Nonlinear scaling schemes for Lennard-Jones interactions in free energy calculations.

Alchemical free energy calculations provide a means for the accurate determination of free energies from atomistic simulations and are increasingly used as a tool for computational studies of protein-ligand interactions. Much attention has been placed on efficient ways to deal with the "endpoint singularity" effect that can cause simulation instabilities when changing the number of atoms. In this study we compare the performance of linear and several nonlinear transformation methods, among them separation shifted "soft core" scaling, for a popular test system, the hydration free energy of an amino acid side chain. All the nonlinear methods yield similar results if extensive sampling is performed, but soft core scaling provides smooth lambda curves that are best suited for commonly used numerical integration schemes. Additionally, results from a more flexible solute, hexane, will also be discussed.

[1]  Thomas Steinbrecher,et al.  A multistep approach to structure-based drug design: studying ligand binding at the human neutrophil elastase. , 2006, Journal of medicinal chemistry.

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

[3]  Vincenzo Mollica,et al.  Group contributions to the thermodynamic properties of non-ionic organic solutes in dilute aqueous solution , 1981 .

[4]  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.

[5]  Benoît Roux,et al.  Calculation of Standard Binding Free Energies:  Aromatic Molecules in the T4 Lysozyme L99A Mutant. , 2006, Journal of chemical theory and computation.

[6]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[7]  Arieh Ben-Naim,et al.  Solvation thermodynamics of nonionic solutes , 1984 .

[8]  Wei Zhang,et al.  A point‐charge force field for molecular mechanics simulations of proteins based on condensed‐phase quantum mechanical calculations , 2003, J. Comput. Chem..

[9]  Shantenu Jha,et al.  Grid-based steered thermodynamic integration accelerates the calculation of binding free energies , 2005, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  K. Shing,et al.  The chemical potential in dense fluids and fluid mixtures via computer simulation , 1982 .

[11]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[12]  T. Darden,et al.  A smooth particle mesh Ewald method , 1995 .

[13]  Donald Hamelberg,et al.  Standard free energy of releasing a localized water molecule from the binding pockets of proteins: double-decoupling method. , 2004, Journal of the American Chemical Society.

[14]  D. Kofke.  Free energy methods in molecular simulation , 2005 .

[15]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[16]  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.

[17]  Peter A. Kollman,et al.  The lag between the Hamiltonian and the system configuration in free energy perturbation calculations , 1989 .

[18]  Abraham M Lenhoff,et al.  Solvation free energy of amino acids and side-chain analogues. , 2007, The journal of physical chemistry. B.

[19]  H. Berendsen,et al.  THERMODYNAMICS OF CAVITY FORMATION IN WATER - A MOLECULAR-DYNAMICS STUDY , 1982 .

[20]  M. L. Connolly.  Analytical molecular surface calculation , 1983 .

[21]  Wei Yang,et al.  Generalized ensembles serve to improve the convergence of free energy simulations , 2003 .

[22]  Jed W. Pitera,et al.  A Comparison of Non-Bonded Scaling Approaches for Free Energy Calculations , 2002 .

[23]  A. Mark,et al.  Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations , 1994 .

[24]  Giorgio Colombo,et al.  Computer simulations of biomolecular systems , 2006 .

[25]  Test of the overlap ratio method on the calculation of the aqueous hydration free energy difference between acetone and dimethylamine , 1988 .

[26]  J. Hine,et al.  Structural effects on rates and equilibriums. XIX. Intrinsic hydrophilic character of organic compounds. Correlations in terms of structural contributions , 1975 .

[27]  Arnaud Blondel,et al.  Ensemble variance in free energy calculations by thermodynamic integration: Theory, optimal “Alchemical” path, and practical solutions , 2004, J. Comput. Chem..

[28]  Wei Yang,et al.  Forging the missing link in free energy estimations: λ-WHAM in thermodynamic integration, overlap histogramming, and free energy perturbation , 2007 .

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

[30]  Ching-Lung Lin,et al.  Free energy of solvation of a small Lennard–Jones particle , 1994, J. Comput. Chem..

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

[32]  Thomas Simonson,et al.  Free energy of particle insertion , 1993 .

[33]  K. Dill,et al.  Predicting absolute ligand binding free energies to a simple model site. , 2007, Journal of molecular biology.

[34]  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 .

[35]  Greg L. Hura,et al.  Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew. , 2004, The Journal of chemical physics.

[36]  Martin Zacharias,et al.  Holonomic constraint contributions to free energy differences from thermodynamic integration molecular dynamics simulations , 1992 .

[37]  K. Sharp,et al.  Accurate Calculation of Hydration Free Energies Using Macroscopic Solvent Models , 1994 .

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

[39]  Christophe Chipot,et al.  Can free energy calculations be fast and accurate at the same time? Binding of low-affinity, non-peptide inhibitors to the SH2 domain of the src protein , 2005, J. Comput. Aided Mol. Des..

[40]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[41]  J. Perram,et al.  Perturbation theory for the two-centre Lennard-Jones fluid using a spherically averaged reference potential , 1980 .

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

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

[44]  W. L. Jorgensen.  The Many Roles of Computation in Drug Discovery , 2004, Science.

[45]  J. Ponder,et al.  Force fields for protein simulations. , 2003, Advances in protein chemistry.

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

[47]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[48]  Donald G. Truhlar,et al.  MODEL FOR AQUEOUS SOLVATION BASED ON CLASS IV ATOMIC CHARGES AND FIRST SOLVATION SHELL EFFECTS , 1996 .

[49]  D. Beveridge,et al.  Free energy via molecular simulation: applications to chemical and biomolecular systems. , 1989, Annual review of biophysics and biophysical chemistry.

[50]  R. C. Weast.  CRC Handbook of Chemistry and Physics , 1973 .

[51]  Peter A. Kollman,et al.  A new method for carrying out free energy perturbation calculations: Dynamically modified windows , 1989 .

[52]  P M Cullis,et al.  Affinities of amino acid side chains for solvent water. , 1981, Biochemistry.

[53]  Thomas Steinbrecher,et al.  Bornyl (3,4,5-trihydroxy)-cinnamate--an optimized human neutrophil elastase inhibitor designed by free energy calculations. , 2008, Bioorganic & medicinal chemistry.