The conformational properties of α,β‐dehydroamino acids with a C‐terminal ester group

α,β‐Dehydroamino acid esters occur in nature. To investigate their conformational properties, a systematic theoretical analysis was performed on the model molecules Ac‐ΔXaa‐OMe [ΔXaa = ΔAla, (E)‐ΔAbu, (Z)‐ΔAbu, ΔVal] at the B3LYP/6‐311+ + G(d,p) level in the gas phase as well as in chloroform and water solutions with the self‐consistent reaction field‐polarisable continuum model method. The Fourier transform IR spectra in CCl₄ and CHCl₃ have been analysed as well as the analogous solid state conformations drawn from The Cambridge Structural Database. The ΔAla residue has a considerable tendency to adopt planar conformations C5 (?, ψ ≈ ? 180°, 180°) and β2 (?, ψ ≈ ? 180°, 0°), regardless of the environment. The ΔVal residue prefers the conformation β2 (?, ψ ≈ ? 120°, 0°) in a low polar environment, but the conformations α (?, ψ ≈ ? 55°, 35°) and β (?, ψ ≈ ? 55°, 145°) when the polarity increases. The ΔAbu residues reveal intermediate properties, but their conformational dispositions depend on configuration of the side chain of residue: (E)‐ΔAbu is similar to ΔAla, whereas (Z)‐ΔAbu to ΔVal. Results indicate that the low‐energy conformation β2 is the characteristic feature of dehydroamino acid esters. The studied molecules constitute conformational patterns for dehydroamino acid esters with various side chain substituents in either or both Z and E positions. Copyright © 2011 European Peptide Society and John Wiley & Sons, Ltd.     

Crystal structure of a tripeptide,L-alanyl-glycyl-glycine and its relevance to the poly(glycine)-II type of conformation

A tripeptide molecule, L -alanyl-glycyl-glycine, crystallizes in the form of a left-handed helix with (?,ψ) = ?83°, 170°. A pseudohexagonal packing arrangement and interchain hydrogen-bonded interactions are reminiscent of the model for the structure of poly(glycine)-II. Observations of certain intermolecular interactions appear to be relevant to the stereochemical assumptions incorporated in the models proposed for poly(glycine)-II and related polypeptides.     

Theoretical π-π* absorption and circular dichroic spectra of polypeptide β-structures

Absorption and circular dichroic (CD) spectra of the π-π* transition near 200 nm are calculated for poly(Gly), poly(Ala), poly(Abu), and poly(Val) in the β_P (paralle) and β_A (antiparallel) pleated-sheet structures using the dipole interaction model and including interactions among all atoms; optical parameters were obtained from previous studies of related molecules. Most of the calculations are for structures with one or three chains of six residues each. The oscillator strength and splitting of the π-π* modes are found to be affected only to a small extent by variations in side-chain structure and conformation, whereas the CD spectrum is very sensitive to these variations. Poly(Gly) and poly(Ala) β-structures in uniform, planar lattices do not show sufficient rotational strength to account for observed CD spectra. Poly(Abu) and poly(Val) β-structures in uniform, planar lattices show rotational strengths comparable to experiment when χ¹ is near ?60° for β_A-structures or in a broad range near 140° for β_P-structures. Poly(Ala) in uniformly twisted β_A- and β_P-structures or in irregular β_A-structures corresponding to regions of the crystal structure of concanavalin A also show enhanced rotational strengths in the principal π-π* CD band. Absorption and CD spectra calculated for poly(Abu) in uniform β_A- and β_P-structures are compared with experimental data on poly(Lys) in the β-form, assuming side-chain conformations in Abu that maximize the intensity of the principal CD band. The calculations for the β_A-form show the better agreement with experiment for both types of spectra.     

Theoretical π-π* absorption and circular dichroic spectra of helical poly(L-proline) forms I and II

Absorption and CD spectra of the π-π* transition near 200 nm are calculated for helical (Pro)_n I and II (n = 6, 10) using the dipole interaction model, including interactions among all atoms, with optical parameters obtained from previous studies of related molecules. Calculated spectra for (Ala)_n and (Pro)_n in the same conformation show marked differences. The spectra for (Pro)_n are sensitive to side-chain structure but are found to agree reasonably well with exeriment for forms I and II when the side-chain C? C bond length is set at 1.54 Å, with structural data otherwise obtained from x-ray diffraction studies.     

Conformational studies of linear β-D-1,4′-mannan and galactan

The nonbonded interaction energy of disaccharides, mannobiose and galactobiose and polysaccharides mannan and galactan have been computed as a function of dihedral angles (?,ψ). The conformation (40°, ?20°) has been preferred for the mannan chain from nonbonded interaction energy considerations. The O₅…O₃′ type of intramolecular hydrogen bond has been found to be possible in the above conformation. Comparison of the allowed region of mannan with those of cellulose and xylan indicates that the monomer unit, in mannan chain has slightly higher freedom of rotation than that of cellulose and less than that of xylan. As in cellulose and mannan, the freedom of rotation of the monomer units in β-1,4′ galactan is highly restricted. Unlike mannan (which prefers an extended conformation) the β-1,4′ galactan prefers a helical conformation similar to amylose. Just as in amylose the O₂…O₃′ type hydrogen bond between contiguous residues is also possible in β-1,4′ galactan.     

Crystallographic characterization of the α,γ C12 helix in hybrid peptide sequences

The solid‐state conformations of two αγ hybrid peptides Boc‐[Aib‐γ⁴(R)Ile]₄‐OMe 1 and Boc‐[Aib‐γ⁴(R)Ile]₅‐OMe 2 are described. Peptides 1 and 2 adopt C₁₂‐helical conformations in crystals. The structure of octapeptide 1 is stabilized by six intramolecular 4 → 1 hydrogen bonds, forming 12 atom C₁₂ motifs. The structure of peptide 2 reveals the formation of eight successive C₁₂ hydrogen‐bonded turns. Average backbone dihedral angles for αγ C₁₂ helices are peptide 1 , Aib; φ (°) = ?57.2 ± 0.8, ψ (°) = ?44.5 ± 4.7; γ⁴(R)Ile; φ (°) = ?127.3 ± 7.3, θ₁ (°) = 58.5 ± 12.1, θ₂ (°) = 67.6 ± 10.1, ψ (°) = ?126.2 ± 16.1; peptide 2 , Aib; φ (°) = ?58.8 ± 5.1, ψ (°) = ?40.3 ± 5.5; ψ⁴(R)Ile; φ (°) = ?123.9 ± 2.7, θ₁ (°) = 53.3 θ 4.9, θ ₂ (°) = 61.2 ± 1.6, ψ (°) = ?121.8 ± 5.1. The tendency of γ⁴‐substituted residues to adopt gauche–gauche conformations about the C^α–C^β and C^β–C^γ bonds facilitates helical folding. The αγ C₁₂ helix is a backbone expanded analog of α peptide 3₁₀ helix. The hydrogen bond parameters for α peptide 3₁₀ and α‐helices are compared with those for αγ hybrid C₁₂ helix. Copyright © 2016 European Peptide Society and John Wiley & Sons.     

Transformation of the ϕ-ψ plot for proteins to a new representation with local helicity and peptide torsional angles as variables

A new representation of protein structure is obtained by the angular coordinate transformations η_i = (?_i+1?ψ_i)/2 and ξ_i = ?_i+1+ψ_i with careful mathematical attention to the cyclical boundary conditions of all of the variables involved. From published ?-ψ data it is possible to obtain a new η-ξ plot. As the angle ξ_i is varied from – 180° through 0° to + 180° in this plot, the local helicity of the polypeptide chain changes continuously and contiguously without sudden reversals in handedness. The variable, η_i, gives the torsional position of the ith peptide group. Some peptide groups in proteins, such as the second peptide residue in a type II β-turn, are nonhydrogen-bonded and can undergo considerable torsional oscillation. In such cases the η angle should be represented by a line whose length reflects the allowed dynamical variations in the peptide torsional position. Certain peptide residues in proteins may be able to undergo a complete torsional rotation of 360°. Such residues would be represented on the η-ξ plot as a straight line across the plot parallel to the abscissa. Other examples of the possible usefulness of this plot are also given.     

Chain length dependent transition of 310- to α-helix of Boc-(Ala-Aib)n-OMe

An apolar synthetic octapeptide, Boc-(Ala-Aib)₄-OMe, was crystallized in the triclinic space group P1 with cell dimensions a = 11.558 Å, b = 11.643 Å, c = 9.650 Å, α = 120.220°, β = 107.000°, γ = 90.430°, V = 1055.889 ų, Z = 1, C₃₄H₆₀O₁₁N₈·H₂O. The calculated crystal density was 1.217 g/cm³ and the absorption coefficient ? was 6.1. All the intrahelical hydrogen bonds are of the 3₁₀ type, but the torsion angles, ? and ψ, of Ala(5) and Ala(7) deviate from the standard values. The distortion of the 3₁₀-helix at the C-terminal half is due to accommodation of the bulky Boc group of an adjacent peptide in the nacking. A water molecule is held between the N-terminal of one peptide and the C-terminal of the other. The oxygen atom of water forms hydrogen bonds with N (1) -H and N (2) -H, which are not involved in the intrahelical hydrogen bonds. The hydrogen atoms of water also formed hydrogen bonds with carbonyl oxygens of the adjacent peptide molecule. On the other hand, ¹H-nmr analysis revealed that the octapeptide took an α-helical structure in a CD₃CN solution. The longer peptides, Boc-(Ala-Aib)₆-OMe and Boc-(Ala-Aib)₈-OMe, were also shown to take an α-helical structure in a CD₃CN solution. An α-helical conformation of the hexadecapeptide in the solid state was suggested by x-ray analysis of the crystalline structure. Thus, the critical length for transition from the 3₁₀- to α-helix of Boc-(Ala-Aib)_n-OMe is 8. © 1993 John Wiley & Sons, Inc.     

The potential energy surface of methyl 2-O-(α-D-mannopyranosyl)-α-D-mannopyranoside in aqueous solution: Conclusions derived from optical rotation

The optical rotation of methyl 2-O -(α-D -mannopyranosyl)-α-D -mannopyranoside is calculated semiempirically as a function of the linkage dihedral angles ? (H1-C1-O1-C2′) and ψ (C1-O1-C2′-H2′). Although the rotation calculated for the global energy minimum conformation found in several rigid-residue modeling calculations (?,ψ = ?40°,?20°) is in good agreement with the observed solution rotation, the observed rotation is also compatible with the limited flexibility inferred from more recent relaxed residue modeling calculations on a structurally related rhamnose disaccharide © 1994 John Wiley & Sons, Inc.     

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.     

Characterization of proline-containing α-helix (helix F model of bacteriorhodopsin) by molecular dynamics studies

Many of the bilayer spanning segments of membrane transport proteins contain proline residues, and most of them are believed to occur in α-helical form. A proline residue in the middle of an α-helix is known to produce a bend in the helix, and recent studies have focused on characterizing such a bend at atomic level. In the present case, molecular dynamics (MD) studies are carried out on helix F model of bacteriorhodopsin (BR) Ace-(Ala)₇-Trp-(Ala)₂-Tyr-Pro-(Ala)₂-Trp-(Ala)₈-NHMe and compared with Ace-(Ala)₇-Trp-(Ala)₂-Tyr-(Ala)₃-Trp-(Ala)₈-NHMe in which the proline is replaced by alanine. The bend in the helix is characterized by structural parameters such as kink angle (α), wobble angle (θ), virtual torsion angle (ρ), and the hydrogen bond distance d (O_p?3 … N_p+1). The average values and the flexibility involved in these parameters are evaluated. The correlation among the bend related parameters are estimated. The equilibrium side chain orientations of tryptophan and tyrosine residues are discussed and compared with those found in the recently proposed model of bacteriorhodopsin. Finally, a detailed characterization of the bend in terms of secondary structures such as α_I, α_II and goniometric helices are discussed, which can be useful in the interpretation of the experimental results on the secondary structures of membrane proteins involving the proline residue. © 1993 Wiley-Liss, Inc.     

α-Hydroxymethylserine as a peptide building block: synthetic and structural aspects

A synthetic methodology has been developed for peptide bond formation with α-hydroxmethylserine as the carboxyl or amino component and also for the preparation of homo-sequences. The key intermediate, O,O-protected α-hydroxymethylserine in the form of an isopropylidene derivative, is easily accessible and represents the first example of a heterocyclic C^α,α-disubstituted amino acid containing an 1,3-dioxane ring. The use of this intermediate facilitates protection of the sterically hindered amino and carboxyl groups and is advantageous for the coupling and deprotection steps. X-ray structure determination of Z-HmS(Ipr)–Ala–OMe revealed that the two crystallographically independent molecules present in the asymmetric unit adopt an S-shaped conformation. In the one molecule the achiral HmS(Ipr) residue has the torsion angle values (ϕ==61.4°,ψ=40.8°) in the left-handed helical region of the Ramachandran map, while in the second molecule the negative torsion angles (ϕ=−60.1°, ψ=–44.4°) are associated with the right-handed helix. © 1998 European Peptide Society and John Wiley & Sons, Ltd.     

Polynucleotide folding in yeast tRNAPhe: elucidation of short-, medium-, and long-range interactions of sugar-phosphate-sugar backbone and base using a "blocked" nucleotide probe

It has recently been proposed that the repeating backbone nucleotide may be regarded as consisting of two blocks of equal magnitude representable by two virtual bonds. Implicit consideration of the nucleotide (ψ,ψ) and internucleotide (ω′,ω) geometry that generate variety in polynucleotide conformations, and of the constancy of the repeating structural moieties (P-C4′ and C4′-P) independent of the above rotations, has enabled us to utilize this scheme in the study of ordered structures such as di-, oligonucleotides and, most significantly, tRNA. The polynucleotide folding dictated by short-, intermediate-, and long-range interactions in the monoclinic and orthorhombic forms is described and compared through circular plots depicting the virtual bond torsions and distance plots constructed independently for backbone as well as bases. The torsions and the bond angles associated with the virtual bonds afford a clear distinction between ordered helical segments from loops and bends of tRNA. Lower virtual bond torsions (?60° to 60°) concomitant with higher values of virtual bond angles characterize various bend regions, while torsions around 160°–210° typify ordered helical strands. The distance plot elucidates the type of interaction associated with various sub-structures (helix–helix, helix–loop, and loop–loop) that form the constituents of different structural domains. Several other features such as the manifestation of the P₁₀ loop and the approximate twofold symmetry in the tRNA molecule are conspicuous on the distance plot.     

Molecular motion in poly(β-benzyl-L-aspartate)

As the temperature of solid poly(β-benzyl-L -aspartate) (PBLA), (CO.NH.CH.-CH₂COOCH₂C₆H₅)_n, in the α-helieal form is raised from ?150 °C, tlie line width and second moment of the proton magnetic resonance (PMR) signal decrease in stages until the conformational transition to the ω-helix occurs at about 90 °C. A similar temperature dependence of the PMR parameters is observed as the transformed polymer is cooled. Below ?100°C (where the lattice is presumed to be rigid), the measured second moments are 9.5 Oe² and 10.7 Oe² for the α and ω forms, respectively. Second moments, calculated from the Van Vleck formula for the rigid lattice and also estimated for possible motional cases in which the polymer is taken to be in the ω form, are compared with the PMH data. By combination with the results of X-ray diffraction and infrared spectroscopic measurements, a tentative explanation can be made of the types of motion occurring in PBLA.     

Nuclear magnetic resonance study of the impact of ribose 2′-O-methylation on the aqueous solution conformation of cytidylyl-(3′ → 5′)-cytidine

In order to obtain information about the conformational characteristics at the nearestneighbor level in the 2′-O-methylated region of t-RNA, as well as in the bizarre 5′-terminus of eucaryotic mRNA, a detailed nuclear magnetic resonance study of 2′-O-methyl-cytidylyl-(3′ → 5′)-cytidine (CmpC) was conducted. Proton spectra were recorded at 270 MHz in the Fourier mode in D₂O solutions, 0.01M, pD 7.3 in the temperature range 5–80°C. Complete accurate sets of nmr parameters were derived for each of the nucleotidyl units by a combination of homo-nuclear decouplings and simulation iteration methods. The data were translated into conformational parameters using procedures developed in earlier studies from these laboratories. It is shown that the ribofuranose ring exists at a ²E ? ³E equilibrium with clear preference [(75–80)%] for the ³E mode. The C(4′)-C(5′) and C(5′)-O(5′) bonds form a stable conformational network with outspoken preference for conformers in which Ψ₁, Ψ₂ ? 60° and ?₂ ? 180°. The orientation of the 3′-phosphate and 2′-O-methyl groups is such that ?₁′ ? 210° and ?″ ? 60°. The phosphodiester bonds are flexible and shift trends for base, H(1′), and H(5″) suggest the existence of a conformational blend of right-handed stack (g^?g^?), left-handed stack (g⁺g⁺), and unstacked arrays (tg^? and tg⁺). Elevation of temperature perturbs the ²E ? ³E equilibrium accompanied with modest depopulation of ψ₁, ψ₂ ? 60° and ?₂ ? 180° conformers. The major effect of elevation of temperature is in the increase of unstacked arrays at the expense of g^?g^? and g⁺g⁺ conformers. The shift trend of Cmp-H(3′) with temperature shows that torsional variation about O(3′)-P is facilitated by increase in temperature and the preferred rotamer about O(3′)-P in the unstacked form is t (ω₁′ = 180°). A detailed comparison of the aqueous solution conformations of CpC and CmpC reveals that 2′-O-methylation causes: (i) a reduction in the magnitude of _χ1; (ii) an increase in the population of ³E pucker at the 3′-nucleotidyl unit; and (iii) modest perturbations in the O(3′)-P and P-O(5′) bond conformations. Comparison of the aqueous solution conformations of AmpA and CmpC makes clear that the conformational properties of pyrimidine-pyrimidine and purine-purine dimers which carry a 2′-O-methylated 3′-nucleotidyl unit are significantly different.     

Conformational features of oligocellulose acetates in the solid state and their implications for the structures of cellulose triacetate

The crystal data on cellobiose octaacetate and cellotriose undecaacetate are compared in an effort to analyze what information available from crystal structures of oligosaccharides can be used to arrive at the three-dimensional structure of the related polysaccharides. This comparison points out the remarkable behavior of the reducing end of both molecules. The glycosidic torsion angles (?,ψ) around the reducing and the middle residues in the disaccharide and in the trisaccharide have values around 45° and 14°, while the conformational angles about the nonreducing residues in cellotriose acetate are 24° and ?20°. The conformations of the primary acetate groups on the two nonreducing residues are similar, but they differ from those observed for the acetate groups belonging to the reducing residues. The possibility of a 2₁ symmetry axis between contiguous triacetate residues within the oligosaccharide is examined, along with a comparison of the molecular packing found in the oligomer structures. Conformational energy calculations have been performed on two dimeric entities derived from cellotriose acetate. The isoenergy maps show the drastic influence of the relative orientations of the primary acetate groups. It is proposed that the nonreducing dimer, as found in the crystal structure of cellotriose acetate, most nearly expresses the “polymer averaged” interactions for contiguous residues in cellulose triacetate.     

Conformation of poly(L-lysine) homologs in solution

The effect of the number of methylene groups in the side chains on the conformation of polypeptides is assessed for three poly(L -lysine) homologs with R = –(CH₂)_nNH₂. Circular dichroism studies show a pH-induced helix–coil transition in 0.05 M KCl with midpoints at 9.6, 9.0, and 8.7 for n = 5, 6, and 7, respectively, as compared with 10.1 for (Lys)_x (n = 4). Homologs with n = 6 and 7 could be partially helical even when the side groups are fully charged (with n = 7, the compound is highly aggregated above pH 9.1). Thus, the longer the number of methylene groups the more stable is the helical conformation of these homologs. Potentiometric titration of the n = 5 homolog gives a ΔG° of ?310 cal/mol (residue) for the uncharged coil-to-helix transition at 25°C. The corresponding ΔH° and ΔS° are ?1740 cal/mol (residue) and ?4.8 e.u./mol (residue). Unlike (Lys)_x, the uncharged helix-to-β transition is slow and incomplete even after heating at 80°C for 1 hr. Addition of methanol enhances the helical formation in neutral solution with midpoints at 72, 52, and 27% methanol (v/v) for n = 5, 6, and 7, respectively [cf. 88% for (Lys)_x]. Addition of sodium dodecyl sulfate induces a coil-to-helix transition for all three homologs in contrast with the β form of (Lys)_x under similar conditions.     

Experimental and theoretical investigation of the molecular and electronic structure of 5-(4-aminophenyl)-4-(3-methyl-3-phenylcyclobutyl)thiazol-2-amine

The title molecule, 5-(4-aminophenyl)-4-(3-methyl-3-phenylcyclobutyl)thiazol-2-amine (C₂₀H₂₁N₃S), was prepared and characterized by ¹H-NMR, ¹³C-NMR, IR and single-crystal X-ray diffraction. The compound crystallizes in the monoclinic space group P2₁/c with a?=?9.4350(5) Å, b?=?11.2796(6) Å, c?=?18.4170(8) Å and β?=?113.378(3)°. In addition to the molecular geometry from X-ray experiment, the molecular geometry, vibrational frequencies, gauge including atomic orbital (GIAO) ¹H- and ¹³C-NMR chemical shift values and atomic charges distribution of the title compound in the ground state have been calculated using the Hartree–Fock (HF) and density functional method (DFT) (B3LYP) with 6-31G(d) basis set. To determine conformational flexibility, molecular energy profile of the title compound was obtained by semi-empirical (AM1) calculations with respect to two selected degrees of torsional freedom, which were varied from ?180° to +180° in steps of 10°. Besides, frontier molecular orbitals (FMO) analysis was performed by the B3LYP/6-31G(d) method.     

Helix-coil equilibria of poly (rA) · poly (rU)

Absorbance melting curves of the double-stranded (rA) · (rU) helix, made with fractionated homopolynucleotides of matched length, have been obtained over a 15-fold range of [Na⁺] and 30° range of temperature. An excellent fit of the observed profiles was obtained with theoretical curves calculated on the basis of the simplest interpretation for the occurrence of particular equilibria [1–3]; the complete molecular partition function being evaluated by the power series method developed by Applequist [4–6]. The stability constant was evaluated from literature values for the calorimetric enthalpy. The loop closure exponent was best represented by 2.22 ± 0.04 for the mismatching loop mode of melting and 1.22 for the matching mode and was independent of [Na⁺] and temperature. Assuming the applicability of the nonintersecting random walk value of 1.9 ± 0.1, these results would suggest a slight bias toward matched loop formation during melting of homopolynucleotides that might be expected to form only mismatched loops. The value of the stacking parameter at 60°C was only ~6% higher than that at 30°C, 0.0221 (0.0184 for the matching case). Calculated melting curves indicate the occurrence of a fifth-order phase transition when the mean helix length is only ~13 base-pairs, or about one full turn of the helix.     

Determination of the relaxation time of the helix–coil transition of poly(γ-benzyl-L-glutamate) by the nmr technique

NMR measurements of poly(γ-benzyl-L -glutamate) are reported in several different strengths of magnetic field to determine the relaxation time of the helix–coil transition. Nmr spectra of various samples had line shapes varying from the double to single, depending on the extent of the polydispersity of the sample. This result indicated that the correct line shape of a polypeptide is obscured in the overlapping of multipeaks, which are due to the heterogeneity of the molecular weight in the sample. Thus, the conventional line-shape analysis could not be applied to the kinetic study of the helix–coil transition of polypeptides without consideration of this polydispersity effect on the line shape. To overcome this difficulty, we measured linewidths of nmr spectra for fairly monodisperse samples, using various nmr spectrometers, having field strengths from 60 to 220 MHz. The results were analyzed by a quadratic equation, which involves an additional term proportional to the frequency difference of two sites. The equation differs from the conventional quadratic equation, usually utilized in the case of the fast-exchange limit, only in this additional term. This modification is required to evaluate correctly the unusual broadening of the linewidth resulting from the polydispersity effect and to determine the relaxation time reflected in nmr. Nmr spectra of three samples (DP-35, 85, and 250) were measured by 220-, 100-, and 60-MHz spectrometers in trifluoroacetic acid/chloroform at 28°C and linewidths were analyzed. Relaxation times of the helix–coil transition obtained at the transition midpoint are 2.5 × 10^?4, 7 × 10^?4, and 1.1 × 10^?3 sec, for DP-35, 85, and 250, respectively.