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 packing code for α-helical structure and protein design

This work demonstrates that all packing in α-helices can be simplified to repetitive patterns of a single motif: the knob-socket. Using the precision of Voronoi Polyhedra/Delauney Tessellations to identify contacts, the knob-socket is a four-residue tetrahedral motif: a knob residue on one α-helix packs into the three-residue socket on another α-helix. The principle of the knob-socket model relates the packing between levels of protein structure: the intra-helical packing arrangements within secondary structure that permit inter-helix tertiary packing interactions. Within an α-helix, the three-residue sockets arrange residues into a uniform packing lattice. Inter-helix packing results from a definable pattern of interdigitated knob-socket motifs between two α-helices. Furthermore, the knob-socket model classifies three types of sockets: (1) free, favoring only intra-helical packing; (2) filled, favoring inter-helical interactions; and (3) non, disfavoring α-helical structure. The amino acid propensities in these three socket classes essentially represent an amino acid code for structure in α-helical packing. Using this code, we used a novel yet straightforward approach for the design of α-helical structure to validate the knob-socket model. Unique sequences for three peptides were created to produce a predicted amount of α-helical structure: mostly helical, some helical, and no helix. These three peptides were synthesized, and helical content was assessed using CD spectroscopy. The measured α-helicity of each peptide was consistent with the expected predictions. These results and analysis demonstrate that the knob-socket motif functions as the basic unit of packing and presents an intuitive tool to decipher the rules governing packing in protein structure.     

Tertiary structural constraints on protein evolutionary diversity: templates, key residues and structure prediction

The pattern of residue substitution in divergently evolving families of globular proteins is highly variable. At each position in a fold there are constraints on the identities of amino acids from both the three-dimensional structure and the function of the protein. To characterize and quantify the structural constraints, we have made a comparative analysis of families of homologous globular proteins. Residues are classified according to amino acid type, secondary structure, accessibility of the sidechain, and existence of hydrogen bonds from sidechain to other sidechains or peptide carbonyl or amide functions. There are distinct patterns of substitution especially where residues are both solvent inaccessible and hydrogen bonded through their sidechains. The patterns of residue substitution can be used to construct templates or to identify 'key' residues if one or more structures are known. Conversely, analysis of conversation and substitution across a large family of aligned sequences in terms of substitution profiles can allow prediction of tertiary environment or indicate a functional role. Similar analyses can be used to test the validity of putative structures if several homologous sequences are available.     

Packing-based difference of structural features between thermophilic and mesophilic proteins

Twenty pairs of thermophilic and mesophilic proteins were compared in terms of residue packing distribution to obtain structural features related to protein thermostability. Based on residue packing concept, structural features of residues such as residue packing distribution, inner/outer position, secondary structure and water solvation were investigated. The statistical tests revealed that higher frequency in well-packed state of residues, lower frequency in exposed state and higher frequency in well-packed state of inner positioned residues, and higher frequency in well-packed state of 3/10 helix residues could be general structural features thermophilic proteins have.     

Environment-specific amino acid substitution tables: tertiary templates and prediction of protein folds.

The local environment of an amino acid in a folded protein determines the acceptability of mutations at that position. In order to characterize and quantify these structural constraints, we have made a comparative analysis of families of homologous proteins. Residues in each structure are classified according to amino acid type, secondary structure, accessibility of the side chain, and existence of hydrogen bonds from the side chains. Analysis of the pattern of observed substitutions as a function of local environment shows that there are distinct patterns, especially for buried polar residues. The substitution data tables are available on diskette with Protein Science. Given the fold of a protein, one is able to predict sequences compatible with the fold (profiles or templates) and potentially to discriminate between a correctly folded and misfolded protein. Conversely, analysis of residue variation across a family of aligned sequences in terms of substitution profiles can allow prediction of secondary structure or tertiary environment.     

Improving prediction of helix–helix packing in membrane proteins using predicted contact numbers as restraints

One of the challenging problems in tertiary structure prediction of helical membrane proteins (HMPs) is the determination of rotation of α‐helices around the helix normal. Incorrect prediction of helix rotations substantially disrupts native residue–residue contacts while inducing only a relatively small effect on the overall fold. We previously developed a method for predicting residue contact numbers (CNs), which measure the local packing density of residues within the protein tertiary structure. In this study, we tested the idea of incorporating predicted CNs as restraints to guide the sampling of helix rotation. For a benchmark set of 15 HMPs with simple to rather complicated folds, the average contact recovery (CR) of best‐sampled models was improved for all targets, the likelihood of sampling models with CR greater than 20% was increased for 13 targets, and the average RMSD100 of best‐sampled models was improved for 12 targets. This study demonstrated that explicit incorporation of CNs as restraints improves the prediction of helix–helix packing. Proteins 2017; 85:1212–1221. © 2017 Wiley Periodicals, Inc.     

Alanine-scanning mutagenesis of the beta-sheet region of phage T4 lysozyme suggests that tertiary context has a dominant effect on beta-sheet formation

In general, alpha-helical conformations in proteins depend in large part on the amino acid residues within the helix and their proximal interactions. For example, an alanine residue has a high propensity to adopt an alpha-helical conformation, whereas that of a glycine residue is low. The sequence preferences for beta-sheet formation are less obvious. To identify the factors that influence beta-sheet conformation, a series of scanning polyalanine mutations were made within the strands and associated turns of the beta-sheet region in T4 lysozyme. For each construct the stability of the folded protein was reduced substantially, consistent with removal of native packing interactions. However, the crystal structures showed that each of the mutants retained the beta-sheet conformation. These results suggest that the structure of the beta-sheet region of T4 lysozyme is maintained to a substantial extent by tertiary interactions with the surrounding parts of the protein. Such tertiary interactions may be important in determining the structures of beta-sheets in general.     

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.     

Small-World Communication of Residues and Significance for Protein Dynamics

It is not merely the position of residues that is critically important for a protein's function and stability, but also their interactions. We illustrate, by using a network construction on a set of 595 nonhomologous proteins, that regular packing is preserved in short-range interactions, but short average path lengths are achieved through some long-range contacts. Thus, lying between the two extremes of regularity and randomness, residues in folded proteins are distributed according to a “small-world” topology. Using this topology, we show that the core residues have the same local packing arrangements irrespective of protein size. Furthermore, we find that the average shortest path lengths are highly correlated with residue fluctuations, providing a link between the spatial arrangement of the residues and protein dynamics.     

Structure of the YibK methyltransferase from Haemophilus influenzae (HI0766): a cofactor bound at a site formed by a knot

Despite the suitability of various lattice geometries for coarse-grained modeling of proteins, the actual packing geometry of residues in folded structures has remained largely unexplored. A strong tendency to assume a regular packing geometry is shown here by optimally reorienting and superimposing clusters of neighboring residues from databank structures examined on a coarse-grained (single-site-per-residue) scale. The orientation function (or order parameter) of the examined coordination clusters with respect to fcc lattice directions is found to be 0.82. The observed geometry, which may be termed an incomplete distorted face-centered cubic (fcc) packing, is apparently favored by the drive to maximize packing density, in a fashion analogous to the way identical spheres pack densely and follow fcc geometry. About 2/3 of all residues obey this packing geometry, while the remainder occupy other context-dependent positions. The preferred coordination directions show relatively small variations over the various amino acid types, consistent with uniform residue viewpoint. Both the extremes of solvent-exposed and completely buried residue neighborhoods approximate the same generic packing, the only difference being in the numbers (and not the orientations) of coordination sites that are occupied (or left void for solvent occupancy). We observe the prevalence of a rather uniform (tight) residue packing density throughout the structure, including even the residues packed near solvent-exposed regions. The observed orientation distribution reveals an underlying, intrinsic orientation lattice for proteins.     

Mechanism of protein folding

The high structural resolution of the main transition states for the formation of native structure for the six small proteins of which Phi-values for a large set of mutants have become available, barstar, barnase, chymotrypsin inhibitor 2, Arc repressor, the src SH3 domain, and a tetrameric p53 domain reveals that for the first 5 of these proteins: (1) Residues that belong to regular secondary structure have a significantly larger average fraction of native structural consolidation than residues in loops; (2) on the other hand, secondary and tertiary structures have built up to the same degree, or at least a high degree, but nonuniformly distributed over the molecule; (3) the most consolidated parts of each protein molecule in the transition state cluster together, and these clusters contain a significantly higher percentage of residues that belong to regular secondary structure than the rest of the molecule. These observations further reconcile the framework model with the nucleation-condensation mechanism for folding: The amazing speed of protein folding can be understood as caused by the catalytic effect of the formation of clusters of residues which have particularly high preferences for the early formation of regular secondary structure in the presence of significant amounts of tertiary structure interactions.     

Effect of spatial coupling of amino acid residues on the possibility of mutational substitution in globular proteins

Amino acid residues can be divided into similar groups by frequencies of interreplacements in the evolutionary pathway and by trends to spatial contacts at the tertiary structures of globular proteins. Each residue was compared to the cluster of spatial surrounding--the totality of residues spacially drawn together. 5210 clusters in 32 unhomologous proteins with established tertiary structure and 6447 clusters formed only by variables amino acid residues were analysed. Spatial contacts among residues were studied depending on the secondary structure and the amount of residues in a cluster. It was assumed that functionally admissible mutations may be defined, first of all, by the degree of neighboring of amino acid residues in the spatial surrounding.     

Voronoi and Voronoi-related tessellations in studies of protein structure and interaction

The three-dimensional structure of a protein can be modeled by a set of polyhedra drawn around its atoms or residues. The tessellation invented by Voronoi in 1908, and other tessellations of space derived from it, provide versatile representations of three-dimensional structures. In recent years, they have been used to investigate a series of issues relating to proteins: atom and residue volumes, packing, folding, interactions and binding.     

Detection of secondary structure elements in proteins by hydrophobic cluster analysis.

Hydrophobic cluster analysis (HCA) is a protein sequence comparison method based on alpha-helical representations of the sequences where the size, shape and orientation of the clusters of hydrophobic residues are primarily compared. The effectiveness of HCA has been suggested to originate from its potential ability to focus on the residues forming the hydrophobic core of globular proteins. We have addressed the robustness of the bidimensional representation used for HCA in its ability to detect the regular secondary structure elements of proteins. Various parameters have been studied such as those governing cluster size and limits, the hydrophobic residues constituting the clusters as well as the potential shift of the cluster positions with respect to the position of the regular secondary structure elements. The following results have been found to support the alpha-helical bidimensional representation used in HCA: (i) there is a positive correlation (clearly above background noise) between the hydrophobic clusters and the regular secondary structure elements in proteins; (ii) the hydrophobic clusters are centred on the regular secondary structure elements; (iii) the pitch of the helical representation which gives the best correspondence is that of an alpha-helix. The correspondence between hydrophobic clusters and regular secondary structure elements suggests a way to implement variable gap penalties during the automatic alignment of protein sequences.     

Fast structure alignment for protein databank searching.

A fast method is described for searching and analyzing the protein structure databank. It uses secondary structure followed by residue matching to compare protein structures and is developed from a previous structural alignment method based on dynamic programming. Linear representations of secondary structures are derived and their features compared to identify equivalent elements in two proteins. The secondary structure alignment then constrains the residue alignment, which compares only residues within aligned secondary structures and with similar buried areas and torsional angles. The initial secondary structure alignment improves accuracy and provides a means of filtering out unrelated proteins before the slower residue alignment stage. It is possible to search or sort the protein structure databank very quickly using just secondary structure comparisons. A search through 720 structures with a probe protein of 10 secondary structures required 1.7 CPU hours on a Sun 4/280. Alternatively, combined secondary structure and residue alignments, with a cutoff on the secondary structure score to remove pairs of unrelated proteins from further analysis, took 10.1 CPU hours. The method was applied in searches on different classes of proteins and to cluster a subset of the databank into structurally related groups. Relationships were consistent with known families of protein structure.     

Identification of amino acids involved in protein structural uniqueness: implication for de novo protein design

Structural uniqueness is characteristic of native proteins and is essential to express their biological functions. The major factors that bring about the uniqueness are specific interactions between hydrophobic residues and their unique packing in the protein core. To find the origin of the uniqueness in their amino acid sequences, we analyzed the distribution of the side chain rotational isomers (rotamers) of hydrophobic amino acids in protein tertiary structures and derived deltaS(contact), the conformational-entropy changes of side chains by residue-residue contacts in each secondary structure. The deltaS(contact) values indicate distinct tendencies of the residue pairs to restrict side chain conformation by inter-residue contacts. Of the hydrophobic residues in alpha-helices, aliphatic residues (Leu, Val, Ile) strongly restrict the side chain conformations of each other. In beta-sheets, Met is most strongly restricted by contact with Ile, whereas Leu, Val and Ile are less affected by other residues in contact than those in alpha-helices. In designed and native protein variants, deltaS(contact) was found to correlate with the folding-unfolding cooperativity. Thus, it can be used as a specificity parameter for designing artificial proteins with a unique structure.     

Contribution of tryptophan residues to the CD spectrum of the extracellular domain of human tissue factor: application in folding studies and prediction of secondary structure.

The contribution to the circular dichroism (CD) spectrum made by each of the four Trp residues in the extracellular domain of human tissue factor, sTF (s designates soluble), was determined from difference CD spectra. The individual Trp CD spectra showed that all four residues contributed to the CD spectrum in almost the entire wavelength region investigated (180-305 nm). The sum of the individual spectra of each Trp residue in the near-UV region was qualitatively identical to the wild-type spectrum, clearly demonstrating that the Trp residues are the major contributors to the spectrum in this wavelength region. Trp CD bands interfere with the peptide bands in the far-UV region, leading to uncertainty in the predictions of the amounts of various types of secondary structure. Accordingly, the best prediction of secondary sTF structure content was achieved using a hypothetical Trp-free CD spectrum obtained after subtraction of all individual Trp spectra from the wild-type spectrum. The mutated Trp residues were also exploited as intrinsic probes to monitor the formation of local native-like tertiary structure by kinetic near-UV CD measurements. The global folding reaction was followed in parallel with a novel functional assay that registered the recovery of cofactor activity, i.e. stimulation of the amidolytic activity of Factor VIIa. From these measurements, it was found that sTF appears to regain FVIIa cofactor activity before the final side-chain packing of the Trp residues. The combined kinetic refolding results suggest that the compact asymmetric environments of the individual Trp residues in sTF are formed simultaneously, leading to the conclusion that the native tertiary structure of the whole protein is formed in a cooperative manner.     

Helix-helix packing and interfacial pairwise interactions of residues in membrane proteins

Helix-helix packing plays a critical role in maintaining the tertiary structures of helical membrane proteins. By examining the overall distribution of voids and pockets in the transmembrane (TM) regions of helical membrane proteins, we found that bacteriorhodopsin and halorhodopsin are the most tightly packed, whereas mechanosensitive channel is the least tightly packed. Large residues F, W, and H have the highest propensity to be in a TM void or a pocket, whereas small residues such as S, G, A, and T are least likely to be found in a void or a pocket. The coordination number for non-bonded interactions for each of the residue types is found to correlate with the size of the residue. To assess specific interhelical interactions between residues, we have developed a new computational method to characterize nearest neighboring atoms that are in physical contact. Using an atom-based probabilistic model, we estimate the membrane helical interfacial pairwise (MHIP) propensity. We found that there are many residue pairs that have high propensity for interhelical interactions, but disulfide bonds are rarely found in the TM regions. The high propensity pairs include residue pairs between an aromatic residue and a basic residue (W-R, W-H, and Y-K). In addition, many residue pairs have high propensity to form interhelical polar-polar atomic contacts, for example, residue pairs between two ionizable residues, between one ionizable residue and one N or Q. Soluble proteins do not share this pattern of diverse polar-polar interhelical interaction. Exploratory analysis by clustering of the MHIP values suggests that residues similar in side-chain branchness, cyclic structures, and size tend to have correlated behavior in participating interhelical interactions. A chi-square test rejects the null hypothesis that membrane protein and soluble protein have the same distribution of interhelical pairwise propensity. This observation may help us to understand the folding mechanism of membrane proteins.