure anti-parallel configuration. The H-bonding
network in the crystal file of Top7 (PDB code 1QYS) is such that
residue 4 forms a closed ring with 23, which is the alternative that
leads to the maximum number of H-bonds.
But also notice that there are also other alternatives which are
energetically "close", for example:
3 -> [ 46:K+][ 47:R+][ 48:V ][ 49:R+][ 50:I ][ 51:S ][ 52:I ][ 53:T ][ 54:A ]
1 <- [ 12:D-][ 11:D-][ 10:I ][ 9:N ][ 8:V ][ 7:Q ][ 6:V ][ 5:Q ][ 4:I ]
2 -> [ 15:K+][ 16:N ][ 17:F@][ 18:D-][ 19:Y@][ 20:T ][ 21:Y@][ 22:T ][ 23:V ]
5 <- [ 94:L ][ 93:Q ][ 92:G ][ 91:E-][ 90:V ][ 89:T ][ 88:V ][ 87:T ][ 86:D-]
4 -> [ 78:D-][ 79:I ][ 80:N ][ 81:V ][ 82:T ][ 83:F@][ 84:D-]
Pairing Energy: -21.31 kcal/mol
Hydrophobicity Energy: -26.17 kcal/mol
(Face 1 Hydrophobicity Score: +17.32)
(Face 2 Hydrophobicity Score: -21.56)
H-bonding Energy: -20.00 kcal/mol
(Alternative 1: 32 H-bonds [ 23 with 4] Energy: -10.00 kcal/mol)
(Alternative 2: 36 H-bonds [ 4 with 54] Energy: -20.00 kcal/mol)
---------------------------------------
Total Sheet Energy: -71.84 kcal/mol
As you can notice, each of the sheets present the same amino-acids on
the same faces; we cannot discard any of them based on the fact that a
sheet has a less hydrophobic face. Also, each of these sheets can host
as much as 36 H-bonds, so here too we cannot pick the best sheet based
on the number of H-bonds. Interestingly, both topologies introduce a
pair of networked salt bridges (15:K-12:D-46:K), which is
electrostatically more stable than isolated salt bridges [6] (here the
energy calculations do not account for this stabilizing effect). Also
of interest is the fact that both topologies should prevent amyloid
fibril formation by hosting an unpaired charged residue in their
border strands [7]. However, the second alternative, even though it
scores close to the first one, is such that the two alpha-helices are
on opposite sides of the sheet, and thus one of them will be in
contact with the less favoured 18:D-91:E unbalanced negative charges.
You can grab the source code here:
Further instructions can be found in the main .C file. I would
appreaciate to be informed of any source code modifications so I can
merge them into the current sources and that everyone has the latest
and best features.
Last source code update: 20/12/2004.
- (20/12/2004) Corrected the allowed topologies now using spin.
- (22/11/2004) Added H-bonding energy calculations.
- (22/11/2004) Corrected the recursive residue spin assignments.
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[1] S. Lifson, C. Sander, Antiparallel and parallel beta-strands differ in amino acid residue preferences, Nature 282 (1979) 109-111.
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[2] S. Lifson, C. Sander, Specific recognition in the tertiary structure of beta-sheets of proteins, J. Mol. Biol. 139 (1980) 627-639.
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[3] H. Zhu, W. Braun, Sequence specificity, statistical potentials, and three-dimensional structure prediction with self-correcting distance geometry calculations of beta-sheet formation in proteins, Protein Sci. 8 (1999) 326-342.
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[4] J. F. Richardson, D. C. Richardson, Principles and patterns of protein conformation, Plenum Press, New York, 1989, Ch. 1, pp. 1-98.
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[5] D. N. Boobbyer, P. J. Goodford, P. M. McWhinnie, R. C. Wade, New hydrogen-bond potentials for use in determining energetically favorable binding sites on molecules of known structure, J. Med. Chem. 32 (1989) 1083-1094.
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[6] S. Kumar, R. Nussinov, Salt bridge stability in monomeric proteins, J Mol Biol. 293 (1999) 1241-55.
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[7] J. S. Richardson, D. C. Richardson, Natural beta-sheet proteins use negative design to avoid edge-to-edge aggregation, PNAS 99 (2002) 2754-9.
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[8] R. A. Sayle, E. J. Milner-White, Rasmol: Biomolecular graphics for all, Trends Biol. Sci. 20 (1995) 374-376.
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[2] P. J. Kraulis, Molscript: a program to produce both detailed and schematic plots of protein structures, Journal of Applied Crystallography 24 (1991) 946-950.
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[9] E. A. Merritt, D. J. Bacon, Raster3D: Photorealistic Molecular Graphics, Methods in Enzymology 277 (1997) 505-524.
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[10] W. Kabsch, C. Sander, Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features, Biopolymers 22 (1983) 2577-2637.
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[11] H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, P. E. Bourne, The Protein Data Bank, Nucl. Acids Res. 28 (2000) 235-242.
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[12] B. Kuhlman, G. Dantas, G. C. Ireton, G. Varani, B. L. Stoddard, D. Baker, Design of a novel globular protein fold with atomic-level accuracy, Science 302 (2003) 1364-1368.
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[13] G. Wang, R. L. Dunbrack Jr, PISCES: a protein sequence culling server, Bioinformatics 19 (2003) 1589-1591.
The X-Ray resolution is 2.0 A, R-Factor at 0.25 and no more than 25% sequence identity. As of the 7th Feb. 2004 it contained 1966 chains.
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[14] M. Parisien, F. Major, A new catalog of protein beta-sheets, Unpublished. See Beta-Spider.
Marc Parisien
Created: 26/10/2004 Last update: 22/11/2004
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