Induction of Peptide Bond Dipoles Drives Cooperative Helix Formation in the (AAQAA)3 Peptide

Cooperativity is a central feature in the formation of secondary structures in proteins. However, the driving forces behind this cooperativity are poorly understood. The present work shows that the cooperativity of helix formation in the acetyl-(AAQAA)₃-NH₂ peptide is significantly enhanced using an empirical force field that explicitly includes the treatment of electronic polarizability. Polarizable simulations yield helical content consistent with experimental measurements and indicate that the dependence of helical content on temperature is improved over additive models, though further sampling is required to fully validate this conclusion. Cooperativity is indicated by the peptide sampling either the coiled state or long helices with relatively low populations of short helices. The cooperativity is shown to be associated with enhanced dipole moments of the peptide backbone upon helix formation. These results indicate the polarizable force field to more accurately model peptide-folding cooperativity based on its physically realistic treatment of electronic polarizability.     

Peptide design: Crystal structure of a helical peptide module attached to a potentially nonhelical amino terminal segment

The peptide Boc-Gly-Dpg-Gly-Val-Ala-Leu-Aib-Val-Ala-Leu-OMe has been designed to examine the structural consequences of placing a short segment with a low helix propensity at the amino terminus of a helical heptapeptide module. The Gly-Dpg-Gly segment is a potential connecting element in the synthetic construction of a helix-linker-helix motif. Crystal parameters for the peptide are P2₁, a = 8.651(3) Å, b = 46.826(13) Å, c = 16.245 Å, β = 90.13(3)*, Z = 4; 2 independent molecules/asymmetric unit. The structure reveals almost identical conformations for the two independent molecules. The backbone is completely helical for residues 2–9, with one 4 → 1 hydrogen bond and six 5 → 1 hydrogen bonds. The α,α-di-n-propylglycine residue adopts a helical conformation. Gly(1) adopts an extended conformation resulting in a nonhelical N-terminus, with the Boc group swinging away from the helix. The lateral association of helices in the b axis direction is unusual in that the helix axes are directed up or down (parallel or antiparallel) by pairs: ↓↓↑↑↓↓, etc. © 1996 John Wiley & Sons, Inc.     

Design of stable α‐helices using global sequence optimization

The rational design of peptide and protein helices is not only of practical importance for protein engineering but also is a useful approach in attempts to improve our understanding of protein folding. Recent modifications of theoretical models of helix‐coil transitions allow accurate predictions of the helix stability of monomeric peptides in water and provide new possibilities for protein design. We report here a new method for the design of α‐helices in peptides and proteins using AGADIR, the statistical mechanical theory for helix‐coil transitions in monomeric peptides and the tunneling algorithm of global optimization of multidimensional functions for optimization of amino acid sequences. CD measurements of helical content of peptides with optimized sequences indicate that the helical potential of protein amino acids is high enough to allow formation of stable α‐helices in peptides as short as of 10 residues in length. The results show the maximum achievable helix content (HC) of short peptides with fully optimized sequences at 5 °C is expected to be ～70–75%. Under certain conditions the method can be a powerful practical tool for protein engineering. Unlike traditional approaches that are often used to increase protein stability by adding a few favorable interactions to the protein structure, this method deals with all possible sequences of protein helices and selects the best one from them. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.     

The sequence TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase displays structural ambivalence and interconverts between alpha-helical and beta-hairpin conformations mediated by collapsed conformational states.

The peptide TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase adopts a helical conformation in the crystal structure and is a site for two hydrated helical segments, which are thought to be helical folding intermediates. Overlapping sequences of four to five residues from the peptide, sample both helical and strand conformations in known protein structures, which are dissimilar to glyceraldehyde-3-phosphate dehydrogenase suggesting that the peptide may have a structural ambivalence. Molecular dynamics simulations of the peptide sequence performed for a total simulation time of 1.2 micros, starting from the various initial conformations using GROMOS96 force field under NVT conditions, show that the peptide samples a large number of conformational forms with transitions from alpha-helix to beta-hairpin and vice versa. The peptide, therefore, displays a structural ambivalence. The mechanism from alpha-helix to beta-hairpin transition and vice versa reveals that the compact bends and turns conformational forms mediate such conformational transitions. These compact structures including helices and hairpins have similar hydrophobic radius of gyration (Rgh) values suggesting that similar hydrophobic interactions govern these conformational forms. The distribution of conformational energies is Gaussian with helix sampling lowest energy followed by the hairpins and coil. The lowest potential energy of the full helix may enable the peptide to take up helical conformation in the crystal structure of the glyceraldehyde-3-phosphate dehydrogenase, even though the peptide has a preference for hairpin too. The relevance of folding and unfolding events observed in our simulations to hydrophobic collapse model of protein folding are discussed.     

High-Resolution Crystal Structures of Protein Helices Reconciled with Three-Centered Hydrogen Bonds and Multipole Electrostatics

Theoretical and experimental evidence for non-linear hydrogen bonds in protein helices is ubiquitous. In particular, amide three-centered hydrogen bonds are common features of helices in high-resolution crystal structures of proteins. These high-resolution structures (1.0 to 1.5 Å nominal crystallographic resolution) position backbone atoms without significant bias from modeling constraints and identify Φ = -62°, ψ = -43 as the consensus backbone torsional angles of protein helices. These torsional angles preserve the atomic positions of α-β carbons of the classic Pauling α-helix while allowing the amide carbonyls to form bifurcated hydrogen bonds as first suggested by Némethy et al. in 1967. Molecular dynamics simulations of a capped 12-residue oligoalanine in water with AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications), a second-generation force field that includes multipole electrostatics and polarizability, reproduces the experimentally observed high-resolution helical conformation and correctly reorients the amide-bond carbonyls into bifurcated hydrogen bonds. This simple modification of backbone torsional angles reconciles experimental and theoretical views to provide a unified view of amide three-centered hydrogen bonds as crucial components of protein helices. The reason why they have been overlooked by structural biologists depends on the small crankshaft-like changes in orientation of the amide bond that allows maintenance of the overall helical parameters (helix pitch (p) and residues per turn (n)). The Pauling 3.6₁₃ α-helix fits the high-resolution experimental data with the minor exception of the amide-carbonyl electron density, but the previously associated backbone torsional angles (Φ, Ψ) needed slight modification to be reconciled with three-atom centered H-bonds and multipole electrostatics. Thus, a new standard helix, the 3.6_13/10-, Némethy- or N-helix, is proposed. Due to the use of constraints from monopole force fields and assumed secondary structures used in low-resolution refinement of electron density of proteins, such structures in the PDB often show linear hydrogen bonding.     

Inclusion of Many-Body Effects in the Additive CHARMM Protein CMAP Potential Results in Enhanced Cooperativity of α-Helix and β-Hairpin Formation

Folding simulations on peptides and proteins using empirical force fields have demonstrated the sensitivity of the results to details of the backbone potential. A recently revised version of the additive CHARMM protein force field, which includes optimization of the backbone CMAP potential to achieve good balance between different types of secondary structure, correcting the α-helical bias present in the former CHARMM22/CMAP energy function, is shown to result in improved cooperativity for the helix-coil transition. This is due to retention of the empirical corrections introduced in the original CMAP to reproduce folded protein structures—corrections that capture many-body effects missing from an energy surface fitted to gas phase calculations on dipeptides. The experimental temperature dependence of helix formation in (AAQAA)₃ and parameters for helix nucleation and elongation are in much better agreement with experiment than those obtained with other recent force fields. In contrast, CMAP parameters derived by fitting to a vacuum quantum mechanical surface for the alanine dipeptide do not reproduce the enhanced cooperativity, showing that the empirical backbone corrections, and not some other feature of the force field, are responsible. We also find that the cooperativity of β-hairpin formation is much improved relative to other force fields we have studied. Comparison with (ϕ,ψ) distributions from the Protein Data Bank further justifies the inclusion of many-body effects in the CMAP. These results suggest that the revised energy function will be suitable for both simulations of unfolded or intrinsically disordered proteins and for investigating protein-folding mechanisms.     

Conformational preferences of a short Aib/Ala‐based water‐soluble peptide as a function of temperature

The amino acid Aib predisposes a peptide to be helical with context‐dependent preference for either 3₁₀‐ or α‐ or a mixed helical conformation. Short peptides also show an inherent tendency to be unfolded. To characterize helical and unfolded states adopted by water‐soluble Aib‐containing peptides, the conformational preference of Ac‐Ala‐Aib‐Ala‐Lys‐Ala‐Aib‐Lys‐Ala‐Lys‐Ala‐Aib‐Tyr‐NH₂ was determined by CD, NMR and MD simulations as a function of temperature. Temperature‐dependent CD data indicated the contribution of two major components, each an admixture of helical and extended/polyproline II structures. Both right‐ and left‐handed helical conformations were detected from deconvolution of CD data and ¹³C NMR experiments. The presence of a helical backbone, more pronounced at the N‐terminal, and a temperature‐induced shift in α‐helix/3₁₀‐helix equilibrium, more pronounced at the C‐terminal, emerged from NMR data. Starting from polyproline II, the N‐terminal of the peptide folded into a helical backbone in MD simulations within 5 ns at 60°C. Longer simulations showed a mixed‐helical backbone to be stable over the entire peptide at 5°C while at 60°C the mixed‐helix was either stable at the N‐terminus or occurred in short stretches through out the peptide, along with a significant population of polyproline II. Our results point towards conformational heterogeneity of water‐soluble Aib‐based peptide helices and the associated subtleties. The problem of analyzing CD and NMR data of both left‐ and right‐handed helices are discussed, especially the validity of the ellipticity ratio [θ]₂₂₂/[θ]₂₀₇, as a reporter of α‐/3₁₀‐ population ratio, in right‐ and left‐handed helical mixtures. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Helix stability of oligoglycine,oligoalanine, and oligo‐β‐alanine dodecamers reflected by hydrogen‐bond persistence

Helices are important structural/recognition elements in proteins and peptides. Stability and conformational differences between helices composed of α‐ and β‐amino acids as scaffolds for mimicry of helix recognition has become a theme in medicinal chemistry. Furthermore, helices formed by β‐amino acids are experimentally more stable than those formed by α‐amino acids. This is paradoxical because the larger sizes of the hydrogen‐bonding rings required by the extra methylene groups should lead to entropic destabilization. In this study, molecular dynamics simulations using the second‐generation force field, AMOEBA (Ponder, J.W., et al., Current status of the AMOEBA polarizable force field. J Phys Chem B, 2010. 114 (8): p. 2549–64.) explored the stability and hydrogen‐bonding patterns of capped oligo‐β‐alanine, oligoalanine, and oligoglycine dodecamers in water. The MD simulations showed that oligo‐β‐alanine has strong acceptor+2 hydrogen bonds, but surprisingly did not contain a large content of 3₁₂‐helical structures, possibly due to the sparse distribution of the 3₁₂‐helical structure and other structures with acceptor+2 hydrogen bonds. On the other hand, despite its backbone flexibility, the β‐alanine dodecamer had more stable and persistent <3.0 Å hydrogen bonds. Its structure was dominated more by multicentered hydrogen bonds than either oligoglycine or oligoalanine helices. The 3₁ (PII) helical structure, prevalent in oligoglycine and oligoalanine, does not appear to be stable in oligo‐β‐alanine indicating its competition with other structures (stacking structure as indicated by MD analyses). These differences are among the factors that shape helical structural preferences and the relative stabilities of these three oligopeptides. Proteins 2014; 82:3043–3061. © 2014 Wiley Periodicals, Inc.     

Conformation and interactions of uteroglobin fragments 4–14 and 49–65 in aqueous solution containing surfactant micelles

The conformation of two fragments of rabbit uteroglobin is described. The peptides are PRFAHVIENLL and PQTTRENIMKLTEKIVK, corresponding to helices I and IV in the crystal structure. CD shows that both peptides interact with sodium dodecyl sulfate (SDS) micelles and change their conformation to an α-helix. The helical content estimated from the CD band at 222 nm is about 40% in each peptide. Surface tension measurements show that both peptides lower the critical micellar concentration (cmc) of SDS, with a more dramatic effect in the case of helix I. This peptide by itself acts as a surfactant, and is able to interact with SDS even below the observed cmc, forming β aggregates. Proton magnetic resonance (¹H-nmr) suggests that flexible helices are present. The longest helical stretches compatible with ¹H-nmr data extend from Phe⁶ to Leu¹⁴ for helix I and from Arg⁵³ to Ile⁶³ for helix IV. © 1993 John Wiley & Sons, Inc.     

Stable interactions between the transmembrane domains of the adenosine A2A receptor

G-protein-coupled receptors (GPCRs) must properly insert and fold in the membrane to adopt a stable native structure and become biologically active. The interactions between transmembrane (TM) helices are believed to play a major role in these processes. Previous studies in our group showed that specific interactions between TM helices occur, leading to an increase in helical content, especially in weakly helical TM domains, suggesting that helix–helix interactions in addition to helix–lipid interactions facilitate helix formation. They also demonstrated that TM peptides interact in a similar fashion in micelles and lipid vesicles, as they exhibit relatively similar thermal stability and α-helicity inserted in SDS micelles to that observed in liposomes. In this study, we perform an analysis of pairwise interactions between peptides corresponding to the seven TM domains of the human A_2A receptor (A_2AR). We used a combination of Förster resonance energy transfer (FRET) measurement and circular dichroism (CD) spectroscopy to detect and analyze these interactions in detergent micelles. We found that strong and specific interactions occur in only seven of the 28 possible peptide pairs. Furthermore, not all interactions, identified by FRET, lead to a change in helicity. Our results identify stabilizing contacts that are likely related to the stability of the receptor and that are consistent with what is known about the three-dimensional structure and stability of rhodopsin and the β₂ adrenergic receptor.     

Interaction of an Amphiphilic Peptide with a Phospholipid Bilayer Surface by Molecular Dynamics Simulation Study

Abstract

Corticotropin-releasing factor (CRF) is the principal neuroregulator of adrenocorticotropic hormone (ACTH) secretion. Previous experiments have demonstrated that CRF binds avidly to the surface of single egg phosphatidylcholine vesicles and its amphiphilic secondary structure might play an important role in the function. In this study, the interaction of the residues 13–41 in human CRF with the surface of a DOPC bilayer was investigated by molecular dynamics (MD) simulation in order to understand the role of the membrane surface in the formation of the amphiphilic α helix as well as to determine the effects of the peptide on the lipid bilayer. The model used included 60 DOPC molecules, 1 helical peptide (CRF_13–41) on the bilayer surface, and explicit waters of solvation in the lipid polar head group regions, together with constant-volume periodic boundary conditions in three dimensions. The MD simulation was carried out for 510 ps. In addition, CRF_13–41, initially in a helical form, was simulated in vacuo as a control. The results indicate that while it was completely unstable in vacuo, the peptide helical form was generally maintained on the bilayer surface, but with distortions near the terminal ends. The peptide was confined to the bilayer headgroup/water region, similar to that reported from neutron diffraction measurement of tripeptides bound to the phosphatidylcholine bilayer surface (Ref 1). The amphiphilicity of the peptide matched that of the bilayer headgroup environment, with the hydrophilic side oriented toward water and the hydrophobic side making contact with the bilayer hydrocarbon core. These results support the hypothesis that the amphiphilic environment of a membrane surface is important in the induction of peptide amphiphilic α-helical secondary structure. Two major effects of the peptide on the lipids were found: the first CH₂ segment in the lipid chains was significantly disordered and the lipid headgroup distribution was broadened towards the water region.     

Polynucleotides. 13. Stoichiometric and thermodynamic studies of polynucleotide helices with non-complementary residues

Stoichiometry and thermodynamic properties of polyadenylate–polyuridylate helices containing varying proportions of near-randomly distributed non-complementary uridine residues were charactrized from an analysis of their mixing curves and melting profiles measured at 259 nm and at appropriate longer wavelength isochromic points. The noncomplementary residues in this homopolymer–copolymer system (in which the homopolymer has the capacity to readjust with respect to the residues with which it is in opposition) show absolute preference for an extrahelical conformation even when situated in … AAUAA … sequences and must occur therefore as single loops. As the frequency of extrahelical residues in creases, the electrostatic energy of these complexes becomes greater, and is particularly severe for the three-stranded helices. Thus, an adenyl-ate-uridylate copolymer containing 35.2 mole percent uridine residues does not form a three-stranded complex with polyuridylate even in 0.7M Na⁺at O°C. The imperfections introduced into the helix lattice by extrahelical residues decrease the cooperativity of thermal denaturation as well as T_m. However, for the helices with extrahelical residues in low frequency (～1 per helix turn) only small increases in concentration of charge-neutralizing ions are required to bring T_m to the level of their perfect analogs. Two-stranded helices with a higher density of extra helical residues (～5 per helix turn) show [Na⁺] dependence of T_m characteristic of perfect three-stranded helices. These findings together with the absence of an effect of these imperfections on the hypochromicity per base-pair suggest only minimal disruption of helix continuity or distortion of stacking interactions that normally in volve the base pairs or triplets.     

Medium-dependence of the secondary structure of exendin-4 and glucagon-like-peptide-1.

Exendin-4 is a natural, 39-residue peptide first isolated from the salivary secretions of a Gila Monster (Heloderma suspectum) that has some pharmacological properties similar to glucagon-like-peptide-1 (GLP-1). This paper reports differences in the structural preferences of these two peptides. For GLP-1 in aqueous buffer (pH 3.5 or 5.9), the concentration dependence of circular dichroism spectra suggests that substantial helicity results only as a consequence of helix bundle formation. In contrast, exendin-4 is significantly helical in aqueous buffer even at the lowest concentration examined (2.3 microM). The pH dependence of the helical signal for exendin-4 indicates that helicity is enhanced by a more favorable sequence alignment of oppositely charged sidechains. Both peptides become more helical upon addition of either lipid micelles or fluoroalcohols. The stabilities of the helices were assessed from the thermal gradient of ellipticity (partial differential theta(221)/partial differential T values); on this basis, the exendin helix does not melt appreciably until temperatures significantly above ambient. The extent of helix formation for exendin-4 in aqueous buffer (and the thermal stability of the resulting helix) suggests the presence of a stable helix-capping interaction which was localized to the C-terminal segment by NMR studies of NH exchange protection. Solvent effects on the thermal stability of the helix indicate that the C-terminal capping interaction is hydrophobic in nature. The absence of this C-capping interaction and the presence of a flexible, helix-destabilizing glycine at residue 16 in GLP-1 are the likely causes of the greater fragility of the monomeric helical state of GLP-1. The intramolecular hydrophobic clustering in exendin-4 also appears to decrease the extent of helical aggregate formation.     

Structures of the transmembrane helices of the G-protein coupled receptor, rhodopsin.

An hypothesis is tested that individual peptides corresponding to the transmembrane helices of the membrane protein, rhodopsin, would form helices in solution similar to those in the native protein. Peptides containing the sequences of helices 1, 4 and 5 of rhodopsin were synthesized. Two peptides, with overlapping sequences at their termini, were synthesized to cover each of the helices. The peptides from helix 1 and helix 4 were helical throughout most of their length. The N- and C-termini of all the peptides were disordered and proline caused opening of the helical structure in both helix 1 and helix 4. The peptides from helix 5 were helical in the middle segment of each peptide, with larger disordered regions in the N- and C-termini than for helices 1 and 4. These observations show that there is a strong helical propensity in the amino acid sequences corresponding to the transmembrane domain of this G-protein coupled receptor. In the case of the peptides from helix 4, it was possible to superimpose the structures of the overlapping sequences to produce a construct covering the whole of the sequence of helix 4 of rhodopsin. As similar superposition for the peptides from helix 1 also produced a construct, but somewhat less successfully because of the disordering in the region of sequence overlap. This latter problem was more severe for helix 5 and therefore a single peptide was synthesized for the entire sequence of this helix, and its structure determined. It proved to be helical throughout. Comparison of all these structures with the recent crystal structure of rhodopsin revealed that the peptide structures mimicked the structures seen in the whole protein. Thus similar studies of peptides may provide useful information on the secondary structure of other transmembrane proteins built around helical bundles.     

Conformational preferences of helix foldamers of γ‐peptides based on 2‐(aminomethyl)cyclohexanecarboxylic acid

The conformational preferences of helix foldamers having different sizes of the H‐bonded pseudocycles have been studied for di‐ to octa‐γ^2,3‐peptides based on 2‐(aminomethyl)cyclohexanecarboxylic acid (γAmc₆) with a cyclohexyl constraint on the C^α–C^β bond using density functional methods. The helical structures of the γAmc₆ oligopeptides with homochiral configurations are known to be much stable than those with heterochiral configurations in the gas phase and in solution (chloroform and water). In particular, it is found that the (P/M)?2.5₁₄‐helices are most preferred in the gas phase and in chloroform, whereas the (P/M)?2.3₁₂‐helices become most populated in water due to the larger helix dipole moments. As the peptide sequence becomes longer, the helix propensities of 14‐ and 12‐helices are found to increase both in the gas phase and in solution. The γAmc₆ peptides longer than octapeptide are expected to exist as a mixture of 12‐ and 14‐helices with the similar populations in water. The mean backbone torsion angles and helical parameters of the 14‐helix foldamers of γAmc₆ oligopeptides are quite similar to those of 2‐aminocyclohexylacetic acid oligopeptides and γ^2,3,4‐aminobutyric acid tetrapeptide in the solid state, despite the different substituents on the backbone. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 87–95, 2014.     

Conformational features of a hexapeptide model Ac-TGAAKA-NH2 corresponding to a hydrated alpha helical segment from glyceraldehyde 3-phosphate dehydrogenase: implications for the role of turns in helix folding

Recent analysis of alpha helices in protein crystal structures, available in literature, revealed hydrated alpha helical segments in which, water molecule breaks open helix 5-->1 hydrogen bond by inserting itself, hydrogen bonds to both C=O and NH groups of helix hydrogen bond without disrupting the helix hydrogen bond, and hydrogen bonds to either C=O or NH of helix hydrogen bond. These hydrated segments display a variety of turn conformations and are thought to be 'folding intermediates' trapped during folding-unfolding of alpha helices. A role for reverse turns is implicated in the folding of alpha helices. We considered a hexapeptide model Ac-1TGAAKA6-NH2 from glyceraldehyde 3-phosphate dehydrogenase, corresponding to a hydrated helical segment to assess its role in helix folding. The sequence is a site for two 'folding intermediates'. The conformational features of the model peptide have been investigated by 1H 2D NMR techniques and quantum mechanical perturbative configuration interaction over localized orbitals (PCILO) method. Theoretical modeling largely correlates with experimental observations. Based upon the amide proton temperature coefficients, the observed d alpha n(i, i + 1), d alpha n(i, i + 2), dnn(i, i + 1), d beta n(i, i + 1) NOEs and the results from theoretical modeling, we conclude that the residues of the peptide sample alpha helical and neck regions of the Ramachandran phi, psi map with reduced conformational entropy and there is a potential for turn conformations at N and C terminal ends of the peptide. The role of reduced conformational entropy and turn potential in helix formation have been discussed. We conclude that the peptide sequence can serve as a 'folding intermediate' in the helix folding of glyceraldehyde 3-phosphate dehydrogenase.     

Structural basis of folding cooperativity in model proteins: insights from a microcanonical perspective

Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.     

Conformational change of the triple-helical structure. IV. Kinetics of the helix-folding of (Pro-Pro-Gly)n (n = 10, 12, and 15)

The kinetic curves of the helix-refolding of (PPG)_n (n = 10, 12, and 15) were analyzed with an all-or-none model. The Arrhenius plot of the overall rate constant of the helixfolding k_F showed a negative activation energy at high temperature. With the aid of a sequential model, it was concluded that the reason for the anomaly was the instability of short helices (shorter than seven helical units in a trimeric molecule), and/or the more rapid rates of helix-folding and helix-opening for shorter helices. The rate constant of the formation of one helical unit composed of three tripeptides at an end of a long helix was calculated to be 10^2–4 sec^?1. It was much smaller than that for other kinds of helices, such as an α helix (10¹⁰ sec^?1) or a double helix of nucleic acids (10^7–9sec^?1).