A Comprehensive Analytical Treatment of Continuum Electrostatics

An analytical treatment of the continuum model for electrostatic solvation is presented and shown to be in good agreement with numerical finite-difference continuum calculations for the same system. Because the analytic method, called ACE, is relatively fast and yields a pairwise potential from which gradients and second derivatives can be obtained, its use with molecular mechanics/molecular dynamics programs will be possible. For calculating the self-energies of molecules in aqueous solution, a new analytic method is introduced. It is based on a continuum electrostatics model in which charges are defined as Gaussian charge distributions, rather than point charges, and in which the solute interior is described by a continuous density function. The self-energy potential is a pairwise energy function which only depends on charges, interatomic distances, and the effective, solvent-inaccessible volumes of the atoms. The potential is derived by integrating the energy density of the electric field and termed the integrated field (IF) method. A combination of the analytic self-energy potential with the generalized Born equation for charge−charge interactions,1-3 termed analytic continuum electrostatics (ACE) potential, makes possible an analytic treatment of the electrostatic contribution to solvation. The focusing of field lines is included. The IF method is applied to the calculation of self-energies of all charges on a series of small organic compounds and the protein bovine pancreatic trypsin inhibitor (BPTI). The agreement with self-energies as calculated using a finite-difference program is excellent for small molecules and satisfactory for BPTI. Application of the combined ACE potential to the calculation of solvation energies of small compounds shows good agreement with results of finite-difference calculations. The potential on a plane through the protein superoxide dismutase using ACE and a finite-difference program is in good agreement. For the calculation of the solvation energies of small molecules (20 atoms), ACE is more than 3 orders of magnitude faster than the program UHBD91 which was used for all numerical continuum electrostatics calculations; for BPTI, the speedup is more than 2 orders of magnitude.