The double cubic lattice method: Efficient approaches to numerical integration of surface area and volume and to dot surface contouring of molecular assemblies

Abstract

The double cubic lattice method (DCLM) is an accurate and rapid approach for computing numerically molecular surface areas (such as the solvent accessible or van der Waals surface) and the volume and compactness of molecular assemblies and for generating dot surfaces. The algorithm has no special memory requirements and can be easily implemented. The computation speed is extremely high, making interactive calculation of surfaces, volumes, and dot surfaces for systems of 1000 and more atoms possible on single-processor workstations. The algorithm can be easily parallelized. The DCLM is an algorithmic variant of the approach proposed by Shrake and Rupley (J. Mol. Biol., 79,351-371,1973). However, the application of two cubic lattices-one for grouping neighboring atomic centers and the other for grouping neighboring surface dots of an atom-results in a drastic reduction of central processing unit (CPU) time consumption by avoiding redundant distance checks. This is most *Author to whom all correspondence should be addressed at European Molecular Biology Laboratory, Postfach 10.2209, Meyerhofstrasse 1, D-69012 Heidelberg, Germany. Frank Eisenhaber is a visiting scientist at the EMBL, Heidelberg. noticeable for compact conformations. For instance, the calculation of the solvent accessible surface area of the crystal conformation of bovine pancreatic trypsin inhibitor (entry 4PTI of the Brookhaven Protein Data Bank, 362-point sphere for all 454 nonhydrogen atoms) takes less than 1 second (on a single R3000 processor of an SGI 4D/480, about 5 MFLOP). The DCLM does not depend on the spherical point distribution applied. The quality of unit sphere tesselations is discussed. We propose new ways of subdivision based on the icosahedron and dodecahedron, which achieve constantly low ratios of longest to shortest arcs over the whole frequency range. The DCLM is the method of choice, especially for large molecular complexes and high point densities. Its speed has been compared to the fastest techniques known to the authors, and it was found to be superior, especially when also taking into account the small memory requirement and the flexibility of the algorithm. The program text may be obtained on request. 0

A fully atomistic computer simulation study of cold denaturation of a β-hairpin

“…On decreasing temperature, however, the colddenatured sate population grows and eventually this state becomes the lowest free-energy minimum at low temperatures. The most plausible conformation of the cold-denatured state of MrH1 retains relatively a compact backbone structure somewhat close to that of the native state, but exhibits a significant loss of , change of average potential energy between water and protein; DU water F!D , change of average water potential energy; DH F-D , system enthalpy change; DSASA F-D , change of average solvent accessible surface area on unfolding 26 . In this energy decomposition, the contribution from electrostatic interactions in the K-space was neglected.…”

“…Investigations of free-energy landscapes during cold denaturation are of interest, because tracing topographical changes of the free-energy surface on cooling can provide clear views on the cold-denaturation-like phenomenon. As proper reaction coordinates for free-energy representations, we employed the number of the native backbone hydrogen bond (N HB ) and the solvent accessible surface area of the non-polar component (SASA_np) 26 . The free-energy surfaces at several temperatures obtained from tip4p/2005 are given as functions of (RMSD, N HB ) (Fig.…”

“…During cold denaturation, this weakening hydrophobic force can disrupt the native hydrophobic cluster of the b-hairpin peptide. Thus, non-polar groups of MrH1, if exposed to water, will increase their SASA 26 . This behaviour is clearly illustrated in the free-energy surface of (RMSD, SASA_np) (Fig.…”

JavaProtein Dossier: a novel web-based data visualization tool for comprehensive analysis of protein structure

“…At the same time, the Gold Sting server is also responsible for calculating a number of macromolecular properties for each PDB structure: electrostatic potential is calculated using modified Delphi (12) software (details will be discussed elsewhere); curvature is calculated using the SurfRace (13) software; solvent accessible area for each protein chain and for the whole molecular complex is calculated using the Surfv (14) software, adapted to our own requirements; secondary structure identification is calculated according to DSSP (15) and STRIDE (16); intra-and interchain amino acid contacts as well as protein-DNA interaction are calculated using our own software, 'contacts'; hydrophobicity is assigned according to Radzicka and Wolfenden (17); dihedral angles are calculated by our own 'Ramachandran' program; and PROSITE patterns are identified using the Ps_Scan (18) software. The 'Sponge' and 'Density' parameters are calculated using the double cubic lattice method (19) in combination with public library procedures such as those of the BALL's library (Biochemical Algorithms Libraryhttp://voyager.bioinf.uni-sb.de/OK/BALL) and our own code (details to be described elsewhere). In addition, we used the Rate4Site (20) software to calculate the 'Evolutionary Pressure' parameter shown within the J PD Conservation row.…”

Backbone assignment of proteins with known structure using residual dipolar couplings

“…In this gird search 1116 uniformly distributed alignment tensor orientations are systematically sampled (Eisenhaber et al, 1995) and for each orientation the deviation D(i, j ) between experimental and back-calculated RDCs is determined (equation 1). All sampled orientations are ranked according to their corresponding D(i, j ) values and the …”