Helix-coil transition theory including long-range electrostatic interactions: application to globular proteins

An extension of the Zimm–Bragg two-state theory for the helix–coil transition in polypeptides, which takes into account the effect of peptide charge–dipole interactions on helix stability, is presented. This new theory incorporates these interactions in an expression that is parameterized on recently obtained experimental data on polypeptides for which electrostatic effects are known to influence helix content. Unlike previous two-state or multistate models, which are parameterized on protein x-ray data, the present theoretical treatment in independent of such protein data. The theoretical model is applied to a series of peptides derived from the C-peptide of ribonuclease A, which have been the object of recent spectroscopic studies. The new theoretical approach can account for most of the structural information derived from studies of these C-peptides, and for overall average helix probabilities that are close in magnitude to those observed for these polypeptides in solution. An application of this new formulation for the prediction of the locations of α-helices in globular proteins from their amino acid sequence is also presented.     

The contribution of residue ion pairs to the helical stability of a model peptide.

Comparative CD measurements were made on the model helical peptides acetylYEAAAKEAXAKEAAAKAamide and acetylYEAAAEKAXAKEAAAKAamide in which X represents a nonaromatic nonionic residue. The former peptide contains three potential i, i + 4 complementary ion pairs at neutral pH, while the latter peptide contains one potential complementary and two potential antagonistic i, i + 4 ion pairs. The effect of pH and ionic strength on the mean residue ellipticity of these peptides was measured at 222 nm and 0 degrees C. These measurements were analyzed assuming a common two-state helix/coil transition and only i, i, + 4 ion-pair interactions. The analyses suggest that the central ion pairs do modulate helical content while the peripheral ion pairs do not, presumably due to the location of the peripheral ion pairs in the frayed ends of the helix. The complementary central ion pair stabilizes the helix by about 0.4 kcal/mole and the antagonistic central ion pair destabilizes the helix by about 0.2 kcal/mole.     

Analysis of peptides for helical prediction

Two terminally blocked peptides, acetylAETAAAKFLRQHMamide and acetylAETSSSRYLRQHMamide, were obtained by solid-phase synthesis, purified by reversed-phase chromatography, and characterized by fast atom bombardment mass spectrometry. Both peptides were soluble in aqueous solutions and remained monomeric over the concentration range examined. Changes in the temperature, pH, and trifluoroethanol concentration of solutions of each peptide produced changes in the far-ultraviolet circular dichroic spectrum characteristic of a two-state helix/coil transition. The limiting mean residue ellipticity of the coil and helix form of each peptide was estimated by addition of the denaturant guanidinium chloride at elevated temperature and by addition of trifluoroethanol at subzero temperatures, respectively. The midpoint for the thermal transition of the peptide SSSRY is lowered by about 30 degrees C relative to that of peptide AAAKF, in qualitative agreement from predictions based on helix probabilities of amino acid residues. The magnitude of the change observed in the midpoint of the thermal transitions suggests that the effect of single amino acid replacements on helix formation should be experimentally measurable.     

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.     

Thermodynamic model of secondary structure for α-helical peptides and proteins

A thermodynamic model describing formation of α-helices by peptides and proteins in the absence of specific tertiary interactions has been developed. The model combines free energy terms defining α-helix stability in aqueous solution and terms describing immersion of every helix or fragment of coil into a micelle or a nonpolar droplet created by the rest of protein to calculate averaged or lowest energy partitioning of the peptide chain into helical and coil fragments. The α-helix energy in water was calculated with parameters derived from peptide substitution and protein engineering data and using estimates of nonpolar contact areas between side chains. The energy of nonspecific hydrophobic interactions was estimated considering each α-helix or fragment of coil as freely floating in the spherical micelle or droplet, and using water/cyclohexane (for micelles) or adjustable (for proteins) side-chain transfer energies. The model was verified for 96 and 36 peptides studied by ¹H-nmr spectroscopy in aqueous solution and in the presence of micelles, respectively ([set I] and [set 2]) and for 30 mostly α-helical globular proteins ([set 3]). For peptides, the experimental helix locations were identified from the published medium-range nuclear Overhauser effects detected by ¹H-nmr spectroscopy. For sets 1, 2, and 3, respectively, 93, 100, and 97% of helices were identified with average errors in calculation of helix boundaries of 1.3, 2.0, and 4.1 residues per helix and an average percentage of correctly calculated helix—coil states of 93, 89, and 81%, respectively. Analysis of adjustable parameters of the model (the entropy and enthalpy of the helix—coil transition, the transfer energy of the helix backbone, and parameters of the bound coil), determined by minimization of the average helix boundary deviation for each set of peptides or proteins, demonstrates that, unlike micelles, the interior of the effective protein droplet has solubility characteristics different from that for cyclohexane, does not bind fragments of coil, and lacks interfacial area. © 1997 John Wiley & Sons, Inc. Biopoly 42: 239–269, 1997     

Carbon-13 and proton NMR studies of helix-coil transition of poly(gamma-benzyl-L-glutamate).

The helix–coil conformational transition undergone by poly(γ-benzyl-L -glutamate) in solutions of trifluoroacetic acid and deuterated chloroform was studied by proton and carbon-13 nmr. The results indicate that in the case of the solvent-induced helix–coil transition, the side chain assumes a helical conformation before the backbone. In the thermally induced helix–coil transition, the results indicate the existence of an intermediate state, which is between the α-helix and random coil and is free from intramolecular hydrogen bonding.     

Helix–coil transitions in a simple polypeptide model

A simplified model of a polypeptide chain is described. Each residue is represented by a single interaction center. The energy of the chain and the force acting on each residue are given as a function of the residue coordinates. Terms to approximate the effect of solvent and the stabilization energy of helix formation are included. The model is used to study equilibrium and dynamical aspects of the helix–coil transition. The equilibrium properties examined include helix–coil equilibrium constants and their dependence on chain position. Dynamical properties are examined by a stochastic simulation of the Brownian motion of the chain in its solvent surroundings. Correlations in the motions of the residues are found to have an important influence on the helix–coil transition rates.     

On the double peak of NMR in the helix—coil transition region

To attempt to resolve the controversy over “fast” and “slow” helix–coil transition rates in polypeptides, nuclear magnetic resonance spectra were measured for monodisperse poly-γ-benzyl-L -glutamate (PBLG). These results were compared with simulated line spectra which were computed by taking the molecular-weight distribution into consideration. Broad but single peaks have been observed in 220 mHz nmr for the α-CH and NH proton resonance spectra in the transition region. The shape of the line changes with the extent of polydispersity. Assuming a fast conversion rate, a molecular model of the helix–coil transition simulates these results. Consequently, the double peak which has been observed in the nmr of polypeptides at the helix–coil transition region is shown to result from the polydispersity in molecular weight.     

Validity of the "two-state" hypothesis for conformational transitions of proteins

The theory, character, and properties of cooperative transitions are developed with special reference to the abrupt changes of state which occur in protein solutions. Comparisons of helix–coil processes and protein conformational reactions show that though cooperation dominates both of these processes, there are important differences. Tests of two types for the validity of the two-state approximation are presented with specific applications to proteins. Available experimental evidence demonstrates that the thermally induced reversible transitions of ribonuclease, α-chymotrypsin, and chymotrypsinogen A under conditions thus far examined are two-state processes.     

Effect of central-residue replacements on the helical stability of a monomeric peptide

The peptide acetylYEAAAKEARAKEAAAKAamide exhibits the dichroic features characteristic of a monomeric helix/coil transition in aqueous solution. Nineteen variants of this peptide each containing a different residue at position 9 were prepared by solid-phase peptide synthesis and purified by reversed-phase chromatography. The thermal dependence of the far-ultraviolet dichroic spectrum of each of these peptides except that containing proline is characteristic for an alpha-helix/coil transition. The relative stability of the helical forms of these peptides does not correlate with the preference of the variable amino acid to occupy a middle position in a protein helix. It is likely that the specific interactions of the variable residue with its local environment obscure any inherent preference of the residue to reside in an alpha-helix.     

Simulation of α-helix–coil transitions in simplified polyvaline: Equilibrium properties and brownian dynamics

A quantitative understanding of helix–coil dynamics will help explain their role in protein folding and in folded proteins. As a contribution to the understanding, the equilibrium and dynamical aspects of the helix–coil transition in polyvaline have been studied by computer simulation using a simplified model of the polypeptide chain. Each amino acid residue is treated as a single quasiparticle in an effective potential that approximates the potential of mean force in solution. The equilibrium properties examined include the helix–coil transition and its dependence on chain position and well depth at the coil–helix interface. A stochastic simulation of the Brownian motion of the chain in its solvent surroundings has been used to investigate dynamical properties. Time histories of the dihedral angles have been used to study the behavior of the helical structure. Auto and cross-correlation functions have been calculated from the time histories and from the state (helix or coil) functions of the residues with relaxation times of tens to hundreds of picoseconds. Helix–coil rate constants of tens of ns^?1 were found for both directions of the transition. © 1993 John Wiley & Sons, Inc.     

The role of PII conformations in the calculation of peptide fractional helix content.

Changes in the temperature, pH, ionic strength, or denaturant concentration of aqueous solutions of the monomeric non-alpha-helical peptide acetylYEAAAKEAPAKEAAAKAamide generate changes in its dichroic spectrum characteristic for a conformational transition. This transition has the characteristic features of a residue PII/unstructured conformational equilibrium in which PII denotes an extended left-handed helical conformation and unstructured denotes all the remaining conformations in a random coil ensemble. Replacement of the proline residue facilitates population of residues in an alpha-helical conformation. However, the ellipticity values for these non-proline peptides merge with the ellipticity of the proline peptide as the population of residues in the alpha-helix conformation is diminished. This convergence suggests that all residues in a host/guest peptide series of the same length share a common PII/unstructured conformational equilibrium in a given solvent. We propose that the fractional helix content of peptides within such a series may be estimated by using a two-state calculation in which the ellipticity for the non-alpha-helix conformations is provided by a peptide having a central proline guest residue.     

The effect of polydispersity on the nuclear magnetic resonance spectra of poly-gamma-benzyl-L-glutamate

The effect of poly dispersity on the nuclear magnetic resonance spectra of samples of poly-γ-benzyl-L -glutamateein the helix–random coil transition is studied. In the transitionregion the α-CH proton resonance shows two peaks whose behavior does not change appreciably upon fractionation by gel permeation chromatography. Theoretical spectra were computed with both a polydispersity model of the transition and a model for slow nucleationof helix from completely random coil molecules. The results suggest that the double peak behavior in the nmr spectra results from a slow rate of helix nucleation rather than polydispersity.     

Study of helix-coil transition of DNA by dielectric constant measurement

The thermal helix–coil transition of DNA was studied by means of dielectric constant measurements. The dielectric dispersion of native helical DNA is characterized by a large dielectric increment and a large relaxation time, whereas that of denatured coil DNA is characterized by a small dielectric increment and a small relaxation time. The dielectric dispersion of partially denatured DNA is of particular interest. At the intermediate stage of the helix–coil transition, dispersion curves which are different from either that of helix DNA or that of coil DNA appear. This is particularly pronounced for large DNA. This indicates the presence of an intermediate form of DNA. Flow birefringence measurements were carried out simultaneously. The negative birefringence of helical DNA diminishes as the helix–coil transition proceeds. However, the extinction angle remains constant, as long as it can be measured. These results indicate the absence of intermediate forms during the helix–coil transition. The discrepancy between dielectric and birefringence measurements can be resolved by assuming that the intermediate forms are not birefringent. The size distribution of native DNA and of the indicated intermediate form of DNA was studied. It is found that a logarithmic normal distribution function explains the distribution of size of DNA reasonably well.     

Correlation between computed conformational properties of cytochrome c peptides and their antigenicity in a T-lymphocyte proliferation assay

By means of conformational energy calculations, we previously showed that the antigenic strength of a series of oligopeptides (derived from the carboxyl terminal sequence of cytochrome c) in a T-lymphocyte proliferation assay depends on their ability to adopt the α-helix conformation. Using experimentally determined statistical weights (within the framework of the Zimm–Bragg theory for the helix–coil transition), here we present a simple free energy analysis of the ability of these peptides to adopt the α-helix conformation in water. The experimental statistical weights have been modified to include the effect of long-range charge–dipole interactions on helix stability. We find that there is a close correlation between the tendency of a peptide to adopt the α-helix conformation and its ability to stimulate antigen-primed T cells. The shortest peptide with a tendency to adopt the α-helix conformation is also the shortest one that exhibits antigenic activity. The rapid and simple method presented here can thus be used to predict relative antigenicities for different peptides derived from cytochrome c.     

Electric birefringence of poly-L-lysine hydrobromide in methanol-water mixtures and helix-coil transition induced by high electric fields

The electric birefringence of poly-L -lysine hydrobromide in methanol–water mixtures has been measured at 25 °C over a wide range of field strengths by use of the rectangular pulse technique. An abrupt change in the specific Kerr constant was observed between 87 and 90 vol % methanol, corresponding to the solvent-induced helix–coil transition. The specific Kerr constant increased rapidly with dilution in the random coil form, and more slowly in the helical conformation. The field strength dependence of the bire fringence at various concentrations, for both the helical and coil conformations, can be described by a common orientation function, which resembles the theoretical one for the case of permanent dipole moment orientation. This is interpreted in terms of the saturation of ion–atmosphere polarization. The optical anisotropy for the helical conformation was much larger than that for the coil form. Anomalous birefringence signals were observed above a critical field strength (about 5 kV/cm) in 90 vol % methanol. The birefringence passed through a maximum and began to decrease slowly before the pulse terminated, reaching a steady-state value. This steady-state value was closer to that of the coil in the coil in the limit of very high fields. The results indicate that a transition from the charged helix to the charged coil is induced by high electric fields in the transition region. This effect can be explained on the basis of the polarization mechanism proposed by Neumann and Katchalasky.     

Structure of aggregates and helix-coil transition of polypeptides by dielectric measurements. II. Poly-D,L-phenylalanine and poly-beta-benzyl-L-aspartate in chloroform-dichloroacetic acid mixtures

The dielectric absorption of poly-DL -phenylalanine and poly-γ-benzyl-L -aspartate (PLAB) was measured in very dilute solutions to determine the type of molecular association and to locate the helix–coil transition. Both polypeptides were present as associated helices in chloroform. The mode of aggregation, which was determined by measuring the dipole moment and the critical frequency, did not depend on the polarity of the side chain but rather on that of the solvent. In both polymers, the dissociation of the aggregates in chloroform was observed on addition of small amounts of dichloroacetic acid; further addition of the acid lead to the helix–coil transition. No second region of dielectric absorption that might be related to the kinetics of the transition was found during the helix–coil transition of PBLA.     

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.     

Dielectric dispersion of the -helix at the transition region to random coil

Dielectric studies have been carried out for the helix–coil transition of poly-β-benzyl-L -aspartate with m-cresol as a solvent. The transition of the solute molecules has been sharply reflected as a characteristic change in the dielectric dispersion curves in changing temperature. Two polarizations, one having a low and the other a high critical frequency, have appeared. According to theoretical considerations of a model of a broken helix, the former is found to come from the orientation. of helical sequences and the latter from the chemical relaxation due to the helix–coil transition. It also seems likely that the unfolded chain may have a polarizability which could not be neglected at the high-temperature side of the transition.