Richard A. Friesner

A hierarchical approach to all-atom protein loop prediction

The application of all‐atom force fields (and explicit or implicit solvent models) to protein homology‐modeling tasks such as side‐chain and loop prediction remains challenging both because of the expense of the individual energy calculations and because of the difficulty of sampling the rugged all‐atom energy surface. Here we address this challenge for the problem of loop prediction through the development of numerous new algorithms, with an emphasis on multiscale and hierarchical techniques. As a first step in evaluating the performance of our loop prediction algorithm, we have applied it to the problem of reconstructing loops in native structures; we also explicitly include crystal packing to provide a fair comparison with crystal structures. In brief, large numbers of loops are generated by using a dihedral angle‐based buildup procedure followed by iterative cycles of clustering, side‐chain optimization, and complete energy minimization of selected loop structures. We evaluate this method by using the largest test set yet used for validation of a loop prediction method, with a total of 833 loops ranging from 4 to 12 residues in length. Average/median backbone root‐mean‐square deviations (RMSDs) to the native structures (superimposing the body of the protein, not the loop itself) are 0.42/0.24 Å for 5 residue loops, 1.00/0.44 Å for 8 residue loops, and 2.47/1.83 Å for 11 residue loops. Median RMSDs are substantially lower than the averages because of a small number of outliers; the causes of these failures are examined in some detail, and many can be attributed to errors in assignment of protonation states of titratable residues, omission of ligands from the simulation, and, in a few cases, probable errors in the experimentally determined structures. When these obvious problems in the data sets are filtered out, average RMSDs to the native structures improve to 0.43 Å for 5 residue loops, 0.84 Å for 8 residue loops, and 1.63 Å for 11 residue loops. In the vast majority of cases, the method locates energy minima that are lower than or equal to that of the minimized native loop, thus indicating that sampling rarely limits prediction accuracy. The overall results are, to our knowledge, the best reported to date, and we attribute this success to the combination of an accurate all‐atom energy function, efficient methods for loop buildup and side‐chain optimization, and, especially for the longer loops, the hierarchical refinement protocol. Proteins 2004;55:000–000.

On the Role of the Crystal Environment in Determining Protein Side-chain Conformations

The role of crystal packing in determining the observed conformations of amino acid side-chains in protein crystals is investigated by (1) analysis of a database of proteins that have been crystallized in different unit cells (space group or unit cell dimensions) and (2) theoretical predictions of side-chain conformations with the crystal environment explicitly represented. Both of these approaches indicate that the crystal environment plays an important role in determining the conformations of polar side-chains on the surfaces of proteins. Inclusion of the crystal environment permits a more sensitive measurement of the achievable accuracy of side-chain prediction programs, when validating against structures obtained by X-ray crystallography. Our side-chain prediction program uses an all-atom force field and a Generalized Born model of solvation and is thus capable of modeling simple packing effects (i.e. van der Waals interactions), electrostatic effects, and desolvation, which are all important mechanisms by which the crystal environment impacts observed side-chain conformations. Our results are also relevant to the understanding of changes in side-chain conformation that may result from ligand docking and protein-protein association, insofar as the results reveal how side-chain conformations change in response to their local environment.

A Mixed Quantum Mechanics/Molecular Mechanics (qm/mm) Method for Large-Scale Modeling of Chemistry in Protein Environments

A QM–MM method, using our previously developed frozen orbital QM–MM interface methodolgy, is presented as a general, accurate, and computationally efficient model for studying chemical problems in a protein environment. The method, its parametrization, and a preliminary application to modeling cytochrome P‐450 chemistry are presented.

Combined fluctuating charge and polarizable dipole models: Application to a five-site water potential function

We present a general formalism for polarizable electrostatics based on fluctuating bond-charge increments and polarizable dipoles and its application to a five-site model for water. The parametrization is based largely on quantum-chemical calculations and should be easily transferable to other molecules. To examine basis-set effects we parametrized two models from two sets of quantum calculations, using the aug-cc-pVTZ and aug-cc-pVQZ basis sets. We computed several gas-phase and condensed-phase properties and compared with experiment or ab initio calculations as available. The models are quite similar and give condensed-phase properties at ambient conditions that are in reasonable accord with experiment, but evince errors consistent with a liquid-state dipole moment that is slightly too large. The model fit to the aug-cc-pVTZ basis set has a smaller liquid-phase dipole moment and thus gives a somewhat better description of liquid water at ambient conditions. This model also performs well away from room t...

Peripheral heme substituents control the hydrogen-atom abstraction chemistry in cytochromes P450

We elucidate the hydroxylation of camphor by cytochrome P450 with the use of density functional and mixed quantum mechanics/molecular mechanics methods. Our results reveal that the enzyme catalyzes the hydrogen-atom abstraction step with a remarkably low free-energy barrier. This result provides a satisfactory explanation for the experimental failure to trap the proposed catalytically competent high-valent heme Fe(IV) oxo (oxyferryl) species responsible for this hydroxylation chemistry. The primary and previously unappreciated contribution to stabilization of the transition state is the interaction of positively charged residues in the active-site cavity with carboxylate groups on the heme periphery. A similar stabilization found in dioxygen binding to hemerythrin, albeit with reversed polarity, suggests that this mechanism for controlling the relative energetics of redox-active intermediates and transition states in metalloproteins may be widespread in nature.

Frozen orbital QM/MM methods for density functional theory

Abstract We have developed a density functional (DFT) version of our quantum chemistry/molecular mechanics (QM/MM) methodology based on using frozen molecular orbitals as the interface between the QM and MM regions. The methodology is distinguished from previous frozen orbital work by the availability of an accurate analytical gradient for ab initio methods and by the construction of a QM/MM interface capable of reproducing both deprotonation energies and conformational energetics around the frozen bond via fitting of interface parameters to a small model molecule. Results are presented for several test cases, including the alanine tetrapeptide and four amino acid side chains. Excellent agreement between fully QM DFT calculations and the QM/MM calculations is obtained for both conformational energetics and deprotonation energies in all cases.

High-resolution prediction of protein helix positions and orientations

We have developed a new method for predicting helix positions in globular proteins that is intended primarily for comparative modeling and other applications where high precision is required. Unlike helix packing algorithms designed for ab initio folding, we assume that knowledge is available about the qualitative placement of all helices. However, even among homologous proteins, the corresponding helices can demonstrate substantial differences in positions and orientations, and for this reason, improperly positioned helices can contribute significantly to the overall backbone root‐mean‐square deviation (RMSD) of comparative models. A helix packing algorithm for use in comparative modeling must obtain high precision to be useful, and for this reason we utilize an all‐atom protein force field (OPLS) and a Generalized Born continuum solvent model. To reduce the computational expense associated with using a detailed, physics‐based energy function, we have developed new hierarchical and multiscale algorithms for sampling the helices and flanking loops. We validate the method using a test suite of 33 cases, which are drawn from a diverse set of high‐resolution crystal structures. The helix positions are reproduced with an average backbone RMSD of 0.6 Å, while the average backbone RMSD of the complete loop–helix–loop region (i.e., the helix with the surrounding loops, which are also repredicted) is 1.3 Å. Proteins 2004;55:000–000.

A computationally inexpensive modification of the point dipole electrostatic polarization model for molecular simulations

We present an approximation, which allows reduction of computational resources needed to explicitly incorporate electrostatic polarization into molecular simulations utilizing empirical force fields. The proposed method is employed to compute three‐body energies of molecular complexes with dipolar electrostatic probes, gas‐phase dimerization energies, and pure liquid properties for five systems that are important in biophysical and organic simulations—water, methanol, methylamine, methanethiol, and acetamide. In all the cases, the three‐body energies agreed with high level ab initio data within 0.07 kcal/mol, dimerization energies—within 0.43 kcal/mol (except for the special case of the CH3SH), and computed heats of vaporization and densities differed from the experimental results by less than 2%. Moreover, because the presented method allows a significant reduction in computational cost, we were able to carry out the liquid‐state calculations with Monte Carlo technique. Comparison with the full‐scale point dipole method showed that the computational time was reduced by 3.5 to more than 20 times, depending on the system in hand and on the desired level of the full‐scale model accuracy, while the difference in energetic results between the full‐scale and the presented approximate model was not great in the most cases. Comparison with the nonpolarizable OPLS‐AA force field for all the substances involved and with the polarizable POL3 and q90 models for water and methanol, respectively, demonstrates that the presented technique allows reduction of computational cost with no sacrifice of accuracy. We hope that the proposed method will be of benefit to research employing molecular modeling technique in the biophysical and physical organic chemistry areas.

Computational methods for protein folding

Statistical Analysis of Protein Folding Kinetics (A. Dinner, et al). Insights into Specific Problems in Protein Folding Using Simple Concepts (D. Thirumalai, et al.). Protein Recognition by Sequence--to--Structure Fitness: Bridging Efficiency and Capacity of Threading Models (J. Meller and R. Elber). A Unified Approach to the Prediction of Protein Structure and Function (J. Skolnick and A. Kolinski). Knowledge--Based Prediction of Protein Tertiary Structure (P. LHeureux, et al.). Ab Initio Protein Structure Prediction Using a Size--Dependent Tertiary Folding Potential (V. Eyrich, et al.). Deterministic Global Optimization and Ab Initio Approaches for the Structure Prediction of Polypeptides, Dynamics of Protein Folding, and Protein--Protein Interactions (J. Klepeis, et al.). Detecting Native Protein Folds Among Large Decoy Sites with the OPLS All--Atom Potential and the Surface Generalized Born Solvent Model (A. Wallqvist, et al.). Author Index. Subject Index.

Efficient pseudospectral methods for density functional calculations

Novel improvements of the pseudospectral method for assembling the Coulomb operator are discussed. These improvements consist of a fast atom centered multipole method and a variation of the Head–Gordan J-engine analytic integral evaluation. The details of the methodology are discussed and performance evaluations presented for larger molecules within the context of DFT energy and gradient calculations.