Conformational changes due to vicinal glycosylation: The branched α-l-Rhap(1–2)[β-d-Galp(1–3)]-β-d-Glc1-OMe trisaccharide compared with its parent disaccharides*

Conformations of the α-l -Rhap(1-2)-β-d -Glc1-OMe and β-d -Galp(1-3)-β-d -Glc1-OMe disaccharides and the branched title trisaccharide were examined in DMSO-d₆ solution by ¹H-nmr. The distance mapping procedure was based on rotating frame nuclear Overhauser effect (NOE) constraints involving C- and O-linked protons, and hydrogen-bond constraints manifested by the splitting of the OH nmr signals for partially deuteriated samples. An “isotopomer-selected NOE” method for the unequivocal identification of mutually hydrogen-bonded hydroxyl groups was suggested. The length of hydrogen bonds thus detected is considered the only one motionally nonaveraged nmr-derived constraint. Molecular mechanics and molecular dynamics methods were used to model the conformational properties of the studied oligosaccharides. Complex conformational search, relying on a regular Φ,Ψ-grid based scanning of the conformational space of the selected glycosidic linkage, combined with simultaneous modeling of different allowed orientations of the pendant groups and the third, neighboring sugar residue, has been carried out. Energy minimizations were performed for each member of the Φ,Ψ grid generated set of conformations. Conformational clustering has been done to group the minimized conformations into families with similar values of glycosidic torsion angles. Several stable syn and anti conformations were found for the 1→2 and 1→3 bonds in the studied disaccharides. Vicinal glycosylation affected strongly the occupancy of conformational states in both branches of the title trisaccharide. The preferred conformational family of the trisaccharide (with average Φ,Ψ values of 38°, 17° for the 1→2 and 48°, 1° for the 1→3 bond, respectively) was shown by nmr to be stabilized by intramolecular hydrogen bonding between the nonbonded Rha and Gal residues. © 1998 John Wiley & Sons, Inc. Biopoly 46: 417–432, 1998     

Peptides containing the sulfonamide junction: Synthesis,structure, and conformation of Z-Tau-Pro-Phe-NHiPr

The taurine (Tau) containing tripeptide derivative Z-Tau-Pro-Phe-NHiPr (1) has been synthesized as suitable sulfonamido-pseudopeptide model to investigate formation and conformational properties of folded secondary structures stabilized by intramolecular H bonds directly involving the sulfonamide junction. In the crystal the pseudopeptide 1 adopts a type I β-turn with the Pro and Phe residues located at the (i + 1) and (i + 2) corner positions, respectively. The turn is stabilized by a 4 → 1 H bond engaging one of the SO₂ oxygen atoms and the isopropylamide NH. In CDCl₃ solution the β-turn folding is accompanied by a γ-turn centered at the Pro and involving a 3 → 1 H bond between the SO₂ and the Phe NH. A comparison of the structural and conformational properties found in 1 with those of the already known sulfonamido-pseudopeptides, with particular reference to the models containing the Tau-Pro junction, is also reported. © 1997 John Wiley & Sons, Inc. Biopoly 41: 555–567, 1997.     

Conformational flexibility and loss of structural rigidity for a model hexapeptide,GRGDTP: 1H‐NMR and molecular dynamics studies

The NMR and molecular dynamics methods are used to study the conformations of a hexapeptide, GRGDTP, which has been shown to be accessible to various types of cell‐adhesion based cellular behaviors such as cell‐to‐matrix interactions, cell differentiation, immunogenicity development, gene expression, angiogenesis, metastasis, sex determination and gamete fusion. ¹H‐NMR results indicate the existence of weak 5→2 hydrogen bonded β‐turn type‐III. Molecular simulation studies using a mixed protocol of distance geometry, constrained minimization, restrained molecular dynamics followed by energy minimization resulted additional conformations that include about 64% of population of inverse γ‐turn (HB, 3→1) and about 35% population of γ‐turn (HB, 4→2). The inter‐proton distances observed in γ‐and inverse γ‐turns are also consistent with the NMR constraints. The variable internal hydrogen bonding due to γ‐turns initiated at Gly 1 and Arg 2 , and its tendency to inter‐convert between γ‐and inverse γ‐turn conformations imply that the peptide is flexible in nature. © 2013 Wiley Periodicals, Inc. Biopolymers 99: 460–471, 2013.     

β-Turn conformations in crystal structures of model peptides containing α,α-Di-n-propylglycine and α,α-Di-n-butylglycine

The crystal state conformations of three peptides containing the α,α-dialkylated residues. α,α-di-n-propylglycine (Dpg) and α,α-di-n-butylglycine (Dbg), have been established by x-ray diffraction. Boc-Ala-Dpg-Alu-OMe (I) and Boc-Ala-Dbg-Ala-OMe (III) adopt distorted type II β-turn conformations with Ala (1) and Dpg/Dbg (2) as the corner residues. In both peptides the conformational angles at the Dxg residue (I: ? = 66.2°, ψ = 19.3°; III: ? = 66.5°. ψ = 21.1°) deviate appreciably from ideal values for the i + 2 residue in a type II β-turn. In both peptides the observed (N…O) distances between the Boc CO and Ala (3) NH groups are far too long (1: 3.44 Å: III: 3.63 Å) for an intramolecular 4 → 1 hydrogen bond. Boc-Ala-Dpg-Ata-NHMe (II) crystallizes with two independent molecules in the asymmetric unit. Both molecules HA and HB adopt consecutive β-turn (type III-III in HA and type III-I in IIB) or incipient 3₁₀-helical structures, stabilized by two intramolecular 4 → 1 hydrogen bonds. In all four molecules the bond angle N-C^α-C′ (τ) at the Dxg residues are ≥ 110°. The observation of conformational angles in the helical region of ?,ψ space at these residues is consistent with theoretical predictions. © 1995 John Wiley & Sons, Inc.     

Comparisons of the conformational biases imposed by trans-2,3-methanomethionine and α-methylmethionine

A comparative study of four peptidomimetics of the sequence Phe-Met-Arg-Phe-amide (FMRFa) was performed to compare the conformational bias caused by trans-2,3-methanomethionine and α-methylmethionine stereoisomers. The specific compounds studied were F[(2S,3S)-cyclo-M] RFa, F[(2R,3R)-cyclo-M]RFa, F[(S)-α-MeM]RFa, and F[(R)-α-MeM]RFa. Molecular simulations based on CHARMm 22 indicate that γ-turn, inverse γ-turn, and α-helical conformations about the cyclo-M residue are accessible to the two F[cyclo-M]RFa stereoisomers. Similar calculations for F[(S)-α-MeM]RFa, and F[(R)-α-MeM]RFa indicate that the α-methylamino acids tend to favor α-helical conformations. The nmr data is presented for the four peptidomimetics. Most informative were the rotating frame nuclear Overhauser effect cross peaks between the NH protons proximal to the methionine surrogates, and the C_β hydrogens. Overall, these nmr data indicate F[(2S,3S)-cyclo-M]RFa and F[(2R,3R)-cyclo-M]RFa preferentially adopt inverse γ-turn and γ-turn conformations, respectively, whereas F[(S)-α-MeM]RFa and F[(R)-α-MeM]RFa tend to form partial left- and right-handed helical structures (although energy differences between the two turn structures, and between the two helical structures are likely to be small). It is suggested that the wider NH-C_α-CO angle of cyclopropane amino acids and their more severe steric requirements around the C_β carbons force the peptidomimetic N- and C-termini into the same region of conformational space. This favors C⁷ turns in the cyclopropane amino acid series relative to the less constrained α-methyl derivatives. © 1997 John Wiley & Sons, Inc. Biopoly 42: 439–453, 1997     

Folding of aminosuccinyl peptides: Thermodynamic data from temperature dependent circular dichroism measurements

The conformational equilibrium of aminosuccinyl peptides between extended conformations and an intramolecularly hydrogen bonded type II′ β-turn conformation has been studied on the peptide Boc-L -Asu-Gly-L -Ala-OMe (Asu = aminosuccinyl residue) by means of temperature dependence of circular dichroism spectra. Owing to the peculiar chiroptical and conformational properties of the Asu residue, this technique proved to be very useful for deriving thermodynamic data for the above folding process. The value of ΔH⁰ (?6.6 kJ mol^?1), obtained for the peptide studied in a chloroformacetonitrile mixture, shows that the lower energy of the folded conformer is primarily due to the characteristic intramolecular hydrogen bond of the β turns. © 1995 Wiley-Liss, Inc.     

Studies of conformational isomerism in α-melanocyte stimulating hormone by design of cyclic analogues

Results of energy calculations for α-MSH (α-melanocyte stimulating hormone, Ac-Ser¹-Tyr²-Ser³-Met⁴-Glu⁵-His⁶-Phe⁷-Arg⁸-Trp⁹-Gly¹⁰-Lys¹¹-Pro¹²-Val¹³-NH₂) and [D -Phe⁷]α-MSH were used for design of cyclic peptides with the general aim to stabilize different conformational isomers of the parent compound. The minimal structural modifications of the conformationally flexible Gly¹⁰ residue, as substitutions for L -Ala, D -Ala, or Aib (replacing of hydrogen atoms by methyl groups), were applied to obtain octa- and heptapeptide analogues of α-MSH(4–11) and α-MSH(5–11), which were cyclized by lactam bridges between the side chains in positions 5 and 11. Some of these analogues, namely those with substitutions of the Gly¹⁰ residue with L -Ala or Aib, showed biological activity potencies on frog skin comparable to the potency of the parent tridecapeptide hormone. Additional energy calculations for designed cyclic analogues were used for further refinement of the model for the biologically active conformations of the His-Phe-Arg-Trp “message” sequence within the sequences of α-MSH and [D -Phe⁷]α-MSH. In such conformations the aromatic moieties of the side chains of the His⁶, L/D -Phe⁷, and Trp⁹ residues form a continuous hydrophobic “surface,” presumably interacting with a complementary receptor site. This feature is characteristic for low-energy conformers of active cyclic analogues, but it is absent in the case of inactive analogues. This particular spatial arrangement of functional groups involved in the message sequence is very close for α-MSH and [D -Phe⁷]α-MSH, as well as for biologically active cyclic analogues despite differences of dihedral angle values for corresponding low-energy conformations. © 1998 John Wiley & Sons, Inc. Biopoly 46: 155–167, 1998     

Conformational interconversions in peptide β-turns: Discrimination between enantiomeric conformations by chiral perturbation

The crystal structure of the model tripeptide Boc-Aib-Gly-Leu-OMe ( 1 ) reveals two independent molecules in the asymmetric unit that adopt “enantiomeric” type I and type I′ β-turn conformations with the Aib and Gly residues occupying the corner (i + 1 and i + 2) positions. ¹³C cross polarization and magic angle sample spinning spectra in the solid state also support the coexistence of two conformational species. ¹³C-nmr in CDCl₃ establishes the presence of a single species or rapid exchange between conformations. 400 MHz ¹H-nmr provides evidence for conformational exchange involving a major and minor species, with β-turn conformations supported by the low solvent exposure of Leu(3) NH and the observation of N_iH ↔ N_i+1H nuclear Overhauser effects. CD bands in the region 190–230 nm are positive, supporting a major population of type I′ β-turns. The isomeric peptide, Boc-Gly-Leu-Aib-OMe ( 2 ), adopts an “open” type II′ β-turn conformation in crystals. Solid state and solution nmr support population of a single conformational species. Chiral perturbation introduced outside the folded region of peptides may provide a means of modulating screw sense in achiral sequences. © 1998 John Wiley & Sons, Inc. Biopoly 45: 191–202, 1998     

Crystal Structure and Molecular Conformation of the Cyclic Hexapeptide cyclo-(Gly-Aib-Gly)2

We have synthesized and crystallized the cyclic peptide (Gly-Aib-Gly) ₂. Its structure has been determined by conventional X-ray diffracti on methods. In the crystal it adopts a conformation with one β-turn (type I) and its mirror image at the other side of the ring. All conformation al angles are similar to those reported for these amino acid residues. In particular the Aib residue has a conformation intermediate between α- and 3₁₀-helical conformations. The ring is an adequate model for the β-turn conformation. A molecule of formic acid is found in the crystal which shows a very short hydrogen bond with one of the glycine carbonyl groups.     

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     

The structure of the ends of α-helices in globular proteins: effect of additional hydrogen bonds and implications for helix formation

We prepared a set of about 2000 α-helices from a relational database of high-resolution three-dimensional structures of globular proteins, and identified additional main chain i ← i+3 hydrogen bonds at the ends of the helices (i.e., where the hydrogen bonding potential is not fulfilled by canonical i ← i+4 hydrogen bonds). About one-third of α-helices have such additional hydrogen bonds at the N-terminus, and more than half do so at the C-terminus. Although many of these additional hydrogen bonds at the C-terminus are associated with Schellman loops, the majority are not. We compared the dihedral angles at the termini of α-helices having or lacking the additional hydrogen bonds. Significant differences were found, especially at the C-terminus, where the dihedral angles at positions C2 and C1 in the absence of additional hydrogen bonds deviate substantially from those occurring within the α-helix. Using a novel approach we show how the structure of the C-terminus of the α-helix can emerge from that of constituent overlapping α-turns and β-turns, which individually show a variation in dihedral angles at different positions. We have also considered the direction of propagation of the α-helix using this approach. If one assumes that helices start as a single α-turn and grow by successive addition of further α-turns, the paths for growth in the N → C and C → N directions differ in a way that suggests that extension in the C → N direction is favored.     

Chain length effects on helix-hairpin distribution in short peptides with Aib-DAla and Aib-Aib segments

The Aib-D Ala dipeptide segment has a tendency to form both type-I'/III' and type-I/III β-turns. The occurrence of prime turns facilitates the formation of β-hairpin conformations, while type-I/III turns can nucleate helix formation. The octapeptide Boc-Leu-Phe-Val-Aib-DAla-Leu-Phe-Val-OMe (1) has been previously shown to form a β-hairpin in the crystalline state and in solution. The effects of sequence truncation have been examined using the model peptides Boc-Phe-Val-Aib-Xxx-Leu-Phe-NHMe (2, 6), Boc-Val-Aib-Xxx-Leu-NHMe (3, 7), and Boc-Aib-Xxx-NHMe (4, 8), where Xxx=DAla, Aib. For peptides with central Aib-Aib segments, Boc-Phe-Val-Aib-Aib-Leu-Phe-NHMe (6), Boc-Val-Aib-Aib-Leu-NHMe (7), and Boc-Aib-Aib-NHMe (8) helical conformations have been established by NMR studies in both hydrogen bonding (CD3OH) and non-hydrogen bonding (CDCl3) solvents. In contrast, the corresponding hexapeptide Boc-Phe-Val-Aib-DAla-Leu-Phe-Val-NHMe (2) favors helical conformations in CDCl3 and β-hairpin conformations in CD3 OH. The β-turn conformations (type-I'/III) stabilized by intramolecular 4→1 hydrogen bonds are observed for the peptide Boc-Aib-D Ala-NHMe (4) and Boc-Aib-Aib-NHMe (8) in crystals. The tetrapeptide Boc-Val-Aib-Aib-Leu-NHMe (7) adopts an incipient 3(10)-helical conformation stabilized by three 4→1 hydrogen bonds. The peptide Boc-Val-Aib-DAla-Leu-NHMe (3) adopts a novel α-turn conformation, stabilized by three intramolecular hydrogen bonds (two 4→1 and one 5→1). The Aib-DAla segment adopts a type-I' β-turn conformation. The observation of an NOE between Val (1) NH?HNCH3 (5) in CD3OH suggests, that the solid state conformation is maintained in methanol solutions.     

Studies on Hydrogen Bonds Part V-Hydrogen Bonding in Energy Minimization Studies of Peptides

Abstract

An energy term, representing the N—H…O type of hydrogen bond, which is a function of the hydrogen bond length (R) and angle (θ) has been introduced in an energy minimization program, taking into consideration its interpolation with the non-bonded energy for borderline values of R and θ. The details of the mathematical formulation of the derivatives of the hydrogen bond function as applicable to the energy minimization have been given. The minimization technique has been applied to hydrogen bonded two and three linked peptide units (γ-turns and β-turns), and having Gly, Ala and Pro side chains. Some of the conformational highlights of the resulting minimum energy conformations are a) the occurrence of the expected 4?1 hydrogen bond in all of the β-turn tripeptide sequences and b) the presence of an additional 3?1 hydrogen bond in some of the type I and II tripeptides with the hydrogen bonding scheme in such type I β-turns occurring in a bifurcated form. These and other conformational features have been discussed in the light of experimental evidence and theoretical predictions of other workers.     

Conformational studies of -glucans

A study of the effect of linkage on the possible conformations of di-and polysaccharides of α-D -glucose and also the probable intramolecular hydrogen bonds has been made. The differences in the nature of linkage is shown to effect the energetically preferred conformations; (1 → 2) linkages lead only to righthanded helical conformations, (1 → 3) linkages lead to extended as well as both left and righthanded helical conformations; (1 → 4) linkages lead to both right-and lefthanded wide helical conformations. The possible hydrogen bonds between adjacent residues are also dependent on the nature of the linkage. A comparison of the conformational data of α-D -glucans with those of β-D -glucans has indicated that the favored conformations and hydrogen bonds between contiguous residues in the chain are influenced by the configuration at the anomeric carbon atom in all the three types of polysaccharides. From the energy calculations a probable conformation (?M = ?10°, ψM = ?30°, ?N = ?23°, ψN = ?19°) has also been proposed for crystalline mycodextran in conformity with x-ray data. This conformation contains two types of hydrogen bonds between contiguous residues one between 0–2 and 0–3 atoms at (1 → 4) linkage and the other between 0?2 and 0–4 atoms at (1 → 3) linkage in the chain. The conformation of maltose unit (?10°,?30°) that is likely to occur in the crystalline mycodextran coincides with the minimum energy conformation of maltose.     

The amide III vibrational circular dichroism band as a probe to detect conformational preferences of alanine dipeptide in water

The conformational preferences of blocked alanine dipeptide (ADP), Ac‐Ala‐NHMe, in aqueous solution were studied using vibrational circular dichroism (VCD) together with density functional theory (DFT) calculations. DFT calculations of three most representative conformations of ADP surrounded by six explicit water molecules immersed in a dielectric continuum have proven high sensitivity of amide III VCD band shape that is characteristic for each conformation of the peptide backbone. The polyproline II (P_II) and α_R conformation of ADP are associated with a positive VCD band while β conformation has a negative VCD band in amide III region. Knowing this spectral characteristic of each conformation allows us to assign the experimental amide III VCD spectrum of ADP. Moreover, the amide III region of the VCD spectrum was used to determine the relative populations of conformations of ADP in water. Based on the interpretation of the amide III region of VCD spectrum we have shown that dominant conformation of ADP in water is P_II which is stabilized by hydrogen bonded water molecules between CO and NH groups on the peptide backbone. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 814–818, 2014.     

Three-dimensional features of the bacterial polysaccharide (1 → 4)-β-D-glucuronan: A molecular modeling study

The mutant strain M5N1 CS of Rhizobium meliloti produces, in a Rhizobium complete medium supplemented with fructose and sucrose, a partially acetylated homopolymer of D -glucuronic acid residues linked β-(1 → 4). This polysaccharide forms thermoreversible gels with monovalent salts and thermally stable gels with divalent salts. In order to define the different levels of structural characterization, modeling simulations were performed for both the regular (1 → 4)-β-D -glucuronan and the acetylated derivatives. This required the evaluation of the accessible conformational space for the 16 disaccharides. Detailed conformational analysis was accomplished using the flexible residue of the MM3 molecular mechanics procedure and the results were used to access the configurational statistics of representative polysaccharide chains. Within the potential energy surfaces calculated for each disaccharide, several low energy conformers can be identified. When these conformations are extrapolated to regular polysaccharide structures, they generate polymers with right- and left-handed chirality along with a 2-fold axis. This later arrangement (n = 2, h = 5.16 Å) closely corresponds to that derived from a fiber x-ray diffraction investigation. The insertion of acetyl groups induces changes in the helical features of the polymer. As for the simulation of the configurational properties of (1 → 4)-β-D -glucuronan, an extended disordered chain having a persistence length of 105 Å (corresponding to 22 monomers) is predicted. This agrees with previous conclusions derived from solution study. The inclusion of varying amounts of acetyl groups only slightly perturbs the calculated persistence length. © 1998 John Wiley & Sons, Inc. Biopoly 45: 165–175, 1998     

Introduction of a new scheme for classifying β-turns in protein structures

Protein β-turn classification remains an area of ongoing development in structural biology research. While the commonly used nomenclature defining type I, type II and type IV β-turns was introduced in the 1970s and 1980s, refinements of β-turn type definitions have been introduced as recently as 2019 by Dunbrack, Jr and co-workers who expanded the number of β-turn types to 18 (Shapovalov et al, PLOS Computat. Biol., 15, e1006844, 2019). Based on their analysis of 13 030 turns from 1074 ultrahigh resolution (≤1.2 Å) protein structures, they used a new clustering algorithm to expand the definitions used to classify protein β-turns and introduced a new nomenclature system. We recently encountered a specific problem when classifying β-turns in crystal structures of pentapeptide repeat proteins (PRPs) determined in our lab that are largely composed of β-turns that often lie close to, but just outside of, canonical β-turn regions. To address this problem, we devised a new scheme that merges the Klyne-Prelog stereochemistry nomenclature and definitions with the Ramachandran plot. The resulting Klyne-Prelog-modified Ramachandran plot scheme defines 1296 distinct potential β-turn classifications that cover all possible protein β-turn space with a nomenclature that indicates the stereochemistry of i + 1 and i + 2 backbone dihedral angles. The utility of the new classification scheme was illustrated by re-classification of the β-turns in all known protein structures in the PRP superfamily and further assessed using a database of 16 657 high-resolution protein structures (≤1.5 Å) from which 522 776 β-turns were identified and classified.     

Stereochemistry of peptides containing 1-aminocyclopentanecarboxylic acid (Acc5): Solution and solid-state conformations of Boc-Acc5-Acc5-NHMe

The conformational analysis of a protected homodipeptide of 1-aminocyclopentanecarboxylic acid (Acc⁵) has been carried out. ¹H-nmr studies establish a β-turn conformation for Boc-Acc⁵-Acc⁵-NHMe in chloroform and dimethylsulfoxide solutions involving the methylamide NH in an intramolecular hydrogen bond. Supportive evidence for the formation of an intramolecular hydrogen bond is obtained from ir studies. X-ray diffraction studies reveal a type III β-turn conformation in the solid state stabilized by a 4 → 1 hydrogen bond between the Boc CO and methylamide NH groups. The ?,ψ values for both Acc⁵ residues are close to those expected for an ideal 3₁₀-helical conformation (?? ± 60°, ψ～ ±30°).     

A novel approach to predicting protein structural classes in a (20–1)-D amino acid composition space

The development of prediction methods based on statistical theory generally consists of two parts: one is focused on the exploration of new algorithms, and the other on the improvement of a training database. The current study is devoted to improving the prediction of protein structural classes from both of the two aspects. To explore a new algorithm, a method has been developed that makes allowance for taking into account the coupling effect among different amino acid components of a protein by a covariance matrix. To improve the training database, the selection of proteins is carried out so that they have (1) as many non-homologous structures as possible, and (2) a good quality of structure. Thus, 129 representative proteins are selected. They are classified into 30 α, 30 β, 30 α + β, 30 α/β, and 9 ζ (irregular) proteins according to a new criterion that better reflects the feature of the structural classes concerned. The average accuracy of prediction by the current method for the 4 × 30 regular proteins is 99.2%, and that for 64 independent testing proteins not included in the training database is 95.3%. To further validate its efficiency, a jackknife analysis has been performed for the current method as well as the previous ones, and the results are also much in favor of the current method. To complete the mathematical basis, a theorem is presented and proved in Appendix A that is instructive for understanding the novel method at a deeper level. © 1995 Wiley-Liss, Inc.