A generalized G-SFED continuum solvation free PNAS PLUS energy calculation model Sehan Leea, Kwang-Hwi Chob, Young-Mook Kanga, Harold A. Scheragac,1, and Kyoung Tai Noa,d,1 aDepartment of Biotechnology, Yonsei University, Seoul 120-749, Korea; bDepartment of Bioinformatics, SoongSil University, Seoul 156-743, Korea; cBaker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853-1301; and dBioinformatics and Molecular Design Research Center, Seoul 120-749, Korea Contributed by Harold A. Scheraga, December 20, 2012 (sent for review October 12, 2012) An empirical continuum solvation model, solvation free energy method (23). A polarizable continuum model (PCM), proposed density (SFED), has been developed to calculate solvation free by Tomasi and colleagues (24), casts the quantum mechanical energies of a molecule in the most frequently used solvents. SCRF equations into a boundary element problem with apparent A generalized version of the SFED model, generalized-SFED (G-SFED), surface charges spread on the cavity surface. Three types of PCMs is proposed here to calculate molecular solvation free energies in have been used frequently: the original method, dielectric PCM virtually any solvent. G-SFED provides an accurate and fast gener- (24); integral equation formalism PCM (25–27);andanalter- alized framework without a complicated description of a solution. native model in which the surrounding medium is modeled as a In the model, the solvation free energy of a solute is represented as conductor instead of as a dielectric (28, 29). a linear combination of empirical functions of the solute properties Moreover, some models complement the description of the – representing the effects of solute on various solute solvent interac- solute–solvent interactions by adding the missing nonelectrostatic tions, and the complementary solvent effects on these interactions fl fi terms. Hydrogen bonds are described adequately by density- were re ected in the linear expansion coef cients with a few solvent functional theory exchange-correlation functionals as well as properties. G-SFED works well for a wide range of sizes and polari- by post-Hartree-Fock (HF) methods (30–32). In the classical ties of solute molecules in various solvents as shown by a set of approach, the free energy of hydrogen-bond formation can be 5,753 solvation free energies of diverse combinations of 103 solvents calculated with a product of parameters characteristic of acidity and 890 solutes. Octanol-water partition coefficients of small organic BIOPHYSICS AND and basicity of molecules (33, 34). Solvent-accessible surface compounds and peptides were calculated with G-SFED with accuracy – COMPUTATIONAL BIOLOGY within 0.4 log unit for each group. The G-SFED computation time (SAS) area models are popular choices for nonpolar solute depends linearly on the number of nonhydrogen atoms (n)ina solvent interactions, such as dispersion, repulsion, and cavitation – molecule, O(n). (35 39). The continuum models generally are parameterized for a specific implicit solvent | macromolecules | linear time solvent to reproduce the interactions of the solvent with a variety of solutes. An important advance in continuum approaches is the n accurate description of the effect of solvent on solvation is development of generalized (or universal) solvation models ap- Acrucial for understanding chemical and biological phenom- plicable to any solvent. The conductor-like screening model for ena. Because many peptide and protein drugs are currently being realistic solvation (COSMO-RS) (40) extension of COSMO (41) developed (1, 2), computational efficiency as well as accuracy are derives the polarization charges of the continuum, caused by the very important. Among the different approaches that have been charge distribution of the solute, from a scaled-conductor ap- x used, continuum solvation models are appealing because of the proximation. SM models (SM5A, SM5.42R, SM8, and others) simplified yet accurate description of the solvent effect (3–8). implement the parameterization of atomic surface tension not Continuum solvent models have been developed based on the only in terms of the properties of the atoms of the solute but also – x early work of Born (9), Bell (10), Kirkwood (11), and Onsanger in terms of the solvent properties (42 44). COSMO-RS and SM (12). They focus primarily on the description of the solute either can be applied only to molecules of limited size that can be at the quantum mechanical level or as a classical collection of treated by quantum or semiempirical quantum chemistry. point charges and try to represent the influence of the solvent based on an approximate treatment as a dielectric continuum Significance medium. The charge distribution of the solute induces electric polarization of the surrounding solvent, and the electric field This paper deals with a long-standing problem in biophysics, generated by the polarized solvent, the reaction field, in turn per- which is resolved here. The model has a strong physical back- turbs the solute, leading to a modification of the charge distribution ground and will have a wide range of applications to physical of the solute. This electrostatic problem of the mutual polarization and biological problems. The model proposed in this article, between solute and solvent can be recast by using boundary con- GSFED model, can be used for the solvation free energy cal- ditions at the cavity surface, leading to significant simplifications in culation of most organic solutes in most organic solvents. Since the associated equations. the computing time depends linearly on the size of the molecule, In the classical approaches, most work is concerned with de- the model can be applied easily to large molecules, for example scribing the electrostatic contribution to the solvation in terms of proteins. The model can provide reliable salvation free energies the Poisson–Boltzmann equation (PBE) (13). Several different of experimentally unavailable solute-solvent pairs. computational techniques for solving the PBE have been deve- loped, for example, finite difference methods in which the di- Author contributions: H.A.S. and K.T.N. designed research; S.L. performed research; K.-H.C. and Y.-M.K. contributed new reagents/analytic tools; and S.L. and K.T.N. wrote electric property of the solvent is described in terms of a 3D the paper. – grid around the solute (14 17) and boundary element methods in The authors declare no conflict of interest. which the reaction potential is described by an apparent charge 1To whom correspondence may be addressed. E-mail: [email protected] or ktno@yonsei. spread on the cavity surface (18–22). ac.kr. In the quantum mechanical approaches, the mutual polarization This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. is taken into account by the self-consistent reaction field (SCRF) 1073/pnas.1221940110/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1221940110 PNAS Early Edition | 1of6 Downloaded by guest on September 27, 2021 Theory Solvent εm, ηm, γm, Am, Bm The solvation free energy of a solute s in a solvent m, ΔGsolv, was m m i ε , η m described by two steps: ( ) forming a solute-shaped cavity in the ε , ηm k l polarizable solvent and calculating the cavitation free energy, r r jk il ΔGcav, and (ii) transferring the charge distribution of the solute rjl rik from the gas phase to the cavity and calculating the interaction, ΔGinter, between the polarizable solvent and the polarizable sol- R R ute. Because the continuum models used the potential of mean vdw S force produced by the solute to calculate ΔG , the contribution q , a q , a inter i i j j to the hydrogen bond, especially from proton tunneling, always is underestimated. Therefore, the contribution of hydrogen bonds s s Solute A , B to solvation, ΔGHB, is calculated independently of other possible solute–solvent interactions: ΔG ¼ ΔG þ ΔG þ ΔG : [1] SAS van der Waals Surface solv inter HB cav To calculate ΔGinter,(i) the solute molecule is represented by Fig. 1. The solute and solvent of a solution are described as an assemblage polarizable atoms with point charges at the center of the atoms of interacting compartments. rik is the distance between the ith atom and ii the kth surface fragment on the SAS of the solute, and γm is the macroscopic in the solute, and ( ) the solvent is represented by an SAS, and surface tension of the solvent. A dielectric constant, «m, and a refractive each surface unit, represented by a dot in Fig. 1, has an average index, ηm, of the solvent are placed at the grid points on the SAS. Hydrogen- dipole and an average induced dipole described by macroscopic bond acidity and basicity of the solvent, Am and Bm, and of the solute, As and solvent properties. Bs, represent the contribution of a hydrogen bond. The electric field produced by the solute aligns the dipoles and induced dipoles on the surface, and the aligned dipoles and in- duced dipoles of the solvent perturb the electron distribution of Previously, we demonstrated that the solvation free energy each atom of the solute. This perturbed electron distribution in fi density (SFED) model is an ef cient one for the description of the solute, described by the change of net atomic charge of each molecular properties in solution with a linear combination of atom, which is proportional to the effective atomic polarizability, – empirical functions of the solute properties (45 50). However, interacts with the aligned dipoles and the induced dipoles on the parameterization of the linear expansion coefficients, opti- the surface. mized for each solvent, limits the application of the model to To describe ΔGinter, which originates from the phenomena de- solvents for which the coefficients were determined. Here we scribed above, previous work (45–50) was carried out to find a present the generalized SFED (G-SFED) model to calculate the proper functional form for ΔGinter.