The mathematical graph theory has been applied to protein
beta-sheets. These beta-sheets can be encoded in graphs, where
vertices are the residues of the beta-sheet and the edges are the
various topological relations between the residues. The topological
relations can be one of 1) covalent peptidic bond between adjacent
residues. 2) H-bond between residues of distinct strands. 3)
Beta-sheet partnership; residues that are side-by-side in the
beta-sheet. These topological features happen to be calculated by the
program DSSP . The topological graphs, along with their associated
3-D atomic coordinates, of proteins found in PDB  have been
compiled in a database. Given a beta-sheet topological graph, the
Beta-Sheet Builder program will seek the database for subgraph
isomorphism and output the 3-D coordinates of the graphs that matches
the given input graph. That way it is possible to go from a 2-D
beta-sheet description to a 3-D atomic model. The difference between
the Beta-Sheet Builder and the Beta-Sheet Proposer is that the
Builder is less limited on the generation of topologies since the
input sheet graph is split into pairs of strands. The Builder is thus
able to build beta-sheet unobserved yet in PDB, as long as each pair
of strands can be found in the PDB. A perfect example is Baker's Top7
beta-sheet ; although the complete beta-sheet has not been in PDB
Select, the Builder is able to generate 3D coordinates for that sheet
since each strand pairs are fairly numerous in PDB. See article for more details.
What is Beta-Sheet Builder?
The featured beta-sheet is from the monocyte chemoattractant protein 1
(MCP-1) (PDB code 1DOK). The result of the execution should give you
26 solutions, i.e. PDB files (named '1DOK-000001.pdb'...). The beta-sheet
database has been compiled from the beta-sheet annotation of the
program DSSP .
The program's parameter needs further explanations:
- The last parameter (here 1.0) is the output structure cache and
it's value is in Angstroms. Each time a complete 3D structure is
generated it is compared to all the ones in the structure cache. If it
is different enough from all these structures then it is outputted as
a solution and the new structure is put in the cache with the
others. This is to prevent from having thousands of similar solutions,
as any good backtracking algorithm can yield!
- The second to last parameter (here 9999) is the maximum number of
3D structures in any backtrack sets. This is to limit the backtrack
tree size. It would be better to limit the backtrack sets using a
measure of structure similarity instead, like the RMSD.
- The third to last parameter (here 0.3) is the minimum RMSD between
instances in the same backtrack set. This value is in Angstroms. In
order for a new 3D structure of a strand pair to be part of the
backtrack it must be at least this value apart from all the previously
loaded pairs. This is to prevent from having too similar pair
structures in the backtrack sets that would end up generating similar
beta-sheets. Lower values increases the database loading time and
yield bigger backtrack tree. Start with high values like 1.0 Angstroms
and work your way downward to acceptable database loading time.
- The fourth to last parameter (here 0.6) is the peptidic link
tolerance for deformation. Here we accept peptidic links of 1.32 +/-
- The fifth to last parameter (here 0.5) is the maximum RMSD value
accepted on the superposition of the common strand when zipping 2
strand pairs togheter. Higher values gives more solutions but the
resulting beta-sheets will have more distorded peptidic bonds.
- The sixth to last parameter (here ./pairs.25.dssp.dat) is the file
name of the strand pairs database. For a bigger database use the
alternative one (Step 2b).
- The seventh to last paramater (here ./1DOK.1.stm) is the beta-sheet
topology graph which gives a 2D representation of what has to be built
in 3D. Download Baker's Top7
The following 3D structures have been generated with this command:
./psb.exe ./baker.stm ./pairs.25.bspider.dat 0.5 0.5 0.4 9999 1.0
Figure 1:579 beta-sheet 3D models for Baker's Top7
beta-sheet (PDB code 1QYS) . Each beta-sheet is at least 1.0A apart
from all the other beta-sheets. The sheets are aligned on the [13-19]
strand, which is a border strand. The figure was produced with RasMol
A) Side 1 view.
B) Side 2 view.
C) N-terminal side view.
D) C-terminal side view.
Figure 2: Accuracy test of the
Beta-Sheet Builder on the beta-sheet of 1TML. The crystal structure
has light grey cylinders while best RMSD (0.83A) structure has dark
grey ones. Strand ribbons are pictured for the crystal structure. The
image was produced using RasMol , Molscript  and Raster3D .
Figure 3: Flexibility test of the
Beta-Sheet Builder on the beta-sheet of 1TML. The crystal structure is
in red while the worst RMSD rebuilt structure is in blue. Both
structures are aligned along the strand 40 to 42. The high RMSD
(7.88A) comes from the fact that the rebuilt structure chooses a
different path as soon as the third strand from the top. The image was
produced using RasMol , Molscript  and Raster3D .
 R. A. Sayle, E. J. Milner-White, Rasmol: Biomolecular graphics for all, Trends Biol. Sci. 20 (1995) 374-376.
 P. J. Kraulis, Molscript: a program to produce both detailed and schematic plots of protein structures, Journal of Applied Crystallography 24 (1991) 946-950.
 E. A. Merritt, D. J. Bacon, Raster3D: Photorealistic Molecular Graphics, Methods in Enzymology 277 (1997) 505-524.
 W. Kabsch, C. Sander, Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features, Biopolymers 22 (1983) 2577-2637.
 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.
 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.
 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.
 M. Parisien, F. Major, A new catalog of protein beta-sheets, Unpublished. See Beta-Spider.
Created: 23/09/2004 Last update: 23/09/2004
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