Abstract of the paper [Vorobjev 1997]: The SIMS method generates the smooth molecular surface by rolling two probe spheres. A solvent probe sphere is rolled over the molecule and produces the Richards-Connolly molecular surface (MS), which envelops the solvent-excluded volume of the molecule. In deep crevices, Connolly's method of calculating the MS has two deficiencies. First, it produces self-intersecting parts of the molecular surface, which have to be removed to obtain the correct MS. Second, the correct MS is not smooth, i.e. the direction of the normal vector of the MS is not continuous, and, some points of the MS are singular. We present an exact method to remove self-intersecting parts and to smooth the singular regions of the MS. The singular MS is smoothed by rolling a smoothing probe sphere over the inward side of the singular MS. The MS in the vicinity of singularities is replaced with the reentrant surface of the smoothing probe sphere. The smoothing method does not disturb the topology of a singular MS and the smooth MS is a better approximation of the dielectric border between high dielectric solvent and low dielectric molecular interior. The SIMS method generates a smooth molecular dot surface which has a quasi-uniform dot distribution in two orthogonal directions on the molecular surface, and which is invariant to rotation of the molecule and stable to a change in the molecular conformation, and which can be used in a variety of implicit methods of modeling solvent effects. The SIMS program is faster than the Connolly MS program and in a matter of seconds generates a smooth dot MS of a 200 residue protein.
The following data was collected according to the rules set on the project specs web page. Only user-level time was measured excluding any system calls and IO that the kernel might perform on behalf of the process. The reading of the PDBs and the output of the results in the program was not timed but rather the section where the calculations are performed only. For measuring the time, the fortran intrinsic call etime() was employed.
Timing of Various PDB files with SIMS |
| PDB file
140D.pdb 4INS.pdb 16VP.pdb 1a34.pdb 148d.pdb 1A4G.pdb 1AFV.pdb 4HMG.pdb 1IAS.pdb 1I84.pdb unknown.pdb 1HVU.pdb 1jmu.pdb None4.pdb 1h1k.pdb 2btv.pdb |
Atoms
527 1181 2637 3479 5856 6641 9024 12243 13181 16580 18236 21416 23657 25977 40008 48336 |
Time
1.020 s 1.830 s 3.810 s 6.140 s 443.250 s 8.340 s 15.940 s 22.710 s 27.190 s 43.440 s 39.680 s 116.230 s 58.080 s 66.370 s 113.580 s 115.200 s |
Output data
140D 4INS 16VP 1a34 148d 1A4G 1AFV 4HMG 1IAS 1I84 unknown 1HVU 1jmu None4 1h1k 2btv |
Abstract of the paper [Barber 1996]: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains non-extreme points, and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of "thick" facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
Timing of Various PDB files with QHULL |
| PDB file
140D.pdb 4INS.pdb 16VP.pdb 1a34.pdb 148d.pdb 1A4G.pdb 1AFV.pdb 4HMG.pdb 1IAS.pdb 1I84.pdb unknown.pdb 1HVU.pdb 1jmu.pdb None4.pdb 1h1k.pdb 2btv.pdb |
Points
527 829 2457 2969 5856 6072 9022 11862 13106 16492 17896 21416 23268 25224 40008 49061 |
Time
0.040 s 0.080 s 0.260 s 0.410 s 0.660 s 0.720 s 1.080 s 1.460 s 1.560 s 2.010 s 2.220 s 2.520 s 2.970 s 3.190 s 4.710 s 6.330 s |
Output data
140D 4INS 16VP 1a34 148d 1A4G 1AFV 4HMG 1IAS 1I84 unknown 1HVU 1jmu None4 1h1k 2btv |
The models summary shows that the best fit is the one graphed below (see detailed report):