Solvation Free Energy of Biomacromolecules: Parameters for a Modified Generalized Born Model Consistent with the AMBER Force Field B. Jayaram, † D. Sprous, and D. L. Beveridge* Department of Chemistry, Wesleyan UniVersity, Middletown, Connecticut 06459 ReceiVed: April 27, 1998 The generalized Born (GB) model provides rapid estimates of the electrostatic free energies of solvation for diverse molecules and molecular ions. This method is expected to be of considerable utility for studies of solvation in macromolecular and biological systems. Calculations on biological molecules are typically based on empirical energy functions, each of which have their own prescriptions for determining net atomic charges. For maximum compatibility, GB parameters tailored to specific force fields are required. The development of parameters compatible with the AMBER force field is described. The method is used to estimate free energies of A and B form structures of DNA obtained from molecular dynamics simulations. The results provide an account of the conformational preferences of right-handed DNA in solution. I. Introduction Generalized Born (GB) theory 1-4 is the basis of a computa- tional method for estimating the electrostatic free energies of solvation of diverse molecules and molecular ions. In the GB model, a molecule in solution is represented as a set of point charges set in spherical cavities embedded in a polarizable dielectric continuum. GB calculations can be considered as a means of approximating finite difference Poisson-Boltzmann 5 free energies and related quantities. Previous studies have demonstrated that the GB method together with a simple treatment of nonelectrostatic effects can estimate solvation free energies that are generally within 5% of observed values, 1,4 and a recent modification, the MGB method, 6 has extended the purview of the GB theory to pK shifts of dicarboxylic acids as well as hydration energies. The essential simplicity of the GB method results in rapid computation times in numerical calculations, and thus its extension to macromolecular and biological solvation problems is readily feasible. However, macromolecular energy calcula- tions are typically based on empirical energy functions such as AMBER, 7 CHARMM, 8 or GROMOS, 9 each of which have their own prescription for specifying the net atomic charges on the individual atoms of the system. For a GB model to be successful on these systems, it is necessary that the effective GB radii for each atom type be parametrized in a manner fully consistent with the net atomic charges intrinsic to the assumed energy function. We describe herein the nature of the reparam- etrization process necessary to achieve this consonance and report the parameters required to obtain the effective Born radii compatible with the recently proposed force field of Cornell et al., 10 incorporated into the AMBER suite of programs. 7 The reparametrized GB model is found to reproduce solvation free energies of 32 molecules, chosen as prototypes of protein and nucleic acid constituents, with a mean unsigned error of <1 kcal. Preliminary application of the method to treat the solvent dependent conformational preferences of a right-handed B-DNA double helix is described. II. Background The generalized Born model treats a molecule as a discrete set of overlapping charged spheres imbedded in a polarizable dielectric continuum. The defining equations of the Generalized Born theory are as follows: Equation 1 expresses the total electrostatic free energy G es of a molecular system in kcal/mol as a sum of the Coulomb interaction energies between each pair of charges q i and q j separated by a distance r ij in a solvent of dielectric constant ǫ (the first term) and the Born solvation (self) energy of each individual charge (the second term). The R i in eq 1 are the Born radii, which are treated as disposable parameters. In eq 2, the free energy is rewritten as a sum of Coulomb interaction energies in a vacuum and polarization free energy G pol . The GB polarization energy captures all the electrostatic effects due to solvent in one single term (eq 3), with a judicious choice of the effective distance parameter f GB as provided by eq 4. The * Author for correspondence. E-mail: dbeveridge@wesleyan.edu. Fax: (860) 685-2211. Tel.: (860) 685-2575. † On leave from Department of Chemistry, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India. 9571 J. Phys. Chem. B 1998, 102, 9571-9576 10.1021/jp982007x CCC: $15.00 © 1998 American Chemical Society Published on Web 11/03/1998 hvordan bredde påvirker klimaet ?