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

An amino-domino model described by a cross-peptide-bond Ramachandran plot defines amino acid pairs as local structural units

Protein structure, both at the global and local level, dictates function. Proteins fold from chains of amino acids, forming secondary structures, α-helices and β-strands, that, at least for globular proteins, subsequently fold into a three-dimensional structure. Here, we show that a Ramachandran-type plot focusing on the two dihedral angles separated by the peptide bond, and entirely contained within an amino acid pair, defines a local structural unit. We further demonstrate the usefulness of this cross-peptide-bond Ramachandran plot by showing that it captures β-turn conformations in coil regions, that traditional Ramachandran plot outliers fall into occupied regions of our plot, and that thermophilic proteins prefer specific amino acid pair conformations. Further, we demonstrate experimentally that the effect of a point mutation on backbone conformation and protein stability depends on the amino acid pair context, i.e., the identity of the adjacent amino acid, in a manner predictable by our method.

Unconstrained generation of synthetic antibody-antigen structures to guide machine learning methodology for antibody specificity prediction

Machine learning (ML) is a key technology for accurate prediction of antibody-antigen binding. Two orthogonal problems hinder the application of ML to antibody-specificity prediction and the benchmarking thereof: the lack of a unified ML formalization of immunological antibody-specificity prediction problems and the unavailability of large-scale synthetic datasets to benchmark real-world relevant ML methods and dataset design. Here we developed the Absolut! software suite that enables parameter-based unconstrained generation of synthetic lattice-based three-dimensional antibody-antigen-binding structures with ground-truth access to conformational paratope, epitope and affinity. We formalized common immunological antibody-specificity prediction problems as ML tasks and confirmed that for both sequence- and structure-based tasks, accuracy-based rankings of ML methods trained on experimental data hold for ML methods trained on Absolut!-generated data. The Absolut! framework has the potential to enable real-world relevant development and benchmarking of ML strategies for biotherapeutics design.

A compact vocabulary of paratope-epitope interactions enables predictability of antibody-antigen binding

Antibody-antigen binding relies on the specific interaction of amino acids at the paratope-epitope interface. The predictability of antibody-antigen binding is a prerequisite for de novo antibody and (neo-)epitope design. A fundamental premise for the predictability of antibody-antigen binding is the existence of paratope-epitope interaction motifs that are universally shared among antibody-antigen structures. In a dataset of non-redundant antibody-antigen structures, we identify structural interaction motifs, which together compose a commonly shared structure-based vocabulary of paratope-epitope interactions. We show that this vocabulary enables the machine learnability of antibody-antigen binding on the paratope-epitope level using generative machine learning. The vocabulary (1) is compact, less than 10⁴ motifs; (2) distinct from non-immune protein-protein interactions; and (3) mediates specific oligo- and polyreactive interactions between paratope-epitope pairs. Our work leverages combined structure- and sequence-based learning to demonstrate that machine-learning-driven predictive paratope and epitope engineering is feasible.

A complete Fourier-synthesis-based backbone-conformation-dependent library for proteins

While broadening the applicability of (φ/ψ)-dependent target values for the bond angles in the peptide backbone, sequence/conformation categories with too few residues to analyze via previous methods were encountered. Here, a method of describing a conformation-dependent library (CDL) using two-dimensional Fourier coefficients is reported where the number of coefficients for individual categories is determined via complete cross-validation. Sample sizes are increased further by selective blending of categories with similar patterns of conformational dependence. An additional advantage of the Fourier-synthesis-based CDL is that it uses continuous functions and has no artifactual steps near the edges of populated regions of φ/ψ space. A set of libraries for the seven main-chain bond angles, along with the ω and ζ angles, was created based on a set of Fourier analyses of 48 368 residues selected from high-resolution models in the wwPDB. This new library encompasses both trans- and cis-peptide bonds and outperforms currently used discrete CDLs.

Systematic Exploration of Protein Conformational Space Using a Distance Geometry Approach

The optimization approaches classically used during the determination of protein structure encounter various difficulties, especially when the size of the conformational space is large. Indeed, in such a case, algorithmic convergence criteria are more difficult to set up. Moreover, the size of the search space makes it difficult to achieve a complete exploration. The interval branch-and-prune (iBP) approach, based on the reformulation of the distance geometry problem (DGP) provides a theoretical frame for the generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of interatomic distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, immediately disappear as distance measurement errors are introduced. Here we propose an improvement of this approach: threading-augmented interval branch-and-prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using self-organizing maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are a uniform covalent geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and a few long-range distances. For most of the proteins smaller than 50 residues and interval widths of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 Å with respect to the initial protein conformation. The efficiency of the TAiBP approach for proteins larger than 50 residues will require the use of nonuniform covalent geometry and may have benefits from the recent development of residue-specific force-fields.

Atomic Motif Recognition in (Bio)Polymers: Benchmarks From the Protein Data Bank

Rationalizing the structure and structure-property relations for complex materials such as polymers or biomolecules relies heavily on the identification of local atomic motifs, e.g., hydrogen bonds and secondary structure patterns, that are seen as building blocks of more complex supramolecular and mesoscopic structures. Over the past few decades, several automated procedures have been developed to identify these motifs in proteins given the atomic structure. Being based on a very precise understanding of the specific interactions, these heuristic criteria formulate the question in a way that implies the answer, by defining a list of motifs based on those that are known to be naturally occurring. This makes them less likely to identify unexpected phenomena, such as the occurrence of recurrent motifs in disordered segments of proteins, and less suitable to be applied to different polymers whose structure is not driven by hydrogen bonds, or even to polypeptides when appearing in unusual, non-biological conditions. Here we discuss how unsupervised machine learning schemes can be used to recognize patterns based exclusively on the frequency with which different motifs occur, taking high-resolution structures from the Protein Data Bank as benchmarks. We first discuss the application of a density-based motif recognition scheme in combination with traditional representations of protein structure (namely, interatomic distances and backbone dihedrals). Then, we proceed one step further toward an entirely unbiased scheme by using as input a structural representation based on the atomic density and by employing supervised classification to objectively assess the role played by the representation in determining the nature of atomic-scale patterns.

A new clustering and nomenclature for beta turns derived from high-resolution protein structures

Protein loops connect regular secondary structures and contain 4-residue beta turns which represent 63% of the residues in loops. The commonly used classification of beta turns (Type I, I’, II, II’, VIa1, VIa2, VIb, and VIII) was developed in the 1970s and 1980s from analysis of a small number of proteins of average resolution, and represents only two thirds of beta turns observed in proteins (with a generic class Type IV representing the rest). We present a new clustering of beta-turn conformations from a set of 13,030 turns from 1074 ultra-high resolution protein structures (≤1.2 Å). Our clustering is derived from applying the DBSCAN and k-medoids algorithms to this data set with a metric commonly used in directional statistics applied to the set of dihedral angles from the second and third residues of each turn. We define 18 turn types compared to the 8 classical turn types in common use. We propose a new 2-letter nomenclature for all 18 beta-turn types using Ramachandran region names for the two central residues (e.g., ‘A’ and ‘D’ for alpha regions on the left side of the Ramachandran map and ‘a’ and ‘d’ for equivalent regions on the right-hand side; classical Type I turns are ‘AD’ turns and Type I’ turns are ‘ad’). We identify 11 new types of beta turn, 5 of which are sub-types of classical beta-turn types. Up-to-date statistics, probability densities of conformations, and sequence profiles of beta turns in loops were collected and analyzed. A library of turn types, BetaTurnLib18, and cross-platform software, BetaTurnTool18, which identifies turns in an input protein structure, are freely available and redistributable from dunbrack.fccc.edu/betaturn and github.com/sh-maxim/BetaTurn18. Given the ubiquitous nature of beta turns, this comprehensive study updates understanding of beta turns and should also provide useful tools for protein structure determination, refinement, and prediction programs.

Folded proteins consist of elements of regular secondary structure, such as alpha helices and beta sheets connected by irregular structures called loops. Loops have a varying length and typically contain U-shaped beta turns which abruptly change the direction of the chain. Beta turns are formed by four sequential amino acid residues and adopt specific conformations which have been classified into eight types since the 1970s. Based on a larger set of very detailed protein structures and thorough statistical data analysis, the previous set of beta-turn types was revised to include 7 existing turn types, 5 subtypes of the existing turns, and 6 new types. Their properties and amino-acid sequence propensities are analyzed. We propose a self-explanatory turn nomenclature, based on the conformations of residues 2 and 3 of the beta turn, that is much easier to remember than the old nomenclature. We developed a library of 18 turn types and software to assign them to an input protein structure. The software and new turn types should advance fundamental understanding of protein structure as well as benefit applications for protein structure prediction, determination, and refinement.

Structural insights into a thermostable variant of human carbonic anhydrase II

Carbonic anhydrase is an enzyme of interest for many biotechnological developments including carbon sequestration. These applications often require harsh conditions, so there is a need for the development of thermostable variants. One of the most thermostable human carbonic anhydrase II (HCAIIts) variants was patented in 2006. Here, we report the ultra-high resolution crystal structure of HCAIIts. The structural changes seen are consistent with each of the six mutations involved acting largely independently and variously resulting in increased H-bonding, improved packing, and reduced side chain entropy loss on folding to yield the increased stability. We further suggest that for four of the mutations, improvements in backbone conformational energetics is also a contributor and that considerations of such conformational propensities of individual amino acids are often overlooked.

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

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

Experimental conformational energy maps of proteins and peptides

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

Left-handed polyproline-II helix revisited: proteins causing proteopathies

Left-handed polyproline-II type helix is a regular conformation of polypeptide chain not only of fibrous, but also of folded and natively unfolded proteins and peptides. It is the only class of regular secondary structure substantially represented in non-fibrous proteins and peptides on a par with right-handed alpha-helix and beta-structure. In this study, we have shown that polyproline-II helix is abundant in several peptides and proteins involved in proteopathies, the amyloid-beta peptides, protein tau and prion protein. Polyproline-II helices form two interaction sites in the amyloid-beta peptides, which are pivotal for pathogenesis of Alzheimer's disease (AD). It also with high probability is the structure of the majority of tau phosphorylation sites, important for tau hyperphosphorylation and formation of neurofibrillary tangles, a hallmark of AD. Polyproline-II helices form large parts of the structure of the folded domain of prion protein. They can undergo conversion to beta-structure as a result of relatively small change of one torsional angle of polypeptide chain. We hypothesize that in prions and amyloids, in general polyproline-II helices can serve as structural elements of the normal structure as well as dormant nuclei of structure conversion, and thus play important role in structure changes leading to the formation of fibrils.

Optimization of Protein Backbone Dihedral Angles by Means of Hamiltonian Reweighting

Molecular dynamics simulations depend critically on the accuracy of the underlying force fields in properly representing biomolecules. Hence, it is crucial to validate the force-field parameter sets in this respect. In the context of the GROMOS force field, this is usually achieved by comparing simulation data to experimental observables for small molecules. In this study, we develop new amino acid backbone dihedral angle potential energy parameters based on the widely used 54A7 parameter set by matching to experimental J values and secondary structure propensity scales. In order to find the most appropriate backbone parameters, close to 100 000 different combinations of parameters have been screened. However, since the sheer number of combinations considered prohibits actual molecular dynamics simulations for each of them, we instead predicted the values for every combination using Hamiltonian reweighting. While the original 54A7 parameter set fails to reproduce the experimental data, we are able to provide parameters that match significantly better. However, to ensure applicability in the context of larger peptides and full proteins, further studies have to be undertaken.

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.

Dihedral-based segment identification and classification of biopolymers I: proteins

A new structure classification scheme for biopolymers is introduced, which is solely based on main-chain dihedral angles. It is shown that by dividing a biopolymer into segments containing two central residues, a local classification can be performed. The method is referred to as DISICL, short for Dihedral-based Segment Identification and Classification. Compared to other popular secondary structure classification programs, DISICL is more detailed as it offers 18 distinct structural classes, which may be simplified into a classification in terms of seven more general classes. It was designed with an eye to analyzing subtle structural changes as observed in molecular dynamics simulations of biomolecular systems. Here, the DISICL algorithm is used to classify two databases of protein structures, jointly containing more than 10 million segments. The data is compared to two alternative approaches in terms of the amount of classified residues, average occurrence and length of structural elements, and pair wise matches of the classifications by the different programs. In an accompanying paper (Nagy, G.; Oostenbrink, C. Dihedral-based segment identification and classification of biopolymers II: Polynucleotides. J. Chem. Inf. Model. 2013, DOI: 10.1021/ci400542n), the analysis of polynucleotides is described and applied. Overall, DISICL represents a potentially useful tool to analyze biopolymer structures at a high level of detail.

Two-dimensional heterospectral correlation analysis of the redox-induced conformational transition in cytochrome c using surface-enhanced Raman and infrared absorption spectroscopies on a two-layer gold surface

The heme protein cytochrome c adsorbed to a two-layer gold surface modified with a self-assembled monolayer of 2-mercaptoethanol was analyzed using a two-dimensional (2D) heterospectral correlation analysis that combined surface-enhanced infrared absorption spectroscopy (SEIRAS) and surface-enhanced Raman spectroscopy (SERS). Stepwise increasing electric potentials were applied to alter the redox state of the protein and to induce conformational changes within the protein backbone. We demonstrate herein that 2D heterospectral correlation analysis is a particularly suitable and useful technique for the study of heme-containing proteins as the two spectroscopies address different portions of the protein. Thus, by correlating SERS and SEIRAS data in a 2D plot, we can obtain a deeper understanding of the conformational changes occurring at the redox center and in the supporting protein backbone during the electron transfer process. The correlation analyses are complemented by molecular dynamics calculations to explore the intramolecular interactions.