Improved side-chain modeling for protein-protein docking

Success in high-resolution protein-protein docking requires accurate modeling of side-chain conformations at the interface. Most current methods either leave side chains fixed in the conformations observed in the unbound protein structures or allow the side chains to sample a set of discrete rotamer conformations. Here we describe a rapid and efficient method for sampling off-rotamer side-chain conformations by torsion space minimization during protein-protein docking starting from discrete rotamer libraries supplemented with side-chain conformations taken from the unbound structures, and show that the new method improves side-chain modeling and increases the energetic discrimination between good and bad models. Analysis of the distribution of side-chain interaction energies within and between the two protein partners shows that the new method leads to more native-like distributions of interaction energies and that the neglect of side-chain entropy produces a small but measurable increase in the number of residues whose interaction energy cannot compensate for the entropic cost of side-chain freezing at the interface. The power of the method is highlighted by a number of predictions of unprecedented accuracy in the recent CAPRI (Critical Assessment of PRedicted Interactions) blind test of protein-protein docking methods.     

Accuracy of side-chain prediction upon near-native protein backbones generated by ab initio folding methods

The ab initio folding problem can be divided into two sequential tasks of approximately equal computational complexity: the generation of native-like backbone folds and the positioning of side chains upon these backbones. The prediction of side-chain conformation in this context is challenging, because at best only the near-native global fold of the protein is known. To test the effect of displacements in the protein backbones on side-chain prediction for folds generated ab initio, sets of near-native backbones (≤ 4 Å Cα RMS error) for four small proteins were generated by two methods. The steric environment surrounding each residue was probed by placing the side chains in the native conformation on each of these decoys, followed by torsion-space optimization to remove steric clashes on a rigid backbone. We observe that on average 40% of the χ1 angles were displaced by 40° or more, effectively setting the limits in accuracy for side-chain modeling under these conditions. Three different algorithms were subsequently used for prediction of side-chain conformation. The average prediction accuracy for the three methods was remarkably similar: 49% to 51% of the χ1 angles were predicted correctly overall (33% to 36% of the χ1+2 angles). Interestingly, when the inter-side-chain interactions were disregarded, the mean accuracy increased. A consensus approach is described, in which side-chain conformations are defined based on the most frequently predicted χ angles for a given method upon each set of near-native backbones. We find that consensus modeling, which de facto includes backbone flexibility, improves side-chain prediction: χ1 accuracy improved to 51–54% (36–42% of χ1+2). Implications of a consensus method for ab initio protein structure prediction are discussed. Proteins 33:204–217, 1998. © 1998 Wiley-Liss, Inc.     

A graph-theory algorithm for rapid protein side-chain prediction

Fast and accurate side-chain conformation prediction is important for homology modeling, ab initio protein structure prediction, and protein design applications. Many methods have been presented, although only a few computer programs are publicly available. The SCWRL program is one such method and is widely used because of its speed, accuracy, and ease of use. A new algorithm for SCWRL is presented that uses results from graph theory to solve the combinatorial problem encountered in the side-chain prediction problem. In this method, side chains are represented as vertices in an undirected graph. Any two residues that have rotamers with nonzero interaction energies are considered to have an edge in the graph. The resulting graph can be partitioned into connected subgraphs with no edges between them. These subgraphs can in turn be broken into biconnected components, which are graphs that cannot be disconnected by removal of a single vertex. The combinatorial problem is reduced to finding the minimum energy of these small biconnected components and combining the results to identify the global minimum energy conformation. This algorithm is able to complete predictions on a set of 180 proteins with 34342 side chains in <7 min of computer time. The total chi(1) and chi(1 + 2) dihedral angle accuracies are 82.6% and 73.7% using a simple energy function based on the backbone-dependent rotamer library and a linear repulsive steric energy. The new algorithm will allow for use of SCWRL in more demanding applications such as sequence design and ab initio structure prediction, as well addition of a more complex energy function and conformational flexibility, leading to increased accuracy.     

Conformational analysis of d-tubocurarine: Implications for minimal dimensions of its binding site within ion channels

All the minimum-energy conformations of d-tubocurarine were calculated by the method of molecular mechanics. The energy was minimized from 413 closed forms of the 18-member ring. The set of minimum-energy conformations includes 10 forms with energies less than 6 kcal/mol from the most stable one. Among the four lowest minimum-energy conformations, two forms correspond to those known from X-ray studies, whereas two conformations were not detected experimentally earlier. The flexibility of d-tubocurarine was estimated by calculating six paths of interconversion between the four lowest minimum-energy conformations. Using a molecular graphics technique, it was found that the most extended minimum-energy conformation of d-tubocurarine may fit in an ion channel of a rectangular profile of 8.7 × 11.2 Å, while one tetrahydroisoquinoline head may fit a profile as small as 6.9 × 11.0 Å. A possible model of d-tubocurarine location within the ion channel of the neuronal nicotinic acetylcholine receptor is suggested.     

Effects of initial settings on computational protein–ligand docking accuracies for several docking programs

In this study, the influences of initial settings, i.e. initial conformations, configurations and docking parameters, on docking results were investigated. The conformations used in the study were generated by the CAMDAS program. After the conformational search calculations, five structures were selected from the conformer groups according to their conformation energies and root mean square deviations against crystal structures; for example, the lowest energy conformer, as well as the closest and farthest conformers to the crystal structure, was retrieved. Several docking parameter settings were used (default, high speed, generating 50 poses). In this study, docking calculations were conducted using the GOLD, eHiTS, AutoDock, AutoDock vina, FRED and DOCK programs. The success rates of GOLD, eHiTS and FRED were better than those of AutoDock, AutoDock vina and DOCK. The docking results using the farthest conformations were worse than those obtained using other conformations, indicating that some conformation search for the ligand molecule should be performed before the docking calculations.     

Docking and DFT Studies to explore the Topoisomerase II ATP Pocket employing 3-Substituted 2,6-Piperazindiones for drug design

Topoisomerases (Topos) are very important protein targets for drug design in cancer treatment. Human Topo type IIα (hTopo IIα) has been widely studied experimentally and theoretically. Here, we performed protein rigid/flexible side-chain docking to study a set of thirty-nine 3-substituted-2,6-piperazindiones (labelled 1a, (R)-[(2–20)a] and (S)-[(2–20)b]) derived from α-amino acids. To explain the ligand–protein complexes at the electronic level [using the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO) energies], density functional theory calculations were carried out. Finally, to show adenosine triphosphate (ATP) binding-site constituents, the Q-SiteFinder program was used. The docking results showed that all of the test compounds bind to the ATP-binding site on hTopo IIα. Recognition is mediated by the formation of several hydrogen bond acceptors or donators. This site was the largest (631 Å³) according to the Q-SiteFinder program. When using the protein rigid docking protocol, compound 13a derived from (R)-Lys showed the highest affinity. However, when a flexible side-chain docking protocol was used, the compound with the highest affinity was 16a, derived from (R)-Trp. Frontier molecular orbital studies showed that the HOMO of the ligand interacts with the LUMO located at side-chain residues from the protein-binding site. The HOMO of the binding site interacts with the LUMO of the ligand. We conclude that some ligand properties including the hindrance effect, hydrogen bonds, π–π interactions and stereogenic centres are important for the ligand to be recognised by the ATP-binding site of hTopo IIα.     

Ligand-induced conformational changes: improved predictions of ligand binding conformations and affinities

A computational docking strategy using multiple conformations of the target protein is discussed and evaluated. A series of low molecular weight, competitive, nonpeptide protein tyrosine phosphatase inhibitors are considered for which the x-ray crystallographic structures in complex with protein tyrosine phosphatase 1B (PTP1B) are known. To obtain a quantitative measure of the impact of conformational changes induced by the inhibitors, these were docked to the active site region of various structures of PTP1B using the docking program FlexX. Firstly, the inhibitors were docked to a PTP1B crystal structure cocrystallized with a hexapeptide. The estimated binding energies for various docking modes as well as the RMS differences between the docked compounds and the crystallographic structure were calculated. In this scenario the estimated binding energies were not predictive inasmuch as docking modes with low estimated binding energies corresponded to relatively large RMS differences when aligned with the corresponding crystal structure. Secondly, the inhibitors were docked to their parent protein structures in which they were cocrystallized. In this case, there was a good correlation between low predicted binding energy and a correct docking mode. Thirdly, to improve the predictability of the docking procedure in the general case, where only a single target protein structure is known, we evaluate an approach which takes possible protein side-chain conformational changes into account. Here, side chains exposed to the active site were considered in their allowed rotamer conformations and protein models containing all possible combinations of side-chain rotamers were generated. To evaluate which of these modeled active sites is the most likely binding site conformation for a certain inhibitor, the inhibitors were docked against all active site models. The receptor rotamer model corresponding to the lowest estimated binding energy is taken as the top candidate. Using this protocol, correct inhibitor binding modes could successfully be discriminated from proposed incorrect binding modes. Moreover, the ranking of the estimated ligand binding energies was in good agreement with experimentally observed binding affinities.     

Docking and scoring with alternative side-chain conformations

We describe a scoring and modeling procedure for docking ligands into protein models that have either modeled or flexible side-chain conformations. Our methodical contribution comprises a procedure for generating new potentials of mean force for the ROTA scoring function which we have introduced previously for optimizing side-chain conformations with the tool IRECS. The ROTA potentials are specially trained to tolerate small-scale positional errors of atoms that are characteristic of (i) side-chain conformations that are modeled using a sparse rotamer library and (ii) ligand conformations that are generated using a docking program. We generated both rigid and flexible protein models with our side-chain prediction tool IRECS and docked ligands to proteins using the scoring function ROTA and the docking programs FlexX (for rigid side chains) and FlexE (for flexible side chains). We validated our approach on the forty screening targets of the DUD database. The validation shows that the ROTA potentials are especially well suited for estimating the binding affinity of ligands to proteins. The results also show that our procedure can compensate for the performance decrease in screening that occurs when using protein models with side chains modeled with a rotamer library instead of using X-ray structures. The average runtime per ligand of our method is 168 seconds on an Opteron V20z, which is fast enough to allow virtual screening of compound libraries for drug candidates.     

Side-chain flexibility in protein-ligand binding: the minimal rotation hypothesis

The goal of this work is to learn from nature about the magnitudes of side-chain motions that occur when proteins bind small organic molecules, and model these motions to improve the prediction of protein-ligand complexes. Following analysis of protein side-chain motions upon ligand binding in 63 complexes, we tested the ability of the docking tool SLIDE to model these motions without being restricted to rotameric transitions or deciding which side chains should be considered as flexible. The model tested is that side-chain conformational changes involving more atoms or larger rotations are likely to be more costly and less prevalent than small motions due to energy barriers between rotamers and the potential of large motions to cause new steric clashes. Accordingly, SLIDE adjusts the protein and ligand side groups as little as necessary to achieve steric complementarity. We tested the hypothesis that small motions are sufficient to achieve good dockings using 63 ligands and the apo structures of 20 different proteins and compared SLIDE side-chain rotations to those experimentally observed. None of these proteins undergoes major main-chain conformational change upon ligand binding, ensuring that side-chain flexibility modeling is not required to compensate for main-chain motions. Although more frugal in the number of side-chain rotations performed, this model substantially mimics the experimentally observed motions. Most side chains do not shift to a new rotamer, and small motions are both necessary and sufficient to predict the correct binding orientation and most protein-ligand interactions for the 20 proteins analyzed.     

Hydrophobic Core Formation and Dehydration in Protein Folding Studied by Generalized-Ensemble Simulations

Despite its small size, chicken villin headpiece subdomain HP36 folds into the native structure with a stable hydrophobic core within several microseconds. How such a small protein keeps up its conformational stability and fast folding in solution is an important issue for understanding molecular mechanisms of protein folding. In this study, we performed multicanonical replica-exchange simulations of HP36 in explicit water, starting from a fully extended conformation. We observed at least five events of HP36 folding into nativelike conformations. The smallest backbone root mean-square deviation from the crystal structure was 1.1 Å. In the nativelike conformations, the stably formed hydrophobic core was fully dehydrated. Statistical analyses of the simulation trajectories show the following sequential events in folding of HP36: 1), Helix 3 is formed at the earliest stage; 2), the backbone and the side chains near the loop between Helices 2 and 3 take nativelike conformations; and 3), the side-chain packing at the hydrophobic core and the dehydration of the core side chains take place simultaneously at the later stage of folding. This sequence suggests that the initial folding nucleus is not necessarily the same as the hydrophobic core, consistent with a recent experimental ϕ-value analysis.     

Side-chain conformation in poly(γ-phenethyl-L-glutamate)

X-ray diffraction and energy-minimization results are reported for poly(γ-phenethyl-L -glutamate). Orthorhombic unit-cell parameters of drawn fibers are a = 15.4 Å, b = 26.6 Å, c = 54.4 Å. Atomic coordinates are derived for an α-helix peptide conformation that corresponds to a calculated side-chain internal energy minimum. The side-chain conformation correlates well with the electron density projection; the side chains wrap around the α-helical main chain with the phenethyl ester group directed toward the N-terminus. The para-axis of the benzene ring is inclined at an angle nearly nearly normal to the helix axis. The x-ray structure factors calculated for this model, when compared to the 10 observed structure factors, yield a crystallographic reliability index of R = 0.23.     

Benchmarking of TASSER_2.0: an improved protein structure prediction algorithm with more accurate predicted contact restraints

To improve tertiary structure predictions of more difficult targets, the next generation of TASSER, TASSER_2.0, has been developed. TASSER_2.0 incorporates more accurate side-chain contact restraint predictions from a new approach, the composite-sequence method, based on consensus restraints generated by an improved threading algorithm, PROSPECTOR_3.5, which uses computationally evolved and wild-type template sequences as input. TASSER_2.0 was tested on a large-scale, benchmark set of 2591 nonhomologous, single domain proteins ≤200 residues that cover the Protein Data Bank at 35% pairwise sequence identity. Compared with the average fraction of accurately predicted side-chain contacts of 0.37 using PROSPECTOR_3.5 with wild-type template sequences, the average accuracy of the composite-sequence method increases to 0.60. The resulting TASSER_2.0 models are closer to their native structures, with an average root mean-square deviation of 4.99 Å compared to the 5.31 Å result of TASSER. Defining a successful prediction as a model with a root mean-square deviation to native <6.5 Å, the success rate of TASSER_2.0 (TASSER) for Medium targets (targets with good templates/poor alignments) is 74.3% (64.7%) and 40.8% (35.5%) for the Hard targets (incorrect templates/alignments). For Easy targets (good templates/alignments), the success rate slightly increases from 86.3% to 88.4%.     

Protein design simulations suggest that side-chain conformational entropy is not a strong determinant of amino acid environmental preferences

Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein.     

An algorithm for determining the conformation of polypeptide segments in proteins by systematic search

The feasibility of determining the conformation of segments of a polypeptide chain up to six residues in length in globular proteins by means of a systematic search through the possible conformations has been investigated. Trial conformations are generated by using representative sets of phi, psi, and chi angles that have been derived from an examination of the distributions of these angles in refined protein structures. A set of filters based on simple rules that protein structures obey is used to reduce the number of conformations to a manageable total. The most important filters are the maintenance of chain integrity and the avoidance of too-short van der Waals contacts with the rest of the protein and with other portions of the segment under construction. The procedure is intended to be used with approximate models so that allowance is made throughout for errors in the rest of the structure. All possible main chains are first constructed and then all possible side-chain conformations are built onto each of these. The electrostatic energy, including a solvent screening term, and the exposed hydrophobic area are evaluated for each accepted conformation. The method has been tested on two segments of chain in the trypsin like enzyme from Streptomyces griseus. It is found that there is a wide spread of energies among the accepted conformations, and the lowest energy ones have satisfactorily small root mean square deviations from the X-ray structure.     

A Free-Energy Approach for All-Atom Protein Simulation

All-atom free-energy methods offer a promising alternative to kinetic molecular mechanics simulations of protein folding and association. Here we report an accurate, transferable all-atom biophysical force field (PFF02) that stabilizes the native conformation of a wide range of proteins as the global optimum of the free-energy landscape. For 32 proteins of the ROSETTA decoy set and six proteins that we have previously folded with PFF01, we find near-native conformations with an average backbone RMSD of 2.14 Å to the native conformation and an average Z-score of −3.46 to the corresponding decoy set. We used nonequilibrium sampling techniques starting from completely extended conformations to exhaustively sample the energy surface of three nonhomologous hairpin-peptides, a three-stranded β-sheet, the all-helical 40 amino-acid HIV accessory protein, and a zinc-finger ββα motif, and find near-native conformations for the minimal energy for each protein. Using a massively parallel evolutionary algorithm, we also obtain a near-native low-energy conformation for the 54 amino-acid engrailed homeodomain. Our force field thus stabilized near-native conformations for a total of 20 proteins of all structure classes with an average RMSD of only 3.06 Å to their respective experimental conformations.     

Protein-protein docking with a reduced protein model accounting for side-chain flexibility

A protein-protein docking approach has been developed based on a reduced protein representation with up to three pseudo atoms per amino acid residue. Docking is performed by energy minimization in rotational and translational degrees of freedom. The reduced protein representation allows an efficient search for docking minima on the protein surfaces within. During docking, an effective energy function between pseudo atoms has been used based on amino acid size and physico-chemical character. Energy minimization of protein test complexes in the reduced representation results in geometries close to experiment with backbone root mean square deviations (RMSDs) of approximately 1 to 3 A for the mobile protein partner from the experimental geometry. For most test cases, the energy-minimized experimental structure scores among the top five energy minima in systematic docking studies when using both partners in their bound conformations. To account for side-chain conformational changes in case of using unbound protein conformations, a multicopy approach has been used to select the most favorable side-chain conformation during the docking process. The multicopy approach significantly improves the docking performance, using unbound (apo) binding partners without a significant increase in computer time. For most docking test systems using unbound partners, and without accounting for any information about the known binding geometry, a solution within approximately 2 to 3.5 A RMSD of the full mobile partner from the experimental geometry was found among the 40 top-scoring complexes. The approach could be extended to include protein loop flexibility, and might also be useful for docking of modeled protein structures.     

Selecting near-native conformations in homology modeling: the role of molecular mechanics and solvation terms

A free energy function, combining molecular mechanics energy with empirical solvation and entropic terms, is used for ranking near-native conformations that occur in the conformational search steps of homology modeling, i.e., side-chain search and loop closure calculations. Correlations between the free energy and RMS deviation from the X-ray structure are established. It is shown that generally both molecular mechanics and solvation/entropic terms should be included in the potential. The identification of near-native backbone conformations is accomplished primarily by the molecular mechanics term that becomes the dominant contribution to the free energy if the backbone is even slightly strained, as frequently occurs in loop closure calculations. Both terms become equally important if a sufficiently accurate backbone conformation is found. Finally, the selection of the best side-chain positions for a fixed backbone is almost completely governed by the solvation term. The discriminatory power of the combined potential is demonstrated by evaluating the free energies of protein models submitted to the first meeting on Critical Assessment of techniques for protein Structure Prediction (CASP1), and comparing them to the free energies of the native conformations.     

Normal-mode-analysis-monitored energy minimization procedure for generating small-molecule bound conformations

The energy minimization of a small molecule alone does not automatically stop at a local minimum of the potential energy surface of the molecule if the minimum is shallow, thus leading to folding of the molecule and consequently hampering the generation of the bound conformation of a guest in the absence of its host. This questions the practicality of virtual screening methods that use conformations at local minima of their potential energy surfaces (local minimum conformations) as potential bound conformations. Here we report a normal-mode-analysis-monitored energy minimization (NEM) procedure that generates local minimum conformations as potential bound conformations. Of 22 selected guest-host complex crystal structures with guest structures possessing up to four rotatable bonds, all complexes were reproduced, with guest mass-weighted root mean square deviations of <1.0 A, through docking with the NEM-generated guest local minimum conformations. An analysis of the potential energies of these local minimum conformations showed that 22 (100%), 18 (82%), 16 (73%), and 12 (55%) of the 22 guest bound conformations in the crystal structures had conformational strain energies of less than or equal to 3.8, 2.0, 0.6, and 0.0 kcal/mol, respectively. These results suggest that (1) the NEM procedure can generate small-molecule bound conformations, and (2) guests adopt low-strain-energy conformations for complexation, thus supporting the virtual screening methods that use local minimum conformations.     

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.     

Side-chain modeling with an optimized scoring function

Modeling side-chain conformations on a fixed protein backbone has a wide application in structure prediction and molecular design. Each effort in this field requires decisions about a rotamer set, scoring function, and search strategy. We have developed a new and simple scoring function, which operates on side-chain rotamers and consists of the following energy terms: contact surface, volume overlap, backbone dependency, electrostatic interactions, and desolvation energy. The weights of these energy terms were optimized to achieve the minimal average root mean square (rms) deviation between the lowest energy rotamer and real side-chain conformation on a training set of high-resolution protein structures. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. We obtained prediction accuracy of 90.4% for chi(1), 78.3% for chi(1 + 2), and 1.18 A overall rms deviation. Furthermore, the derived scoring function combined with a Monte Carlo search algorithm was used to place all side chains onto a protein backbone simultaneously. The average prediction accuracy was 87.9% for chi(1), 73.2% for chi(1 + 2), and 1.34 A rms deviation for 30 protein structures. Our approach was compared with available side-chain construction methods and showed improvement over the best among them: 4.4% for chi(1), 4.7% for chi(1 + 2), and 0.21 A for rms deviation. We hypothesize that the scoring function instead of the search strategy is the main obstacle in side-chain modeling. Additionally, we show that a more detailed rotamer library is expected to increase chi(1 + 2) prediction accuracy but may have little effect on chi(1) prediction accuracy.