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

The impact of side-chain packing on protein docking refinement

We study the impact of optimizing the side-chain positions in the interface region between two proteins during the process of binding. Mathematically, the problem is similar to side-chain prediction, which has been extensively explored in the process of protein structure prediction. The protein-protein docking application, however, has a number of characteristics that necessitate different algorithmic and implementation choices. In this work, we implement a distributed approximate algorithm that can be implemented on multiprocessor architectures and enables a trade-off between accuracy and running speed. We report computational results on benchmarks of enzyme-inhibitor and other types of complexes, establishing that the side-chain flexibility our algorithm introduces substantially improves the performance of docking protocols. Furthermore, we establish that the inclusion of unbound side-chain conformers in the side-chain positioning problem is critical in these performance improvements. The code is available to the community under open source license.

ITScorePro: an efficient scoring program for evaluating the energy scores of protein structures for structure prediction

One important component in protein structure prediction is to evaluate the free energy of a given conformation. Given the enormous number of possible conformations for a sequence, it is extremely challenging to quickly and accurately score the energies of these conformations and predict a reasonable structure within a practical computational time. Here, we describe an efficient program for energy evaluation, referred to as ITScorePro (Copyright © 2012). The energy scoring function in the ITScorePro program is based on the distance-dependent, pairwise atomic potentials for protein structure prediction that we recently derived by using statistical mechanics principles (Huang and Zou, Proteins 79:2648-2661, 2011). ITScorePro is a stand-alone program and can also be easily implemented in other software suites for protein structure prediction.

Statistical mechanics-based method to extract atomic distance-dependent potentials from protein structures

In this study, we have developed a statistical mechanics-based iterative method to extract statistical atomic interaction potentials from known, nonredundant protein structures. Our method circumvents the long-standing reference state problem in deriving traditional knowledge-based scoring functions, by using rapid iterations through a physical, global convergence function. The rapid convergence of this physics-based method, unlike other parameter optimization methods, warrants the feasibility of deriving distance-dependent, all-atom statistical potentials to keep the scoring accuracy. The derived potentials, referred to as ITScore/Pro, have been validated using three diverse benchmarks: the high-resolution decoy set, the AMBER benchmark decoy set, and the CASP8 decoy set. Significant improvement in performance has been achieved. Finally, comparisons between the potentials of our model and potentials of a knowledge-based scoring function with a randomized reference state have revealed the reason for the better performance of our scoring function, which could provide useful insight into the development of other physical scoring functions. The potentials developed in this study are generally applicable for structural selection in protein structure prediction.

Discovery of entry inhibitors for HIV-1 via a new de novo protein design framework

A new (to our knowledge) de novo design framework with a ranking metric based on approximate binding affinity calculations is introduced and applied to the discovery of what we believe are novel HIV-1 entry inhibitors. The framework consists of two stages: a sequence selection stage and a validation stage. The sequence selection stage produces a rank-ordered list of amino-acid sequences by solving an integer programming sequence selection model. The validation stage consists of fold specificity and approximate binding affinity calculations. The designed peptidic inhibitors are 12-amino-acids-long and target the hydrophobic core of gp41. A number of the best-predicted sequences were synthesized and their inhibition of HIV-1 was tested in cell culture. All peptides examined showed inhibitory activity when compared with no drug present, and the novel peptide sequences outperformed the native template sequence used for the design. The best sequence showed micromolar inhibition, which is a 3-15-fold improvement over the native sequence, depending on the donor. In addition, the best sequence equally inhibited wild-type and Enfuvirtide-resistant virus strains.

Novel nonlinear knowledge-based mean force potentials based on machine learning

The prediction of 3D structures of proteins from amino acid sequences is one of the most challenging problems in molecular biology. An essential task for solving this problem with coarse-grained models is to deduce effective interaction potentials. The development and evaluation of new energy functions is critical to accurately modeling the properties of biological macromolecules. Knowledge-based mean force potentials are derived from statistical analysis of proteins of known structures. Current knowledge-based potentials are almost in the form of weighted linear sum of interaction pairs. In this study, a class of novel nonlinear knowledge-based mean force potentials is presented. The potential parameters are obtained by nonlinear classifiers, instead of relative frequencies of interaction pairs against a reference state or linear classifiers. The support vector machine is used to derive the potential parameters on data sets that contain both native structures and decoy structures. Five knowledge-based mean force Boltzmann-based or linear potentials are introduced and their corresponding nonlinear potentials are implemented. They are the DIH potential (single-body residue-level Boltzmann-based potential), the DFIRE-SCM potential (two-body residue-level Boltzmann-based potential), the FS potential (two-body atom-level Boltzmann-based potential), the HR potential (two-body residue-level linear potential), and the T32S3 potential (two-body atom-level linear potential). Experiments are performed on well-established decoy sets, including the LKF data set, the CASP7 data set, and the Decoys “R”Us data set. The evaluation metrics include the energy Z score and the ability of each potential to discriminate native structures from a set of decoy structures. Experimental results show that all nonlinear potentials significantly outperform the corresponding Boltzmann-based or linear potentials, and the proposed discriminative framework is effective in developing knowledge-based mean force potentials. The nonlinear potentials can be widely used for ab initio protein structure prediction, model quality assessment, protein docking, and other challenging problems in computational biology.

Incorporating Ab Initio energy into threading approaches for protein structure prediction

Background

Native structures of proteins are formed essentially due to the combining effects of local and distant (in the sense of sequence) interactions among residues. These interaction information are, explicitly or implicitly, encoded into the scoring function in protein structure prediction approaches—threading approaches usually measure an alignment in the sense that how well a sequence adopts an existing structure; while the energy functions in Ab Initio methods are designed to measure how likely a conformation is near-native. Encouraging progress has been observed in structure refinement where knowledge-based or physics-based potentials are designed to capture distant interactions. Thus, it is interesting to investigate whether distant interaction information captured by the Ab Initio energy function can be used to improve threading, especially for the weakly/distant homologous templates.

Results

In this paper, we investigate the possibility to improve alignment-generating through incorporating distant interaction information into the alignment scoring function in a nontrivial approach. Specifically, the distant interaction information is introduced through employing an Ab Initio energy function to evaluate the “partial” decoy built from an alignment. Subsequently, a local search algorithm is utilized to optimize the scoring function.

Experimental results demonstrate that with distant interaction items, the quality of generated alignments are improved on 68 out of 127 query-template pairs in Prosup benchmark. In addition, compared with state-to-art threading methods, our method performs better on alignment accuracy comparison.

Conclusions

Incorporating Ab Initio energy functions into threading can greatly improve alignment accuracy.

Extending the PRIME model for protein aggregation to all 20 amino acids

We extend PRIME, an intermediate-resolution protein model previously used in simulations of the aggregation of polyalanine and polyglutamine, to the description of the geometry and energetics of peptides containing all 20 amino acid residues. The 20 amino acid side chains are classified into 14 groups according to their hydrophobicity, polarity, size, charge, and potential for side chain hydrogen bonding. The parameters for extended PRIME, called PRIME 20, include hydrogen-bonding energies, side chain interaction range and energy, and excluded volume. The parameters are obtained by applying a perceptron-learning algorithm and a modified stochastic learning algorithm that optimizes the energy gap between 711 known native states from the PDB and decoy structures generated by gapless threading. The number of independent pair interaction parameters is chosen to be small enough to be physically meaningful yet large enough to give reasonably accurate results in discriminating decoys from native structures. The most physically meaningful results are obtained with 19 energy parameters.

Simulating protein folding initiation sites using an alpha-carbon-only knowledge-based force field

Protein folding is a hierarchical process where structure forms locally first, then globally. Some short sequence segments initiate folding through strong structural preferences that are independent of their three-dimensional context in proteins. We have constructed a knowledge-based force field in which the energy functions are conditional on local sequence patterns, as expressed in the hidden Markov model for local structure (HMMSTR). Carbon-alpha force field (CALF) builds sequence specific statistical potentials based on database frequencies for alpha-carbon virtual bond opening and dihedral angles, pair-wise contacts and hydrogen bond donor-acceptor pairs, and simulates folding via Brownian dynamics. We introduce hydrogen bond donor and acceptor potentials as alpha-carbon probability fields that are conditional on the predicted local sequence. Constant temperature simulations were carried out using 27 peptides selected as putative folding initiation sites, each 12 residues in length, representing several different local structure motifs. Each 0.6 micros trajectory was clustered based on structure. Simulation convergence or representativeness was assessed by subdividing trajectories and comparing clusters. For 21 of the 27 sequences, the largest cluster made up more than half of the total trajectory. Of these 21 sequences, 14 had cluster centers that were at most 2.6 A root mean square deviation (RMSD) from their native structure in the corresponding full-length protein. To assess the adequacy of the energy function on nonlocal interactions, 11 full length native structures were relaxed using Brownian dynamics simulations. Equilibrated structures deviated from their native states but retained their overall topology and compactness. A simple potential that folds proteins locally and stabilizes proteins globally may enable a more realistic understanding of hierarchical folding pathways.

Optimizing energy potential for protein fold recognition with parametric evaluation function

In this paper, a new optimization method is proposed to determine a simplified energy potential for protein fold recognition, which consists of the residue-residue contact, hydrophobicity, and pseudodihedral potentials. With a parametric evaluation function method, the Z-scores of all the proteins in a training set are optimized simultaneously to obtain the best parameter set of the potential. For this multi-objective and multi-constraint problem, the new optimization scheme is very effective. The derived potential is then tested on two high-quality decoy sets and compared with other classical fold recognition potentials. With the simplified energy potential, we achieve a high level of discrimination capability between correct and incorrect folds.

A simple Calpha-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C(alpha)-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.

Probabilistic models and machine learning in structural bioinformatics

Structural bioinformatics is concerned with the molecular structure of biomacromolecules on a genomic scale, using computational methods. Classic problems in structural bioinformatics include the prediction of protein and RNA structure from sequence, the design of artificial proteins or enzymes, and the automated analysis and comparison of biomacromolecules in atomic detail. The determination of macromolecular structure from experimental data (for example coming from nuclear magnetic resonance, X-ray crystallography or small angle X-ray scattering) has close ties with the field of structural bioinformatics. Recently, probabilistic models and machine learning methods based on Bayesian principles are providing efficient and rigorous solutions to challenging problems that were long regarded as intractable. In this review, I will highlight some important recent developments in the prediction, analysis and experimental determination of macromolecular structure that are based on such methods. These developments include generative models of protein structure, the estimation of the parameters of energy functions that are used in structure prediction, the superposition of macromolecules and structure determination methods that are based on inference. Although this review is not exhaustive, I believe the selected topics give a good impression of the exciting new, probabilistic road the field of structural bioinformatics is taking.

Distance dependent centroid to centroid force fields using high resolution decoys

Simplified force fields play an important role in protein structure prediction and de novo protein design by requiring less computational effort than detailed atomistic potentials. A side chain centroid based, distance dependent pairwise interaction potential has been developed. A linear programming based formulation was used in which non-native "decoy" conformers are forced to take a higher energy compared with the corresponding native structure. This model was trained on an enhanced and diverse protein set. High quality decoy structures were generated for approximately 1400 nonhomologous proteins using torsion angle dynamics along with restricted variations of the hydrophobic cores of the native structure. The resulting decoy set was used to train the model yielding two different side chain centroid based force fields that differ in the way distance dependence has been used to calculate energy parameters. These force fields were tested on an independent set of 148 test proteins with 500 decoy structures for each protein. The side chain centroid force fields were successful in correctly identifying approximately 86% native structures. The Z-scores produced by the proposed centroid-centroid distance dependent force fields improved compared with other distance dependent C(alpha)-C(alpha) or side chain based force fields.

Dissecting contact potentials for proteins: relative contributions of individual amino acids

Knowledge-based contact potentials are routinely used in fold recognition, binding of peptides to proteins, structure prediction, and coarse-grained models to probe protein folding kinetics. The dominant physical forces embodied in the contact potentials are revealed by eigenvalue analysis of the matrices, whose elements describe the strengths of interaction between amino acid side chains. We propose a general method to rank quantitatively the importance of various inter-residue interactions represented in the currently popular pair contact potentials. Eigenvalue analysis and correlation diagrams are used to rank the inter-residue pair interactions with respect to the magnitude of their relative contributions to the contact potentials. The amino acid ranking is shown to be consistent with a mean field approximation that is used to reconstruct the original contact potentials from the most relevant amino acids for several contact potentials. By providing a general, relative ranking score for amino acids, this method permits a detailed, quantitative comparison of various contact interaction schemes. For most contact potentials, between 7 and 9 amino acids of varying chemical character are needed to accurately reconstruct the full matrix. By correlating the identified important amino acid residues in contact potentials and analysis of about 7800 structural domains in the CATH database we predict that it is important to model accurately interactions between small hydrophobic residues. In addition, only potentials that take interactions involving the protein backbone into account can predict dense packing in protein structures.

Mutations affecting the oligomerization interface of G-protein-coupled receptors revealed by a novel de novo protein design framework

Specific functional and pharmacological properties have recently been ascribed to G-protein-coupled receptor (GPCR) dimers/oligomers. Because the association of two identical or two distinct GPCR monomers seems to be required to elicit receptor function, it is necessary to understand the exact nature of this interaction. We present here a novel method for de novo protein design and its application to the prediction of mutations that can stabilize or destabilize a GPCR dimer while maintaining the monomer's native fold. To test the efficacy of this new method, the dimer of the single-spanned transmembrane domain of glycophorin A was used as a model system. Experimental data from mutagenesis of the helix-helix interface are compared with computational predictions at that interface, and the model's results are found to be consistent with the experimental findings. A flexible template was developed for the rhodopsin homodimer at atomic resolution and used to predict sets of three and five mutations. The results are found to be consistent across eight case studies, with favored mutations at each position. Mutation sets predicted to be the most disruptive at the dimerization interface are found to be less specific to the flexible template than sets predicted to be less disruptive.

Toward full-sequence de novo protein design with flexible templates for human beta-defensin-2

In this article, we introduce and apply our de novo protein design framework, which observes true backbone flexibility, to the redesign of human beta-defensin-2, a 41-residue cationic antimicrobial peptide of the innate immune system. The flexible design templates are generated using molecular dynamics simulations with both Generalized Born implicit solvation and explicit water molecules. These backbone templates were employed in addition to the x-ray crystal structure for designing human beta-defensin-2. The computational efficiency of our framework was demonstrated with the full-sequence design of the peptide with flexible backbone templates, corresponding to the mutation of all positions except the native cysteines.

OPUS-Ca: a knowledge-based potential function requiring only Calpha positions

In this paper, we report a knowledge-based potential function, named the OPUS-Ca potential, that requires only Calpha positions as input. The contributions from other atomic positions were established from pseudo-positions artificially built from a Calpha trace for auxiliary purposes. The potential function is formed based on seven major representative molecular interactions in proteins: distance-dependent pairwise energy with orientational preference, hydrogen bonding energy, short-range energy, packing energy, tri-peptide packing energy, three-body energy, and solvation energy. From the testing of decoy recognition on a number of commonly used decoy sets, it is shown that the new potential function outperforms all known Calpha-based potentials and most other coarse-grained ones that require more information than Calpha positions. We hope that this potential function adds a new tool for protein structural modeling.

Potential function of simplified protein models for discriminating native proteins from decoys: combining contact interaction and local sequence-dependent geometry

An effective potential function is critical for protein structure prediction and folding simulation. For simplified models of proteins where coordinates of only Ca atoms need to be specified, an accurate potential function is important. Such a simplified model is essential for efficient search of conformational space. In this work, we present a formulation of potential function for simplified representations of protein structures. It is based on the combination of descriptors derived from residue-residue contact and sequence-dependent local geometry. The optimal weight coefficients for contact and local geometry is obtained through optimization by maximizing margins among native and decoy structures. The latter are generated by chain growth and by gapless threading. The performance of the potential function in blind test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. This potential function have comparable or better performance than several residue-based potential functions that require in addition coordinates of side chain centers or coordinates of all side chain atoms.

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.

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.

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.

Optimal design of protein docking potentials: efficiency and limitations

Protein-protein docking is a challenging computational problem in functional genomics, particularly when one or both proteins undergo conformational change(s) upon binding. The major challenge is to define scoring function soft enough to tolerate these changes and specific enough to distinguish between near-native and "misdocked" conformations. Using a linear programming technique, we derived protein docking potentials (PDPs) that comply with this requirement. We considered a set of 63 nonredundant complexes to this aim, and generated 400,000 putative docked complexes (decoys) based on shape complementarity criterion for each complex. The PDPs were required to yield for the native (correctly docked) structure a potential energy lower than those of all the nonnative (misdocked) structures. The energy constraints applied to all complexes led to ca. 25 million inequalities, the simultaneous solution of which yielded an optimal set of PDPs that discriminated the correctly docked (up to 4.0 A root-mean-square deviation from known complex structure) structure among the 85 top-ranking (0.02%) decoys in 59/63 examined bound-bound cases. The high performance of the potentials was further verified in jackknife tests and by ranking putative docked conformation submitted to CAPRI. In addition to their utility in identifying correctly folded complexes, the PDPs reveal biologically meaningful features that distinguish docking potentials from folding potentials.

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.