Improved modeling of side-chains in proteins with rotamer-based methods: a flexible rotamer model

Side-chain modeling has a widespread application in many current methods for protein tertiary structure determination, prediction, and design. Of the existing side-chain modeling methods, rotamer-based methods are the fastest and most efficient. Classically, a rotamer is conceived as a single, rigid conformation of an amino acid sidechain. Here, we present a flexible rotamer model in which a rotamer is a continuous ensemble of conformations that cluster around the classic rigid rotamer. We have developed a thermodynamically based method for calculating effective energies for the flexible rotamer. These energies have a one-to-one correspondence with the potential energies of the rigid rotamer. Therefore, the flexible rotamer model is completely general and may be used with any rotamer-based method in substitution of the rigid rotamer model. We have compared the performance of the flexible and rigid rotamer models with one side-chain modeling method in particular (the self-consistent mean field theory method) on a set of 20 high quality crystallographic protein structures. For the flexible rotamer model, we obtained average predictions of 85.8% for chi1, 76.5% for chi1+2 and 1.34 A for root-mean-square deviation (RMSD); the corresponding values for core residues were 93.0%, 87.7% and 0.70 A, respectively. These values represent improvements of 7.3% for chi1, 8.1% for chi1+2 and 0.23 A for RMSD over the predictions obtained with the rigid rotamer model under otherwise identical conditions; the corresponding improvements for core residues were 6.9%, 10.5% and 0.43 A, respectively. We found that the predictions obtained with the flexible rotamer model were also significantly better than those obtained for the same set of proteins with another state-of-the-art side-chain placement method in the literature, especially for core residues. The flexible rotamer model represents a considerable improvement over the classic rigid rotamer model. It can, therefore, be used with considerable advantage in all rotamer-based methods commonly applied to protein tertiary structure determination, prediction, and design and also in predictions of free energies in mutational studies.     

Triathlon for energy functions: Who is the winner for design of protein–protein interactions?

Computational prediction of stabilizing mutations into monomeric proteins has become an almost ordinary task. Yet, computational stabilization of protein–protein complexes remains a challenge. Design of protein–protein interactions (PPIs) is impeded by the absence of an energy function that could reliably reproduce all favorable interactions between the binding partners. In this work, we present three energy functions: one function that was trained on monomeric proteins, while the other two were optimized by different techniques to predict side-chain conformations in a dataset of PPIs. The performances of these energy functions are evaluated in three different tasks related to design of PPIs: predicting side-chain conformations in PPIs, recovering native binding-interface sequences, and predicting changes in free energy of binding due to mutations. Our findings show that both functions optimized on side-chain repacking in PPIs are more suitable for PPI design compared to the function trained on monomeric proteins. Yet, no function performs best at all three tasks. Comparison of the three energy functions and their performances revealed that (1) burial of polar atoms should not be penalized significantly in PPI design as in single-protein design and (2) contribution of electrostatic interactions should be increased several-fold when switching from single-protein to PPI design. In addition, the use of a softer van der Waals potential is beneficial in cases when backbone flexibility is important. All things considered, we define an energy function that captures most of the nuances of the binding energetics and hence, should be used in future for design of PPIs.     

Monte Carlo refinement of rigid-body protein docking structures with backbone displacement and side-chain optimization

Structures of hitherto unknown protein complexes can be predicted by docking the solved protein monomers. Here, we present a method to refine initial docking estimates of protein complex structures by a Monte Carlo approach including rigid-body moves and side-chain optimization. The energy function used is comprised of van der Waals, Coulomb, and atomic contact energy terms. During the simulation, we gradually shift from a novel smoothed van der Waals potential, which prevents trapping in local energy minima, to the standard Lennard-Jones potential. Following the simulation, the conformations are clustered to obtain the final predictions. Using only the first 100 decoys generated by a fast Fourier transform (FFT)-based rigid-body docking method, our refinement procedure is able to generate near-native structures (interface RMSD <2.5 A) as first model in 14 of 59 cases in a benchmark set. In most cases, clear binding funnels around the native structure can be observed. The results show the potential of Monte Carlo refinement methods and emphasize their applicability for protein-protein docking.     

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.     

Construction of side-chains in homology modelling. Application to the C-terminal lobe of rhizopuspepsin

A detailed and rule-based side-chain modelling procedure for globular proteins is presented. It uses the conformational information contained in a homologous (template) structure as a starting point and includes recipes for atom placement and for checking and improving the atomic positions. The scheme does not rely on intuitive judgements or visual examination of the model during construction or refinement. It comprises four stages; the first three are relatively simple and the fourth is more complex. In the first stage, initial conformations for as many atoms as possible are transferred from the template structure based on the application of trends reported previously. Second, these trends are used to correct poor van der Waals overlaps. Third, the remaining side-chains atoms (those for which no information is contained in the template) are placed by evaluating their rigid rotation, van der Waals surfaces. The fourth stage consists of a hierarchial series of conformational checks. They involve the evaluation of individual residue energies in the absence and presence of the rest of the protein relative to statistical trends observed in the template structure, the comparison of hydrogen-bonding patterns and side-chain accessibilities in the model and template and brief energy minimization followed by an evaluation of the rigid rotation potential energy surfaces of each side-chain. The checks pinpoint "incorrectly" modelled side-chains, suggest conformational changes and provide a means for determining the portions of the model that are likely to be correct and those likely to be in error. The procedure developed in the paper is tested by modelling the side-chains of the C-terminal lobe of the aspartyl proteinase rhizopuspepsin, using the rhizopuspepsin backbone and the homologous protein, penicillopepsin, as a template for the side-chains. The resultant model was compared to the high-resolution X-ray structure of rhizopuspepsin. Using penicillopepsin data only (stage I), 58% of the chi 1 dihedrals and 44% of the chi 2 dihedrals were modelled correctly. Once poor van der Waals overlaps had been corrected and all of the atoms had been placed (stages II and III), 86% of the chi 1 dihedrals and 75% of the chi 2 dihedrals were correct. After the refinement had been completed (stage IV), 92% of the chi 1 dihedrals and 81% of the chi 2 dihedrals were correctly positioned.(ABSTRACT TRUNCATED AT 400 WORDS)     

Improved side-chain prediction accuracy using an ab initio potential energy function and a very large rotamer library

Accurate prediction of the placement and comformations of protein side chains given only the backbone trace has a wide range of uses in protein design, structure prediction, and functional analysis. Prediction has most often relied on discrete rotamer libraries so that rapid fitness of side-chain rotamers can be assessed against some scoring function. Scoring functions are generally based on experimental parameters from small-molecule studies or empirical parameters based on determined protein structures. Here, we describe the NCN algorithm for predicting the placement of side chains. A predominantly first-principles approach was taken to develop the potential energy function incorporating van der Waals and electrostatics based on the OPLS parameters, and a hydrogen bonding term. The only empirical knowledge used is the frequency of rotameric states from the PDB. The rotamer library includes nearly 50,000 rotamers, and is the most extensive discrete library used to date. Although the computational time tends to be longer than most other algorithms, the overall accuracy exceeds all algorithms in the literature when placing rotamers on an accurate backbone trace. Considering only the most buried residues, 80% of the total residues tested, the placement accuracy reaches 92% for chi(1), and 83% for chi(1 + 2), and an overall RMS deviation of 1 A. Additionally, we show that if information is available to restrict chi(1) to one rotamer well, then this algorithm can generate structures with an average RMS deviation of 1.0 A for all heavy side-chains atoms and a corresponding overall chi(1 + 2) accuracy of 85.0%.     

Combination of scoring functions improves discrimination in protein-protein docking

Two structure-based potentials are used for both filtering (i.e., selecting a subset of conformations generated by rigid-body docking), and rescoring and ranking the selected conformations. ACP (atomic contact potential) is an atom-level extension of the Miyazawa-Jernigan potential parameterized on protein structures, whereas RPScore (residue pair potential score) is a residue-level potential, based on interactions in protein-protein complexes. These potentials are combined with other energy terms and applied to 13 sets of protein decoys, as well as to the results of docking 10 pairs of unbound proteins. For both potentials, the ability to discriminate between near-native and non-native docked structures is substantially improved by refining the structures and by adding a van der Waals energy term. It is observed that ACP and RPScore complement each other in a number of ways (e.g., although RPScore yields more hits than ACP, mainly as a result of its better performance for charged complexes, ACP usually ranks the near-native complexes better). As a general solution to the protein-docking problem, we have found that the best discrimination strategies combine either an RPScore filter with an ACP-based scoring function, or an ACP-based filter with an RPScore-based scoring function. Thus, ACP and RPScore capture complementary structural information, and combining them in a multistage postprocessing protocol provides substantially better discrimination than the use of the same potential for both filtering and ranking the docked conformations.     

Free energy landscapes of two model peptides: α-helical and β-hairpin peptides explored with Brownian dynamics simulation

We applied an atomistic Brownian dynamics (BD) simulation with multiple time step method for the folding simulation of a 13-mer α-helical peptide and a 12-mer β-hairpin peptide, giving successful folding simulations. In this model, the driving energy contribution towards folding came from both electrostatic and van der Waals interactions for the α-helical peptide and from van der Waals interactions for the β-hairpin peptide. Although, many non-native structures having the same or lower energy than that of native structure were observed, the folded states formed the most populated cluster when the structures obtained by the BD simulations were subjected to the cluster analysis based on distance-based root mean square deviation of side-chains between different structures. This result indicates that we can predict the native structures from conformations sampled by BD simulation.     

Protein-surface interactions

This article describes an energy-based approach to protein adsorption, focusing on the energies involved in the interactions between a protein and a surface. Mathematical modeling and simulation based on this approach allow an improved understanding of the conditions that favor or prevent adsorption of a protein onto a surface and that can play a significant role in the design of material surfaces that interact with biological tissues according to specific needs. Biocompatibility with respect to fluids in motion, such as blood, is the main foreseeable application of our work. The considered energies are the van der Waals energy, the electrostatic energy, and the hydrophobic or hydrophilic energy. Moreover, the motion of the medium in which particles are immersed is also taken into account, considering the drag effect of the motion of the fluid on the particle, leading to a kinetic contribution to the total energy. It is shown that the adsorption behavior is not mainly determined by the van der Waals energy and by the double layer energy, but that a significant role is also played by the hydrophobic or hydrophilic energy. These results support the findings of experimental studies.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Protonate3D: assignment of ionization states and hydrogen coordinates to macromolecular structures

A new method, called Protonate3D, is presented for the automated prediction of hydrogen coordinates given the 3D coordinates of the heavy atoms of a macromolecular structure. Protonate3D considers side-chain "flip," rotamer, tautomer, and ionization states of all chemical groups, ligands, and solvent, provided suitable templates are available in a parameter file. The energy model includes van der Waals, Coulomb, solvation, rotamer, tautomer, and titration effects. The results of computational validation experiments suggest that Protonate3D can accurately predict the location of hydrogen atoms in macromolecular structures.     

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

Understanding beta-hairpin formation by molecular dynamics simulations of unfolding

We have studied the mechanism of formation of a 16-residue beta-hairpin from the protein GB1 using molecular dynamics simulations in an aqueous environment. The analysis of unfolding trajectories at high temperatures suggests a refolding pathway consisting of several transient intermediates. The changes in the interaction energies of residues are related with the structural changes during the unfolding of the hairpin. The electrostatic energies of the residues in the turn region are found to be responsible for the transition between the folded state and the hydrophobic core state. The van der Waals interaction energies of the residues in the hydrophobic core reflect the behavior of the radius of gyration of the core region. We have examined the opposing influences of the protein-protein (PP) energy, which favors the native state, and the protein-solvent (PS) energy, which favors unfolding, in the formation of the beta-hairpin structure. It is found that the behavior of the electrostatic components of PP and PS energies reflects the structural changes associated with the loss of backbone hydrogen bonding. Relative changes in the PP and PS van der Waals interactions are related with the disruption of the hydrophobic core of a protein. The results of the simulations support the hydrophobic collapse mechanism of beta-hairpin folding.     

Poisson–Boltzmann model analysis of binding mRNA cap analogues to the translation initiation factor eIF4E

The electrostatic free energy of binding of two analogues of the 5′-mRNA cap, differing in size and electric charge, to the wild type and mutated eukaryotic initiation factor eIF4E was computed using the finite difference solutions to the Poisson–Boltzmann equation. Two definitions of the solute–solvent dielectric boundary were used: van der Waals model, solvent exclusion (SE) model. The computed electrostatic energies were supplemented by estimations of the non polar and entropic contributions. A comparison with experimental data for the investigated systems was done. It appears that the SE model with additional contribution fits experimental findings better than the van der Waals model does.     

The penultimate rotamer library

All published rotamer libraries contain some rotamers that exhibit impossible internal atomic overlaps if built in ideal geometry with all hydrogen atoms. Removal of uncertain residues (mainly those with B-factors >/=40 or van der Waals overlaps >/=0.4 A) greatly improves the clustering of rotamer populations. Asn, Gln, or His side chains additionally benefit from flipping of their planar terminal groups when required by atomic overlaps or H-bonding. Sensitivity to skew and to the boundaries of chi angle bins is avoided by using modes rather than traditional mean values. Rotamer definitions are listed both as the modal values and in a preferred version that maximizes common atoms between related rotamers. The resulting library shows significant differences from previous ones, differences validated by considering the likelihood of systematic misfitting of models to electron density maps and by plotting changes in rotamer frequency with B-factor. Few rotamers now show atomic overlaps in ideal geometry; those overlaps are relatively small and can be understood in terms of bond angle distortions compensated by favorable interactions. The new library covers 94.5% of examples in the highest quality protein data with 153 rotamers and can make a significant contribution to improving the accuracy of new structures. Proteins 2000;40:389-408.     

ROSETTALIGAND: protein-small molecule docking with full side-chain flexibility

Protein-small molecule docking algorithms provide a means to model the structure of protein-small molecule complexes in structural detail and play an important role in drug development. In recent years the necessity of simulating protein side-chain flexibility for an accurate prediction of the protein-small molecule interfaces has become apparent, and an increasing number of docking algorithms probe different approaches to include protein flexibility. Here we describe a new method for docking small molecules into protein binding sites employing a Monte Carlo minimization procedure in which the rigid body position and orientation of the small molecule and the protein side-chain conformations are optimized simultaneously. The energy function comprises van der Waals (VDW) interactions, an implicit solvation model, an explicit orientation hydrogen bonding potential, and an electrostatics model. In an evaluation of the scoring function the computed energy correlated with experimental small molecule binding energy with a correlation coefficient of 0.63 across a diverse set of 229 protein- small molecule complexes. The docking method produced lowest energy models with a root mean square deviation (RMSD) smaller than 2 A in 71 out of 100 protein-small molecule crystal structure complexes (self-docking). In cross-docking calculations in which both protein side-chain and small molecule internal degrees of freedom were varied the lowest energy predictions had RMSDs less than 2 A in 14 of 20 test cases.     

Protein docking using continuum electrostatics and geometric fit

The computer program DOT quickly finds low-energy docked structures for two proteins by performing a systematic search over six degrees of freedom. A novel feature of DOT is its energy function, which is the sum of both a Poisson-Boltzmann electrostatic energy and a van der Waals energy, each represented as a grid-based correlation function. DOT evaluates the energy of interaction for many orientations of the moving molecule and maintains separate lists scored by either the electrostatic energy, the van der Waals energy or the composite sum of both. The free energy is obtained by summing the Boltzmann factor over all rotations at each grid point. Three important findings are presented. First, for a wide variety of protein-protein interactions, the composite-energy function is shown to produce larger clusters of correct answers than found by scoring with either van der Waals energy (geometric fit) or electrostatic energy alone. Second, free-energy clusters are demonstrated to be indicators of binding sites. Third, the contributions of electrostatic and attractive van der Waals energies to the total energy term appropriately reflect the nature of the various types of protein-protein interactions studied.