Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.

[1]  M. Dewar,et al.  Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters , 1977 .

[2]  Jerry M. Parks,et al.  Quantum mechanics/molecular mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: sequential sampling and optimization on the potential of mean force surface. , 2008, The Journal of chemical physics.

[3]  M. Rami Reddy,et al.  Ab initio quantum mechanics‐based free energy perturbation method for calculating relative solvation free energies , 2007, J. Comput. Chem..

[4]  Bernard R Brooks,et al.  Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations. , 2015, Biochimica et biophysica acta.

[5]  Stefan Grimme,et al.  Benchmarking of London Dispersion-Accounting Density Functional Theory Methods on Very Large Molecular Complexes. , 2013, Journal of chemical theory and computation.

[6]  Justin L. MacCallum,et al.  Calculation of the water–cyclohexane transfer free energies of neutral amino acid side‐chain analogs using the OPLS all‐atom force field , 2003, J. Comput. Chem..

[7]  Stefan Bruckner,et al.  Unorthodox uses of Bennett's acceptance ratio method , 2009, J. Comput. Chem..

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

[9]  Wei Yang,et al.  Practically Efficient QM/MM Alchemical Free Energy Simulations: The Orthogonal Space Random Walk Strategy. , 2010, Journal of chemical theory and computation.

[10]  J. Guthrie,et al.  A blind challenge for computational solvation free energies: introduction and overview. , 2009, The journal of physical chemistry. B.

[11]  Darrin M York,et al.  An Efficient Linear-Scaling Ewald Method for Long-Range Electrostatic Interactions in Combined QM/MM Calculations. , 2005, Journal of chemical theory and computation.

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

[13]  F. J. Luque,et al.  Induced dipole moment and atomic charges based on average electrostatic potentials in aqueous solution , 1993 .

[14]  Walter Thiel,et al.  Beyond the MNDO model: Methodical considerations and numerical results , 1993, J. Comput. Chem..

[15]  Shawn T. Brown,et al.  Advances in methods and algorithms in a modern quantum chemistry program package. , 2006, Physical chemistry chemical physics : PCCP.

[16]  Bernard R Brooks,et al.  Calculations of Solvation Free Energy through Energy Reweighting from Molecular Mechanics to Quantum Mechanics. , 2016, Journal of chemical theory and computation.

[17]  David L Mobley,et al.  Predicting small-molecule solvation free energies: an informal blind test for computational chemistry. , 2008, Journal of medicinal chemistry.

[18]  Arieh Warshel,et al.  Ab Initio Free Energy Perturbation Calculations of Solvation Free Energy Using the Frozen Density Functional Approach , 1994 .

[19]  Christopher J. Woods,et al.  A "Stepping Stone" Approach for Obtaining Quantum Free Energies of Hydration. , 2015, The journal of physical chemistry. B.

[20]  David L. Mobley,et al.  Blind prediction of solvation free energies from the SAMPL4 challenge , 2014, Journal of Computer-Aided Molecular Design.

[21]  J. Koenderink.  Q… , 2014, Les noms officiels des communes de Wallonie, de Bruxelles-Capitale et de la communaute germanophone.

[22]  Bernard R. Brooks,et al.  Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations , 2011, Journal of Computer-Aided Molecular Design.

[23]  Gerhard König,et al.  Non‐Boltzmann sampling and Bennett's acceptance ratio method: How to profit from bending the rules , 2011, J. Comput. Chem..

[24]  Julien Michel,et al.  A simple QM/MM approach for capturing polarization effects in protein-ligand binding free energy calculations. , 2011, The journal of physical chemistry. B.

[25]  H. Berendsen,et al.  ALGORITHMS FOR MACROMOLECULAR DYNAMICS AND CONSTRAINT DYNAMICS , 1977 .

[26]  Wei Yang,et al.  QM/MM Alchemical Free Energy Simulations: Challenges and Recent Developments , 2010 .

[27]  Guohui Li,et al.  Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes. , 2006, The journal of physical chemistry. B.

[28]  Walter Thiel,et al.  OMx-D: semiempirical methods with orthogonalization and dispersion corrections. Implementation and biochemical application. , 2008, Physical chemistry chemical physics : PCCP.

[29]  J. Peter Guthrie,et al.  SAMPL4, a blind challenge for computational solvation free energies: the compounds considered , 2014, Journal of Computer-Aided Molecular Design.

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

[31]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .

[32]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[33]  Ulf Ryde,et al.  Quantum mechanical free energy barrier for an enzymatic reaction. , 2005, Physical review letters.

[34]  Samuel Genheden,et al.  Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model , 2015, J. Comput. Chem..

[35]  Bogdan I. Iorga,et al.  Prediction of hydration free energies for aliphatic and aromatic chloro derivatives using molecular dynamics simulations with the OPLS-AA force field , 2012, Journal of Computer-Aided Molecular Design.

[36]  Colin D. Brown,et al.  LogD: lipophilicity for ionisable compounds. , 2008, Chemosphere.

[37]  Arieh Warshel,et al.  Paradynamics: an effective and reliable model for ab initio QM/MM free-energy calculations and related tasks. , 2011, The journal of physical chemistry. B.

[38]  Ronald M. Levy,et al.  Prediction of SAMPL3 host-guest affinities with the binding energy distribution analysis method (BEDAM) , 2012, Journal of Computer-Aided Molecular Design.

[39]  Matthew T. Geballe,et al.  The SAMPL3 blind prediction challenge: transfer energy overview , 2012, Journal of Computer-Aided Molecular Design.

[40]  Y. Sugita,et al.  Multidimensional replica-exchange method for free-energy calculations , 2000, cond-mat/0009120.

[41]  Paul K. Weiner,et al.  Ground states of molecules , 1972 .

[42]  Andreas Klamt,et al.  Blind prediction test of free energies of hydration with COSMO-RS , 2010, J. Comput. Aided Mol. Des..

[43]  Ricardo A. Mata,et al.  Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host–guest binding energies , 2014, Journal of Computer-Aided Molecular Design.

[44]  William L. Jorgensen,et al.  PDDG/PM3 and PDDG/MNDO: Improved semiempirical methods , 2002, J. Comput. Chem..

[45]  Bernard R. Brooks,et al.  Interfacing Q‐Chem and CHARMM to perform QM/MM reaction path calculations , 2007, J. Comput. Chem..

[46]  Walter Thiel,et al.  QM/MM Free-Energy Perturbation Compared to Thermodynamic Integration and Umbrella Sampling:  Application to an Enzymatic Reaction. , 2006, Journal of chemical theory and computation.

[47]  Walter Thiel,et al.  Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters , 2016, Journal of chemical theory and computation.

[48]  U. Singh,et al.  Development of a quantum mechanics-based free-energy perturbation method: use in the calculation of relative solvation free energies. , 2004, Journal of the American Chemical Society.

[49]  Michael K. Gilson,et al.  Blind prediction of host–guest binding affinities: a new SAMPL3 challenge , 2012, Journal of Computer-Aided Molecular Design.

[50]  Andrew C Simmonett,et al.  Efficient treatment of induced dipoles. , 2015, The Journal of chemical physics.

[51]  Jiali Gao,et al.  HYBRID AB INITIO QM/MM SIMULATION OF N-METHYLACETAMIDE IN AQUEOUS SOLUTION , 1997 .

[52]  Jonathan W Essex,et al.  Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies. , 2013, The journal of physical chemistry. B.

[53]  Pär Söderhjelm,et al.  Converging ligand‐binding free energies obtained with free‐energy perturbations at the quantum mechanical level , 2016, J. Comput. Chem..

[54]  Ulf Ryde,et al.  Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations. , 2012, Physical chemistry chemical physics : PCCP.

[55]  Mirjam Scholten,et al.  Semiempirische Verfahren mit Orthogonalisierungskorrekturen: Die OM3 Methode , 2003 .

[56]  James Andrew McCammon,et al.  Thermodynamic integration to predict host-guest binding affinities , 2012, Journal of Computer-Aided Molecular Design.

[57]  Bernard R. Brooks,et al.  Blind prediction of distribution in the SAMPL5 challenge with QM based protomer and pKa corrections , 2016, Journal of Computer-Aided Molecular Design.

[58]  Wei Yang,et al.  Chaperoned alchemical free energy simulations: a general method for QM, MM, and QM/MM potentials. , 2004, The Journal of chemical physics.

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

[60]  Alexander D. MacKerell,et al.  CHARMM general force field: A force field for drug‐like molecules compatible with the CHARMM all‐atom additive biological force fields , 2009, J. Comput. Chem..

[61]  Donald G. Truhlar,et al.  Prediction of SAMPL2 aqueous solvation free energies and tautomeric ratios using the SM8, SM8AD, and SMD solvation models , 2010, J. Comput. Aided Mol. Des..

[62]  Milan Hodoscek,et al.  Efficiently computing pathway free energies: New approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes. , 2015, Biochimica et biophysica acta.

[63]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[64]  Walter Thiel,et al.  Extension of MNDO to d Orbitals: Parameters and Results for the Second-Row Elements and for the Zinc Group , 1996 .

[65]  J. Gao,et al.  A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations. , 1992, Science.

[66]  Walter Thiel.  The MNDOC method, a correlated version of the MNDO model , 1981 .

[67]  Julien Michel,et al.  Prediction of partition coefficients by multiscale hybrid atomic-level/coarse-grain simulations. , 2008, The journal of physical chemistry. B.

[68]  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..

[69]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[70]  Stefan Bruckner,et al.  Efficiency of alchemical free energy simulations. I. A practical comparison of the exponential formula, thermodynamic integration, and Bennett's acceptance ratio method , 2011, J. Comput. Chem..

[71]  Donald G Truhlar,et al.  Performance of SM6, SM8, and SMD on the SAMPL1 test set for the prediction of small-molecule solvation free energies. , 2009, The journal of physical chemistry. B.

[72]  Bernard R Brooks,et al.  Computational scheme for pH‐dependent binding free energy calculation with explicit solvent , 2015, Protein science : a publication of the Protein Society.

[73]  M. Karplus,et al.  Simulation of activation free energies in molecular systems , 1996 .

[74]  T. Straatsma,et al.  Separation‐shifted scaling, a new scaling method for Lennard‐Jones interactions in thermodynamic integration , 1994 .

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

[76]  Jianpeng Ma,et al.  CHARMM: The biomolecular simulation program , 2009, J. Comput. Chem..

[77]  Kenneth M. Merz,et al.  Calculation of solvation free energies using a density functional/molecular dynamics coupled potential , 1993 .

[78]  Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation. , 2013, The Journal of chemical physics.

[79]  Christopher J. Woods,et al.  Compatibility of Quantum Chemical Methods and Empirical (MM) Water Models in Quantum Mechanics/Molecular Mechanics Liquid Water Simulations , 2010 .

[80]  Wei Yang,et al.  Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: a general algorithm and its extension for free energy calculation on rugged energy surface. , 2007, The Journal of chemical physics.

[81]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[82]  R. Wolfenden,et al.  On the probability of finding a water molecule in a nonpolar cavity. , 1994, Science.

[83]  Arieh Warshel,et al.  Ab Initio QM/MM Simulation with Proper Sampling: “First Principle” Calculations of the Free Energy of the Autodissociation of Water in Aqueous Solution , 2002 .

[84]  Samuel Genheden,et al.  Predicting Partition Coefficients with a Simple All-Atom/Coarse-Grained Hybrid Model. , 2016, Journal of chemical theory and computation.

[85]  Alessandra Villa,et al.  Calculation of the free energy of solvation for neutral analogs of amino acid side chains , 2002, J. Comput. Chem..

[86]  Gerhard König,et al.  Hydration free energies of amino acids: why side chain analog data are not enough. , 2009, The journal of physical chemistry. B.

[87]  Andrew C Simmonett,et al.  An efficient algorithm for multipole energies and derivatives based on spherical harmonics and extensions to particle mesh Ewald. , 2014, The Journal of chemical physics.

[88]  Christopher J. Woods,et al.  An efficient method for the calculation of quantum mechanics/molecular mechanics free energies. , 2008, The Journal of chemical physics.

[89]  Andreas Klamt,et al.  Prediction of free energies of hydration with COSMO-RS on the SAMPL3 data set , 2012, Journal of Computer-Aided Molecular Design.

[90]  J. Stewart.  Optimization of parameters for semiempirical methods I. Method , 1989 .

[91]  H Lee Woodcock,et al.  Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems. , 2015, The journal of physical chemistry letters.

[92]  Jonathan W Essex,et al.  Direct validation of the single step classical to quantum free energy perturbation. , 2015, The journal of physical chemistry. B.

[93]  Walter Thiel,et al.  Orthogonalization corrections for semiempirical methods , 2000 .

[94]  Ye Mei,et al.  Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4 , 2014, Journal of Computer-Aided Molecular Design.

[95]  James J P Stewart,et al.  Optimization of parameters for semiempirical methods IV: extension of MNDO, AM1, and PM3 to more main group elements , 2004, Journal of molecular modeling.

[96]  Hao Hu,et al.  Elucidating solvent contributions to solution reactions with ab initio QM/MM methods. , 2010, The journal of physical chemistry. B.

[97]  Walter Thiel,et al.  QM/MM methods for biomolecular systems. , 2009, Angewandte Chemie.

[98]  James Andrew McCammon,et al.  Ligand-receptor interactions , 1984, Comput. Chem..

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

[100]  Stefan Grimme,et al.  Effect of the damping function in dispersion corrected density functional theory , 2011, J. Comput. Chem..

[101]  David L. Mobley,et al.  Measuring experimental cyclohexane-water distribution coefficients for the SAMPL5 challenge , 2016, bioRxiv.

[102]  P. Strevens.  Iii , 1985 .

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

[104]  Bernard R Brooks,et al.  Comparison of Methods To Reweight from Classical Molecular Simulations to QM/MM Potentials. , 2016, Journal of chemical theory and computation.

[105]  Paul Robustelli,et al.  Water dispersion interactions strongly influence simulated structural properties of disordered protein states. , 2015, The journal of physical chemistry. B.

[106]  Gerhard König,et al.  Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes , 2014, Journal of chemical theory and computation.

[107]  Charles W. Kehoe,et al.  Testing the semi-explicit assembly solvation model in the SAMPL3 community blind test , 2012, Journal of Computer-Aided Molecular Design.

[108]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[109]  Weitao Yang,et al.  QM/MM Minimum Free Energy Path: Methodology and Application to Triosephosphate Isomerase. , 2007, Journal of chemical theory and computation.

[110]  U. Ryde,et al.  Ligand-Binding Affinity Estimates Supported by Quantum-Mechanical Methods. , 2016, Chemical reviews.

[111]  Ulf Ryde,et al.  Accurate QM/MM Free Energy Calculations of Enzyme Reactions:  Methylation by Catechol O-Methyltransferase. , 2005, Journal of chemical theory and computation.

[112]  Weitao Yang,et al.  Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach. , 2008, The Journal of chemical physics.

[113]  Pavlo O. Dral,et al.  Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks for Ground-State Properties , 2016, Journal of chemical theory and computation.

[114]  Andrew C Simmonett,et al.  Computation of Hydration Free Energies Using the Multiple Environment Single System Quantum Mechanical/Molecular Mechanical Method. , 2016, Journal of chemical theory and computation.

[115]  Enhancing QM/MM molecular dynamics sampling in explicit environments via an orthogonal-space-random-walk-based strategy. , 2011, The journal of physical chemistry. B.

[116]  Arieh Warshel,et al.  Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies , 1992 .

[117]  Helmut Bönnemann.  Preface: 5th German Ferrofluid Workshop, held 25–27 June 2003, at the Max‐Planck‐Institut für Kohlenforschung, Mülheim a.d. Ruhr, Germany , 2004 .