Mark A. DePristo

Simultaneous determination of protein structure and dynamics

We present a protocol for the experimental determination of ensembles of protein conformations that represent simultaneously the native structure and its associated dynamics. The procedure combines the strengths of nuclear magnetic resonance spectroscopy—for obtaining experimental information at the atomic level about the structural and dynamical features of proteins—with the ability of molecular dynamics simulations to explore a wide range of protein conformations. We illustrate the method for human ubiquitin in solution and find that there is considerable conformational heterogeneity throughout the protein structure. The interior atoms of the protein are tightly packed in each individual conformation that contributes to the ensemble but their overall behaviour can be described as having a significant degree of liquid-like character. The protocol is completely general and should lead to significant advances in our ability to understand and utilize the structures of native proteins.

Ab Initio Construction of Polypeptide Fragments: Efficient Generation of Accurate, Representative Ensembles

We describe a novel method to generate ensembles of conformations of the main‐chain atoms {N, Cα, C, O, Cβ} for a sequence of amino acids within the context of a fixed protein framework. Each conformation satisfies fundamental stereo‐chemical restraints such as idealized geometry, favorable ϕ/ψ angles, and excluded volume. The ensembles include conformations both near and far from the native structure. Algorithms for effective conformational sampling and constant time overlap detection permit the generation of thousands of distinct conformations in minutes. Unlike previous approaches, our method samples dihedral angles from fine‐grained ϕ/ψ state sets, which we demonstrate is superior to exhaustive enumeration from coarse ϕ/ψ sets. Applied to a large set of loop structures, our method samples consistently near‐native conformations, averaging 0.4, 1.1, and 2.2 Å main‐chain root‐mean‐square deviations for four, eight, and twelve residue long loops, respectively. The ensembles make ideal decoy sets to assess the discriminatory power of a selection method. Using these decoy sets, we conclude that quality of anchor geometry cannot reliably identify near‐native conformations, though the selection results are comparable to previous loop prediction methods. In a subsequent study (de Bakker et al.: Proteins 2003;51:21–40), we demonstrate that the AMBER forcefield with the Generalized Born solvation model identifies near‐native conformations significantly better than previous methods. Proteins 2003;51:41–55.

Ab Initio Construction of Polypeptide Fragments: Accuracy of Loop Decoy Discrimination by an All-Atom Statistical Potential and the AMBER Force Field With the Generalized Born Solvation Model

The accuracy of model selection from decoy ensembles of protein loop conformations was explored by comparing the performance of the Samudrala–Moult all‐atom statistical potential (RAPDF) and the AMBER molecular mechanics force field, including the Generalized Born/surface area solvation model. Large ensembles of consistent loop conformations, represented at atomic detail with idealized geometry, were generated for a large test set of protein loops of 2 to 12 residues long by a novel ab initio method called RAPPER that relies on fine‐grained residue‐specific phi/psi propensity tables for conformational sampling. Ranking the conformers on the basis of RAPDF scores resulted in selected conformers that had an average global, non‐superimposed RMSD for all heavy mainchain atoms ranging from 1.2 Å for 4‐mers to 2.9 Å for 8‐mers to 6.2 Å for 12‐mers. After filtering on the basis of anchor geometry and RAPDF scores, ranking by energy minimization of the AMBER/GBSA potential energy function selected conformers that had global RMSD values of 0.5 Å for 4‐mers, 2.3 Å for 8‐mers, and 5.0 Å for 12‐mers. Minimized fragments had, on average, consistently lower RMSD values (by 0.1 Å) than their initial conformations. The importance of the Generalized Born solvation energy term is reflected by the observation that the average RMSD accuracy for all loop lengths was worse when this term is omitted. There are, however, still many cases where the AMBER gas‐phase minimization selected conformers of lower RMSD than the AMBER/GBSA minimization. The AMBER/GBSA energy function had better correlation with RMSD to native than the RAPDF. When the ensembles were supplemented with conformations extracted from experimental structures, a dramatic improvement in selection accuracy was observed at longer lengths (average RMSD of 1.3 Å for 8‐mers) when scoring with the AMBER/GBSA force field. This work provides the basis for a promising hybrid approach of ab initio and knowledge‐based methods for loop modeling. Proteins 2003;51:21–40.

Is one solution good enough

VOLUME 13 NUMBER 3 MARCH 2006 NATURE STRUCTURAL & MOLECULAR BIOLOGY To the Editor: Three-dimensional structures of proteins, nucleic acids and other macromolecules are central to understanding biology. They provide a basis for understanding catalytic mechanisms, ligand binding and interactions in multicomponent assemblies. Macromolecular structures are essential for modeling of such phenomena as molecular dynamics and docking of ligands. They are also the basis for virtual screening in lead discovery and lead optimization in drug, vaccine and agrochemical design. In macromolecular crystallography, it is conventional to represent the conformation of a macromolecule as a single structure unless strong evidence is available for specific alternative conformations. This convention unfortunately results in little indication of either accuracy or conformational heterogeneity in the crystal structures deposited in the Protein Data Bank (PDB)1. It leaves the users of crystallographic structures in a difficult situation, as they are not able to quantify the uncertainties in any calculations that make use of these structures. Users of crystallographic structures can attempt to identify atoms that have high uncertainty or heterogeneity using indirect evidence such as high values of atomic displacement parameters (B-factors), implausible geometric features and low local correlations of model and electron density. None of these approaches, however, gives a direct measure of the uncertainty in the model or the heterogeneity present in the crystal. A more suitable representation of a macromolecular crystal structure would be an ensemble of models. The range of structures in the ensemble would represent the range of structures that should be considered by any user of the structural information. There is precedent for this representation of a protein structure, most notably from the field of NMR, where structural ensembles are routinely deposited, but also from molecular dynamics and from within the field of crystallography itself through the study of static ensembles2–4. The ever-increasing computational processing power available, combined with the pre-existing and emerging automated methods5,6 for structure determination, principally driven by the structural genomics initiatives, means the production of collections of models is now a realistic and relatively effortless procedure. Although structure determination, deposition and subsequent analysis of X-ray crystal structures have largely been conducted using single models, multiple conformers have occasionally been deposited in the PDB1. It is ironic that coordinates for multiple conformers are submitted principally for high-resolution datasets, where there is the least disorder. This is of course because more parameters are required to define multiple conformers and their definition requires more experimental observations or higher resolution. Nevertheless, the structures that would most benefit from multiplemodel descriptions are those at medium or low resolution, which typically have multiple conformers occurring over space or time, and for which the uncertainty in placing atomic coordinates is highest. A crystallographic ensemble can represent one of two possibilities. First, there may be several individual structures that are equally compatible with the data when considered one at a time; these can be thought of as describing the uncertainty of the experimental data. Second, it can represent spatial heterogeneity and dynamics, showing a set of structures that, taken over time and across the different unit cells, are compatible with the data. Obviously, such ensembles can reflect aspects of both factors, and at present we are unable to distinguish between the two, but in any case the collection demonstrates the inappropriateness of specification of a model as a single species. We urge those producing crystallographic models to deposit an ensemble of solutions wherever possible. At a practical level, the deposition procedure would require only minor modifications, because many of the processes for handling model ensembles already exist for NMR. A ‘best’ model can be presented by the depositor, separate from the ensemble; this can be either a composite of the ensemble members or the single member that has the best fit to the experimental data as assessed either by standard crystallographic measures or by methods similar to those used by the NMR community, that is, a mean structure that is then subjected to energy minimization or the closest structure to the centroid of the clustered ensemble7. The method by which the ensembles were produced should also be noted, as this may affect which of the two types of ensembles is presented. For example, if a real-space model generation and refinement protocol is used to fit conformers one at a time into the same experimental map, then the individual members of the resultant ensemble may all be approximately equally compatible with the data, and their differences may primarily reflect experimental uncertainty. By contrast, if the models are fit as a group to the data, then the variation among models may also reflect spatial heterogeneity or dynamics. Providing a range of models allows a measure of confidence to be taken into account when carrying out any calculations on a structure. This is particularly relevant for mediumand lower-resolution structures, where the uncertainty, and possibly the heterogeneity as well, cannot be accounted for by exploring only the very local energy landscape represented by the B-factor model, but requires a more global exploration of the conformational landscape. We note that the use of multiple models allows a fuller and potentially more accurate representation of the true underlying structure than does a single model8. The availability of crystallographic ensemble data would have a considerable impact on all structural studies by providing a more rigorous framework to evaluate the certainty of structure-based inferences. Such ensembles would be especially valuable in structural bioinformatics and rational drug design. For example, they would alter how local environments around residues9 are calculated and considered; this would have an impact on structural alignments, fold recognition, prediction of protein-protein interactions and docking. An ensemble of conformations should Is one solution good enough? CO R R E S P O N D E N C E

Discrete restraint‐based protein modeling and the Cα‐trace problem

We present a novel de novo method to generate protein models from sparse, discretized restraints on the conformation of the main chain and side chain atoms. We focus on Cα‐trace generation, the problem of constructing an accurate and complete model from approximate knowledge of the positions of the Cα atoms and, in some cases, the side chain centroids. Spatial restraints on the Cα atoms and side chain centroids are supplemented by constraints on main chain geometry, φ/ξ angles, rotameric side chain conformations, and inter‐atomic separations derived from analyses of known protein structures. A novel conformational search algorithm, combining features of tree‐search and genetic algorithms, generates models consistent with these restraints by propensity‐weighted dihedral angle sampling. Models with ideal geometry, good φ/ξ angles, and no inter‐atomic overlaps are produced with 0.8 Å main chain and, with side chain centroid restraints, 1.0 Å all‐atom root‐mean‐square deviation (RMSD) from the crystal structure over a diverse set of target proteins. The mean model derived from 50 independently generated models is closer to the crystal structure than any individual model, with 0.5 Å main chain RMSD under only Cα restraints and 0.7 Å all‐atom RMSD under both Cα and centroid restraints. The method is insensitive to randomly distributed errors of up to 4 Å in the Cα restraints. The conformational search algorithm is efficient, with computational cost increasing linearly with protein size. Issues relating to decoy set generation, experimental structure determination, efficiency of conformational sampling, and homology modeling are discussed.