Physical-chemical determinants of coil conformations in globular proteins

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

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

Ramachandran maps for side chains in globular proteins

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

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.

Extension of the classical classification of β-turns

The functional properties of a protein primarily depend on its three-dimensional (3D) structure. These properties have classically been assigned, visualized and analysed on the basis of protein secondary structures. The β-turn is the third most important secondary structure after helices and β-strands. β-turns have been classified according to the values of the dihedral angles φ and ψ of the central residue. Conventionally, eight different types of β-turns have been defined, whereas those that cannot be defined are classified as type IV β-turns. This classification remains the most widely used. Nonetheless, the miscellaneous type IV β-turns represent 1/3^rd of β-turn residues. An unsupervised specific clustering approach was designed to search for recurrent new turns in the type IV category. The classical rules of β-turn type assignment were central to the approach. The four most frequently occurring clusters defined the new β-turn types. Unexpectedly, these types, designated IV₁, IV₂, IV₃ and IV₄, represent half of the type IV β-turns and occur more frequently than many of the previously established types. These types show convincing particularities, in terms of both structures and sequences that allow for the classical β-turn classification to be extended for the first time in 25 years.

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.

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.

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.

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.

Assignment of PolyProline II conformation and analysis of sequence--structure relationship

BACKGROUND

Secondary structures are elements of great importance in structural biology, biochemistry and bioinformatics. They are broadly composed of two repetitive structures namely α-helices and β-sheets, apart from turns, and the rest is associated to coil. These repetitive secondary structures have specific and conserved biophysical and geometric properties. PolyProline II (PPII) helix is yet another interesting repetitive structure which is less frequent and not usually associated with stabilizing interactions. Recent studies have shown that PPII frequency is higher than expected, and they could have an important role in protein-protein interactions.

METHODOLOGY/PRINCIPAL FINDINGS

A major factor that limits the study of PPII is that its assignment cannot be carried out with the most commonly used secondary structure assignment methods (SSAMs). The purpose of this work is to propose a PPII assignment methodology that can be defined in the frame of DSSP secondary structure assignment. Considering the ambiguity in PPII assignments by different methods, a consensus assignment strategy was utilized. To define the most consensual rule of PPII assignment, three SSAMs that can assign PPII, were compared and analyzed. The assignment rule was defined to have a maximum coverage of all assignments made by these SSAMs. Not many constraints were added to the assignment and only PPII helices of at least 2 residues length are defined.

CONCLUSIONS/SIGNIFICANCE

The simple rules designed in this study for characterizing PPII conformation, lead to the assignment of 5% of all amino as PPII. Sequence-structure relationships associated with PPII, defined by the different SSAMs, underline few striking differences. A specific study of amino acid preferences in their N and C-cap regions was carried out as their solvent accessibility and contact patterns. Thus the assignment of PPII can be coupled with DSSP and thus opens a simple way for further analysis in this field.

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.