Approximate solvent-accessible surface areas from tetrahedrally directed neighbor densities

A fast analytical formula (TDND) has been derived for the calculation of approximate atomic and molecular solvent-accessible surface areas (SASA), as well as the first and second derivatives of these quantities with respect to atomic coordinates. Extending the work of Stouten et al. (Molecular Simulation, 1993, Vol. 10, pp. 97-120), as well as our own (Journal of Computational Chemistry, 1999, Vol. 20, pp. 586-596), the method makes use of a Gaussian function to calculate the neighbor density in four tetrahedral directions in three-dimensional space, sometimes twice with different orientations. SASA and first derivatives of the 2366 heavy atoms of penicillopepsin are computed in 0.13 s on an SGI R10000/194 MHz processor. When second derivatives are computed as well, the total time is 0.23 s. This is considerably faster than timings reported previously for other algorithms. Based on a parameterization set of nineteen compounds of different size (11-4346 atoms) and class (organics, proteins, DNA, and various complexes) consisting of a total 23,197 atoms, the method exhibits relative errors in the range 0.2-12.6% for total molecular surface areas and average absolute atomic surface area deviations in the range 1.7 to 3.6 A(2).