Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ϕ and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010

[1]  Hideaki Fujitani,et al.  High-Level ab Initio Calculations To Improve Protein Backbone Dihedral Parameters. , 2009, Journal of chemical theory and computation.

[2]  C. Almbladh,et al.  Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues. , 1985, Physical review. B, Condensed matter.

[3]  Giovanni Scalmani,et al.  Energies, structures, and electronic properties of molecules in solution with the C‐PCM solvation model , 2003, J. Comput. Chem..

[4]  Stefan Grimme,et al.  Accurate description of van der Waals complexes by density functional theory including empirical corrections , 2004, J. Comput. Chem..

[5]  Warren J. Hehre,et al.  AB INITIO Molecular Orbital Theory , 1986 .

[6]  P M Cullis,et al.  Affinities of amino acid side chains for solvent water. , 1981, Biochemistry.

[7]  Leo Frederick Holroyd,et al.  Insufficient description of dispersion in B3LYP and large basis set superposition errors in MP2 calculations can hide peptide conformers , 2007 .

[8]  F. Jensen,et al.  Force Field Modeling of Amino Acid Conformational Energies. , 2007, Journal of chemical theory and computation.

[9]  P. Hobza,et al.  Phenylalanyl-Glycyl-Phenylalanine Tripeptide: A Model System for Aromatic-Aromatic Side Chain Interactions in Proteins. , 2009, Journal of chemical theory and computation.

[10]  T. Mourik.  Assessment of Density Functionals for Intramolecular Dispersion-Rich Interactions. , 2008, Journal of chemical theory and computation.

[11]  S. Grimme,et al.  Benzenium-ethene complex: a fundamental problem for standard second-order Møller-Plesset theory. , 2009, The journal of physical chemistry. A.

[12]  G. Scuseria,et al.  Assessment of a long-range corrected hybrid functional. , 2006, The Journal of chemical physics.

[13]  Qin Wu,et al.  Empirical correction to density functional theory for van der Waals interactions , 2002 .

[14]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[15]  R. Wolfenden,et al.  Interaction of the peptide bond with solvent water: a vapor phase analysis. , 1978, Biochemistry.

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

[17]  Donald G Truhlar,et al.  Performance of SM6, SM8, and SMD on the SAMPL1 test set for the prediction of small-molecule solvation free energies. , 2009, The journal of physical chemistry. B.

[18]  T. van Mourik,et al.  Structure of the gas-phase glycine tripeptide. , 2010, Physical chemistry chemical physics : PCCP.

[19]  V. Spiwok,et al.  Potential-energy and free-energy surfaces of glycyl-phenylalanyl-alanine (GFA) tripeptide: experiment and theory. , 2008, Chemistry.

[20]  Yan Zhao,et al.  Density Functionals for Noncovalent Interaction Energies of Biological Importance. , 2007, Journal of chemical theory and computation.

[21]  V. Barone,et al.  Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model , 1998 .

[22]  S. Grimme,et al.  "Mindless" DFT Benchmarking. , 2009, Journal of chemical theory and computation.

[23]  Joo Yun Lee,et al.  Conformational preferences and pKa value of cysteine residue. , 2008, Journal of Physical Chemistry B.

[24]  Petros Koumoutsakos,et al.  Dispersion corrections to density functionals for water aromatic interactions. , 2004, The Journal of chemical physics.

[25]  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..

[26]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[27]  Jacopo Tomasi,et al.  A new definition of cavities for the computation of solvation free energies by the polarizable continuum model , 1997 .

[28]  M. Head‐Gordon,et al.  Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. , 2008, Physical chemistry chemical physics : PCCP.

[29]  Jacopo Tomasi,et al.  Evaluation of Solvent Effects in Isotropic and Anisotropic Dielectrics and in Ionic Solutions with a Unified Integral Equation Method: Theoretical Bases, Computational Implementation, and Numerical Applications , 1997 .

[30]  Jacopo Tomasi,et al.  A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics , 1997 .

[31]  J. Vondrášek,et al.  Structure and IR spectrum of phenylalanyl-glycyl-glycine tripetide in the gas-phase: IR/UV experiments, ab initio quantum chemical calculations, and molecular dynamic simulations. , 2005, Chemistry.

[32]  K N Houk,et al.  Benchmarking the Conductor-like Polarizable Continuum Model (CPCM) for Aqueous Solvation Free Energies of Neutral and Ionic Organic Molecules. , 2005, Journal of chemical theory and computation.

[33]  H. Scheraga,et al.  Conformational analysis of the 20 naturally occurring amino acid residues using ECEPP. , 1977, Macromolecules.

[34]  Harold A. Scheraga,et al.  Free energies of hydration of solute molecules. 3. Application of the hydration shell model to charged organic molecules , 1987 .

[35]  E. Beausoleil,et al.  Steric Effects on the Amide Isomer Equilibrium of Prolyl Peptides. Synthesis and Conformational Analysis of N-Acetyl-5-tert-butylproline N‘-Methylamides , 1996 .

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

[37]  Giovanni Scalmani,et al.  New developments in the polarizable continuum model for quantum mechanical and classical calculations on molecules in solution , 2002 .

[38]  Tanja van Mourik,et al.  Basis set superposition error effects cause the apparent nonexistence of the ethene/benzenium ion complex on the MP2 potential energy surface. , 2008 .

[39]  Donald G. Truhlar,et al.  PARAMETRIZED MODEL FOR AQUEOUS FREE ENERGIES OF SOLVATION USING GEOMETRY-DEPENDENT ATOMIC SURFACE TENSIONS WITH IMPLICIT ELECTROSTATICS , 1997 .

[40]  S. Grimme,et al.  Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability. , 2007, Physical chemistry chemical physics : PCCP.

[41]  T. van Mourik,et al.  Comparison of ab initio and DFT electronic structure methods for peptides containing an aromatic ring: effect of dispersion and BSSE. , 2007, The journal of physical chemistry. A.

[42]  Saroj K. Nayak,et al.  Towards extending the applicability of density functional theory to weakly bound systems , 2001 .

[43]  Y. Kang.  Conformational preferences of non-prolyl and prolyl residues. , 2006, The journal of physical chemistry. B.

[44]  Pavel Hobza,et al.  On the convergence of the (ΔECCSD(T)−ΔEMP2) term for complexes with multiple H-bonds , 2002 .

[45]  Fabio Della Sala,et al.  Asymptotic behavior of the Kohn-Sham exchange potential. , 2002, Physical review letters.

[46]  Young Kee Kang,et al.  Ab initio MO and density functional studies on trans and cis conformers of N-methylacetamide , 2001 .

[47]  David A. Dixon,et al.  Conformational Study of the Alanine Dipeptide at the MP2 and DFT Levels , 2002 .

[48]  C. Cramer,et al.  Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. , 2009, The journal of physical chemistry. B.

[49]  K. Kopple,et al.  Solvent-dependent conformational distributions of some dipeptides , 1980 .

[50]  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 .

[51]  Jirí Cerný,et al.  Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. , 2006, Physical chemistry chemical physics : PCCP.