Intramolecular interaction energies in model alanine and glycine tetrapeptides. Evaluation of anisotropy, polarization, and correlation effects. A parallel ab initio HF/MP2, DFT, and polarizable molecular mechanics study

An extension of the SIBFA polarizable molecular mechanics procedure to flexible oligopeptides is reported. The procedure is evaluated by computing the relative conformational energies, δEconf, of the alanine tetrapeptide in 10 representative conformations, which were originally derived by Beachy et al. (J Am Chem Soc 1997, 119, 5908) to benchmark molecular mechanics procedures with respect to ab initio computations. In the present study, a particular emphasis is on the separable nature of the components of the energy and the particular impact of the polarization energy component on δEconf. We perform comparisons with respect to single‐point HF, DFT, LMP2, and MP2 computations done at the SIBFA‐derived energy minima. Such comparisons are made first for the 10 conformers derived from ϕ/ψ torsional angle energy‐minimization (the rigid rotor approach), and, in a second step, after allowing additional relaxation of the Cα centered valence angles. In both series of energy‐minimization, the SIBFA δEconf compared best with the LMP2 results using the 6‐311G** basis set, the rms being 1.3 kcal/mol. In the absence of the polarization component, the rms is 3.5 kcal/mol. In both series of minimizations, the magnitudes of δEconf, computed as differences with respect to the most stable conformer taken as energy zero, decrease along the series: HF > DFT > LMP2 > SIBFA > MP2, indicative of increasing stabilization of the most highly folded conformers. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 823–834, 2004

[1]  Peter Pulay,et al.  Efficient elimination of basis set superposition errors by the local correlation method: Accurate ab initio studies of the water dimer , 1993 .

[2]  William H. Fink,et al.  Frozen fragment reduced variational space analysis of hydrogen bonding interactions. Application to the water dimer , 1987 .

[3]  Enhanced intramolecular amide-amide hydrogen bonding through cooperativity , 1996 .

[4]  S. Nilar,et al.  Hydrogen-Bonding Capabilities Based on Polarizability Studies of Model Peptide Systems , 1995 .

[5]  Sarah L. Price,et al.  A TRANSFERABLE DISTRIBUTED MULTIPOLE MODEL FOR THE ELECTROSTATIC INTERACTIONS OF PEPTIDES AND AMIDES , 1990 .

[6]  A. Becke Correlation energy of an inhomogeneous electron gas: A coordinate‐space model , 1988 .

[7]  Theoretical studies of molecular conformation. II: Application of the SIBFA procedure to molecules containing carbonyl and carboxylate oxygens and amide nitrogens , 1985 .

[8]  Nohad Gresh,et al.  A theoretical study of nonadditive effects in four water tetramers , 1998 .

[9]  T. Simonson,et al.  Macromolecular electrostatics: continuum models and their growing pains. , 2001, Current opinion in structural biology.

[10]  Laurent Emmanuel Dardenne,et al.  Reassociation of fragments using multicentered multipolar expansions: peptide junction treatments to investigate electrostatic properties of proteins , 2001, J. Comput. Chem..

[11]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[12]  N. Špačková,et al.  Theoretical Study of Binding of Hydrated Zn(II) and Mg(II) Cations to 5‘-Guanosine Monophosphate. Toward Polarizable Molecular Mechanics for DNA and RNA , 2003 .

[13]  R. Ludwig,et al.  Quantum Cluster Equilibrium Theory of Liquids: Temperature Dependence of Hydrogen Bonding in Liquid N-Methylacetamide Studied by IR Spectra , 1998 .

[14]  P. Claverie,et al.  Improvements of the continuum model. 1. Application to the calculation of the vaporization thermodynamic quantities of nonassociated liquids , 1988 .

[15]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

[16]  Steven J. Stuart,et al.  Dynamical fluctuating charge force fields: Application to liquid water , 1994 .

[17]  Dennis R. Salahub,et al.  Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation , 1992 .

[18]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[19]  J. Perdew,et al.  Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. , 1986, Physical review. B, Condensed matter.

[20]  J. Markley,et al.  Theoretical Studies of Protium/Deuterium Fractionation Factors and Cooperative Hydrogen Bonding in Peptides , 1995 .

[21]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[22]  JENS ANTONY,et al.  Binding of D‐ and L‐captopril inhibitors to metallo‐β‐lactamase studied by polarizable molecular mechanics and quantum mechanics , 2002, J. Comput. Chem..

[23]  Nohad Gresh,et al.  Energetics of Zn2+ binding to a series of biologically relevant ligands: A molecular mechanics investigation grounded on ab initio self‐consistent field supermolecular computations , 1995, J. Comput. Chem..

[24]  Nohad Gresh,et al.  Conformation‐dependent intermolecular interaction energies of the triphosphate anion with divalent metal cations. Application to the ATP‐binding site of a binuclear bacterial enzyme. A parallel quantum chemical and polarizable molecular mechanics investigation , 2004, J. Comput. Chem..

[25]  Ioannis N. Demetropoulos,et al.  Merlin - a portable system for multidimensional minimization , 1987 .

[26]  P. Reinhardt The decomposition of intermolecular interaction energies in localized orbitals — critical analysis and an invariance , 2003 .

[27]  M. Alderton,et al.  Distributed multipole analysis , 2006 .

[28]  Robert Rein,et al.  On Physical Properties and Interactions of Polyatomic Molecules: With Application to Molecular Recognition in Biology , 1973 .

[29]  Ruhong Zhou,et al.  Parametrizing a polarizable force field from ab initio data. I. The fluctuating point charge model , 1999 .

[30]  W. Goddard,et al.  Charge equilibration for molecular dynamics simulations , 1991 .

[31]  David Feller,et al.  Hydrogen bond energy of the water dimer , 1996 .

[32]  J. P. Malrieu,et al.  Localization and Delocalization in Quantum Chemistry , 1975 .

[33]  S. Kafafi,et al.  Ab initio determination of the structure of the active site of a metalloenzyme: Metal substitution in phosphotriesterase using density functional methods , 1999 .

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

[35]  R Rein,et al.  Point charge representation of multicenter multipole moments in calculation of electrostatic properties , 1993, Theoretica chimica acta.

[36]  E. Oelkers,et al.  Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: dissociation constants for supercritical alkali metal halides at temperatures from 400 to 800.degree.C and pressures from 500 to 4000 bar , 1988 .

[37]  P. Claverie,et al.  The exact multicenter multipolar part of a molecular charge distribution and its simplified representations , 1988 .

[38]  S. Suhai Cooperative effects in hydrogen bonding: Fourth‐order many‐body perturbation theory studies of water oligomers and of an infinite water chain as a model for ice , 1994 .

[39]  Nohad Gresh,et al.  Intermolecular interactions: Elaboration on an additive procedure including an explicit charge-transfer contribution , 1986 .

[40]  Nohad Gresh,et al.  Joint quantum chemical and polarizable molecular mechanics investigation of formate complexes with penta‐ and hexahydrated Zn2+: Comparison between energetics of model bidentate, monodentate, and through‐water Zn2+ binding modes and evaluation of nonadditivity effects , 1999 .

[41]  W. Andrzej Sokalski,et al.  Intramolecular electrostatic interactions studied by cumulative atomic multipole moment expansion with improved convergence , 1994 .

[42]  Nohad Gresh,et al.  Conformational properties of a model alanyl dipeptide and of alanine‐derived oligopeptides: Effects of solvation in water and in organic solvents—A combined SIBFA/continuum reaction field, ab initio self‐consistent field, and density functional theory investigation , 1998 .

[43]  Nohad Gresh,et al.  Critical Role of Anisotropy for the Dimerization Energies of Two Protein−Protein Recognition Motifs: cis-N-Methylacetamide versus a β-Sheet Conformer of Alanine Dipeptide. A Joint ab Initio, Density Functional Theory, and Molecular Mechanics Investigation , 1999 .

[44]  Nohad Gresh,et al.  Modeling of Copper(II) Complexes with the SIBFA Polarizable Molecular Mechanics Procedure. Application to a New Class of HIV-1 Protease Inhibitors , 2003 .

[45]  W. J. Stevens,et al.  Transferability of molecular distributed polarizabilities from a simple localized orbital based method , 1989 .

[46]  Nohad Gresh,et al.  Comparative binding energetics of Mg2+, Ca2+, Zn2+, and Cd2+ to biologically relevant ligands: Combined ab initio SCF supermolecule and molecular mechanics investigation , 1996, J. Comput. Chem..

[47]  Dennis R. Salahub,et al.  Extension of the LAP functional to include parallel spin correlation , 1997 .

[48]  W. A. Sokalski,et al.  Correlated molecular and cumulative atomic multipole moments , 1987 .

[49]  Hong Guo,et al.  Cooperative Hydrogen Bonding and Enzyme Catalysis. , 1998, Angewandte Chemie.

[50]  Richard A. Friesner,et al.  Pseudospectral localized Mo/ller–Plesset methods: Theory and calculation of conformational energies , 1995 .

[51]  Peter Pulay,et al.  The local correlation treatment. II. Implementation and tests , 1988 .

[52]  Ulrich Sternberg,et al.  New approach to the semiempirical calculation of atomic charges for polypeptides and large molecular systems , 1994, J. Comput. Chem..

[53]  Nohad Gresh,et al.  Many-Body Effects in Systems of Peptide Hydrogen-Bonded Networks and Their Contributions to Ligand Binding: A Comparison of the Performances of DFT and Polarizable Molecular Mechanics , 2000 .

[54]  Ulf Berg,et al.  Inter‐ and intramolecular potential for the N‐formylglycinamide‐water system. A comparison between theoretical modeling and empirical force fields , 2003, J. Comput. Chem..

[55]  J. Perdew,et al.  Erratum: Density-functional approximation for the correlation energy of the inhomogeneous electron gas , 1986, Physical review. B, Condensed matter.

[56]  P Hobza,et al.  Structure, energetics, and dynamics of the nucleic Acid base pairs: nonempirical ab initio calculations. , 1999, Chemical reviews.

[57]  P. Kollman,et al.  How well does a restrained electrostatic potential (RESP) model perform in calculating conformational energies of organic and biological molecules? , 2000 .

[58]  Guntram Rauhut,et al.  Local Treatment of Electron Correlation in Molecular Clusters: Structures and Stabilities of (H2O)n, n = 2−4 , 1998 .

[59]  Martin Karplus,et al.  Ab initio studies of hydrogen bonding of N-methylacetamide: structure, cooperativity, and internal rotational barriers , 1992 .

[60]  Nohad Gresh,et al.  Interaction of neutral and zwitterionic glycine with Zn2+ in gas phase: ab initio and SIBFA molecular mechanics calculations , 2000 .

[61]  Nohad Gresh,et al.  Model, Multiply Hydrogen-Bonded Water Oligomers (N = 3−20). How Closely Can a Separable, ab Initio-Grounded Molecular Mechanics Procedure Reproduce the Results of Supermolecule Quantum Chemical Computations? , 1997 .

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

[63]  Walter Thiel,et al.  Description of peptide and protein secondary structures employing semiempirical methods , 2001 .

[64]  W. Andrzej Sokalski,et al.  Analysis of the transferability of atomic multipoles for amino acids in modeling macromolecular charge distribution from fragments , 2001, J. Comput. Chem..

[65]  J. Dannenberg,et al.  Cooperativity in amide hydrogen bonding chains: implications for protein-folding models. , 2001, Journal of the American Chemical Society.

[66]  Yun-Dong Wu,et al.  Theoretical study of sheets formed by β‐peptides , 2002, J. Comput. Chem..

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

[68]  Y. D. Wu,et al.  A theoretical study on the origin of cooperativity in the formation of 3(10)- and alpha-helices. , 2001, Journal of the American Chemical Society.

[69]  P. Claverie,et al.  Theoretical studies of molecular conformation. Derivation of an additive procedure for the computation of intramolecular interaction energies. Comparison withab initio SCF computations , 1984 .

[70]  R. Lavery,et al.  The calculation of molecular electrostatic potential from a multipole expansion based on localized orbitals and developed at their centroids: Accuracy and applicability for macromolecular computations , 1982 .

[71]  Martin Karplus,et al.  Solvent Influence on the Stability of the Peptide Hydrogen Bond: A Supramolecular Cooperative Effect , 1994 .

[72]  Harry A. Stern,et al.  Development of a polarizable force field for proteins via ab initio quantum chemistry: First generation model and gas phase tests , 2002, J. Comput. Chem..

[73]  R. Rein,et al.  Quantitative examination of the approximations in the monopole and dipole theories of intermolecular interactions. , 1972, Journal of theoretical biology.

[74]  Peter Pulay,et al.  Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method , 1987 .

[75]  M. Leboeuf,et al.  Energetics and Structure in Model Neutral, Anionic, and Cationic Hydrogen-Bonded Complexes: Combined Ab Initio SCF/MP2 Supermolecular, Density Functional, and Molecular Mechanics Investigation , 1994 .

[76]  A Simple Coupling Scheme between Hartree−Fock and Local Spin-Density Functional Theories , 1998 .

[77]  Curt M. Breneman,et al.  Transferable atom equivalent multicentered multipole expansion method , 2003, J. Comput. Chem..

[78]  Jay W. Ponder,et al.  Accurate modeling of the intramolecular electrostatic energy of proteins , 1995, J. Comput. Chem..

[79]  Hitoshi Yamamoto,et al.  Solid-state13C NMR study on order → disorder phase transition in oleic acid , 2004 .

[80]  D. R. Garmer,et al.  Modeling of inhibitor–metalloenzyme interactions and selectivity using molecular mechanics grounded in quantum chemistry , 1998, Proteins.

[81]  Harold Basch,et al.  Compact effective potentials and efficient shared‐exponent basis sets for the first‐ and second‐row atoms , 1984 .

[82]  Richard A. Friesner,et al.  Accurate ab Initio Quantum Chemical Determination of the Relative Energetics of Peptide Conformations and Assessment of Empirical Force Fields , 1997 .

[83]  R Rein,et al.  Ab initio study of the electrostatic multipole nature of torsional potentials in CH3SSCH3, CH3SSH, and HOOH. , 1991, International journal of quantum chemistry. Quantum biology symposium : proceedings of the International Symposium on Quantum Biology and Quantum Pharmacology. International Symposium on Quantum Biology and Quantum Pharmacology.

[84]  Nohad Gresh,et al.  Intramolecular chelation of Zn2+ by α‐ and β‐mercaptocarboxamides. A parallel ab initio and polarizable molecular mechanics investigation. Assessment of the role of multipole transferability , 2001, J. Comput. Chem..

[85]  Susan K. Gregurick,et al.  Computation of the Electronic and Spectroscopic Properties of Carbohydrates Using Novel Density Functional and Vibrational Self-Consistent Field Methods , 1999 .

[86]  Sarah L. Price,et al.  Electrostatic models for polypeptides: can we assume transferability? , 1992 .

[87]  Nohad Gresh,et al.  Parallel ab initio and molecular mechanics investigation of polycoordinated Zn(II) complexes with model hard and soft ligands: Variations of binding energy and of its components with number and charges of ligands , 2000, J. Comput. Chem..