Rotamer strain as a determinant of protein structural specificity

We present direct evidence for a change in protein structural specificity due to hydrophobic core packing. High resolution structural analysis of a designed core variant of ubiquitin reveals that the protein is in slow exchange between two conformations. Examination of side-chain rotamers indicates that this dynamic response and the lower stability of the protein are coupled to greater strain and mobility in the core. The results suggest that manipulating the level of side-chain strain may be one way of fine tuning the stability and specificity of proteins.     

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%.     

Beyond the rotamer library: genetic algorithm combined with the disturbing mutation process for upbuilding protein side-chains

The disturbing genetic algorithm, incorporating the disturbing mutation process into the genetic algorithm flow, has been developed to extend the searching space of side-chain conformations and to improve the quality of the rotamer library. Moreover, the growing generation amount idea, simulating the real situation of the natural evolution, is introduced to improve the searching speed. In the calculations using the pseudo energy scoring function of the root mean squared deviation, the disturbing genetic algorithm method has been shown to be highly efficient. With the real energy function based on AMBER force field, the program has been applied to rebuilding side-chain conformations of 25 high-quality crystallographic structures of single-protein and protein-protein complexes. The averaged root mean standard deviation of atom coordinates in side-chains and veracities of the torsion angles of chi(1) and chi(1) + chi(2) are 1.165 A, 88.2 and 72.9% for the buried residues, respectively, and 1.493 A, 79.2 and 64.7% for all residues, showing that the method has equal precision to the program SCWRL, whereas it performs better in the prediction of buried residues and protein-protein interfaces. This method has been successfully used in redesigning the interface of the Basnase-Barstar complex, indicating that it will have extensive application in protein design, protein sequence and structure relationship studies, and research on protein-protein interaction.     

Steric and electronic interactions controlling the cis/trans isomer equilibrium at X‐pro tertiary amide motifs in solution

A systematic understanding of the noncovalent interactions that influence the structures of the cis conformers and the equilibrium between the cis and the trans conformers, of the X‐Pro tertiary amide motifs, is presented based on analyses of ¹H‐, ¹³C‐NMR and FTIR absorption spectra of two sets of homologous peptides, X‐Pro‐Aib‐OMe and X‐Pro‐NH‐Me (where X is acetyl, propionyl, isobutyryl and pivaloyl), in solvents of varying polarities. First, this work shows that the cis conformers of any X‐Pro tertiary amide motif, including Piv‐Pro, are accessible in the new motifs X‐Pro‐Aib‐OMe, in solution. These conformers are uniquely observable by FTIR spectroscopy at ambient temperatures and by NMR spectroscopy from temperatures as high as 273 K. This is made possible by the persistent presence of n_i‐1→π_i* interactions at Aib, which also influence the disappearance of steric effects at these cis X‐Pro rotamers. Second, contrary to conventional understanding, the energy contribution of steric effects to the cis/trans equilibrium at the X‐Pro motifs is found to be nonvariant (0.54 ± 0.02 kcal/mol) with increase in steric bulk on the X group. Third, the current studies provide direct evidence for the weak intramolecular interactions namely the n_i‐1→π_i*, the N_Pro???H_i+1 (C₅a), and the C₇ hydrogen bond that operate and influence the structures, stabilities, and dynamics between different conformational states of X‐Pro tertiary amide motifs. NMR and IR spectral data suggest that the cis conformers of X‐Pro motifs are ensembles of short‐lived rotamers about the C′_X–N_Pro bond. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 66–77, 2014.     

Role of the structural context in selection of hydrophobic side-chain rotamers in a- and d-positions of α-helices

It was demonstrated for the first time that the distribution of side-chain rotamers in the a-and d-positions of α-helices of coiled-coil (cc) proteins follows a certain trend, rather then being random. For instance, most side chains adopt t rotamers in the a-positions and g^? rotamers in the d-positions of helical dimers. Vice versa, most side chains adopt g^? rotamers in the a-positions and t rotamers in the d-positions of tetramers. It was concluded that selection of the side-chain rotamers depends on the packing of α-helices and, consequently, depends on the structural context.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

Optimization of rotamers prior to template minimization improves stability predictions made by computational protein design

Computational protein design (CPD) predictions are highly dependent on the structure of the input template used. However, it is unclear how small differences in template geometry translate to large differences in stability prediction accuracy. Herein, we explored how structural changes to the input template affect the outcome of stability predictions by CPD. To do this, we prepared alternate templates by Rotamer Optimization followed by energy Minimization (ROM) and used them to recapitulate the stability of 84 protein G domain β1 mutant sequences. In the ROM process, side-chain rotamers for wild-type (WT) or mutant sequences are optimized on crystal or nuclear magnetic resonance (NMR) structures prior to template minimization, resulting in alternate structures termed ROM templates. We show that use of ROM templates prepared from sequences known to be stable results predominantly in improved prediction accuracy compared to using the minimized crystal or NMR structures. Conversely, ROM templates prepared from sequences that are less stable than the WT reduce prediction accuracy by increasing the number of false positives. These observed changes in prediction outcomes are attributed to differences in side-chain contacts made by rotamers in ROM templates. Finally, we show that ROM templates prepared from sequences that are unfolded or that adopt a nonnative fold result in the selective enrichment of sequences that are also unfolded or that adopt a nonnative fold, respectively. Our results demonstrate the existence of a rotamer bias caused by the input template that can be harnessed to skew predictions toward sequences displaying desired characteristics.     

Relating side-chain mobility in proteins to rotameric transitions: Insights from molecular dynamics simulations and NMR

The dynamic aspect of proteins is fundamental to understanding protein stability and function. One of the goals of NMR studies of side-chain dynamics in proteins is to relate spin relaxation rates to discrete conformational states and the timescales of interconversion between those states. Reported here is a physical analysis of side-chain dynamics that occur on a timescale commensurate with monitoring by ²H spin relaxation within methyl groups. Motivated by observations made from tens-of-nanoseconds long MD simulations on the small protein eglin c in explicit solvent, we propose a simple molecular mechanics-based model for the motions of side-chain methyl groups. By using a Boltzmann distribution within rotamers, and by considering the transitions between different rotamer states, the model semi-quantitatively correlates the population of rotamer states with ‘model-free’ order parameters typically fitted from NMR relaxation experiments. Two easy-to-use, analytical expressions are given for converting S²_axis’ values (order parameter for C–CH₃ bond) into side-chain rotamer populations. These predict that S²_axis’ values below 0.8 result from population of more than one rotameric state. The relations are shown to predict rotameric sampling with reasonable accuracy on the ps–ns timescale for eglin c and are validated for longer timescales on ubiquitin, for which side-chain residual dipolar coupling (RDC) data have been collected.     

Environment-dependent long-range structural distortion in a temperature-sensitive point mutant

Extensive environment-dependent rearrangement of the helix-turn-helix DNA recognition region and adjacent L-tryptophan binding pocket is reported in the crystal structure of dimeric E. coli trp aporepressor with point mutation Leu75Phe. In one of two subunits, the eight residues immediately C-terminal to the mutation are shifted forward in helical register by three positions, and the five following residues form an extrahelical loop accommodating the register shift. In contrast, the second subunit has wildtype-like conformation, as do both subunits in an isomorphous wildtype control structure. Treated together as an ensemble pair, the distorted and wildtype-like conformations of the mutant apoprotein agree more fully than either conformation alone with previously reported NOE measurements, and account more completely for its diverse biochemical and biophysical properties. The register-shifted segment Ile79-Ala80-Thr81-Ile82-Thr83 is helical in both conformations despite low helical propensity, suggesting an important structural role for the steric constraints imposed by β-branched residues in helical conformation.