Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO)

A fast analytical formula was derived for the calculation of approximate atomic and molecular van der Waals (vdWSA), and solvent-accessible surface areas (SASAs), as well as the first and second derivatives of these quantities with respect to atomic coordinates. This method makes use of linear combinations of terms composed from pairwise overlaps of hard spheres; therefore, we term this the LCPO method for linear combination of pairwise overlaps. For higher performance, neighbor-list reduction (NLR) was applied as a preprocessing step. Eighteen compounds of different sizes (8–2366 atoms) and classes (organic, proteins, DNA, and various complexes) were chosen as representative test cases. LCPO/NLR computed the SASA and first derivatives of penicillopepsin, a protein with 2366 atoms, in 0.87 s (0.22 s for the creation of the neighbor list, 0.35 s for NLR, and 0.30 s for SASA and first derivatives) on an SGI R10000/194 Mhz processor. This appears comparable to or better than timings reported previously for other algorithms. The vdWSAs were in good agreement with the numerical results: relative errors for total molecular surface areas ranged from 0.1 to 2.0% and average absolute atomic surface area deviations from 0.3 to 0.7 Å2. For SASAs without NLR, the LCPO method exhibited relative errors in the range of 0.4–9.2% for total molecular surface areas and average absolute atomic surface area deviations of 2.0–2.7 Å2; with NLR the relative molecular errors ranged from 0.1 to 7.8% and the average absolute atomic surface area deviation from 1.6 to 3.0 Å2. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 217–230, 1999