Transcript allometric scaling

Protein Structural Domain Assignment with
a Delaunay Tessellation Derived Lattice
Abstract: A method of protein structural domain assignment using an
Ising/Potts-like model on a lattice derived from the Delaunay tessellation of
a protein structure is described. The method is very simple and agrees well
with previously published methods.
Todd J.Taylor, Iosif I.Vaisman
[email protected], [email protected]
Cα Delaunay tessellation of phosphoglycerate kinase
(16pk) with no edge cutoff and with a 10Å cutoff
Protein structures have been analyzed with a technique from computational geometry known as Delaunay
tessellation (DT). Each amino acid is abstracted to a point and the points are then joined by edges to form
a set of non-overlapping, irregular, space-filling tetrahedra each having the property that the sphere on the
surface of which all four vertices reside does not contain a vertex from any other tetrahedron.
The union of the surface faces of the tessellated protein forms the convex hull of the Cα point set. Surface
irregularities are ‘paved over’ by long edges (20Å+) which form contacts between residue pairs that are too
far apart to be ‘true’ neighbors. It is sometimes expedient therefore to impose an edge length cutoff in the
DT analysis.
Protein domain assignment and DePot
Structural domains: Wetlaufer (1973), Definition - continuous segment(s) of the main
chain that form a compact, stable structure with a hydrophobic core and potentially
could fold and function independently from the rest of the structure
Delaunay-Potts: Sequence of domain labels is S={s1,s2, …, sN} , initialized to
residue numbers.
sit+1 = sit + U[∑ J(sit ,sjt ) ] , i =1, …, N , where j varies over the Delaunay neighbors
of i and U(x) = x/|x|
Pick residue at random and immediately update (asynchronous updating). Iterate
until shape of domain label profile meets ending 'stairstep' criteria.
1 if sj > si and dij ≤ r
J(sit ,sjt ) =
-1 if sj < si and dij ≤ r
cutoff distance r, typically 8.5-12Å
0 if dij > r
Smooth in a window around residue i, replacing the label at i with the median in the
window. Post-processing fine tunes assignment: no domains smaller than 40
residues, no domain boundary cuts a beta sheet.
Schematic of Delaunay-Potts (DePot) procedure
domain 1
domain 2
Example assignments and evolution of domain labels
2lao
Expert
DALI
CATH
PDP
DomainParser2
3DEE
DDBASE
Islam
SCOP
DOMS
DePot
1avhA
Expert
DALI
CATH
PDP
DomainParser2
3DEE
DDBASE
Islam
SCOP
DOMS
DePot
domain1
1-90,191-238
1-89,193-240
1-90,192-238
1-90,192-238
1-89,193-240
1-89,193-238
5-91,188-237
1-88,196-238
1-238
1-90,192-238
1-91,186-238
domain1
3-87
3-86,247-320
14-86
3-140,247-320
3-89,247-320
14-86
3-87
3-87
3-320
3-73
3-87
domain2
91-190
90-192
91-191
91-191
90-192
90-192
92-185
89-195
91-191
92-185
domain2
88-167
87-145
87-160
141-246
90-145
87-160
88-157
88-245
domain3 domain4
168-246 247-320
146-246
161-246 247-318
146-246
161-246
158-246
246-320
247-320
247-320
74-159
88-160
160-223
161-247
224-320
248-320
Performance on combined Jones, Taylor, and
Veretnik test set wrt expert assignment
DALI
CATH
PDP
Domain Parser
3DEE
DDBASE
Islam
SCOP
DOMS
DePot
Rand
0.80
0.88
0.81
0.80
0.91
0.79
0.81
0.78
0.75
0.80
VI
0.53
0.38
0.54
0.53
0.32
0.61
0.53
0.55
0.62
0.53
overlap
0.97
0.96
0.94
0.97
0.97
0.94
0.95
0.97
0.96
0.98
same #
0.56
0.76
0.63
0.56
0.81
0.61
0.59
0.58
0.52
0.59
Depot along with several other methods was tested on a set of 100 structures from
three previously published domain assignment papers. The overlap score (used
before in the literature) was used to measure similarity wrt expert assignments as
well as two other scoring schemes, not applied to domain assignment before from
the clustering literature.
Selected references
[1] Singh RK, Tropsha A, Vaisman II (1996) Delaunay tessellation of proteins: four body nearest-neighbor
propensities of amino acid residues. J Comput Biol 3(2):213-21.
[2] Taylor TJ, Vaisman II (2006) Protein structural domain assignment with a Delaunay tessellation
derived lattice, Proceedings of the 3rd International Symposium on Voronoi Diagrams in Science and
Engineering.
[3] Taylor WR (1999) Protein structural domain identification. Protein Eng 12: 203-16.
[4] Veretnik S, Bourne PE, Alexandrov NN, Shindyalov IN (2004) Toward consistent assignment of
protein domains in proteins. J Mol Biol 339: 647-678.
[5] Holland TA, Veretnik S, Shindyalov IN, Bourne PE. (2006) Partitioning protein structures into
domains: why is it so difficult? J Mol Biol. 361(3):562-590.
[6] Jones S, Stewart M, Michie A, Swindells MB, Orengo C, Thornton JM (1998) Domain assignment for
protein structures using a consensus approach: characterization and analysis. Protein Sci 7: 233-242.
[7] Okabe A (2000) Spatial tessellations : concepts and applications of Voronoi diagrams. Wiley
Acknowledgements
W.R. Taylor for the DOMS method and code.
Stella Veretnik for discussions regarding her work with domain assignment.
NSF for funding.
Assignment server
http://proteins.binf.gmu.edu/iv-software.html