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.     

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.     

Comparison of alpha-helix stability in peptides having a negatively or positively charged residue block attached either to the N- or C-terminus of an alpha-helix: the electrostatic contribution and anisotropic stability of the alpha-helix

An estimation of the thermodynamic effects of a charged random coil, which is attached either to the N- or C-terminus of polyalanine, upon alpha-helix stability is attempted. A temperature-induced helix-coil transition of Ala20Lys20Phe and Lys20Ala20Phe was studied under various conditions of salt concentration and pH. By combining the results with previous ones for Ala20Glu20Phe and Glu20Ala20Phe, which have opposite electric charges to the present system [S. Ihara et al. (1982) Biopolymers 21, 131-145], the free energy of the coil to helix transition of the polyalanine block could be separated into two terms--one term for the electrostatic interaction of electric charges in the random-coil block with the alpha-helix dipole, and a second term for the intrinsic stability of the helix. The first term indicates the significance of the helix dipole-charge interactions, which affects the helix stability depending on the attaching side of the charged block and on the sign of the charges. This clearly shows the anisotropic stability of the alpha-helix. Furthermore, analysis of the dependence of these thermodynamic quantities on salt concentrations showed, assuming that the effect of the attached electric charges was symmetric (in other words, the absolute values of the electrostatic interaction terms were independent of the sign of electric charges), that the intrinsic stability of the alpha-helix was dependent on which side of the helix was attached to the random coil: a random coil attached to the N-terminus of the alpha-helix had little effect while that attached to a C-terminal significantly destabilized the helix.     

Electro-optical studies on the electric field-induced helix-to-coil transition of poly(l-ornithine hydrobromide) in methanol/water mixtures

Transient electric birefringence and circular dichroism measurements have been made on poly(L-ornithine hydrobromide) in methanol/water mixtures of various compositions. The specific Kerr constant and the molar ellipticity at 222 nm underwent an abrupt change between 93 and 98% (v/v) methanol at 25°C corresponding to a solvent-induced helix-coil transition. Anomalous birefringence transients were observed at high electric fields between 96 and 98% (v/v) methanol, i.e. on the helix side of the transition region. The double logarithmic plots of the steady-state specific birefringence versus the square of field strength for different solvent compositions could be superimposed on one another by horizontal and vertical shifts, except for the range where anomalous birefringence transient were observed. This behavior served to determine the threshold field strength. The results indicate that a conformational change from the charged helix to the charged coils is induced by high electric fields in this system, as in the cases of poly(L-lysine hydrobromide) and poly(L-αγ-diaminobutyric acid hydrochloride) in methanol/water mixtures.     

Electric field effect on the helix–coil transition of poly(L-α,γ-diaminobutyric acid hydrochloride) in methanol/water mixtures

Transient electric birefringence of poly(L -α,γ-diaminobutyric acid hydrochloride) in methanol/water mixtures has been measured over a wide range of field strengths and solvent compositions and at different polymer concentrations and temperatures. The molar ellipticity at 222 nm and the specific Kerr constant underwent an abrupt change between 75 and 80 vol % methanol at 25°C, accompanied by a solvent-induced helix–coil transition. Anomalous birefringence transients were observed between 78 and 80 vol% methanol above threshold field strengths. The double logarithmic plots of the steady-state specific birefringence versus the square of field strength for different solvent compositions and polymer concentrations could be superimposed by shifting them horizontally along the abscissa and vertically along the ordinate except for the range where anomalous transients were observed. The threshold field strength could be estimated from the point at which a downward deviation occurred. It increased with increasing polymer concentration and with increasing methanol content on the verge of the transition region. The results were interpreted as indicating that a conformational change from the charged helix to the charged coil is induced by high fields in this system, as in the case of poly(L -lysine hydrobromide) in methanol/water mixtures.     

Relationship between helix-coil transition and gene organization of ColE1 plasmid DNA. Differential scanning calorimetric and theoretical studies

Differential scanning calorimetry (DSC) was carried out to analyze the transition of helix to coil state of DNA, using ColE1 DNA molecules digested with EcoRI. The DSC curves showed multimodal transition, consisting of nine to 11 peaks over a temperature range, depending on the ionic strength of the DNA solution. These DSC curves were essentially in good agreement with the optical melting curves of ColE1 DNA. The theoretical melting profiles of ColE1 DNA were predicted from calculations based on the helix-coil transition theory and the nucleotide sequence of the DNA. These profiles resembled the DSC curves and made it possible to assign the peaks seen in the DSC curves to the helix-coil transition of particular regions of the nucleotide sequence of ColE1. The helix-coil transition of each of the small genes gave rise to a single peak in the DSC curve, while the helix-coil transition of large genes contributed to two or more peaks in the DSC curve. This multimodal transition within a single coding region might correspond to the melting of individual segments encoding the different domains of the proteins. The helix-coil transition at the specific sites including ori, the origin of replication of ColE1, was also found to occur in a particular temperature range. DSC, a simple method, is thus useful for analyzing the multimodal helix-coil transition of DNA, and for providing information on the genetic organization of DNA.     

Electric field-induced conformational change of poly(L-lysine) studied by transient electric birefringence

Transient electric birefringence measurements on poly(L -lysine hydrobromide) in methanol–water mixtures have been carried out at various solvent compositions in the vicinity of the helix–coil transition region (from 87 to 98 vol % methanol). Anomalous birefringence transients were observed between 90 and 95 vol % methanol above a threshold field strength. A distinct difference between the responses to weak and strong electric fields was noticed over a narrow range of the solvent composition. The effects of polymer concentration and temperature on the field-strength dependence of the birefringence were studied at a solvent composition of 90 vol % methanol where the anomalous transients appeared most clearly. The double logarithmic plots of the steady-state specific birefringence versus the square of field strength for different concentrations and temperatures could be superimposed by shifting them horizontally along the abscissa. The threshold field strength which was determined from the shift factor decreased with decreasing concentration. The results provide further evidence that strong electric fields can cause a helix–coil transition in this system under favorable conditions.     

Temperature dependence of the thermodynamics of helix-coil transition

The temperature-induced helix to coil transition in a series of host peptides was monitored using circular dichroism spectroscopy (CD) and differential scanning calorimetry (DSC). Combination of these two techniques allowed direct determination of the enthalpy of helix-coil transition for the studied peptides. It was found that the enthalpy of the helix-coil transition differs for different peptides and this difference is related to the difference in the temperature for the midpoint of helix-coil transition. The enthalpy of the helix-coil transition decreases with the increase in temperature, thus providing the first experimental estimate for the heat capacity changes upon helix-coil transition, DeltaC(p). The values for DeltaC(p) of helix-coil transition are found to be negative, which is in contrast to the positive DeltaC(p) for protein unfolding. Analysis suggests that this negative DeltaC(p) of helix-coil transition is due to the exposure of the polar peptide backbone to solvent upon helix unfolding.     

On the displacement of cooperative transitions of linear biopolymers by an electric field

A basic theory for equilibrium properties of cooperative transitions (particularly helix–coil transformations) of sufficiently long linear biopolymers under the influence of an electric field is developed. General relations for the calculation of the distribution of uninterrupted sequences of elementary subunit states (e.g., helical fragments) as well as the overall degree of transition θ are given. Strong cooperativity is found to permit simplifications. It is shown that only in this case can a practically significant field effect be expected. Numerical results are presented for a special example of experimental interest.     

Predicting helical segments in proteins by a helix-coil transition theory with parameters derived from a structural database of proteins

A novel helix-coil transition theory has been developed. This new theory contains more types of interactions than similar theories developed earlier. The parameters of the models were obtained from a database of 351 nonhomologous proteins. No manual adjustment of the parameters was performed. The interaction parameters obtained in this manner were found to be physically meaningful, consistent with current understanding of helix stabilizing/destabilizing interactions. Novel insights into helix stabilizing/destabilizing interactions have also emerged from this analysis. The theory developed here worked well in sorting out helical residues from amino acid sequences. If the theory was forced to make prediction on every residue of a given amino acid sequence, its performance was the best among ten other secondary structural prediction algorithms in distinguishing helical residues from nonhelical ones. The theory worked even better if one only required it to make prediction on residues that were “predictable” (identifiable by the theory); >90% predictive reliability could be achieved. The helical residues or segments identified by the helix-coil transition theory can be used as secondary structural contraints to speed up the prediction of the three-dimensional structure of a protein by reducing the dimension of a computational protein folding problem. Possible further improvements of this helix-coil transition theory are also discussed. Proteins 28:344–359, 1997. © 1997 Wiley-Liss, Inc.     

Kinetics of helix-coil transition of polypeptides in solution by the relaxation methods

Relaxation phenomena were studied in aqueous solutions of poly (alpha-L-glutamic acid) (Glu)n and poly (alpha-L-lysine) (Lys)n under various conditions using the electric field pulse method with detection by conductivity change. The relaxation time for the (Glu)n has a maximum value at the midpoint of the helix-coil transition. Some possible mechanisms are discussed and the observed relaxation phenomenon is attributed to the helix-coil transition. In the case of (Lys)n, the relaxation time as a function of pH exhibits two maxima. One is assigned to a proton transfer reaction and the other to the helix-coil transition. Using the Schwarz's theory the rate constants of the helix growth step for both (Glu)n and (Lys)n are estimated. The difference in the activation parameters for (Glu)n and (Lys)n is discussed.     

Continuum electrostatics of the C-peptide: anatomy of the problem.

A computational study of the role of all ionizable groups of the C-peptide in its helix-coil transition is performed within the framework of continuum electrostatics. The method employed in our computations involves a numeric solution of the Poisson equation with the Boundary Element Method. Our calculations correctly predict the experimentally observed trends in the helix-coil equilibrium of the C-peptide, and suggest that the mechanisms involved are more complex than usually presumed in the literature. Our results suggest that electrostatic interactions in the unfolded conformation are often more important than in the helix, total electrostatic contribution to the helix-coil transition due to the side chains of the C-peptide destabilizes the helix, changes in the helix stability produced by the changes in the ionization state of the side chains are dominated by side chain effects, the effect of the helix dipole on the energetics of the helix-coil transition of the C-peptide is either minor or similar to other contributions in magnitude; while the formation of a salt bridge is electrostatically favorable, formation of the hydrogen bond between a charged and a polar side chains is not. Factors limiting the accuracy of the computations are discussed.     

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.     

Effect of side-chain hydrophobic bonding on the stability of homopolyamino acid alpha-helices: conformational studies of poly-l-leucine in water

The conformational properties of block copolymers of poly-L -leucine in water have been examined. The degree of polymerization of the poly-L -leucine block was 11 and 21, respectively, for samples prepared by the Merrifield procedure, and 56 for a sample prepared by the polymerization of leucine N-carboxyanhydride. The optical rotatory dispersion parameter b₀ was used to obtain the helix content θ_h at various temperatures. Application of the Lifson-Roig theory gave the following parameters for the transition of a residue from a coil to a helical state: v = 0.05–0.011, ΔH = +100 cal/mole, ΔS = +0.70–1.00 e. u. These parameters, as well as those for other polyamino acids, are accounted for by hydrophobic bonds involving the nonpolar side chains in the helical and randomly coiled forms. From the data for poly-L -alanine and theoretical values of the thermodynamic parameters for hydrophobic bond formation, the parameters for formation of a polyglycine helix are computed. By separating the contributions of the backbone, it is possible to obtain a set of thermodynamic parameters for the side-chain contributions of a number of polyamino acids. Increased size of the nonpolar side chain (with a larger contribution from hydrophobic bonding) makes a larger contribution to the stability of the α-helix which is reflected, among other ways, in a higher helix content at given temperature.     

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.     

Kinetic properties and the electric field effect of the helix-coil transition of poly(gamma-benzyl L-glutamate) determined from dielectric relaxation measurements

Dielectric relaxation of poly(γ-benzyl L -glutamate) in solution has been studied in the 5 kcps-10 Mcps range for various values of the helix content. The results give first experimental evidence for three effects of major significance. (1) The system exhibits dielectric relaxation due to a chemical rate process (namely helix formation). This confirms recent theoretical predictions. (2) The mean relaxation time τ* of the helix–coil transition could be evaluated as a function of the degree of transition. The results are in excellent agreement with a previously developed theory. At the midpoint of transition it is found τ*_max = 5 × 10^?7 sec. The elementary process of helical growth turns out to be practically diffusion-controlled (with a rate constant of hydrogen bond formation of 1.3 × 10¹⁰ sec^?1). (3) There is a considerable electric field effect of the helix–coil transition. This indicates that conformation changes in biological systems could be potentially caused by direct action of an electric field.     

Stabilizing nonpolar/polar side-chain interactions in the alpha-helix.

A simplistic, yet often used, view of protein stability is that amino acids attract other amino acids with similar polarity, whereas nonpolar and polar side chains repel. Here we show that nonpolar/polar interactions, namely Val or Ile bonding to Lys or Arg in alpha-helices, can in fact be stabilizing. Residues spaced i, i + 4 in alpha-helices are on the same face of the helix, with potential to favorably interact and stabilize the structure. We observe that the nonpolar/polar pairs Ile-Lys, Ile-Arg, and Val-Lys occur in protein helices more often than expected when spaced i, i + 4. Partially helical peptides containing pairs of nonpolar/polar residues were synthesized. Controls with i, i + 5 spacing have the residues on opposite faces of the helix and are less helical than the test peptides with the i, i + 4 interactions. Experimental circular dichroism results were analyzed with helix-coil theory to calculate the free energy for the interactions. All three stabilize the helix with DeltaG between -0.14 and -0.32 kcal x mol(-1). The interactions are hydrophobic with contacts between Val or Ile and the alkyl groups in Arg or Lys. Side chains such as Lys and Arg can thus interact favorably with both polar and nonpolar residues.     

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.     

Adsorption of polypeptides on the solid surface. II. Effect of secondary chain structure and helix–coil transition

The theory of adsorption of semistiff chains on a planar surface developed by the authors previously has been used to consider the helix–coil transition in single-stranded macromolecule interacting with an adsorbent plane. The cases of nonselective interaction when the adsorption energy is independent of the unit conformation (a) and selective interaction with only helical (b) or coiled (c) sequences active in adsorption were investigated. In case (b) the existence of secondary structure favors chain bonding to the surface. This leads to the increase in the stability of the helical state and complete polypeptide chain spiralization. The profile of the conformational helix–coil transition acquires an asymmetrical shape inherent to the second-order phase transition. In case (c) the bonding of a partially helical chain to the surface is similar to the adsorption of Gaussian coils and is accompanied by the destruction of secondary structure, this destruction being appreciable even if the helical state in space was favorable.