Structures, basins, and energies: a deconstruction of the Protein Coil Library

Exploring LCST- and UCST-like Behavior of Branched Molecules Bearing Repeat Units of Elastin-like Peptides as Side Components

Elastin-like peptides (ELPs) exhibit lower critical solution temperature (LCST)-type behavior, being soluble at low temperatures and insoluble at high temperatures. While the properties of linear, long-chain ELPs are well-studied, short-chain ELPs, especially those with branched architectures, have been less explored. Herein, to obtain further insights into multimeric short ELPs, we investigated the temperature-responsive properties of branched molecules composed of a repeating pentapeptide unit of short ELPs, Phe-Pro-Gly-Val-Gly, as side components and oligo(Glu) as a backbone structure. In turbidimetry experiments, the branched ELPs showed LCST-like behavior similar to conventional ELPs and upper critical solution temperature (UCST)-like behavior, which are rarely observed in ELPs. In addition, the morphological aspects and mechanisms underlying the temperature-responsiveness were investigated. We observed that spherical aggregates formed, and the branched ELPs underwent structural changes through the self-assembly process. This study demonstrates the unique temperature-responsiveness of branched short ELPs, providing new insights into the future development and use of ELPs with tailored properties.

Structural Insights into Ciona intestinalis Septins: Complexes Suggest a Mechanism for Nucleotide-dependent Interfacial Cross-talk

Septins are filamentous nucleotide-binding proteins which can associate with membranes in a curvature-dependent manner leading to structural remodelling and barrier formation. Ciona intestinalis, a model for exploring the development and evolution of the chordate lineage, has only four septin-coding genes within its genome. These represent orthologues of the four classical mammalian subgroups, making it a minimalist non-redundant model for studying the modular assembly of septins into linear oligomers and thereby filamentous polymers. Here, we show that C. intestinalis septins present a similar biochemistry to their human orthologues and also provide the cryo-EM structures of an octamer, a hexamer and a tetrameric sub-complex. The octamer, which has the canonical arrangement (2-6-7-9-9-7-6-2) clearly shows an exposed NC-interface at its termini enabling copolymerization with hexamers into mixed filaments. Indeed, only combinations of septins which had CiSEPT2 occupying the terminal position were able to assemble into filaments via NC-interface association. The CiSEPT7-CiSEPT9 tetramer is the smallest septin particle to be solved by Cryo-EM to date and its good resolution (2.7 Å) provides a well-defined view of the central NC-interface. On the other hand, the CiSEPT7-CiSEPT9 G-interface shows signs of fragility permitting toggling between hexamers and octamers, similar to that seen in human septins but not in yeast. The new structures provide insights concerning the molecular mechanism for cross-talk between adjacent interfaces. This indicates that C. intestinalis may represent a valuable tool for future studies, fulfilling the requirements of a complete but simpler system to understand the mechanisms behind the assembly and dynamics of septin filaments.

Fluid protein fold space and its implications

Fold-switching proteins, which remodel their secondary and tertiary structures in response to cellular stimuli, suggest a new view of protein fold space. For decades, experimental evidence has indicated that protein fold space is discrete: dissimilar folds are encoded by dissimilar amino acid sequences. Challenging this assumption, fold-switching proteins interconnect discrete groups of dissimilar protein folds, making protein fold space fluid. Three recent observations support the concept of fluid fold space: (1) some amino acid sequences interconvert between folds with distinct secondary structures, (2) some naturally occurring sequences have switched folds by stepwise mutation, and (3) fold switching is evolutionarily selected and likely confers advantage. These observations indicate that minor amino acid sequence modifications can transform protein structure and function. Consequently, proteomic structural and functional diversity may be expanded by alternative splicing, small nucleotide polymorphisms, post-translational modifications, and modified translation rates.

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.

Structural and Energetic Characterization of the Denatured State from the Perspectives of Peptides, the Coil Library, and Intrinsically Disordered Proteins

The α and polyproline II (PPII) basins are the two most populated regions of the Ramachandran map when constructed from the protein coil library, a widely used denatured state model built from the segments of irregular structure found in the Protein Data Bank. This indicates the α and PPII conformations are dominant components of the ensembles of denatured structures that exist in solution for biological proteins, an observation supported in part by structural studies of short, and thus unfolded, peptides. Although intrinsic conformational propensities have been determined experimentally for the common amino acids in short peptides, and estimated from surveys of the protein coil library, the ability of these intrinsic conformational propensities to quantitatively reproduce structural behavior in intrinsically disordered proteins (IDPs), an increasingly important class of proteins in cell function, has thus far proven elusive to establish. Recently, we demonstrated that the sequence dependence of the mean hydrodynamic size of IDPs in water and the impact of heat on the coil dimensions, provide access to both the sequence dependence and thermodynamic energies that are associated with biases for the α and PPII backbone conformations. Here, we compare results from peptide-based studies of intrinsic conformational propensities and surveys of the protein coil library to those of the sequence-based analysis of heat effects on IDP hydrodynamic size, showing that a common structural and thermodynamic description of the protein denatured state is obtained.

Impact of Heat on Coil Hydrodynamic Size Yields the Energetics of Denatured State Conformational Bias

Conformational equilibria in the protein denatured state have key roles regulating folding, stability, and function. The extent of conformational bias in the protein denatured state under folding conditions, however, has thus far proven elusive to quantify, particularly with regard to its sequence dependence and energetic character. To better understand the structural preferences of the denatured state, we analyzed both the sequence dependence to the mean hydrodynamic size of disordered proteins in water and the impact of heat on the coil dimensions, showing that the sequence dependence and thermodynamic energies associated with intrinsic biases for the α and polyproline II (PPII) backbone conformations can be obtained. Experiments that evaluate how the hydrodynamic size changes with compositional changes in the protein reveal amino acid specific preferences for PPII that are in good quantitative agreement with calorimetry-measured values from unfolded peptides and those inferred by survey of the protein coil library. At temperatures above 25 °C, the denatured state follows the predictions of a PPII-dominant ensemble. Heat effects on coil hydrodynamic size indicate the α bias is comparable to the PPII bias at cold temperatures. Though historically thought to give poor resolution to structural details, the hydrodynamic size of the unfolded state is found to be an effective reporter on the extent of the biases for the α and PPII backbone conformations.

Conformation Dependence of Diphenylalanine Self-Assembly Structures and Dynamics: Insights from Hybrid-Resolution Simulations

The molecular design of peptide-assembled nanostructures relies on extensive knowledge pertaining to the relationship between conformational features of peptide constituents and their behavior regarding self-assembly, and characterizing the conformational details of peptides during their self-assembly is experimentally challenging. Here, we demonstrate that a hybrid-resolution modeling method can be employed to investigate the role that conformation plays during the assembly of terminally capped diphenylalanines (FF) through microsecond simulations of hundreds or thousands of peptides. Our simulations discovered tubular or vesicular nanostructures that were consistent with experimental observation while reproducing critical self-assembly concentration and secondary structure contents in the assemblies that were measured in our experiments. The atomic details provided by our method allowed us to uncover diverse FF conformations and conformation dependence of assembled nanostructures. We found that the assembled morphologies and the molecular packing of FFs in the observed assemblies are linked closely with side-chain angle and peptide bond orientation, respectively. Of various conformations accessible to soluble FFs, only a select few are compatible with the assembled morphologies in water. A conformation resembling a FF crystal, in particular, became predominant due to its ability to permit highly ordered and energetically favorable FF packing in aqueous assemblies. Strikingly, several conformations incompatible with the assemblies arose transiently as intermediates, facilitating key steps of the assembly process. The molecular rationale behind the role of these intermediate conformations were further explained. Collectively, the structural details reported here advance the understanding of the FF self-assembly mechanism, and our method shows promise for studying peptide-assembled nanostructures and their rational design.

Computational design of structured loops for new protein functions

The ability to engineer the precise geometries, fine-tuned energetics and subtle dynamics that are characteristic of functional proteins is a major unsolved challenge in the field of computational protein design. In natural proteins, functional sites exhibiting these properties often feature structured loops. However, unlike the elements of secondary structures that comprise idealized protein folds, structured loops have been difficult to design computationally. Addressing this shortcoming in a general way is a necessary first step towards the routine design of protein function. In this perspective, we will describe the progress that has been made on this problem and discuss how recent advances in the field of loop structure prediction can be harnessed and applied to the inverse problem of computational loop design.

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.

An n→π* Interaction in the Bound Substrate of Aspartic Proteases Replicates the Oxyanion Hole

Aspartic proteases regulate many biological processes and are prominent targets for therapeutic intervention. Structural studies have captured intermediates along the reaction pathway, including the Michaelis complex and tetrahedral intermediate. Using a Ramachandran analysis of these structures, we discovered that residues occupying the P1 and P1' positions (which flank the scissile peptide bond) adopt the dihedral angle of an inverse γ-turn and polyproline type-II helix, respectively. Computational analyses reveal that the polyproline type-II helix engenders an n→π* interaction in which the oxygen of the scissile peptide bond is the donor. This interaction stabilizes the negative charge that develops in the tetrahedral intermediate, much like the oxyanion hole of serine proteases. The inverse γ-turn serves to twist the scissile peptide bond, vacating the carbonyl π* orbital and facilitating its hydration. These previously unappreciated interactions entail a form of substrate-assisted catalysis and offer opportunities for drug design.

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.

Conformational Analysis of n→π* Interactions in Collagen Triple Helix Models

Ab initio calculations of three models of collagen at positions Pro-Pro-Gly (1), Pro-Gly-Pro (2), and Gly-Pro-Pro (3) were performed to assess the conformational variation of n→π* contributions to the stability of the collagen triple helix. Full conformational analyses by relaxed potential-energy scans of the Ψ dihedral angle of the central residue in models 1, 2, and 3 revealed the presence of several n→π* interactions. In model 2, with Gly as the central residue, both the Φ and Ψ dihedral angles of Gly were scanned. Most minima of each model contained one or two n→π* interactions, with pyramidalization at the π* carbon. We also observed pyramidalization at the n→π* donor amide nitrogens. Minima with hydrogen-bond or non-native n→π* interactions compete with the collagen stabilizing n→π* interactions. The collagen-like n→ re-π* conformation was found as the global minimum only in model 3. The global minimum of 1 had a 5-membered ring hydrogen bond with an additional weak n→ si-π* interaction. The global minimum of 2 was in the extended conformation. We predict that the n→π* interactions found in native collagen, while individually small, cumulatively contribute to the stability of the triple helix conformation of collagen.

Crystal Structures of Expanded Poly(l-leucine) Isomers Containing Bis(pyridine)silver(I) Moieties: Precise Formation of Secondary Structure Depending on the Side Chain

Precise construction of a three-dimensional molecular structure is key for functional macromolecules, such as enzymes or proteins. Previously, a new concept, "expanded poly(α-amino acid)s" containing rigid spacers, was proposed for strategic construction of chiral helices. Herein, expanded poly(l-leucine) isomers containing bis(pyridine)silver(I) moieties were synthesized, and their crystal structures were determined by X-ray analysis. Each expanded polypeptide forms a unique secondary structure, a left-handed 6₁ helix or zigzag chain (2₁ helix), precisely depending on the chemical structure of the side chain, that is, slight branching. Distinct conformations were indicated by two main areas in the Ramachandran plot. These results suggest that the appropriate selection of the amino acid sequence and rigid spacers will lead to a new expanded protein with a tailor-made three-dimensional structure and desired functions.

A random forest learning assisted "divide and conquer" approach for peptide conformation search

Computational determination of peptide conformations is challenging as it is a problem of finding minima in a high-dimensional space. The "divide and conquer" approach is promising for reliably reducing the search space size. A random forest learning model is proposed here to expand the scope of applicability of the "divide and conquer" approach. A random forest classification algorithm is used to characterize the distributions of the backbone φ-ψ units ("words"). A random forest supervised learning model is developed to analyze the combinations of the φ-ψ units ("grammar"). It is found that amino acid residues may be grouped as equivalent "words", while the φ-ψ combinations in low-energy peptide conformations follow a distinct "grammar". The finding of equivalent words empowers the "divide and conquer" method with the flexibility of fragment substitution. The learnt grammar is used to improve the efficiency of the "divide and conquer" method by removing unfavorable φ-ψ combinations without the need of dedicated human effort. The machine learning assisted search method is illustrated by efficiently searching the conformations of GGG/AAA/GGGG/AAAA/GGGGG through assembling the structures of GFG/GFGG. Moreover, the computational cost of the new method is shown to increase rather slowly with the peptide length.

Modeling the Early Stages of Phase Separation in Disordered Elastin-like Proteins

Elastin-like proteins (ELPs) are known to undergo liquid-liquid phase separation reversibly above a concentration-dependent transition temperature. Previous studies suggested that, as temperature increases, ELPs experience an increased propensity for type II β-turns. However, how the ELPs behave below the phase transition temperature itself is still elusive. Here, we investigate the importance of β-turn formation during the early stages of ELP self-association. We examined the behavior of two ELPs, a 150-repeat construct that had been investigated previously (ELP[V5G3A2-150] as well as a new 40-repeat construct (ELP40) suitable for nuclear magnetic resonance measurements. Structural analysis of ELP40 reveals a disordered conformation, and chemical shifts throughout the sequence are insensitive to changes in temperature over 20°C. However, a low population of β-turn conformation cannot be ruled out based on chemical shifts alone. To examine the structural consequences of β-turns in ELPs, a series of structural ensembles of ELP[V5G3A2-150] were generated, incorporating differing amounts of β-turn bias throughout the chain. To mimic the early stages of the phase change, two monomers were paired, assuming preferential interaction at β-turn regions. This approach was justified by the observation that buried hydrophobic turns are commonly observed to interact in the Protein Data Bank. After dimerization, the ensemble-averaged hydrodynamic properties were calculated for each degree of β-turn bias, and the results were compared with analytical ultracentrifugation experiments at various temperatures. We find that the temperature dependence of the sedimentation coefficient (s20,wo) can be reproduced by increasing the β-turn content in the structural ensemble. This analysis allows us to estimate the presence of β-turns and weak associations under experimental conditions. Because disordered proteins frequently exhibit weak biases in secondary structure propensity, these experimentally-driven ensemble calculations may complement existing methods for modeling disordered proteins generally.

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.

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.

An amino acid code for irregular and mixed protein packing

To advance our understanding of protein tertiary structure, the development of the knob-socket model is completed in an analysis of the packing in irregular coil and turn secondary structure packing as well as between mixed secondary structure. The knob-socket model simplifies packing based on repeated patterns of two motifs: a three-residue socket for packing within secondary (2°) structure and a four-residue knob-socket for tertiary (3°) packing. For coil and turn secondary structure, knob-sockets allow identification of a correlation between amino acid composition and tertiary arrangements in space. Coil contributes almost as much as α-helices to tertiary packing. In irregular sockets, Gly, Pro, Asp, and Ser are favored, while in irregular knobs, the preference order is Arg, Asp, Pro, Asn, Thr, Leu, and Gly. Cys, His,Met, and Trp are not favored in either. In mixed packing, the knob amino acid preferences are a function of the socket that they are packing into, whereas the amino acid composition of the sockets does not depend on the secondary structure of the knob. A unique motif of a coil knob with an XYZ β-sheet socket may potentially function to inhibit β-sheet extension. In addition, analysis of the preferred crossing angles for strands within a β-sheet and mixed α-helice/β-sheet identifies canonical packing patterns useful in protein design. Lastly, the knob-socket model abstracts the complexity of protein tertiary structure into an intuitive packing surface topology map.

Sparsely populated residue conformations in protein structures: revisiting "experimental" Ramachandran maps

The Ramachandran map clearly delineates the regions of accessible conformational (φ-ψ) space for amino acid residues in proteins. Experimental distributions of φ, ψ values in high-resolution protein structures, reveal sparsely populated zones within fully allowed regions and distinct clusters in apparently disallowed regions. Conformational space has been divided into 14 distinct bins. Residues adopting these relatively rare conformations are presented and amino acid propensities for these regions are estimated. Inspection of specific examples in a completely "arid", fully allowed region in the top left quadrant establishes that side-chain and backbone interactions may provide the energetic compensation necessary for populating this region of φ-ψ space. Asn, Asp, and His residues showed the highest propensities in this region. The two distinct clusters in the bottom right quadrant which are formally disallowed on strict steric considerations correspond to the gamma turn (C7 axial) conformation (Bin 12) and the i + 1 position of Type II' β turns (Bin 13). Of the 516 non-Gly residues in Bin 13, 384 occupied the i + 1 position of Type II' β turns. Further examination of these turn segments revealed a high propensity to occur at the N-terminus of helices and as a tight turn in β hairpins. The β strand-helix motif with the Type II' β turn as a connecting element was also found in as many as 57 examples.

The intrinsic conformational features of amino acids from a protein coil library and their applications in force field development

The local conformational (φ, ψ, χ) preferences of amino acid residues remain an active research area, which are important for the development of protein force fields. In this perspective article, we first summarize spectroscopic studies of alanine-based short peptides in aqueous solution. While most studies indicate a preference for the P(II) conformation in the unfolded state over α and β conformations, significant variations are also observed. A statistical analysis from various coil libraries of high-resolution protein structures is then summarized, which gives a more coherent view of the local conformational features. The φ, ψ, χ distributions of the 20 amino acids have been obtained from a protein coil library, considering both backbone and side-chain conformational preferences. The intrinsic side-chain χ(1) rotamer preference and χ(1)-dependent Ramachandran plot can be generally understood by combining the interaction of the side-chain Cγ/Oγ atom with two neighboring backbone peptide groups. Current all-atom force fields such as AMBER ff99sb-ILDN, ff03 and OPLS-AA/L do not reproduce these distributions well. A method has been developed by combining the φ, ψ plot of alanine with the influence of side-chain χ(1) rotamers to derive the local conformational features of various amino acids. It has been further applied to improve the OPLS-AA force field. The modified force field (OPLS-AA/C) reproduces experimental (3)J coupling constants for various short peptides quite well. It also better reproduces the temperature-dependence of the helix-coil transition for alanine-based peptides. The new force field can fold a series of peptides and proteins with various secondary structures to their experimental structures. MD simulations of several globular proteins using the improved force field give significantly less deviation (RMSD) to experimental structures. The results indicate that the local conformational features from coil libraries are valuable for the development of balanced protein force fields.

Reducing the dimensionality of the protein-folding search problem

How does a folding protein negotiate a vast, featureless conformational landscape and adopt its native structure in biological real time? Motivated by this search problem, we developed a novel algorithm to compare protein structures. Procedures to identify structural analogs are typically conducted in three-dimensional space: the tertiary structure of a target protein is matched against each candidate in a database of structures, and goodness of fit is evaluated by a distance-based measure, such as the root-mean-square distance between target and candidate. This is an expensive approach because three-dimensional space is complex. Here, we transform the problem into a simpler one-dimensional procedure. Specifically, we identify and label the 11 most populated residue basins in a database of high-resolution protein structures. Using this 11-letter alphabet, any protein's three-dimensional structure can be transformed into a one-dimensional string by mapping each residue onto its corresponding basin. Similarity between the resultant basin strings can then be evaluated by conventional sequence-based comparison. The disorder → order folding transition is abridged on both sides. At the onset, folding conditions necessitate formation of hydrogen-bonded scaffold elements on which proteins are assembled, severely restricting the magnitude of accessible conformational space. Near the end, chain topology is established prior to emergence of the close-packed native state. At this latter stage of folding, the chain remains molten, and residues populate natural basins that are approximated by the 11 basins derived here. In essence, our algorithm reduces the protein-folding search problem to mapping the amino acid sequence onto a restricted basin string.

A thermodynamic definition of protein domains

Protein domains are conspicuous structural units in globular proteins, and their identification has been a topic of intense biochemical interest dating back to the earliest crystal structures. Numerous disparate domain identification algorithms have been proposed, all involving some combination of visual intuition and/or structure-based decomposition. Instead, we present a rigorous, thermodynamically-based approach that redefines domains as cooperative chain segments. In greater detail, most small proteins fold with high cooperativity, meaning that the equilibrium population is dominated by completely folded and completely unfolded molecules, with a negligible subpopulation of partially folded intermediates. Here, we redefine structural domains in thermodynamic terms as cooperative folding units, based on m-values, which measure the cooperativity of a protein or its substructures. In our analysis, a domain is equated to a contiguous segment of the folded protein whose m-value is largely unaffected when that segment is excised from its parent structure. Defined in this way, a domain is a self-contained cooperative unit; i.e., its cooperativity depends primarily upon intrasegment interactions, not intersegment interactions. Implementing this concept computationally, the domains in a large representative set of proteins were identified; all exhibit consistency with experimental findings. Specifically, our domain divisions correspond to the experimentally determined equilibrium folding intermediates in a set of nine proteins. The approach was also proofed against a representative set of 71 additional proteins, again with confirmatory results. Our reframed interpretation of a protein domain transforms an indeterminate structural phenomenon into a quantifiable molecular property grounded in solution thermodynamics.

Assessment of the intrinsic conformational preferences of dipeptide amino acids in aqueous solution by combined umbrella sampling/MBAR statistics. A comparison with experimental results

The propensities of 19 amino acid dipeptides have been calculated by a distributed umbrella sampling molecular dynamics simulation procedure using the OPLS-AA force field. The potential of mean force maps was estimated with the multiple Bennett acceptance ratio statistics. The resulting propensities compare satisfactorily well with very recently published experimental data on equivalent systems. In particular, α conformation-probabilities for all of the dipeptides remain much lower than either β or P(II) propensities. This result is in agreement with most experimental data for dipeptides. However, it is also in contrast with most simulation studies performed so far with other force fields, where α conformations result even more probable than P(II) or β ones. We discuss the behavior of the OPLS-AA force field, which can be useful for the improvement of this model in reproducing the recent experimental observations on amino acid dipeptides.

(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.

J-coupling constants for a trialanine peptide as a function of dihedral angles calculated by density functional theory over the full Ramachandran space

We present 13 (3)J, seven (2)J and four (1)J coupling constants (24 in all) calculated using B3LYP/D95** as a function of the φ and ψ Ramachandran dihedral angles of the acetyl(Ala)(3)NH(2) capped trialanine peptide over the entire Ramachandran space. With the exception of three of these J couplings, all show significant dependence upon both dihedral angles. For each J coupling considered, a two dimensional grid with respect to φ and ψ angles can be used to interpolate the values for any pair of φ and ψ values. Such simple interpolation is shown to be very accurate. Most of these calculated J couplings should prove useful for improving the accuracy of the determination of peptide and protein structures from NMR measurements in solution over that provided by the common procedure of treating the J couplings as functions of a single dihedral angle by means of Karplus-type fittings.

Accessing the disallowed conformations of peptides employing amide-to-imidate modification

Selective modification of the C-terminal amide in peptides to dihydrooxazine (a novel stable imidate isostere) by intramolecular nucleophilic cyclo-O-alkylation of the corresponding N-(3-bromopropyl)amides results in constraining of the C-terminal residue in natively disallowed conformations both in crystals and in solution.

Counting peptide-water hydrogen bonds in unfolded proteins

It is often assumed that the peptide backbone forms a substantial number of additional hydrogen bonds when a protein unfolds. We challenge that assumption in this article. Early surveys of hydrogen bonding in proteins of known structure typically found that most, but not all, backbone polar groups are satisfied, either by intramolecular partners or by water. When the protein is folded, these groups form approximately two hydrogen bonds per peptide unit, one donor or acceptor for each carbonyl oxygen or amide hydrogen, respectively. But when unfolded, the backbone chain is often believed to form three hydrogen bonds per peptide unit, one partner for each oxygen lone pair or amide hydrogen. This assumption is based on the properties of small model compounds, like N-methylacetamide, or simply accepted as self-evident fact. If valid, a chain of N residues would have approximately 2N backbone hydrogen bonds when folded but 3N backbone hydrogen bonds when unfolded, a sufficient difference to overshadow any uncertainties involved in calculating these per-residue averages. Here, we use exhaustive conformational sampling to monitor the number of H-bonds in a statistically adequate population of blocked polyalanyl-six-mers as the solvent quality ranges from good to poor. Solvent quality is represented by a scalar parameter used to Boltzmann-weight the population energy. Recent experimental studies show that a repeating (Gly-Ser) polypeptide undergoes a denaturant-induced expansion accompanied by breaking intramolecular peptide H-bonds. Results from our simulations augment this experimental finding by showing that the number of H-bonds is approximately conserved during such expansion⇋compaction transitions.

Populations of the three major backbone conformations in 19 amino acid dipeptides

The amide III region of the peptide infrared and Raman spectra has been used to determine the relative populations of the three major backbone conformations (P(II), β, and α(R)) in 19 amino acid dipeptides. The results provide a benchmark for force field or other methods of predicting backbone conformations in flexible peptides. There are three resolvable backbone bands in the amide III region. The major population is either P(II) or β for all dipeptides except Gly, whereas the α(R) population is measurable but always minor (≤ 10%) for 18 dipeptides. (The Gly ϕ,ψ map is complex and so is the interpretation of the amide III bands of Gly.) There are substantial differences in the relative β and P(II) populations among the 19 dipeptides. The band frequencies have been assigned as P(II), 1,317-1,306 cm(-1); α(R), 1,304-1,294 cm(-1); and β, 1,294-1,270 cm(-1). The three bands were measured by both attenuated total reflection spectroscopy and by Raman spectroscopy. Consistent results, both for band frequency and relative population, were obtained by both spectroscopic methods. The β and P(II) bands were assigned from the dependence of the (3)J(H(N),H(α)) coupling constant (known for all 19 dipeptides) on the relative β population. The P(II) band assignment agrees with one made earlier from Raman optical activity data. The temperature dependences of the relative β and P(II) populations fit the standard model with Boltzmann-weighted energies for alanine and leucine between 30 and 60 °C.

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.

A fresh look at the Ramachandran plot and the occurrence of standard structures in proteins

The Ramachandran plot is among the most central concepts in structural biology, seen in publications and textbooks alike. However, with the increasing numbers of known protein-structures and greater accuracy of ultra-high resolution protein structures, we are still learning more about the basic principles of protein structure. Here we use high fidelity conformational information to explore novel ways, such a geo-style and wrapped Ramachandran plots, to convey some of the basic aspects of the Ramachandran plot and of protein conformation. We point out the pressing need for a standard nomenclature for peptide conformation and propose such a nomenclature. Finally, we summarize some recent conceptual advances related to the building blocks of protein structure. The results for linear groups imply the need for substantive revisions in how the basics of protein structure are handled.

Physical-chemical determinants of coil conformations in globular proteins

We present a method with the potential to generate a library of coil segments from first principles. Proteins are built from alpha-helices and/or beta-strands interconnected by these coil segments. Here, we investigate the conformational determinants of short coil segments, with particular emphasis on chain turns. Toward this goal, we extracted a comprehensive set of two-, three-, and four-residue turns from X-ray-elucidated proteins and classified them by conformation. A remarkably small number of unique conformers account for most of this experimentally determined set, whereas remaining members span a large number of rare conformers, many occurring only once in the entire protein database. Factors determining conformation were identified via Metropolis Monte Carlo simulations devised to test the effectiveness of various energy terms. Simulated structures were validated by comparison to experimental counterparts. After filtering rare conformers, we found that 98% of the remaining experimentally determined turn population could be reproduced by applying a hydrogen bond energy term to an exhaustively generated ensemble of clash-free conformers in which no backbone polar group lacks a hydrogen-bond partner. Further, at least 90% of longer coil segments, ranging from 5- to 20 residues, were found to be structural composites of these shorter primitives. These results are pertinent to protein structure prediction, where approaches can be divided into either empirical or ab initio methods. Empirical methods use database-derived information; ab initio methods rely on physical-chemical principles exclusively. Replacing the database-derived coil library with one generated from first principles would transform any empirically based method into its corresponding ab initio homologue.

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.

Backbone statistical potential from local sequence-structure interactions in protein loops

Native proteins have been optimized by evolution simultaneously for structure and sequence. Structural databases reflect this interdependency. In this paper, we present a new statistical potential for a reduced backbone representation that has both structure and sequence characteristics as variables. We use information from structural data available in the Protein Coil Library, selected on the basis of resolution and refinement factor. In these structures, the nonlocal interactions are randomly distributed and, thus, average out in statistics, so structural propensities due to local backbone-based interactions can be studied separately. We collect data in the form of local sequence-specific phi-psi backbone dihedral pairs. From these data, we construct dihedral probability density functions (DPDFs) that quantify any adjacent phi-psi pair distribution in the context of all possible combinations of local residue types. We use a probabilistic analysis to deduce how the correlations encoded in the various DPDFs as well as in residue frequencies propagate along the sequence and can be cumulated in a statistical potential capable of efficiently scoring a loop by its backbone conformation and sequence only. Our potential is able to identify with high accuracy the native structure of a loop with a given sequence among possible alternative conformations from sets of well-constructed decoys. Conversely, the potential can also be used for sequence prediction problems and is shown to score the native sequence of a given loop structure among the most fit of the possible sequence combinations. Applications for both structure prediction and sequence design are discussed.

Predicting dihedral angle probability distributions for protein coil residues from primary sequence using neural networks

Background

Predicting the three-dimensional structure of a protein from its amino acid sequence is currently one of the most challenging problems in bioinformatics. The internal structure of helices and sheets is highly recurrent and help reduce the search space significantly. However, random coil segments make up nearly 40% of proteins and they do not have any apparent recurrent patterns, which complicates overall prediction accuracy of protein structure prediction methods. Luckily, previous work has indicated that coil segments are in fact not completely random in structure and flanking residues do seem to have a significant influence on the dihedral angles adopted by the individual amino acids in coil segments. In this work we attempt to predict a probability distribution of these dihedral angles based on the flanking residues. While attempts to predict dihedral angles of coil segments have been done previously, none have, to our knowledge, presented comparable results for the probability distribution of dihedral angles.

Results

In this paper we develop an artificial neural network that uses an input-window of amino acids to predict a dihedral angle probability distribution for the middle residue in the input-window. The trained neural network shows a significant improvement (4-68%) in predicting the most probable bin (covering a 30° × 30° area of the dihedral angle space) for all amino acids in the data set compared to baseline statistics. An accuracy comparable to that of secondary structure prediction (≈ 80%) is achieved by observing the 20 bins with highest output values.

Conclusion

Many different protein structure prediction methods exist and each uses different tools and auxiliary predictions to help determine the native structure. In this work the sequence is used to predict local context dependent dihedral angle propensities in coil-regions. This predicted distribution can potentially improve tertiary structure prediction methods that are based on sampling the backbone dihedral angles of individual amino acids. The predicted distribution may also help predict local structure fragments used in fragment assembly methods.

On the occurrence of linear groups in proteins

Linear groups-polypeptide conformations based on a single repeating phi,psi-pair-are a foundational concept in protein structure, yet how they are presented in textbooks is based largely on theoretical studies from the early days of protein structure analysis. Now, ultra-high resolution protein structures provide a resource for an accurate empirical and systematic assessment of the linear groups that truly exist in proteins. Here, a purely conformation-based survey of linear groups shows that only three distinct phi,psi-regions occur: a diverse set of extended conformations mostly present as beta-strands, a broad population of polyproline-II-like spirals, and a tight cluster that includes the highly populated alpha-helix and the conformationally-similar but much less populated 3(10)-helix. Rare, short left-handed alpha-/3(10)-helical turns with repeating phi,psi-angles occur, but none are longer than three residues. Misperceptions dispelled by this study are the existence of 2.2(7)- and pi-helices as linear groups, the existence of specific ideal phi,psi-angles for each linear group, and the existence of a substantive difference in the phi,psi-preferences for parallel versus antiparallel beta-strands. This study provides a concrete basis for updating and enhancing how we think about and teach the basics of protein structure.

Backbone conformational dependence of peptide acidity

Electrostatic interactions at the protein surface yield over a billion-fold range of amide hydrogen exchange rates. This range is equivalent to the maximal degree of attenuation in exchange rates that have been shown to occur for amides buried within the protein interior. Continuum dielectric analysis of Ala-Ala, Ala-Gly, Gly-Ala and trans-Pro-Ala peptide conformer acidities predicts that the relative orientation of the two neighboring peptide groups can account for a million-fold variation in hydroxide-catalyzed hydrogen exchange rates. As in previous protein studies, an internal dielectric value of 3 was found to be applicable to simple model peptides, presumably reflecting the short lifetime of the peptide anion intermediate. Despite the million-fold range in conformer acidities, the small differences in the experimental exchange rates for these peptides are accurately predicted. Ala-Ala conformers with an extended N-terminal residue and the C-terminal residue in the alpha conformation are predicted to account for over 60% of the overall hydrogen exchange reaction, despite constituting only 12% of the protein coil population.