The Flory isolated-pair hypothesis is not valid for polypeptide chains: implications for protein folding

Architectonic principles of polyproline II helix bundle protein domains

Glycine rich polyproline II helix assemblies are an emerging class of natural domains found in several proteins with different functions and diverse origins. The distinct properties of these domains relative to those composed of α-helices and β-sheets could make glycine-rich polyproline II helix assemblies a useful building block for protein design. Whereas the high population of polyproline II conformers in disordered state ensembles could facilitate glycine-rich polyproline II helix folding, the architectonic bases of these structures are not well known. Here, we compare and analyze their structures to uncover common features. These protein domains are found to be highly tolerant of distinct flanking sequences. This speaks to the robustness of this fold and strongly suggests that glycine rich polyproline II assemblies could be grafted with other protein domains to engineer new structures and functions. These domains are also well packed with few or no cavities. Moreover, a significant trend towards antiparallel helix configuration is observed in all these domains and could provide stabilizing interactions among macrodipoles. Finally, extensive networks of Cα-H···OC hydrogen bonds are detected in these domains. Despite their diverse evolutionary origins and activities, glycine-rich polyproline II helix assemblies share architectonic features which could help design novel proteins.

From isolated polyelectrolytes to star-like assemblies: the role of sequence heterogeneity on the statistical structure of the intrinsically disordered neurofilament-low tail domain

Intrinsically disordered proteins (IDPs) are a subset of proteins that lack stable secondary structure. Given their polymeric nature, previous mean-field approximations have been used to describe the statistical structure of IDPs. However, the amino-acid sequence heterogeneity and complex intermolecular interaction network have significantly impeded the ability to get proper approximations. One such case is the intrinsically disordered tail domain of neurofilament low (NFLt), which comprises a 50 residue-long uncharged domain followed by a 96 residue-long negatively charged domain. Here, we measure two NFLt variants to identify the impact of the NFLt two main subdomains on its complex interactions and statistical structure. Using synchrotron small-angle x-ray scattering, we find that the uncharged domain of the NFLt induces attractive interactions that cause it to self-assemble into star-like polymer brushes. On the other hand, when the uncharged domain is truncated, the remaining charged N-terminal domains remain isolated in solution with typical polyelectrolyte characteristics. We further discuss how competing long- and short-ranged interactions within the polymer brushes dominate their ensemble structure and, in turn, their implications on previously observed phenomena in NFL native and diseased states.

High-Accuracy Prediction of Stabilizing Surface Mutations to the Three-Helix Bundle, UBA(1), with EmCAST

The accurate modeling of energetic contributions to protein structure is a fundamental challenge in computational approaches to protein analysis and design. We describe a general computational method, EmCAST (empirical Cα stabilization), to score and optimize the sequence to the structure in proteins. The method relies on an empirical potential derived from the database of the Cα dihedral angle preferences for all possible four-residue sequences, using the data available in the Protein Data Bank. Our method produces stability predictions that naturally correlate one-to-one with the experimental results for solvent-exposed mutation sites. EmCAST predicted four mutations that increased the stability of a three-helix bundle, UBA(1), from 2.4 to 4.8 kcal/mol by optimizing residues in both helices and turns. For a set of eight variants, the predicted and experimental stabilizations correlate very well (R2 = 0.97) with a slope near 1 and with a 0.16 kcal/mol standard error for EmCAST predictions. Tests against literature data for the stability effects of surface-exposed mutations show that EmCAST outperforms the existing stability prediction methods. UBA(1) variants were crystallized to verify and analyze their structures at an atomic resolution. Thermodynamic and kinetic folding experiments were performed to determine the magnitude and mechanism of stabilization. Our method has the potential to enable the rapid, rational optimization of natural proteins, expand the analysis of the sequence/structure relationship, and supplement the existing protein design strategies.

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.

The neuropeptide galanin adopts an irregular secondary structure

Human galanin is a 30-residue neuropeptide targeted for development of analgesics, antidepressants, and anticonvulsants. While previous work from our group and others has already produced significant insights into galanin's N-terminal region, no extant structures of galanin in databases include its full-length sequence and the function of its C-terminus remains ambiguous. We report the NMR solution structure of full-length human galanin C-terminal amide, determined from 2D ¹H-¹H COSY, TOCSY, and ROESY NMR data. Galanin adopts an irregular helical structure across its N-terminus, likely the average of several coiling states. We present the NMR structure of a peptide encompassing the C-terminus of galanin as a stand-alone fragment. The C-terminus of full-length galanin appears to indirectly assist the intramolecular association of hydrophobic sidechains within its N-terminus, remotely rigidifying their position when compared to previously studied N-terminal galanin fragments. By contrast, there is flexibility in the C-terminus of galanin, characterized by two i to i + 2 hydrogen-bonded turns within an otherwise dynamic backbone. The C-terminal portion of the peptide renders it soluble, and plays a hitherto undescribed biophysical role in pre-organizing the galanin receptor binding epitope. We speculate that hydrophilic microdomains of signaling peptides, hormones, and perhaps intrinsically disordered proteins may also function similarly.

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.

Reframing the Protein Folding Problem: Entropy as Organizer

It has been a long-standing conviction that a protein's native fold is selected from a vast number of conformers by the optimal constellation of enthalpically favorable interactions. In marked contrast, this Perspective introduces a different mechanism, one that emphasizes conformational entropy as the principal organizer in protein folding while proposing that the conventional view is incomplete. This mechanism stems from the realization that hydrogen bond satisfaction is a thermodynamic necessity. In particular, a backbone hydrogen bond may add little to the stability of the native state, but a completely unsatisfied backbone hydrogen bond would be dramatically destabilizing, shifting the U(nfolded) ⇌ N(ative) equilibrium far to the left. If even a single backbone polar group is satisfied by solvent when unfolded but buried and unsatisfied when folded, that energy penalty alone, approximately +5 kcal/mol, would rival almost the entire free energy of protein stabilization, typically between -5 and -15 kcal/mol under physiological conditions. Consequently, upon folding, buried backbone polar groups must form hydrogen bonds, and they do so by assembling scaffolds of α-helices and/or strands of β-sheet, the only conformers in which, with rare exception, hydrogen bond donors and acceptors are exactly balanced. In addition, only a few thousand viable scaffold topologies are possible for a typical protein domain. This thermodynamic imperative winnows the folding population by culling conformers with unsatisfied hydrogen bonds, thereby reducing the entropy cost of folding. Importantly, conformational restrictions imposed by backbone···backbone hydrogen bonding in the scaffold are sequence-independent, enabling mutation─and thus evolution─without sacrificing the structure.

Repeating Aspartic Acid Residues Prefer Turn-like Conformations in the Unfolded State: Implications for Early Protein Folding

Protein folding can be described as a motion of the polypeptide chain in a potential energy funnel, where the conformational manifold is narrowed as the chain traverses from a completely unfolded state until it reaches the folded (native) state. The initial folding stages set the tone for this process by substantially narrowing the manifold of accessible conformations. In an ideally unfolded state with no long-range stabilizing forces, local conformations (i.e., residual structures) are likely to drive the folding process. While most amino acid residues tend to predominantly adopt extended structures in unfolded proteins and peptides, aspartic acid exhibits a relatively high intrinsic preference for turn-forming conformations. Regions in an unfolded polypeptide or protein that are rich in aspartic acid residues may therefore be crucial sites for protein folding steps. By combining NMR and vibrational spectroscopies, we observed that the conformational sampling of multiple sequentially neighbored aspartic acid residues in the model peptides GDDG and GDDDG even show an on average higher propensity for turn-forming structures than the intrinsic reference system D in GDG, which suggests that nearest neighbor interactions between adjacent aspartic acid residues stabilize local turn-forming structures. In the presence of the unlike neighbor phenylalanine, nearest neighbor interactions are of a totally different nature in that it they decrease the turn-forming propensities and mutually increase the sampling of polyproline II (pPII) conformations. We hypothesize the structural role of aspartic residues in intrinsically disordered proteins in general, and particularly in small linear motifs, that are very much determined by their respective neighbors.

Protein folding - seeing is deceiving

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical-chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α-helices and strands of β-sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen-bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of "frustration" is largely eliminated and the Levinthal paradox is resolved. Putting the "bottom line" at the top: it is likely that hydrogen-bond satisfaction represents a largely under-appreciated parameter in protein folding models.

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.

Process, Outcomes and Possible Elimination of Aggregation with Special Reference to Heme Proteins; Likely Remediations of Proteinopathies

Protein folding is a natural phenomenon through which a linear polypeptide possessing necessary information attains three-dimension functionally active conformation. This is a complex and multistep process and therefore, the presence of several intermediary structures could be speculated as a result of protein folding. In in vivo, this folding process is governed by the assistance of other proteins called molecular chaperones and heat shock proteins. Due to the mechanism of protein folding, these intermediary structures remain major challenge for modern biology. Mutation in gene encoding amino acid can cause adverse environmental conditions which may result in misfolding of the linear polypeptide followed by the formation of aggregates and amyloidosis. Aggregation contributes to the pathophysiology of several maladies including diabetes mellitus, Huntington's and Alzheimer's disease. The propensity of native structure to form aggregated and fibrillar assemblies is a hallmark of amyloidosis. During aggregation of a protein, transition from α helix to β sheet is observed, and mainly β sheeted structure is visualised in a mature fibril. Heme proteins are very crucial for major life activities like transport of oxygen and carbon dioxide, synthesis of ATP, role in electron transport chain, and detoxification of free radicals formed during biochemical reactions. Any structural variation in the heme proteins may lead to a fatal response. Hence characterization of the folding intermediates becomes crucial. The characterization has been deciphered with the help of strong denaturants like acetonitrile and TFE. Moreover, possible role of elimination of these aggregates and prevention of protein denaturation is also discussed. Current review deals with the basic process and mechanism of the protein folding in general and the ultimate outcomes of the protein misfolding. Since Native conformation of heme proteins is essential for some vital activities as listed above, we have discussed possible prevention of denaturation and aggregation of heme proteins such as Hb, cyt c, catalase & peroxidase.

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.

Understanding and applications of Ser/Gly linkers in protein engineering

Peptide linkers consisting of repeats of glycine and serine residues are commonly chosen by protein engineers to introduce flexible and hydrophilic spacers between protein domains. Given the popularity of these linkers, gaining a quantitative insight in their conformational behavior is important to understand the effect on functional properties of fusion proteins, including energy transfer efficiency in luminescent sensor proteins, intramolecular domain interactions and (multivalent) binding. In this chapter, we discuss how the conformational behavior of Ser/Gly linkers can be described using random coil models, and how measuring FRET as a function of linker length can be used to obtain empirical values for the stiffness of linkers containing different Ser-to-Gly ratios. Subsequently, we show how these models and the experimentally determined linker stiffness can be used to explain and predict the functional properties of multidomain proteins, providing useful rules-of-thumb and design tools for optimal linker engineering.

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.

Do Molecular Dynamics Force Fields Capture Conformational Dynamics of Alanine in Water?

We examine the ability of six molecular dynamics (MD) force fields (Amber ff14SB, Amber ff99SBnmr1, Amber ff03ws, OPLS-AA/L, OPLS-AA/M, and CHARMM36) to reproduce conformational ensembles of the central alanine in GAG and AAA in a way that is consistent with five (GAG) or six (AAA) J coupling constants and amide I' profiles. MD-derived Ramachandran plots for all six force fields under study differ from those obtained by the Gaussian fit to experimental data in three major ways: (i) the polyproline II (pPII) basin in the Ramachandran plot is too concentrated, (ii) the antiparallel β (aβ) basin is overpopulated, and (iii) the transitional β (βt) basin is underpopulated. Amber ff14SB outperforms the other five MD force fields and yields the highest pPII populations of the central alanine residue in GAG (55%) and AAA (63%), in good agreement with the predictions of the Gaussian model (59 and 76%). The analysis of the hydration layer around the central alanine residue reveals considerable reorientation of water molecules and reduction in both the average number of water molecules and the average number of water-water hydrogen bonds when glycines (in GAG) are replaced by alanines (in AAA), elucidating water-mediated nearest neighbor effects on alanine's conformational dynamics.

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.

Improvements to the ABSINTH Force Field for Proteins Based on Experimentally Derived Amino Acid Specific Backbone Conformational Statistics

We present an improved version of the ABSINTH implicit solvation model and force field paradigm (termed ABSINTH-C) by incorporating a grid-based term that bootstraps against experimentally derived and computationally optimized conformational statistics for blocked amino acids. These statistics provide high-resolution descriptions of the intrinsic backbone dihedral angle preferences for all 20 amino acids. The original ABSINTH model generates Ramachandran plots that are too shallow in terms of the basin structures and too permissive in terms of dihedral angle preferences. We bootstrap against the reference optimized landscapes and incorporate CMAP-like residue-specific terms that help us reproduce the intrinsic dihedral angle preferences of individual amino acids. These corrections that lead to ABSINTH-C are achieved by balancing the incorporation of the new residue-specific terms with the accuracies inherent to the original ABSINTH model. We demonstrate the robustness of ABSINTH-C through a series of examples to highlight the preservation of accuracies as well as examples that demonstrate the improvements. Our efforts show how the recent experimentally derived and computationally optimized coil-library landscapes can be used as a touchstone for quantifying errors and making improvements to 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.

Tuning the Flexibility of Glycine-Serine Linkers To Allow Rational Design of Multidomain Proteins

Flexible polypeptide linkers composed of glycine and serine are important components of engineered multidomain proteins. We have previously shown that the conformational properties of Gly-Gly-Ser repeat linkers can be quantitatively understood by comparing experimentally determined Förster resonance energy transfer (FRET) efficiencies of ECFP-linker-EYFP proteins to theoretical FRET efficiencies calculated using wormlike chain and Gaussian chain models. Here we extend this analysis to include linkers with different glycine contents. We determined the FRET efficiencies of ECFP-linker-EYFP proteins with linkers ranging in length from 25 to 73 amino acids and with glycine contents of 33.3% (GSSGSS), 16.7% (GSSSSSS), and 0% (SSSSSSS). The FRET efficiency decreased with an increasing linker length and was overall lower for linkers with less glycine. Modeling the linkers using the WLC model revealed that the experimentally observed FRET efficiencies were consistent with persistence lengths of 4.5, 4.8, and 6.2 Å for the GSSGSS, GSSSSS, and SSSSSS linkers, respectively. The observed increase in linker stiffness with reduced glycine content is much less pronounced than that predicted by a classical model developed by Flory and co-workers. We discuss possible reasons for this discrepancy as well as implications for using the stiffer linkers to control the effective concentrations of connected domains in engineered multidomain proteins.

Conformational Heterogeneity and FRET Data Interpretation for Dimensions of Unfolded Proteins

A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible-heterogeneous as well as homogeneous-conformational distributions are taken into account without prejudgment, a single value of average transfer efficiency 〈E〉 between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration 〈R_g〉. Here we utilize unbiased conformational statistics from a coarse-grained explicit-chain model to establish a general logical framework to quantify this fundamental ambiguity in smFRET inference. As an application, we address the long-standing controversy regarding the denaturant dependence of 〈R_g〉 of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that 〈R_g〉 of unfolded Protein L is highly sensitive to [GuHCl], but data from SAXS suggested a near-constant 〈R_g〉 irrespective of [GuHCl]. Strikingly, our analysis indicates that although the reported 〈E〉 values for Protein L at [GuHCl] = 1 and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian R_g² distributions consistent with these two 〈E〉 values overlap by as much as 75%. Our findings suggest, in general, that the smFRET-SAXS discrepancy regarding unfolded protein dimensions likely arise from highly heterogeneous conformational ensembles at low or zero denaturant, and that additional experimental probes are needed to ascertain the nature of this heterogeneity.

Statistical description of the denatured structure of a single protein, staphylococcal nuclease, by FRET analysis

Structural characterization of fully unfolded proteins is essential for understanding not only protein-folding mechanisms, but also the structures of intrinsically disordered proteins. Because an unfolded protein can assume all possible conformations, statistical descriptions of its structure are most appropriate. For this purpose, we applied Förster resonance energy transfer (FRET) analysis to fully unfolded staphylococcal nuclease. Artificial amino acids labeled with a FRET donor or acceptor were introduced by an amber codon and a four-base codon respectively. Eight double-labeled proteins were prepared, purified, and subjected to FRET analysis in 6 M urea. The observed behavior could be explained by a power law, R = αN^0.44, where R, and N are the distance and the number of residues between donor and acceptor, and α is a coefficient. The index was smaller than the value expected for an excluded-volume random coil, 0.588, indicating that the fully unfolded proteins were more compact than polypeptides in good solvent. The FRET efficiency in the native state did not necessarily correlate to the distance obtained from crystal structure, suggesting that other factors such as the orientation factor made a substantial contribution to FRET.

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.

Beyond basins: φ,ψ preferences of a residue depend heavily on the φ,ψ values of its neighbors

The Ramachandran plot distributions of nonglycine residues from experimentally determined structures are routinely described as grouping into one of six major basins: β, PII , α, αL , ξ and γ'. Recent work describing the most common conformations adopted by pairs of residues in folded proteins [i.e., (φ,ψ)2 -motifs] showed that commonly described major basins are not true single thermodynamic basins, but are composed of distinct subregions that are associated with various conformations of either the preceding or following neighbor residue. Here, as documentation of the extent to which the conformational preferences of a central residue are influenced by the conformations of its two neighbors, we present a set of φ,ψ-plots that are delimited simultaneously by the φ,ψ-angles of its neighboring residues on both sides. The level of influence seen here is typically greater than the influence associated with considering the identities of neighboring residues, implying that the use of this heretofore untapped information can improve the accuracy of structure prediction algorithms and low resolution protein structure refinement.

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.

The effect of chirality and steric hindrance on intrinsic backbone conformational propensities: tools for protein design

The conformational propensities of amino acids are an amalgamation of sequence effects, environmental effects and underlying intrinsic behavior. Many have attempted to investigate neighboring residue effects to aid in our understanding of protein folding and improve structure prediction efforts, especially with respect to difficult to characterize states, such as disordered or unfolded states. Host-guest peptide series are a useful tool in examining the propensities of the amino acids free from the surrounding protein structure. Here, we compare the distributions of the backbone dihedral angles (φ/ψ) of the 20 proteogenic amino acids in two different sequence contexts using the AAXAA and GGXGG host-guest pentapeptide series. We further examine their intrinsic behaviors across three environmental contexts: water at 298 K, water at 498 K, and 8 M urea at 298 K. The GGXGG systems provide the intrinsic amino acid propensities devoid of any conformational context. The alanine residues in the AAXAA series enforce backbone chirality, thereby providing a model of the intrinsic behavior of amino acids in a protein chain. Our results show modest differences in φ/ψ distributions due to the steric constraints of the Ala side chains, the magnitudes of which are dependent on the denaturing conditions. One of the strongest factors modulating φ/ψ distributions was the protonation of titratable side chains, and the largest differences observed were in the amino acid propensities for the rarely sampled αL region.

Energy Landscape of Pentapeptides in a Higher-Order (ϕ,ψ) Conformational Subspace

The potential energy landscape of pentapeptides was mapped in a collective coordinate principal conformational subspace derived from principal component analysis of a nonredundant representative set of protein structures from the PDB. Three pentapeptide sequences that are known to be distinct in terms of their secondary structure characteristics, (Ala)5, (Gly)5, and Val.Asn.Thr.Phe.Val, were considered. Partitioning the landscapes into different energy valleys allowed for calculation of the relative propensities of the peptide secondary structures in a statistical mechanical framework. The distribution of the observed conformations of pentapeptide data showed good correspondence to the topology of the energy landscape of the (Ala)5 sequence where, in accord with reported trends, the α-helix showed a predominant propensity at 298 K. The topography of the landscapes indicates that the stabilization of the α-helix in the (Ala)5 sequence is enthalpic in nature while entropic factors are important for stabilization of the β-sheet in the Val.Asn.Thr.Phe.Val sequence. The results indicate that local interactions within small pentapeptide segments can lead to conformational preference of one secondary structure over the other where account of conformational entropy is important in order to reveal such preference. The method, therefore, can provide critical structural information for ab initio protein folding methods.

Quantifying Protein Disorder through Measures of Excess Conformational Entropy

Intrinsically disordered proteins (IDPs) and proteins with a large degree of disorder are abundant in the proteomes of eukaryotes and viruses, and play a vital role in cellular homeostasis and disease. One fundamental question that has been raised on IDPs is the process by which they offset the entropic penalty involved in transitioning from a heterogeneous ensemble of conformations to a much smaller collection of binding-competent states. However, this has been a difficult problem to address, as the effective entropic cost of fixing residues in a folded-like conformation from disordered amino acid neighborhoods is itself not known. Moreover, there are several examples where the sequence complexity of disordered regions is as high as well-folded regions. Disorder in such cases therefore arises from excess conformational entropy determined entirely by correlated sequence effects, an entropic code that is yet to be identified. Here, we explore these issues by exploiting the order-disorder transitions of a helix in Pbx-Homeodomain together with a dual entropy statistical mechanical model to estimate the magnitude and sign of the excess conformational entropy of residues in disordered regions. We find that a mere 2.1-fold increase in the number of allowed conformations per residue (∼0.7kBT favoring the unfolded state) relative to a well-folded sequence, or ∼2(N) additional conformations for a N-residue sequence, is sufficient to promote disorder under physiological conditions. We show that this estimate is quite robust and helps in rationalizing the thermodynamic signatures of disordered regions in important regulatory proteins, modeling the conformational folding-binding landscapes of IDPs, quantifying the stability effects characteristic of disordered protein loops and their subtle roles in determining the partitioning of folding flux in ordered domains. In effect, the dual entropy model we propose provides a statistical thermodynamic basis for the relative conformational propensities of amino acids in folded and disordered environments in proteins. Our work thus lays the foundation for understanding and quantifying protein disorder through measures of excess conformational entropy.

The importance of cooperative interactions and a solid-state paradigm to proteins: what Peptide chemists can learn from molecular crystals

Proteins and peptides in solution or in vivo share properties with both liquids and solids. More often than not, they are studied using the liquid paradigm rather than that of a solid. Studies of molecular crystals illustrate how the use of a solid paradigm may change the way that we consider these important molecules. Cooperative interactions, particularly those involving H-bonding, play much more important roles in the solid than in the liquid paradigms, as molecular crystals clearly illustrate. Using the solid rather than the liquid paradigm for proteins and peptides includes these cooperative interactions while application of the liquid paradigm tends to ignore or minimize them. Use of the solid paradigm has important implications for basic principles that are often implied about peptide and protein chemistry, such as the importance of entropy in protein folding and the nature of the hydrophobic effect. Understanding the folded states of peptides and proteins (especially alpha-helices) often requires the solid paradigm, whereas understanding unfolded states does not. Both theoretical and experimental studies of the energetics of protein and peptide folding require comparison to a suitable standard. Our perspective on these energetics depends on the reasonable choice of reference. The use of multiple reference states, particularly that of component amino acids in the gas phase, is proposed.

Dynamic Protein Interaction Networks and New Structural Paradigms in Signaling

Understanding signaling and other complex biological processes requires elucidating the critical roles of intrinsically disordered proteins (IDPs) and regions (IDRs), which represent ∼30% of the proteome and enable unique regulatory mechanisms. In this review, we describe the structural heterogeneity of disordered proteins that underpins these mechanisms and the latest progress in obtaining structural descriptions of conformational ensembles of disordered proteins that are needed for linking structure and dynamics to function. We describe the diverse interactions of IDPs that can have unusual characteristics such as "ultrasensitivity" and "regulated folding and unfolding". We also summarize the mounting data showing that large-scale assembly and protein phase separation occurs within a variety of signaling complexes and cellular structures. In addition, we discuss efforts to therapeutically target disordered proteins with small molecules. Overall, we interpret the remodeling of disordered state ensembles due to binding and post-translational modifications within an expanded framework for allostery that provides significant insights into how disordered proteins transmit biological information.

Correlation Analysis of Trp-Cage Dynamics in Folded and Unfolded States

A fundamental and still debated problem is how folded structures of proteins are related to their unfolded state. Besides the classical view, in which a large number of conformations characterize the unfolded state while the folded one is dominated by a single structure, recently a reassessment of the denatured state has been suggested. A growing amount of evidence indicates that not only the folded but also the unfolded state is at least partially organized. Here, we try to answer the question of how different protein dynamics is in folded and unfolded states by performing all-atom molecular dynamics simulations on the model protein Trp-cage. Random matrix theory inspired analysis of the correlation matrices has been carried out. The spectra of these correlation matrices show that the low rank modes of Trp-cage dynamics are outside of the limit expected for a random system both in folded and in unfolded conditions. These findings shed light on the nature of the unfolded state of the proteins, suggesting that it is much less random than previously thought.

Sequence- and Temperature-Dependent Properties of Unfolded and Disordered Proteins from Atomistic Simulations

We use all-atom molecular simulation with explicit solvent to study the properties of selected intrinsically disordered proteins and unfolded states of foldable proteins, which include chain dimensions and shape, secondary structure propensity, solvent accessible surface area, and contact formation. We find that the qualitative scaling behavior of the chains matches expectations from theory under ambient conditions. In particular, unfolded globular proteins tend to be more collapsed under the same conditions than charged disordered sequences of the same length. However, inclusion of explicit solvent in addition naturally captures temperature-dependent solvation effects, which results in an initial collapse of the chains as temperature is increased, in qualitative agreement with experiment. There is a universal origin to the collapse, revealed in the change of hydration of individual residues as a function of temperature: namely, that the initial collapse is driven by unfavorable solvation free energy of individual residues, which in turn has a strong temperature dependence. We also observe that in unfolded globular proteins, increased temperature also initially favors formation of native-like (rather than non-native-like) structure. Our results help to establish how sequence encodes the degree of intrinsic disorder or order as well as its response to changes in environmental conditions.

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.

Secondary structure assignment for conformationally irregular peptides: comparison between DSSP, STRIDE and KAKSI

Secondary structure assignment codes were built to explore the regularities associated with the periodic motifs of proteins, such as those in backbone dihedral angles or in hydrogen bonds between backbone atoms. Precise structure assignment is challenging because real-life secondary structures are susceptible to bending, twist, fraying and other deformations that can distance them from their geometrical prototypes. Although results from codes such as DSSP and STRIDE converge in well-ordered structures, the agreement between the secondary structure assignments is known to deteriorate as the conformations become more distorted. Conformationally irregular peptides therefore offer a great opportunity to explore the differences between these codes. This is especially important for unfolded proteins and intrinsically disordered proteins, which are known to exhibit residual and/or transient secondary structure whose characterization is challenging. In this work, we have carried out Molecular Dynamics simulations of (relatively) disordered peptides, specifically gp41659-671 (ELLELDKWASLWN), the homopeptide polyasparagine (N18), and polyasparagine dimers. We have analyzed the resulting conformations with DSSP and STRIDE, based on hydrogen-bond patterns (and dihedral angles for STRIDE), and KAKSI, based on α-Carbon distances; and carefully characterized the differences in structural assignments. The full-sequence Segment Overlap (SOV) scores, that quantify the agreement between two secondary structure assignments, vary from 70% for gp41659-671 (STRIDE as reference) to 49% for N18 (DSSP as reference). Major differences are observed in turns, in the distinction between α and 310 helices, and in short parallel-sheet segments.

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.

Quantifying the Sources of Kinetic Frustration in Folding Simulations of Small Proteins

Experiments and atomistic simulations of polypeptides have revealed structural intermediates that promote or inhibit conformational transitions to the native state during folding. We invoke a concept of “kinetic frustration” to quantify the prevalence and impact of these behaviors on folding rates within a large set of atomistic simulation data for 10 fast-folding proteins, where each protein’s conformational space is represented as a Markov state model of conformational transitions. Our graph theoretic approach addresses what conformational features correlate with folding inhibition and therefore permits comparison among features within a single protein network and also more generally between proteins. Nonnative contacts and nonnative secondary structure formation can thus be quantitatively implicated in inhibiting folding for several of the tested peptides.

A cooperative jack model of random coil-to-elongation transition of the FH1 domain by profilin binding explains formin motor behavior in actin polymerization

Filopodia are essential for the development of neuronal growth cones, cell polarity and cell migration. Their protrusions are powered by the polymerization of actin filaments linked to the plasma membrane, catalyzed by formin proteins. The acceleration of polymerization depends on the number of profilin-actins binding with the formin-FH1 domain. Biophysical characterization of the disordered formin-FH1 domain remains a challenge. We analyzed the conformational distribution of the diaphanous-related formin mDia1-FH1 bound with one to six profilins. We found a coil-to-elongation transition in the FH1 domain. We propose a cooperative "jack" model for the Formin-Homology-1 (FH1) domain of formins stacked by profilin-actins.

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.