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.     

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. Proteins 2015; 83:2147–2161. © 2015 Wiley Periodicals, Inc.     

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.     

An amino acid code to define a protein's tertiary packing surface

One difficult aspect of the protein‐folding problem is characterizing the nonspecific interactions that define packing in protein tertiary structure. To better understand tertiary structure, this work extends the knob‐socket model by classifying the interactions of a single knob residue packed into a set of contiguous sockets, or a pocket made up of 4 or more residues. The knob‐socket construct allows for a symbolic two‐dimensional mapping of pockets. The two‐dimensional mapping of pockets provides a simple method to investigate the variety of pocket shapes to understand the geometry of protein tertiary surfaces. The diversity of pocket geometries can be organized into groups of pockets that share a common core, which suggests that some interactions in pockets are ancillary to packing. Further analysis of pocket geometries displays a preferred configuration that is right‐handed in α‐helices and left‐handed in β‐sheets. The amino acid composition of pockets illustrates the importance of nonpolar amino acids in packing as well as position specificity. As expected, all pocket shapes prefer to pack with hydrophobic knobs; however, knobs are not selective for the pockets they pack. Investigating side‐chain rotamer preferences for certain pocket shapes uncovers no strong correlations. These findings allow a simple vocabulary based on knobs and sockets to describe protein tertiary packing that supports improved analysis, design, and prediction of protein structure. Proteins 2016; 84:201–216. © 2015 Wiley Periodicals, Inc.     

The crystal structure of a TIR domain from Arabidopsis thaliana reveals a conserved helical region unique to plants

Plants use a highly evolved immune system to exhibit defense response against microbial infections. The plant TIR domain, together with the nucleotide‐binding (NB) domain and/or a LRR region, forms a type of molecule, named resistance (R) proteins, that interact with microbial effector proteins and elicit hypersensitive responses against infection. Here, we report the first crystal structure of a plant TIR domain from Arabidopsis thaliana (AtTIR) solved at a resolution of 2.0 Å. The structure consists of five β‐strands forming a parallel β‐sheet at the core of the protein. The β‐strands are connected by a series of α‐helices and the overall fold mimics closely that of other mammalian and bacterial TIR domains. However, the region of the αD‐helix reveals significant differences when compared with other TIR structures, especially the αD3‐helix that corresponds to an insertion only present in plant TIR domains. Available mutagenesis data suggest that several conserved and exposed residues in this region are involved in the plant TIR signaling function.     

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     

Structural trees for protein superfamilies

Structural trees for large protein superfamilies, such as β proteins with the aligned β sheet packing, β proteins with the orthogonal packing of α helices, two-layer and three-layer α/β proteins, have been constructed. The structural motifs having unique overall folds and a unique handedness are taken as root structures of the trees. The larger protein structures of each superfamily are obtained by a stepwise addition of α helices and/or β strands to the corresponding root motif, taking into account a restricted set of rules inferred from known principles of the protein structure. Among these rules, prohibition of crossing connections, attention to handedness and compactness, and a requirement for α helices to be packed in α-helical layers and β strands in β layers are the most important. Proteins and domains whose structures can be obtained by stepwise addition of α helices and/or β strands to the same root motif can be grouped into one structural class or a superfamily. Proteins and domains found within branches of a structural tree can be grouped into subclasses or subfamilies. Levels of structural similarity between different proteins can easily be observed by visual inspection. Within one branch, protein structures having a higher position in the tree include the structures located lower. Proteins and domains of different branches have the structure located in the branching point as the common fold. Proteins 28:241–260, 1997. © 1997 Wiley-Liss Inc.     

Solution structures and backbone dynamics of the ribosomal protein S6 and its permutant P54‐55

The ribosomal protein S6 from Thermus thermophilus has served as a model system for the study of protein folding, especially for understanding the effects of circular permutations of secondary structure elements. This study presents the structure of a permutant protein, the 96‐residue P^54‐55, and the structure of its 101‐residue parent protein S6^wt in solution. The data also characterizes the effects of circular permutation on the backbone dynamics of S6. Consistent with crystallographic data on S6^wt, the overall solution structures of both P^54‐55 and S6^wt show a β‐sheet of four antiparallel β‐strands with two α‐helices packed on one side of the sheet. In clear contrast to the crystal data, however, the solution structure of S6^wt reveals a disordered loop in the region between β‐strands 2 and 3 (Leu43‐Phe60) instead of a well‐ordered stretch and associated hydrophobic mini‐core observed in the crystal structure. Moreover, the data for P^54‐55 show that the joined wild‐type N‐ and C‐terminals form a dynamically robust stretch with a hairpin structure that complies with the in silico design. Taken together, the results explain why the loop region of the S6^wt structure is relatively insensitive to mutational perturbations, and why P^54‐55 is more stable than S6^wt: the permutant incision at Lys54‐Asp55 is energetically neutral by being located in an already disordered loop whereas the new hairpin between the wild‐type N‐ and C‐termini is stabilizing.     

Geometrical principles of homomeric β‐barrels and β‐helices: Application to modeling amyloid protofilaments

Examples of homomeric β‐helices and β‐barrels have recently emerged. Here we generalize the theory for the shear number in β‐barrels to encompass β‐helices and homomeric structures. We introduce the concept of the “β‐strip,” the set of parallel or antiparallel neighboring strands, from which the whole helix can be generated giving it n‐fold rotational symmetry. In this context, the shear number is interpreted as the sum around the helix of the fixed register shift between neighboring identical β‐strips. Using this approach, we have derived relationships between helical width, pitch, angle between strand direction and helical axis, mass per length, register shift, and number of strands. The validity and unifying power of the method is demonstrated with known structures including α‐hemolysin, T4 phage spike, cylindrin, and the HET‐s(218‐289) prion. From reported dimensions measured by X‐ray fiber diffraction on amyloid fibrils, the relationships can be used to predict the register shift and the number of strands within amyloid protofilaments. This was used to construct models of transthyretin and Alzheimer β(40) amyloid protofilaments that comprise a single strip of in‐register β‐strands folded into a “β‐strip helix.” Results suggest both stabilization of an individual β‐strip helix and growth by addition of further β‐strip helices can involve the same pair of sequence segments associating with β‐sheet hydrogen bonding at the same register shift. This process would be aided by a repeat sequence. Hence, understanding how the register shift (as the distance between repeat sequences) relates to helical dimensions will be useful for nanotube design.     

Discovery of a significant,nontopological preference for antiparallel alignment of helices with parallel regions in sheets

To help elucidate the role of secondary structure packing preferences in protein folding, here we present an analysis of the packing geometry observed between alpha-helices and between alpha-helices and beta-sheets in 1316 diverse, nonredundant protein structures. Finite-length vectors were fit to the alpha-carbon atoms in each of the helices and strands, and the packing angle between the vectors, Omega, was determined at the closest point of approach within each helix-helix or helix-sheet pair. Helix-sheet interactions were found in 391 of the proteins, and the distributions of Omega values were calculated for all the helix-sheet and helix-helix interactions. The packing angle preferences for helix-helix interactions are similar to those previously observed. However, analysis of helix-strand packing preferences uncovered a remarkable tendency for helices to align antiparallel to parallel regions of beta-sheets, independent of the topological constraints or prevalence of beta-alpha-beta motifs in the proteins. This packing angle preference is significantly diminished in helix interactions involving mixed and antiparallel beta-sheets, suggesting a role for helix-sheet dipole alignment in guiding supersecondary structure formation in protein folding. This knowledge of preferred packing angles can be used to guide the engineering of stable protein modules.     

Crystal structure of a tripeptide containing aminocyclododecane carboxylic acid: a supramolecular twisted parallel β‐sheet in crystals

The crystal structure of a tripeptide Boc‐Leu‐Val‐Ac₁₂c‐OMe ( 1 ) is determined, which incorporates a bulky 1‐aminocyclododecane‐1‐carboxylic acid (Ac₁₂c) side chain. The peptide adopts a semi‐extended backbone conformation for Leu and Val residues, while the backbone torsion angles of the C^α,α‐dialkylated residue Ac₁₂c are in the helical region of the Ramachandran map. The molecular packing of 1 revealed a unique supramolecular twisted parallel β‐sheet coiling into a helical architecture in crystals, with the bulky hydrophobic Ac₁₂c side chains projecting outward the helical column. This arrangement resembles the packing of peptide helices in crystal structures. Although short oligopeptides often assemble as parallel or anti‐parallel β‐sheet in crystals, twisted or helical β‐sheet formation has been observed in a few examples of dipeptide crystal structures. Peptide 1 presents the first example of a tripeptide showing twisted β‐sheet assembly in crystals. Copyright © 2016 European Peptide Society and John Wiley & Sons, Ltd.     

The ensemble folding kinetics of the FBP28 WW domain revealed by an all-atom Monte Carlo simulation in a knowledge-based potential

In this work, we apply a detailed all‐atom model with a transferable knowledge‐based potential to study the folding kinetics of Formin‐Binding protein, FBP28, which is a canonical three‐stranded β‐sheet WW domain. Replica exchange Monte Carlo simulations starting from random coils find native‐like (Cα RMSD of 2.68 Å) lowest energy structure. We also study the folding kinetics of FBP28 WW domain by performing a large number of ab initio Monte Carlo folding simulations. Using these trajectories, we examine the order of formation of two β‐hairpins, the folding mechanism of each individual β‐hairpin, and transition state ensemble (TSE) of FBP28 WW domain and compare our results with experimental data and previous computational studies. To obtain detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Further, a rigorous P_fold analysis is used to obtain representative samples of the TSEs showing good quantitative agreement between experimental and simulated Φ values. Our analysis shows that the turn structure between first and second β strands is a partially stable structural motif that gets formed before entering the TSE in FBP28 WW domain and there exist two major pathways for the folding of FBP28 WW domain, which differ in the order and mechanism of hairpin formation. Proteins 2011. © 2011 Wiley‐Liss, Inc.     

The presence of non‐native helical structure in the unfolding of a beta‐sheet protein MPT63

MPT63, a major secreted protein from Mycobacterium tuberculosis, has been shown to have immunogenic properties and has been implicated in virulence. MPT63 is a β‐sandwich protein containing 11 β strands and a very short stretch of 3₁₀ helix. The detailed experimental and computational study reported here investigates the equilibrium unfolding transition of MPT63. It is shown that in spite of being a complete β‐sheet protein, MPT63 has a strong propensity toward helix structures in its early intermediates. Far UV‐CD and FTIR spectra clearly suggest that the low‐pH intermediate of MTP63 has enhanced helical content, while fluorescence correlation spectroscopy suggests a significant contraction. Molecular dynamics simulation complements the experimental results indicating that the unfolded state of MPT63 traverses through intermediate forms with increased helical characteristics. It is found that this early intermediate contains exposed hydrophobic surface, and is aggregation prone. Although MPT63 is a complete β‐sheet protein in its native form, the present findings suggest that the secondary structure preferences of the local interactions in early folding pathway may not always follow the native conformation. Furthermore, the Gly25Ala mutant supports the proposed hypothesis by increasing the non‐native helical propensity of the protein structure.     

Folding of Top7 in unbiased all‐atom Monte Carlo simulations

For computational studies of protein folding, proteins with both helical and β‐sheet secondary structure elements are very challenging, as they expose subtle biases of the physical models. Here, we present reproducible folding of a 92 residue α/β protein (residues 3–94 of Top7, PDB ID: 1QYS) in computer simulations starting from random initial conformations using a transferable physical model which has been previously shown to describe the folding and thermodynamic properties of about 20 other smaller proteins of different folds. Top7 is a de novo designed protein with two α‐helices and a five stranded β‐sheet. Experimentally, it is known to be unusually stable for its size, and its folding transition distinctly deviates from the two‐state behavior commonly seen in natural single domain proteins. In our all‐atom implicit solvent parallel tempering Monte Carlo simulations, Top7 shows a rapid transition to a group of states with high native‐like secondary structure, and a much slower subsequent transition to the native state with a root mean square deviation of about 3.5 Å from the experimentally determined structure. Consistent with experiments, we find Top7 to be thermally extremely stable, although the simulations also find a large number of very stable non‐native states with high native‐like secondary structure. Proteins 2013; 81:1446–1456. © 2013 Wiley Periodicals, Inc.     

Plasmid replication initiator RepB forms a hexamer reminiscent of ring helicases and has mobile nuclease domains

RepB initiates plasmid rolling‐circle replication by binding to a triple 11‐bp direct repeat (bind locus) and cleaving the DNA at a specific distant site located in a hairpin loop within the nic locus of the origin. The structure of native full‐length RepB reveals a hexameric ring molecule, where each protomer has two domains. The origin‐binding and catalytic domains show a three‐layer α–β–α sandwich fold. The active site is positioned at one of the faces of the β‐sheet and coordinates a Mn²⁺ ion at short distance from the essential nucleophilic Y99. The oligomerization domains (ODs), each consisting of four α‐helices, together define a compact ring with a central channel, a feature found in ring helicases. The toroidal arrangement of RepB suggests that, similar to ring helicases, it encircles one of the DNA strands during replication to confer processivity to the replisome complex. The catalytic domains appear to be highly mobile with respect to ODs. This mobility may account for the adaptation of the protein to two distinct DNA recognition sites.     

Amyloidogenic sequences in native protein structures

Numerous short peptides have been shown to form β‐sheet amyloid aggregates in vitro. Proteins that contain such sequences are likely to be problematic for a cell, due to their potential to aggregate into toxic structures. We investigated the structures of 30 proteins containing 45 sequences known to form amyloid, to see how the proteins cope with the presence of these potentially toxic sequences, studying secondary structure, hydrogen‐bonding, solvent accessible surface area and hydrophobicity. We identified two mechanisms by which proteins avoid aggregation: Firstly, amyloidogenic sequences are often found within helices, despite their inherent preference to form β structure. Helices may offer a selective advantage, since in order to form amyloid the sequence will presumably have to first unfold and then refold into a β structure. Secondly, amyloidogenic sequences that are found in β structure are usually buried within the protein. Surface exposed amyloidogenic sequences are not tolerated in strands, presumably because they lead to protein aggregation via assembly of the amyloidogenic regions. The use of α‐helices, where amyloidogenic sequences are forced into helix, despite their intrinsic preference for β structure, is thus a widespread mechanism to avoid protein aggregation.     

DNA self-fitting: the double helix directs the geometry of its supramolecular assembly.

Groove-backbone interaction is a natural and biologically relevant mechanism for the specific assembly of B-DNA double helices. Crystal engineering and crystal packing analysis of oligonucleotides of different sizes and sequences reveal that the sequence-dependent self-fitting of B-DNA helices is a dominant constraint for their ordered assembly. It can override the other intermolecular interactions and impose the overall geometry of the packing. Analysis of experimental examples of architectural motifs formed by the geometric combination of self-fitted DNA segments leads to general rules for DNA assembly. Like a directing piece for a supramolecular 'construction set', the double helix imposes a limited number of geometric solutions. These basic architectural constraints could direct, in a codified manner, the formation of higher-order structures. DNA architectural motifs exhibit new structural and electrostatic properties which could have some implications for their molecular recognition by proteins acting on DNA.     

Re‐engineering a β‐lactamase using prototype peptides from a library of local structural motifs

B. licheniformis exo‐small β‐lactamase (ESBL) has a complex architecture with twelve α helices and a five‐stranded beta sheet. We replaced, separately or simultaneously, three of the ESBL α helices with prototype amphiphatic helices from a catalog of secondary structure elements. Although the substitutes bear no sequence similarity to the originals and pertain to unrelated protein families, all the engineered ESBL variants were found able to fold in native like structures with in vitro and in vivo enzymic activity. The triple substituted variant resembles a primitive protein, with folding defects such as a strong tendency to oligomerization and very low stability; however it mimics a non homologous recombinant abandoning the family sequence space while preserving fold. The results test protein folding and evolution theories.     

A polymetamorphic protein

Arc repressor is a homodimeric protein with a ribbon‐helix–helix fold. A single polar‐to‐hydrophobic substitution (N11L) at a solvent‐exposed position leads to population of an alternate dimeric fold in which 3₁₀ helices replace a β‐sheet. Here we find that the variant Q9V/N11L/R13V (S‐VLV), with two additional polar‐to‐hydrophobic surface mutations in the same β‐sheet, forms a highly stable, reversibly folded octamer with approximately half the?α‐helical content of wild‐type Arc. At low protein concentration and low ionic strength, S‐VLV also populates both dimeric topologies previously observed for N11L, as judged by NMR chemical shift comparisons. Thus, accumulation of simple hydrophobic mutations in Arc progressively reduces fold specificity, leading first to a sequence with two folds and then to a manifold bridge sequence with at least three different topologies. Residues 9–14 of S‐VLV form a highly hydrophobic stretch that is predicted to be amyloidogenic, but we do not observe aggregates of higher order than octamer. Increases in sequence hydrophobicity can promote amyloid aggregation but also exert broader and more complex effects on fold specificity. Altered native folds, changes in fold coupled to oligomerization, toxic pre‐amyloid oligomers, and amyloid fibrils may represent a near continuum of accessible alternatives in protein structure space.