Thermodynamic parameters of helix-coil transition in polypeptide chains. I. Poly-(L-glutamic acid)

The helix-coil transitions for poly(L -glutamic acid) (PGA) in 0.2M NaCl and in its mixture with dioxane were studied by the methods of spectropolarimetry, viscometry, and potentiometric titration at different temperatures from 8 to 50°C. The enthalpy and entropy differences between the helical and coillike states of uncharged PGA molecules were determined from the curves of potentiometric titration. The temperature dependence of the cooperativity parameter σ was determined by two methods: from the sharpness of transition and from the dependence of the intrinsic viscosity on the helical content in the transition region. In 0.2MNaCl, σ= (2.5 ± 0.5) × 10^?3 and practically does not depend on temperature, i.e., the cooperativity of the helix-coil transition is connected mainly with the entropy decrease in initiating helical regions (ΔS_i ≈ ?12 is mole of helical regions). On the contrary, initiation of a helical region in the water-organic solvent mixture is accompanied by a considerable enthalpy increase.     

Calorimetric study of the order-disorder conformational transition in succinoglycan

Thermally induced order-disorder conformational transition in succinoglycan was studied using the method of high-sensitivity differential scanning microcalorimetry within the range of polysaccharide concentrations from 0.1 to 3.5 mg mL⁻¹ at NaCl concentrations 0, 0.01, and 0.1M. The positions and shapes of the excess heat capacity curves depended substantially on both the NaCl and polysaccharide concentrations. At low polysaccharide concentrations in salt-free solution the experimental curves were closely approximated by the two-state model suggesting the transition mechanism to be of the single helix-coil type. With increasing polysaccharide and/or NaCl concentration, the experimental curves changed significantly in symmetry, which indicated a changing transition mechanism. At high polysaccharide concentrations or in the presence of the salt, the order-disorder transition of succinoglycan was shown to include two stages: the cooperative dissociation of the helix dimer and subsequent two-state melting of the helix monomer. The dependence of thermodynamic parameters for the dissociation and melting of helix structures in succinoglycan on NaCl and polysaccharide concentrations was obtained by fitting the experimental excess heat capacity curves. The cooperativity parameter σ for the single helix-coil transition as well as the average length of the helix segment of succinoglycan were calculated. Some features of succinoglycan ordering in solution are discussed. © 1996 John Wiley & Sons, Inc.     

Helix-coil stability constants for the naturally occurring amino acids in water. XII. Asparagine parameters from random poly(hydroxybutylglutamine-co-L-asparagine)

The synthesis and characterization of water-soluble random copolymers containing L -asparagine with N⁵-(4-hydroxybutyl)-L -glutamine, and the thermally induced helix-coil transitions of these copolymers in water, are described. The incorporation of L -asparagine was found to decrease the helix content of the polymers in water at all temperatures. The Zimm-Bragg parameters σ and s for the helix-coil transition in poly(L -asparagine) in water were deduced from an analysis of the copolymer melting curves in the manner described in earlier papers. The computed values of s indicate that asparagine destabilizes helical sequences at all temperatures in the range 0–60°C.     

Experimental thermodynamics of the helix--random coil transition. 3. Determination of the transition enthalpies of the helical complexes poly(I+C) and poly I in solution

The enthalpies of the helix-coil transitions of the ordered polynucleotide systems of poly(inosinic acid)–poly(cytidylic acid) [poly(I + C)], (helical duplex), and of poly (inosinic acid) [poly(I + I + I)], (proposed secondary structure: a triple-stranded helical complex), were determined by using an adiabatic twin-vessel differential calorimeter. Measuring the temperature course of the heat capacity of the aqueous polymer solutions, the enthalpy values for the dissociation of the helical duplex poly (I + C) and the three-stranded helical complex poly(I + 1 + 1), respectively, were obtained by evaluating the additional heat capacity involved in the conformational change of the polynucleotide system in the transition range. The ΔH values of the helix-coil transition of poly (I + C) resulting from the analysis of the calorimetric measurements vary between the limits 6.5 ± 0.4 kcal/mole (I + C) and 8.4 ± 0.4 kcal/mole (I + C). depending on the variation of the cation concentration ranging from 0.063 mole cations kg H₂O to 1.003 mole cations/kg H₂O. The calorimetric investigation of an aqueous poly I solution (cation concentration 1.0 mole/kg H₂O) yielded the enthalpy value ΔH = 1.9 ± 0.4 kcal/mole (I), a result which has been interpreted qualitatively following current models of inter- and intramolecular forces of biologically significant macromolecules. Additional information on the transition behavior of poly(I+ C)Was obtained by ultraviolet and infrared absorption measurements.     

Solution properties of synthetic polypeptides. V. Helix–coil transition in poly(β-benzyl L-aspartate)

Simple approximate expressions have been derived from the theory of Zimm and Bragg for use in the analysis of experimental data on the helix-coil transition in polypeptide. On the basis of the resulting expressions practical procedures are proposed to determine two basic parameters characterizing a thermally induced transition, i.e., helix initiation parameter σ and enthalpy change for helix formation, ΔH. They have been applied to the data for poly(β-benzyl L -aspartate) (PBLA) with the result: σ = 1.6 × 10^?4 and ΔH = ?450 cal/mole for PBLA in m-cresol; σ = 0.6 × 10^?4 and ΔH = 260 cal/mole for PBLA in chloroform containing 5.7 vol-% of dichloroacetic acid. This result gives evidence that σ may change not only from one polypeptide to another but also for a given polypeptide in different solvents. The change in limiting viscosity number [η] accompanying the transition was measured in the same solvents. The curve of [η] versus helical content had a relatively monotonic shape for the chloroformdichloroacetic acid solutions as compared with that for the m-cresol solutions, indicating that [η] depended largely on σ. Provided that [η] is a direct measure of the mean-square radius of gyration, 〈S²〉, the results are consistent with the theoretical predictions of Nagai and of Miller and Flory for 〈S²〉.     

Thermal and charge-induced coil to -helix transition of poly-L-glutamic acid and random L-glutamic acid-L-alanine copolymers

Thermal and charge induced random coil to α-helix transitions of poly-L -glutamic acid (PGA) were measured by optical rotatory dispersion in various solvents. The data of PGA in 0.1M Nacl were analyzed by the Zimm-Rice theory. Enthalpy and entropy changes for the coil-to-helix transition in the unionized state were obtained: ΔH° = ?1020 ± 100 cal/residue mole; ΔH° = ?3.0 ± 0.4 e.u./residue mole. The initiation parameter, σ, of the Zimm-Rice theory was given by a value of 5 ± 1 × 10^-3. Random copolymers of L -glutamic acid and L -alanine containing 10, 30, and 40 molar percents of alanyl residue were synthesized. Stabilities of α-helix of the copolymers were compared to that of PGA. In water and water-ethanol solutions, stabilities of the polymers were almost equal after the simple correction about the ionized charge density of the polymers. In 0.1 M NaCl solution these copolymers showed some deviations from the transition curve of PGA, which would suggest the hydrophobic contribution of the alanyl residues.     

Stability of the helical conformation of random L-alanine-L-lysine copolymers in aqueous solution

The potentiometric titration of random copolymers of L -lysine and L -alanine containing 0–35% alanine was carried out. The standard free-energy change for the transition of coil to helix was calculated from the titration curve, and was treated by taking account of first-neighbor interactions. For uncharged lysine ΔG° = ?140 cal/mole, and for alanine ΔG° = ?50 cal/mole in 0.06M NaBr at 25°C, indicating that the alanine helix is thermodynamically less stable than the lysine helix. The randomness in co-polymerization was confirmed by trypsin treatment.     

Side-chain effect on conformation of ionizable polypeptides in aqueous solution

In order to study the effect of side-chain length on the conformation of polypeptides, conformational changes of various ionic polypeptides with various lengths of side chain, poly-N^ε-glutaryl-L -lysine (PGL), poly-N^δ-glutaryl-L -ornithine (PGO), poly-N^ε-succinyl-L -lysine (PSL), and poly-N^δ-succinyl-L -ornithine (PGO), were investigated by ORD, potentiometric titration, and dilatometric measurements in aqueous solution. The results of optical rotation and potentiometric titration measurements indicate strongly that the α-helix stability increases in the sequence PSO < PSL ～ PGO < PGL, which corresponds to increased side-chain length. The volume change associated with the helix–coil transition also increased in the above sequence. This series of polymers seems to be more hydrophobic compared with poly-L -glutamic acid or poly-L -lysine, as suggested from the values of enthalpy and entropy changes for coil–helix transitions.     

Solution properties of synthetic polypeptides. 18. Helix-coil transition of poly-N5-(2-hydroxyethyl)L-glutamine

The helix–coil transition of poly-N⁵-(2-hydroxyethyl)L -glutamine (PHEG) in aqueous isopropanol was examined by means of optical rotatory dispersion (ORD) and intrinsic viscosity [η] measurements. The Zimm–Bragg parameters σ and s for the transition were determined from the ORD data as a function of molecular weight. It was found that the transition was characterized by a relatively low cooperativity; the values of \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt \sigma $\end{document} were in the range from 0.039 to 0.066, depending on the solvent composition. These σ values are much larger than those reported for other polypeptide–solvent systems. The transition enthalpy was negative and its magnitude varied with the solvent composition, with a maximum of 620 cal/mol at 40 wt% isopropanol. The curve of [η] versus helical content for a high-molecular-weight sample exhibited a very broad minimum, and this behavior was attributed to the low cooperativity of the transition.     

Helix-coil stability constants for the naturally occuring amino acids in water. XIV. Methionine parameters from random poly(hydroxypropylglutamine,L-Methionine)

Water-soluble, random copolymers containing L -methionine and N⁵-(3-hydroxypropyl)-L -glutamine have been prepared, fractionated, and characterized. The thermally induced helix-coil transitions of these copolymers in water have been investigated, and it has been found that incorporation of L-methionine increases the helix content of the polymers at all temperatures in the range of 0–60°C. The Zimm-Bragg parameters σ and s for the helix-coil transition in poly(L -methionine) in water were deduced from an analysis of the melting curves of the copolymers using the methods described in earlier papers.     

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.     

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.     

Nonadditivity in conformational entropy upon molecular rigidification reveals a universal mechanism affecting folding cooperativity

Previously, we employed a Maxwell counting distance constraint model (McDCM) to describe α-helix formation in polypeptides. Unlike classical helix-coil transition theories, the folding mechanism derives from nonadditivity in conformational entropy caused by rigidification of molecular structure as intramolecular cross-linking interactions form along the backbone. For example, when a hydrogen bond forms within a flexible region, both energy and conformational entropy decrease. However, no conformational entropy is lost when the region is already rigid because atomic motions are not constrained further. Unlike classical zipper models, the same mechanism also describes a coil-to-β-hairpin transition. Special topological features of the helix and hairpin structures allow the McDCM to be solved exactly. Taking full advantage of the fact that Maxwell constraint counting is a mean field approximation applied to the distribution of cross-linking interactions, we present an exact transfer matrix method that does not require any special topological feature. Upon application of the model to proteins, cooperativity within the folding transition is yet again appropriately described. Notwithstanding other contributing factors such as the hydrophobic effect, this simple model identifies a universal mechanism for cooperativity within polypeptide and protein-folding transitions, and it elucidates scaling laws describing hydrogen-bond patterns observed in secondary structure. In particular, the native state should have roughly twice as many constraints as there are degrees of freedom in the coil state to ensure high fidelity in two-state folding cooperativity, which is empirically observed.     

Transition temperature and enthalpy change dependence on stabilizing and destabilizing ions in the helix–coil transition in native tendon collagen

The transition temperatures t_t and enthalpy changes ΔH in the helix–coil transition of solid tendon collagen soaked in a solution containing one of the following stabilizing or destabilizing agents, HCHO, NaF, NaCl, NaI, NaBr, NaOH, NH₂CONH₂, CaCl₂, MgCl₂, were measured as a function of molar concentration by a calorimetric method. The temperature and the enthalpy changes accompanying the transition behaved in a similar manner: when the t_t was depressed by the presence of ions, similar behaviour was observed in ΔH. Both parameters (t_t and ΔH) increased for HCHO, and decreased for NaF and NaCl at concentrations lower than 0.2 M. Above 0.2 M they increased for NaF and NaCl, and decreased in the presence of the other reagents listed above. The average t_t and the ΔH observed in collagen soaked in water were 63.5°C and 12.3 cal/g, respectively. In addition to the parameters mentioned above, the molar effectiveness of the various reagents was obtained for the cases where there was a linear relationship between the t_t and molar concentration of the reagent in the solution. Since both the t_t and the ΔH were observed to vary, the entropy change (ΔS) accompanying the transition was calculated using thermodynamic relations. In order to explain the ΔS observed as a function of ionic concentration, the thermodynamic relationships have been obtained from a partition function under suitable assumptions. Since the partition function is dependent on the number of hydrogen bonds responsible for collagen stability, the result obtained has been compared with the values predicted by the two most quoted models for collagen. The present study is in accordance with the Ramachandran model for collagen structure, which predicts more than one hydrogen bond per three residues.     

Conformational change of poly-N epsilon-glutaryl-L-lysine and poly-N epsilon-succinyl-L-lysine in aqueous salt solutions

The conformational changes of poly-N^ε-glutaryl-L -lysine (PGL) and poly-N^ε-succinyl-L -lysine (PSL) in various salt solutions were studied by use of ORD and potentiometric titration measurements. The addition of alkali metal salts to the fully ionized PGL or PSL solution caused helix formation. The helical content of the polymers increases in the following sequences: at salt concentration 0–2 M, CsCl < KCl < LiCl < NaCl; and at 2–3 M, LiCl < CsCl < KCl ～ NaCl. The preferential binding of the solvent components with various alkali metal salts of PGL or PSL was measured in LiCl, NaCl, and KCl solutions by means of equilibrium dialysis and differential refractometry. It was found that with increasing salt concentration, the polymers were preferentially hydrated in NaCl and KCl soultions; however the salt was preferentially bound to the polymers in LiCl solution. Such preferential binding was suggested to be closely related to conformational change. The addition of CaCl₂ to polymer solutions led to the stabilization of the helical structure of PGL or PSL.     

Thermodynamic parameters of the helix-coil transition in polypeptide chains. III. Random copolymers of L-leucine and L-glutamic acid.

Conformational transitions induced by pH changes in random copolymers of leucine and glutamic acid have been studied. Significant differences were observed in the potentiometric titration curves of copolymers with small (up to 4%) and large leucine contents. The helical stability of copolymers with small leucine content, determined from titration curves by the Zimm and Rice method, decreases slightly with an increase in the leucine content, whereas the helical stability of copolymers with large leucine content increases sharply with an increase of the leucine content. It is shown that copolymers with large leucine content aggregate in the region of transition into the helical state, but the increase of their helical state stability is not connected with intermolecular aggregation, as it was also observed for a nonaggregating fraction isolated from one of the copolymers by gel chromatography. A conclusion is made that the helix–coil equilibrium constant s for leucine does not itself exceed the s constant for uncharged polyglutamic acid. The stabilization of the helical state in copolymers with large leucine content is due to intramolecular aggregation of helices in these copolymers. The analysis of the leucine residue distribution between helical and nonhelical regions in globular proteins also gives no real arguments to ascribe special helix-forming properties to leucine.     

Cooperative nonenzymic base recognition II. thermodynamics of the helix-coil transition of oligoadenylic + oligouridylic acids

The properties of oligonucleotide helices of adeuylic- and uridylic acid oligomers have been investigated by measurements of hypo-and hyperchromieity. High ionic strengths favor the formation of triple helices. Thus, the double helix-coil transition can be studied (without interference by triple helices) only at low ionic-strength. A “phase diagram” is given representing the T_m-values of the various transitions at different ionic strengths for the system A(pA)₁₇ + U(pU)₁₇. Oligonucleolides of chain lengths <8 always form both double and triple helices at the nucleotide concentrations required for base pairing. For this reason the double helix-coil transition without coupling of the triple helix equilibrium can only be measured for chain lengths higher than 7. Melting curves corresponding to this transition have been determined for chain lengths 8, 9, 10, 11, 14 and 18 at different concentrations. An increase in nucleotide concentration leads to an increase in melting temperature. The shorter the chain length the lower the T_m-value and the broader the helix-coil transition. The experimental transition curves have been analysed according to a staggering zipper model with consideration of the stacking of the adeuylic acid single strands and the electrostatic repulsion of tlip phosphate charges on opposite strands. The temperature dependence of the nucleation parameter has been accounted for by a slacking factor x. The stacking factor expresses the magnitude of the stacking enthalpy. By curve fitting xwas computed to be 0.7, corresponding to a stacking enthalpy of about S kcal/mole. The model described allows the reproduction of the experimental transition curves with relatively high accuracy. In an appendix the thermodynamic parameters of the stacking equilibrium of poly A and of the helix-coil equilibria of poly A + poly U at neutral pH are calculated (ΔH_A = ?7.9 kcal/mole for the poly A stacking and ΔH₁₂ = ?10.9 kcal/mole for the formation of the double helix from the randomly coiled single strands). A formula for the configurational entropy of polymers derived by Flory on the basis of a liquid lattice model is adapted to calculate the stacking entropies of adenylic oligomers.     

Monte Carlo studies on potentiometric titration of poly(glutamic acid)

The potentiometric titration of poly(glutamic acid) with special attention to its helix-coil transition is investigated in terms of the previously developed Monte Carlo method. The simulations of the potentiometric titration are carried out for helical and coiled form of the peptide, separately. A cylindrical rod with spherical ionizable groups is adopted as each conformational model of poly(glutamic acid) molecule. A spherical charge with a hard core potential is assumed as a mobile hydrated ion. The helix-coil transition curves are analyzed by the Zimm-Bragg theory. A satisfactory agreement is achieved for the titration curves with the experimental data in most cases. The significance and the limitations of the simulation method are discussed.     

The random coil leads to beta transition of copolymers of L-lysine and L-valine: potentiometric titration and circular dichroism studies.

A series of copolymers of L -lysine and L -valine [poly(L -lysine^f L -valine^100-f)] containing 0–13% L -valine have been studied, in 0.10M KF solution, using potentiometric titration and circular dichroism spectroscopy. Incorporation of increasing amounts of valine into the copolymers favors β-sheet formation over α-helix formation at high pH and room temperature. The titrations were analyzed using the method of Zimm and Rice and the partial free energy (ΔG⁰_cβ) for the coil-to-β-sheet transition for valine is estimated at 900 cal/mole at 25°C. From the temperature dependence of the free energy, the partial enthalpy, ΔH⁰_cβ, and entropy, ΔS⁰_cβ, of the transition for valine is estimated to be 854 cal/mole and 6.0 e.u., respectively. The corresponding partial thermodynamic parameters for L -lysine are in agreement with published results. The fraction of β-sheet versus pH has been calculated for poly(L -lysine^86.8 L -valine^13.2) at 25.0°C using the titration data; data obtained from circular dichroism spectroscopy for the same copolymer are in good accord. It is concluded from these results that L -valine is a very strong β-sheet forming amino acid. Furthermore, these results indicate that the Zimm–Rice method is applicable to transitions between the coil and β-sheet states for a polypeptide containing two different residues.     

Relaxation kinetics of the helix-coil transition of a self-complementary ribo-oligonucleotide: A7U7

Relaxation measurements on the kinetics of the double helix to coil transition for the self-complementary ribo-oligonucleotide A₇U₇ are reported over a concentration range of 6.9 μM to 19.6 μM in single strand in 1 M NaCl. The rate constants for helix formation are about 2 × 10⁶ M^?1 s^?1 and decrease with increasing temperature yielding an activation enthalpy of ?6 $\text{kcal}\text{mole}$. The rate constants for helix dissociation range from 3 to 250 s^?1 and increase with increasing temperature yielding an activation enthalpy of +45 $\text{kcal}\text{mole}$. The kinetic data reported here for 1 M NaCl is compared with previously published results obtained at lower salt concentrations. These data are discussed in terms of the quantitative effect of ionic strength on the kinetics of helix-coil transitions in oligo- and polynucleotides.