An amino acid code for β‐sheet packing structure

To understand the relationship between protein sequence and structure, this work extends the knob‐socket model in an investigation of β‐sheet packing. Over a comprehensive set of β‐sheet folds, the contacts between residues were used to identify packing cliques: sets of residues that all contact each other. These packing cliques were then classified based on size and contact order. From this analysis, the two types of four‐residue packing cliques necessary to describe β‐sheet packing were characterized. Both occur between two adjacent hydrogen bonded β‐strands. First, defining the secondary structure packing within β‐sheets, the combined socket or XY:HG pocket consists of four residues i, i+2 on one strand and j, j+2 on the other. Second, characterizing the tertiary packing between β‐sheets, the knob‐socket XY:H+B consists of a three‐residue XY:H socket (i, i+2 on one strand and j on the other) packed against a knob B residue (residue k distant in sequence). Depending on the packing depth of the knob B residue, two types of knob‐sockets are found: side‐chain and main‐chain sockets. The amino acid composition of the pockets and knob‐sockets reveal the sequence specificity of β‐sheet packing. For β‐sheet formation, the XY:HG pocket clearly shows sequence specificity of amino acids. For tertiary packing, the XY:H+B side‐chain and main‐chain sockets exhibit distinct amino acid preferences at each position. These relationships define an amino acid code for β‐sheet structure and provide an intuitive topological mapping of β‐sheet packing. Proteins 2014; 82:2128–2140. © 2014 Wiley Periodicals, Inc.     

β‐Bulges: Extensive structural analyses of β‐sheets irregularities

β‐Sheets are quite frequent in protein structures and are stabilized by regular main‐chain hydrogen bond patterns. Irregularities in β‐sheets, named β‐bulges, are distorted regions between two consecutive hydrogen bonds. They disrupt the classical alternation of side chain direction and can alter the directionality of β‐strands. They are implicated in protein‐protein interactions and are introduced to avoid β‐strand aggregation. Five different types of β‐bulges are defined. Previous studies on β‐bulges were performed on a limited number of protein structures or one specific family. These studies evoked a potential conservation during evolution. In this work, we analyze the β‐bulge distribution and conservation in terms of local backbone conformations and amino acid composition. Our dataset consists of 66 times more β‐bulges than the last systematic study (Chan et al. Protein Science 1993, 2:1574–1590). Novel amino acid preferences are underlined and local structure conformations are highlighted by the use of a structural alphabet. We observed that β‐bulges are preferably localized at the N‐ and C‐termini of β‐strands, but contrary to the earlier studies, no significant conservation of β‐bulges was observed among structural homologues. Displacement of β‐bulges along the sequence was also investigated by Molecular Dynamics simulations.     

Boosting protein stability with the computational design of β‐sheet surfaces

β‐sheets often have one face packed against the core of the protein and the other facing solvent. Mutational studies have indicated that the solvent‐facing residues can contribute significantly to protein stability, and that the preferred amino acid at each sequence position is dependent on the precise structure of the protein backbone and the identity of the neighboring amino acids. This suggests that the most advantageous methods for designing β‐sheet surfaces will be approaches that take into account the multiple energetic factors at play including side chain rotamer preferences, van der Waals forces, electrostatics, and desolvation effects. Here, we show that the protein design software Rosetta, which models these energetic factors, can be used to dramatically increase protein stability by optimizing interactions on the surfaces of small β‐sheet proteins. Two design variants of the β‐sandwich protein from tenascin were made with 7 and 14 mutations respectively on its β‐sheet surfaces. These changes raised the thermal midpoint for unfolding from 45°C to 64°C and 74°C. Additionally, we tested an empirical approach based on increasing the number of potential salt bridges on the surfaces of the β‐sheets. This was not a robust strategy for increasing stability, as three of the four variants tested were unfolded.     

The stability of cylindrin β‐barrel amyloid oligomer models—A molecular dynamics study

Small‐soluble amyloid oligomers are believed to play a significant role in the pathology of amyloid diseases. Recently, the atomic structure of a toxic oligomer formed by an 11 residue and its tandem repeat was found to have an out‐off register antiparallel β‐strands in the shape of a β‐barrel. In the present article we investigate the effect of mutations in the hydrophobic cores on the structure and dynamic of the β‐barrels using all atom multiple molecular dynamics simulations with an explicit solvent. Extending previous experiments with molecular dynamics simulations we systematically test how stability and formation of cylindrin depends on the interplay between hydrophobicity and steric effects of the core residues. We find that strong hydrophobic interactions between geometrically fitting residues keep the strands (both in register and out‐off‐register interface) in close proximity, which in turn stabilizes the side‐chain and main‐chain hydrogen bonds, and the salt bridges on the outer surface along the weak out‐of‐register interface. Our simulations also indicate presence of water molecules in the hydrophobic interior of the cylindrin β‐barrel.Proteins 2013. © 2013 Wiley Periodicals, Inc.     

Structures of single‐layer β‐sheet proteins evolved from β‐hairpin repeats

Free‐standing single‐layer β‐sheets are extremely rare in naturally occurring proteins, even though β‐sheet motifs are ubiquitous. Here we report the crystal structures of three homologous, single‐layer, anti‐parallel β‐sheet proteins, comprised of three or four twisted β‐hairpin repeats. The structures reveal that, in addition to the hydrogen bond network characteristic of β‐sheets, additional hydrophobic interactions mediated by small clusters of residues adjacent to the turns likely play a significant role in the structural stability and compensate for the lack of a compact hydrophobic core. These structures enabled identification of a family of secreted proteins that are broadly distributed in bacteria from the human gut microbiome and are putatively involved in the metabolism of complex carbohydrates. A conserved surface patch, rich in solvent‐exposed tyrosine residues, was identified on the concave surface of the β‐sheet. These new modular single‐layer β‐sheet proteins may serve as a new model system for studying folding and design of β‐rich proteins.     

Local sequence of protein β‐strands influences twist and bend angles

β‐Sheet twisting is thought to be mainly determined by interstrand hydrogen bonds with little contribution from side chains, but some proteins have large, flat β‐sheets, suggesting that side chains influence β‐structures. We therefore investigated the relationship between amino acid composition and twists or bends of β‐strands. We calculated and statistically analyzed the twist and bend angles of short frames of β‐strands in known protein structures. The most frequent twist angles were strongly negatively correlated with the proportion of hydrophilic amino acid residues. The majority of hydrophilic residues (except serine and threonine) were found in the edge regions of β‐strands, suggesting that the side chains of these residues likely do not affect β‐strand structure. In contrast, the majority of serine, threonine, and asparagine side‐chains in β‐strands made contacts with a nitrogen atom of the main chain, suggesting that these residues suppress β‐strand twisting. Proteins 2014; 82:1484–1493. © 2014 Wiley Periodicals, Inc.     

Sequence determinants of thermodynamic stability in a WW domain—An all‐β‐sheet protein

The stabilities of 66 sequence variants of the human Pin1 WW domain have been determined by equilibrium thermal denaturation experiments. All 34 residues composing the hPin1 WW three‐stranded β‐sheet structure could be replaced one at a time with at least one different natural or non‐natural amino acid residue without leading to an unfolded protein. Alanine substitutions at only four positions within the hPin1 WW domain lead to a partially or completely unfolded protein—in the absence of a physiological ligand. The side chains of these four residues form a conserved, partially solvent‐inaccessible, continuous hydrophobic minicore comprising the N‐ and C‐termini. Ala mutations at five other residues, three of which constitute the ligand binding patch on the concave side of the β‐sheet, significantly destabilize the hPin1 WW domain without leading to an unfolded protein. The remaining mutations affect protein stability only slightly, suggesting that only a small subset of side chain interactions within the hPin1 WW domain are mandatory for acquiring and maintaining a stable, cooperatively folded β‐sheet structure.     

Helix‐sheet packing in proteins

The three‐dimensional structure of a protein is organized around the packing of its secondary structure elements. Although much is known about the packing geometry observed between α‐helices and between β‐sheets, there has been little progress on characterizing helix–sheet interactions. We present an analysis of the conformation of αβ₂ motifs in proteins, corresponding to all occurrences of helices in contact with two strands that are hydrogen bonded. The geometry of the αβ₂ motif is characterized by the azimuthal angle θ between the helix axis and an average vector representing the two strands, the elevation angle ψ between the helix axis and the plane containing the two strands, and the distance D between the helix and the strands. We observe that the helix tends to align to the two strands, with a preference for an antiparallel orientation if the two strands are parallel; this preference is diminished for other topologies of the β‐sheet. Side‐chain packing at the interface between the helix and the strands is mostly hydrophobic, with a preference for aliphatic amino acids in the strand and aromatic amino acids in the helix. From the knowledge of the geometry and amino acid propensities of αβ₂ motifs in proteins, we have derived different statistical potentials that are shown to be efficient in picking native‐like conformations among a set of non‐native conformations in well‐known decoy datasets. The information on the geometry of αβ₂ motifs as well as the related statistical potentials have applications in the field of protein structure prediction. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

BuildBeta—A system for automatically constructing beta sheets

We describe a method that can thoroughly sample a protein conformational space given the protein primary sequence of amino acids and secondary structure predictions. Specifically, we target proteins with β‐sheets because they are particularly challenging for ab initio protein structure prediction because of the complexity of sampling long‐range strand pairings. Using some basic packing principles, inverse kinematics (IK), and β‐pairing scores, this method creates all possible β‐sheet arrangements including those that have the correct packing of β‐strands. It uses the IK algorithms of ProteinShop to move α‐helices and β‐strands as rigid bodies by rotating the dihedral angles in the coil regions. Our results show that our approach produces structures that are within 4–6 Å RMSD of the native one regardless of the protein size and β‐sheet topology although this number may increase if the protein has long loops or complex α‐helical regions. Proteins 2010. © Published 2009 Wiley‐Liss, Inc.     

Protein β-Sheet Nucleation Is Driven by Local Modular Formation

Despite its central role in the protein folding process, the specific mechanism(s) behind β-sheet formation has yet to be determined. For example, whether the nucleation of β-sheets, often containing strands separated in sequence by many residues, is local or not remains hotly debated. Here, we investigate the initial nucleation step of β-sheet formation by performing an analysis of the smallest β-sheets in a non-redundant dataset on the grounds that the smallest sheets, having undergone little growth after nucleation, will be enriched for nucleating characteristics. We find that the residue propensities are similar for small and large β-sheets as are their interstrand pairing preferences, suggesting that nucleation is not primarily driven by specific residues or interacting pairs. Instead, an examination of the structural environments of the two-stranded sheets shows that virtually all of them are contained in single, compact structural modules, or when multiple modules are present, one or both of the chain termini are involved. We, therefore, find that β-nucleation is a local phenomenon resulting either from sequential or topological proximity. We propose that β-nucleation is a result of two opposite factors; that is, the relative rigidity of an associated folding module that holds two stretches of coil close together in topology coupled with sufficient chain flexibility that enables the stretches of coil to bring their backbones in close proximity. Our findings lend support to the hydrophobic zipper model of protein folding (Dill, K. A., Fiebig, K. M., and Chan, H. S. (1993) Proc. Natl. Acad. Sci. U.S.A. 90, 1942–1946). Implications for protein folding are discussed.     

Determination of the secondary structural elements of chicken liver fatty acid binding protein by two‐dimensional homonuclear NMR

A conformational study in solution of the fatty acid binding protein from chicken liver is presented. The nearly complete sequence‐specific ¹H resonance assignment was achieved from homonuclear two‐dimensional nmr experiments using a sample of native protein. The principal elements of secondary structure were identified: 10 antiparallel β‐strands and one helical segment followed by a turn comprising 5 residues. These elements correspond closely with those of the crystal structure of the related protein, and two new secondary structural features obtained from the nmr data are the β‐sheet conformation between the first and the last β‐strand in the protein sequence, as well as a helical loop at the N‐terminus of the polypeptide chain. © 1999 John Wiley & Sons, Inc. Biopoly 50: 1–11, 1999     

Rotameric preferences of a protein spin label at edge‐strand β‐sheet sites

Protein spin labeling to yield the nitroxide‐based R1 side chain is a powerful method to measure protein dynamics and structure by electron spin resonance. However, R1 measurements are complicated by the flexibility of the side chain. While analysis approaches for solvent‐exposed α‐helical environment have been developed to partially account for flexibility, similar work in β‐sheets is lacking. The goal of this study is to provide the first essential steps for understanding the conformational preferences of R1 within edge β‐strands using X‐ray crystallography and double electron electron resonance (DEER) distance measurements. Crystal structures yielded seven rotamers for a non‐hydrogen‐bonded site and three rotamers for a hydrogen‐bonded site. The observed rotamers indicate contextual differences in R1 conformational preferences compared to other solvent‐exposed environments. For the DEER measurements, each strand site was paired with the same α‐helical site elsewhere on the protein. The most probable distance observed by DEER is rationalized based on the rotamers observed in the crystal structure. Additionally, the appropriateness of common molecular modeling methods that account for R1 conformational preferences are assessed for the β‐sheet environment. These results show that interpretation of R1 behavior in β‐sheets is difficult and indicate further development is needed for these computational methods to correctly relate DEER distances to protein structure at edge β‐strand sites.     

PackHelix: a tool for helix-sheet packing during protein structure prediction

The three‐dimensional structure of a protein is organized around the packing of its secondary structure elements. Predicting the topology and constructing the geometry of structural motifs involving α‐helices and/or β‐strands are therefore key steps for accurate prediction of protein structure. While many efforts have focused on how to pack helices and on how to sample exhaustively the topologies and geometries of multiple strands forming a β‐sheet in a protein, there has been little progress on generating native‐like packings of helices on sheets. We describe a method that can generate the packing of multiple helices on a given β‐sheet for αβα sandwich type protein folds. This method mines the results of a statistical analysis of the conformations of αβ₂ motifs in protein structures to provide input values for the geometric attributes of the packing of a helix on a sheet. It then proceeds with a geometric builder that generates multiple arrangements of the helices on the sheet of interest by sampling through these values and performing consistency checks that guarantee proper loop geometry between the helices and the strands, minimal number of collisions between the helices, and proper formation of a hydrophobic core. The method is implemented as a module of ProteinShop. Our results show that it produces structures that are within 4–6 Å RMSD of the native one, regardless of the number of helices that need to be packed, though this number may increase if the protein has several helices between two consecutive strands in the sequence that pack on the sheet formed by these two strands. Proteins 2011; Published 2011 Wiley‐Liss, Inc.     

Rules for connectivity of secondary structure elements in protein: Two–layer αβ sandwiches

In protein structures, the fold is described according to the spatial arrangement of secondary structure elements (SSEs: α‐helices and β‐strands) and their connectivity. The connectivity or the pattern of links among SSEs is one of the most important factors for understanding the variety of protein folds. In this study, we introduced the connectivity strings that encode the connectivities by using the types, positions, and connections of SSEs, and computationally enumerated all the connectivities of two‐layer αβ sandwiches. The calculated connectivities were compared with those in natural proteins determined using MICAN, a nonsequential structure comparison method. For 2α‐4β, among 23,000 of all connectivities, only 48 were free from irregular connectivities such as loop crossing. Of these, only 20 were found in natural proteins and the superfamilies were biased toward certain types of connectivities. A similar disproportional distribution was confirmed for most of other spatial arrangements of SSEs in the two‐layer αβ sandwiches. We found two connectivity rules that explain the bias well: the abundances of interlayer connecting loops that bridge SSEs in the distinct layers; and nonlocal β‐strand pairs, two spatially adjacent β‐strands located at discontinuous positions in the amino acid sequence. A two‐dimensional plot of these two properties indicated that the two connectivity rules are not independent, which may be interpreted as a rule for the cooperativity of proteins.     

Structural motifs in which β‐strands are clipped together with the П‐like module

In this study, the structural motifs that can be represented as combinations of small motifs such as β‐hairpins, S‐, and Z‐like β‐sheets and βαβ‐units, and the П‐like module are described and analyzed. The П‐module consists of connected elements of the β‐strand‐loop‐β‐strand type arranged in space so that its overall fold resembles a clip or the Greek letter П. In proteins, the П‐module itself and the structural motifs containing it exhibit unique overall folds and have specific sequence patterns of the key hydrophobic, hydrophilic and glycine residues. All this together enables us to conclude that these structural motifs can fold independently of the remaining part of the molecule and can act as nuclei and/or “ready‐made” building blocks in protein folding.     

Optimization of a β‐sheet‐cap for long loop closure

Protein loops make up a large portion of the secondary structure in nature. But very little is known concerning loop closure dynamics and the effects of loop composition on fold stability. We have designed a small system with stable β‐sheet structures, including features that allow us to probe these questions. Using paired Trp residues that form aromatic clusters on folding, we are able to stabilize two β‐strands connected by varying loop lengths and composition (an example sequence: R W ITVTI – loop – KKIRV W E). Using NMR and CD, both fold stability and folding dynamics can be investigated for these systems. With the 16 residue loop peptide (sequence: R W ITVTI‐(GGGGKK)₂GGGG‐KKIRV W E) remaining folded (ΔG_U = 1.6 kJ/mol at 295K). To increase stability and extend the series to longer loops, we added an additional Trp/Trp pair in the loop flanking position. With this addition to the strands, the 16 residue loop (sequence: R W ITVRI W ‐(GGGGKK)₂GGGG‐ W KTIRV W E) supports a remarkably stable β‐sheet (ΔG_U = 6.3 kJ/mol at 295 K, T_m = ～55°C). Given the abundance of loops in binding motifs and between secondary structures, these constructs can be powerful tools for peptide chemists to study loop effects; with the Trp/Trp pair providing spectroscopic probes for assessing both stability and dynamics by NMR.     

Molecular mechanism of β-sheet self-organization at water-hydrophobic interfaces

The capacity to form β‐sheet structure and to self‐organize into amyloid aggregates is a property shared by many proteins. Severe neurodegenerative pathologies such as Alzheimer's disease are thought to involve the interaction of amyloidogenic protein oligomers with neuronal membranes. To understand the experimentally observed catalysis of amyloid formation by lipid membranes and other water‐hydrophobic interfaces, we examine the physico‐chemical basis of peptide adsorption and aggregation in a model membrane using atomistic molecular simulations. Blocked octapeptides with simple, repetitive sequences, (Gly‐Ala)₄, and (Gly‐Val)₄, are used as models of β‐sheet‐forming polypeptide chains found in the core of amyloid fibrils. In the presence of an n‐octane phase mimicking the core of lipid membranes, the peptides spontaneously partition at the octane‐water interface. The adsorption of nonpolar sidechains displaces the peptides' conformational equilibrium from a heterogeneous ensemble characterized by a high degree of structural disorder toward a more ordered ensemble favoring β‐hairpins and elongated β‐strands. At the interface, peptides spontaneously aggregate and rapidly evolve β‐sheet structure on a 10 to 100 ns time scale, while aqueous aggregates remain amorphous. Catalysis of β‐sheet formation results from the combination of the hydrophobic effect and of reduced conformational entropy of the polypeptide chain. While the former drives interfacial partition and displaces the conformational equilibrium of monomeric peptides, the planar interface further facilitates β‐sheet organization by increasing peptide concentration and reducing the dimensionality of self‐assembly from three to two. These findings suggest a general mechanism for the formation of β‐sheets on the surface of globular proteins and for amyloid self‐organization at hydrophobic interfaces. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Possible Hydrophobic Region in Myelin Basic Protein Consisting of an Orthogonally Packed β-Sheet

Theoretical analysis was carried out to determine how the approximately 20% of beta-structure observed in the 18.5 kilodalton (kDa) myelin basic protein (MBP) could be organized into a relatively stable beta-sheet. The beta-sheet is presumed to consist of the five most hydrophobic segments of polypeptide chain, which have beta-structure potential. These correspond approximately to sequences 15-21, 37-45, 84-92, 106-112, and 148-154 (rabbit MBP sequence numbering) and constitute beta-strands a, b, c, d, and e, respectively. A number of constraints are imposed upon the sheet; e.g., it should have the same topology in all MBP forms (21.5, 18.5, 17, and 14 kDa); strand e should lie at the sheet edge; strands b, c, and d should be ordered sequentially; the sheet formed by strands a, b, c, and d should be antiparallel; a maximum of the nonpolar surface area should be removed from the aqueous milieu; and charged side chains should be solvent-accessible. On the basis of these constraints it is possible to propose six orthogonally packed beta-sheets having different topologies. If strand e is restricted to an antiparallel alignment, the number of different sheets is reduced to four. Each of these sheets can form a relatively compact hydrophobic globular region. Two of the strands (a and e) can undergo transitions to alpha-helix without disrupting the structure of the remaining sheet bcd or producing major topologic rearrangements of the polypeptide chain.     

Structural properties of amyloid β(1‐40) dimer explored by replica exchange molecular dynamics simulations

Replica exchange molecular dynamics simulations (300 ns) were used to study the dimerization of amyloid β(1‐40) (Aβ(1‐40)) polypeptide. Configurational entropy calculations revealed that at physiological temperature (310 K, 37°C) dynamic dimers are formed by randomly docked monomers. Free energy of binding of the two chains to each other was ?93.56 ± 6.341 kJ mol^?1. Prevalence of random coil conformations was found for both chains with the exceptions of increased β‐sheet content from residues 16‐21 and 29‐32 of chain A and residues 15‐21 and 30‐33 of chain B with β‐turn/β‐bend conformations in both chains from residues 1‐16, 21‐29 of chain A, 1‐16, and 21‐29 of chain B. There is a mixed β‐turn/β‐sheet region from residues 33‐38 of both chains. Analysis of intra‐ and interchain residue distances shows that, although the individual chains are highly flexible, the dimer system stays in a loosely packed antiparallel β‐sheet configuration with contacts between residues 17‐21 of chain A with residues 17‐21 and 31‐36 of chain B as well as residues 31‐36 of chain A with residues 17‐21 and 31‐36 of chain B. Based on dihedral principal component analysis, the antiparallel β‐sheet‐loop‐β‐sheet conformational motif is favored for many low energy sampled conformations. Our results show that Aβ(1‐40) can form dynamic dimers in aqueous solution that have significant conformational flexibility and are stabilized by collapse of the central and C‐terminal hydrophobic cores with the expected β‐sheet‐loop‐β‐sheet conformational motif. Proteins 2017; 85:1024–1045. © 2017 Wiley Periodicals, Inc.     

Analyses of the general rule on residue pair frequencies in local amino acid sequences of soluble,ordered proteins

The amino acid sequences of soluble, ordered proteins with stable structures have evolved due to biological and physical requirements, thus distinguishing them from random sequences. Previous analyses have focused on extracting the features that frequently appear in protein substructures, such as α‐helix and β‐sheet, but the universal features of protein sequences have not been addressed. To clarify the differences between native protein sequences and random sequences, we analyzed 7368 soluble, ordered protein sequences, by inspecting the observed and expected occurrences of 400 amino acid pairs in local proximity, up to 10 residues along the sequence in comparison with their expected occurrence in random sequence. We found the trend that the hydrophobic residue pairs and the polar residue pairs are significantly decreased, whereas the pairs between a hydrophobic residue and a polar residue are increased. This trend was universally observed regardless of the secondary structure content but was not observed in protein sequences that include intrinsically disordered regions, indicating that it can be a general rule of protein foldability. The possible benefits of this rule are discussed from the viewpoints of protein aggregation and disorder, which are both caused by low‐complexity regions of hydrophobic or polar residues.