Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: Case study of relative binding free energies of fructose‐1,6‐bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase‐AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional‐ and QM/MM‐FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase‐AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011

[1]  J N Weinstein,et al.  Relative differences in the binding free energies of human immunodeficiency virus 1 protease inhibitors: a thermodynamic cycle-perturbation approach. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[2]  M. Erion,et al.  Fructose-1,6-bisphosphatase inhibitors. 1. Purine phosphonic acids as novel AMP mimics. , 2009, Journal of medicinal chemistry.

[3]  M. Rami Reddy,et al.  Computer-Assisted Scanning of Ligand Interactions: Analysis of the Fructose 1,6-Bisphosphatase−AMP Complex Using Free Energy Calculations , 2000 .

[4]  M. Erion,et al.  Calculation of relative binding free energy differences for fructose 1,6-bisphosphatase inhibitors using the thermodynamic cycle perturbation approach. , 2001, Journal of the American Chemical Society.

[5]  U. Singh,et al.  Hydrophobic hydration: A free energy perturbation study , 1989 .

[6]  Arieh Warshel,et al.  Towards accurate ab initio QM/MM calculations of free-energy profiles of enzymatic reactions. , 2006, The journal of physical chemistry. B.

[7]  David A. Kofke,et al.  Accuracy of free-energy perturbation calculations in molecular simulation. II. Heuristics , 2001 .

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

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

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

[11]  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 .

[12]  W. Lipscomb,et al.  Discovery of potent and specific fructose-1,6-bisphosphatase inhibitors and a series of orally-bioavailable phosphoramidase-sensitive prodrugs for the treatment of type 2 diabetes. , 2007, Journal of the American Chemical Society.

[13]  Structural aspects of the allosteric inhibition of fructose-1,6-bisphosphatase by AMP: the binding of both the substrate analogue 2,5-anhydro-D-glucitol 1,6-bisphosphate and catalytic metal ions monitored by X-ray crystallography. , 1995 .

[14]  M. Rami Reddy,et al.  Relative solvation free energies calculated using an ab initio QM/MM-based free energy perturbation method: dependence of results on simulation length , 2009, J. Comput. Aided Mol. Des..

[15]  M. Berkowitz,et al.  The dielectric constant of SPC/E water , 1989 .

[16]  M. Erion,et al.  Computer-aided drug design strategies used in the discovery of fructose 1, 6-bisphosphatase inhibitors. , 2005, Current pharmaceutical design.

[17]  P. A. Bash,et al.  Calculation of the relative change in binding free energy of a protein-inhibitor complex. , 1987, Science.

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

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

[20]  U. Singh,et al.  A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: Applications to the CH3Cl + Cl− exchange reaction and gas phase protonation of polyethers , 1986 .

[21]  J Tirado-Rives,et al.  Estimation of binding affinities for HEPT and nevirapine analogues with HIV-1 reverse transcriptase via Monte Carlo simulations. , 2001, Journal of medicinal chemistry.

[22]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.

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

[24]  Jiali Gao,et al.  Combined QM/MM study of the mechanism and kinetic isotope effect of the nucleophilic substitution reaction in haloalkane dehalogenase. , 2003, Journal of the American Chemical Society.

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

[26]  U. C. Singh,et al.  Free energy perturbation studies on inhibitor binding to HIV-1 proteinase , 1992 .

[27]  Jiali Gao,et al.  Polarization and charge-transfer effects in aqueous solution via ab initio QM/MM simulations. , 2006, The journal of physical chemistry. B.

[28]  M. Erion,et al.  Relative binding affinities of fructose-1,6-bisphosphatase inhibitors calculated using a quantum mechanics-based free energy perturbation method. , 2007, Journal of the American Chemical Society.

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

[30]  Arieh Warshel,et al.  Simulation of enzyme reactions using valence bond force fields and other hybrid quantum/classical approaches , 1993 .

[31]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[32]  U. Singh,et al.  A free energy perturbation study of solvation in methanol and dimethyl sulfoxide , 1990 .

[33]  U. Singh.  Probing the salt bridge in the dihydrofolate reductase-methotrexate complex by using the coordinate-coupled free-energy perturbation method. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Tao Jiang,et al.  MB06322 (CS-917): A potent and selective inhibitor of fructose 1,6-bisphosphatase for controlling gluconeogenesis in type 2 diabetes , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[35]  F. Young.  Biochemistry , 1955, The Indian Medical Gazette.

[36]  S. Benkovic,et al.  Mechanism of action of fructose 1,6-bisphosphatase. , 1982, Advances in enzymology and related areas of molecular biology.

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

[38]  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.

[39]  T. Straatsma,et al.  THE MISSING TERM IN EFFECTIVE PAIR POTENTIALS , 1987 .

[40]  W. Lipscomb,et al.  Structure-guided design of AMP mimics that inhibit fructose-1,6-bisphosphatase with high affinity and specificity. , 2007, Journal of the American Chemical Society.

[41]  J. Straub,et al.  Proteins : energy, heat and signal flow , 2009 .

[42]  Peter A. Kollman,et al.  The overlooked bond‐stretching contribution in free energy perturbation calculations , 1991 .

[43]  M. Rami Reddy,et al.  Calculation of relative solvation free energy differences by thermodynamic perturbation method: Dependence of free energy results on simulation length , 1999, J. Comput. Chem..

[44]  W. L. Jorgensen,et al.  Monte Carlo simulation of differences in free energies of hydration , 1985 .

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

[46]  J. Andrew McCammon,et al.  Free energy difference calculations by thermodynamic integration: Difficulties in obtaining a precise value , 1991 .

[47]  U. Singh,et al.  A free-energy perturbation study of the binding of methotrexate to mutants of dihydrofolate reductase. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[48]  N. Burton,et al.  Catalytic Mechanism of the Enzyme Papain: Predictions with a Hybrid Quantum Mechanical/Molecular Mechanical Potential , 1997 .