allometric scaling

1
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 todd.taylor_at_nist.go
v, ivaisman_at_gmu.edu
2
Ca 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 Ca 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.
3
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
Ss1,s2, , sN , initialized to residue
numbers. sit1 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 gt si
and dij r J(sit ,sjt ) -1 if sj lt si
and dij r cutoff distance r, typically
8.5-12Å 0 if dij gt
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.
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Schematic of Delaunay-Potts (DePot) procedure
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Example assignments and evolution of domain labels
2lao domain1 domain2
Expert 1-90,191-238 91-190
DALI 1-89,193-240 90-192
CATH 1-90,192-238 91-191
PDP 1-90,192-238 91-191
DomainParser2 1-89,193-240 90-192
3DEE 1-89,193-238 90-192
DDBASE 5-91,188-237 92-185
Islam 1-88,196-238 89-195
SCOP 1-238
DOMS 1-90,192-238 91-191
DePot 1-91,186-238 92-185
1avhA domain1 domain2 domain3 domain4
Expert 3-87 88-167 168-246 247-320
DALI 3-86,247-320 87-145 146-246
CATH 14-86 87-160 161-246 247-318
PDP 3-140,247-320 141-246
DomainParser2 3-89,247-320 90-145 146-246
3DEE 14-86 87-160 161-246 247-320
DDBASE 3-87 88-157 158-246 247-320
Islam 3-87 88-245 246-320
SCOP 3-320
DOMS 3-73 74-159 160-223 224-320
DePot 3-87 88-160 161-247 248-320
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Performance on combined Jones, Taylor, and
Veretnik test set wrt expert assignment
same
overlap
VI
Rand
0.56
0.97
0.53
0.80
DALI
0.76
0.96
0.38
0.88
CATH
0.63
0.94
0.54
0.81
PDP
0.56
0.97
0.53
0.80
Domain Parser
0.81
0.97
0.32
0.91
3DEE
0.61
0.94
0.61
0.79
DDBASE
0.59
0.95
0.53
0.81
Islam
0.58
0.97
0.55
0.78
SCOP
0.52
0.96
0.62
0.75
DOMS
0.59
0.98
0.53
0.80
DePot
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.
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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