A complete set of intermolecular potential functions has been developed for use in computer simulations of proteins in their native environment. Parameters are reported for 25 peptide residues as well as the common neutral and charged terminal groups. The potential functions have the simple Coulomb plus Lennard-Jones form and are compatible with the widely used models for water, TIP4P, TIP3P, and SPC. The parameters were obtained and tested primarily in conjunction with Monte Carlo statistical mechanics simulations of 36 pure organic liquids and numerous aqueous solutions of organic ions representative of subunits in the side chains and backbones of proteins. Bond stretch, angle bend, and torsional terms have been adopted from the AMBER united-atom force field. As reported here, further testing has involved studies of conformational energy surfaces and optimizations of the crystal structures for four cyclic hexapeptides and a cyclic pentapeptide. The average root-mean-square deviation from the X-ray structures of the crystals is only 0.17 A for the atomic positions and 3% for the unit cell volumes. A more critical test was then provided by performing energy minimizations for the complete crystal of the protein crambin, including 182 water molecules that were initially placed via a Monte Carlo simulation. The resultant root-mean-square deviation for the non-hydrogen atoms is still ca. 0.2 A and the variation in the errors for charged, polar, and nonpolar residues is small. Improvement is apparent over the AMBER united-atom force field which has previously been demonstrated to be superior to many alternatives. Computer simulations are undoubtedly destined to became an increasingly important means for investigating the structures and dynamics of biomolecular systems.' At the heart of such theoretical calculations are the force fields that describe the interatomic interactions and the mechanics of deformations of the molecules.* There is also little doubt that there will be a continual evolution in force fields with added complexity and improved performance paralleling the availability of computer resources. Our own efforts in this area over the last few years have resulted in the OPLS potential functions for proteins whose development and performance are summarized here. These potential functions have a simple form and they have been parametrized directly to reproduce experimental thermodynamic and structural data on fluids. Consequently, they are computationally efficient and their description of proteins in solution or crystalline environments should be superior to many alterantives that have been developed with limited condensed-phase data. The latter point is pursued here primarily through calculations on the crystal structures for four cyclic hexapeptides, a cyclic pentapeptide, and the protein crambin. Improvements are apparent in comparison to the AMBER united-atom force field3 which has previously been shown to be superior to many alternative^.^ (1) Beveridge, D. L., Jorgensen, W. L., Eds. Ann. N.Y. Acad. Sci. 1986, 482. ( 2 ) For reviews, see: (a) Levitt, M. Annu. Reu. Biophys. Eioeng. 1982, 11, 251. (b) McCammon, J. A. Rep. Prog. Phys. 1984, 47, 1. (3) Weiner, S. J.; Kollman, P. A.; Case, D. A,; Singh, U. C.; Ghio, C.; Alagona, G.; Profeta, S.; Weiner, P. J. Am. Chem. SOC. 1984, 106, 765. Parametrization The peptide residues of proteins contain readily identifiable organic subunits such as amides, hydrocarbons, alcohols, thioethers, etc. In view of this and since data are available on the corresponding pure organic liquids, our approach to developing a force field for proteins was to build it up from parameters demonstrated to yield good descriptions of organic liquids. U1timately, the force field would need to treat both intramolecular terms for bond stretches, angle bends, and torsions, as well as the intermolecular and intramolecular nonbonded interactions. The latter are generally accepted to be the most difficult part of the problem and have been our focus.3 A simple, computationally efficient form was chosen to represent the nonbonded interactions through Coulomb and Lennard-Jones terms interacting between sites centered on nuclei (eq 1). Thus, the intermolecular inter-

The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin.

Geometrical validation around the Calpha is described, with a new Cbeta measure and updated Ramachandran plot. Deviation of the observed Cbeta atom from ideal position provides a single measure encapsulating the major structure-validation information contained in bond angle distortions. Cbeta deviation is sensitive to incompatibilities between sidechain and backbone caused by misfit conformations or inappropriate refinement restraints. A new phi,psi plot using density-dependent smoothing for 81,234 non-Gly, non-Pro, and non-prePro residues with B < 30 from 500 high-resolution proteins shows sharp boundaries at critical edges and clear delineation between large empty areas and regions that are allowed but disfavored. One such region is the gamma-turn conformation near +75 degrees,-60 degrees, counted as forbidden by common structure-validation programs; however, it occurs in well-ordered parts of good structures, it is overrepresented near functional sites, and strain is partly compensated by the gamma-turn H-bond. Favored and allowed phi,psi regions are also defined for Pro, pre-Pro, and Gly (important because Gly phi,psi angles are more permissive but less accurately determined). Details of these accurate empirical distributions are poorly predicted by previous theoretical calculations, including a region left of alpha-helix, which rates as favorable in energy yet rarely occurs. A proposed factor explaining this discrepancy is that crowding of the two-peptide NHs permits donating only a single H-bond. New calculations by Hu et al. [Proteins 2002 (this issue)] for Ala and Gly dipeptides, using mixed quantum mechanics and molecular mechanics, fit our nonrepetitive data in excellent detail. To run our geometrical evaluations on a user-uploaded file, see MOLPROBITY (http://kinemage.biochem.duke.edu) or RAMPAGE (http://www-cryst.bioc.cam.ac.uk/rampage).

Structure validation by Calpha geometry: phi,psi and Cbeta deviation.

Computational studies of proteins based on empirical force fields represent a powerful tool to obtain structure-function relationships at an atomic level, and are central in current efforts to solve the protein folding problem. The results from studies applying these tools are, however, dependent on the quality of the force fields used. In particular, accurate treatment of the peptide backbone is crucial to achieve representative conformational distributions in simulation studies. To improve the treatment of the peptide backbone, quantum mechanical (QM) and molecular mechanical (MM) calculations were undertaken on the alanine, glycine, and proline dipeptides, and the results from these calculations were combined with molecular dynamics (MD) simulations of proteins in crystal and aqueous environments. QM potential energy maps of the alanine and glycine dipeptides at the LMP2/cc-pVxZ//MP2/6-31G* levels, where x = D, T, and Q, were determined, and are compared to available QM studies on these molecules. The LMP2/cc-pVQZ//MP2/6-31G* energy surfaces for all three dipeptides were then used to improve the MM treatment of the dipeptides. These improvements included additional parameter optimization via Monte Carlo simulated annealing and extension of the potential energy function to contain peptide backbone phi, psi dihedral crossterms or a phi, psi grid-based energy correction term. Simultaneously, MD simulations of up to seven proteins in their crystalline environments were used to validate the force field enhancements. Comparison with QM and crystallographic data showed that an additional optimization of the phi, psi dihedral parameters along with the grid-based energy correction were required to yield significant improvements over the CHARMM22 force field. However, systematic deviations in the treatment of phi and psi in the helical and sheet regions were evident. Accordingly, empirical adjustments were made to the grid-based energy correction for alanine and glycine to account for these systematic differences. These adjustments lead to greater deviations from QM data for the two dipeptides but also yielded improved agreement with experimental crystallographic data. These improvements enhance the quality of the CHARMM force field in treating proteins. This extension of the potential energy function is anticipated to facilitate improved treatment of biological macromolecules via MM approaches in general.

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.

A new derivation of the GLYCAM06 force field, which removes its previous specificity for carbohydrates, and its dependency on the AMBER force field and parameters, is presented. All pertinent force field terms have been explicitly specified and so no default or generic parameters are employed. The new GLYCAM is no longer limited to any particular class of biomolecules, but is extendible to all molecular classes in the spirit of a small-molecule force field. The torsion terms in the present work were all derived from quantum mechanical data from a collection of minimal molecular fragments and related small molecules. For carbohydrates, there is now a single parameter set applicable to both alpha- and beta-anomers and to all monosaccharide ring sizes and conformations. We demonstrate that deriving dihedral parameters by fitting to QM data for internal rotational energy curves for representative small molecules generally leads to correct rotamer populations in molecular dynamics simulations, and that this approach removes the need for phase corrections in the dihedral terms. However, we note that there are cases where this approach is inadequate. Reported here are the basic components of the new force field as well as an illustration of its extension to carbohydrates. In addition to reproducing the gas-phase properties of an array of small test molecules, condensed-phase simulations employing GLYCAM06 are shown to reproduce rotamer populations for key small molecules and representative biopolymer building blocks in explicit water, as well as crystalline lattice properties, such as unit cell dimensions, and vibrational frequencies.

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GLYCAM06: a generalizable biomolecular force field. Carbohydrates.

Fragment molecular orbital method: an approximate computational method for large molecules

The ab initio gradient revolution in structural chemistry: The importance of local molecular geometries and the efficacy of joint quantum mechanical and experimental procedures

Investigations concerning the apparent contradiction between the microwave structure and the ab initio calculations of glycine

The molecular structures of four conformations of N‐acetyl–N′‐methyl glycyl amide were refined by geometrically unconstrained ab initio gradient relaxation on the 4–21G level. The most stable form I contains a seven‐membered ring closed by hydrogen bonding. A second local minimum II is less than 1 kcal/mol above I and represents the fully extended form with a five‐membered hydrogen bonded ring. The two other minima refined, III and IV, are open forms which are 4–5 kcal/mol less stable than I. The refined geometries make it possible to estimate the significance of local geometries, in contrast to standard geometry, in the various conformations. It is found that bond distances in different conformations can vary by up to 0.02 A, and important backbone bond angles can vary by up to 7°. Except for the symmetrical form II, small deviations from amide planarity (H–N–C = 0 angles of 3–10°) are the rule, even though the equilibrium structure of the unperturbed amide group in 4–21G space is planar. It can be concl...

Ab initio studies of structural features not easily amenable to experiment. 23. Molecular structures and conformational analysis of the dipeptide N‐acetyl‐N′‐methyl glycyl amide and the significance of local geometries for peptide structures

Energies of rotational isomers of n-alkanes are largely determined by the number of individual gauche bonds (G). However, according to molecular mechanics calculations (MM2), within a group of rotamers with equal number of G bonds, there are characteristic energy variations due to cooperative effects involving sequences of several bonds. For example, the energy is increased by inserting a trans bond (T) between two consecutive G bonds of the same sign (e.g., TGGG<GTGG in n-heptane), and special long-range repulsive interactions seem to exist between G and G', a gauche bond of opposite sign, in a GTG' sequence (e.g., GTG<GTG' in n-hexane). With use of ab initio MP4SDQ/6-31G*//6-31G* energies and geometries of ethane to n-hexane

Investigation of intramolecular interactions in n-alkanes. Cooperative energy increments associated with GG and GTG' [G = gauche, T = trans] sequences

CH bond length variations due to the intramolecular environment: a comparison of the results obtained by the method of isolated CH stretching frequencies and by ab initio gradient calculations

Lothar Schäfer

Papers

The ab initio gradient revolution in structural chemistry: The importance of local molecular geometries and the efficacy of joint quantum mechanical and experimental procedures

Investigations concerning the apparent contradiction between the microwave structure and the ab initio calculations of glycine

Ab initio studies of structural features not easily amenable to experiment. 23. Molecular structures and conformational analysis of the dipeptide N‐acetyl‐N′‐methyl glycyl amide and the significance of local geometries for peptide structures

Investigation of intramolecular interactions in n-alkanes. Cooperative energy increments associated with GG and GTG' [G = gauche, T = trans] sequences

CH bond length variations due to the intramolecular environment: a comparison of the results obtained by the method of isolated CH stretching frequencies and by ab initio gradient calculations