Disorder and order in unfolded and disordered peptides and proteins: A view derived from tripeptide conformational analysis. II. Tripeptides with short side chains populating asx and β‐type like turn conformations

In the preceding paper, we found that ensembles of tripeptides with long or bulky chains can include up to 20% of various turns. Here, we determine the structural and thermodynamic characteristics of GxG peptides with short polar and/or ionizable central residues (D, N, C), whose conformational distributions exhibit higher than average percentage (>20%) of turn conformations. To probe the side‐chain conformations of these peptides, we determined the ³J(H^α,H^β) coupling constants and derived the population of three rotamers with χ₁‐angles of ?60°, 180° and 60°, which were correlated with residue propensities by DFT‐calculations. For protonated GDG, the rotamer distribution provides additional evidence for asx‐turns. A comparison of vibrational spectra and NMR coupling constants of protonated GDG, ionized GDG, and the protonated aspartic acid dipeptide revealed that side chain protonation increases the pPII content at the expense of turn populations. The charged terminal groups, however, have negligible influence on the conformational properties of the central residue. Like protonated GDG, cationic GCG samples asx‐turns to a significant extent. The temperature dependence of the UVCD spectra and ³J(H^NH^α) constants suggest that the turn populations of GDG and GNG are practically temperature‐independent, indicating enthalpic and entropic stabilization. The temperature‐independent J‐coupling and UVCD spectra of GNG require a three‐state model. Our results indicate that short side chains with hydrogen bonding capability in GxG segments of proteins may serve as hinge regions for establishing compact structures of unfolded proteins and peptides. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

IR investigation on dehydrophenylalanine containing model peptides in helical conformation deposited on a crystal surface

Fourier transform ir spectra have been recorded for three 3₁₀‐helical and one α‐helical pentapeptides containing dehydrophenylalanine, in a thin solid film, in order to find marker bands for various secondary structures encountered in peptides containing dehydroaminoacids. The peptide solutions were deposited and dried as thin film on zinc selenide crystal surface. This convenient sampling method has provided reliable estimates of peptide secondary structure in solid state. Detailed vibrational assignments in the spectral region between 1200–1700 cm⁻¹ are reported. In this region, peptide amide I, II, and III vibrations occur. Spectra–structure correlation has been presented based on the amide modes. Comparison of the ir spectra with available crystal structure data provides qualitative support for assignments of ir bands to 3₁₀‐helical structure and α‐helical structure in dehydrophenylalanine containing pentapeptides. Band frequency assignments for 3₁₀‐helical conformation are consistent for all three peptides. All the assignments agree closely with the theoretical predictions. The spectral differences between 3₁₀‐helical peptides and the α‐helical peptide have been highlighted. These findings demonstrate that a method based on ir spectroscopy can be developed for a useful approximation of three‐dimensional structure of dehydropeptides in solid state. © 1999 John Wiley & Sons, Inc. Biopoly 50: 595–601, 1999     

Insights into the helix‐sense inversion of poly(β‐phenethyl‐L‐aspartate) by two‐dimensional Raman correlation spectroscopy

In this study, the transition process of the helix‐sense inversion of poly(β‐phenethyl‐L‐aspartate) was investigated by Raman scattering and 2‐dimensional correlation spectroscopy. Temperature‐dependent Raman spectra were obtained during the helix‐sense inversion. The results of 2‐dimensional correlation analysis in the spectral regions of 1600‐1800 and 3200‐3400 cm^?1 showed that the intensity changes of the side‐chain ester C═O stretching bands occurred prior to those of amide A and amide I bands in the unwinding process of αR‐helix on heating. The sequential order of the intensity changes for amide A, amide I, and the side‐chain ester C═O stretching bands during the inversion process was determined. It was found that the conformation change of the side chain occurred prior to that of the main chain for the αR‐helix on heating. Thus, we concluded that the transformation of the backbone chain from right‐handed to left‐handed is triggered by the conformational change of the side chains.     

VCD Robustness of the Amide‐I and Amide‐II Vibrational Modes of Small Peptide Models

The rotational strengths and the robustness values of amide‐I and amide‐II vibrational modes of For(AA)_nNHMe (where AA is Val, Asn, Asp, or Cys, n = 1–5 for Val and Asn; n = 1 for Asp and Cys) model peptides with α‐helix and β‐sheet backbone conformations were computed by density functional methods. The robustness results verify empirical rules drawn from experiments and from computed rotational strengths linking amide‐I and amide‐II patterns in the vibrational circular dichroism (VCD) spectra of peptides with their backbone structures. For peptides with at least three residues (n ≥ 3) these characteristic patterns from coupled amide vibrational modes have robust signatures. For shorter peptide models many vibrational modes are nonrobust, and the robust modes can be dependent on the residues or on their side chain conformations in addition to backbone conformations. These robust VCD bands, however, provide information for the detailed structural analysis of these smaller systems. Chirality 27:625–634, 2015 © 2015 Wiley Periodicals, Inc.     

Fourier transform infrared studies of ribonuclease in H2O and 2H2O solutions

Fourier transform infrared transmission spectra have been obtained of the enzyme ribonuclease in both H₂O and ²H₂O. The resolution of the spectra have been enhanced by Fourier self-deconvolution procedures. The infrared spectrum of ribonuclease changes during exchange of the enzyme's amide hydrogens for deuterium and the exchange has been followed in the amide I and amide II spectral regions. The amide I band shifts towards lower wavenumbers during both the fast and slow phases of hydrogen exchange and the interpretation of these shifts has aided the band assignments. In particular these studies have allowed an assignment to be made for the high frequency component of the β-strand absorption that differs from that proposed previously. This paper represents the first example of the use of deconvoluted Fourier transform infrared spectra in conjunction with hydrogen-deuterium exchange in order to aid in the assignment of a proteins's infrared bands.     

Ribonuclease Activity of the Peptides with Alternating Arginine and Leucine Residues Conjugated to Tetrathymidilate

RNA cleaving conjugates have been prepared by attachment of oligodeoxyribonucleotide TTTT to peptides containing arginine, leucine, proline and serine residues. The highest activity was displayed by the conjugates containing peptides with alternating arginine and leucine residues (LR)₄G‐amide. Ribonuclease activity of the conjugates pep‐T₄ decreases in the order T₄‐(LR)₄G > T₄‐(LR)₂G > T₄‐(LLRR)2G > T₄‐(LR)₂PRLRG > S₂R₃‐Hmda‐T₄ ≥ R₅ ≠ (LR)₃. According to CD spectra, the free peptide (LR)₄G‐amide in water solution at neutral pH and physiological ionic strength has no pronounced secondary structure whereas conjugated to oligonucleotide it acquires a folding similar to α‐helix.     

Vibrational and chiroptical spectroscopic characterization of γ‐turn model cyclic tetrapeptides containing two β‐Ala residues

The optical spectroscopic characterization of γ‐turns in solution is uncertain and their distinction from β‐turns is often difficult. This work reports systematic ECD and vibrational circular dichroism (VCD) spectroscopic studies on γ‐turn model cyclic tetrapeptides cyclo(Ala‐β‐Ala‐Pro‐β‐Ala) ( 1 ), cyclo(Pro‐β‐Ala‐Pro‐β‐Ala) ( 2 ) and cyclo(Ala‐β‐Ala‐Ala‐β‐Ala) ( 3 ). Conformational analysis performed at the 6‐31G(d)/B3LYP level of theory using an adequate PCM solvent model predicted one predominant conformer for 1‐3 , featuring two inverse γ‐turns. The ECD spectra in ACN of 1 and 2 are characterized by a negative n→π* band near 230 nm and a positive π→π* band below 200 nm with a long wavelength shoulder. The ECD spectra in TFE of 1‐3 show similar spectra with blue‐shifted bands. The VCD spectra in ACN‐d₃ of 1 and 2 show a +/?/+/? amide I sign pattern resulting from four uncoupled vibrations in the case of 1 and a sequence of two positive couplets in the case of 2 . A ?/+/+/? amide I VCD pattern was measured for 3 in TFE‐d₂. All three peptides give a positive couplet or couplet‐like feature (+/?) in the amide II region. VCD spectroscopy, in agreement with theoretical calculations revealed that low frequency amide I vibrations (at ～1630 cm^?1 or below) are indicative of a C₇ H‐bonded inverse γ‐turns with Pro in position 2, while γ‐turns encompassing Ala absorb at higher frequency (above 1645 cm^?1). Chirality, 2010. © 2010 Wiley‐Liss, Inc.     

Steric and electronic interactions controlling the cis/trans isomer equilibrium at X‐pro tertiary amide motifs in solution

A systematic understanding of the noncovalent interactions that influence the structures of the cis conformers and the equilibrium between the cis and the trans conformers, of the X‐Pro tertiary amide motifs, is presented based on analyses of ¹H‐, ¹³C‐NMR and FTIR absorption spectra of two sets of homologous peptides, X‐Pro‐Aib‐OMe and X‐Pro‐NH‐Me (where X is acetyl, propionyl, isobutyryl and pivaloyl), in solvents of varying polarities. First, this work shows that the cis conformers of any X‐Pro tertiary amide motif, including Piv‐Pro, are accessible in the new motifs X‐Pro‐Aib‐OMe, in solution. These conformers are uniquely observable by FTIR spectroscopy at ambient temperatures and by NMR spectroscopy from temperatures as high as 273 K. This is made possible by the persistent presence of n_i‐1→π_i* interactions at Aib, which also influence the disappearance of steric effects at these cis X‐Pro rotamers. Second, contrary to conventional understanding, the energy contribution of steric effects to the cis/trans equilibrium at the X‐Pro motifs is found to be nonvariant (0.54 ± 0.02 kcal/mol) with increase in steric bulk on the X group. Third, the current studies provide direct evidence for the weak intramolecular interactions namely the n_i‐1→π_i*, the N_Pro???H_i+1 (C₅a), and the C₇ hydrogen bond that operate and influence the structures, stabilities, and dynamics between different conformational states of X‐Pro tertiary amide motifs. NMR and IR spectral data suggest that the cis conformers of X‐Pro motifs are ensembles of short‐lived rotamers about the C′_X–N_Pro bond. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 66–77, 2014.     

Cationic oligopeptides with the repeating sequence L‐lysyl‐L‐alanyl‐L‐alanine: conformational and thermal stability study using optical spectroscopic methods

The infrared (IR), vibrational circular dichroism (VCD), and electronic circular dichroism (ECD) spectra of short cationic sequential peptides (L ‐Lys‐L ‐Ala‐L ‐Ala)_n (n = 1, 2, and 3) were measured over a range of temperatures (20–90 °C) in aqueous solution at near‐neutral pH values in order to investigate their solution conformations and thermally induced conformational changes. VCD spectra of all three oligopeptides measured in the amide I′ region indicate the presence of extended helical polyproline II (PPII)‐like conformation at room temperature. UV‐ECD spectra confirmed this conclusion. Thus, the oligopeptides adopt a PPII‐like conformation, independent of the length of the peptide chain. However, the optimized dihedral angles ? and ψ are within the range ?82 to ?107° and 143–154°, respectively, and differ from the canonical PPII values. At elevated temperatures, the observed intensity and bandshape variations in the VCD and ECD spectra show that the PPII‐like conformation of the Lys‐Ala‐Ala sequence is still preferred, being in equilibrium with an unordered conformer at near‐neutral pH values within the range of temperatures from 20 to 90 °C. This finding was obtained from analysis of the temperature‐dependent spectra using the singular value decomposition method. The study presents KAA‐containing oligopeptides as conformationally stable models of biologically important cationic peptides and proteins. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.     

Laser Raman spectroscopic analysis of angiotensin peptides' conformation

In this study we examined the conformation and side chain environments of angiotensins I, II, III, and [Sar¹-Ile⁵-Ala⁸]angiotensin II using laser Raman spectroscopy. The positions of the amide I bands for all four peptides were found between 1664 and 1673 cm^?1. D₂O exchange studies confirmed the positions of the amide I and amide III bands. The positions of the amide I bands for all the angiotensins were found at approximately 1665 cm^?1 and the amide III bands were all located between 1265 and 1278 cm^?1. From the positions and intensities of the amide I and III bands we concluded that all peptides share the same overall conformation consisting of β-turn structure. Spectral analysis indicated that although the spectra for all the peptides were qualitatively identical there was evidence that the angiotensin conformations were more flexible in the aqueous phase than the solid phase. Examination of the $\text{850}\text{830}$ cm^?1 tyrosine doublet suggested that the tyrosine residue in the peptides is exposed to the solvent environment and becomes more exposed as the peptide length is decreased. Therefore, there are some localized conformational differences among the angiotensins. The conformational data yielded by this study leads us to conclude that the various biological properties ascribed to the angiotensins are not due to different conformations of the peptides. The biological differences could perhaps be attributed to localized interactions of the individual amino acid residues with themselves and with the hormone receptors.     

1H-N.m.r. and c.d. investigation of the histidine side chain conformation in small peptides

Three series of model peptides containing histidine have been examined by ¹H-n.m.r. and c.d. spectroscopy: X-His peptides with X = Gly, Ala, Leu; His-X peptides with X = Gly, Ala, Leu, Ser, Lys, Phe, Tyr; and Pro-His-X peptides with X = Gly; Ala; Leu; Val; Phe; Tyr, C.d. spectra were obtained for pH values between 1 and 11 to give titration curves [θ] vs. pH; ¹H-n.m.r. spectra were recorded at four selected pH values corresponding to defined ionic species. ¹H-n.m.r. spectra in Me₂SO of the NH₃⁺, Imid⁺, COO^? ionic state (pH 4.5) were also obtained. The histidine side chain conformation in the various peptides and the changing ionic states is reflected in the ³J_αβ,β′ coupling constants, the Δδ ββ′ anisochrony values and the c.d. histidine chromophore contribution at 215 nm, and qualitative and semiquantitative correlations can be established between these parameters. Whereas the histidine side chain conformation is quite different in each of the three series, and varies with the ionic state and environment, it is practically identical for each peptide within a series: the nature of the X-residue does not exert any influence on the histidine side chain conformational behaviour. Thus, the classical rotamer distribution R I > R II > R III which is due to steric factors is usually observed unless specific intramolecular interactions such as hydrogen or ionic bonds override these.     

A 13C-NMR study on the conformational and dynamical properties of a cereal seed storage protein,C-hordein,and its model peptides

We have recorded the ¹³C CP-MAS and DD-MAS nmr spectra of dry and hydrated barley storage protein, C-hordein, as a model for wheat S-poor prolamins, together with those of model synthetic peptides (Pro)₂(Gln)₆(I) and (Pro-Gln-Gln-Pro-Phe-Pro-Gln-Gln)₃(II) under dry or hydrated conditions. The spectral features of C-hordein as well as these peptides were appreciably different from each other depending on the extent of hydration, reflecting different domains that adopt different types of conformations as well as dynamics. In particular, considerable proportions of the peak intensities were lost in the CP-MAS spectra, and well-resolved ¹³C-nmr signals emerged in DD-MAS nmr spectra owing to acquisition of molecular motions by swelling. It was shown that local β-turn or (Pro)_n type II conformation is more preferable for individual Pro residues and β-sheet type conformation is dominant for individual Gln residues in the dry and hydrated systems. In addition, two types of Gln environments are originated in C-hordein that differ in their mobility. Further, ¹³C spin-lattice relaxation times (T₁'s) of C- hordein and peptide II were reduced by more than one order of magnitude by hydration, reflecting the presence of well-swollen molecular chains. In contrast, theT₁ values of peptide I upon hydration remained one third of those in the dry state. Carbon-resolved proton spin-lattice relaxation times in the rotating frame (T_1ρ's) were also decreased by about 50% upon hydration, although these parameters were less sensitive as compared to T₁ values. In addition, the ¹³C-nmr signals of the aromatic side chain of Phe residues disappeared on hydration owing to interference between the frequency of the acquired flip-flop motion and the proton decoupling frequency. This information gives a new insight into establishing the structural properties of the studied protein system. A model may be put forward for a gel-type structure in which the more rigid part of the system involves intermolecular hydrogen-bonded Gln side chains as well as some hydrophobic “pockets” involving Pro and Phe residues. The liquid-like domain is characterized by considerable backbone and side-chain motion as well as rapid ring-puckering motion in Pro residues. © 1997 John Wiley & Sons, Inc.     

Comparative study of conformational behaviour of leucine and methionine enkephalinamides by1H-nuclear magnetic resonance spectroscopy

The conformational proclivity of leucine and methionine enkephalinamides in deuterated dimethyl sulphoxide has been investigated using proton magnetic resonance at 500 MHz. The resonances from the spin system of the various amino acid residues have been assigned from the 2-dimensional correlated spectroscopy spectra. The temperature variation of the amide proton shifts indicates that none of the amide proton is intramolecularly hydrogen-bonded or solvent-shielded. The analysis of vicinal coupling constants,³J_{HN.C 2}H,along with temperature coefficients and the absence of characteristic nuclear Overhauser effect cross peaks between the NH protons reveal that there is no evidence of the chain folding in these molecules. However, the observation of nuclear Overhauser effect cross peaks between the NH and the C^αH of the preceding residue indicates preference for extended backbone conformation with preferred side chain orientations particularly of Tyr and Phe in both [Leu⁵]- and [Met⁵]-enkephalinamides.     

Characterization of β-bend ribbon spiral forming peptides using electronic and vibrational CD

Terminally blocked (L-Pro-Aib)_n and Aib-(L-Pro-Aib)_n sequential oligopeptides are known to form right-handed β-bend ribbon spirals under a variety of experimental conditions. Here we describe the results of a complete CD and ir characterization of this subtype of 3₁₀-helical structure. The electronic CD spectra were obtained in solvents of different polarity in the 260-180 nm region. The vibrational CD and Fourier transform ir (FTIR) spectra were measured in deuterochloroform solution in the amide I and amide II (1750-1500 cm^?1) regions. The critical chain length for full development of the β-bend ribbon spiral structure is found to be five to six residues. Spectral effects related to concentration-induced stabilization of the structures of the longer peptides were seen in the resolution-enhanced FTIR spectra. Comparison to previous studies of (Aib)_n and (Pro)_n oligomers indicate that the low frequency of the amide I mode is due to the interaction of secondary and tertiary amide bonds and not to a strong difference in conformation from a regular 3₁₀-helix. © 1995 John Wiley & Sons, Inc.     

Infrared and visible emissions of rare‐earth‐doped CeO2 phosphor

This paper reports the synthesis and characterization of Er³⁺‐doped CeO₂ phosphor with variable concentrations of erbium. The sample was synthesized using a solid‐state reaction method, which is useful for the large‐scale production of phosphors and is also eco‐friendly. The prepared sample was characterized using an X‐ray diffraction (XRD) technique. The XRD pattern confirmed that sample has the pure cubic fluorite crystal structure of CeO₂. The crystallite size of the prepared phosphor was determined by Scherer's formula and the crystallite size giving an intense XRD peak is 40.06 nm. The surface morphology of the phosphor was determined by field emission gun scanning electron microscopy (FEGSEM). From the FEGSEM image, good surface morphology with some agglomerates was found. The functional group in the prepared sample was analysed by Fourier transform infrared (FTIR) spectroscopy. All samples prepared with variable concentrations of Er³⁺ (0.1–2 mol%) were studied by photoluminescence analysis and it was found that the excitation spectra of the prepared phosphor shows broad excitation centred at 251 nm. Emission spectra at different concentrations of Er³⁺ show strong peaks at 413 and 470 nm and a weaker peak at 594 nm. The dominant peaks at 413 and 470 nm are caused by the allowed electronic transition ⁴S_3/2 → ⁴I_15/2 and the weaker transition at 594 nm is due to the transition ⁴ F_9/2 → ⁴I_15/2. Spectrophotometric determinations of peaks were evaluated using the Commission Internationale de I'Eclairage (CIE) technique. The emission spectra were also observed using an infrared (IR) laser 980 nm source, and three distinct peaks were found in the IR region at 848, 870 and 980 nm. The prepared phosphor has utility for application in display devices. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthetic pentapeptides inhibiting autophosphorylation of insulin receptor in a non‐ATP‐competitive mechanism

In an attempt to develop non‐ATP‐competitive inhibitors of the autophosphorylation of IR, the effects of the synthetic peptides, Ac‐DIY¹¹⁵⁸ET‐NH₂ and Ac‐DY¹¹⁶²Y¹¹⁶³RK‐NH₂, on the phosphorylation of IR were studied in vitro. The peptides were derived from the amino‐acid sequence in the activation loop of IR. They inhibited the autophosphorylation of IR to 20.5 and 40.7%, respectively, at 4000 µM . The Asp/Asn‐ and Glu/Gln‐substituted peptides, Ac‐NIYQT‐NH₂ and Ac‐NYYRK‐NH₂, more potently inhibited the autophosphorylation than did the corresponding parent peptides. The inhibitory potencies of the substituted peptides were decreased with increasing concentrations of ATP, indicating that these peptides employ an ATP‐competitive mechanism in inhibiting the autophosphorylation of IR. In contrast, those of the parent peptides were not affected. Mass spectrometry showed that the parent peptides were phosphorylated by IR, suggesting that they interact with the catalytic loop. Moreover, docking simulations predicted that the substituted peptides would interact with the ATP‐binding region of IR, whereas their parent peptides would interact with the catalytic loop of IR. Thus, Ac‐DIYET‐NH₂ and Ac‐DYYRK‐NH₂ are expected to be non‐ATP‐competitive inhibitors. These peptides could contribute to the development of a drug employing a novel mechanism. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.     

Preferred side‐chain conformation of arginine residues in a triple‐helical structure

The crystal structure of the triple‐helical peptide (Pro‐Hyp‐Gly)₃‐Pro‐Arg‐Gly‐(Pro‐Hyp‐Gly)₄ (POG3‐PRG‐POG4) was determined at 1.45 Å resolution. POG3‐PRG‐POG4 was designed to permit investigation of the side‐chain conformation of the Arg residues in a triple‐helical structure. Because of the alternative structure of one of three Arg residues, four side‐chain conformations were observed in an asymmetric unit. Among them, three adopt a ttg^?t conformation and the other adopts a tg^?g^?t conformation. A statistical analysis of 80 Arg residues in various triple‐helical peptides showed that, unlike those in globular proteins, they preferentially adopt a tt conformation for χ₁ and χ₂, as observed in POG3‐PRG‐POG4. This conformation permits van der Waals contacts between the side‐chain atoms of Arg and the main‐chain atoms of the adjacent strand in the same molecule. Unlike many other host–guest peptides, in which there is a significant difference between the helical twists in the guest and the host peptides, POG3‐PRG‐POG4 shows a marked difference between the helical twists in the N‐terminal peptide and those in the C‐terminal peptide, separated near the Arg residue. This suggested that the unique side‐chain conformation of the Arg residue affects not only the conformation of the guest peptide, but also the conformation of the peptide away from the Arg residue. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1000–1009, 2014.     

Structural analysis of some soluble elastins by means of FT‐IR and 2D IR correlation spectroscopy

Fourier transform infrared (FT‐IR) spectroscopy combined with 2D correlation spectroscopy has been used to offer some information about stability and structure of some soluble elastins. Temperature has been chosen as the perturbation to monitor the infrared behavior of various soluble elastins, namely, α‐elastin p, α‐elastin, and k‐elastin. In the 3800–2700 cm^?1 region, the H‐containing groups were analyzed. The bonded hydroxyls are found to decrease prior to the NH‐related hydrogen bonds and also to the conformational reorganization of hydrocarbon chains. The transition temperatures were evaluated and they were found to agree with those obtained from DSC data. The FTIR spectra and their 2nd derivatives denote that α‐ elastins exhibited amide‐I, ‐II and ‐III bands at 1656, 1539 and 1236 cm^?1, respectively, while in k‐elastin these bands were found at 1652 cm^?1 for amide I, 1540 cm^?1 for amide II and 1248 cm^?1 for amide III. The macroscopic IR finger‐print method, which combines: general IR spectra, secondary derivative spectra, and 2D‐IR correlation spectra, is useful to discriminate different elastins. Thus using the differences of the position and intensity of the bands from “fingerprint region” of studied elastins, which include the peaks assigned to C?O, C? C groups from α‐helix, β‐turn, and the peaks assigned to the amide groups, it is possible to identify and discriminate elastins from each others. Furthermore, the pattern of 2D‐IR correlation spectra under thermal perturbation, allow their direct identification and discrimination. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 1072–1084, 2010. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com