Investigations into sequence and conformational dependence of backbone entropy, inter-basin dynamics and the Flory isolated-pair hypothesis for peptides

What are the minimal folding seeds in proteins? Experimental and theoretical assessment of secondary structure propensities of small peptide fragments

Certain peptide sequences, some of them as short as amino acid triplets, are significantly overpopulated in specific secondary structure motifs in folded protein structures. For example, 74% of the EAM triplet is found in α-helices, and only 3% occurs in the extended parts of proteins (typically β-sheets). In contrast, other triplets (such as VIV and IYI) appear almost exclusively in extended parts (79% and 69%, respectively). In order to determine whether such preferences are structurally encoded in a particular peptide fragment or appear only at the level of a complex protein structure, NMR, VCD, and ECD experiments were carried out on selected tripeptides: EAM (denoted as pro-'α-helical' in proteins), KAM(α), ALA(α), DIC(α), EKF(α), IYI(pro-β-sheet or more generally, pro-extended), and VIV(β), and the reference α-helical CATWEAMEKCK undecapeptide. The experimental data were in very good agreement with extensive quantum mechanical conformational sampling. Altogether, we clearly showed that the pro-helical vs. pro-extended propensities start to emerge already at the level of tripeptides and can be fully developed at longer sequences. We postulate that certain short peptide sequences can be considered minimal "folding seeds". Admittedly, the inherent secondary structure propensity can be overruled by the large intramolecular interaction energies within the folded and compact protein structures. Still, the correlation of experimental and computational data presented herein suggests that the secondary structure propensity should be considered as one of the key factors that may lead to understanding the underlying physico-chemical principles of protein structure and folding from the first principles.

The relevance of short peptides for an understanding of unfolded and intrinsically disordered proteins

Over the last thirty years the unfolded state of proteins has attracted considerable interest owing to the discovery of intrinsically disordered proteins which perform a plethora of functions despite resembling unfolded proteins to a significant extent. Research on both, unfolded and disordered proteins has revealed that their conformational properties can deviate locally from random coil behavior. In this context results from work on short oligopeptides suggest that individual amino acid residues sample the sterically allowed fraction of the Ramachandran plot to a different extent. Alanine has been found to exhibit a peculiarity in that it has a very high propensity for adopting polyproline II like conformations. This Perspectives article reviews work on short peptides aimed at exploring the Ramachandran distributions of amino acid residues in different contexts with experimental and computational means. Based on the thus provided overview the article discussed to what extent short peptides can serve as tools for exploring unfolded and disordered proteins and as benchmarks for the development of a molecular dynamics force field.

Statistical proofs of the interdependence between nearest neighbor effects on polypeptide backbone conformations

Backbone dihedral angles ϕ and ψ are the main structural descriptors of proteins and peptides. The distribution of these angles has been investigated over decades as they are essential for the validation and refinement of experimental measurements, as well as for structure prediction and design methods. The dependence of these distributions, not only on the nature of each amino acid but also on that of the closest neighbors, has been the subject of numerous studies. Although neighbor-dependent distributions are nowadays generally accepted as a good model, there is still some controversy about the combined effects of left and right neighbors. We have investigated this question using rigorous methods based on recently-developed statistical techniques. Our results unambiguously demonstrate that the influence of left and right neighbors cannot be considered independently. Consequently, three-residue fragments should be considered as the minimal building blocks to investigate polypeptide sequence-structure relationships.

Exhaustive Mapping of the Conformational Space of Natural Dipeptides by the DFT-D3//COSMO-RS Method

We extensively mapped energy landscapes and conformations of 22 (including three His protonation states) proteinogenic α-amino acids in trans configuration and the corresponding 484 (22²) dipeptides. To mimic the environment in a protein chain, the N- and C-termini of the studied systems were capped with acetyl and N-methylamide groups, respectively. We systematically varied the main chain dihedral angles (ϕ, ψ) by 40° steps and all side chain angles by 90° or 120° steps. We optimized the molecular geometries with the GFN2-xTB semiempirical (SQM) method and performed single point density functional theory calculations at the BP86-D3/DGauss-DZVP//COSMO-RS level in water, 1-octanol, N,N-dimethylformamide, and n-hexane. For each restrained (nonequilibrium) structure, we also calculated energy gradients (in water) and natural atomic charges. The exhaustive and unprecedented QM-based sampling enabled us to construct Ramachandran plots of quantum mechanical (QM(BP86-D3)//COSMO-RS) energies calculated on SQM structures, for all 506 (484 dipeptides and 22 amino acids) studied systems. We showed how the character of an amino acid side chain influences the conformational space of single amino acids and dipeptides. With clustering techniques, we were able to identify unique minima of amino acids and dipeptides (i.e., minima on the GFN2-xTB potential energy surfaces) and analyze the distribution of their BP86-D3//COSMO-RS conformational energies in all four solvents. We also derived an empirical formula for the number of unique minima based on the overall number of rotatable bonds within each peptide. The final peptide conformer data set (PeptideCs) comprises over 400 million structures, all of them annotated with QM(BP86-D3)//COSMO-RS energies. Thanks to its completeness and unbiased nature, the PeptideCs can serve, inter alia, as a data set for the validation of new methods for predicting the energy landscapes of protein structures. This data set may also prove to be useful in the development and reparameterization of biomolecular force fields. The data set is deposited at Figshare (10.25452/figshare.plus.19607172) and can be accessed using a simple web interface at http://peptidecs.uochb.cas.cz.

Exploring Nearest Neighbor Interactions and Their Influence on the Gibbs Energy Landscape of Unfolded Proteins and Peptides

The Flory isolated pair hypothesis (IPH) is one of the corner stones of the random coil model, which is generally invoked to describe the conformational dynamics of unfolded and intrinsically disordered proteins (IDPs). It stipulates, that individual residues sample the entire sterically allowed space of the Ramachandran plot without exhibiting any correlations with the conformational dynamics of its neighbors. However, multiple lines of computational, bioinformatic and experimental evidence suggest that nearest neighbors have a significant influence on the conformational sampling of amino acid residues. This implies that the conformational entropy of unfolded polypeptides and proteins is much less than one would expect based on the Ramachandran plots of individual residues. A further implication is that the Gibbs energies of residues in unfolded proteins or polypeptides are not additive. This review provides an overview of what is currently known and what has yet to be explored regarding nearest neighbor interactions in unfolded proteins.

Randomizing of Oligopeptide Conformations by Nearest Neighbor Interactions between Amino Acid Residues

Flory’s random coil model assumes that conformational fluctuations of amino acid residues in unfolded poly(oligo)peptides and proteins are uncorrelated (isolated pair hypothesis, IPH). This implies that conformational energies, entropies and solvation free energies are all additive. Nearly 25 years ago, analyses of coil libraries cast some doubt on this notion, in that they revealed that aromatic, but also β-branched side chains, could change the ³J(H^NH^Cα) coupling of their neighbors. Since then, multiple bioinformatical, computational and experimental studies have revealed that conformational propensities of amino acids in unfolded peptides and proteins depend on their nearest neighbors. We used recently reported and newly obtained Ramachandran plots of tetra- and pentapeptides with non-terminal homo- and heterosequences of amino acid residues to quantitatively determine nearest neighbor coupling between them with a Ising type model. Results reveal that, depending on the choice of amino acid residue pairs, nearest neighbor interactions either stabilize or destabilize pairs of polyproline II and β-strand conformations. This leads to a redistribution of population between these conformations and a reduction in conformational entropy. Interactions between residues in polyproline II and turn(helix)-forming conformations seem to be cooperative in most cases, but the respective interaction parameters are subject to large statistical errors.

Advancing Rational Control of Peptide-Surface Complexes

Understanding peptide-surface interactions is crucial for programming self-assembly of peptides at surfaces and in realizing their applications, such as biosensors and biomimetic materials. In this study, we developed insights into the dependence of a residue's interaction with a surface on its neighboring residue in a tripeptide using molecular dynamics simulations. This knowledge is integral for designing rational mutations to control peptide-surface complexes. Using graphene as our model surface, we estimated the free energy of adsorption (ΔA_ads) and extracted predominant conformations of 26 tripeptides with the motif LNR-CR-Gly, where LNR and CR are variable left-neighboring and central residues, respectively. We considered a combination of strongly adsorbing (Phe, Trp, and Arg) and weakly adsorbing (Ala, Val, Leu, Ser, and Thr) amino acids on graphene identified in a prior study to form the tripeptides. Our results indicate that ΔA_ads of a tripeptide cannot be estimated as the sum of ΔA_ads of each residue indicating that the residues in a tripeptide do not behave as independent entities. We observed that the contributions from the strongly adsorbing amino acids were dominant, which suggests that such residues could be used for strengthening peptide-graphene interactions irrespective of their neighboring residues. In contrast, the adsorption of weakly adsorbing central residues is dependent on their neighboring residues. Our structural analysis revealed that the dihedral angles of LNR are more correlated with that of CR in the adsorbed state than in bulk state. Together with ΔA_ads trends, this implies that different backbone structures of a given CR can be accessed for a similar ΔA_ads by varying the LNR. Therefore, incorporation of context effects in designing mutations can lead to desired peptide structure at surfaces. Our results also emphasize that these cooperative effects in ΔA_ads and structure are not easily predicted a priori. The collective results have applications in guiding rational mutagenesis techniques to control orientation of peptides at surfaces and in developing peptide structure prediction algorithms in adsorbed state from its sequence.

Short peptides as predictors for the structure of polyarginine sequences in disordered proteins

Intrinsically disordered proteins and intrinsically disordered regions are frequently enriched in charged amino acids. Intrinsically disordered regions are regularly involved in important biological processes in which one or more charged residues is the driving force behind a protein-biomolecule interaction. Several lines of experimental and computational evidence suggest that polypeptides and proteins that carry high net charges have a high preference for extended conformations with average end-to-end distances exceeding expectations for self-avoiding random coils. Here, we show that charged arginine residues even in short glycine-capped model peptides (GRRG and GRRRG) significantly affect the conformational propensities of each other when compared with the intrinsic propensities of a mostly unperturbed arginine in the tripeptide GRG. A conformational analysis based on experimentally determined J-coupling constants from heteronuclear NMR spectroscopy and amide I' band profiles from vibrational spectroscopy reveals that nearest-neighbor interactions stabilize extended β-strand conformations at the expense of polyproline II and turn conformations. The results from molecular dynamics simulations with a CHARMM36m force field and TIP3P water reproduce our results only to a limited extent. The use of the Ramachandran distribution of the central residue of GRRRG in a calculation of end-to-end distances of polyarginines of different length yielded the expected power law behavior. The scaling coefficient of 0.66 suggests that such peptides would be more extended than predicted by a self-avoiding random walk. Our findings thus support in principle theoretical predictions.

On the Role of Entropy in the Stabilization of α-Helices

Protein folding evolves by exploring the conformational space with a subtle balance between enthalpy and entropy changes which eventually leads to a decrease of free energy upon reaching the folded structure. A complete understanding of this process requires, therefore, a deep insight into both contributions to free energy. In this work, we clarify the role of entropy in favoring the stabilization of folded structures in polyalanine peptides with up to 12 residues. We use a novel method referred to as K2V that allows us to obtain the potential-energy landscapes in terms of residue conformations extracted from molecular dynamics simulations at conformational equilibrium and yields folding thermodynamic magnitudes, which are in agreement with the experimental data available. Our results demonstrate that the folded structures of the larger polyalanine chains are stabilized with respect to the folded structures of the shorter chains by both an energetic contribution coming from the formation of the intramolecular hydrogen bonds and an entropic contribution coming from an increase of the entropy of the solvent with approximate weights of 60 and 40%, respectively, thus unveiling a key piece in the puzzle of protein folding. In addition, the ability of the K2V method to provide the enthalpic and entropic contributions for individual residues along the peptide chain makes it clear that the energetic and entropic stabilizations are basically governed by the nearest neighbor residue conformations, with the folding propensity being rationalized in terms of triads of residues.

Helix-Coil Transition at a Glycine Following a Nascent α-Helix: A Synergetic Guidance Mechanism for Helix Growth

A detailed understanding of forces guiding the rapid folding of a polypeptide from an apparently random coil state to an ordered α-helical structure following the rate-limiting preorganization of the initial three residue backbones into helical conformation is imperative to comprehending and regulating protein folding and for the rational design of biological mimetics. However, several details of this process are still unknown. First, although the helix-coil transition was proposed to originate at the residue level (J. Chem. Phys. 1959, 31, 526-535; J. Chem. Phys. 1961, 34, 1963-1974), all helix-folding studies have only established it between time-averaged bulk states of a long-lived helix and several transiently populated random coils, along the whole helix model sequence. Second, the predominant thermodynamic forces driving either this two-state transition or the faster helix growth following helix nucleation are still unclear. Third, the conformational space of the random coil state is not well-defined unlike its corresponding α-helix. Here we investigate the restrictions placed on the conformational space of a Gly residue backbone, as a result of it immediately succeeding a nascent α-helical turn. Analyses of the temperature-dependent 1D-, 2D-NMR, FT-IR, and CD spectra and GROMACS MD simulation trajectory of a Gly residue backbone following a model α-helical turn, which is artificially rigidified by a covalent hydrogen bond surrogate, reveal that: (i) the α-helical turn guides the ϕ torsion of the Gly exclusively into either a predominantly populated entropically favored α-helical (α-ϕ) state or a scarcely populated random coil (RC-ϕ) state; (ii) the α-ϕ state of Gly in turn favors the stability of the preceding α-helical turn, while the RC-ϕ state disrupts it, revealing an entropy-driven synergetic guidance for helix growth in the residue following helix nucleation. The applicability of a current synergetic guidance mechanism to explain rapid helix growth in folded and unfolded states of proteins and helical peptides is discussed.

Glycine in Water Favors the Polyproline II State

Conformational preferences of amino acid residues in water are determined by the backbone and side-chain properties. Alanine is known for its high polyproline II (pPII) propensity. The question of relative contributions of the backbone and side chain to the conformational preferences of alanine and other amino acid residues in water is not fully resolved. Because glycine lacks a heavy-atom side chain, glycine-based peptides can be used to examine to which extent the backbone properties affect the conformational space. Here, we use published spectroscopic data for the central glycine residue of cationic triglycine in water to demonstrate that its conformational space is dominated by the pPII state. We assess three commonly used molecular dynamics (MD) force fields with respect to their ability to capture the conformational preferences of the central glycine residue in triglycine. We show that pPII is the mesostate that enables the functional backbone groups of the central residue to form the most hydrogen bonds with water. Our results indicate that the pPII propensity of the central glycine in GGG is comparable to that of alanine in GAG, implying that the water-backbone hydrogen bonding is responsible for the high pPII content of these residues.

Interplay between Conformational Strain and Intramolecular Interaction in Protein Structures: Which of Them Is Evolutionarily Conserved?

By computing strain energies of peptide fragments within protein structures and their intramolecular interaction energies, we attempt to reveal general biophysical trends behind the secondary structure formation in the context of protein evolution. Our "protein basis set" consisted of 1143 representatives of different folds obtained from curated SCOPe database, and for each member of the set, the strain and intramolecular energy was calculated on the "rolling tripeptide" basis, employing the DFT-D3/COSMO-RS method for the former and the QM-calibrated force field method (MM) for the latter. The calculated data, strain and interactions, were correlated with the conservation of amino acid residues in secondary structure elements and also with the level of the residue burial within the protein three-dimensional structure. It allowed us to formulate several observations concerning fundamental differences between two main secondary structure motifs: α-helices and β-strands. We have shown that a strong interaction is one of the determining characteristics of the β-sheet formation, at least at the level of tripeptides (and likely penta- or heptapeptides, too), and that the β-strand is a prevailing secondary structure in the strongly-interacting regions of the protein folds conserved by evolution. On the other hand, low strain was neither proven to be an important physicochemical property conserved by evolution nor does it correlate with the propensity for the α-helix and β-strand. Finally, it has been demonstrated that the strong interaction has a certain level of connection with residue burial; however, we demonstrate that these two characteristics should be rather regarded as two complementary factors. These findings represent an important contribution to understanding protein folding from first principles, which is a complementary approach to ongoing efforts to solve the protein folding problem by knowledge-based approaches and machine-learning.

Anticooperative Nearest-Neighbor Interactions between Residues in Unfolded Peptides and Proteins

Growing evidence suggests that the conformational distributions of amino acid residues in unfolded peptides and proteins depend on the nature of the nearest neighbors. To explore whether the underlying interactions would lead to a breakdown of the isolated pair hypothesis of the classical random coil model, we further analyzed the conformational propensities that were recently obtained for the two guest residues (x,y) of GxyG tetrapeptides. We constructed a statistical thermodynamics model that allows for cooperative as well as for anticooperative interactions between adjacent residues adopting either a polyproline II or a β-strand conformation. Our analysis reveals that the nearest-neighbor interactions between most of the central residues in the investigated GxyG peptides are anticooperative. Interaction Gibbs energies are rather large at high temperatures (350 K), at which point many proteins undergo thermal unfolding. At room temperature, these interaction energies are less pronounced. We used the obtained interaction parameter in a Zimm-Bragg/Ising-type approach to calculate the temperature dependence of the ultraviolet circular dichroism (CD) of the MAX3 peptide, which is predominantly built by KV repeats. The agreement between simulation and experimental data was found to be satisfactory. Finally, we analyzed the temperature dependence of the CD and ³J(H^NH^α) parameters of the amyloid β_1-9 fragment. The results of this analysis and a more qualitative consideration of the temperature dependence of denatured proteins probed by CD spectroscopy further corroborate the dominance of anticooperative nearest-neighbor interactions. Generally, our results show that unfolded peptides-and most likely also proteins-exhibit some similarity with antiferromagnetic systems.

Experimentally Derived and Computationally Optimized Backbone Conformational Statistics for Blocked Amino Acids

Experimentally derived, amino acid specific backbone dihedral angle distributions are invaluable for modeling data-driven conformational equilibria of proteins and for enabling quantitative assessments of the accuracies of molecular mechanics force fields. The protein coil library that is extracted from analysis of high-resolution structures of proteins has served as a useful proxy for quantifying intrinsic and context-dependent conformational distributions of amino acids. However, data that go into coil libraries will have hidden biases, and ad hoc procedures must be used to remove these biases. Here, we combine high-resolution biased information from protein structural databases with unbiased low-resolution information from spectroscopic measurements of blocked amino acids to obtain experimentally derived and computationally optimized coil-library landscapes for each of the 20 naturally occurring amino acids. Quantitative descriptions of conformational distributions require parsing of data into conformational basins with defined envelopes, centers, and statistical weights. We develop and deploy a numerical method to extract conformational basins. The weights of conformational basins are optimized to reproduce quantitative inferences drawn from spectroscopic experiments for blocked amino acids. The optimized distributions serve as touchstones for assessments of intrinsic conformational preferences and for quantitative comparisons of molecular mechanics force fields.

Ramachandran maps for side chains in globular proteins

The Ramachandran plot for backbone ϕ,ψ-angles in a blocked monopeptide has played a central role in understanding protein structure. Curiously, a similar analysis for side chain χ-angles has been comparatively neglected. Instead, efforts have focused on compiling various types of side chain libraries extracted from proteins of known structure. Departing from this trend, the following analysis presents backbone-based maps of side chains in blocked monopeptides. As in the original ϕ,ψ-plot, these maps are derived solely from hard-sphere steric repulsion. Remarkably, the side chain biases exhibit marked similarities to corresponding biases seen in high-resolution protein structures. Consequently, some of the entropic cost for side chain localization in proteins is prepaid prior to the onset of folding events because conformational bias is built into the chain at the covalent level. Furthermore, side chain conformations are seen to experience fewer steric restrictions for backbone conformations in either the α or β basins, those map regions where repetitive ϕ,ψ-angles result in α-helices or strands of β-sheet, respectively. Here, these α and β basins are entropically favored for steric reasons alone; a blocked monopeptide is too short to accommodate the peptide hydrogen bonds that stabilize repetitive secondary structure. Thus, despite differing energetics, α/β-basins are favored for both monopeptides and repetitive secondary structure, underpinning an energetically unfrustrated compatibility between these two levels of protein structure.

Using chirality to probe the conformational dynamics and assembly of intrinsically disordered amyloid proteins

Intrinsically disordered protein (IDP) conformers occupy large regions of conformational space and display relatively flat energy surfaces. Amyloid-forming IDPs, unlike natively folded proteins, have folding trajectories that frequently involve movements up shallow energy gradients prior to the “downhill” folding leading to fibril formation. We suggest that structural perturbations caused by chiral inversions of amino acid side-chains may be especially valuable in elucidating these pathways of IDP folding. Chiral inversions are subtle in that they do not change side-chain size, flexibility, hydropathy, charge, or polarizability. They allow focus to be placed solely on the question of how changes in amino acid side-chain orientation, and the resultant alterations in peptide backbone structure, affect a peptide’s conformational landscape (Ramachandran space). If specific inversions affect folding and assembly, then the sites involved likely are important in mediating these processes. We suggest here a “focused chiral mutant library” approach for the unbiased study of amyloid-forming IDPs.

Construction and comparison of the statistical coil states of unfolded and intrinsically disordered proteins from nearest-neighbor corrected conformational propensities of short peptides

Assessing the influence of nearest neighbors on the conformational ensemble of amino acid residues in unfolded and intrinsically disordered proteins and peptides is pivotal for a thorough understanding of the statistical coil state of unfolded proteins as well as of the energetics of the folding process. Research aimed at exploring nearest neighbor interactions has mostly focused on the analysis of restricted coil libraries that reflect conformational distributions in loops connecting more regular secondary structure segments. Recently, however, Toal et al. reported an experimentally based structural analysis of selected xy-pairs in GxyG tetrapeptides, which revealed quantitative information about conformational changes induced by nearest-neighbor interactions (Eur. J. Chem., 2015, 21, 5173-5192). Here, we perform analyses of Ramachandran plots of xy-pairs in GxyG and in coil libraries (Ting et al., PLOS CompBiol, 2010, 6, e1000763) using Hellinger distances as a quantitative measure of dissimilarities between Ramachandran distributions. Our analysis reveals that nearest-neighbor effects inferred from the above coil library are much less pronounced than corresponding structural changes observed for GxyG peptides. To determine whether nearest-neighbor induced conformational changes observed for GxyG can be utilized for the analysis of unfolded proteins, we analyzed sets of ³J(H^HH^α) coupling constants of three different unfolded proteins, namely the 130-residue fragment of the Staphylococcus aureus fibronectin-binding protein (FnBPc), denatured hen lysozyme, and the htau40 protein. For the first two proteins we found statistically meaningful correlations between predicted nearest-neighbor induced changes of ³J(H^HH^α) and experimentally observed deviations from corresponding coupling constants of GxG peptides in water, which we used as reference system with minimal nearest-neighbor interactions. This observation is in line with the NMR based understanding of these proteins being predominantly statistical coils. For htau40, however, which is known to exhibit residual structure and large deviations form statistical coil expectations, these correlations are weak or absent. Our results thus underscore the importance of nearest-neighbor interactions for a complete physical description of an ideal statistical coil state of a protein.

Slow Interconversion in a Heterogeneous Unfolded-State Ensemble of Outer-Membrane Phospholipase A

Structural and dynamic investigations of unfolded proteins are important for understanding protein-folding mechanisms as well as the interactions of unfolded polypeptide chains with other cell components. In the case of outer-membrane proteins (OMPs), unfolded-state properties are of particular physiological relevance, because these proteins remain unfolded for extended periods of time during their biogenesis and rely on interactions with binding partners to support proper folding. Using a combination of ensemble and single-molecule spectroscopy, we have scrutinized the unfolded state of outer-membrane phospholipase A (OmpLA) to provide a detailed view of its structural dynamics on timescales from nanoseconds to milliseconds. We find that even under strongly denaturing conditions and in the absence of residual secondary structure, OmpLA populates an ensemble of slowly (>100 ms) interconverting and conformationally heterogeneous unfolded states that lack the fast chain-reconfiguration motions expected for an unstructured, fully unfolded chain. The drastically slowed sampling of potentially folding-competent states, as compared with a random-coil polypeptide, may contribute to the slow in vitro folding kinetics observed for many OMPs. In vivo, however, slow intramolecular long-range dynamics might be advantageous for entropically favored binding of unfolded OMPs to chaperones and, by facilitating conformational selection after release from chaperones, for preserving binding-competent conformations before insertion into the outer membrane.

Dihedral angle preferences of amino acid residues forming various non-local interactions in proteins

In theory, a polypeptide chain can adopt a vast number of conformations, each corresponding to a set of backbone rotation angles. Many of these conformations are excluded due to steric overlaps. Ramachandran and coworkers were the first to look into this problem by plotting backbone dihedral angles in a two-dimensional plot. The conformational space in the Ramachandran map is further refined by considering the energetic contributions of various non-bonded interactions. Alternatively, the conformation adopted by a polypeptide chain may also be examined by investigating interactions between the residues. Since the Ramachandran map essentially focuses on local interactions (residues closer in sequence), out of interest, we have analyzed the dihedral angle preferences of residues that make non-local interactions (residues far away in sequence and closer in space) in the folded structures of proteins. The non-local interactions have been grouped into different types such as hydrogen bond, van der Waals interactions between hydrophobic groups, ion pairs (salt bridges), and ππ-stacking interactions. The results show the propensity of amino acid residues in proteins forming local and non-local interactions. Our results point to the vital role of different types of non-local interactions and their effect on dihedral angles in forming secondary and tertiary structural elements to adopt their native fold.

Experimental conformational energy maps of proteins and peptides

We have presented an extensive analysis of the peptide backbone dihedral angles in the PDB structures and computed experimental Ramachandran plots for their distributions seen under a various constraints on X-ray resolution, representativeness at different sequence identity percentages, and hydrogen bonding distances. These experimental distributions have been converted into isoenergy contour plots using the approach employed previously by F. M. Pohl. This has led to the identification of energetically favored minima in the Ramachandran (ϕ, ψ) plots in which global minima are predominantly observed either in the right-handed α-helical or the polyproline II regions. Further, we have identified low energy pathways for transitions between various minima in the (ϕ,ψ) plots. We have compared and presented the experimental plots with published theoretical plots obtained from both molecular mechanics and quantum mechanical approaches. In addition, we have developed and employed a root mean square deviation (RMSD) metric for isoenergy contours in various ranges, as a measure (in kcal.mol^-1 ) to compare any two plots and determine the extent of correlation and similarity between their isoenergy contours. In general, we observe a greater degree of compatibility with experimental plots for energy maps obtained from molecular mechanics methods compared to most quantum mechanical methods. The experimental energy plots we have investigated could be helpful in refining protein structures obtained from X-ray, NMR, and electron microscopy and in refining force field parameters to enable simulations of peptide and protein structures that have higher degree of consistency with experiments. Proteins 2017; 85:979-1001. © 2017 Wiley Periodicals, Inc.

Experimental and Computational Analysis of Protein Stabilization by Gly-to-d-Ala Substitution: A Convolution of Native State and Unfolded State Effects

The rational and predictable enhancement of protein stability is an important goal in protein design. Most efforts target the folded state, however stability is the free energy difference between the folded and unfolded states thus both are suitable targets. Strategies directed at the unfolded state usually seek to decrease chain entropy by introducing cross-links or by replacing glycines. Cross-linking has led to mixed results. Replacement of glycine with an l-amino acid, while reducing the entropy of the unfolded state, can introduce unfavorable steric interactions in the folded state, since glycine is often found in conformations that require a positive φ angle such as helical C-capping motifs or type I' and II″ β-turns. l-Amino acids are strongly disfavored in these conformations, but d-amino acids are not. However, there are few reported examples and conflicting results have been obtained when glycines are replaced with d-Ala. We critically examine the effect of Gly-to-d-Ala substitutions on protein stability using experimental approaches together with molecular dynamics simulations and free energy calculations. The data, together with a survey of high resolution structures, show that the vast majority of proteins can be stabilized by substitution of C-capping glycines with d-Ala. Sites suitable for substitutions can be identified via sequence alignment with a high degree of success. Steric clashes in the native state due to the new side chain are rarely observed, but are likely responsible for the destabilizing or null effect observed for the small subset of Gly-to-d-Ala substitutions which are not stabilizing. Changes in backbone solvation play less of a role. Favorable candidates for d-Ala substitution can be identified using a rapid algorithm based on molecular mechanics.

A closer look into the α-helix basin

α-Helices are the most abundant structures found within proteins and play an important role in the determination of the global structure of proteins and their function. Representation of α-helical structures with the common (φ, ψ) dihedrals, as in Ramachandran maps, does not provide informative details regarding the helical structure apart for the abstract geometric meaning of the dihedrals. We present an alternative coordinate system that describes helical conformations in terms of residues per turn (ρ) and angle (ϑ) between backbone carbonyls relative to the helix direction through an approximate linear transformation between the two coordinates system (φ, ψ and ρ, ϑ). In this way, valuable information on the helical structure becomes directly available. Analysis of α-helical conformations acquired from the Protein Data Bank (PDB) demonstrates that a conformational energy function of the α-helix backbone can be harmonically approximated on the (ρ, ϑ) space, which is not applicable to the (φ, ψ) space due to the diagonal distribution of the conformations. The observed trends of helical conformations obtained from the PDB are captured by four conceptual simulations that theoretically examine the effects of residue bulkiness, external electric field, and externally applied mechanical forces. Flory’s isolated pair hypothesis is shown to be partially correct for α-helical conformations.

Molecular Dynamics Simulations of 441 Two-Residue Peptides in Aqueous Solution: Conformational Preferences and Neighboring Residue Effects with the Amber ff99SB-ildn-NMR Force Field

Understanding the intrinsic conformational preferences of amino acids and the extent to which they are modulated by neighboring residues is a key issue for developing predictive models of protein folding and stability. Here we present the results of 441 independent explicit-solvent MD simulations of all possible two-residue peptides that contain the 20 standard amino acids with histidine modeled in both its neutral and protonated states. (3)J(HNHα) coupling constants and δ(Hα) chemical shifts calculated from the MD simulations correlate quite well with recently published experimental measurements for a corresponding set of two-residue peptides. Neighboring residue effects (NREs) on the average (3)J(HNHα) and δ(Hα) values of adjacent residues are also reasonably well reproduced, with the large NREs exerted experimentally by aromatic residues, in particular, being accurately captured. NREs on the secondary structure preferences of adjacent amino acids have been computed and compared with corresponding effects observed in a coil library and the average β-turn preferences of all amino acid types have been determined. Finally, the intrinsic conformational preferences of histidine, and its NREs on the conformational preferences of adjacent residues, are both shown to be strongly affected by the protonation state of the imidazole ring.

Correct folding of an α-helix and a β-hairpin using a polarized 2D torsional potential

A new modification to the AMBER force field that incorporates the coupled two-dimensional main chain torsion energy has been evaluated for the balanced representation of secondary structures. In this modified AMBER force field (AMBER03(2D)), the main chain torsion energy is represented by 2-dimensional Fourier expansions with parameters fitted to the potential energy surface generated by high-level quantum mechanical calculations of small peptides in solution. Molecular dynamics simulations are performed to study the folding of two model peptides adopting either α-helix or β-hairpin structures. Both peptides are successfully folded into their native structures using an AMBER03(2D) force field with the implementation of a polarization scheme (AMBER03(2D)p). For comparison, simulations using a standard AMBER03 force field with and without polarization, as well as AMBER03(2D) without polarization, fail to fold both peptides successfully. The correction to secondary structure propensity in the AMBER03 force field and the polarization effect are critical to folding Trpzip2; without these factors, a helical structure is obtained. This study strongly suggests that this new force field is capable of providing a more balanced preference for helical and extended conformations. The electrostatic polarization effect is shown to be indispensable to the growth of secondary structures.

Randomizing the unfolded state of peptides (and proteins) by nearest neighbor interactions between unlike residues

To explore the influence of nearest neighbors on conformational biases in unfolded peptides, we combined vibrational and 2D NMR spectroscopy to obtain the conformational distributions of selected "GxyG" host-guest peptides in aqueous solution: GDyG, GSyG, GxLG, GxVG, where x/y=A, K, L, V. Large changes of conformational propensities were observed due to nearest-neighbor interactions, at variance with the isolated pair hypothesis. We found that protonated aspartic acid and serine lose their above-the-average preference for turn-like structures in favor of polyproline II (pPII) populations in the presence of neighbors with bulky side chains. Such residues also decrease the above-the-average pPII preference of alanine. These observations suggest that the underlying mechanism involves a disruption of the hydration shell. Thermodynamic analysis of (3) J(H(N) ,H(α) ) (T) data for each x,y residue reveals that modest changes in the conformational ensemble masks larger changes of enthalpy and entropy governing the pPII↔β equilibrium indicating a significant residue dependent temperature dependence of the peptides' conformational ensembles. These results suggest that nearest-neighbor interactions between unlike residues act as conformational randomizers close to the enthalpy-entropy compensation temperature, eliminating intrinsic biases in favor of largely balanced pPII/β dominated ensembles at physiological temperatures.

Important roles of hydrophobic interactions in folding and charge interactions in misfolding of α-helix bundle protein

An enhanced-sampling molecular dynamics simulation is presented to quantitatively demonstrate the important roles of hydrophobic and charge interactions in the folding and misfolding of α-helix bundle protein, respectively.

Local order in the unfolded state: conformational biases and nearest neighbor interactions

The discovery of Intrinsically Disordered Proteins, which contain significant levels of disorder yet perform complex biologically functions, as well as unwanted aggregation, has motivated numerous experimental and theoretical studies aimed at describing residue-level conformational ensembles. Multiple lines of evidence gathered over the last 15 years strongly suggest that amino acids residues display unique and restricted conformational preferences in the unfolded state of peptides and proteins, contrary to one of the basic assumptions of the canonical random coil model. To fully understand residue level order/disorder, however, one has to gain a quantitative, experimentally based picture of conformational distributions and to determine the physical basis underlying residue-level conformational biases. Here, we review the experimental, computational and bioinformatic evidence for conformational preferences of amino acid residues in (mostly short) peptides that can be utilized as suitable model systems for unfolded states of peptides and proteins. In this context particular attention is paid to the alleged high polyproline II preference of alanine. We discuss how these conformational propensities may be modulated by peptide solvent interactions and so called nearest-neighbor interactions. The relevance of conformational propensities for the protein folding problem and the understanding of IDPs is briefly discussed.

Backbone flexibility of CDR3 and immune recognition of antigens

Conformational entropy is an important component of protein-protein interactions; however, there is no reliable method for computing this parameter. We have developed a statistical measure of residual backbone entropy in folded proteins by using the ϕ-ψ distributions of the 20 amino acids in common secondary structures. The backbone entropy patterns of amino acids within helix, sheet or coil form clusters that recapitulate the branching and hydrogen bonding properties of the side chains in the secondary structure type. The same types of residues in coil and sheet have identical backbone entropies, while helix residues have much smaller conformational entropies. We estimated the backbone entropy change for immunoglobulin complementarity-determining regions (CDRs) from the crystal structures of 34 low-affinity T-cell receptors and 40 high-affinity Fabs as a result of the formation of protein complexes. Surprisingly, we discovered that the computed backbone entropy loss of only the CDR3, but not all CDRs, correlated significantly with the kinetic and affinity constants of the 74 selected complexes. Consequently, we propose a simple algorithm to introduce proline mutations that restrict the conformational flexibility of CDRs and enhance the kinetics and affinity of immunoglobulin interactions. Combining the proline mutations with rationally designed mutants from a previous study led to 2400-fold increase in the affinity of the A6 T-cell receptor for Tax-HLAA2. However, this mutational scheme failed to induce significant binding changes in the already-high-affinity C225-Fab/huEGFR interface. Our results will serve as a roadmap to formulate more effective target functions to design immune complexes with improved biological functions.

A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

Context and force field dependence of the loss of protein backbone entropy upon folding using realistic denatured and native state ensembles

The loss of conformational entropy is the largest unfavorable quantity affecting a protein's stability. We calculate the reduction in the number of backbone conformations upon folding using the distribution of backbone dihedral angles (ϕ,ψ) obtained from an experimentally validated denatured state model, along with all-atom simulations for both the denatured and native states. The average loss of entropy per residue is TΔS(BB)(U-N) = 0.7, 0.9, or 1.1 kcal·mol(-1) at T = 298 K, depending on the force field used, with a 0.6 kcal·mol(-1) dispersion across the sequence. The average equates to a decrease of a factor of 3-7 in the number of conformations available per residue (f = Ω(Denatured)/Ω(Native)) or to a total of f(tot) = 3(n)-7(n) for an n residue protein. Our value is smaller than most previous estimates where f = 7-20, that is, our computed TΔS(BB)(U-N) is smaller by 10-100 kcal mol(-1) for n = 100. The differences emerge from our use of realistic native and denatured state ensembles as well as from the inclusion of accurate local sequence preferences, neighbor effects, and correlated motions (vibrations), in contrast to some previous studies that invoke gross assumptions about the entropy in either or both states. We find that the loss of entropy primarily depends on the local environment and less on properties of the native state, with the exception of α-helical residues in some force fields.

Are ambivalent α-helices entropically driven?

This work is a first attempt to characterise the conformational preference of structurally ambivalent helices in terms of their backbone conformational entropy. Ambivalent sequences conform to two different secondary structures (helix-sheet or helix-random coil or sheet-random coil, etc.) in two different proteins. For variable ambivalent helices, the helical conformations are found to possess less conformational entropy as compared with their non-helical counterparts when the ϕ-ψ dihedral angle range of the entire peptide segment is used to calculate the backbone conformational entropy. The favourable number of native contacts is a primary stabilising factor for these helical conformations. However, an opposite trend is observed when the ϕ-ψ angles of the individual amino acids are used to calculate the backbone conformational entropy. The results show that these peptide segments are rather reluctant to form helices, but are driven to form helices due to the favourable number of native contacts and optimum range of ϕ-ψ angle of the segments. Both procedures are validated by applying on conserved helices in the non-redundant database and their corresponding counterparts in the Structural Classification of Proteins database. Although context is a major determinant in deciding conformations of ambivalent sequences, no significant difference in the conformational entropy of sequences flanking ambivalent helical sequences in helical and non-helical forms is observed in this study. The results may be useful in understanding the structural context and environmental factors which leads to the formation of ambivalent helices and designing de novo proteins.

(φ,ψ)₂ motifs: a purely conformation-based fine-grained enumeration of protein parts at the two-residue level

A deep understanding of protein structure benefits from the use of a variety of classification strategies that enhance our ability to effectively describe local patterns of conformation. Here, we use a clustering algorithm to analyze 76,533 all-trans segments from protein structures solved at 1.2 Å resolution or better to create a purely φ,ψ-based comprehensive empirical categorization of common conformations adopted by two adjacent φ,ψ pairs (i.e., (φ,ψ)(2) motifs). The clustering algorithm works in an origin-shifted four-dimensional space based on the two φ,ψ pairs to yield a parameter-dependent list of (φ,ψ)(2) motifs, in order of their prominence. The results are remarkably distinct from and complementary to the standard hydrogen-bond-centered view of secondary structure. New insights include an unprecedented level of precision in describing the φ,ψ angles of both previously known and novel motifs, ordering of these motifs by their population density, a data-driven recommendation that the standard C(α(i))…C(α(i+3))<7 Å criteria for defining turns be changed to 6.5 Å, identification of β-strand and turn capping motifs, and identification of conformational capping by residues in polypeptide II conformation. We further document that the conformational preferences of a residue are substantially influenced by the conformation of its neighbors, and we suggest that accounting for these dependencies will improve protein modeling accuracy. Although the CUEVAS-4D(r(10)є(14)) 'parts list' presented here is only an initial exploration of the complex (φ,ψ)(2) landscape of proteins, it shows that there is value to be had from this approach, and it opens the door to more in-depth characterizations at the (φ,ψ)(2) level and at higher dimensions.

Automated real-space refinement of protein structures using a realistic backbone move set

Crystals of many important biological macromolecules diffract to limited resolution, rendering accurate model building and refinement difficult and time-consuming. We present a torsional optimization protocol that is applicable to many such situations and combines Protein Data Bank-based torsional optimization with real-space refinement against the electron density derived from crystallography or cryo-electron microscopy. Our method converts moderate- to low-resolution structures at initial (e.g., backbone trace only) or late stages of refinement to structures with increased numbers of hydrogen bonds, improved crystallographic R-factors, and superior backbone geometry. This automated method is applicable to DNA-binding and membrane proteins of any size and will aid studies of structural biology by improving model quality and saving considerable effort. The method can be extended to improve NMR and other structures. Our backbone score and its sequence profile provide an additional standard tool for evaluating structural quality.

Redrawing the Ramachandran plot after inclusion of hydrogen-bonding constraints

A protein backbone has two degrees of conformational freedom per residue, described by its ϕ,ψ-angles. Accordingly, the energy landscape of a blocked peptide unit can be mapped in two dimensions, as shown by Ramachandran, Sasisekharan, and Ramakrishnan almost half a century ago. With atoms approximated as hard spheres, the eponymous Ramachandran plot demonstrated that steric clashes alone eliminate 3/4 of ϕ,ψ-space, a result that has guided all subsequent work. Here, we show that adding hydrogen-bonding constraints to these steric criteria eliminates another substantial region of ϕ,ψ-space for a blocked peptide; for conformers within this region, an amide hydrogen is solvent-inaccessible, depriving it of a hydrogen-bonding partner. Yet, this "forbidden" region is well populated in folded proteins, which can provide longer-range intramolecular hydrogen-bond partners for these otherwise unsatisfied polar groups. Consequently, conformational space expands under folding conditions, a paradigm-shifting realization that prompts an experimentally verifiable conjecture about likely folding pathways.

Influence of side chain conformations on local conformational features of amino acids and implication for force field development

Statistical analysis of coil regions in protein structures has been used to obtain the local backbone phi, psi preferences of amino acids, which agree well with the NMR experiments of unfolded peptides and proteins. We analyzed the conformational features of amino acid residues in a restricted coil library of 4220 high-resolution protein crystal structures. In addition to Gly, Ala, and Pro, the phi, psi distribution (Ramachandran plot) of each amino acid is analyzed with respect to three side chain conformers: g+ (chi(1) approximately -60 degrees), g- (chi(1) approximately 60 degrees), and t (chi(1) approximately 180 degrees). The statistical study indicates that the effect of side chain conformations on phi, psi distributions is even greater than the effect of amino acid types. On the basis of the chi(1), phi, psi conformational preferences, the amino acids in addition to Gly, Pro, and Ala can be divided into five types: (1) ordinary amino acids, (2) Ser, (3) Asp and Asn, (4) Val and Ile, and (5) Thr, each with distinguished chi(1) rotamers. The alpha-helix, beta-sheet, and type-I beta-turn preferences of the different rotamers of various amino acid types can be captured by their intrinsic phi, psi preferences from our coil library. Molecular dynamics simulations of dipeptide Ac-X-NHMe and tetrapeptide Ac-A-X-A-NHMe models give nearly the same side chain rotamer distributions. However, for many amino acids, both OPLS-AA/L and AMBER-FF03 force fields give very different chi(1) rotamer distributions from the coil library. This may partially explain why dipeptide models sometimes cannot reproduce those of protein structures well. The current coil library analysis may be valuable in improving the force field for protein simulations.

Conformations of phenylalanine in the tripeptides AFA and GFG probed by combining MD simulations with NMR, FTIR, polarized Raman, and VCD spectroscopy

Conformational properties of small, flexible peptides are a matter of ongoing interest since they can be considered as models for unfolded proteins. However, the investigation of the conformations of small peptides is challenging as they are ensembles of rapidly interconverting conformers; moreover, the different methods used are prone to different approximations and errors. In order to obtain more reliable results, it is prudent to combine different techniques; here, molecular dynamics (MD) simulations together with nuclear magnetic resonance (NMR), Fourier transform IR (FTIR), polarized Raman, and vibrational circular dichroism (VCD) measurements were used to study the conformational propensity of phenylalanine in the tripeptides AFA and GFG, motivated by the relevance of phenylalanine for the self-aggregation of peptides. The results of this analysis indicate that the F residue predominantly populates the beta-strand (beta) and polyproline II (PPII) conformations in both AFA and GFG. However, while phenylalanine exhibits a propensity for beta-strand conformations in GFG (0.40 < or = beta population < or = 0.69 and 0.29 < or = PPII population < or = 0.42), the substitution of terminal glycines with alanine residues induces a higher population of PPII (0.31 < or = beta population < or = 0.50 and 0.37 < or = PPII population < or = 0.57).

Sidechain conformational dependence of hydrogen exchange in model peptides

Peptide hydrogens that are exposed to solvent in protein X-ray structures exhibit a billion-fold range in hydroxide-catalyzed exchange rates, and these rates have previously been shown to be predictable by continuum dielectric methods to within a factor of 7, based on single protein conformations. When using a protein coil library to model the Boltzmann-weighted conformational distribution for the various N-acetyl-[X-Ala]-N-methylamides and N-acetyl-[Ala-Y]-N-methylamides, the acidity of the central amide in the individual conformers of each peptide spans nearly a million-fold range. Nevertheless, population averaging of these conformer acidities predicts the standard sidechain-dependent hydrogen exchange correction factors for nonpolar model peptides to within a factor of 30% (10(0.11)) with a correlation coefficient r=0.91. Comparison with the analogous continuum dielectric calculations for the other N-acetyl-[X-Y]-N-methylamides indicates that deviations from the isolated residue hypothesis of classical polymer theory predict appreciable errors in the exchange rates for conformationally disordered peptides when the standard sidechain-dependent hydrogen exchange rate correction factors are assumed to be independently additive. Although electronic polarizability generally dominates the dielectric shielding for the approximately 10ps lifetime of peptide ionization, evidence is presented for modest contributions from rapid intrarotamer conformational reorganization of Asn and Gln sidechains.

Neighbor-dependent Ramachandran probability distributions of amino acids developed from a hierarchical Dirichlet process model

Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1) input data size and criteria for structure inclusion (resolution, R-factor, etc.); 2) filtering of suspect conformations and outliers using B-factors or other features; 3) secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included); 4) the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5) whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately) have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp.

The three-dimensional structure of a protein enables it to perform its specific function, which may be catalysis, DNA binding, cell signaling, maintaining cell shape and structure, or one of many other functions. Predicting the structures of proteins is an important goal of computational biology. One way of doing this is to figure out the rules that determine protein structure from protein sequences by determining how local protein sequence is associated with local protein structure. That is, many (but not all) of the interactions that determine protein structure occur between amino acids that are a short distance away from each other in the sequence. This is particularly true in the irregular parts of protein structure, often called loops. In this work, we have performed a statistical analysis of the structure of the protein backbone in loops as a function of the protein sequence. We have determined how an amino acid bends the local backbone due to its amino acid type and the amino acid types of its neighbors. We used a recently developed statistical method that is particularly suited to this problem. The analysis shows that backbone conformation prediction can be improved using the information in the statistical distributions we have developed.

Intrinsic propensities of amino acid residues in GxG peptides inferred from amide I' band profiles and NMR scalar coupling constants

A reliable intrinsic propensity scale of amino acid residues is indispensable for an assessment of how local conformational distributions in the unfolded state can affect the folding of peptides and proteins. Short host-guest peptides, such as GxG tripeptides, are suitable tools for probing such propensities. To explore the conformational distributions sampled by the central amino acid residue in these motifs, we combined vibrational (IR, Raman, and VCD) with NMR spectroscopy. The data were analyzed in terms of a superposition of two-dimensional Gaussian distribution functions in the Ramachandran space pertaining to subensembles of polyproline II, beta-strand, right- and left-handed helical, and gamma-turn-like conformations. The intrinsic propensities of eight amino acid residues (x = A, V, F, L, S, E, K, and M) in GxG peptides were determined as mole fractions of these subensembles. Our results show that alanine adopts primarily (approximately 80%) a PPII-like conformation, while valine and phenylalanine were found to sample PPII and beta-strand-like conformations equally. The centers of the respective beta-strand distributions generally do not coincide with canonical values of dihedral angles of residues in parallel or antiparallel beta-strands. In fact, the distributions for most residues found in the beta-region significantly overlap the PPII-region. A comparison with earlier reported results for trivaline reveals that the terminal valines increase the beta-strand propensity of the central valine residue even further. Of the remaining investigated amino acids, methionine preferred PPII the most (0.64), and E, S, L, and K exhibit moderate (0.56-0.45) PPII propensities. Residues V, F, S, E, and L sample, to a significant extent, a region between the canonical PPII and (antiparallel) beta-strand conformations. This region coincides with the sampling reported for L and V using theoretical predictions (Tran et al. Biochemistry 2005, 44, 11369). The distributions of all investigated residues differ from coil library and computationally predicted distributions in that they do not exhibit a substantial sampling of helical conformations. We conclude that this sampling of helical conformations arises from the context dependence, for example, neighboring residues, in proteins and longer peptides, some of which is long-range.

Statistical potentials for improved structurally constrained evolutionary models

Assessing the influence of three-dimensional protein structure on sequence evolution is a difficult task, mainly because of the assumption of independence between sites required by probabilistic phylogenetic methods. Recently, models that include an explicit treatment of protein structure and site interdependencies have been developed: a statistical potential (an energy-like scoring system for sequence-structure compatibility) is used to evaluate the probability of fixation of a given mutation, assuming a coarse-grained protein structure that is constant through evolution. Yet, due to the novelty of these models and the small degree of overlap between the fields of structural and evolutionary biology, only simple representations of protein structure have been used so far. In this work, we present new forms of statistical potentials using a probabilistic framework recently developed for evolutionary studies. Terms related to pairwise distance interactions, torsion angles, solvent accessibility, and flexibility of the residues are included in the potentials, so as to study the effects of the main factors known to influence protein structure. The new potentials, with a more detailed representation of the protein structure, yield a better fit than the previously used scoring functions, with pairwise interactions contributing to more than half of this improvement. In a phylogenetic context, however, the structurally constrained models are still outperformed by some of the available site-independent models in terms of fit, possibly indicating that alternatives to coarse-grained statistical potentials should be explored in order to better model structural constraints.

A self-consistent description of the conformational behavior of chemically denatured proteins from NMR and small angle scattering

Characterization of the conformational properties of unfolded proteins is essential for understanding the mechanisms of protein folding and misfolding. This information is also fundamental to determining the relationship between flexibility and function in the highly diverse families of intrinsically disordered proteins. Here we present a self-consistent model of conformational sampling of chemically denatured proteins in agreement with experimental data reporting on long-range distance distributions in unfolded proteins using small-angle x-ray scattering and nuclear magnetic resonance pulse-field gradient-based measurements. We find that standard statistical coil models, selected from folded protein databases with secondary structural elements removed, need to be refined to correct backbone dihedral angle sampling of denatured proteins, although they appear to be appropriate for intrinsically disordered proteins. For denatured proteins, pervasive increases in the sampling of more-extended regions of Ramachandran space {50 degrees Collapse

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MESH Headings

• Computer Simulation
• Databases, Protein
• Models, Chemical
• Nuclear Magnetic Resonance, Biomolecular
• Protein Conformation
• Protein Denaturation
• Protein Folding
• Protein Structure, Secondary
• Scattering, Small Angle

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Affiliation(s)

Pau Bernadó Institute for Research in Biomedicine, c/ Baldiri Reixac, Barcelona, Spain
Martin Blackledge Protein Dynamics and Flexibility, Institut de Biologie Structurale, UMR 5075, Commissariat à l'Énergie Atomique-Centre National de la Recherche Scientifique-Université Joseph Fourier, Grenoble, France

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Alpha helical crossovers favor right-handed supersecondary structures by kinetic trapping: the phone cord effect in protein folding

The remarkable predominance of right-handedness in beta-alpha-beta helical crossovers has been previously explained in terms of thermodynamic stability and kinetic accessibility, but a different kinetic trapping mechanism may also play a role. If the beta-sheet contacts are made before the crossover helix is fully formed, and if the backbone angles of the folding helix follows the energetic pathway of least resistance, then the helix would impart a torque on the ends of the two strands. Such a torque would tear apart a left-handed conformation but hold together a right-handed one. Right-handed helical crossovers predominate even in all-alpha proteins, where previous explanations based on the preferred twist of the beta sheet do not apply. Using simple molecular simulations, we can reproduce the right-handed preference in beta-alpha-beta units, without imposing specific beta-strand geometry. The new kinetic trapping mechanism is dubbed the "phone cord effect" because it is reminiscent of the way a helical phone cord forms superhelices to relieve torsional stress. Kinetic trapping explains the presence of a right-handed superhelical preference in alpha helical crossovers and provides a possible folding mechanism for knotted proteins.