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Analyzing the Simplicial Decomposition of Spatial Protein Structures
Rafael Ördög, Zoltán Szabadka, Vince Grolmusz
Aims of our research
AimsEasy to use protein database containing
relevant geometrical data on proteins. (Capable of treating thousands of PDB entries at once.)
Drug discovery by data mining in the database.
Steps of our research
Steps Cleaning and restructuring the PDB (RS-PDB)
Done by Zoltan Szabadka
Creating a database of geometrical & chemo-geometrical data
Under construction in our present research
Discovering rules, and creating learning systems for ligand pre-docking.
Mostly later work
Delaunay Decompositions To find the Delaunay
decomposition of a set, we have used the qhull algorithm, its source is available at: http://www.qhull.org/.
Important properties of Delaunay decompositions Regions are defined
by circum spheres being empty (Region is empty as well)
Regions are tetrahedra except if more than 4 points are on the same sphere.
Important properties of Delaunay decompositions Partition of the convex hull of A. The graph defined by the edges of the
Delaunay regions: Delaunay GraphCan be used for searching closest neighbors
Delaunay decomposition of heavy atoms of the protein in 1n9c with the ligand
Important properties of Delaunay decompositions The “dual” structure can solve the Post
Office problem.Partitioning the city into service areas of
given post offices, so that every one belongs to the closest post office.
Duality here is only theoretical, in practice it is the same structure. (Voronoi diagram.)
Previous work
Singh, Tropsha and Vaisman The point set was chosen to be the set of
Cα atoms of the protein Aim: predict secondary protein structure In contrast: we chose the point set to be
the set of all heavy atoms. (Non hydrogen atoms.)
Volume
Tetrahedrality
Volume and tetrahedrality
Tetrahedrality: 0 for regular tetrahedra, and < 1
i<j(li-lj)2)
(15 (ili / 6)2)
Frequency
Two dimensional temperature plots of the frequency of regions with given volume and tetrahedrality. In all proteins (Our whole database) In a given protein
Volume and tetrahedrality of all regions (Cα atoms)
Volume and tetrahedrality of all regions (Heavy atoms)
Volume and tetrahedrality of all regions
Volume and tetrahedrality of regions with ligand atom
Volume and tetrahedrality of regions with ligand atom
Volume and tetrahedrality of all regions (Heavy atoms)
Classifying by corner atoms
Question: are the different peaks in the earlier plots in connection with the function of the corner atoms?Classification by the symbols of corner atomsClassification by hetid of the residues the
atom is found in. Question: How frequent are different
corner atom sets?
Most frequent corner sets
C C N O25%
C C C O17%
C C C N11%
C C C C10%
C C O O10%
C N O O9%
C N N O6%
C C N N5%
C O O O2%
Other5%
Connection of volume and tetrahedrality corner atom set
Volume and tetrahedrality of all regions (Heavy atoms)
Frequency of metals in different types of tetrahedra
CCNO CNOO CNNO COOO CCNN NNOO NOOO CNNN NNNO OOOO CCCS NNNN CCNS CCSS NOSS
ZN 5 7 3 2 0 14 14 0 38 2 0 0 4 0 32
MG 1 11 4 1 0 15 10 6 5 6 0 5 0 0 0
FE 2 3 0 1 1 0 0 2 0 0 2 1 0 5 0
MN 0 0 0 3 1 3 4 0 4 5 0 0 0 0 0
CA 0 0 0 0 0 0 1 0 2 48 0 0 0 0 0
Ca appears almost exclusively in the vicinity of four Oxygen
Zn prefers NOSS and NNNO type of tetrahedra, but also frequent in CNOO NNOO NOOO
Only Zn was found in NOSS
Thank you
About the geometric extension
Presently we cannot handle: Missing atoms Precision errors, non-tetrahedral regions
The PDB is handled as a juggled input The resulting database can only be used for quality statistical
purposes.
Strongly restricted database. No missing atoms, 2.2 Ǻ resolution, includes protein
5757 such PDB (June 23, 2006 )
Our current research addresses the problems above.
Recent problems For example aromatic rings should be on one
circle, in one plane, hence on one sphere, but they refuse to be: Distortion is minor, not recognizable by eye
Is it just measuring error? Or is it due to the structure around the ring?
In contrast some atoms not expected to fall on one sphere tend to do so.
Structure of the geometric extension Essential:
Corner Reference to the atoms in the RS-PDB
Region the radius and coordinates of the center of the circum sphere volume and tetrahedrality of the tetrahedron three type of bond graphs code hetid, atom name, and symbol set assigned to the regions
corner set and more
Additional: Edge, Neighbor, (Ligand) Atom