Theoretical study of volume changes associated with the helix-coil transition of an alanine-rich peptide in aqueous solution

The changes in the partial molar volume (PMV) associated with the conformational transition of an alanine-rich peptide AK16 from the alpha-helix structure to various random coil structures are calculated by the three-dimensional interaction site model (3D-RISM) theory coupled with the Kirkwood-Buff theory. The volume change is analyzed by decomposing it into contributions from geometry and hydration: the changes in the van der Waals, void, thermal, and interaction volume. The total change in the PMV is positive. This is primarily due to the growth of void space within the peptide, which is canceled in part by the volume reduction resulting from the increase in the electrostatic interaction between the peptide and water molecules. The changes in the void and thermal volume of the coil structures are widely distributed and tend to compensate each other. Additionally, the relations between the hydration volume components and the surface properties are investigated. We categorize coil structures into extended coils with the PMV smaller than helix and general coils with the PMV larger than helix. The pressure therefore can both stabilize and destabilize the coil structures. The latter seems to be a more proper model of random coil structures of the peptide.     

Sequential polypeptides: 5. Statistical mechanical analysis of helix-coil transition in sequential polypeptides

A statistical mechanical theory of the helix-coil transition in sequential polypeptides is developed assuming that the statistical weights of the Zimm-Bragg parameters of a given residue depend on the type of adjacent residues. In the case of a sequential polypeptide consisting of two kinds of residues, the theory describes the helix- coil transition of the polypeptide in terms of the Zimm-Bragg parameters associated with the corresponding residues. The theory is then used to determine this parameter, as a function of temperature, from experimental data for transition temperature as a function of solvent composition, for a series of sequential polypeptides consisting of Glu(OBzl) and Lys(Chz) residues in mixtures of dichloroacetic acid and 1,2-dichlorethane. This parameter is then combined with the Zimm-Bragg parameters for the parent homopolypeptides, and the theory used to predict helix coil transition curves which are in good agreement with the experimental ones for the sequential polypeptides studied.     

Minimum model for the alpha-helix-beta-hairpin transition in proteins

We present a minimal model for proteins, which is able to capture the structural conversion between the alpha-helix and beta-hairpin. In most regimes of the parameter space, the model produces a stable structure at a low temperature; in a few limited regimes of the parameter space, the model displays an beta-hairpin transition as the physical conditions vary. These variations include a perturbation on hydrogen bonding propensity at the middle of the modeled chain, or the change of the hydrophobicity of a designated pair along the chain. Using Monte Carlo simulations, we demonstrate the structural conversion by means of state diagrams, heat capacity maps, and free energy maps.     

Development of the multiple sequence approximation within the AGADIR model of α-helix formation: Comparison with Zimm-Bragg and Lifson-Roig formalisms

In this work we present the development of the multiple sequence approximation (AGADIRms) and the standard one-sequence approximation (AGADIRIs) within the framework of AGADIR's α-helix formation model. The extensive comparison between these new formulations and the original one [AGADIR; v. Muñoz and L. Serrano (1994),Nat. Struct. Biol., Vol. 1, pp. 399–409] indicates that the standard one-sequence approximation is virtually identical to the multiple sequence approximation, while the previously used residue partition function approximation [Muñoz and Serrano (1994); (1995), J. Mol. Biol., Vol. 245, pp. 275–296] is less precise. The calculations of the average helical content performed with AGADIR are precise for peptides of less than 30 residues and progressively diverge from the multiple sequence formulation for longer peptides. The helicity distribution of heteropolypeptides with less than 50% average helical content is also well described, while those of quasi-homopolymers with high helical content tend to be flattened. These inaccuracies lead to an underestimation of 0.017 kcal/mol for the mean-residue enthalpic contribution in AGADIR, as compared to AGADIRms and AGADIRIs. The other energy contributions to α-helix stability are not affected by the original statistical approximation. We also discuss the particularities of the model for α-helix formation utilized in AGADIR and compare it with the classical Zimm-Bragg and Lifson-Roig theories. Moreover, we develop the mathematical relationships between the basic AGADIR energy contributions and helix nucleation and elongation, which permit the quantitative comparison between formalisms. Remarkably, the comparison between AGADIRms and the Lifson-Roig formalism shows that, despite the differences on treating helix/coil cooperativity, both theories give virtually identical results when an equivalent set of parameters is used. This indicates that the helix/coil transition is a solid theory independent of the particularities of the model for α-helix formation. © 1997 John Wiley & Sons, Inc. Biopoly 41: 495–509, 1997.     

Contribution of secondary structure to the heat capacity and enthalpy distribution of the unfolded state in proteins.

We have recently shown that one can construct the enthalpy distribution for protein molecules from experimental knowledge of the temperature dependence of the heat capacity. For many proteins the enthalpy distribution evaluated at the midpoint of the denaturation transition (corresponding to the maximum in the heat capacity vs temperature curve) is broad and biphasic, indicating two different populations of molecules (native and unfolded) with distinctly different enthalpies. At temperatures above the denaturation point, the heat capacity for the unfolded state in many proteins is quite large and using the analysis just mentioned, we obtain a gaussian-like enthalpy distribution that is very broad. A large value of the heat capacity indicates that there are structural changes going on in the unfolded state above the transition temperature. In the present paper we investigate the origin of this large heat capacity by considering the presence of changing amounts of secondary structure (specifically, alpha-helix) in the unfolded state. For this purpose we use the empirical estimates of the Zimm-Bragg sigma and s factors for all of the native amino acids in water as determined by Scheraga and co-workers. Using myoglobin as an example, we calculate probability profiles and distribution functions for the total number of helix states in the specific-sequence molecule. Given the partition function for the specific-sequence molecule, we can then calculate a set of enthalpy moments for the molecule from which we obtain a good estimate of the enthalpy distribution in the unfolded state. This distribution turns out to be quite narrow when compared with the distribution obtained from the raw heat capacity data. We conclude that there must be other major structural changes (backbone and solvent) that are not accounted for by the inclusion of alpha-helix in the unfolded state.     

Helix-coil transition of PrP106-126: molecular dynamic study.

A set of 34 molecular dynamic (MD) simulations totaling 305 ns of simulation time of the prion protein-derived peptide PrP106-126 was performed with both explicit and implicit solvent models. The objective of these simulations is to investigate the relative stability of the alpha-helical conformation of the peptide and the mechanism for conversion from the helix to a random-coil structure. At neutral pH, the wild-type peptide was found to lose its initial helical structure very fast, within a few nanoseconds (ns) from the beginning of the simulations. The helix breaks up in the middle and then unwinds to the termini. The spontaneous transition into the random coil structure is governed by the hydrophobic interaction between His(111) and Val(122). The A117V mutation, which is linked to GSS disease, was found to destabilize the helix conformation of the peptide significantly, leading to a complete loss of helicity approximately 1 ns faster than in the wild-type. Furthermore, the A117V mutant exhibits a different mechanism for helix-coil conversion, wherein the helix begins to break up at the C-terminus and then gradually to unwind towards the N-terminus. In most simulations, the mutation was found to speed up the conversion through an additional hydrophobic interaction between Met(112) and the mutated residue Val(117), an interaction that did not exist in the wild-type peptide. Finally, the beta-sheet conformation of the wild-type peptide was found to be less stable at acidic pH due to a destabilization of the His(111)-Val(122), since at acidic pH this histidine is protonated and is unlikely to participate in hydrophobic interaction.     

Application of the nearest-neighbor Ising model to the helix-coil transition of polypeptides in mixed organic solvents.

Using the formalism of nearest-neighbor Ising model and assuming that the allowed states for a monomeric unity of a polypeptide chain in solutions containing strong acids are E (helix), C (coil), and CS (solvent-bonded coil), the partition function of the system was deduced analytically. Equations were obtained which permitted the prediction of the characteristic thermodynamic behavior of the helix–coil transition under these conditions. These equations were used to examine critically the possible correlations between experimental data obtained using different techniques. Particular attention was devoted to quantities called “transition enthalpies,” obtained from the slope of the transition curves at the point where the helix fraction is one-half (ΔH), or for measurements of the heat of solution of the polymer over the total range of solvent composition (ΔH), or from heat capacity measurements taken at various temperatures (ΔH). Literature data of ΔH(j = opt, sol, cal) for the system poly-γ-benzyl-L -glutamate in mixtures of dichloroacetic acid and 1,2-dichloroethane were carefully analyzed.     

Equilibrium thermal transitions of collagen model peptides

The folding of collagen in vitro is very slow and presents difficulties in reaching equilibrium, a feature that may have implications for in vivo collagen function. Peptides serve as good model systems for examining equilibrium thermal transitions in the collagen triple helix. Investigations were carried out to ascertain whether a range of synthetic triple-helical peptides of varying sequences can reach equilibrium, and whether the triple helix to unfolded monomer transition approximates a two-state model. The thermal transitions for all peptides studied are fully reversible given sufficient time. Isothermal experiments were carried out to obtain relaxation times at different temperatures. The slowest relaxation times, on the order of 10-15 h, were observed at the beginning of transitions, and were shown to result from self-association limited by the low concentration of free monomers, rather than cis-trans isomerization. Although the fit of the CD equilibrium transition curves and the concentration dependence of T(m) values support a two-state model, the more rigorous comparison of the calorimetric enthalpy to the van't Hoff enthalpy indicates the two-state approximation is not ideal. Previous reports of melting curves of triple-helical host-guest peptides are shown to be a two-state kinetic transition, rather than an equilibrium transition.     

Kinetics of the helix/coil transition of the collagen-like peptide (Pro-Hyp-Gly)10

This article measures the rates of folding and unfolding of the collagen-like peptide (Pro-Hyp-Gly)(10) over overlapping concentration and temperature ranges. The data allow calculation of the orders of the folding and the unfolding reactions, the effective Arrhenius activation energies, and numerical solution of the differential equation controlling the helix/coil transition during temperature scanning. The resulting predictions of helicity closely followed DSC measurements of the peptide in both up- and down-scanning modes, confirming the validity of the theoretical equations governing the kinetics of the folding/unfolding process. In both up- and down-scanning, three regions were apparent: "quasistatic," "rate," and "mixed." At very low scanning rates, a quasistatic region revealed a broad, short endotherm that was independent of scanning rate, but dependent on concentration and equal to the equilibrium endotherm. At high up-scanning rates, the "rate region" endotherm was sharp and tall and T(max) increased with scanning rate. In down-scanning, the "rate peak" was very broad and very short and T(max) decreased with scanning rate. The "mixed region" showed nascent "rate" and nascent "quasistatic" peaks, which were evident in the same up-scan under certain conditions. Comparison of (Pro-Hyp-Gly)(10) and (Pro-Pro-Gly)(10) showed that the higher temperature stability of (Pro-Hyp-Gly)(10) is due mainly to its slower rate of unfolding and higher activation energy.     

Generalized Poland-Scheraga model for DNA hybridization

The Poland-Scheraga (PS) model for the helix-coil transition of DNA considers the statistical mechanics of the binding (or hybridization) of two complementary strands of DNA of equal length, with the restriction that only bases with the same index along the strands are allowed to bind. In this article, we extend this model by relaxing these constraints: We propose a generalization of the PS model that allows for the binding of two strands of unequal lengths N1 and N2 with unrelated sequences. We study in particular (i) the effect of mismatches on the hybridization of complementary strands, (ii) the hybridization of noncomplementary strands (as resulting from point mutations) of unequal lengths N1 and N2. The use of a Fixman-Freire scheme scales down the computational complexity of our algorithm from O(N1(2)N2(2) to O(N1N2). The simulation of complementary strands of a few kilo base pairs yields results almost identical to the PS model. For short strands of equal or unequal lengths, the binding displays a strong sensitivity to mutations. This model may be relevant to the experimental protocol in DNA microarrays, and more generally to the molecular recognition of DNA fragments. It also provides a physical implementation of sequence alignments.     

alpha-helix formation: discontinuous molecular dynamics on an intermediate-resolution protein model.

An intermediate-resolution model of small, homogeneous peptides is introduced, and discontinuous molecular dynamics simulation is applied to study secondary structure formation. Physically, each model residue consists of a detailed three-bead backbone and a simplified single-bead side-chain. Excluded volume and hydrogen bond interactions are constructed with discontinuous (i.e., hard-sphere and square-well) potentials. Simulation results show that the backbone motion of the model is limited to realistic regions of Phi-Psi conformational space. Model polyalanine chains undergo a locally cooperative transition to form alpha-helices that are stabilized by backbone hydrogen bonding, while model polyglycine chains tend to adopt nonhelical structures. When side-chain size is increased beyond a critical diameter, steric interactions prevent formation of long alpha-helices. These trends in helicity as a function of residue type have been well documented by experimental, theoretical, and simulation studies and demonstrate the ability of the intermediate-resolution model developed in this work to accurately mimic realistic peptide behavior. The efficient algorithm used permits observation of the complete helix-coil transition within 15 min on a single-processor workstation, suggesting that simulations of very long times are possible with this model.     

Crystal structure of (Gly-Pro-Hyp)(9) : implications for the collagen molecular model

Collagens have long been believed to adopt a triple‐stranded molecular structure with a 10/3 symmetry (ten triplet units in three turns) and an axial repeat of 29 Å. This belief even persisted after an alternative structure with a 7/2 symmetry (seven triplet units in two turns) with an axial repeat of 20 Å had been proposed. The uncertainty regarding the helical symmetry of collagens is attributed to inadequate X‐ray fiber diffraction data. Therefore, for better understanding of the collagen helix, single‐crystal analyses of peptides with simplified characteristic amino acid sequences and similar compositions to collagens have long been awaited. Here we report the crystal structure of (Gly‐Pro‐Hyp)₉ peptide at a resolution of 1.45 Å. The repeating unit of this peptide, Gly‐Pro‐Hyp, is the most typical sequence present in collagens, and it has been used as a basic repeating unit in fiber diffraction analyses of collagen. The (Gly‐Pro‐Hyp)₉ peptide adopts a triple‐stranded structure with an average helical symmetry close to the ideal 7/2 helical model for collagen. This observation strongly suggests that the average molecular structure of collagen is not the accepted Rich and Crick 10/3 helical model but is a 7/2 helical conformation. © 2012 Wiley Periodicals, Inc. Biopolymers 97: 607–616, 2012.     

A thermodynamic model for the helix-coil transition coupled to dimerization of short coiled-coil peptides.

A simple thermodynamic formalism is presented to model the conformational transition between a random-coil monomeric peptide and a coiled-coil helical dimer. The coiled-coil helical dimer is the structure of a class of proteins also called leucine zipper, which has been studied intensively in recent years. Our model, which is appropriate particularly for short peptides, is an alternative to the theory developed by Skolnick and Holtzer. Using the present formalism, we discuss the multi-equilibriatory nature of this transition and provide an explanation for the apparent two-state behavior of coiled-coil formation when the helix-coil transition is coupled to dimerization. It is found that such coupling between multi-equilibria and a true two-state transition can simplify the data analysis, but care must be taken in using the overall association constant to determine helix propensities (w) of single residues. Successful use of the two-state model does not imply that the helix-coil transition is all-or-none. The all-or-none assumption can provide good numerical estimates when w is around unity (0.35 < or = w < or = 1.35), but when w is small (w < 0.01), similar estimations can lead to large errors. The theory of the helix-coil transition in denaturation experiments is also discussed.     

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56?Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.     

Helix-helix interconversion rates of short 13C-labeled helical peptides as measured by dynamic NMR spectroscopy

The rates at which a peptide hexamer and a peptide octamer interconvert between left- and right-handed helical forms in CD2Cl2 solution have been characterized by 13C dynamic NMR (DNMR) spectroscopy. The peptide esters studied are Fmoc-(Aib)n-OtBu (n = 6 and 8), where Fmoc is 9-fluorenylmethyoxycarbonyl and Aib is the strongly helix-forming residue alpha-aminoisobutyric acid. Because the Aib residue is itself achiral, homooligomers of this residue form a 50/50 mixture of enantiomeric 3(10)-helices in solution. It has been demonstrated (R.-P. Hummel, C. Toniolo, and G. Jung, Angewandte Chemie International Edition, 1987, Vol. 26, pp. 1150-1152) that oligomers of Aib interconvert on the millisecond timescale. We have performed lineshape analysis of 13C-NMR spectra collected for our peptides enriched with 13C at a single residue. Rate constants for the octamer range from 6 s(-1) at 196 K to about 56,500 s(-1) at 320 K. At all temperatures, the hexamer interconverts about three times faster than the octamer. Eyring plots of the data reveal experimentally indistinguishable DeltaH++ values for the hexamer and octamer of 37.8 +/- 0.6 and 37.6 +/- 0.4 kJ mol(-1) respectively. The difference in the rates of interconversion is dictated by entropic factors. The hexamer and octamer exhibit negative DeltaS++ values of -29.0(-1) +/- 2.5 and -37.3 +/- 1.7 J K(-1) mol(-1), respectively. A mechanism for the helix-helix interconversion is proposed. and calculated DeltaG++ values are compared to the estimate for a decamer undergoing a helix-helix interconversion.     

Oligopeptide-mediated helix stabilization of model peptides in aqueous solution.

Oligopeptide-mediated helix stabilization of peptides in hydrophobic solutions was previously found by NMR and CD spectroscopic studies. The oligopeptide included the hydrophobic amino acids found in its parent peptide and were interposed by relevant basic oracidic amino acids. The strength of the interactions depended on the amino acid sequences. However, no helix-stabilizing effect was seen for the peptides in phosphate buffer solution, because the peptides assumed a random-coil structure. In order to ascertain whether the helix-stabilizing effect of an oligopeptide on its parent peptide could operate in aqueous solution, model peptides EK17 (Ac-AEAAAAEAAAKAAAAKA-NH2) and IFM17 (Ac-AEAAAAEIFMKAAAAKA-NH2) that may assume an alpha-helix in aqueous solutions were synthesized. Interactions were examined between various oligopeptides (EAAAK, KAAAE, EIFMK, KIFME, KIFMK and EYYEE) and EK17 or IFM17 in phosphate buffer and in 80% trifluoroethanol (TFE)-20% H2O solutions by CD spectra. EAAAK had little effect on the secondary structures of EK17 in both buffer and TFE solutions, while KAAAE, which has the reverse amino acid sequence of EAAAK, had a marked helix-destabilizing effect on EK17 in TFE. EIFMK and KIFME were found to stabilize the alpha-helical structure of EK17 in phosphate buffer solutions, whereas KIFMK and EYYEE destabilized the alpha-helical structure of EK17. EIFMK and KIFME had no effect on IFM17, because unexpectedly, IFM17 had appreciable amounts of beta-sheet structure in buffer solution. It was concluded that in order for the helix-stabilizing (1) the model peptide, the alpha-helical conformation of which is to be stabilized, should essentially assume an alpha-helical structure by nature, and (2) the hydrophobicity of the side-chains of the oligopeptide should be high enough for the oligopeptide to perform stable specific side chain-side chain intermolecular hydrophobic interactions with the model peptide.     

Coil-helix transition of iota-carrageenan as a function of chain regularity

A series of iota-carrageenans containing different amounts of nu-carrageenan (0-23 monomer %) have been prepared from neutrally extracted carrageenan of Eucheuma denticulatum. nu-Carrageenan is the biochemical precursor of iota-carrageenan. The conformational order-disorder transition and rheological properties of these carrageenans were studied using optical rotation, rheometry, size exclusion chromatography coupled to multiangle laser light scattering, and high-sensitivity differential scanning calorimetry. The helix forming capacity of iota-carrageenan turns out to decrease monotonously with increasing amount of nu-units. In contrast, the rheological properties of iota-carrageenan are remarkably enhanced by the presence of a small amount of nu-units, yielding a maximum twofold increase in G' at 3% nu-units. It is concluded that the structure-forming capacity of iota-carrageenan, containing a small amount of nu-carrageenan, is significantly higher than that of pure iota-carrageenan. This phenomenon is explained in terms of the balance between the helical content and the number of cross-links between chains, taking into consideration the fact that nu-units introduce "kinks" in the chain conformation enabling neighboring chains to connect. Increasing amounts of nu-units increase the number of cross-links in the network, resulting in increased gel strength. On the other hand, a reduced length of the helical strands weakens the cross-links between the different chains and, consequently, the gel.     

Stacking and hydrogen bonding: DNA cooperativity at melting

By taking into account base-base stacking interactions we improve the Generalized Model of Polypeptide Chain (GMPC). Based on a one-dimensional Potts-like model with many-particle interactions, the GMPC describes the helix-coil transition in both polypeptides and polynucleotides. In the framework of the GMPC we show that correctly introduced nearest-neighbor stacking interactions against the background of hydrogen bonding lead to increased stability (melting temperature) and, unexpectedly, to decreased cooperativity (maximal correlation length). The increase in stability is explained as due to an additional stabilizing interaction (stacking) and the surprising decrease in cooperativity is seen as a result of mixing of contributions of hydrogen bonding and stacking.     

The role of alpha-, 3(10)-, and pi-helix in helix-->coil transitions

The conformational equilibrium between 3(10)- and alpha-helical structure has been studied via high-resolution NMR spectroscopy by Millhauser and coworkers using the MW peptide Ac-AMAAKAWAAKA AAARA-NH2. Their 750-MHz nuclear Overhauser effect spectroscopy (NOESY) spectra were interpreted to reflect appreciable populations of 3(10)-helix throughout the peptide, with the greatest contribution at the N and C termini. The presence of simultaneous alphaN(i,i + 2) and alphaN(i,i + 4) NOE cross-peaks was proposed to represent conformational averaging between 3(10)- and alpha-helical structures. In this study, we describe 25-nsec molecular dynamics simulations of the MW peptide at 298 K, using both an 8 A and a 10 A force-shifted nonbonded cutoff. The ensemble averages of both simulations are in reasonable agreement with the experimental helical content from circular dichroism (CD), the (3)J(HNalpha) coupling constants, and the 57 observed NOEs. Analysis of the structures from both simulations revealed very little formation of contiguous i --> i + 3 hydrogen bonds (3(10)-helix); however, there was a large population of bifurcated i --> i + 3 and i --> i + 4 alpha-helical hydrogen bonds. In addition, both simulations contained considerable populations of pi-helix (i --> i + 5 hydrogen bonds). Individual turns formed over residues 1-9, which we predict contribute to the intensities of the experimentally observed alphaN(i,i + 2) NOEs. Here we show how sampling of both folded and unfolded structures can provide a structural framework for deconvolution of the conformational contributions to experimental ensemble averages.