Exploring the interactions of gliadins with model membranes: Effect of confined geometry and interfaces

Mechanisms leading to the assembly of wheat storage proteins into proteins bodies within the endoplasmic reticulum (ER) of endosperm cells are unresolved today. In this work, physical chemistry parameters which could be involved in these processes were explored. To model the confined environment of proteins within the ER, the dynamic behavior of γ‐gliadins inserted inside lyotropic lamellar phases was studied using FRAP experiments. The evolution of the diffusion coefficient as a function of the lamellar periodicity enabled to propose the hypothesis of an interaction between γ‐gliadins and membranes. This interaction was further studied with the help of phospholipid Langmuir monolayers. γ‐ and ω‐gliadins were injected under DMPC and DMPG monolayers and the two‐dimensional (2D) systems were studied by Brewster angle microscopy (BAM), polarization modulation infrared reflection‐absorption spectroscopy (PM‐IRRAS), and surface tension measurements. Results showed that both gliadins adsorbed under phospholipid monolayers, considered as biological membrane models, and formed micrometer‐sized domains at equilibrium. However, their thicknesses, probed by reflectance measurements, were different: ω‐gliadins aggregates displayed a constant thickness, consistent with a monolayer, while the thickness of γ‐gliadins aggregates increased with the quantity of protein injected. These different behaviors could find some explanations in the difference of aminoacid sequence distribution: an alternate repeated ‐ unrepeated domain within γ‐gliadin sequence, while one unique repeated domain was present within ω‐gliadin sequence. All these findings enabled to propose a model of gliadins self‐assembly via a membrane interface and to highlight the predominant role of wheat prolamin repeated domain in the membrane interaction. In the biological context, these results would mean that the repeated domain could be considered as an anchor for the interaction with the ER membrane and a nucleus point for the formation and growth of protein bodies within endosperm cells. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 610–622, 2009. 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     

Changes in the quaternary structure of amelogenin when adsorbed onto surfaces

Amelogenin is a unique protein that self‐assembles into spherical aggregates called “nanospheres” and is believed to be involved in controlling the formation of the highly anisotropic and ordered hydroxyapatite crystallites that form enamel. The adsorption behavior of amelogenin onto substrates is of great interest because protein‐surface interactions are critical to its function. We report studies of the adsorption of amelogenin onto self‐assembled monolayers containing COOH end group functionality as well as single crystal fluoroapatite, a biologically relevant surface. We found that although our solutions contained only nanospheres of narrow size distribution, smaller structures such as dimers or trimers were observed on the hydrophilic surfaces. This suggests that amelogenin can adsorb onto surfaces as small structures that “shed” or disassemble from the nanospheres that are present in solution. © 2008 Wiley Periodicals, Inc. Biopolymers 91: 103–107, 2009. 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     

Interaction of α‐gliadin with polyanions: Design considerations for sequestrants used in supportive treatment of celiac disease

Copolymers of sodium 4‐styrene sulfonate (SS) and hydroxyethyl methacrylate (HEMA) were investigated as sequestrants of α‐gliadin, a gluten protein, for the treatment of gluten intolerance. The interactions of α‐gliadin with poly(SS) and poly(HEMA‐co‐SS) with 9 and 26 mol% SS content were studied at gastric (1.2) and intestinal (6.8) pH using circular dichroism and measurements of turbidity, dynamic light scattering and zeta potential. The interactions and their influence on α‐gliadin secondary and aggregated structures depended mainly on the ratio of polymer negative and protein positive charges at pH 1.2, and on polymer SS content at polymer concentrations providing in excess of negative charges at either pH. Poly(SS) could not form complex particles with α‐gliadin in a sufficient excess of negative charges. Copolymerization with HEMA enhanced the formation of complex particles. Poly(HEMA‐co‐SS) with intermediate SS content was found to be the most effective sequestrant for α‐gliadin. This study provides insight into design considerations for polymer sequestrants used in the supportive treatment of celiac disease. © 2009 Wiley Periodicals, Inc. Biopolymers 93:418–428, 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     

Influence of surface and protein modification on immunoglobulin G adsorption observed by scanning force microscopy.

Scanning force microscopy has been used successfully to produce images of individual protein molecules. However, one of the problems with this approach has been the high mobility of the proteins caused by the interaction between the sample and the scanning tip. To stabilize the proteins we have modified the adsorption properties of immunoglobulin G on graphite and mica surfaces. We have used two approaches: first, we applied glow discharge treatment to the surface to increase the hydrophilicity, favoring adhesion of hydrophilic protein molecules; second, we used the arginine modifying reagent phenylglyoxal to increase the protein hydrophobicity and thus enhance its adherence to hydrophobic surfaces. We used scanning force microscopy to show that the glow discharge treatment favors a more homogeneous distribution and stronger adherence of the protein molecules to the graphite surface. Chemical modification of the immunoglobulin caused increased aggregation of the proteins on the surface but did not improve the adherence to graphite. On mica, clusters of modified immunoglobulins were also observed and their adsorption was reduced. These results underline the importance of the surface hydrophobicity and charge in controlling the distribution of proteins on the surface.     

Correlation between surface morphology and surface forces of protein A adsorbed on mica.

We have investigated the morphology and surface forces of protein A adsorbed on mica surface in the protein solutions of various concentrations. The force-distance curves, measured with a surface force apparatus (SFA), were interpreted in terms of two different regimens: a "large-distance" regimen in which an electrostatic double-layer force dominates, and an "adsorbed layer" regimen in which a force of steric origin dominates. To further clarify the forces of steric origin, the surface morphology of the adsorbed protein layer was investigated with an atomic force microscope (AFM) because the steric repulsive forces are strongly affected by the adsorption mode of protein A molecules on mica. At lower protein concentrations (2 ppm, 10 ppm), protein A molecules were adsorbed "side-on" parallel to the mica surfaces, forming a monolayer of approximately 2.5 nm. AFM images at higher concentrations (30 ppm, 100 ppm) showed protruding structures over the monolayer, which revealed that the adsorbed protein A molecules had one end oriented into the solution, with the remainder of each molecule adsorbed side-on to the mica surface. These extending ends of protein A overlapped each other and formed a "quasi-double layer" over the mica surface. These AFM images proved the existence of a monolayer of protein A molecules at low concentrations and a "quasi-double layer" with occasional protrusions at high concentrations, which were consistent with the adsorption mode observed in the force-distance curves.     

Determination of the secondary structure of proteins in different environments by FTIR-ATR spectroscopy and PLS regression

The secondary structures of proteins (alpha-helical, beta-sheet, beta-turn, and random coil) in the solid state and when bound to polymer beads, containing immobilized phenyl and butyl ligands such as those as commonly employed in hydrophobic interaction chromatography, have been investigated using FTIR-ATR spectroscopy and partial least squares (PLS) methods. Proteins with known structural features were used as models, including 12 proteins in the solid state and 7 proteins adsorbed onto the hydrophobic surfaces. A strong PLS correlation was achieved between predictions derived from the experimental data for 4 proteins adsorbed onto the phenyl-modified beads and reference data obtained from the X-ray crystallographic structures with r(2) values of 0.9974, 0.9864, 0.9924, and 0.9743 for alpha-helical, beta-sheet, beta-turn, and random coiled structures, respectively. On the other hand, proteins adsorbed onto the butyl sorbent underwent greater secondary structural changes compared to the phenyl sorbent as evidenced from the poorer PLS r(2) values (r(2) are 0.9658, 0.9106, 0.9571, and 0.9340). The results thus indicate that the secondary structures for these proteins were more affected by the butyl sorbent, whereas the secondary structure remains relatively unchanged for the proteins adsorbed onto the phenyl sorbent. This study has important ramifications for understanding the nature of protein secondary structural changes following adsorption onto hydrophobic sorbent surfaces. This knowledge could also enable the development of useful protocols for enhancing the chromatographic purification of proteins in their native bioactive states. (c) 2008 Wiley Periodicals, Inc. Biopolymers 89: 895-905, 2008.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.     

Oligoglycine surface structures: molecular dynamics simulation

The full-atomic molecular dynamics (MD) simulation of adsorption mode for diantennary oligoglycines [H-Gly4-NH(CH2)5]2 onto graphite and mica surface is described. The resulting structure of adsorption layers is analyzed. The peptide second structure motives have been studied by both STRIDE (structural identification) and DSSP (dictionary of secondary structure of proteins) methods. The obtained results confirm the possibility of polyglycine II (PGII) structure formation in diantennary oligoglycine (DAOG) monolayers deposited onto graphite surface, which was earlier estimated based on atomic-force microscopy measurements.     

Effect of supporting substrates on the structure of DNA and DNA-trivaline complexes studied by atomic force microscopy

Linear DNA, circular DNA, and circular DNA complexes with trivaline (TV), a synthetic oligopeptide, were imaged by atomic force microscopy (AFM) using mica as a conventional supporting substrate and modified highly ordered pyrolytic graphite (HOPG) as an alternative substrate. A method of modifying the HOPG surface was developed that enabled the adsorption of DNA and DNA-TV complexes onto this surface. On mica, both purified DNA and DNA-TV complexes were shown to undergo significant structural distortions: DNA molecules decrease in height and DNA-TP displays substantial changes in the shape of its circular compact structures. Use of the HOPG support helps preserve the structural integrity of the complexes and increase the measured height of DNA molecules up to 2 nm. AFM with the HOPG support was shown to efficiently reveal the particular points of the complexes where, according to known models of their organization, a great number of bent DNA fibers meet. These results provide additional information on DNA organization in its complexes with TV and are also of methodological interest, since the use of the modified HOPG may widen the possibilities of AFM in studying DNA and its complexes with various ligands.     

Comparing four different approaches for the determination of inter‐residue interactions provides insight for the structure prediction of helical membrane proteins

Studying inter‐residue interactions provides insight into the folding and stability of both soluble and membrane proteins and is essential for developing computational tools for protein structure prediction. As the first step, various approaches for elucidating such interactions within protein structures have been proposed and proven useful. Since different approaches may grasp different aspects of protein structural folds, it is of interest to systematically compare them. In this work, we applied four approaches for determining inter‐residue interactions to the analysis of three distinct structure datasets of helical membrane proteins and compared their correlation to the three individual quality measures of structures in these datasets. These datasets included one of 35 structures of rhodopsin receptors and bacterial rhodopsins determined at various resolutions, one derived from the HOMEP benchmark dataset previously reported, and one comprising of 139 homology models. It was found that the correlation between the average number of inter‐residue interactions obtained by applying the four approaches and the available structure quality measures varied quite significantly among them. The best correlation was achieved by the approach focusing exclusively on favorable inter‐residue interactions. These results provide interesting insight for the development of objective quality measure for the structure prediction of helical membrane proteins. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 547–556, 2009. 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     

Rational shape engineering of the filamentous protein γ prefoldin through incremental gene truncation

An enticing possibility in nanotechnology is to use proteins as templates for the positioning of molecules in regular patterns with nanometer precision over large surface areas. However, the ability to redesign protein quaternary structure to construct new shapes remains underdeveloped. In the present work, we have engineered the dimensions of a filamentous protein, the γ prefoldin (γ PFD) from the hyperthermophile Methanocaldococcus jannaschii, and have achieved controllable attachment of filaments in a specific orientation on a carbon surface. Four different constructs of γ PFD were generated in which the coiled coils extending from the association domain are progressively truncated. Three of the truncation constructs form well‐defined filaments with predictable dimensions according to transmission electron microscopy. Two of these constructs had 2D persistence lengths similar to that of γ PFD at 300–740 nm. In contrast, the 2D persistence length of the shortest truncation mutant was 3500 nm, indicating that the filament adsorbs along a different axis than the other constructs with its two rows of coiled coils facing out from the surface. The elastic moduli of the filaments range from 0.7–2.1 GPa, similar to rigid plastics and within the lower limit for proteins whose primary intermolecular interaction is hydrogen bonding. These results demonstrate a versatile approach for controlling the overall dimensions and surface orientation of protein filaments, and expand the toolbox by which to tune two overall dimensions in protein space for the creation of templated materials over a wide variety of conditions. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 496–503, 2009. 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     

Adsorption of DNA to mica mediated by divalent counterions: a theoretical and experimental study

The adsorption of DNA molecules onto a flat mica surface is a necessary step to perform atomic force microscopy studies of DNA conformation and observe DNA-protein interactions in physiological environment. However, the phenomenon that pulls DNA molecules onto the surface is still not understood. This is a crucial issue because the DNA/surface interactions could affect the DNA biological functions. In this paper we develop a model that can explain the mechanism of the DNA adsorption onto mica. This model suggests that DNA attraction is due to the sharing of the DNA and mica counterions. The correlations between divalent counterions on both the negatively charged DNA and the mica surface can generate a net attraction force whereas the correlations between monovalent counterions are ineffective in the DNA attraction. DNA binding is then dependent on the fractional surface densities of the divalent and monovalent cations, which can compete for the mica surface and DNA neutralizations. In addition, the attraction can be enhanced when the mica has been pretreated by transition metal cations (Ni(2+), Zn(2+)). Mica pretreatment simultaneously enhances the DNA attraction and reduces the repulsive contribution due to the electrical double-layer force. We also perform end-to-end distance measurement of DNA chains to study the binding strength. The DNA binding strength appears to be constant for a fixed fractional surface density of the divalent cations at low ionic strength (I < 0.1 M) as predicted by the model. However, at higher ionic strength, the binding is weakened by the screening effect of the ions. Then, some equations were derived to describe the binding of a polyelectrolyte onto a charged surface. The electrostatic attraction due to the sharing of counterions is particularly effective if the polyelectrolyte and the surface have nearly the same surface charge density. This characteristic of the attraction force can explain the success of mica for performing single DNA molecule observation by AFM. In addition, we explain how a reversible binding of the DNA molecules can be obtained with a pretreated mica surface.     

Effect of Supporting Substrates on the Structure of DNA and DNA–Trivaline Complexes Studied by Atomic Force Microscopy

Linear DNA, circular DNA, and circular DNA complexes with trivaline (TV), a synthetic oligopeptide, were imaged by atomic force microscopy (AFM) using mica as a conventional supporting substrate and modified highly ordered pyrolytic graphite (HOPG) as an alternative substrate. A method of modifying the HOPG surface was developed that enabled the adsorption of DNA and DNA–TV complexes onto this surface. On mica, both purified DNA and DNA–TV complexes were shown to undergo significant structural distortions: DNA molecules decrease in height and DNA–TV displays substantial changes in the shape of its circular compact structures. Use of the HOPG support helps preserve the structural integrity of the complexes and increase the measured height of DNA molecules up to 2 nm. AFM with the HOPG support was shown to efficiently reveal the particular points of the complexes where, according to known models of their organization, a great number of bent DNA fibers meet. These results provide additional information on DNA organization in its complexes with TV and are also of methodological interest, since the use of the modified HOPG may widen the possibilities of AFM in studying DNA and its complexes with various ligands.     

Uncover the conserved property underlying sequence‐distant and structure‐similar proteins

It is widely accepted that a protein's sequence determines its structure. The surprising finding that proteins of distant sequence can adopt similar 3D structures has raised interesting questions regarding underlying conserved properties that are essential for protein folding and stability. Uncovering the conserved properties may shed light on the folding mechanism of proteins and help with the development of computational tools for protein structure prediction. We compiled and analyzed a structure pair dataset of 66 high‐resolution and low sequence identity (16–38%) soluble proteins. Structure deviation for each pair was confirmed by calculating its C_α SiMax value and comparing its potential energy per residue. Analysis of favorable inter‐residue interactions for each structure pair indicated that the average number of inter‐residue interactions within each structure represents a conserved feature of homologous structures of distant sequence. Detailed comparison of individual types of interactions showed that the average number of either hydrophobic or hydrogen bonding interactions remains unchanged for each structure pair. These findings should be of help to improving the quality of homology models based on templates of low sequence identity, thus broadening the application of homology modeling techniques for protein studies. © 2009 Wiley Periodicals, Inc. Biopolymers 93: 340–347, 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     

Fate of prions in soil: adsorption kinetics of recombinant unglycosylated ovine prion protein onto mica in laminar flow conditions and subsequent desorption

Prions can be disseminated in soils. Their interaction with soil minerals is a key factor for the assessment of risks associated with the transport of their infectivity. We did not examine here the infectivity itself but the adsorption kinetics of an ovine recombinant prion protein (ovine PrPrec), as a noninfectious model protein, on muscovite mica, a phyllosilicate with surface properties analogous to soil clays, in conditions of laminar flow through a channel. The protein was labeled with (125)I, and its adsorption examined between pH 4.0 and 9.0. At wall shear rate 100 s(-1), we found the process to be controlled mainly by transport at the beginning of the adsorption process. Additional experiments at 1000 s(-1) (pH 5 and 6) determined that the diffusion coefficient was in accordance with the hydrodynamic radius measured by size exclusion chromatography. The pseudo-plateau of the interfacial concentration with time was compatible with more than a monolayer and suggests the presence of aggregates. Desorption was not observed in the presence of buffer between pH 4 and 9 and sheep plasma, while the addition of alkaline detergent or 10(-1) M NaOH allowed an almost complete removal from the interface. The ensemble of results suggests that the largely irreversible adsorption of the ovine PrPrec onto mica is mainly due to electrostatic attraction between the protein and the highly negatively charged mica surface. Possible consequences for the mode of dissemination of prion proteins in soils are indicated.     

Enzymatic activity and thermal stability of metallo proteins in hydrated ionic liquids

Hydrated choline dihydrogen phosphate (Hy[ch][dhp]) containing 30 wt% water was investigated as a novel protein solvent. The Hy[ch][dhp] dissolved some metallo proteins (cytochrome c, peroxidase, ascorbate oxidase, azurin, pseudoazurin and fructose dehydrogenase) without any modification. These proteins retained the surroundings of the active site after dissolution in Hy[ch][dhp]. Some metallo proteins were found to retain their activity in the Hy[ch][dhp]. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 1093–1099, 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     

Adsorption of viral matrix protein M1 in acidic medium

Adsorption of viral matrix protein M1 on the self-assembled monolayer of carboxyhexadecanthiol molecules simulating the surface of the cell membrane was studied by surface plasmon resonance refractometry technique. It was shown that in the acidic medium (pH 4.0) the fraction of irreversibly adsorbed protein increases with time. The protein formed a monolayer on the surface in concentration range from 50 to 500 nM. It was found that the amount of the adsorbed protein increased more than 3 times in this range. An important observation is that even at the lowest concentrations of the protein its molecules totally occupied the entire surface of the substrate, and a further protein addition did not lead to its further adsorption. To explain this phenomena, it was suggested that the number of M1 bonds with the surface increases during the adsorption, which leads to spreading of the protein molecules. Apparently, this effect is caused by the intrinsic disorder of the C-domain of the protein. It is hypothesized that the disassembly of the protein-lipid envelope of the influenza virus in the acidic medium does not result from desorption of the M1, but it is caused by the weakening of protein-protein bonds.     

PM-IRRAS investigation of the interaction of serum albumin and fibrinogen with a biomedical-grade stainless steel 316LVM surface

Polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) was applied to investigate the interaction of bovine serum albumin (BSA) and fibrinogen with a biomedical-grade 316LVM stainless steel surface, in terms of the adsorption thermodynamics and adsorption-induced secondary structure changes of the proteins. Highly negative apparent Gibbs energy of adsorption values revealed a spontaneous adsorption of both proteins onto the surface, accompanied by significant changes in their secondary structure. It was determined that, at saturated surface coverages, lateral interactions between the adsorbed BSA molecules induced rather extensive secondary structure changes. Fibrinogen's two coiled coils appeared to undergo negligible secondary structure changes upon adsorption of the protein, while large structural rearrangements of the protein's globular domains occurred upon adsorption. The secondary structure of adsorbed fibrinogen was not influenced by lateral interactions between the adsorbed fibrinogen molecules. PM-IRRAS was deemed to be viable for investigating protein adsorption and for obtaining information on adsorption-induced changes in their secondary structures.     

Dissecting membrane protein architecture: An annotation of structural complexity

α‐Helical membrane proteins exist in an anisotropic environment which strongly influences their folding, stability, and architecture, which is far more complex than a simple bundle of transmembrane helices, notably due to helix deformations, prosthetic groups and extramembrane structures. However, the role and the distribution of such heterogeneity in the supra molecular organization of membrane proteins remains poorly investigated. Using a nonredundant subset of α‐helical membrane proteins, we have annotated and analyze the statistics of several types of new elements such as incomplete helices, intramembrane loops, helical extensions of helical transmembrane domains, extracellular loops, and helices lying parallel to the membrane surface. The relevance of the annotation scheme was studied using residue composition, statistics, physical chemistry, and symmetry of their distribution in relation to the immediate membrane environment. Calculation of hydrophobicity using different scales show that different structural elements appear to have affinities coherent with their position in the membrane. Examination of the annotation scheme suggests that there is considerable information content in the amino acid compositions of the different elements suggesting that it might be useful for structural prediction. More importantly, the proposed annotation will help to decipher the complex hierarchy of interactions involved in membrane protein architecture. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 815–829, 2009. 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     

Interplay between protein homeostasis networks in protein aggregation and proteotoxicity

The misfolding and aggregation of disease proteins is characteristic of numerous neurodegenerative diseases. Particular neuronal populations are more vulnerable to proteotoxicity while others are more apt to tolerate the misfolding and aggregation of disease proteins. Thus, the cellular environment must play a significant role in determining whether disease proteins are converted into toxic or benign forms. The endomembrane network of eukaryotes divides the cell into different subcellular compartments that possess distinct sets of molecular chaperones and protein interaction networks. Chaperones act as agonists and antagonists of disease protein aggregation to prevent the accumulation of toxic intermediates in the aggregation pathway. Interacting partners can also modulate the conformation and localization of disease proteins and thereby influence proteotoxicity. Thus, interplay between these protein homeostasis network components can modulate the self‐association of disease proteins and determine whether they elicit a toxic or benign outcome. © 2009 Wiley Periodicals, Inc. Biopolymers 93: 229–236, 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     

Importance of the spatial display of charged residues in heparin–peptide interactions

Many studies have examined consensus sequences required for protein‐glycosaminoglycan interactions. Through the synthesis of helical heparin binding peptides, this study probes the relationship between spatial arrangement of positive charge and heparin binding affinity. Peptides with a linear distribution of positive charge along one face of the α‐helix had the highest affinity for heparin. Moving the basic residues away from a single face resulted in drastic changes in heparin binding affinity of up to three orders of magnitude. These findings demonstrate that amino acid sequences, different from the known heparin binding consensus sequences, will form high affinity protein‐heparin binding interactions when the charged residues are aligned linearly. © 2009 Wiley Periodicals, Inc. Biopolymers 93: 290–298, 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