Structure of aggregates and helix-coil transition of polypeptides by dielectric measurements. I. Poly-gamma-benzyl-L-glutamate in dioxane and dioxane-dichloroacetic acid

Dielectric dispersion measurements on poly-γ-benzyl-L -glutamate (PBLG) in dioxane and dioxane–dichloroacetic acid (DCA) mixtures in the frequency range 200 Hz–2 MHz were made in order to study the structure of molecular aggregates. The structure of aggregates is explained on the basis of the variation of dipole moment and relaxation time with degree of aggregation. PBLG was found to form linear head-to-tail-type aggregates in dioxane. These aggregates gradually reduce in size without loosing their α-helical structure during the process of disaggregation obtained by either adding DCA to the solution in dioxane or by heating. It was confirmed that the addition of 30 wt % DCA completely destroys the aggregation of PBLG in dioxane at 30°C. Thermal disaggregation, however, was not complete even at a temperature approaching the boiling point of the solvent. A reaction scheme for aggregation is proposed and equilibrium constants are calculated at various stages of aggregation. The enthalpy of aggregate formation is found to be ?3 kcal/mol. Results of optical rotatory dispersion measurements of the helix–coil transition in this system are also presented.     

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.     

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.     

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.     

The determination of the thermodynamic parameters of the helix-coil transition of polypeptides by means of dipole moment measurements

The theoretical change of the mean-square dipole moment of a polypeptide during the helix-coil transition is compared with the change in helix content. It is shown that, according to the theory, the determination of the helix initiation parameter σ and the enthalpy of helix formation ΔH can be determined. Experimental data on poly-benzyl-L -gluatamate in two different solvent mixtures are given.     

Enthalpy of helix-coil transitions from heats of solution. II. Poly-epsilon-carbobenzoxy-L-lysine and copolymers with L-phenylalanine

The heal of solution of Poly-ε-carbobenzoxy-L -lysine and of a series of its copolymers with phenylalanine was measured as a function of solvent composition. The enthalpy change of the helix-to-coil transition was estimated for the various cases. The previous findings that side chains do not greatly affect the transition enthalpy is confirmed also in cases having much larger differences in helix stability.     

Thermodynamic parameters of helix-coil transition in polypeptide chains. II. Poly-L-lysine

The helix–coil transitions for poly-L -lysine (PL) were investigated by the methods of spectropolarimetry, viscometry and potentiometric titration in 0.2M NaCl at different temperatures as well as in 0.2MNaBr, 1MKCl, and in mixtures of 0.2MNaCl or NaBr with methanol at room temperature. The enthalpy and entropy differences between the helical and coillike states of uncharged PL molecules in 0.2.M NaCl were determined from the potentiometric titration curves. The cooperativity parameters σ for PL in different solvents were determined by two methods (from the sharpness of the transition and from the dependence of the intrinsic viscosity on the helical content in the transition region). In 0.2MNaCl σ has a value of (2.3 ± 0.5) × 10^?4 and does not depend on temperature, i.e., the cooperativity of the helix-coil transition, as for PGA, is mainly of an entropy origin (the initiating of the helical region is accompanied by the entropy decrease ΔS_i = ?12 eu/mole of helical regions). A comparison of the obtained results for PGA and PL with the molecular theories of the helix-coil transitions shows that the role of dipole-dipole interactions of nonneighboring peptide groups is greatly overestimated in these theories, leading to a considerable enthalpy contribution to the free energy of initiating helical regions which is not observed in the experiment.     

A statistical mechanical study of helix-coil transition in concentrated solutions of polypeptides and proteins

The helix–coil transition in polypeptides was studied by methods of statistical mechanics, taking account of interaction between “melted” amide groups through hydrogen bonds. The statistical sums are calculated in the explicit form for two limit cases: (1) the dilute solution when the main contribution is given by collisions of two particles; (2) “condensation” when contacting macromolecules form a united aggregate. In the first case the transition enthalpy was shown to decrease linearly when the concentration increases, while at the appropriate choice of theoretical parameters, melting temperature and range are almost independent of the concentration. In the second case the structural transition parameters were shown to be independent of the concentration (the saturation effect). These results agree with the experimental data on synthetic polypeptides reported by other authors and with data on some globular proteins (serum and egg albumin) reported in this paper.     

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.     

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.     

Statistical mechanical studies of polypeptides. 1. Theory of the helix-coil transition including right- and left-handed helical states

The Lifson-Roig and Zimm-Bragg theories of the helix–coil transition in polypeptides are generalized to include both right- and left-handed α-helical states. The partition functions for these more general theories are formulated in terms of the parameters u, v_R, V_L, W_R, and w_L for the generalized Lifson-Roig theory and σ_R, σ_L, s_R, and s_L for the generalized Zimm-Bragg theory. Matrix equations are derived for calculating such average molecular properties as the fraction of the amino acid residues hydrogen bonded into right- and left-handed α-helices, the average number of right- and left-handed helical sequences per molecule, the number-average length (in residues) of the right- and left-handed helical sequences, and the degree of solvent binding to the peptide NH and CO groups. These equations are shown to be conveniently adaptable to machine methods of calculation, thus avoiding the difficulty of solving an eigenvalue problem where the secular equation is of a high order. A discussion is given of the various energetic and entropic effects which determine the screw sense and stability of helices and of the extent to which it is valid to interpret experimental data by adjustment of the parameters of these statistical mechanical theories which include in their formulation only near-neighbor interactions between residues.     

On the controversy over "fast" and "slow" helix-coil transition rates in polypeptides

The controversy over “fast” and “slow” helix-coil transition rates in polypeptides is discussed. The “slow” results are derived from the assumption that multiple NMR spectra of α-CH and NH groups arise from chemical exchange. In this paper it is shown that such spectra may be obtained without invoking chemical exchange. The multiplicity arises from the difference in helicity of amino acid residues near the ends of the chain by comparison with amino acid residues nearer the middle, and from a polydispersity in molecular weight. As a consequence of this analysis, support is given to the “fast” transition rates.     

Intramolecular alpha-helix-beta-structure-random coil transition in polypeptides. II. Dynamic case

The conformational changes of polypeptides which are capable of forming the alpha-helix. beta-structure and random coil (or the unordered) conformations are discussed. The kinetics of this system are studied as the time evolution of the probabilities describing the conformational states of the system. The time behavior of the average numbers of the alpha-helix and the beta-structure reveals the existence of intermediate states which are not found and not stable at equilibrium. These intermediates make the kinetics of this system more complex. Such situations can occur in protein folding and unfolding processes in such a way that a conformation absent in the tertiary structure appears in the intermediate stages and disappears finally, and the time course of the reaction is described by the sum of two or more exponential terms, in other words, the protein folding and unfolding processes display multiphasic kinetics. These intermediates, which are formed by short-range interactions, may usually be destroyed but sometimes can be stabilized by medium- and long-range interactions and remain stable for a fairly long time in the process of renaturation in real proteins.     

Enthalpy of helix-coil transition from heat of solutions. 3. Poly-N- -carbobenzoxy-L-ornithine and poly-N- -carbobenzoxy-L- , -aminobutyric acid

The helix-to-coil transition in dichloroethane–dichloroacetic acid (DCE–DCA) mixtures for poly-N-δ-carbobenzoxy-L -ornithine (PCBO) and for poly-N-γ-carbobenzoxy-L α,γ-aminobutyric acid (PCBBA) have been studied by ORD and the “heat of solution” method. The results provide strong evidence for the existence of a very specific side-chain/side-chain interaction in PCBBA, which is discussed on the basis of a detailed structural model. The main sources of enthalpy and entropy changes in helix-coil transitions of uncharged homopolypeptides in DCE–DCA mixtures are also discussed briefly.     

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.     

Electric birefringence of ionized polypeptides in solution and the effect of high electric fields on the helix-coil transition

Electric birefringence and circular dichroism measurements have been made on solutions of two po!y (L-lysine) homologs. The specific Kerr constant and the molar ellipticity at 222 nm of poly (L-alpha, gamma-diaminobutyric acid hydrochloride) in methanol/water mixtures underwent an abrupt change between 75 and 80 vol% methanol at 25 degrees C, corresponding to a solvent-induced helix-coil transition. On the helix side of the transition region, i.e., between 78 and 80 vol% methanol, anomalous birefringence transients indicative of field-induced helix-to-coil transition were observed at high fields. In the case of poly (L-ornithine hydrobromide) in methanol/water mixtures, a helix-coil transition was induced between 93 and 98 vol% methanol and anomalous birefringence transients were observed between 96 and 98 vol% methanol. The double logarithmic plots of the steady-state specific birefringence versus the square of field strength for various solvent compositions and polymer concentrations could be superimposed on one another by horizontal and vertical shifts, except for the range where anomalous birefringence transients were observed. This enabled us to estimate the threshold field strength.