All-atom Statistical Potential Research Articles

Computational Protocol for Assessing the Optimal Pixel Size to Improve the Accuracy of Single-particle Cryo-electron Microscopy Maps.

Cryo-electron microscopy (cryo-EM) single-particle analysis has come a long way in achieving atomic-level resolution when imaging biomolecules. To obtain the best possible three-dimensional (3D) structure in cryo-EM, many parameters have to be carefully considered. Here we address the often-overlooked parameter of the pixel size, which describes the magnification of the image produced by the experiment. While efforts are made to refine and validate this parameter in the analysis of cryo-EM experimental data, there is no systematic protocol in place. Since the pixel size parameter can have an impact on the resolution and accuracy of a cryo-EM map, and the atomic resolution 3D structure models derived from it, we propose a computational protocol to estimate the appropriate pixel size parameter. In our protocol, we fit and refine atomic structures against cryo-EM maps at multiple pixel sizes. The resulting fitted and refined structures are evaluated using the GOAP (generalized orientation-dependent, all-atom statistical potential) score, which we found to perform better than other commonly used functions, such as Molprobity and the correlation coefficient from refinement. Finally, we describe the efficacy of this protocol in retrieving appropriate pixel sizes for several examples; simulated data based on yeast elongation factor 2 and experimental data from Gro-EL chaperone, beta-galactosidase, and the TRPV1 ion channel.

OPUS-DOSP: A Distance- and Orientation-Dependent All-Atom Potential Derived from Side-Chain Packing

We report a new distance- and orientation-dependent, all-atom statistical potential derived from side-chain packing, named OPUS-DOSP, for protein structure modeling. The framework of OPUS-DOSP is based on OPUS-PSP, previously developed by us [JMB (2008), 376, 288–301], with refinement and new features. In particular, distance or orientation contribution is considered depending on the range of contact distance. A new auxiliary function in energy function is also introduced, in addition to the traditional Boltzmann term, in order to adjust the contributions of extreme cases. OPUS-DOSP was tested on 11 decoy sets commonly used for statistical potential benchmarking. Among 278 native structures, 239 and 249 native structures were recognized by OPUS-DOSP without and with the auxiliary function, respectively. The results show that OPUS-DOSP has an increased decoy recognition capability comparing with those of other relevant potentials to date.

GOAP: A Generalized Orientation-Dependent, All-Atom Statistical Potential for Protein Structure Prediction

An accurate scoring function is a key component for successful protein structure prediction. To address this important unsolved problem, we develop a generalized orientation and distance-dependent all-atom statistical potential. The new statistical potential, generalized orientation-dependent all-atom potential (GOAP), depends on the relative orientation of the planes associated with each heavy atom in interacting pairs. GOAP is a generalization of previous orientation-dependent potentials that consider only representative atoms or blocks of side-chain or polar atoms. GOAP is decomposed into distance- and angle-dependent contributions. The DFIRE distance-scaled finite ideal gas reference state is employed for the distance-dependent component of GOAP. GOAP was tested on 11 commonly used decoy sets containing 278 targets, and recognized 226 native structures as best from the decoys, whereas DFIRE recognized 127 targets. The major improvement comes from decoy sets that have homology-modeled structures that are close to native (all within ∼4.0 Å) or from the ROSETTA ab initio decoy set. For these two kinds of decoys, orientation-independent DFIRE or only side-chain orientation-dependent RWplus performed poorly. Although the OPUS-PSP block-based orientation-dependent, side-chain atom contact potential performs much better (recognizing 196 targets) than DFIRE, RWplus, and dDFIRE, it is still ∼15% worse than GOAP. Thus, GOAP is a promising advance in knowledge-based, all-atom statistical potentials. GOAP is available for download at http://cssb.biology.gatech.edu/GOAP.

Explicit Orientation Dependence in Empirical Potentials and Its Significance to Side-Chain Modeling

Protein structure modeling and prediction have important applications throughout the biological sciences, from the design of pharmaceuticals to the elucidation of enzyme mechanisms. At the core of most protein modeling is an energy function, the minimum of which represents the free energy "cost" for forming a correct protein structure. The most commonly used energy functions are knowledge-based statistical potential functions; that is, they are empirically derived from statistical analysis of a set of high-resolution protein structures. When that kind of potential function is constructed, the anisotropic orientation dependence between the interacting groups is a critical component for accurately representing key molecular interactions, such as those involved in protein side-chain packing. In the literature, however, many potential functions are limited in their ability to describe orientation dependence. In all-atom potentials, they typically ignore heterogeneous chemical-bond connectivity. In coarse-grained potentials, such as (semi)-residue-based potentials, the simplified representation of residues often reduces the sensitivity of the potential to side-chain orientation. Recently, in an effort to maximally capture the orientation dependence in side-chain interactions, a new type of all-atom statistical potential was developed: OPUS-PSP (potential derived from side-chain packing). The key feature of this potential is its explicit description of orientation dependence in molecular interactions, which is achieved with a basis set of 19 rigid-body blocks extracted from the chemical structures of 20 amino acid residues. This basis set is specifically designed to maximally capture the essential elements of orientation dependence in molecular packing interactions. The potential is constructed from the orientation-specific packing statistics of pairs of those blocks in a nonredundant structural database. On decoy set tests, OPUS-PSP significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and its consistency in achieving high Z scores across decoy sets. The application of OPUS-PSP to conformational modeling of side chains has led to another method, called OPUS-Rota. In terms of combined speed and accuracy, OPUS-Rota outperforms all of the other methods in modeling side-chain conformation. In this Account, we briefly outline the basic scheme of the OPUS-PSP potential and its application to side-chain modeling via OPUS-Rota. Future perspectives on the modeling of orientation dependence are also discussed. The computer programs for OPUS-PSP and OPUS-Rota can be downloaded at http://sigler.bioch.bcm.tmc.edu/MaLab . They are free for academic users.

Fold prediction of VP24 protein of Ebola and Marburg viruses using de novo fragment assembly

Virus particle 24 (VP24) is the smallest protein of the Ebola and Marburg virus genomes. Recent experiments show that Ebola VP24 blocks binding of tyrosine-phosphorylated STAT-1 homodimer (PY-STAT1) to the NPI-1 subfamily of importin alpha, thereby preventing nuclear accumulation of this interferon-promoting transcription factor which, in turn, reduces the innate immune response of the host target. Lacking an experimental structure for VP24, we applied de novo protein structure prediction using the fragment assembly-based Rosetta method to classify its fold topology and better understand its biological function. Filtering and ranking of models were performed with the DFIRE all-atom statistical potential and the CHARMM22 force field with a generalized Born solvent model. From 40,000 Rosetta-generated structures and selective comparisons with the SCOP database, a structural match to two of our top 10-ranking models was the Armadillo repeat fold topology. Specific members of this fold family include importin alpha, importin beta, and exportin. We propose that, unlike the nuclear import of host cargo, VP24 lacks a classical nuclear localization signal (NLS) and targets importin alpha in a similar manner to the observed heterodimeric complex with exportin, thereby interfering with the auto-inhibitory NLS on importin alpha and blocking peripheral docking sites for PY-STAT1 assembly.

Reduced Cβstatistical potentials can outperform all-atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.

Minimalist Representations and the Importance of Nearest Neighbor Effects in Protein Folding Simulations

In order to investigate the level of representation required to simulate folding and predict structure, we test the ability of a variety of reduced representations to identify native states in decoy libraries and to recover the native structure given the advanced knowledge of the very broad native Ramachandran basin assignments. Simplifications include the removal of the entire side-chain or the retention of only the C β atoms. Scoring functions are derived from an all-atom statistical potential that distinguishes between atoms and different residue types. Structures are obtained by minimizing the scoring function with a computationally rapid simulated annealing algorithm. Results are compared for simulations in which backbone conformations are sampled from a Protein Data Bank-based backbone rotamer library generated by either ignoring or including a dependence on the identity and conformation of the neighboring residues. Only when the C β atoms and nearest neighbor effects are included do the lowest energy structures generally fall within 4 Å of the native backbone root-mean square deviation (RMSD), despite the initial configuration being highly expanded with an average RMSD ≥ 10 Å. The side-chains are reinserted into the C β models with minimal steric clash. Therefore, the detailed, all-atom information lost in descending to a C β-level representation is recaptured to a large measure using backbone dihedral angle sampling that includes nearest neighbor effects and an appropriate scoring function.

Characterization of the Structure of RAMP1 by Mutagenesis and Molecular Modeling

Receptor activity modifying proteins (RAMPs) are a family of single-pass transmembrane proteins that dimerize with G-protein-coupled receptors. They may alter the ligand recognition properties of the receptors (particularly for the calcitonin receptor-like receptor, CLR). Very little structural information is available about RAMPs. Here, an ab initio model has been generated for the extracellular domain of RAMP1. The disulfide bond arrangement (Cys 27-Cys 82, Cys 40-Cys 72, and Cys 57-Cys 104) was determined by site-directed mutagenesis. The secondary structure ( α-helices from residues 29–51, 60–80, and 87–100) was established from a consensus of predictive routines. Using these constraints, an assemblage of 25,000 structures was constructed and these were ranked using an all-atom statistical potential. The best 1000 conformations were energy minimized. The lowest scoring model was refined by molecular dynamics simulation. To validate our strategy, the same methods were applied to three proteins of known structure; PDB:1HP8, PDB:1V54 chain H (residues 21–85), and PDB:1T0P. When compared to the crystal structures, the models had root mean-square deviations of 3.8 Å, 4.1 Å, and 4.0 Å, respectively. The model of RAMP1 suggested that Phe 93, Tyr 100, and Phe 101 form a binding interface for CLR, whereas Trp 74 and Phe 92 may interact with ligands that bind to the CLR/RAMP1 heterodimer.

Accurate and efficient loop selections by the DFIRE-based all-atom statistical potential.

The conformations of loops are determined by the water-mediated interactions between amino acid residues. Energy functions that describe the interactions can be derived either from physical principles (physical-based energy function) or statistical analysis of known protein structures (knowledge-based statistical potentials). It is commonly believed that statistical potentials are appropriate for coarse-grained representation of proteins but are not as accurate as physical-based potentials when atomic resolution is required. Several recent applications of physical-based energy functions to loop selections appear to support this view. In this article, we apply a recently developed DFIRE-based statistical potential to three different loop decoy sets (RAPPER, Jacobson, and Forrest-Woolf sets). Together with a rotamer library for side-chain optimization, the performance of DFIRE-based potential in the RAPPER decoy set (385 loop targets) is comparable to that of AMBER/GBSA for short loops (two to eight residues). The DFIRE is more accurate for longer loops (9 to 12 residues). Similar trend is observed when comparing DFIRE with another physical-based OPLS/SGB-NP energy function in the large Jacobson decoy set (788 loop targets). In the Forrest-Woolf decoy set for the loops of membrane proteins, the DFIRE potential performs substantially better than the combination of the CHARMM force field with several solvation models. The results suggest that a single-term DFIRE-statistical energy function can provide an accurate loop prediction at a fraction of computing cost required for more complicate physical-based energy functions. A Web server for academic users is established for loop selection at the softwares/services section of the Web site http://theory.med.buffalo.edu/.