Solvation Model Based on Weighted Solvent Accessible Surface Area

Transcription

1 J. Phys. Chem. B 2001, 105, Solvation Model Based on Weighted Solvent Accessible Surface Area Junmei Wang, Wei Wang, Shuanghong Huo, Matthew Lee, and Peter A. Kollman* Department of Pharmaceutical Chemistry UniVersity of California, San Francisco, California ReceiVed: January 22, 2001; In Final Form: March 5, 2001 We have developed a fast procedure to predict solvation free energies for both organic and biological molecules. This solvation model is based on weighted solvent accessible surface area (WSAS). Least-squares fittings have been applied to optimize the weights of SAS for different atom types in order to reproduce the experimental solvation free energies. Good agreement with experimental results has been obtained. For the 184-molecule set (model I), for which there are experimental solvation free energies in 1-octanol, we have achieved an average error of 0.36 kcal/mol, better than that of the SM5.42R universal solvation model 1 by Li et al. For the 245-molecule set (model II) that has experimental aqueous solvation free energies, our WSAS model achieves an average error of 0.48 kcal/mol, marginally larger than that of Li s model (0.46 kcal/mol). We have used a 401-molecule set, the largest training set (model IV) that we know of solvation model development, to derive the SAS weights in order to reproduce the experimental solvation free energies in water. For this model, we have achieved an average unsigned error of 0.54 kcal/mol and an RMS error of 0.79 kcal/mol.the advantage of this model lies in its simplicity and independence of charge models. We have successfully applied this model to predict the relative binding free energies for the five binding modes of HIV-1RT/ efavirenz. The most favorable binding mode, which has an RMSD of 1.1 Å (for 54 C R around the binding site) compared to the crystal structure, has a binding free energy at least 10 kcal/mol more negative than the other binding modes. Moreover, the solvation free energies with WSAS have a high correlation (the correlation coefficient is 0.92) to the solvation free energies calculated by the Poisson-Boltzmann/surface area (PBSA) model. As an efficient and fast approach, WASA is also attractive for protein modeling and protein folding studies. We have applied this model to predict the solvation free energies of the 36-mer villin headpiece subdomain in its native structure, a compact folding intermediate, and a random coil. The rank order of the solvation free energies and the free energies for the three kinds of conformational clusters are in reasonable agreement with those found by MM-PBSA, a widely used solvation free energy model. Introduction Solvation free energies in aqueous solution are important for structural and metabolic equilibria and kinetics. 2-5 For example, in enzyme catalysis, substrates are often dehydrated, and thus, the free energies of desolvation are important contributors to the free energies of activation. The electrostatic energy in a molecular mechanical model is usually coupled with the electrostatic part of the solvation free energy. Unfavorable solvation free energies of associating nonpolar groups may lead to hydrophobic stabilization of their mutual complexes, although the electrostatic energy may not be so favorable. On the other hand, a favorable electrostatic energy does not always mean a high affinity, owing to the high solvation free energy penalty. Thus, the solvation free energy plays an important role in both protein-ligand association and the protein folding. How to treat the solvation effect efficiently and accurately is a long-term challenge in computational chemistry. At this point, there have been many different solvation models developed to address this problem, from the very simple atom and fragmentadditive models 6,7 to methods that treating solvent molecules explicitly In 1975, Hine and Mookerjee developed a simple solvation model 6 based on the assumption that the solvation free energy is fragment additive. Therefore, in their model, the * To whom correspondence should be addressed. Tel: (415) (pak). Fax: (415) s: Pak@cgl.ucsf.edu. Web site: solvation free energy of a given molecule is the sum of the solvation free energy of all the fragments. Hansch and Leo also developed a similar solvation model 7 to predict the water/ 1-octanol partition coefficients of organic compounds. The additivity assumption of the above models work well for small organic molecules but has some problems when applied to medium and large molecules. In 1986, Eisenberg and McLachlan developed a simple solvation model 11 using the solvent accessible surface area to estimate the solvation free energies of proteins, and their model is still widely used today owning to its simplicity. In 1997, Hawkins, Cramer and Truhlar 12 developed an aqueous solvation model using geometry-dependent atomic surface tensions with implicit electrostatics. Unlike Eisenberg-McLachlan s model, this model applied a more complicated procedure to calculate the atomic surface tensions and there are three types of parameters needed to be parametrized (17 nonlinear parameters, 9 van der Waals radii, and 23 linear surface tension coefficients). In 1998, this model was extended to other solvents. 13 It is believed that the solvation free energy of a molecule is made up of two parts: the electrostatic contribution and the nonpolar contribution 2-5, The latter contribution is usually modeled as proportional to the solvent accessible surface area. For most molecules, the electrostatic term dominates the total solvation free energy. All of the above solvation models are charge method independent and the electrostatic contribution of the solvation free energy is implicitly incorporated into the parameters. To more ac /jp CCC: $ American Chemical Society Published on Web 05/05/2001

2 5056 J. Phys. Chem. B, Vol. 105, No. 21, 2001 Wang et al. curately predict the solvation free energy, it is necessary to calculate the screening energy (the electrostatic part) using a more physically rigorous approach. The most popular models for screening energy calculations are the Generalized Born model (GB), the Poisson-Boltzmann (PB) model, 14,15 and the conductor-like models (COSMO) Although these models have a somewhat different theoretical basis, after appropriate parametrization, the electrostatic solvation effect can be well represented by each of these models and be applied in molecular docking, binding free energy calculations and protein folding studies One problem of those methods is that they are charge dependent, and the parameters developed with one charge method may not be transferable to others. Another problem is that these models are quite time-consuming compared to the fragment and surface area based models, especially for the PB and the conductor-like models. In this work, we have developed a new solvation model based on the weighted solvent accessible surface area (WSAS) using a rather large molecular set (387 neutral molecules and 14 ions). The solvation free energy is evaluated using the following equation. G WSAS ) i ) 0 j ) 0 where m is the number of the atom types for a given model; w i is the solvation free energy weight of atom type i; n i are the number of atoms with atom type i in a molecule, and S j is the solvent accessible surface area of atom j. Although the basic idea is similar to the Eisenberg- McLachlan model, 11 the two models are quite different. The Eisenberg-McLachlan model has been mainly used to study the original conformational dependent solvation free energies of proteins. The parameters were derived using the water/octanol distribution coefficients of 20 amino acids. On the other hand, we have used the aqueous solvation free energies to develop our parameters not only for amino acid analogues but also for organic molecules. Therefore, our model has more potential applications. For example, it can be used to calculate the relative binding free energy of protein/ligand complexes, whereas the Eisenberg-Mclachlan model cannot be used in this fashion. Second, we have used a very large training set to derive the parameters for different atom types, whereas the Eisenberg- McLachlan model only applied a limited number of experimental data to fit the weight parameters for five basic atom types (C, N/O, O-, N+, S). The third difference is that we have used a probe radius of 0.6 Å to generate the solvent accessible surface (SAS), whereas Eisenberg-McLachlan model used a probe radius of 1.4 Å. Because, in both of the models, the contribution from the intrinsic charges is completely neglected, smaller probe radii and inclusion of more atom types allow the electrostatic solvent effect to be better represented. In the following, we will discuss how we parametrized this solvation model. Two applications of this model, to binding free energy calculation and protein folding analysis, will also be presented. Methodology Solvent Accessible Surface (SAS) Area Calculations. The molecules were built up with the SYBYL software package 35 of Tripos Inc. and optimized using the MMFF94 force field with MMFF charges. 36 For each molecule, only the global minimum conformation was used in the SAS calculation and the subsequent parametrization. Simple conformational searches m n i w i S j (1) were performed for some molecules in cases where the global minimum conformation was not obvious. Molecular surface areas were calculated using the MSMS program 37 and the probe radius was set to 0.6 Å with density of 3.0 vertex/å 2. For each atom, the atomic SAS in each surface component were added together. In the next step, we applied an automated atom type determination program 38 to judge the atom types for given molecules. The solvation free energies were then estimated by eq 1. Least-Squares Fitting Procedure. Least-squares fittings were applied to derive the solvation free energy weights, w i in eq 1. There are two different procedures to perform the fittings: one may derive all the parameters simultaneously or derive them step-by-step. For the latter, one first derives the parameters of a certain compound class, such as hydrocarbons, and the developed parameters are transferred to other compound classes without change during the subsequent fittings. We found that the first procedure is superior because it avoids the biases aroused from the order in which the compound classes are fitted. With the first fitting procedure, we worked out the parameters for four different solvation models. In models I and II, all the molecules investigated are from Li et al. s training sets for their SM5.42R models. However, in model I, all the molecules (184) have the experimental solvation free energies in 1-octanol, whereas the molecules (245) in model II have aqueous solvation free energies. We presented the two models for comparison purpose. Unlike the Generalized Born model and the Poisson- Boltzmann model, there is no dielectric constants introduced in our simple WSAS model; therefore, the parameters developed for one solvent cannot be transferred to other solvents. For other two-solvation models, apart from all the molecules in model II, we extended our molecular set by including another 142 neutral molecules and 14 charged ones that have aqueous solvation free energies. In model III, we divided our whole molecule set excluding charged molecules into training set (293 molecules) and test set (94 molecules). The purpose is to investigate how well do the parameters developed with the training set transfer to the test set. In model IV, we developed the parameters using all the molecules including the charged ones available in this work, which were then used for binding free energy calculations in the following two applications. Relative Binding Free Energy Calculations with WSAS. In another work, 39 we combined molecular docking and molecular dynamics simulations to model the complex of HIV- 1RT/efavirenz, for which the crystal structure has been solved by Dupont Pharmaceuticals, but not published. We performed 500 pico-second MD simulations for the five binding modes suggested by the flexible docking and estimated the binding free energies for each binding mode using the MM-PBSA approach. In this work, instead of using PBSA, a more timeconsuming solvation free energy approach, we applied WSAS to estimate the relative binding free energies for the five binding mode with the same snapshots as used in the MM-PBSA analysis. Energy-Analysis on the MD Trajectories of Villin Headpiece. In 1998, Duan and Kollman 40 carried out a 1-µs molecular dynamics folding simulation for villin headpiece with explicit water. They found a very stable folding intermediate (from ns), which is closer to the native structure than any other structure found along the trajectory. Subsequently, Lee et al. 34 applied MM-PBSA to analyze both a 1-µs trajectory and a 100 ns native trajectory. They found that the free energy of the folding intermediate was less favorable than that of the native one, but much more favorable than the unfolded random coil

3 Weighted Solvent Accessible Surface Area J. Phys. Chem. B, Vol. 105, No. 21, TABLE 1: Definitions of Atom Types Used in Solvation Free Energy Calculation, 1-47 Are the Basic Atom Types and Are Special Atom Types for Ions no. atom type symbol explanation 1 CT3 sp 3 carbon attached by three hydrogens 2 CT2 sp 3 carbon attached by two hydrogens 3 CT1 sp 3 carbon attached by one hydrogens 4 CT sp 3 carbon connected with four heavy atoms 5 CA sp 2 aromatic carbon 6 CD2 sp 2 carbon attached by two hydrogens 7 CD1 sp 2 carbon attached by one hydrogens 8 CD sp 2 carbon without hydrogens attached 9 CS sp 1 carbon 10 CO carbon in the carbonyl function group 11 CN sp 2 carbon in the amide function group 12 F any fluorine 13 Cl any chlorine 14 Br any bromine 15 I any iodine 16 HCT3 hydrogen connected to sp 3 carbon that has three electron withdrawn group 17 HCT2 hydrogen connected to sp 3 carbon that has two electron withdrawn group 18 HCT1 hydrogen connected to sp 3 carbon that has one electron withdrawn group 19 HCT hydrogen connected to sp 3 carbon that has no electron withdrawn group 20 HCD2 hydrogen connected to sp 2 carbon that has two electron withdrawn group 21 HCD1 hydrogen connected to sp 2 carbon that has one electron withdrawn group 22 HCD hydrogen connected to sp 2 carbon that has no electron withdrawn group 23 HCA hydrogen connected to aromatic carbon 24 HCS hydrogen connected to sp carbon 25 HO hydrogen connected to oxygen 26 HN hydrogen connected to nitrogen 27 HS hydrogen connected to sulfur 28 OH hydroxyl oxygen in alcohol 29 OC ether oxygen 30 O oxygen in carbonyl function group 31 OS sp 3 oxygen in ester 32 OOH hydroxyl oxygen in acid 33 SH sulfur in thiols 34 SS sulfur in disulfide and thioether 35 SP sp2 S connected to phosphate 36 NS sp nitrogen 37 ND2 sp2 nitrogen in the heteroring with two connected atoms 38 ND3 sp2 nitrogen in the heteroring with three connected atoms 39 NO nitrogen connected to oxygen 40 NH2 amide nitrogen with two attached hydrogens 41 NH1 amide nitrogen with one attached hydrogen 42 N amide nitrogen without attached hydrogens 43 NTH2 amine nitrogen with two attached hydrogens 44 NTH amine nitrogen with one attached hydrogen 45 NT amine nitrogen without attached hydrogen 46 P3 phosphate with three connected atoms 47 P4 phosphate with four connected atoms 48 O- acetate ion and propionate ion 49 OA- p-cresole ion and C 6H 5O - 50 S- C 6H 5S- and CH 3S- 51 HN+ hydrogen connected to charged nitrogen 52 NT+ sp3 nitrogen cation 53 ND+ sp2 nitrogen cation, such as methyl-imidazolium 54 N+ N-p-guanidinium ( ns). For the solvation free energy, the sequence order for the three conformation cluster is the opposite of the free energy, i.e., G solvation native > G solvation intermediate > G solvation random coil. In this work, we performed energy analysis for the two MD trajectories with WSAS substituting for PBSA. Results and Discussion Atom Type Definition. The solvation free energy is made up of two parts: the electrostatic and the nonpolar (cavity and van der Waals) contributions. The electrostatic part, which is charge-method dependent, can be evaluated using several different models, such as finite difference Poisson-Boltzmann (FDPB), dielectric screening Poisson-Boltzmann (DSPB), the Generalized Born (GB), and the conductor-like screening models The nonpolar part can be simply estimated using the total solvation accessible surface area (SAS), according to the formula G ) γ A + b, where g and b are constants, and A is SAS. For WSAS, the two contributions are considered simultaneously, and the electrostatic part is taken into account implicitly using different atom types. In principle, atoms that are the same atom type should bear similar charges. With this in mind, we selected the atom types in the following way. We began with only a few very basic atom types and introduced specific ones only if they could reduce the error significantly. After introducing new atom types, it was necessary to check whether one was overfitting the data or not. Table 1 lists the entire set of atom types in our WASA models. Probe Radius. In other solvation models (PBSA, GBSA,

4 5058 J. Phys. Chem. B, Vol. 105, No. 21, 2001 Wang et al. TABLE 2: Solvation Free Energies of Organic Compounds a no. compound name model(i) model(ii) model(iii) model(iv) expt (a) expt (b) 1 Methane Ethane Propane b Cyclopropane methyl propane b ,2-dimethyl propane b n-butane ,2-dimethylbutane 1.26 b Cyclopentane n-pentane methylpentane methyl pentane ,4-dimethyl pentane b ,2,4-trimethyl pentane Methylcyclopentane n-hexane Cyclohexane b Methylcyclohexane Cis-1,2-dimethylcyclohexane n-heptane b n-octane b Ethylene Propylene methyl propene b butene methyl-2-butene 1.21 b methyl-1-butene pentene Trans-2-pentene methyl-1-pentene Cyclopentene hexene Cyclohexene Trans-2-heptene methylcyclohexene octene ,3-butadiene methyl-1,3-butadiene ,3-dimethyl-1,3-butadiene ,4-pentadiene 1.72 b ,5-hexadiene Acetylene Propyne butyne pentyne hexyne b heptyne octyne nonyne 0.38 b Butenyne Benzene Toluene ,2,4-trimethylbenzene Ethylbenzene m-xylene o-xylene b p-xylene Propylbenzene propylbenzene b Butylbenzene butylbenzene tert-butylbenzene tert-amylbenzene Naphthalene b Anthracene Phenanthrene Acenaphthene b p-chlorotoluene b

5 Weighted Solvent Accessible Surface Area J. Phys. Chem. B, Vol. 105, No. 21, TABLE 2: (Continued) no. compound name model(i) model(ii) model(iii) model(iv) expt (a) expt (b) 69 Fluoromethane ,1-difluoroethane Trifluoromethane Tetrafluoromethane Hexafluoroethane Octafluoropropane b Fluorobenzene chloro-1,1,1-trifluoroethane Chlorofluoromethane b Chlorodifluoromethane Chlorotrifluoromethane Dichlorodifluoromethane Fluorotrichloromethane ,1,2-trichloro-1,2,2-trifluoroethane ,1,2,2-tetrachlorodifluoroethane 0.74 b ,1,2-trichlorotrifluoroethane Chloropentafluoroethane ,1-dichorotetrafluoroethane ,2-dichlorotetrafluoroethane 1.93 b bromo-1-chloro-2,2,2-trifluoroethane b Bromotrifluoromethane b bromo-1,2,2,2-tetrafluoroethane Chloromethane Dichloromethane b Trichloromethane Tetrachloromethane Chloroethane ,1-dichloroethane E-1,2-dichloroethane b ,1,1-trichloroethane ,1,2-trichloroethane ,1,1,2-tetrachloroethane ,1,2,2-tetrachloroethane Pentachloroethane Hexachloroethane b chloropropane chloropropane b ,2-dichloropropane ,3-dichloropropane chlorobutane chlorobutane ,1-dichlorobutane chloropentane chloropentane chloropentane Chloroethylene Cis-1,2-dichloroethylene Trans-1,2-dichloroethylene Trichloroethylene b Tetrachloroethylene chloropropane b Chlorobenzene Chlorotoluene o-chlorotoluene ,2-dichlorobenzene ,3-dichlorobenzene b ,4-dichlorobenzene ,2?-dichlorobiphenyl ,3-dichlorobiphenyl b ,2,3?-trichlorobiphenyl Bromotrichloromethane b chloro-2-bromoethane b Bromomethane Dibromomethane b Tribromomethane Bromoethane ,2-dibromoethane bromopropane bromopropane ,2-dibromopropane ,3-dibromopropane

6 5060 J. Phys. Chem. B, Vol. 105, No. 21, 2001 Wang et al. TABLE 2: (Continued) no. compound name model(i) model(ii) model(iii) model(iv) expt (a) expt (b) bromo-2-methylpropane b bromobutane bromo-isobutane bromo-3-methylbutane bromopentane bromopropene Bromobenzene ,4-dibromobenzne b p-bromotoluene bromo-2-ethylbenzene b o-bromocumene Iodomethane Diiodomethane Iodoethane b iodopropane iodopropane b iodobutane iodopentane Iodobenzene b Methanol Ethanol ,2,2-trifluoroethanol Ethylene glycol propanol b propanol ,1,1-trifluoro-2-propanol ,2,3,3-tetrafluoropropanol ,2,3,3,3-pentafluoropropanol b Hexafluoro-2-propanol methyl-1-propanol b butanol butanol tert-butyl alcohol methyl-1-butanol methyl butanol b methyl-2-butanol ,3-dimethylbutanol pentanol pentanol pentanol methyl-1-pentanol methyl-2-pentanol methyl-3-pentanol methyl-2-pentanol b Cyclopentanol b hexanol hexanol Cyclohexanol heptanol b Cycloheptanol heptanol octanol decanol Allyl alcohol Cyclopentanol Phenol bromophenol b nitrophenol tert-butylphenol cresol cresol cresol b ,2,2-trifluoroethanol p-bromophenol methoxyethanol Dimethoxymethane b Methyl propyl ether b Methyl isopropyl ether Methyl tert-butyl ether b Diethyl ether

7 Weighted Solvent Accessible Surface Area J. Phys. Chem. B, Vol. 105, No. 21, TABLE 2: (Continued) no. compound name model(i) model(ii) model(iii) model(iv) expt (a) expt (b) 210 Ethyl propyl ether Dipropyl ether b Diisopropyl ether b di-n-butyl ether Tetrahydrofuran methyltetrahydrofuran b Anisole Ethyl phenyl ether ,1-diethoxyethane ,2-dimethoxyethane ,2-diethoxyethane ,3-dioxolane ,4-dioxane ,2,2-trifluoroethyl vinyl ether chloro-2,2,2-trifluoroethyl difluoromethyl ether b ,1-dichloro-2,2-difluoroethylmethyl ether Formaldehyde Acetaldehyde Propanal b Butanal Pentanal Hexanal Heptanal b Octanal Nonanal Trans-2-butenal Trans-2-hexenal b Trans-2-octenal Trans,trans-2,4-hexadienal Benzaldehyde m-hydroxybenzaldehyde p-hydroxybenzaldehyde Acetone butanone b methyl-2-butanone ,3-dimethylbutanone pentanone b pentanone methyl-2-pentanone ,4-dimethyl-3-pentanone b Cyclopentanone hexanone heptanone heptanone b octanone nonanone nonanone undecanone Acetophenone Acetic acid Propionic acid b Butyric acid Pentanoic acid Hexanoic acid amino-3,5,6-trichloropyridine-2-carboxylic acid b Methyl formate Ethyl formate Propyl formate Methyl acetate b Isopropyl formate Isobutyl formate Isoamyl formate Ethyl acetate b Propyl acetate Isopropyl acetate Butyl acetate Isobutyl acetate Amyl acetate b Isoamyl acetate

8 5062 J. Phys. Chem. B, Vol. 105, No. 21, 2001 Wang et al. TABLE 2: (Continued) no. compound name model(i) model(ii) model(iii) model(iv) expt (a) expt (b) 279 Hexyl acetate Methyl propionae Ethyl propionate Propyl propionate Isopropyl propionate Amyl propionate Methyl butyrate b Ethyl butyrate Propyl butyrate Methyl pentanoate Ethyl pentanoate Methyl hexanonate Ethyl heptanoate b Methyl octanoate Methyl benzoate Methylamine Ethylamine Propylamine b Butylamine Pentylamine Hexylamine Dimethylamine b Diethylamine Dipropylamine Dibutylamine Trimethylamine Triethylamine b Azetidine Piperazine N,n?-dimethylpiperazine b N-methylpiperazine Aniline ,1-dimethyl-3-phenyl urea N? N-dimethyl aniline Ethylenediamine HydrazineHydrazine methoxyethanamine b Morpholine b N-methylmorpholine n-methylpyrrolidine n-methylpiperidine Pyrrolidine Piperidine Pyridine methylpyridine methylpyridine b methylpyridine ethylpyridine ethylpyridine b ethylpyridine ,3-dimethylpyridine ,4-dimethylpyridine b ,5-dimethylpyridine ,6-dimethylpyridine ,4-dimethylpyridine ,5-dimethylpyridine b ,4-dimethylpyridine b ,5-dimethylpyridine methylpyrazine b ethylpyrazine isobutylpyrazine ethyl-3-methoxypyrazine isobutyl-3-methoxypyrazine methyladenine methylthymine Methylindole Methylimidazole N-propyl guanidine Acetonitrile Propionitrile b

9 Weighted Solvent Accessible Surface Area J. Phys. Chem. B, Vol. 105, No. 21, TABLE 2: (Continued) no. compound name model(i) model(ii) model(iii) model(iv) expt (a) expt (b) 349 Butyronitrile Nitroethane Benzonitrile ,6-dichlorobenzonitrile b ,5-dibromo-4-hydroxybenzonitrile nitropropane nitropropane b nitrobutane Nitrobenzene nitrotoluene nitrotoluene N N-dimethyl formamide N-methylformamide Acetamide E-N-methylacetamide Z-N-methylacetamide Propionamide b Methanethiol Ethanethiol propanethiol b Thiophenol Thioanisole Dimethyl sulfide Diethyl sulfide Methyl ethyl sulfide Dipropyl sulfide Bis(2-chloroethyl) sulfide b Dimethyl disulfide b Diethyl disulfide Trimethyl phosphate Triethyl phosphate b Tripropyl phosphate ,2-dichloroethenyl dimethyl phosphate Dimethyl-4-bromo-2,5-dichlorophenyl thiophosphate b Dimethyl 2,4,5-trichlorophenyl thiophosphate Dimethyl 4-nitrophenyl thiophosphate b Dimethyl 5-(4-chloro) bicyclo[3.2.0] heptyl phosphate Diethyl 2,4-dichlorophenyl thiophosphate Dimethyl 3-methyl-4-thiomethoxyphenyl thiophosphate Ethyl 4-cyanophenyl phenylthiophosphonate Diethyl 4-nitrophenyl thiophosphonate o-ethyl o?-4-bromo-2-chlorophenyl s-propyl phosphorothioate b Ammonium CH 3NH (CH 3) 2NH (CH 3) 3NH C 6H 5NH N-butylammonium Methyl imidazolium N-p-guanidinium Methylthiol ion C 6H 5S Acetate ion Propionate ion C 6H 5O p-cresole ion a Expt (a) lists the solvation free energies in water (Refs 1, 6, 12, and 46) and (b) lists the solvation free energies in 1-octanol (Ref 1). b Compounds in test set for model 3. etc.), a probe radius of 1.4 Å is usually applied for SAS calculation. However, in this work, a probe radius of 0.6 was used. The reason is that with a smaller probe radius, a more precise description of the surface area can be achieved compared to that with a larger probe radius. For large molecules, the interior atoms, although, they have no accessible surface area, can still make a contribution to the electrostatic solvation free energy. However, in WSAS, those contributions are totally neglected. This deficiency of the simple models can be partially reduced by using a smaller probe radius. Moreover, a probe radius of 0.6 is still in the reliable radius range for the MSMS program. In the following, we also gave an example of how the probe radius affecting the performance of the WSAS models. Solvation Models. Table 2 lists all the solvation free energies

10 5064 J. Phys. Chem. B, Vol. 105, No. 21, 2001 Wang et al. TABLE 3: Performance of WSAS (Mode 4) by Solute Function Class a model I model IV solute class no. of solute unsigned mean error RMS error no. of solute unsigned mean error RMS error alkanes alkenes alkynes aromatic hydrocarbons fluorides chlorides bromides iodinates alcohols ethers aldehydes ketones acids esters amines amides nitriles nitro compounds compounds with N in heterorings compounds with S compounds with P ions total a All the errors are in kcal/mol. for four WSAS models. In model I, 184 molecules for which there are experimental solvation free energies in 1-octanol were studied. The WSAS model achieves an unsigned average error of 0.36 kcal/mol better than those of the SM5.42R universal solvation models (0.56 and 0.58 for SM5.42R/AM1 and SM5.42R/PM3, respectively). In model II, a 245-molecule set with aqueous solvation free energies, used as the training set by Li et al. 1 for their SM5.42R models, were investigated for comparison. Finally, our model and the universal solvation models achieve very similar performances: WSAS has a marginally larger unsigned average error than that of SM5.42R (0.48 vs 0.46 kcal/mol (SM5.42R/AM1 and SM5.42R/PM3)), but a slightly smaller RMS error (0.64 vs 0.66 (SM5.42R/AM1) and 0.68 (SM5.42R/PM3) kcal/mol). To investigate how the probe radius affects the fitting results, we also developed another model with the same molecular set of model II, for which the solvent accessible surface areas were calculated with a probe radius of 1.4 Å, a commonly-used probe radius for water molecule. In this model, both the unsigned average error and the RMS error are significantly larger than those in model II, which are 0.67 and 0.89 kcal/mol, respectively. Compared to the mode II, the solvation free energies of some branched molecules are significantly worse because of the reason stated above. Models III and IV, the largest molecule sets in aqueous solvation free energy studies that we know, were applied to perform parametrizations. The molecule sets of model III (387) and IV (401) are same except that model IV includes 14 ions. For model III, the molecule set was further divided into a training set (293) and a test set (94). The WSAS model gives unsigned average errors of 0.50 and 0.66 kcal/mol for the training set and test set, respectively. In total, the average error for the 387 molecules is kcal/mol, marginally larger than that of model IV (0.536 kcal/mol) without considering the ions. For the 14 ions, we achieved an average error of 0.53 kcal/ mol. That means the fitting procedure is reliable and no overfitting has occurred. For model IV, 47 independent variables entered the fitting procedure, and this number is a somewhat larger than that in the SM5.42 models (10 radii and 28 surface-tension coefficients). It is reasonable because our simple models need more variables to represent the electrostatic solvation energies. Compared to the SM5.0R, in which the electrostatic effect was implicit treated, the two models achieved similar performances and the mean unsigned errors are (this work) vs 0.57 (SM5.0R) kcal/mol. Table 3 lists the unsigned average errors for models I and IV by compound classes. The result of model IV is further summarized by the scatter plot in Figure 1. The correlation coefficient is 0.97 and the slope and intercept are 0.94 and -0.15, respectively. Table 4 lists the parameters for all of the four models. In the following applications of WSAS, we always used the parameters in model IV. Relative Binding Free Energy Calculations on HIV-1RT/ efavirenz. Table 5 lists the results of energy analyses with MM- WSAS and MM-PBSA. Binding mode I has the most favorable binding free energy (with or without intramolecular energy correction) in both of the models, which is about 10 and 7 kcal/ mol more favorable than the second best mode, respectively. Because of the neglect of the contribution of the intrinsic Figure 1. Calculated and experimental solvation free energies for the 401-molecule set (model 4)

11 Weighted Solvent Accessible Surface Area J. Phys. Chem. B, Vol. 105, No. 21, TABLE 4: Coefficients of Different Atom Types in Four Solvation Models no. atom type model 1 model 2 mode 3 model 4 1 CT CT CT CT CA CD CD CD CS CO CN F Cl Br I HCT HCT HCT HCT HCD HCD HCD HCA HCS HO HN HS OH OC O OS OOH SH SS SP NS ND ND NO NH NH N NTH NTH NT P P O OA S HN NT ND N charges, the absolute solvation free energy with WSAS is smaller than that of PBSA. However, the solvation free energy with the two models has a high correlation (Figure 2) and the correlation coefficient is 0.92, which means the contribution of the intrinsic charges to the solvation free energy are comparable for the five binding modes and this deficiency of WSAS model may be acceptable if one is only interested in the relative solvation free energy. For the solvation free energy, both of WSAS and PBSA have very similar root-mean-square deviations (RMSD), which are about 2.0 kcal/mol; however, for the binding free energy, MM-PBSA has a somewhat smaller RMSD error than MM-WSAS (about 3.0 kcal/mol) due to the compensation of the electrostatic energies of the MM and the PBSA. We TABLE 5: Summary of Energies from MD Simulations on HIV-1RT/Efavirenz a binding mode mode I mode II mode III mode IV mode V E intra E MM G WSAS G PBSA G b MM-WSAS G MM-PBSA T S G c a G b G a G b a All the energies are in kcal/mol. b G MM-WSAS ) E MM - G WSAS; G MM-PBSA ) E MM - G PBSA. c G a ) G MM-WSAS - T S; G b ) G MM-PBSA - T S; G a and G b are corrected binding free energies by adding the relative intramolecular energy of the ligand to G a and G b, respectively. Figure 2. Relationship of the solvation free energies by WSAS and PBSA for the five binding mode of HIV-1RT/ efavirenz. The correlation coefficient, slope, and intercept are 0.92, 0.84, and 2.62, respectively. believe WSAS can be applied efficiently in evaluating the binding free energies for multiple ligands in a database. We also carried out the solvation free energies of the five binding modes with the Eisenberg-McLachlan s model. In their model, the solvation free energy weighs (in kcal/mol/å 2 ) of five basic atom types (C (0.016), N/O (-0.006), O- (-0.024), N+ (0.050), and S(0.021)) were derived with the solvation free energies of 20 amino acids, which were estimated using the distribution coefficients of octanol/water. Because there are no parameters for fluorine and chlorine in their model, we simply borrowed the parameters from model IV, which are kcal/ mol/å 2 for fluorine and kcal/mol/å 2 for chlorine. Considering that the hydrogen is treated implicitly in Eisenberg-McLachlan s model, we deleted all of the hydrogens and applied the united atom radii in the MSMS program for SAS calculations. The following are the solvation free energies for the five binding modes in sequence: 8.0, 7.3, 7.5, 7.4, and 7.2 kcal/mol. It is clear that the solvation energies with this model cannot be well discriminated and the rank order is not satisfactory either. The reason lies in the fact that their model is too simple, and the parameters fitted with the distribution coefficients in other than the gas/water system may not be proper for this kind of calculations. Energy Analysis on Villin Headpiece. Table 6 lists the energy analyses results for two MD trajectories of villin headpiece using both MM-WSAS and MM-PBSA. The RMSD of each energy term is indicated in the followed parenthesis. Overall, for the three conformational clusters (the native, the

12 5066 J. Phys. Chem. B, Vol. 105, No. 21, 2001 Wang et al. TABLE 6: Summary of Energies from MD Simulations on Villin Headpiece ensemble native (1-100 ns) folding-intermediate ( ns) unfolded coil ( ns) E MM (35.7) (38.0) (61.4) G WSAS (24.9) (24.5) (38.9) G PBSA (31.9) (31.6) (54.5) TS (3.8) (2.0) (5.6) G MM-WSAS (33.2) (31.4) (47.1) G MM-PBSA (15.9) (15.7) (17.2) G b G a All the energies are in kcal/mol. b G 1 ) G MM-WSAS - TS; G 2 ) G MM-PBSA - TS. folding intermediate, and the unfolded random coil), the two solvation models give similar trends both for the solvation free energy and the free energy when the entropy contribution was also included. Quantitatively, the WSAS model makes the folding intermediate almost as stable as the native, whereas PBSA finds a large free energy gap between these two structures. Similar to the binding free energy calculation, the free energy with WSAS has a somewhat larger fluctuation, although for the solvation free energy, WSAS is actually more stable than PBSA (the RMSD of WSAS is about 60% of that of PBSA). The reason lies in the fact that the solvent accessible surface area is not as sensitive to the conformations along the MD trajectories as are the screening energies. Usually, the RMS deviation of screening energy is about 1% of the total screening energy in the MM-PBSA analysis, whereas the RMS of SAS is smaller than that of 0.5%. WSAS is nonetheless an attractive solvation model, especially for very large systems with many structures to be evaluated. For example, in protein modeling, both the threading and the ab initio prediction approaches need to evaluate hundreds, even thousands, of conformations. With WSAS, one can filter some unfavorable conformations (improper folding structures, too many buriedcharge conformations) first. Then, one focuses on the more promising conformations using more physically rigorous approaches. Other Applications of WSAS. Apart from the two applications discussed above, WSAS could be also very useful in other areas. For small- and medium-sized molecules, few atoms are completely buried, so this model can give very accurate solvation free energies. Therefore, the solvation free energies with this model could be applied as the parameters in QSAR studies. In QSAR, Hansch-Leo s solvation free energy models, 7 which intend to reproduce the distribution coefficient of the molecules between 1-octanol/water, are widely used. The WSAS model based on gas/water partitioning, could be an alternative model for such studies. Finally, this model can be used to calculate the atomic hydrophobic dipolar moments µ 11 described by eq 2, where n is the total number of atoms in a group, r i is a vector form the origin to the atom i; S i is the solvent accessible surface area of atom i; w i is the solvation free energy weight of atom i; and the brackets indicate the mean value of all the atoms in the group. Eisenberg-McLachlan 11 noted that the hydrophobic dipolar moments of neighboring segments of secondary structure tend to oppose each other in correctly folded proteins, but not in incorrectly folded ones, and that the hydrophobic moments can be used to classify helices (on the basis of amino acid sequences) and to detect periodicities. With the hydrophobic moment, one can detect incorrectly folded structures. In the future work, we will apply this model to calculate the relative binding free energy for a set of protein complexes and incorporate this model into a docking program n n µ ) w i S i r i - w i S i r i (2) i ) 1 i ) 1 Conclusions In this work, we have developed a fast and efficient solvation model based on atomic solvent accessible surface area. For model I, where the training set has 184 molecules with experimental solvation free energies in 1-octanol, WSAS achieves an unsigned average error of 0.36 kcal/mol, better than those of SM5.42R universal solvation model. For model II, both the WSAS and the universal solvation models achieve similar performances in reproducing the experimental aqueous solvation free energies for 245 molecules and the unsigned average error is about 0.46 kcal/mol with WSAS. In model III and IV, we have studied the largest molecule set for aqueous solvation free energy studies that we know. For model III, the whole molecule set has been separated into training set (293 molecules) and test set (94 molecules). Although the training set has a little lower unsigned average error (0.50 kcal/mol) compared to that of test set (0.66 kcal/mol), the overall unsigned average error (0.538 kcal/mol) is very close that of the Model IV (0.536 kcal/ mol), in which the parameters were derived using all the molecules. We have applied WSAS in predicting the relative binding free energies for the five binding modes of HIV-1RT/efavirenz. With this model, the correct binding mode has a binding free energy at least 10 kcal/mol favorable than other binding modes. Moreover, the solvation free energies calculated with WSAS have a high correlation to those calculated by PBSA. Considering WSAS is a much faster solvation model than PBSA, it could be useful to implement WSAS in docking programs to take into account the solvation effect on ligand binding. We have also applied WSAS in perform the energy analysis for the native and 1-µs MD trajectories of villin headpiece. For the three conformational clusters (the native, the folding intermediate, the unfolded random coil), we achieved the same solvation free energy and free energy trends as PBSA. Although this model has some larger inherent error in the calculation of absolute free energies compared to MM-PBSA, considering the simplicity and the very small computer time cost, WSAS could still be an attracting solvation model, especially for very large systems and with many structures to be evaluated. Acknowledgment. P.A.K. is grateful to acknowledge research support from the NIH (GM and GM (E. Arnold, P. I.)). References and Notes (1) Li, J.; Zhu, T.; Hawkins, G. D.; Winget, P.; Liotard, D. A.; Cramer, C. J. Theor. Chem. Acc. 1999, 103, (2) Honig, B.; Nicholls, A. Science 1995, 268, (3) Gilson, M. K.; Honig, B. Proteins 1998, 4, (4) Cramer, C. J.; Truhlar, D. G. Chem. ReV. 1999, 99, (5) Cramer, C. J.; Truhlar, D. G. Science 1992, 256, (6) Hine, J.; Mookerjee, P. K. J. Org. Chem. 1975, 40, (7) Hansch, C.; Leo, A. Exploring QSAR; American Chemical Society: Washington, DC (8) Kollman, P. A. Chem. ReV, 1993, 93, (9) Miller, J. L.; Kollman, P. A. J. Phys. Chem. 1996, 100, (10) Meng, E. C.; Caldwell, J. W.; Kollman, P. A. J. Phys. Chem. B 1996, 100, (11) Eisenberg, D.; McLachlan, A. D. Nature 1986, 319, (12) Hawkins, G. D.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 1997, 101,