• Molecular Surfaces Calculation

ABSTRACT: Presented here is an analysis of the performance of Delaunay-tree 3 for computing delaunay triangulations, and of VEGA (running under Linux 7.2) for computing molecular surfaces.

This software creates Delaunay triangulations of an input set of atoms using a randomized algorithm

"This code iplement a randomized algorithm, that is performances are good if the points are inserted in random order."

A sample result of using Delaunay Tree on some molecules is as follows:

Results forsome other atoms using del-tree3 are as below:

============================================
Name:   | Number of atoms: | time in seconds:
--------------------------------------------
1A4G.pdb       6072                  2
1IAS.pdb      13106                  7
4HMG.pdb      11862                 10
1jmu.pdb      23268                 16
2btv.pdb      49061                256
=============================================

Graph of the above

Computation of Molecular Surface using Vega

The following was the result of computing molecular surfaces of some molecules

NAME        no. of atoms  Time taken (user time)
================================================
140D.pdb       527             6.580s
4INS.pdb       829            32.040s
16VP.pdb      2457           148.980s
1a34.pdb      2970           322.760s
1A4G.pdb      6072          2762.070s
4HMG.pdb     11862         13264.730s
===============================================
=============================================================================================================================
SUMMARY:

Rank	Model           StdError         Residual Sum           Residual Avg.       	RSS	        R^2	         Ra^2
1	a*x^2+b*x+c	30.14028474	-7.176481631E-013	-1.196080272E-013	2725.310293	0.9999802699	0.9999671166
=============================================================================================================================

Second order polynomial fit of the above.

• C++ code to parse .pb files for x, y, z (command prompt name input) parse .PDB files 1

• same as above, but file names are stored in a file called input parse .PDB files 2

• Totrov, M. and Abagyan, R.: The Contour-Buildup Algorithm to Calculate the Analytical Molecular Surface


• M.C. Rivara and N. Hitschfeld: LEPP-Delaunay algorithm: a robust tool for producing size-optimal quality triangulations. Proceedings of the 8th Annual International Meshing Roundtable. October 1999, South Lake Tahoe, California, USA, pp: 205,220


• Guibas, L. and Stolfi, J.: "Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams" ACM transactions on Graphics, 4:74-23, April 1985.
• A. Goede, R. Preissner, C. Frommel: "Voronoi Cell: New Method for Allocation of Space among Atoms: Elimination of Avoidable Errors in Calculation of Atomic Volume and Density" Journal of Computational Chemistry, 18:1113-1123, 1997
• K. E. I. Hoff, T. Culver, J. Keyser, M. Lin, and D. Manocha: "Fast computation of generalized voronoi diagrams using graphics hardware." ACM SIGGRAPH, 1999.
• N. Amenta, M. Bern, and M. Kamvysselis: " A new voronoi-based surface reconstruction algorithm." Proceedings of SIGGRAPH 98, pages 415--422, July 1998.