Thermodynamic model of secondary structure for α-helical peptides and proteins

A thermodynamic model describing formation of α-helices by peptides and proteins in the absence of specific tertiary interactions has been developed. The model combines free energy terms defining α-helix stability in aqueous solution and terms describing immersion of every helix or fragment of coil into a micelle or a nonpolar droplet created by the rest of protein to calculate averaged or lowest energy partitioning of the peptide chain into helical and coil fragments. The α-helix energy in water was calculated with parameters derived from peptide substitution and protein engineering data and using estimates of nonpolar contact areas between side chains. The energy of nonspecific hydrophobic interactions was estimated considering each α-helix or fragment of coil as freely floating in the spherical micelle or droplet, and using water/cyclohexane (for micelles) or adjustable (for proteins) side-chain transfer energies. The model was verified for 96 and 36 peptides studied by ¹H-nmr spectroscopy in aqueous solution and in the presence of micelles, respectively ([set I] and [set 2]) and for 30 mostly α-helical globular proteins ([set 3]). For peptides, the experimental helix locations were identified from the published medium-range nuclear Overhauser effects detected by ¹H-nmr spectroscopy. For sets 1, 2, and 3, respectively, 93, 100, and 97% of helices were identified with average errors in calculation of helix boundaries of 1.3, 2.0, and 4.1 residues per helix and an average percentage of correctly calculated helix—coil states of 93, 89, and 81%, respectively. Analysis of adjustable parameters of the model (the entropy and enthalpy of the helix—coil transition, the transfer energy of the helix backbone, and parameters of the bound coil), determined by minimization of the average helix boundary deviation for each set of peptides or proteins, demonstrates that, unlike micelles, the interior of the effective protein droplet has solubility characteristics different from that for cyclohexane, does not bind fragments of coil, and lacks interfacial area. © 1997 John Wiley & Sons, Inc. Biopoly 42: 239–269, 1997     

Structural classification of αββ and ββα supersecondary structure units in proteins

We present a fully automatic structural classification of supersecondary structure units, consisting of two hydrogen-bonded β strands, preceded or followed by an α helix. The classification is performed on the spatial arrangement of the secondary structure elements, irrespective of the length and conformation of the intervening loops. The similarity of the arrangements is estimated by a structure alignment procedure that uses as similarity measure the root mean square deviation of superimposed backbone atoms. Applied to a set of 141 well-resolved nonhomologous protein structures, the classification yields 11 families of recurrent arrangements. In addition, fragments that are structurally intermediate between the families are found; they reveal the continuity of the classification. The analysis of the families shows that the α helix and β hairpin axes can adopt virtually all relative orientations, with, however, some preferable orientations; moreover, according to the orientation, preferences in the left/right handedness of the α–β connection are observed. These preferences can be explained by favorable side by side packing of the α helix and the β hairpin, local interactions in the region of the α–β connection or stabilizing environments in the parent protein. Furthermore, fold recognition procedures and structure prediction algorithms coupled to database-derived potentials suggest that the preferable nature of these arrangements does not imply their intrinsic stability. They usually accommodate a large number of sequences, of which only a subset is predicted to stabilize the motif. The motifs predicted as stable could correspond to nuclei formed at the very beginning of the folding process. Proteins 30:193–212, 1998. © 1998 Wiley-Liss, Inc.     

Intrinsic secondary structure propensities of the amino acids,using statistical ϕ–ψ matrices: Comparison with experimental scales

Today there are several different experimental scales for the intrinsic α-helix as well as β-strand, propensities of the 20 amino acids obtained from the thermodynamic analysis of various model systems. These scales do not compare well with those extracted from statistical analysis of three-dimensional structure databases. Possible explanations for this could be the limited size of the databases used, the definitions of intrinsic propensities, or the theoretical approach. Here we report a statistical determination of α-helix and β-strand propensities derived from the analysis of a database of 279 three-dimensional structures. Contrary to what has been generally done, we have considered a particular residue as in α-helix or β-strand conformation by looking only at its dihedral angles (?–ψ matrices). Neither the identity nor the conformation of the surrounding residues in the amino acid sequence has been taken into consideration. Pseudoenergy empirical scales have been calculated from the statistical propensities. These scales agree very well with the experimental ones in relative and absolute terms. Moreover, its correlation with the average of the experimental scales for α-helix or β-strand is as good as the correlations of the individual experimental scales with the average. These results show that by using a large enough database and a proper definition for the secondary structure propensities, it is possible to obtain a scale as good as any of experimental origin. Interestingly the ?–ψ analysis of the Ramachandran plot suggests that the amino acids could have different β-strand propensities in different subregions of the β-strand area. © 1994 Wiley-Liss, Inc.     

Sequence and conformational preferences at termini of α‐helices in membrane proteins: Role of the helix environment

α‐helices are amongst the most common secondary structural elements seen in membrane proteins and are packed in the form of helix bundles. These α‐helices encounter varying external environments (hydrophobic, hydrophilic) that may influence the sequence preferences at their N and C‐termini. The role of the external environment in stabilization of the helix termini in membrane proteins is still unknown. Here we analyze α‐helices in a high‐resolution dataset of integral α‐helical membrane proteins and establish that their sequence and conformational preferences differ from those in globular proteins. We specifically examine these preferences at the N and C‐termini in helices initiating/terminating inside the membrane core as well as in linkers connecting these transmembrane helices. We find that the sequence preferences and structural motifs at capping (Ncap and Ccap) and near‐helical (N' and C') positions are influenced by a combination of features including the membrane environment and the innate helix initiation and termination property of residues forming structural motifs. We also find that a large number of helix termini which do not form any particular capping motif are stabilized by formation of hydrogen bonds and hydrophobic interactions contributed from the neighboring helices in the membrane protein. We further validate the sequence preferences obtained from our analysis with data from an ultradeep sequencing study that identifies evolutionarily conserved amino acids in the rat neurotensin receptor. The results from our analysis provide insights for the secondary structure prediction, modeling and design of membrane proteins. Proteins 2014; 82:3420–3436. © 2014 Wiley Periodicals, Inc.     

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, P_II, α, α_L, 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.     

Helix propensities of the amino acids measured in alanine-based peptides without helix-stabilizing side-chain interactions.

Helix propensities of the amino acids have been measured in alanine-based peptides in the absence of helix-stabilizing side-chain interactions. Fifty-eight peptides have been studied. A modified form of the Lifson-Roig theory for the helix-coil transition, which includes helix capping (Doig AJ, Chakrabartty A, Klingler TM, Baldwin RL, 1994, Biochemistry 33:3396-3403), was used to analyze the results. Substitutions were made at various positions of homologous helical peptides. Helix-capping interactions were found to contribute to helix stability, even when the substitution site was not at the end of the peptide. Analysis of our data with the original Lifson-Roig theory, which neglects capping effects, does not produce as good a fit to the experimental data as does analysis with the modified Lifson-Roig theory. At 0 degrees C, Ala is a strong helix former, Leu and Arg are helix-indifferent, and all other amino acids are helix breakers of varying severity. Because Ala has a small side chain that cannot interact significantly with other side chains, helix formation by Ala is stabilized predominantly by the backbone ("peptide H-bonds"). The implication for protein folding is that formation of peptide H-bonds can largely offset the unfavorable entropy change caused by fixing the peptide backbone. The helix propensities of most amino acids oppose folding; consequently, the majority of isolated helices derived from proteins are unstable, unless specific side-chain interactions stabilize them.     

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.     

Conformational analysis of peptides corresponding to all the secondary structure elements of protein L B1 domain: secondary structure propensities are not conserved in proteins with the same fold.

The solution conformation of three peptides corresponding to the two beta-hairpins and the alpha-helix of the protein L B1 domain have been analyzed by circular dichroism (CD) and nuclear magnetic resonance spectroscopy (NMR). In aqueous solution, the three peptides show low populations of native and non-native locally folded structures, but no well-defined hairpin or helix structures are formed. In 30% aqueous trifluoroethanol (TFE), the peptide corresponding to the alpha-helix adopts a high populated helical conformation three residues longer than in the protein. The hairpin peptides aggregate in TFE, and no significant conformational change occurs in the NMR observable fraction of molecules. These results indicate that the helical peptide has a significant intrinsic tendency to adopt its native structure and that the hairpin sequences seem to be selected as non-helical. This suggests that these sequences favor the structure finally attained in the protein, but the contribution of the local interactions alone is not enough to drive the formation of a detectable population of native secondary structures. This pattern of secondary structure tendencies is different to those observed in two structurally related proteins: ubiquitin and the protein G B1 domain. The only common feature is a certain propensity of the helical segments to form the native structure. These results indicate that for a protein to fold, there is no need for large native-like secondary structure propensities, although a minimum tendency to avoid non-native structures and to favor native ones could be required.     

A hierarchical order within protein structures underlies large separations between strands in β‐sheets

Protein β‐sheets often involve nonlocal interactions between parts of the polypeptide chain that are separated by hundreds of residues, raising the question of how these nonlocal contacts form. A recent study of the smallest β‐sheets found that their formation was not driven by signals hidden in the primary sequence. Instead, the strands in these sheets were either local in sequence, or, when separated by large sequential distances, the intervening residues were found to fold into compact modules that anchored distant parts of the chain in close spatial proximity. Here, we examine larger β‐sheets to investigate the extensibility of this principle. From an analysis of the β‐sheets in a nonredundant protein dataset, we find that a highly ordered hierarchical relationship exists in the intervening structure between nonlocal β‐strands. This observation is almost universal: virtually all β‐sheets, no matter their complexity, appear to adopt an antiparallel model to manage the nonlocal aspects of their assembly, one where the chain, having left the vicinity of an unfinished β‐sheet, retraces its steps via the same route to complete the initial sheet. Exceptions typically involve unstructured regions at chain termini. Moreover, an analysis of the residues involved in nonlocal crossstrand interactions did not produce any evidence of a signal hidden in the sequence that might direct long‐range interactions. These results build on those reported for the smallest sheets, suggesting that sheet formation is either local in sequence or local in space following prior folding events that anchor disparate parts of the chain in close proximity. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

Protein structure and the sequential structure of mRNA: α-Helix and β-sheet signals at the nucleotide level

A direct comparison of experimentally determined protein structures and their corresponding protein coding mRNA sequences has been performed. We examine whether real world data support the hypothesis that clusters of rare codons correlate with the location of structural units in the resulting protein. The degeneracy of the genetic code allows for a biased selection of codons which may control the translational rate of the ribosome, and may thus in vivo have a catalyzing effect on the folding of the polypeptide chain. A complete search for GenBank nucleotide sequences coding for structural entries in the Brookhaven Protein Data Bank produced 719 protein chains with matching mRNA sequence, amino acid sequence, and secondary structure assignment. By neural network analysis, we found strong signals in mRNA sequence regions surrounding helices and sheets. These signals do not originate from the clustering of rare codons, but from the similarity of codons coding for very abundant amino acid residues at the N- and C-termini of helices and sheets. No correlation between the positioning of rare codons and the location of structural units was found. The mRNA signals were also compared with conserved nucleotide features of 16S-like ribosomal RNA sequences and related to mechanisms for maintaining the correct reading frame by the ribosome. © 1996 Wiley-Liss, Inc.     

Folding type-specific secondary structure propensities of amino acids,derived from α-helical, β-sheet, α/β, and α+β proteins of known structures

Folding type-specific secondary structure propensities of 20 naturally occurring amino acids have been derived from α-helical, β-sheet, α/β, and α+β proteins of known structures. These data show that each residue type of amino acids has intrinsic propensities in different regions of secondary structures for different folding types of proteins. Each of the folding types shows markedly different rank ordering, indicating folding type-specific effects on the secondary structure propensities of amino acids. Rigorous statistical tests have been made to validate the folding type-specific effects. It should be noted that α and β proteins have relatively small α-helices and β-strands forming propensities respectively compared with those of α+β and α/β proteins. This may suggest that, with more complex architectures than α and β proteins, α+β and α/β proteins require larger propensities to distinguish from interacting α-helices and β-strands. Our finding of folding type-specific secondary structure propensities suggests that sequence space accessible to each folding type may have differing features. Differing sequence space features might be constrained by topological requirement for each of the folding types. Almost all strong β-sheet forming residues are hydrophobic in character regardless of folding types, thus suggesting the hydrophobicities of side chains as a key determinant of β-sheet structures. In contrast, conformational entropy of side chains is a major determinant of the helical propensities of amino acids, although other interactions such as hydrophobicities and charged interactions cannot be neglected. These results will be helpful to protein design, class-based secondary structure prediction, and protein folding. © 1998 John Wiley & Sons, Inc. Biopoly 45: 35–49, 1998     

Prediction of β-turns in proteins by 1-4 and 2-3 correlation model

A 1–4 and 2–3 residue-correlation model is proposed to predict the β-turns in proteins. The average rate of correct prediction for the 455 β-turn tetrapeptides and 4018 non-β-turn tetrapeptides in the training data base is 80.1%, and that for the 223 β-turn tetrapeptides and 12562 non-β-turn tetrapeptides in the testing data base is 80.9%. Compared with the rates of correct prediction based on the residue-independent model reported previously, the quality of prediction is significantly improved by the new model, implying that the correlation effect between the 1st and the 4th residues and that between the 2nd and 3rd residues along a tetrapeptide are important for forming a β-turn in a protein during the process of its folding. © 1997 John Wiley & Sons, Inc. Biopoly 41: 673–702, 1997     

Folding propensities of peptide fragments of myoglobin.

Myoglobin has been studied extensively as a paradigm for protein folding. As part of an ongoing study of potential folding initiation sites in myoglobin, we have synthetized a series of peptides covering the entire sequence of sperm whale myoglobin. We report here on the conformation preferences of a series of peptides that cover the region from the A helix to the FG turn. Structural propensities were determined using circular dichroism and nuclear magnetic resonance spectroscopy in aqueous solution, trifluoroethanol, and methanol. Peptides corresponding to helical regions in the native protein, namely the B, C, D, and E helices, populate the alpha region of (phi, psi) space in water solution but show no measurable helix formation except in the presence of trifluoroethanol. The F-helix sequence has a much lower propensity to populate helical conformations even in TFE. Despite several attempts, we were not successful in synthesizing a peptide corresponding to the A-helix region that was soluble in water. A peptide termed the AB domain was constructed spanning the A- and B-helix sequences. The AB domain is not soluble in water, but shows extensive helix formation throughout the peptide when dissolved in methanol, with a break in the helix at a site close to the A-B helix junction in the intact folded myoglobin protein. With the exception of one local preference for a turn conformation stabilized by hydrophobic interactions, the peptides corresponding to turns in the folded protein do not measurably populate beta-turn conformations in water, and the addition of trifluoroethanol does not enhance the formation of either helical or turn structure. In contrast to the series of peptides described here, either studies of peptides from the GH region of myoglobin show a marked tendency to populate helical structures (H), nascent helical structures (G), or turn conformations (GH peptide) in water solution. This region, together with the A-helix and part of the B-helix, has been shown to participate in an early folding intermediate. The complete analysis of conformational properties of isolated myoglobin peptides supports the hypothesis that spontaneous secondary structure formation in local regions of the polypeptide may play an important role in the initiation of protein folding.     

Dissecting α-helices: Position-specific analysis of α-helices in globular proteins

An analysis of the amino acid distributions at 15 positions, viz., N“, N′, Ncap, N1, N2, N3, N4, Mid, C4, C3, C2, C1, Ccap, C′, and C” in 1,131 α-helices reveals that each position has its own unique characteristics. In general, natural helix sequences optimize by identifying the residues to be avoided at a given position and minimizing the occurrence of these avoided residues rather than by maximizing the preferred residues at various positions. Ncap is most selective in its choice of residues, with six amino acids (S, D, T, N, G, and P) being preferred at this position and another 11 (V, I, F, A, K, L, Y, R, E, M, and Q) being strongly avoided. Ser, Asp, and Thr are all more preferred at Ncap position than Asn, whose role at helix N-terminus has been highlighted by earlier analyses. Furthermore, Asn is also found to be almost equally preferred at helix C-terminus and a novel structural motif is identified, involving a hydrogen bond formed by N^δ2 of Asn at Ccap or C1 position, with the backbone carbonyl oxygen four residues inside the helix. His also forms a similar motif at the C-terminus. Pro is the most avoided residue in the main body (N4 to C4 positions) and at C-ter-minus, including Ccap of an α-helix. In 1,131 α-helices, no helix contains Pro at C3 or C2 positions. However, Pro is highly favoured at N1 and C′. The doublet X-Pro, with Pro at C′ position and extended backbone conformation for the X residue at Ccap, appears to be a common structural motif for termination of α-helices, in addition to the Schellman motif. Main body of the helix shows a high preference for aliphatic residues Ala, Leu, Val, and Ile, while these are avoided at helix termini. A propensity scale for amino acids to occur in the middle of helices has been obtained. Comparison of this scale with several previously reported scales shows that this scale correlates best with the experimentally determined values. Proteins 31:460–476, 1998. © 1998 Wiley-Liss, Inc.     

Helix propensities of short peptides: molecular dynamics versus bioinformatics

Knowledge-based potential functions for protein structure prediction assume that the frequency of occurrence of a given structure or a contact in the protein database is a measure of its free energy. Here, we put this assumption to test by comparing the results obtained from sequence-structure cluster analysis with those obtained from long all-atom molecular dynamics simulations. Sixty-four eight-residue peptide sequences with varying degrees of similarity to the canonical sequence pattern for amphipathic helix were drawn from known protein structures, regardless of whether they were helical in the protein. Each was simulated using AMBER6.0 for at least 10 ns using explicit waters. The total simulation time was 1176 ns. The resulting trajectories were tested for reproducibility, and the helical content was measured. Natural peptides whose sequences matched the amphipathic helix motif with greater than 50% confidence were significantly more likely to form helix during the course of the simulation than peptides with lower confidence scores. The sequence pattern derived from the simulation data closely resembles the motif pattern derived from the database cluster analysis. The difficulties encountered in sampling conformational space and sequence space simultaneously are discussed.     

A Continuum theory for the prediction of lateral and rotational positioning of α-helices in membrane proteins: Bacteriorhodopsin

We have developed a new method for the prediction of the lateral and the rotational positioning of transmembrane helices, based upon the present status of knowledge about the dominant interaction of the tertiary structure formation. The basic assumption about the interaction is that the interhelix binding is due to the polar interactions and that very short extramembrane loop segments restrict the relative position of the helices. Another assumption is made for the simplification of the prediction that a helix may be regarded as a continuum rod having polar interaction fields around it. The polar interaction field is calculated by a probe helix method, using a copolymer of serine and alanine as probe helices. The lateral position of helices is determined by the strength of the interhelix binding estimated from the polar interaction field together with the length of linking loop segments. The rotational positioning is determined by the polar interaction field, assuming the optimum lateral configuration. The structural change due to the binding of a prosthetic group is calculated, fixing the rotational freedom of a helix that is connected to the prosthetic group. Applying this method to bacteriorhodopsin, the optimum lateral and rotational positioning of transmembrane helices that are very similar to the experimental configuration was obtained. This method was implemented by a software system, which was developed for this work, and automatic calculation became possible for membrane proteins comprised of several transmembrane helices. © 1995 Wiley-Liss, Inc.     

Anion induced conformational preference of CαNN motif residues in functional proteins

Among different ligand binding motifs, anion binding C^αNN motif consisting of peptide backbone atoms of three consecutive residues are observed to be important for recognition of free anions, like sulphate or biphosphate and participate in different key functions. Here we study the interaction of sulphate and biphosphate with C^αNN motif present in different proteins. Instead of total protein, a peptide fragment has been studied keeping C^αNN motif flanked in between other residues. We use classical force field based molecular dynamics simulations to understand the stability of this motif. Our data indicate fluctuations in conformational preferences of the motif residues in absence of the anion. The anion gives stability to one of these conformations. However, the anion induced conformational preferences are highly sequence dependent and specific to the type of anion. In particular, the polar residues are more favourable compared to the other residues for recognising the anion.