The numerical continuum electrostatic method presented previously (Warwicker, J. & Watson, H. C. (1982) J. Mol. Biol., 157, 671-679), is developed with an improved analysis of the protein-solvent system. Inclusion in the model of saturable solvent dielectric, and counterions is discussed and presented. A number of long-range electrostatic field calculations are made on bovine pancreatic trypsin inhibitor to demonstrate the differences between various solvent and counterion models. The long-range potential field, due to polar side-chain and α-helix dipole charge, is calculated for the glycolytic enzyme phosphoglycerate mutase. The positive potential in and around the catalytic cleft region is sufficiently large to suggest that it may play a role in long-range attraction of the enzyme's negatively charged substrates. Analogous systems with charge-charge interactions in solvent water are considered. It is suggested that a long-range enzyme-substrate attractive force-field may, in part, offset the repulsive energy arising from overlap of hydration shells between enzyme and substrate. © 1986 Academic Press Inc. (London) Ltd.