A distance-dependent atomic knowledge-based potential for improved protein structure selection

Protein structure prediction by all-atom free-energy refinement

Background

The reliable prediction of protein tertiary structure from the amino acid sequence remains challenging even for small proteins. We have developed an all-atom free-energy protein forcefield (PFF01) that we could use to fold several small proteins from completely extended conformations. Because the computational cost of de-novo folding studies rises steeply with system size, this approach is unsuitable for structure prediction purposes. We therefore investigate here a low-cost free-energy relaxation protocol for protein structure prediction that combines heuristic methods for model generation with all-atom free-energy relaxation in PFF01.

Results

We use PFF01 to rank and cluster the conformations for 32 proteins generated by ROSETTA. For 22/10 high-quality/low quality decoy sets we select near-native conformations with an average C_α root mean square deviation of 3.03 Å/6.04 Å. The protocol incorporates an inherent reliability indicator that succeeds for 78% of the decoy sets. In over 90% of these cases near-native conformations are selected from the decoy set. This success rate is rationalized by the quality of the decoys and the selectivity of the PFF01 forcefield, which ranks near-native conformations an average 3.06 standard deviations below that of the relaxed decoys (Z-score).

Conclusion

All-atom free-energy relaxation with PFF01 emerges as a powerful low-cost approach toward generic de-novo protein structure prediction. The approach can be applied to large all-atom decoy sets of any origin and requires no preexisting structural information to identify the native conformation. The study provides evidence that a large class of proteins may be foldable by PFF01.

A free-rotating and self-avoiding chain model for deriving statistical potentials based on protein structures

Statistical potentials have been widely used in protein studies despite the much-debated theoretical basis. In this work, we have applied two physical reference states for deriving the statistical potentials based on protein structure features to achieve zero interaction and orthogonalization. The free-rotating chain-based potential applies a local free-rotating chain reference state, which could theoretically be described by the Gaussian distribution. The self-avoiding chain-based potential applies a reference state derived from a database of artificial self-avoiding backbones generated by Monte Carlo simulation. These physical reference states are independent of known protein structures and are based solely on the analytical formulation or simulation method. The new potentials performed better and yielded higher Z-scores and success rates compared to other statistical potentials. The end-to-end distance distribution produced by the self-avoiding chain model was similar to the distance distribution of protein atoms in structure database. This fact may partly explain the basis of the reference states that depend on the atom pair frequency observed in the protein database. The current study showed that a more physical reference model improved the performance of statistical potentials in protein fold recognition, which could also be extended to other types of applications.

Near-native structure refinement using in vacuo energy minimization

One of the greatest shortcomings of macromolecular energy minimization and molecular dynamics techniques is that they generally do not preserve the native structure of proteins as observed by x-ray crystallography. This deformation of the native structure means that these methods are not generally used to refine structures produced by homology-modeling techniques. Here, we use a database of 75 proteins to test the ability of a variety of popular molecular mechanics force fields to maintain the native structure. Minimization from the native structure is a weak test of potential energy functions: It is complemented by a much stronger test in which the same methods are compared for their ability to attract a near-native decoy protein structure toward the native structure. We use a powerfully convergent energy-minimization method and show that, of the traditional molecular mechanics potentials tested, only one showed a modest net improvement over a large data set of structurally diverse proteins. A smooth, differentiable knowledge-based pairwise atomic potential performs better on this test than traditional potential functions. This work is expected to have important implications for protein structure refinement, homology modeling, and structure prediction.

Statistical potential for assessment and prediction of protein structures

Protein structures in the Protein Data Bank provide a wealth of data about the interactions that determine the native states of proteins. Using the probability theory, we derive an atomic distance-dependent statistical potential from a sample of native structures that does not depend on any adjustable parameters (Discrete Optimized Protein Energy, or DOPE). DOPE is based on an improved reference state that corresponds to noninteracting atoms in a homogeneous sphere with the radius dependent on a sample native structure; it thus accounts for the finite and spherical shape of the native structures. The DOPE potential was extracted from a nonredundant set of 1472 crystallographic structures. We tested DOPE and five other scoring functions by the detection of the native state among six multiple target decoy sets, the correlation between the score and model error, and the identification of the most accurate non-native structure in the decoy set. For all decoy sets, DOPE is the best performing function in terms of all criteria, except for a tie in one criterion for one decoy set. To facilitate its use in various applications, such as model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling, DOPE was incorporated into the modeling package MODELLER-8.

Development of a Grid-based statistical potential for protein structure prediction

A key component in protein structure prediction is the development of potentials that can discriminate native or near native structures from the wrong ones. Most previously developed statistical potentials are based on the preferred distances between any pair of residues. Here we explore the possible angle dependence between pairs of residues in addition to their distance dependence. For simplicity, we used a grid based partition of the space and analyzed relative geometric propensity between protein residue pairs. One thousand and nine non-redundant protein structures are studied in this paper. We have attached a local coordinate system to each amino acid, and spatial distributions of its nearby residues are investigated. Within the same distance range, there are clear differences in various grids. We have further developed a grid-based statistical potential, which incorporates both the distance dependence and angle dependence using a quasi-chemical approximation. The potential is tested against 32 decoy sets, and in 25 cases the native structure has the best score. This performance is comparable and in two cases better than best performance from previously developed distance-dependent statistical potentials on residue and atom level.

Energetics of protein-DNA interactions

Protein–DNA interactions are vital for many processes in living cells, especially transcriptional regulation and DNA modification. To further our understanding of these important processes on the microscopic level, it is necessary that theoretical models describe the macromolecular interaction energetics accurately. While several methods have been proposed, there has not been a careful comparison of how well the different methods are able to predict biologically important quantities such as the correct DNA binding sequence, total binding free energy and free energy changes caused by DNA mutation. In addition to carrying out the comparison, we present two important theoretical models developed initially in protein folding that have not yet been tried on protein–DNA interactions. In the process, we find that the results of these knowledge-based potentials show a strong dependence on the interaction distance and the derivation method. Finally, we present a knowledge-based potential that gives comparable or superior results to the best of the other methods, including the molecular mechanics force field AMBER99.

A novel high resolution Calpha--Calpha distance dependent force field based on a high quality decoy set

This work presents a novel C(alpha)--C(alpha) distance dependent force field which is successful in selecting native structures from an ensemble of high resolution near-native conformers. An enhanced and diverse protein set, along with an improved decoy generation technique, contributes to the effectiveness of this potential. High quality decoys were generated for 1489 nonhomologous proteins and used to train an optimization based linear programming formulation. The goal in developing a set of high resolution decoys was to develop a simple, distance-dependent force field that yields the native structure as the lowest energy structure and assigns higher energies to decoy structures that are quite similar as well as those that are less similar. The model also includes a set of physical constraints that were based on experimentally observed physical behavior of the amino acids. The force field was tested on two sets of test decoys not in the training set and was found to excel on all the metrics that are widely used to measure the effectiveness of a force field. The high resolution force field was successful in correctly identifying 113 native structures out of 150 test cases and the average rank obtained for this test was 1.87. All the high resolution structures (training and testing) used for this work are available online and can be downloaded from http://titan.princeton.edu/HRDecoys.

PIPER: an FFT-based protein docking program with pairwise potentials

The Fast Fourier Transform (FFT) correlation approach to protein-protein docking can evaluate the energies of billions of docked conformations on a grid if the energy is described in the form of a correlation function. Here, this restriction is removed, and the approach is efficiently used with pairwise interaction potentials that substantially improve the docking results. The basic idea is approximating the interaction matrix by its eigenvectors corresponding to the few dominant eigenvalues, resulting in an energy expression written as the sum of a few correlation functions, and solving the problem by repeated FFT calculations. In addition to describing how the method is implemented, we present a novel class of structure-based pairwise intermolecular potentials. The DARS (Decoys As the Reference State) potentials are extracted from structures of protein-protein complexes and use large sets of docked conformations as decoys to derive atom pair distributions in the reference state. The current version of the DARS potential works well for enzyme-inhibitor complexes. With the new FFT-based program, DARS provides much better docking results than the earlier approaches, in many cases generating 50% more near-native docked conformations. Although the potential is far from optimal for antibody-antigen pairs, the results are still slightly better than those given by an earlier FFT method. The docking program PIPER is freely available for noncommercial applications.

Structural refinement of protein segments containing secondary structure elements: Local sampling, knowledge-based potentials, and clustering

In this article, we present an iterative, modular optimization (IMO) protocol for the local structure refinement of protein segments containing secondary structure elements (SSEs). The protocol is based on three modules: a torsion-space local sampling algorithm, a knowledge-based potential, and a conformational clustering algorithm. Alternative methods are tested for each module in the protocol. For each segment, random initial conformations were constructed by perturbing the native dihedral angles of loops (and SSEs) of the segment to be refined while keeping the protein body fixed. Two refinement procedures based on molecular mechanics force fields - using either energy minimization or molecular dynamics - were also tested but were found to be less successful than the IMO protocol. We found that DFIRE is a particularly effective knowledge-based potential and that clustering algorithms that are biased by the DFIRE energies improve the overall results. Results were further improved by adding an energy minimization step to the conformations generated with the IMO procedure, suggesting that hybrid strategies that combine both knowledge-based and physical effective energy functions may prove to be particularly effective in future applications.

An all-atom, distance-dependent scoring function for the prediction of protein-DNA interactions from structure

We have developed an all-atom statistical potential function for the prediction of protein-DNA interactions from their structures, and show that this method outperforms similar, lower-resolution statistical potentials in a series of decoy discrimination experiments. The all-atom formalism appears to capture details of atomic interactions that are missed by the lower-resolution methods, with the majority of the discriminatory power arising from its description of short-range atomic contacts. We show that, on average, the method is able to identify 90% of near-native docking decoys within the best-scoring 10% of structures in a given decoy set, and it compares favorably with an optimized physical potential function in a test of structure-based identification of DNA binding-sequences. These results demonstrate that all-atom statistical functions specific to protein-DNA interactions can achieve great discriminatory power despite the limited size of the structural database. They also suggest that the statistical scores may soon be able to achieve accuracy on par with more complex, physical potential functions.

Divergence, recombination and retention of functionality during protein evolution

We have only a vague idea of precisely how protein sequences evolve in the context of protein structure and function. This is primarily because structural and functional contexts are not easily predictable from the primary sequence, and evaluating patterns of evolution at individual residue positions is also difficult. As a result of increasing biodiversity in genomics studies, progress is being made in detecting context-dependent variation in substitution processes, but it remains unclear exactly what context-dependent patterns we should be looking for. To address this, we have been simulating protein evolution in the context of structure and function using lattice models of proteins and ligands (or substrates). These simulations include thermodynamic features of protein stability and population dynamics. We refer to this approach as 'ab initio evolution' to emphasise the fact that the equilibrium details of fitness distributions arise from the physical principles of the system and not from any preconceived notions or arbitrary mathematical distributions. Here, we present results on the retention of functionality in homologous recombinants following population divergence. A central result is that protein structure characteristics can strongly influence recombinant functionality. Exceptional structures with many sequence options evolve quickly and tend to retain functionality--even in highly diverged recombinants. By contrast, the more common structures with fewer sequence options evolve more slowly, but the fitness of recombinants drops off rapidly as homologous proteins diverge. These results have implications for understanding viral evolution, speciation and directed evolutionary experiments. Our analysis of the divergence process can also guide improved methods for accurately approximating folding probabilities in more complex but realistic systems.

Empirical potential function for simplified protein models: combining contact and local sequence-structure descriptors

An effective potential function is critical for protein structure prediction and folding simulation. Simplified protein models such as those requiring only Calpha or backbone atoms are attractive because they enable efficient search of the conformational space. We show residue-specific reduced discrete-state models can represent the backbone conformations of proteins with small RMSD values. However, no potential functions exist that are designed for such simplified protein models. In this study, we develop optimal potential functions by combining contact interaction descriptors and local sequence-structure descriptors. The form of the potential function is a weighted linear sum of all descriptors, and the optimal weight coefficients are obtained through optimization using both native and decoy structures. The performance of the potential function in a test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. Our potential function requiring only backbone atoms or Calpha atoms have comparable or better performance than several residue-based potential functions that require additional coordinates of side-chain centers or coordinates of all side-chain atoms. By reducing the residue alphabets down to size 10 for contact descriptors, the performance of the potential function can be further improved. Our results also suggest that local sequence-structure correlation may play important role in reducing the entropic cost of protein folding.

Novel knowledge-based mean force potential at the profile level

Background

The development and testing of functions for the modeling of protein energetics is an important part of current research aimed at understanding protein structure and function. Knowledge-based mean force potentials are derived from statistical analyses of interacting groups in experimentally determined protein structures. Current knowledge-based mean force potentials are developed at the atom or amino acid level. The evolutionary information contained in the profiles is not investigated. Based on these observations, a class of novel knowledge-based mean force potentials at the profile level has been presented, which uses the evolutionary information of profiles for developing more powerful statistical potentials.

Results

The frequency profiles are directly calculated from the multiple sequence alignments outputted by PSI-BLAST and converted into binary profiles with a probability threshold. As a result, the protein sequences are represented as sequences of binary profiles rather than sequences of amino acids. Similar to the knowledge-based potentials at the residue level, a class of novel potentials at the profile level is introduced. We develop four types of profile-level statistical potentials including distance-dependent, contact, Φ/Ψ dihedral angle and accessible surface statistical potentials. These potentials are first evaluated by the fold assessment between the correct and incorrect models generated by comparative modeling from our own and other groups. They are then used to recognize the native structures from well-constructed decoy sets. Experimental results show that all the knowledge-base mean force potentials at the profile level outperform those at the residue level. Significant improvements are obtained for the distance-dependent and accessible surface potentials (5–6%). The contact and Φ/Ψ dihedral angle potential only get a slight improvement (1–2%). Decoy set evaluation results show that the distance-dependent profile-level potentials even outperform other atom-level potentials. We also demonstrate that profile-level statistical potentials can improve the performance of threading.

Conclusion

The knowledge-base mean force potentials at the profile level can provide better discriminatory ability than those at the residue level, so they will be useful for protein structure prediction and model refinement.

A correlation-based method for the enhancement of scoring functions on funnel-shaped energy landscapes

A correlation-based approach is introduced for enhancing the ability of structure-scoring methods to identify and distinguish native-like conformations. The proposed method relies on a funnel-shaped scoring function that decreases steadily toward the native state. It takes advantage of the idea that the structure from a given ensemble that is closest to the native basin leads to the highest correlation coefficient between a given score and distance to that structure as an approximation of the native state for the entire ensemble. The method is applied successfully to a number of different test cases that demonstrate substantial improvements in the correlation of the score with the distance from the true native state but also result in the selection of more native-like structures compared to the original score.

Dynamic domain threading

A modeling method is described that avoids the need to consider the domain structure of the template used for modeling, and automatically extracts compact fragments of structure that would be of a suitable size to build the model. This aids automation as the size or nature of the template structure can be ignored and does not have to be broken into domain (or multi-domain) units beforehand. The approach leads to the generation of a large number of models each based on slightly differing domain definitions and this variation was further increased by considering alternative secondary structure predictions. Each model, of which there may be thousands, takes the form of a complete alpha-carbon trace and some methods (including residue burial) were investigated for their power to discriminate good models from bad models using decoys. The method is also compared to an earlier retroviral capsid modeling problem for which the X-ray structure is now known. Some potential extensions of the approach to more distant modeling problems are discussed.

Atomically detailed potentials to recognize native and approximate protein structures

Atomically detailed potentials for recognition of protein folds are presented. The potentials consist of pair interactions between atoms. One or three distance steps are used to describe the range of interactions between a pair. Training is carried out with the mathematical programming approach on the decoy sets of Baker, Levitt, and some of our own design. Recognition is required not only for decoy-native structural pairs but also for pairs of decoy and homologous structures. Performance is tested on the targets of CASP5 using templates from the Protein Data Bank, on two test ab initio decoy sets from Skolnick's laboratory, and on decoy sets from Moult's laboratory. We conclude that the newly derived potentials have significant recognition capacity, comparable to the best models derived from other techniques. The new potentials require a significantly smaller number of parameters. The enhanced recognition capacity extends primarily to the identification of structures generated by ab initio simulation and less to the recognition of approximate shapes created by homology.

A knowledge-based scoring function based on residue triplets for protein structure prediction

One of the general paradigms for ab initio protein structure prediction involves sampling the conformational space such that a large set of decoy (candidate) structures are generated and then selecting native-like conformations from those decoys using various scoring functions. In this study, based on a physical/geometric approach first suggested by Banavar and colleagues, we formulate a knowledge-based scoring function, which uses the radii of curvature formed among triplets of residues in a protein conformation. By analyzing its performance on various decoy sets, we determine a good set of parameters--the distance cutoff and the number of distance bins--to use for configuring such a function. Furthermore, we investigate the effect of using various approaches for compiling the prior distribution on the performance of the knowledge-based function. Possible extensions to the current form of the residue triplet scoring function are discussed.

Protein refolding in silico with atom-based statistical potentials and conformational search using a simple genetic algorithm

A distance-dependent atom-pair potential that treats long range and local interactions separately has been developed and optimized to distinguish native protein structures from sets of incorrect or decoy structures. Atoms are divided into 30 types based on chemical properties and relative position in the amino acid side-chains. Several parameters affecting the calculation and evaluation of this statistical potential, such as the reference state, the bin width, cutoff distances between pairs, and the number of residues separating the atom pairs, are adjusted to achieve the best discrimination. The native structure has the lowest energy for 39 of the 40 sets of original ROSETTA decoys (1000 structures per set) and 23 of the 25 improved decoys (approximately 1900 structures per set). Combined with the orientation-dependent backbone hydrogen bonding potential used by ROSETTA and a statistical solvation potential based on the solvent exclusion model of Lazaridis & Karplus, this potential is used as a scoring function for conformational search based on a genetic algorithm method. After unfolding the native structure by changing every phi and psi angle by either +/-3, +/-5 or +/-7 degrees, five small proteins can be efficiently refolded, in some cases to within 0.5 A C(alpha) distance matrix error (DME) to the native state. Although no significant correlation is found between the total energy and structural similarity to the native state, a surprisingly strong correlation exists between the radius of gyration and the DME for low energy structures.

Improvement of statistical potentials and threading score functions using information maximization

We show that statistical potentials and threading score functions, derived from finite data sets, are informatic functions, and that their performance depends on the manner in which data are classified and compressed. The choice of sequence and structural parameters affects estimates of the conditional probabilities P(C|S), the quantification of the effect of sequence S on conformation C, and determines the amount of information extracted from the data set, as measured by information gain. The mathematical link between information gain and mean conformational energy, established in this work using the local backbone potential as model, demonstrates that manipulation of descriptive parameters also alters the "energy" values assigned to native conformation and to decoy structures in the test pool, and consequently, the performance of such statistical potential functions in fold recognition exercises. We show that sequence and structural partitions that maximize information gain also minimize the mean energy of the ensemble of native conformations. Moreover, we establish an informatic basis for the placement of the native score within an energy spectrum given by the decoy pool in a threading exercise. We discover that, among all informatic quantities, information gain is the best predictor of threading success, even better than the standard Z-score. Consequently, the choices of sequence and structural descriptors, extent of compression, and levels of discretization that maximize information gain must also produce the best potential functions. Strategies to optimize these parameters with respect to information extraction are therefore relevant to building better statistical potentials. Last, we demonstrate that the backbone torsion potential, defined by the trimer sequence, can be an effective tool in greatly reducing the set of possible conformations from a vast decoy pool.

SSALN: an alignment algorithm using structure-dependent substitution matrices and gap penalties learned from structurally aligned protein pairs

In template-based modeling of protein structures, the generation of the alignment between the target and the template is a critical step that significantly affects the accuracy of the final model. This paper proposes an alignment algorithm SSALN that learns substitution matrices and position-specific gap penalties from a database of structurally aligned protein pairs. In addition to the amino acid sequence information, secondary structure and solvent accessibility information of a position are used to derive substitution scores and position-specific gap penalties. In a test set of CASP5 targets, SSALN outperforms sequence alignment methods such as a Smith-Waterman algorithm with BLOSUM50 and PSI_BLAST. SSALN also generates better alignments than PSI_BLAST in the CASP6 test set. LOOPP server prediction based on an SSALN alignment is ranked the best for target T0280_1 in CASP6. SSALN is also compared with several threading methods and sequence alignment methods on the ProSup benchmark. SSALN has the highest alignment accuracy among the methods compared. On the Fischer's benchmark, SSALN performs better than CLUSTALW and GenTHREADER, and generates more alignments with accuracy >50%, >60% or >70% than FUGUE, but fewer alignments with accuracy >80% than FUGUE. All the supplemental materials can be found at http://www.cs.cornell.edu/ approximately jianq/research.htm.

The victor/FRST function for model quality estimation

Scoring functions are widely used in the final step of model selection in protein structure prediction. This is of interest both for comparative modeling targets, where it is important to select the best model among a set of many good, "correct" ones, as well as for other (fold recognition or novel fold) targets, where the set may contain many incorrect models. A novel combination of four knowledge-based potentials recognizing different features of native protein structures is introduced and tested. The pairwise, solvation, hydrogen bond, and torsion angle potentials contain largely orthogonal information. Of these, the torsion angle potential is found to show the strongest correlation with model quality. Combining these features with a linear weighting function, it was possible to construct a robust energy function capable of discriminating native-like structures on several benchmarking sets. In a recent blind test (CAFASP-4 MQAP), the scoring function ranked consistently well and was able to reliably distinguish the correct template from an ensemble of high quality decoys in 52 of 70 cases (33 of 34 for comparative modeling). An executable version of the Victor/FRST function for Linux PCs is available for download from the URL http://protein.cribi.unipd.it/frst/.

A new generation of statistical potentials for proteins

We propose a novel and flexible derivation scheme of statistical, database-derived, potentials, which allows one to take simultaneously into account specific correlations between several sequence and structure descriptors. This scheme leads to the decomposition of the total folding free energy of a protein into a sum of lower order terms, thereby giving the possibility to analyze independently each contribution and clarify its significance and importance, to avoid overcounting certain contributions, and to deal more efficiently with the limited size of the database. In addition, this derivation scheme appears as quite general, for many previously developed potentials can be expressed as particular cases of our formalism. We use this formalism as a framework to generate different residue-based energy functions, whose performances are assessed on the basis of their ability to discriminate genuine proteins from decoy models. The optimal potential is generated as a combination of several coupling terms, measuring correlations between residue types, backbone torsion angles, solvent accessibilities, relative positions along the sequence, and interresidue distances. This potential outperforms all tested residue-based potentials, and even several atom-based potentials. Its incorporation in algorithms aiming at predicting protein structure and stability should therefore substantially improve their performances.

In quest of an empirical potential for protein structure prediction

Key to successful protein structure prediction is a potential that recognizes the native state from misfolded structures. Recent advances in empirical potentials based on known protein structures include improved reference states for assessing random interactions, sidechain-orientation-dependent pair potentials, potentials for describing secondary or supersecondary structural preferences and, most importantly, optimization protocols that sculpt the energy landscape to enhance the correlation between native-like features and the energy. Improved clustering algorithms that select native-like structures on the basis of cluster density also resulted in greater prediction accuracy. For template-based modeling, these advances allowed improvement in predicted structures relative to their initial template alignments over a wide range of target-template homology. This represents significant progress and suggests applications to proteome-scale structure prediction.

Protein Structure Evaluation using an All-Atom Energy Based Empirical Scoring Function

Arriving at the native conformation of a polypeptide chain characterized by minimum most free energy is a problem of long standing interest in protein structure prediction endeavors. Owing to the computational requirements in developing free energy estimates, scoring functions--energy based or statistical--have received considerable renewed attention in recent years for distinguishing native structures of proteins from non-native like structures. Several cleverly designed decoy sets, CASP (Critical Assessment of Techniques for Protein Structure Prediction) structures and homology based internet accessible three dimensional model builders are now available for validating the scoring functions. We describe here an all-atom energy based empirical scoring function and examine its performance on a wide series of publicly available decoys. Barring two protein sequences where native structure is ranked second and seventh, native is identified as the lowest energy structure in 67 protein sequences from among 61,659 decoys belonging to 12 different decoy sets. We further illustrate a potential application of the scoring function in bracketing native-like structures of two small mixed alpha/beta globular proteins starting from sequence and secondary structural information. The scoring function has been web enabled at www.scfbio-iitd.res.in/utility/proteomics/energy.jsp.

A decoy set for the thermostable subdomain from chicken villin headpiece, comparison of different free energy estimators

BACKGROUND

Estimators of free energies are routinely used to judge the quality of protein structural models. As these estimators still present inaccuracies, they are frequently evaluated by discriminating native or native-like conformations from large ensembles of so-called decoy structures.

RESULTS

A decoy set is obtained from snapshots taken from 5 long (100 ns) molecular dynamics (MD) simulations of the thermostable subdomain from chicken villin headpiece. An evaluation of the energy of the decoys is given using: i) a residue based contact potential supplemented by a term for the quality of dihedral angles; ii) a recently introduced combination of four statistical scoring functions for model quality estimation (FRST); iii) molecular mechanics with solvation energy estimated either according to the generalized Born surface area (GBSA) or iv) the Poisson-Boltzmann surface area (PBSA) method.

CONCLUSION

The decoy set presented here has the following features which make it attractive for testing energy scoring functions:1) it covers a broad range of RMSD values (from less than 2.0 A to more than 12 A);2) it has been obtained from molecular dynamics trajectories, starting from different non-native-like conformations which have diverse behaviour, with secondary structure elements correctly or incorrectly formed, and in one case folding to a native-like structure. This allows not only for scoring of static structures, but also for studying, using free energy estimators, the kinetics of folding;3) all structures have been obtained from accurate MD simulations in explicit solvent and after molecular mechanics (MM) energy minimization using an implicit solvent method. The quality of the covalent structure therefore does not suffer from steric or covalent problems. The statistical and physical effective energy functions tested on the set behave differently when native simulation snapshots are included or not in the set and when averaging over the trajectory is performed.

Lessons from the design of a novel atomic potential for protein folding

We investigate all-atom potentials of mean force for estimating free energies in protein folding and fold recognition. We search through the space potentials and design novel atomic potentials with a random mixing approximation and a contact-correlated Gaussian approximation of decoy states. We show that the two derived potentials are highly correlated, supporting the use of the random energy model as an accurate statistical description of protein conformational states. The novel atomic potentials perform well in a Z-score and fold decoy recognition test. Furthermore, the designed atomic potential performs slightly and significantly better than atomic potentials derived under a quasi-chemical assumption. While accounting for connectivity correlations between atom types does not improve the performance of the designed potential, we show these correlations lead to ambiguities in the distribution of energetic contributions for atoms on the same residue. Within the confines of the model then, many potentials may exist which stabilize all native folds in subtly different ways. Comparison of different protein conformations under the various atomic potentials reveals both a remarkable degree of correspondence in the estimated free energies and a remarkable degree of correspondence in the identity of the contacts types that make the dominant contributions to the estimated free energies. This consistency may be interpreted as a sign that the design procedure is extracting physically meaningful quantities.

Prediction of protein thermostability with a direction- and distance-dependent knowledge-based potential

The increasing use of enzymes in industrial processes and the importance of understanding protein folding and stability have led to several attempts to predict and quantify the effect of every possible amino acid exchange (mutation) on the thermostability of proteins. In this article we describe a knowledge-based discrimination function that acts as a fast and reliable guide in protein engineering and optimization. The function used consists of two parts, a pairwise energy function based on a distance- and direction-dependent atomic description of the amino acid environment, and a torsion angle energy function. In a first step a training set of 11 proteins including 646 mutant proteins with experimentally determined thermostability was used to optimize the knowledge-based energy functions. The resulting potential function was then tested using a test mutant database consisting of 918 various point mutations introduced in 27 proteins. The best correlation coefficient obtained for the experimental data and the predicted thermostability for the training set is r = 0.81 (561 data points). A total of 76% of the mutations could be predicted correctly as being either stabilizing or destabilizing. The results for the test set are r = 0.74 (747 data points) and 72%, respectively. The global correlation over the combined data (1308 mutants) obtained is 0.78.

Comparison between Generalized-Born and Poisson-Boltzmann methods in physics-based scoring functions for protein structure prediction

Continuum solvent models such as Generalized-Born and Poisson-Boltzmann methods hold the promise to treat solvation effect efficiently and to enable rapid scoring of protein structures when they are combined with physics-based energy functions. Yet, direct comparison of these two approaches on large protein data set is lacking. Building on our previous work with a scoring function based on a Generalized-Born (GB) solvation model, and short molecular-dynamics simulations, we further extended the scoring function to compare with the MM-PBSA method to treat the solvent effect. We benchmarked this scoring function against seven publicly available decoy sets. We found that, somewhat surprisingly, the results of MM-PBSA approach are comparable to the previous GB-based scoring function. We also discussed the effect to the scoring function accuracy due to presence of large ligands and ions in some native structures of the decoy sets.

Polypeptide foldings obtained with effective pair potentials

We present a model of protein folding which is based on a potential function that describes the effective interaction between two amino acids (alanines, in this case). Our model is consistent with the formation of two important secondary structures, namely, an alpha-helix and a beta-ladder. In each case, we estimate the density of states using a random walk in energy space. This function allows the direct calculation of certain thermodynamic properties. By means of the configurational temperature, we also verify that the obtained polypeptides are in their native state.

Development of novel statistical potentials for protein fold recognition

The need to perform large-scale studies of protein fold recognition, structure prediction and protein-protein interactions has led to novel developments of residue-level minimal models of proteins. A minimum requirement for useful protein force-fields is that they be successful in the recognition of native conformations. The balance between the level of detail in describing the specific interactions within proteins and the accuracy obtained using minimal protein models is the focus of many current protein studies. Recent results suggest that the introduction of explicit orientation dependence in a coarse-grained, residue-level model improves the ability of inter-residue potentials to recognize the native state. New statistical and optimization computational algorithms can be used to obtain accurate residue-dependent potentials for use in protein fold recognition and, more importantly, structure prediction.

Geometric cooperativity and anticooperativity of three-body interactions in native proteins

Characterizing multibody interactions of hydrophobic, polar, and ionizable residues in protein is important for understanding the stability of protein structures. We introduce a geometric model for quantifying 3-body interactions in native proteins. With this model, empirical propensity values for many types of 3-body interactions can be reliably estimated from a database of native protein structures, despite the overwhelming presence of pairwise contacts. In addition, we define a nonadditive coefficient that characterizes cooperativity and anticooperativity of residue interactions in native proteins by measuring the deviation of 3-body interactions from 3 independent pairwise interactions. It compares the 3-body propensity value from what would be expected if only pairwise interactions were considered, and highlights the distinction of propensity and cooperativity of 3-body interaction. Based on the geometric model, and what can be inferred from statistical analysis of such a model, we find that hydrophobic interactions and hydrogen-bonding interactions make nonadditive contributions to protein stability, but the nonadditive nature depends on whether such interactions are located in the protein interior or on the protein surface. When located in the interior, many hydrophobic interactions such as those involving alkyl residues are anticooperative. Salt-bridge and regular hydrogen-bonding interactions, such as those involving ionizable residues and polar residues, are cooperative. When located on the protein surface, these salt-bridge and regular hydrogen-bonding interactions are anticooperative, and hydrophobic interactions involving alkyl residues become cooperative. We show with examples that incorporating 3-body interactions improves discrimination of protein native structures against decoy conformations. In addition, analysis of cooperative 3-body interaction may reveal spatial motifs that can suggest specific protein functions.

Protein decoy sets for evaluating energy functions

Energy functions are crucial ingredients of protein tertiary structure prediction methods. Assessing the quality of energy functions is therefore of prime importance. It requires the elaboration of a standard evaluation scheme, whose key elements are: i). sets that contain the native and several non-native structures of proteins (decoys) in order to test whether the energy functions display the expected quality features and ii). measures to evaluate the reliability of energy functions. We present here a survey of the recent advances in these two related fields. In a first part, we analyze and review the large number of decoy sets that are available on the web, and we summarize the characteristics of a challenging decoy set. We then discuss how to define the quality of energy functions and review the measures related to it.

Energy landscapes and solved protein-folding problems

Energy-landscape theory has led to much progress in protein folding kinetics, protein structure prediction and protein design. Funnel landscapes describe protein folding and binding and explain how protein topology determines kinetics. Landscape-optimized energy functions based on bioinformatic input have been used to correctly predict low-resolution protein structures and also to design novel proteins automatically.

Quantitative evaluation of protein-DNA interactions using an optimized knowledge-based potential

Computational evaluation of protein–DNA interaction is important for the identification of DNA-binding sites and genome annotation. It could validate the predicted binding motifs by sequence-based approaches through the calculation of the binding affinity between a protein and DNA. Such an evaluation should take into account structural information to deal with the complicated effects from DNA structural deformation, distance-dependent multi-body interactions and solvation contributions. In this paper, we present a knowledge-based potential built on interactions between protein residues and DNA tri-nucleotides. The potential, which explicitly considers the distance-dependent two-body, three-body and four-body interactions between protein residues and DNA nucleotides, has been optimized in terms of a Z-score. We have applied this knowledge-based potential to evaluate the binding affinities of zinc-finger protein–DNA complexes. The predicted binding affinities are in good agreement with the experimental data (with a correlation coefficient of 0.950). On a larger test set containing 48 protein–DNA complexes with known experimental binding free energies, our potential has achieved a high correlation coefficient of 0.800, when compared with the experimental data. We have also used this potential to identify binding motifs in DNA sequences of transcription factors (TF). The TFs in 79.4% of the known TF–DNA complexes have accurately found their native binding sequences from a large pool of DNA sequences. When tested in a genome-scale search for TF-binding motifs of the cyclic AMP regulatory protein (CRP) of Escherichia coli, this potential ranks all known binding motifs of CRP in the top 15% of all candidate sequences.

The dependence of all-atom statistical potentials on structural training database

An accurate statistical energy function that is suitable for the prediction of protein structures of all classes should be independent of the structural database used for energy extraction. Here, two high-resolution, low-sequence-identity structural databases of 333 alpha-proteins and 271 beta-proteins were built for examining the database dependence of three all-atom statistical energy functions. They are RAPDF (residue-specific all-atom conditional probability discriminatory function), atomic KBP (atomic knowledge-based potential), and DFIRE (statistical potential based on distance-scaled finite ideal-gas reference state). These energy functions differ in the reference states used for energy derivation. The energy functions extracted from the different structural databases are used to select native structures from multiple decoys of 64 alpha-proteins and 28 beta-proteins. The performance in native structure selections indicates that the DFIRE-based energy function is mostly independent of the structural database whereas RAPDF and KBP have a significant dependence. The construction of two additional structural databases of alpha/beta and alpha + beta-proteins further confirmed the weak dependence of DFIRE on the structural databases of various structural classes. The possible source for the difference between the three all-atom statistical energy functions is that the physical reference state of ideal gas used in the DFIRE-based energy function is least dependent on the structural database.

A new hydrogen-bonding potential for the design of protein-RNA interactions predicts specific contacts and discriminates decoys

RNA-binding proteins play many essential roles in the regulation of gene expression in the cell. Despite the significant increase in the number of structures for RNA-protein complexes in the last few years, the molecular basis of specificity remains unclear even for the best-studied protein families. We have developed a distance and orientation-dependent hydrogen-bonding potential based on the statistical analysis of hydrogen-bonding geometries that are observed in high-resolution crystal structures of protein-DNA and protein-RNA complexes. We observe very strong geometrical preferences that reflect significant energetic constraints on the relative placement of hydrogen-bonding atom pairs at protein-nucleic acid interfaces. A scoring function based on the hydrogen-bonding potential discriminates native protein-RNA structures from incorrectly docked decoys with remarkable predictive power. By incorporating the new hydrogen-bonding potential into a physical model of protein-RNA interfaces with full atom representation, we were able to recover native amino acids at protein-RNA interfaces.

An accurate, residue-level, pair potential of mean force for folding and binding based on the distance-scaled, ideal-gas reference state

Structure prediction on a genomic scale requires a simplified energy function that can efficiently sample the conformational space of polypeptide chains. A good energy function at minimum should discriminate native structures against decoys. Here, we show that a recently developed, residue-specific, all-atom knowledge-based potential (167 atomic types) based on distance-scaled, finite ideal-gas reference state (DFIRE-all-atom) can be substantially simplified to 20 residue types located at side-chain center of mass (DFIRE-SCM) without a significant change in its capability of structure discrimination. Using 96 standard multiple decoy sets, we show that there is only a small reduction (from 80% to 78%) in success rate of ranking native structures as the top 1. The success rate is higher than two previously developed, all-atom distance-dependent statistical pair potentials. Applied to structure selections of 21 docking decoys without modification, the DFIRE-SCM potential is 29% more successful in recognizing native complex structures than an all-atom statistical potential trained by a database of dimeric interfaces. The potential also achieves 92% accuracy in distinguishing true dimeric interfaces from artificial crystal interfaces. In addition, the DFIRE potential with the C(alpha) positions as the interaction centers recognizes 123 native structures out of a comprehensive 125-protein TOUCHSTONE decoy set in which each protein has 24,000 decoys with only C(alpha) positions. Furthermore, the performance by DFIRE-SCM on newly established 25 monomeric and 31 docking Rosetta-decoy sets is comparable to (or better than in the case of monomeric decoy sets) that of a recently developed, all-atom Rosetta energy function enhanced with an orientation-dependent hydrogen bonding potential.

Empirical force fields for biological macromolecules: overview and issues

Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.

Single-body residue-level knowledge-based energy score combined with sequence-profile and secondary structure information for fold recognition

An elaborate knowledge-based energy function is designed for fold recognition. It is a residue-level single-body potential so that highly efficient dynamic programming method can be used for alignment optimization. It contains a backbone torsion term, a buried surface term, and a contact-energy term. The energy score combined with sequence profile and secondary structure information leads to an algorithm called SPARKS (Sequence, secondary structure Profiles and Residue-level Knowledge-based energy Score) for fold recognition. Compared with the popular PSI-BLAST, SPARKS is 21% more accurate in sequence-sequence alignment in ProSup benchmark and 10%, 25%, and 20% more sensitive in detecting the family, superfamily, fold similarities in the Lindahl benchmark, respectively. Moreover, it is one of the best methods for sensitivity (the number of correctly recognized proteins), alignment accuracy (based on the MaxSub score), and specificity (the average number of correctly recognized proteins whose scores are higher than the first false positives) in LiveBench 7 among more than twenty servers of non-consensus methods. The simple algorithm used in SPARKS has the potential for further improvement. This highly efficient method can be used for fold recognition on genomic scales. A web server is established for academic users on http://theory.med.buffalo.edu.

Improved protein structure selection using decoy-dependent discriminatory functions

BACKGROUND

A key component in protein structure prediction is a scoring or discriminatory function that can distinguish near-native conformations from misfolded ones. Various types of scoring functions have been developed to accomplish this goal, but their performance is not adequate to solve the structure selection problem. In addition, there is poor correlation between the scores and the accuracy of the generated conformations.

RESULTS

We present a simple and nonparametric formula to estimate the accuracy of predicted conformations (or decoys). This scoring function, called the density score function, evaluates decoy conformations by performing an all-against-all Calpha RMSD (Root Mean Square Deviation) calculation in a given decoy set. We tested the density score function on 83 decoy sets grouped by their generation methods (4state_reduced, fisa, fisa_casp3, lmds, lattice_ssfit, semfold and Rosetta). The density scores have correlations as high as 0.9 with the Calpha RMSDs of the decoy conformations, measured relative to the experimental conformation for each decoy. We previously developed a residue-specific all-atom probability discriminatory function (RAPDF), which compiles statistics from a database of experimentally determined conformations, to aid in structure selection. Here, we present a decoy-dependent discriminatory function called self-RAPDF, where we compiled the atom-atom contact probabilities from all the conformations in a decoy set instead of using an ensemble of native conformations, with a weighting scheme based on the density scores. The self-RAPDF has a higher correlation with Calpha RMSD than RAPDF for 76/83 decoy sets, and selects better near-native conformations for 62/83 decoy sets. Self-RAPDF may be useful not only for selecting near-native conformations from decoy sets, but also for fold simulations and protein structure refinement.

CONCLUSIONS

Both the density score and the self-RAPDF functions are decoy-dependent scoring functions for improved protein structure selection. Their success indicates that information from the ensemble of decoy conformations can be used to derive statistical probabilities and facilitate the identification of near-native structures.

Large-scale prediction of protein geometry and stability changes for arbitrary single point mutations

We have developed a method to both predict the geometry and the relative stability of point mutants that may be used for arbitrary mutations. The geometry optimization procedure was first tested on a new benchmark of 2141 ordered pairs of X-ray crystal structures of proteins that differ by a single point mutation, the largest data set to date. An empirical energy function, which includes terms representing the energy contributions of the folded and denatured proteins and uses the predicted mutant side chain conformation, was fit to a training set consisting of half of a diverse set of 1816 experimental stability values for single point mutations in 81 different proteins. The data included a substantial number of small to large residue mutations not considered by previous prediction studies. After removing 22 (approximately 2%) outliers, the stability calculation gave a standard deviation of 1.08 kcal/mol with a correlation coefficient of 0.82. The prediction method was then tested on the remaining half of the experimental data, giving a standard deviation of 1.10 kcal/mol and covariance of 0.66 for 97% of the test set. A regression fit of the energy function to a subset of 137 mutants, for which both native and mutant structures were available, gave a prediction error comparable to that for the complete training set with predicted side chain conformations. We found that about half of the variation is due to conformation-independent residue contributions. Finally, a fit to the experimental stability data using these residue parameters exclusively suggests guidelines for improving protein stability in the absence of detailed structure information.

A structural pattern-based method for protein fold recognition

A method (SPREK) was developed to evaluate the register of a sequence on a structure based on the matching of structural patterns against a library derived from the protein structure databank. The scores obtained were normalized against random background distributions derived from sequence shuffling and permutation methods. 'Random' structures were also used to evaluate the effectiveness of the method. These were generated by a simple random-walk and a more sophisticated structure prediction method that produced protein-like folds. For comparison with other methods, the performance of the method was assessed using collections of models including decoys and models from the CASP-5 exercise. The performance of SPREK on the decoy models was equivalent to (and sometimes better than) those obtained with more complex approaches. An exception was the two smallest proteins, for which SPREK did not perform well due to a lack of patterns. Using the best parameter combination from trials on decoy models, the CASP models of intermediate difficulty were evaluated by SPREK and the quality of the top scoring model was evaluated by its CASP ranking. Of the 14 targets in this class, half lie in the top 10% (out of around 140 models for each target). The two worst rankings resulted from the selection by our method of a well-packed model that was based on the wrong fold. Of the other poor rankings, one was the smallest protein and the others were the four largest (all over 250 residues).

MMTSB Tool Set: enhanced sampling and multiscale modeling methods for applications in structural biology

We describe the Multiscale Modeling Tools for Structural Biology (MMTSB) Tool Set (https://mmtsb.scripps.edu/software/mmtsbToolSet.html), which is a novel set of utilities and programming libraries that provide new enhanced sampling and multiscale modeling techniques for the simulation of proteins and nucleic acids. The tool set interfaces with the existing molecular modeling packages CHARMM and Amber for classical all-atom simulations, and with MONSSTER for lattice-based low-resolution conformational sampling. In addition, it adds new functionality for the integration and translation between both levels of detail. The replica exchange method is implemented to allow enhanced sampling of both the all-atom and low-resolution models. The tool set aims at applications in structural biology that involve protein or nucleic acid structure prediction, refinement, and/or extended conformational sampling. With structure prediction applications in mind, the tool set also implements a facility that allows the control and application of modeling tasks on a large set of conformations in what we have termed ensemble computing. Ensemble computing encompasses loosely coupled, parallel computation on high-end parallel computers, clustered computational grids and desktop grid environments. This paper describes the design and implementation of the MMTSB Tool Set and illustrates its utility with three typical examples--scoring of a set of predicted protein conformations in order to identify the most native-like structures, ab initio folding of peptides in implicit solvent with the replica exchange method, and the prediction of a missing fragment in a larger protein structure.

A physical reference state unifies the structure-derived potential of mean force for protein folding and binding

Extracting knowledge-based statistical potential from known structures of proteins is proved to be a simple, effective method to obtain an approximate free-energy function. However, the different compositions of amino acid residues at the core, the surface, and the binding interface of proteins prohibited the establishment of a unified statistical potential for folding and binding despite the fact that the physical basis of the interaction (water-mediated interaction between amino acids) is the same. Recently, a physical state of ideal gas, rather than a statistically averaged state, has been used as the reference state for extracting the net interaction energy between amino acid residues of monomeric proteins. Here, we find that this monomer-based potential is more accurate than an existing all-atom knowledge-based potential trained with interfacial structures of dimers in distinguishing native complex structures from docking decoys (100% success rate vs. 52% in 21 dimer/trimer decoy sets). It is also more accurate than a recently developed semiphysical empirical free-energy functional enhanced by an orientation-dependent hydrogen-bonding potential in distinguishing native state from Rosetta docking decoys (94% success rate vs. 74% in 31 antibody-antigen and other complexes based on Z score). In addition, the monomer potential achieved a 93% success rate in distinguishing true dimeric interfaces from artificial crystal interfaces. More importantly, without additional parameters, the potential provides an accurate prediction of binding free energy of protein-peptide and protein-protein complexes (a correlation coefficient of 0.87 and a root-mean-square deviation of 1.76 kcal/mol with 69 experimental data points). This work marks a significant step toward a unified knowledge-based potential that quantitatively captures the common physical principle underlying folding and binding. A Web server for academic users, established for the prediction of binding free energy and the energy evaluation of the protein-protein complexes, may be found at http://theory.med.buffalo.edu.

Relationships between amino acid sequence and backbone torsion angle preferences

Statistical averages and correlations for backbone torsion angles of chymotrypsin inhibitor 2 are calculated by using the Rotational Isomeric States model of chain statistics. Statistical weights of torsional states of phipsi pairs, needed for the statistics of the full chain, are obtained in two different ways: 1) by using knowledge-based pairwise dependent phipsi energy maps from Protein Data Bank (PDB) and 2) by collecting torsion angle data from a large number of random coil configurations of an all-atom protein model with volume exclusion. Results obtained by using PDB data show strong correlations between adjacent torsion angle pairs belonging to both the same and different residues. These correlations favor the choice of the native-state torsion angles, and they are strongly context dependent, determined by the specific amino acid sequence of the protein. Excluded volume or steric clashes, only, do not introduce context-dependent phipsi correlations into the chain that would affect the choice of native-state torsional angles.

A new pairwise folding potential based on improved decoy generation and side-chain packing

A new force field for pairwise residue interactions as a function of C(alpha) to C(alpha) distances is presented. The force field was developed through the solution of a linear programming formulation with large sets of constraints. The constraints are based on the construction of >80,000 low-energy decoys for a set of proteins and requiring the decoy energies for each protein system to be higher than the native conformation of that particular protein. The generation of a robust force field was facilitated by the use of a novel decoy generation process, which involved the rational selection of proteins to add to the training set and included a significant energy minimization of the decoys. The force field was tested on a large set of decoys for various proteins not included in the training set and shown to perform well compared with a leading force field in identifying the native conformation for these proteins.

Application of statistical potentials to protein structure refinement from low resolution ab initio models

Recently ab initio protein structure prediction methods have advanced sufficiently so that they often assemble the correct low resolution structure of the protein. To enhance the speed of conformational search, many ab initio prediction programs adopt a reduced protein representation. However, for drug design purposes, better quality structures are probably needed. To achieve this refinement, it is natural to use a more detailed heavy atom representation. Here, as opposed to costly implicit or explicit solvent molecular dynamics simulations, knowledge-based heavy atom pair potentials were employed. By way of illustration, we tried to improve the quality of the predicted structures obtained from the ab initio prediction program TOUCHSTONE by three methods: local constraint refinement, reduced predicted tertiary contact refinement, and statistical pair potential guided molecular dynamics. Sixty-seven predicted structures from 30 small proteins (less than 150 residues in length) representing different structural classes (alpha, beta, alpha;/beta) were examined. In 33 cases, the root mean square deviation (RMSD) from native structures improved by more than 0.3 A; in 19 cases, the improvement was more than 0.5 A, and sometimes as large as 1 A. In only seven (four) cases did the refinement procedure increase the RMSD by more than 0.3 (0.5) A. For the remaining structures, the refinement procedures changed the structures by less than 0.3 A. While modest, the performance of the current refinement methods is better than the published refinement results obtained using standard molecular dynamics.