Best practices in free energy calculations for drug design.

Free energy calculations are increasingly of interest for computing biophysical properties of novel small molecules of interest in drug design, such as protein-ligand binding affinities and small molecule partition coefficients. However, these calculations are also notoriously difficult to implement correctly. In this article, we review standard methods for computing free energy differences via simulation, discuss current best practices, and examine potential pitfalls for computational researchers without extensive experience in such calculations. We include a variety of examples and tips for how to set up and conduct these calculations, including applications to relative binding affinities and absolute binding free energies.

[1]  Benoît Roux,et al.  Characterization of conformational equilibria through Hamiltonian and temperature replica‐exchange simulations: Assessing entropic and environmental effects , 2007, J. Comput. Chem..

[2]  Niu Huang,et al.  Physics-based methods for studying protein-ligand interactions. , 2007, Current opinion in drug discovery & development.

[3]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[4]  S. Rick,et al.  Increasing the Efficiency of Free Energy Calculations Using Parallel Tempering and Histogram Reweighting. , 2006, Journal of chemical theory and computation.

[5]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[6]  T. Steinbrecher,et al.  Towards accurate free energy calculations in ligand protein-binding studies. , 2010, Current medicinal chemistry.

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

[8]  H. Meirovitch Recent developments in methodologies for calculating the entropy and free energy of biological systems by computer simulation. , 2007, Current opinion in structural biology.

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

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

[11]  Ioannis G. Economou,et al.  Effect of the integration method on the accuracy and computational efficiency of free energy calculations using thermodynamic integration , 2010 .

[12]  Conrad Shyu,et al.  Reducing the bias and uncertainty of free energy estimates by using regression to fit thermodynamic integration data , 2009, J. Comput. Chem..

[13]  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.

[14]  Michael R. Shirts,et al.  Comparison of efficiency and bias of free energies computed by exponential averaging, the Bennett acceptance ratio, and thermodynamic integration. , 2005, The Journal of chemical physics.

[15]  David L Mobley,et al.  Predicting ligand binding affinity with alchemical free energy methods in a polar model binding site. , 2009, Journal of molecular biology.

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

[17]  Stefan Boresch,et al.  The Role of Bonded Terms in Free Energy Simulations. 2. Calculation of Their Influence on Free Energy Differences of Solvation , 1999 .

[18]  A. Pohorille,et al.  Free energy calculations : theory and applications in chemistry and biology , 2007 .

[19]  Wei Yang,et al.  Synergistic approach to improve "alchemical" free energy calculation in rugged energy surface. , 2007, The Journal of chemical physics.

[20]  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 .

[21]  Mark A Olson,et al.  Calculation of absolute protein-ligand binding affinity using path and endpoint approaches. , 2006, Biophysical journal.

[22]  R. Swendsen,et al.  THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method , 1992 .

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

[24]  G. Torrie,et al.  Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling , 1977 .

[25]  Régis Pomès,et al.  Enhancing the accuracy, the efficiency and the scope of free energy simulations. , 2005, Current opinion in structural biology.

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

[27]  Wei Yang,et al.  Simulated scaling method for localized enhanced sampling and simultaneous "alchemical" free energy simulations: a general method for molecular mechanical, quantum mechanical, and quantum mechanical/molecular mechanical simulations. , 2007, The Journal of chemical physics.

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

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

[30]  G. Crooks Path-ensemble averages in systems driven far from equilibrium , 1999, cond-mat/9908420.

[31]  Mika A. Kastenholz,et al.  Computation of methodology-independent ionic solvation free energies from molecular simulations. II. The hydration free energy of the sodium cation. , 2006, The Journal of chemical physics.

[32]  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.

[33]  Christophe Chipot,et al.  Good practices in free-energy calculations. , 2010, The journal of physical chemistry. B.

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

[35]  David L Mobley,et al.  Nonlinear scaling schemes for Lennard-Jones interactions in free energy calculations. , 2007, The Journal of chemical physics.

[36]  C. Dellago,et al.  Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods? , 2005, The journal of physical chemistry. B.

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

[38]  A. Leach Molecular Modelling: Principles and Applications , 1996 .

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

[40]  Charles L. Brooks,et al.  Efficient Sampling of Ligand Orientations and Conformations in Free Energy Calculations Using the λ-Dynamics Method , 2000 .

[41]  D. Pearlman,et al.  Determination of the differential effects of hydrogen bonding and water release on the binding of FK506 to native and Tyr82-->Phe82 FKBP-12 proteins using free energy simulations. , 1995, Journal of molecular biology.

[42]  Christian Bartels,et al.  Multidimensional adaptive umbrella sampling: Applications to main chain and side chain peptide conformations , 1997 .

[43]  Yuko Okamoto,et al.  Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations. , 2003, Journal of molecular graphics & modelling.

[44]  Michael P Eastwood,et al.  Minimizing thermodynamic length to select intermediate states for free-energy calculations and replica-exchange simulations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[47]  Lorna J. Smith,et al.  Assessing equilibration and convergence in biomolecular simulations , 2002, Proteins.

[48]  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..

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

[50]  Lianqing Zheng,et al.  A hybrid recursion method to robustly ensure convergence efficiencies in the simulated scaling based free energy simulations. , 2008, The Journal of chemical physics.

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

[52]  Christopher J. Woods,et al.  Enhanced configurational sampling in binding free-energy calculations , 2003 .

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

[54]  Wei Yang,et al.  Essential energy space random walks to accelerate molecular dynamics simulations: convergence improvements via an adaptive-length self-healing strategy. , 2008, The Journal of chemical physics.

[55]  Jonathan W. Essex,et al.  Prediction of protein–ligand binding affinity by free energy simulations: assumptions, pitfalls and expectations , 2010, J. Comput. Aided Mol. Des..

[56]  F Marty Ytreberg Absolute FKBP binding affinities obtained via nonequilibrium unbinding simulations. , 2009, The Journal of chemical physics.

[57]  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.

[58]  Benoît Roux,et al.  Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations , 2001 .

[59]  Martin Almlöf,et al.  Free energy calculations and ligand binding. , 2003, Advances in protein chemistry.

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

[61]  Michael R. Shirts,et al.  Statistically optimal analysis of samples from multiple equilibrium states. , 2008, The Journal of chemical physics.

[62]  Charles L. Brooks,et al.  Efficient and Flexible Algorithm for Free Energy Calculations Using the λ-Dynamics Approach , 1998 .

[63]  Chris Oostenbrink,et al.  Calculating zeros: Non-equilibrium free energy calculations , 2006 .

[64]  Anthony K. Felts,et al.  Temperature weighted histogram analysis method, replica exchange, and transition paths. , 2005, The journal of physical chemistry. B.

[65]  R. Swendsen,et al.  Comparison of free energy methods for molecular systems. , 2006, The Journal of chemical physics.

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

[67]  Wei Yang,et al.  Energy difference space random walk to achieve fast free energy calculations. , 2008, The Journal of chemical physics.

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

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

[70]  M. Rami Reddy,et al.  Free energy calculations in rational drug design , 2001 .

[71]  Nohad Gresh,et al.  Binding of 5‐phospho‐D‐arabinonohydroxamate and 5‐phospho‐D‐arabinonate inhibitors to zinc phosphomannose isomerase from Candida albicans studied by polarizable molecular mechanics and quantum mechanics , 2007, J. Comput. Chem..

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

[73]  Charles L. Brooks,et al.  λ‐dynamics: A new approach to free energy calculations , 1996 .

[74]  Berend Smit,et al.  Understanding molecular simulation: from algorithms to applications , 1996 .

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

[76]  Jan Hermans,et al.  Change of bond length in free‐energy simulations: Algorithmic improvements, but when is it necessary? , 1994 .

[77]  M. Karplus,et al.  The Jacobian factor in free energy simulations , 1996 .

[78]  J. Andrew McCammon,et al.  Independent-Trajectories Thermodynamic-Integration Free-Energy Changes for Biomolecular Systems: Determinants of H5N1 Avian Influenza Virus Neuraminidase Inhibition by Peramivir , 2009, Journal of chemical theory and computation.

[79]  David L Mobley,et al.  The Confine-and-Release Method: Obtaining Correct Binding Free Energies in the Presence of Protein Conformational Change. , 2007, Journal of chemical theory and computation.

[80]  David A. Kofke,et al.  Appropriate methods to combine forward and reverse free-energy perturbation averages , 2003 .

[81]  Jozef Hritz,et al.  Hamiltonian replica exchange molecular dynamics using soft-core interactions. , 2008, The Journal of chemical physics.

[82]  Mihaly Mezei,et al.  Studies on free energy calculations. I. Thermodynamic integration using a polynomial path , 1993 .