Practically Efficient and Robust Free Energy Calculations: Double-Integration Orthogonal Space Tempering.

The orthogonal space random walk (OSRW) method, which enables synchronous acceleration of the motions of a focused region and its coupled environment, was recently introduced to enhance sampling for free energy simulations. In the present work, the OSRW algorithm is generalized to be the orthogonal space tempering (OST) method via the introduction of the orthogonal space sampling temperature. Moreover, a double-integration recursion method is developed to enable practically efficient and robust OST free energy calculations, and the algorithm is augmented by a novel θ-dynamics approach to realize both the uniform sampling of order parameter spaces and rigorous end point constraints. In the present work, the double-integration OST method is employed to perform alchemical free energy simulations, specifically to calculate the free energy difference between benzyl phosphonate and difluorobenzyl phosphonate in aqueous solution, to estimate the solvation free energy of the octanol molecule, and to predict the nontrivial Barnase-Barstar binding affinity change induced by the Barnase N58A mutation. As demonstrated in these model studies, the DI-OST method can robustly enable practically efficient free energy predictions, particularly when strongly coupled slow environmental transitions are involved.

[1]  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..

[2]  Peter A. Kollman,et al.  Designing an Optimum Guest for a Host Using Multimolecule Free Energy Calculations: Predicting the Best Ligand for Rebek's “Tennis Ball” , 1998 .

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

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

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

[6]  Alexander D. MacKerell,et al.  Extending the treatment of backbone energetics in protein force fields: Limitations of gas‐phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations , 2004, J. Comput. Chem..

[7]  Volodymyr Babin,et al.  Adaptively biased molecular dynamics for free energy calculations. , 2007, The Journal of chemical physics.

[8]  Charles L. Brooks,et al.  λ‐Dynamics free energy simulation methods , 2009, J. Comput. Chem..

[9]  C. Brooks,et al.  Constant‐pH molecular dynamics using continuous titration coordinates , 2004, Proteins.

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

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

[12]  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.

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

[14]  Stefan Boresch,et al.  Unexpected relative aqueous solubilities of a phosphotyrosine analogue and two phosphonate derivatives. , 2005, Journal of the American Chemical Society.

[15]  Wei Yang,et al.  Simultaneous escaping of explicit and hidden free energy barriers: application of the orthogonal space random walk strategy in generalized ensemble based conformational sampling. , 2009, The Journal of chemical physics.

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

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

[18]  P. A. Bash,et al.  Free energy calculations by computer simulation. , 1987, Science.

[19]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[20]  T. Lelièvre,et al.  Long-time convergence of an adaptive biasing force method , 2007, 0706.1695.

[21]  M. Parrinello,et al.  Well-tempered metadynamics: a smoothly converging and tunable free-energy method. , 2008, Physical review letters.

[22]  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.

[23]  S. Nosé,et al.  Constant pressure molecular dynamics for molecular systems , 1983 .

[24]  A. Laio,et al.  Assessing the accuracy of metadynamics. , 2005, The journal of physical chemistry. B.

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

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

[27]  Eric Darve,et al.  Adaptive biasing force method for scalar and vector free energy calculations. , 2008, The Journal of chemical physics.

[28]  Walter Thiel,et al.  Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: "Umbrella integration". , 2005, The Journal of chemical physics.

[29]  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..

[30]  Wei Yang,et al.  Random walk in orthogonal space to achieve efficient free-energy simulation of complex systems , 2008, Proceedings of the National Academy of Sciences.

[31]  Gregory D. Hawkins,et al.  Extension of the platform of applicability of the SM5.42R universal solvation model , 1999 .

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

[33]  Simon Hanna,et al.  Use of thermodynamic integration to calculate the hydration free energies of n-alkanes , 2002 .

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

[35]  Taehoon Kim,et al.  CHARMM‐GUI: A web‐based graphical user interface for CHARMM , 2008, J. Comput. Chem..

[36]  S. Nosé.  A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[37]  Thomas Simonson,et al.  Free energy simulations come of age: protein-ligand recognition. , 2002, Accounts of chemical research.

[38]  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.

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

[40]  Wei Yang,et al.  On the convergence improvement in the metadynamics simulations: a Wang-Landau recursion approach. , 2007, The Journal of chemical physics.

[41]  Wei Yang,et al.  Quantitative computer simulations of biomolecules: A snapshot , 2008, J. Comput. Chem..

[42]  M. Karplus,et al.  Hidden thermodynamics of mutant proteins: a molecular dynamics analysis. , 1989, Science.

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

[44]  Bruce Tidor,et al.  Simulated annealing on free energy surfaces by a combined molecular dynamics and Monte Carlo approach , 1993 .

[45]  G. Ciccotti,et al.  Constrained reaction coordinate dynamics for the simulation of rare events , 1989 .

[46]  William L Jorgensen,et al.  Perspective on Free-Energy Perturbation Calculations for Chemical Equilibria. , 2008, Journal of chemical theory and computation.

[47]  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.

[48]  R. Swendsen,et al.  Adaptive integration method for Monte Carlo simulations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Yingkai Zhang,et al.  Determination of free energy profiles by repository based adaptive umbrella sampling: bridging nonequilibrium and quasiequilibrium simulations. , 2008, The Journal of chemical physics.

[50]  Frédéric Legoll,et al.  Free energy calculations: an efficient adaptive biasing potential method. , 2009, The journal of physical chemistry. B.

[51]  Bruce Tidor,et al.  Barstar is electrostatically optimized for tight binding to barnase , 2001, Nature Structural Biology.

[52]  Eric F Darve,et al.  Calculating free energies using average force , 2001 .

[53]  G Schreiber,et al.  Interaction of barnase with its polypeptide inhibitor barstar studied by protein engineering. , 1993, Biochemistry.

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

[55]  Gregory A Voth,et al.  A Combined Metadynamics and Umbrella Sampling Method for the Calculation of Ion Permeation Free Energy Profiles. , 2011, Journal of chemical theory and computation.

[56]  Arieh Warshel,et al.  Investigation of the free energy functions for electron transfer reactions , 1990 .

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

[58]  Simone Marsili,et al.  Self-healing umbrella sampling: a non-equilibrium approach for quantitative free energy calculations. , 2006, The journal of physical chemistry. B.

[59]  Stewart A. Adcock,et al.  Molecular dynamics: survey of methods for simulating the activity of proteins. , 2006, Chemical reviews.

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

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

[62]  Rudolph A. Marcus,et al.  On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. I , 1956 .

[63]  Christophe Chipot,et al.  Comprar Free Energy Calculations · Theory and Applications in Chemistry and Biology | Chipot, Christophe | 9783540736172 | Springer , 2007 .