Prediction of NMR order parameters in proteins using weighted protein contact-number model

In the NMR experiment, the protein backbone motion can be described by the N–H order parameters. Though protein dynamics is determined by a complex network of atomic interactions, we show that the order parameter of residues can be determined using a very simple method, the weighted protein contact number model. We computed for each Cα atom the number of neighboring Cα atoms weighted by the inverse distance squared between them. We show that the weighted contact number of each residue is directly related to its order parameter. Despite the simplicity of this model, it performs better than the other method. Since we can compute the order parameters directly from the topological properties (such as protein contact number) of protein structures, our study underscores a very direct link between protein topological structure and its dynamics.     

Exploring experimental sources of multiple protein conformations in structure-based drug design

Receptor flexibility must be incorporated into structure-based drug design in order to portray a more accurate representation of a protein in solution. Our approach is to generate pharmacophore models based on multiple conformations of a protein and is very similar to solvent mapping of hot spots. Previously, we had success using computer-generated conformations of apo human immunodeficiency virus-1 protease (HIV-1p). Here, we examine the use of an NMR ensemble versus a collection of crystal structures, and we compare back to our previous study based on computer-generated conformations. To our knowledge, this is the first direct comparison of an NMR ensemble and a collection of crystal structures to incorporate protein flexibility in structure-based drug design. To provide an accurate comparison between the experimental sources, we used bound structures for our multiple protein structure (MPS) pharmacophore models. The models from an NMR ensemble and a collection of crystal structures were both able to discriminate known HIV-1p inhibitors from decoy molecules and displayed superior performance over models created from single conformations of the protein. Although the active-site conformations were already predefined by bound ligands, the use of MPS allows us to overcome the cross-docking problem and generate a model that does not simply reproduce the chemical characteristics of a specific ligand class. We show that there is more structural variation between 28 structures in an NMR ensemble than 90 crystal structures bound to a variety of ligands. MPS models from both sources performed well, but the model determined using the NMR ensemble appeared to be the most general yet accurate representation of the active site. This work encourages the use of NMR models in structure-based design.     

The elastic net algorithm and protein structure prediction

Predicting protein structures from their amino acid sequences is a problem of global optimization. Global optima (native structures) are often sought using stochastic sampling methods such as Monte Carlo or molecular dynamics, but these methods are slow. In contrast, there are fast deterministic methods that find near-optimal solutions of well-known global optimization problems such as the traveling salesman problem (TSP). But fast TSP strategies have yet to be applied to protein folding, because of fundamental differences in the two types of problems. Here, we show how protein folding can be framed in terms of the TSP, to which we apply a variation of the Durbin-Willshaw elastic net optimization strategy. We illustrate using a simple model of proteins with database-derived statistical potentials and predicted secondary structure restraints. This optimization strategy can be applied to many different models and potential functions, and can readily incorporate experimental restraint information. It is also fast; with the simple model used here, the method finds structures that are within 5-6 A all-Calpha-atom RMSD of the known native structures for 40-mers in about 8 s on a PC; 100-mers take about 20 s. The computer time tau scales as tau approximately n, where n is the number of amino acids. This method may prove to be useful for structure refinement and prediction.     

Conserved network properties of helical membrane protein structures and its implication for improving membrane protein homology modeling at the twilight zone

Homology modeling techniques remain an important tool for membrane protein studies and membrane protein-targeted drug development. Due to the paucity of available structure data, an imminent challenge in this field is to develop novel computational methods to help improve the quality of the homology models constructed using template proteins with low sequence identity. In this work, we attempted to address this challenge using the network approach developed in our group. First, a structure pair dataset of 27 high-resolution and low sequence identity (7–36%) comparative TM proteins was compiled by analyzing available X-ray structures of helical membrane proteins. Structure deviation between these pairs was subsequently confirmed by calculating their backbone RMSD and comparing their potential energy per residue. Next, this dataset was further studied using the network approach. Results of these analyses indicated that the network measure applied represents a conserved feature of TM domains of similar folds with various sequence identities. Further comparison of this salient feature between high-resolution template structures and their homology models at the twilight zone suggested a useful method to utilize this property for homology model refinement. These findings should be of help for improving the quality of homology models based on templates with low sequence identity, thus broadening the application of homology modeling techniques in TM protein studies.     

PCASSO: A fast and efficient Cα‐based method for accurately assigning protein secondary structure elements

Proteins are often characterized in terms of their primary, secondary, tertiary, and quaternary structure. Algorithms such as define secondary structure of proteins (DSSP) can automatically assign protein secondary structure based on the backbone hydrogen‐bonding pattern. However, the assignment of secondary structure elements (SSEs) becomes a challenge when only the Cα coordinates are available. In this work, we present protein C‐alpha secondary structure output (PCASSO), a fast and accurate program for assigning protein SSEs using only the Cα positions. PCASSO achieves ～95% accuracy with respect to DSSP and takes ～0.1 s using a single processor to analyze a 1000 residue system with multiple chains. Our approach was compared with current state‐of‐the‐art Cα‐based methods and was found to outperform all of them in both speed and accuracy. A practical application is also presented and discussed. © 2014 Wiley Periodicals, Inc.     

Stochastic pairwise alignments and scoring methods for comparative protein structure modeling

Despite recent advances in fold recognition algorithms that identify template structures with distant homology to the target sequence, the quality of the target-template alignment can be a major problem for distantly related proteins in comparative modeling. Here we report for the first time on the use of ensembles of pairwise alignments obtained by stochastic backtracking as a means to improve three-dimensional comparative protein models. In every one of the 35 cases, the ensemble produced by the program probA resulted in alignments that were closer to the structural alignment than those obtained from the optimal alignment. In addition, we examined the lowest energy structure among these ensembles from four different structural assessment methods and compared these with the optimal and structural alignment model. The structural assessment methods consisted of the DFIRE, DOPE, and ProsaII statistical potential energies and the potential energy from the CHARMM protein force field coupled to a Generalized Born implicit solvent model. The results demonstrate that the generation of alignment ensembles through stochastic backtracking using probA combined with one of the statistical potentials for assessing three-dimensional structures can be used to improve comparative models.     

Fast procedure for reconstruction of full-atom protein models from reduced representations

We introduce PULCHRA, a fast and robust method for the reconstruction of full-atom protein models starting from a reduced protein representation. The algorithm is particularly suitable as an intermediate step between coarse-grained model-based structure prediction and applications requiring an all-atom structure, such as molecular dynamics, protein-ligand docking, structure-based function prediction, or assessment of quality of the predicted structure. The accuracy of the method was tested on a set of high-resolution crystallographic structures as well as on a set of low-resolution protein decoys generated by a protein structure prediction algorithm TASSER. The method is implemented as a standalone program that is available for download from http://cssb.biology.gatech.edu/skolnick/files/PULCHRA.     

Topology-based models and NMR structures in protein folding simulations

Topology-based interaction potentials are simplified models that use the native contacts in the folded structure of a protein to define an energetically unfrustrated folding funnel. They have been widely used to analyze the folding transition and pathways of different proteins through computer simulations. Obviously, they need a reliable, experimentally determined folded structure to define the model interactions. In structures elucidated through NMR spectroscopy, a complex treatment of the raw experimental data usually provides a series of models, a set of different conformations compatible with the available experimental data. Here, we use an efficient coarse-grained simulation technique to independently consider the contact maps from every different NMR model in a protein whose structure has been resolved by the use of NMR spectroscopy. For lambda-Cro repressor, a homodimeric protein, we have analyzed its folding characteristics with a topology-based model. We have focused on the competition between the folding of the individual chains and their binding to form the final quaternary structure. From 20 different NMR models, we find a predominant three-state folding behavior, in agreement with experimental data on the folding pathway for this protein. Individual NMR models, however, show distinct characteristics, which are analyzed both at the level of the interplay between tertiary/quaternary structure formation and also regarding the thermal stability of the tertiary structure of every individual chain.     

The importance of short structural motifs in protein structure analysis

Summary Proteins tend to use recurrent structural motifs on all levels of organization. In this paper we first survey the topics of recurrent motifs on the local secondary structure level and on the global fold level. Then, we focus on the intermediate level which we call the short structural motifs. We were able to identify a set of structural building blocks that are very common in protein structure. We suggest that these building blocks can be used as an important link between the primary sequence and the tertiary structure. In this framework, we present our latest results on the structural variability of the extended strand motifs. We show that extended strands can be divided into three distinct structural classes, each with its own sequence specificity. Other approaches to the study of short structural motifs are reviewed.     

Elastic network normal modes provide a basis for protein structure refinement

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.     

A sampling-based method for ranking protein structural models by integrating multiple scores and features

One of the major challenges in protein tertiary structure prediction is structure quality assessment. In many cases, protein structure prediction tools generate good structural models, but fail to select the best models from a huge number of candidates as the final output. In this study, we developed a sampling-based machine-learning method to rank protein structural models by integrating multiple scores and features. First, features such as predicted secondary structure, solvent accessibility and residue-residue contact information are integrated by two Radial Basis Function (RBF) models trained from different datasets. Then, the two RBF scores and five selected scoring functions developed by others, i.e., Opus-CA, Opus-PSP, DFIRE, RAPDF, and Cheng Score are synthesized by a sampling method. At last, another integrated RBF model ranks the structural models according to the features of sampling distribution. We tested the proposed method by using two different datasets, including the CASP server prediction models of all CASP8 targets and a set of models generated by our in-house software MUFOLD. The test result shows that our method outperforms any individual scoring function on both best model selection, and overall correlation between the predicted ranking and the actual ranking of structural quality.     

Assessment of Semiempirical Quantum Mechanical Methods for the Evaluation of Protein Structures

The ability to discriminate native structures from computer-generated misfolded ones is key to predicting the three-dimensional structure of a protein from its amino acid sequence. Here we describe an assessment of semiempirical methods for discriminating native protein structures from decoy models. The discrimination of decoys entails an analysis of a large number of protein structures, and provides a large-scale validation of quantum mechanical methods and their ability to accurately model proteins. We combine our analysis of semiempirical methods with a comparison of an AMBER force field to discriminate decoys in conjunction with a continuum solvent model. Protein decoys provide a rigorous and reliable benchmark for the evaluation of scoring functions, not only in their ability to accurately identify native structures but also to be computationally tractable to sample a large set of non-native models.     

Diffusion models of protein folding

In theory and in the analysis of experiments, protein folding is often described as diffusion along a single coordinate. We explore here the application of a one-dimensional diffusion model to interpret simulations of protein folding, where the parameters of a model that "best" describes the simulation trajectories are determined using a Bayesian analysis. We discuss the requirements for such a model to be a good approximation to the global dynamics, and several methods for testing its accuracy. For example, one test considers the effect of an added bias potential on the fitted free energies and diffusion coefficients. Such a bias may also be used to extend our approach to determining parameters for the model to systems that would not normally explore the full coordinate range on accessible time scales. Alternatively, the propagators predicted from the model at different "lag" times may be compared with observations from simulation. We then present some applications of the model to protein folding, including Kramers-like turnover in folding rates of coarse-grained models, the effect of non-native interactions on folding, and the effect of the chosen coordinate on the observed position-dependence of the diffusion coefficients. Lastly, we consider how our results are useful for the interpretation of experiments, and how this type of Bayesian analysis may eventually be applied directly to analyse experimental data.     

Boltzmann's principle,knowledge-based mean fields and protein folding. An approach to the computational determination of protein structures

Summary The data base of known protein structures contains a tremendous amount of information on protein-solvent systems. Boltzmann's principle enables the extraction of this information in the form of potentials of mean force. The resulting force field constitutes an energetic model for protein-solvent systems. We outline the basic physical principles of this approach to protein folding and summarize several techniques which are useful in the development of knowledge-based force fields. Among the applications presented are the validation of experimentally determined protein structures, data base searches which aim at the identification of native-like sequence structure pairs, sequence structure alignments and the calculation of protein conformations from amino acid sequences.     

Developing a high-quality scoring function for membrane protein structures based on specific inter-residue interactions

Membrane proteins are of particular biological and pharmaceutical importance, and computational modeling and structure prediction approaches play an important role in studies of membrane proteins. Developing an accurate model quality assessment program is of significance to the structure prediction of membrane proteins. Few such programs are proposed that can be applied to a broad range of membrane protein classes and perform with high accuracy. We developed a new model scoring function Interaction-based Quality assessment (IQ), based on the analysis of four types of inter-residue interactions within the transmembrane domains of helical membrane proteins. This function was tested using three high-quality model sets: all 206 models of GPCR Dock 2008, all 284 models of GPCR Dock 2010, and all 92 helical membrane protein models of the HOMEP set. For all three sets, the scoring function can select the native structures among all of the models with the success rates of 93, 85, and 100% respectively. For comparison, these three model sets were also adopted for a recently published model assessment program for membrane protein structures, ProQM, which gave the success rates of 85, 79, and 92% separately. These results suggested that IQ outperforms ProQM when only the transmembrane regions of the models are considered. This scoring function should be useful for the computational modeling of membrane proteins.     

Prediction of homology model quality with multivariate regression

A new method has been developed for prediction of homology model quality directly from the sequence alignment, using multivariate regression. Hence, the expected quality of future homology models can be estimated using only information about the primary structure. This method has been applied to protein kinases and can easily be extended to other protein families. Homology model quality for a reference set of homology models was verified by comparison to experimental structures, by calculation of root-mean-square deviations (RMSDs) and comparison of interresidue contact areas. The homology model quality measures were then used as dependent variables in a Partial Least Squares (PLS) regression, using a matrix of alignment score profiles found from the Point Accepted Mutation (PAM) 250 similarity matrix as independent variables. This resulted in a regression model that can be used to predict the accuracy of future homology models from the sequence alignment. Using this method, one can identify the target-template combinations that are most likely to give homology models of sufficient quality. Hence, this method can be used to effectively choose the optimal templates to use for the homology modeling. The method's ability to guide the choice of homology modeling templates was verified by comparison of success rates to those obtained using BLAST scores and target-template sequence identities, respectively. The results indicate that the method presented here performs best in choosing the optimal homology modeling templates. Using this method, the optimal template was chosen in 86% of the cases, as compared to 62% using BLAST scores, and 57% using sequence identities. The method presented here can also be used to identify regions of the protein structure that are difficult to model, as well as alignment errors. Hence, this method is a useful tool for ensuring that the best possible homology model is generated.     

PROSIGN: a method for protein secondary structure assignment based on three-dimensional coordinates of consecutive C(alpha) atoms

The automatic assignment of secondary structure from three-dimensional atomic coordinates of proteins is an essential step for the analysis and modeling of protein structures. So different methods based on different criteria have been designed to perform this task. We introduce a new method for protein secondary structure assignment based solely on C(alpha) coordinates. We introduce four certain relations between C(alpha) three-dimensional coordinates of consecutive residues, each of which applies to one of the four regular secondary structure categories: alpha-helix, 3(10)-helix, pi-helix and beta-strand. In our approach, the deviation of the C(alpha) coordinates of each residue from each relation is calculated. Based on these deviation values, secondary structures are assigned to all residues of a protein. We show that our method agrees well with popular methods as DSSP, STRIDE and assignments in PDB files. It is shown that our method gives more information about helix geometry leading to more accurate secondary structure assignment.     

Structure determination of a membrane protein in proteoliposomes

An NMR method for determining the three-dimensional structures of membrane proteins in proteoliposomes is demonstrated by determining the structure of MerFt, the 60-residue helix-loop-helix integral membrane core of the 81-residue mercury transporter MerF. The method merges elements of oriented sample (OS) solid-state NMR and magic angle spinning (MAS) solid-state NMR techniques to measure orientation restraints relative to a single external axis (the bilayer normal) from individual residues in a uniformly (13)C/(15)N labeled protein in unoriented liquid crystalline phospholipid bilayers. The method relies on the fast (>10(5) Hz) rotational diffusion of membrane proteins in bilayers to average the static chemical shift anisotropy and heteronuclear dipole-dipole coupling powder patterns to axially symmetric powder patterns with reduced frequency spans. The frequency associated with the parallel edge of such motionally averaged powder patterns is exactly the same as that measured from the single line resonance in the spectrum of a stationary sample that is macroscopically aligned parallel to the direction of the applied magnetic field. All data are collected on unoriented samples undergoing MAS. Averaging of the homonuclear (13)C/(13)C dipolar couplings, by MAS of the sample, enables the use of uniformly (13)C/(15)N labeled proteins, which provides enhanced sensitivity through direct (13)C detection as well as the use of multidimensional MAS solid-state NMR methods for resolving and assigning resonances. The unique feature of this method is the measurement of orientation restraints that enable the protein structure and orientation to be determined in unoriented proteoliposomes.     

Predicting protein-protein interactions using graph invariants and a neural network

The PDZ domain of proteins mediates a protein-protein interaction by recognizing the hydrophobic C-terminal tail of the target protein. One of the challenges put forth by the DREAM (Discussions on Reverse Engineering Assessment and Methods) 2009 Challenge consists of predicting a position weight matrix (PWM) that describes the specificity profile of five PDZ domains to their target peptides. We consider the primary structures of each of the five PDZ domains as a numerical sequence derived from graph-theoretic models of each of the individual amino acids in the protein sequence. Using available PDZ domain databases to obtain known targets, the graph-theoretic based numerical sequences are then used to train a neural network to recognize their targets. Given the challenge sequences, the target probabilities are computed and a corresponding position weight matrix is derived. In this work we present our method. The results of our method placed second in the DREAM 2009 challenge.