Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at Rint = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 Wiley Periodicals, Inc.

[1]  Takao Otsuka,et al.  Trimer effects in fragment molecular orbital-linear combination of molecular orbitals calculation of one-electron orbitals for biomolecules. , 2013, The Journal of chemical physics.

[2]  Jon Clardy,et al.  DESIGN, SYNTHESIS, AND KINETIC EVALUATION OF HIGH-AFFINITY FKBP LIGANDS AND THE X-RAY CRYSTAL-STRUCTURES OF THEIR COMPLEXES WITH FKBP12. , 1994 .

[3]  Jeremy C. Smith,et al.  Protein/ligand binding free energies calculated with quantum mechanics/molecular mechanics. , 2005, The journal of physical chemistry. B.

[4]  Edward G Hohenstein,et al.  Assessment of the Performance of the M05-2X and M06-2X Exchange-Correlation Functionals for Noncovalent Interactions in Biomolecules. , 2008, Journal of chemical theory and computation.

[5]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[6]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[7]  Troy Van Voorhis,et al.  Benchmark Assessment of the Accuracy of Several van der Waals Density Functionals. , 2012, Journal of chemical theory and computation.

[8]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[9]  Yuri Alexeev,et al.  Geometry Optimization of the Active Site of a Large System with the Fragment Molecular Orbital Method , 2011 .

[10]  Kaori Fukuzawa,et al.  Fragment molecular orbital method: use of approximate electrostatic potential , 2002 .

[11]  Kiyoyuki Terakura,et al.  Molecular orbital calculation of biomolecules with fragment molecular orbitals , 2009 .

[12]  K. Kitaura,et al.  Definition of molecular orbitals in fragment molecular orbital method , 2002 .

[13]  J M Thornton,et al.  LIGPLOT: a program to generate schematic diagrams of protein-ligand interactions. , 1995, Protein engineering.

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

[15]  Yuto Komeiji,et al.  Fragment molecular orbital method: analytical energy gradients , 2001 .

[16]  Kaori Fukuzawa,et al.  Molecular interactions between estrogen receptor and its ligand studied by the ab initio fragment molecular orbital method. , 2006, The journal of physical chemistry. B.

[17]  J. Perdew,et al.  Performance of meta-GGA Functionals on General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions. , 2013, Journal of chemical theory and computation.

[18]  Kazuo Kitaura,et al.  On the accuracy of the 3-body fragment molecular orbital method (FMO) applied to density functional theory , 2004 .

[19]  Hiroaki Tokiwa,et al.  Functions of key residues in the ligand-binding pocket of vitamin D receptor: Fragment molecular orbital interfragment interaction energy analysis , 2006 .

[20]  Shinichiro Nakamura,et al.  Analytic second derivatives of the energy in the fragment molecular orbital method. , 2013, The Journal of chemical physics.

[21]  末永 正彦,et al.  PC GAMESSのための新しい計算化学統合環境 Facio の開発 , 2005 .

[22]  H. Fujitani,et al.  Massively parallel computation of absolute binding free energy with well-equilibrated states. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Kazuo Kitaura,et al.  Pair interaction energy decomposition analysis , 2007, J. Comput. Chem..

[24]  K. Kitaura,et al.  Fragment molecular orbital method: an approximate computational method for large molecules , 1999 .

[25]  Hiroshi Chuman,et al.  QSAR Study of Cyclic Urea Type HIV‐1 PR Inhibitors Using Ab Initio MO Calculation of Their Complex Structures with HIV‐1 PR , 2008 .

[26]  Kotoko Nakata,et al.  Ab initio quantum mechanical study of the binding energies of human estrogen receptor α with its ligands: An application of fragment molecular orbital method , 2005, J. Comput. Chem..

[27]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[28]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[29]  Mark Whittaker,et al.  Prediction of cyclin-dependent kinase 2 inhibitor potency using the fragment molecular orbital method , 2011, J. Cheminformatics.

[30]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[31]  Kazuo Kitaura,et al.  Second order Møller-Plesset perturbation theory based upon the fragment molecular orbital method. , 2004, The Journal of chemical physics.

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

[33]  S. Grimme.  Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies , 2003 .

[34]  Dimitrios G Liakos,et al.  Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods. , 2011, The journal of physical chemistry. A.

[35]  P. Beroza,et al.  Application of a pairwise generalized Born model to proteins and nucleic acids: inclusion of salt effects , 1999 .

[36]  J. Šponer,et al.  Refinement of the AMBER Force Field for Nucleic Acids: Improving the Description of α/γ Conformers , 2007 .

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

[38]  Yutaka Akiyama,et al.  Fragment molecular orbital method: application to polypeptides , 2000 .

[39]  Adrienn Ruzsinszky,et al.  Workhorse semilocal density functional for condensed matter physics and quantum chemistry. , 2009, Physical review letters.

[40]  K. Kitaura,et al.  Multilayer formulation of the fragment molecular orbital method (FMO). , 2005, The journal of physical chemistry. A.

[41]  Kazuo Kitaura,et al.  Multiconfiguration self-consistent-field theory based upon the fragment molecular orbital method. , 2005, The Journal of chemical physics.

[42]  Kohji Itoh,et al.  Correlation Analyses on Binding Affinity of Sialic Acid Analogues and Anti-Influenza Drugs with Human Neuraminidase Using ab Initio MO Calculations on Their Complex Structures - LERE-QSAR Analysis (IV) , 2011, J. Chem. Inf. Model..

[43]  Bing Wang,et al.  The role of quantum mechanics in structure-based drug design. , 2007, Drug discovery today.

[44]  Kazuo Kitaura,et al.  The importance of three-body terms in the fragment molecular orbital method. , 2004, The Journal of chemical physics.

[45]  Kazuo Kitaura,et al.  Molecular recognition mechanism of FK506 binding protein: An all‐electron fragment molecular orbital study , 2007, Proteins.

[46]  Kazuya Ishimura,et al.  Accuracy of the three‐body fragment molecular orbital method applied to Møller–Plesset perturbation theory , 2007, J. Comput. Chem..

[47]  Kenneth M Merz,et al.  A Mixed QM/MM Scoring Function to Predict Protein-Ligand Binding Affinity. , 2010, Journal of chemical theory and computation.

[48]  Hui Li,et al.  The polarizable continuum model (PCM) interfaced with the fragment molecular orbital method (FMO) , 2006, J. Comput. Chem..

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

[50]  Kazuo Kitaura,et al.  Exploring chemistry with the fragment molecular orbital method. , 2012, Physical chemistry chemical physics : PCCP.

[51]  Kazuo Kitaura,et al.  The three-body fragment molecular orbital method for accurate calculations of large systems , 2006 .