Accounting for ligand conformational restriction in calculations of protein-ligand binding affinities.

The conformation adopted by a ligand on binding to a receptor may differ from its lowest-energy conformation in solution. In addition, the bound ligand is more conformationally restricted, which is associated with a configurational entropy loss. The free energy change due to these effects is often neglected or treated crudely in current models for predicting binding affinity. We present a method for estimating this contribution, based on perturbation theory using the quasi-harmonic model of Karplus and Kushick as a reference system. The consistency of the method is checked for small model systems. Subsequently we use the method, along with an estimate for the enthalpic contribution due to ligand-receptor interactions, to calculate relative binding affinities. The AMBER force field and generalized Born implicit solvent model is used. Binding affinities were estimated for a test set of 233 protein-ligand complexes for which crystal structures and measured binding affinities are available. In most cases, the ligand conformation in the bound state was significantly different from the most favorable conformation in solution. In general, the correlation between measured and calculated ligand binding affinities including the free energy change due to ligand conformational change is comparable to or slightly better than that obtained by using an empirically-trained docking score. Both entropic and enthalpic contributions to this free energy change are significant.

[1]  J. Essex,et al.  Hit identification and binding mode predictions by rigorous free energy simulations. , 2008, Journal of medicinal chemistry.

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

[3]  W. L. Jorgensen,et al.  Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids , 1996 .

[4]  Daniel M Zuckerman,et al.  Simple estimation of absolute free energies for biomolecules. , 2006, The Journal of chemical physics.

[5]  T. Bhat,et al.  Structure of HIV-1 protease with KNI-272, a tight-binding transition-state analog containing allophenylnorstatine. , 1995, Structure.

[6]  M. Tyka,et al.  Absolute free-energy calculations of liquids using a harmonic reference state. , 2007, The journal of physical chemistry. B.

[7]  Dusanka Janezic,et al.  Harmonic analysis of large systems. II. Comparison of different protein models , 1995, J. Comput. Chem..

[8]  B. Roux,et al.  Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials. , 2006, Biophysical journal.

[9]  M. Gilson,et al.  Calculation of cyclodextrin binding affinities: energy, entropy, and implications for drug design. , 2004, Biophysical journal.

[10]  C. E. Peishoff,et al.  A critical assessment of docking programs and scoring functions. , 2006, Journal of medicinal chemistry.

[11]  Matthew P. Repasky,et al.  Glide: a new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy. , 2004, Journal of medicinal chemistry.

[12]  Julian Tirado-Rives,et al.  Contribution of conformer focusing to the uncertainty in predicting free energies for protein-ligand binding. , 2006, Journal of medicinal chemistry.

[13]  P. Kollman,et al.  Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. , 2000, Accounts of chemical research.

[14]  On the calculation of absolute free energies from molecular-dynamics or Monte Carlo data. , 2006, The Journal of chemical physics.

[15]  Dusanka Janezic,et al.  Harmonic analysis of large systems. I. Methodology , 1995, J. Comput. Chem..

[16]  M J Sternberg,et al.  Empirical scale of side-chain conformational entropy in protein folding. , 1993, Journal of molecular biology.

[17]  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.

[18]  M. Gilson,et al.  Coordinate Systems and the Calculation of Molecular Properties , 2002 .

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

[20]  Ruhong Zhou,et al.  New Linear Interaction Method for Binding Affinity Calculations Using a Continuum Solvent Model , 2001 .

[21]  K. Dill,et al.  On the use of orientational restraints and symmetry corrections in alchemical free energy calculations. , 2006, The Journal of chemical physics.

[22]  M. Gilson,et al.  Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm. , 2004, Journal of the American Chemical Society.

[23]  Richard B Sessions,et al.  An efficient, path-independent method for free-energy calculations. , 2006, The journal of physical chemistry. B.

[24]  W. C. Still,et al.  The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii , 1997 .

[25]  Johannes C. Hermann,et al.  A combined QM/MM approach to protein--ligand interactions: polarization effects of the HIV-1 protease on selected high affinity inhibitors. , 2004, Journal of medicinal chemistry.

[26]  G. Klebe,et al.  DrugScore(CSD)-knowledge-based scoring function derived from small molecule crystal data with superior recognition rate of near-native ligand poses and better affinity prediction. , 2005, Journal of medicinal chemistry.

[27]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[28]  Araz Jakalian,et al.  Fast, efficient generation of high‐quality atomic charges. AM1‐BCC model: I. Method , 2000 .

[29]  L. Verlet,et al.  Perturbation Theory and Equation of State for Fluids , 1969 .

[30]  M Karplus,et al.  Calculation of free-energy differences by confinement simulations. Application to peptide conformers. , 2009, The journal of physical chemistry. B.

[31]  Kenneth S. Pitzer,et al.  Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation: II. Unsymmetrical Tops Attached to a Rigid Frame , 1946 .

[32]  M. Gilson,et al.  The statistical-thermodynamic basis for computation of binding affinities: a critical review. , 1997, Biophysical journal.

[33]  K. Appelt,et al.  Crystal structures of HIV-1 protease-inhibitor complexes , 1993 .

[34]  Michael R. Shirts,et al.  Direct calculation of the binding free energies of FKBP ligands. , 2005, The Journal of chemical physics.

[35]  P. Charifson,et al.  Conformational analysis of drug-like molecules bound to proteins: an extensive study of ligand reorganization upon binding. , 2004, Journal of medicinal chemistry.

[36]  Michael R. Shirts,et al.  Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods. , 2003, Physical review letters.

[37]  István Kolossváry,et al.  Evaluation of the Molecular Configuration Integral in All Degrees of Freedom for the Direct Calculation of Conformational Free Energies: Prediction of the Anomeric Free Energy of Monosaccharides , 1997 .

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

[39]  B. Roux,et al.  Calculation of absolute protein-ligand binding free energy from computer simulations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[40]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

[41]  K. Dill,et al.  Binding of small-molecule ligands to proteins: "what you see" is not always "what you get". , 2009, Structure.

[42]  M. Gilson,et al.  Calculation of Molecular Configuration Integrals , 2003 .

[43]  K. Merz,et al.  Large-scale validation of a quantum mechanics based scoring function: predicting the binding affinity and the binding mode of a diverse set of protein-ligand complexes. , 2005, Journal of medicinal chemistry.

[44]  David L Mobley,et al.  Treating entropy and conformational changes in implicit solvent simulations of small molecules. , 2008, The journal of physical chemistry. B.

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

[46]  B. Roux,et al.  Computations of standard binding free energies with molecular dynamics simulations. , 2009, The journal of physical chemistry. B.

[47]  M. Gilson,et al.  Calculation of protein-ligand binding affinities. , 2007, Annual review of biophysics and biomolecular structure.

[48]  Gerard Pujadas,et al.  Protein-ligand Docking: A Review of Recent Advances and Future Perspectives , 2008 .

[49]  Michael K Gilson,et al.  Evaluating the Accuracy of the Quasiharmonic Approximation. , 2005, Journal of chemical theory and computation.

[50]  Jonathan C. Horton,et al.  What you see ... , 2001, Nature.

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

[52]  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 .

[53]  Hege S. Beard,et al.  Glide: a new approach for rapid, accurate docking and scoring. 2. Enrichment factors in database screening. , 2004, Journal of medicinal chemistry.

[54]  Renxiao Wang,et al.  The PDBbind database: collection of binding affinities for protein-ligand complexes with known three-dimensional structures. , 2004, Journal of medicinal chemistry.

[55]  Julien Michel,et al.  Protein-ligand binding affinity predictions by implicit solvent simulations: a tool for lead optimization? , 2006, Journal of medicinal chemistry.

[56]  Steven W. Muchmore,et al.  High-Throughput Calculation of Protein-Ligand Binding Affinities: Modification and Adaptation of the MM-PBSA Protocol to Enterprise Grid Computing , 2006, J. Chem. Inf. Model..

[57]  Renxiao Wang,et al.  The PDBbind database: methodologies and updates. , 2005, Journal of medicinal chemistry.

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

[59]  M. Gilson,et al.  Ligand configurational entropy and protein binding , 2007, Proceedings of the National Academy of Sciences.

[60]  Jeremy C. Smith,et al.  Thermodynamic stability of water molecules in the bacteriorhodopsin proton channel: a molecular dynamics free energy perturbation study. , 1996, Biophysical journal.

[61]  J. Aqvist,et al.  A new method for predicting binding affinity in computer-aided drug design. , 1994, Protein engineering.

[62]  Benoît Roux,et al.  Binding specificity of SH2 domains: Insight from free energy simulations , 2009, Proteins.

[63]  D. J. Price,et al.  Assessing scoring functions for protein-ligand interactions. , 2004, Journal of medicinal chemistry.

[64]  Dusanka Janezic,et al.  Harmonic analysis of large systems. III. Comparison with molecular dynamics , 1995, J. Comput. Chem..

[65]  Jeffrey Skolnick,et al.  Assessment of programs for ligand binding affinity prediction , 2008, J. Comput. Chem..

[66]  W. L. Jorgensen.  Free energy calculations: a breakthrough for modeling organic chemistry in solution , 1989 .

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

[68]  Stefan Boresch,et al.  Absolute Binding Free Energies: A Quantitative Approach for Their Calculation , 2003 .

[69]  Daan Frenkel,et al.  New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres , 1984 .