Partial atomic charges and their impact on the free energy of solvation

Free energies of solvation (ΔG) in water and n‐octanol have been computed for common drug molecules by molecular dynamics simulations with an additive fixed‐charge force field. The impact of the electrostatic interactions was investigated by computing the partial atomic charges with four methods that all fit the charges from the quantum mechanically determined electrostatic potential (ESP). Due to the redistribution of electron density that occurs when molecules are transferred from gas phase to condensed phase, the polarization impact was also investigated. By computing the partial atomic charges with the solutes placed in a conductor‐like continuum, the charges were effectively polarized to take the polarization effects into account. No polarization correction term or similar was considered, only the partial atomic charges. Results show that free energies are very sensitive to the choice of atomic charges and that ΔG can differ by several kBT depending on the charge computing method. Inclusion of polarization effects makes the solutes too hydrophilic with most methods and in vacuo charges make the solutes too hydrophobic. The restrained‐ESP methods together with effectively polarized charges perform well in our test set and also when applied to a larger set of molecules. The effect of water models is also highlighted and shows that the conclusions drawn are valid for different three‐point models. Partitioning between an aqueous and a hydrophobic phase is also described better if the two environment's polarization is taken into account, but again the results are sensitive to the charge calculation method. Overall, the results presented here show that effectively polarized charges can improve the description of solvating a drug‐like molecule in a solvent and that the choice of partial atomic charges is crucial to ensure that molecular simulations produce reliable results. © 2012 Wiley Periodicals, Inc.

[1]  Jonathan W. Essex,et al.  Theoretical determination of partition coefficients , 1992 .

[2]  Wilfred F. van Gunsteren,et al.  Basic ingredients of free energy calculations: A review , 2009, J. Comput. Chem..

[3]  Igor V. Tetko,et al.  Prediction of n-Octanol/Water Partition Coefficients from PHYSPROP Database Using Artificial Neural Networks and E-State Indices , 2001, J. Chem. Inf. Comput. Sci..

[4]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[5]  Hans W. Horn,et al.  Accounting for polarization cost when using fixed charge force fields. II. Method and application for computing effect of polarization cost on free energy of hydration. , 2010, The journal of physical chemistry. B.

[6]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

[7]  G. S. Maciel,et al.  Charges derived from electrostatic potentials: Exploring dependence on theory and geometry optimization levels for dipole moments , 2005 .

[8]  David L. Mobley,et al.  Alchemical prediction of hydration free energies for SAMPL , 2012, Journal of Computer-Aided Molecular Design.

[9]  J. Errington,et al.  Determination of Henry's law constants through transition matrix Monte Carlo simulation , 2005 .

[10]  B. Hess,et al.  Hydration thermodynamic properties of amino acid analogues: a systematic comparison of biomolecular force fields and water models. , 2006, The journal of physical chemistry. B.

[11]  Junmei Wang,et al.  Development and testing of a general amber force field , 2004, J. Comput. Chem..

[12]  Michelle Francl,et al.  The Pluses and Minuses of Mapping Atomic Charges to Electrostatic Potentials , 2007 .

[13]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[14]  Jacopo Tomasi,et al.  Geometry optimization of molecular structures in solution by the polarizable continuum model , 1998 .

[15]  Alexander P. Lyubartsev,et al.  Determination of Free Energy from Chemical Potentials: Application of the Expanded Ensemble Method , 1996 .

[16]  S. Nosé.  A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[17]  Miguel Jorge,et al.  1-Octanol/Water Partition Coefficients of n-Alkanes from Molecular Simulations of Absolute Solvation Free Energies. , 2009, Journal of chemical theory and computation.

[18]  Rahman,et al.  Molecular-dynamics study of atomic motions in water. , 1985, Physical review. B, Condensed matter.

[19]  Jonathan W. Essex,et al.  Errors in free-energy perturbation calculations due to neglecting the conformational variation of atomic charges , 1992 .

[20]  David L Mobley,et al.  Alchemical free energy methods for drug discovery: progress and challenges. , 2011, Current opinion in structural biology.

[21]  Giovanni Scalmani,et al.  Energies, structures, and electronic properties of molecules in solution with the C‐PCM solvation model , 2003, J. Comput. Chem..

[22]  Sven P. Jacobsson,et al.  Solubility of Organic Compounds in Water/Octanol Systems. A Expanded Ensemble Molecular Dynamics Simulation Study of log P Parameters , 2001 .

[23]  William L. Jorgensen,et al.  Relative partition coefficients for organic solutes from fluid simulations , 1990 .

[24]  Michael R. Shirts,et al.  Solvation free energies of amino acid side chain analogs for common molecular mechanics water models. , 2005, The Journal of chemical physics.

[25]  Andrew S. Paluch,et al.  Efficient Solvation Free Energy Calculations of Amino Acid Analogs by Expanded Ensemble Molecular Simulation. , 2011, Journal of chemical theory and computation.

[26]  W. Richards,et al.  Theoretical calculation of electrode potentials: Electron‐withdrawing compounds , 1992 .

[27]  Anthony Nicholls,et al.  The SAMPL2 blind prediction challenge: introduction and overview , 2010, J. Comput. Aided Mol. Des..

[28]  David L. Mobley,et al.  Chapter 4 Alchemical Free Energy Calculations: Ready for Prime Time? , 2007 .

[29]  Hans W. Horn,et al.  Accounting for polarization cost when using fixed charge force fields. I. Method for computing energy. , 2010, The journal of physical chemistry. B.

[30]  E. Maginn,et al.  Monte Carlo simulations of gas solubility in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate. , 2005, The journal of physical chemistry. B.

[31]  P. Geerlings,et al.  On the performance of density functional methods for describing atomic populations, dipole moments and infrared intensities , 1996 .

[32]  T. Straatsma,et al.  THE MISSING TERM IN EFFECTIVE PAIR POTENTIALS , 1987 .

[33]  P. Kollman,et al.  A well-behaved electrostatic potential-based method using charge restraints for deriving atomic char , 1993 .

[34]  Alexander P. Lyubartsev,et al.  Free energy calculations for Lennard-Jones systems and water using the expanded ensemble method A Monte Carlo and molecular dynamics simulation study , 1994 .

[35]  C. Breneman,et al.  Determining atom‐centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis , 1990 .

[36]  Alexander P. Lyubartsev,et al.  M.DynaMix – a scalable portable parallel MD simulation package for arbitrary molecular mixtures , 2000 .

[37]  Christophe Chipot,et al.  Free Energy Calculations. The Long and Winding Gilded Road , 2002 .

[38]  Lee,et al.  New Monte Carlo algorithm: Entropic sampling. , 1993, Physical review letters.

[39]  Benoît Roux,et al.  Hydration of Amino Acid Side Chains: Nonpolar and Electrostatic Contributions Calculated from Staged Molecular Dynamics Free Energy Simulations with Explicit Water Molecules , 2004 .

[40]  W. Sherman,et al.  Prediction of Absolute Solvation Free Energies using Molecular Dynamics Free Energy Perturbation and the OPLS Force Field. , 2010, Journal of chemical theory and computation.

[41]  David L Mobley,et al.  Small Molecule Solvation Free Energy: Enhanced Conformational Sampling Using Expanded Ensemble Molecular Dynamics Simulation. , 2011, Journal of chemical theory and computation.

[42]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[43]  Ulf Ryde,et al.  Comparison of methods for deriving atomic charges from the electrostatic potential and moments , 1998 .

[44]  Irwin Oppenheim,et al.  Statistical Mechanical Theory of Transport Processes. VII. The Coefficient of Thermal Conductivity of Monatomic Liquids , 1954 .

[45]  Peter A. Kollman,et al.  FREE ENERGY CALCULATIONS : APPLICATIONS TO CHEMICAL AND BIOCHEMICAL PHENOMENA , 1993 .

[46]  Jaeeon Chang,et al.  The calculation of chemical potential of organic solutes in dense liquid phases by using expanded ensemble Monte Carlo simulations. , 2009, The Journal of chemical physics.

[47]  Charles H. Bennett,et al.  Efficient estimation of free energy differences from Monte Carlo data , 1976 .

[48]  David L Mobley,et al.  Small molecule hydration free energies in explicit solvent: An extensive test of fixed-charge atomistic simulations. , 2009, Journal of chemical theory and computation.

[49]  Andrew S. Paluch,et al.  A method for computing the solubility limit of solids: application to sodium chloride in water and alcohols. , 2010, The Journal of chemical physics.

[50]  A. Leo,et al.  Partition coefficients and their uses , 1971 .

[51]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[52]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[53]  J. Kirkwood.  Statistical Mechanics of Fluid Mixtures , 1935 .

[54]  Christophe Chipot,et al.  Rational determination of charge distributions for free energy calculations , 2003, J. Comput. Chem..

[55]  Piotr Cieplak,et al.  The R.E.D. tools: advances in RESP and ESP charge derivation and force field library building. , 2010, Physical chemistry chemical physics : PCCP.

[56]  Alexei M. Nikitin,et al.  New six‐site acetonitrile model for simulations of liquid acetonitrile and its aqueous mixtures , 2007, J. Comput. Chem..

[57]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[58]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[59]  P. Kollman,et al.  Application of RESP charges to calculate conformational energies, hydrogen bond energies, and free energies of solvation , 1993 .

[60]  L. E. Chirlian,et al.  Atomic charges derived from electrostatic potentials: A detailed study , 1987 .

[61]  Jonathan W. Essex,et al.  Atomic charges for variable molecular conformations , 1992 .

[62]  Ranbir Singh,et al.  J. Mol. Struct. (Theochem) , 1996 .

[63]  David M. Gange,et al.  Charges fit to electrostatic potentials. II. Can atomic charges be unambiguously fit to electrostatic potentials? , 1996 .

[64]  P. Kollman,et al.  Atomic charges derived from semiempirical methods , 1990 .

[65]  R. Zwanzig.  High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases , 1954 .

[66]  Robert J. Woods,et al.  Solvated ensemble averaging in the calculation of partial atomic charges , 2001, J. Comput. Chem..

[67]  David L. Mobley,et al.  Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations , 2010, J. Comput. Aided Mol. Des..

[68]  David L Mobley,et al.  Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent. , 2007, The journal of physical chemistry. B.

[69]  Aatto Laaksonen,et al.  Determination of solvation free energies by adaptive expanded ensemble molecular dynamics. , 2004, The Journal of chemical physics.

[70]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[71]  Benoît Roux,et al.  Computations of Absolute Solvation Free Energies of Small Molecules Using Explicit and Implicit Solvent Model. , 2009, Journal of chemical theory and computation.

[72]  S. Tsuzuki,et al.  Comparison of atomic charge distributions obtained from different procedures: basis set and electron correlation effects , 1996 .

[73]  A. Lyubartsev,et al.  New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles , 1992 .

[74]  D. Vernon.  Inform , 1995, Encyclopedia of the UN Sustainable Development Goals.

[75]  P. Kollman,et al.  An approach to computing electrostatic charges for molecules , 1984 .

[76]  W. L. Jorgensen,et al.  Prediction of Properties from Simulations: Free Energies of Solvation in Hexadecane, Octanol, and Water , 2000 .

[77]  Alexander P. Lyubartsev,et al.  Solvation free energies of methane and alkali halide ion pairs: An expanded ensemble molecular dynamics simulation study , 1998 .

[78]  Sture Nordholm,et al.  In silico prediction of drug solubility: 1. Free energy of hydration. , 2007, The journal of physical chemistry. B.

[79]  Michael R. Shirts,et al.  Extremely precise free energy calculations of amino acid side chain analogs: Comparison of common molecular mechanics force fields for proteins , 2003 .

[80]  Fernando A Escobedo,et al.  Variance minimization of free energy estimates from optimized expanded ensembles. , 2008, The journal of physical chemistry. B.