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.     

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.     

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.     

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.     

Beyond the nearest-neighbor Zimm-Bragg model for helix-coil transition in peptides

The nearest-neighbor (micro = 1) variant of the Zimm and Bragg (ZB) model has been extensively used to describe the helix-coil transition in biopolymers. In this work, we investigate the helix-coil transition for a 21-residue alanine peptide (AP) with the ZB model up to fourth nearest neighbor (micro = 1, 2, 3, and 4). We use a matrix approach that takes into account combinations of any number of helical stretches of any length and therefore gives the exact statistical weight of the chain within the assumptions of the ZB model. The parameters of the model are determined by fitting the temperature-dependent circular dichroism and Fourier transform infrared experimental spectra of the AP. All variants of the model fit the experimental data, thus giving similar results in terms of the macroscopic observables, such as temperature-dependent fractional helicity. However, the resulting microscopic parameters, such as distributions of the individual residue helical probabilities and free energy surfaces, vary significantly depending on the variant of the model. Overall, the mean residue enthalpy and entropy (in the absolute value) both increase with micro, but combined yield essentially the same "effective" value of the ZB propagation parameters for all micro. Greater helical probabilities for individual residues are predicted for larger micro, in particular, near the center of the sequence. The ZB nucleation parameters increase with increasing micro, which results in a lower free energy barrier to helix nucleation and lower apparent "cooperativity" of the transition. The significance of the long-range interactions for the predictions of ZB model for helix-coil transition, the calculated model parameters and the limitations of the model are discussed.     

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.     

Calorimetric measurements of the transition enthalpy of DNA in aqueous urea solutions

The helix-coil equilibrium of DNA is delicately affected by the nature of the solvent. In this investigation the helical secondary structure was destabilized by an increasing concentration of urea. We found a linear dependence of the transition enthalpy deltaH on the urea concentration for calf thymus DNA as well as for salmon sperm DNA.     

Parameters of helix-coil transition theory for alanine-based peptides of varying chain lengths in water.

Thermal unfolding curves have been measured for a series of short alanine-based peptides that contain repeating sequences and varying chain lengths. Standard helix-coil theory successfully fits the observed transition curves, even for these short peptides. The results provide values for sigma, the helix nucleation constant, delta H0, the enthalpy change on helix formation, and for s (0 degree C), the average helix propagation parameter at 0 degree C. The enthalpy change agrees with the value determined calorimetrically. The success of helix-coil theory in describing the unfolding transitions of short peptides in water indicates that helical propensities, or s values, can be determined from substitution experiments in short alanine-based peptides.     

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.     

The triple helix-coil transition of cyanogen-bromide peptides of the α1-chain of the calf-skin collagen

The thermal triple helix-coil transition of the CNBr peptides of the α1-chain of calf-skin collagen was studied optically and calorimetrically. Besides α1CB5, all the peptides were able to form triple-helical structures at low temperatures. The peptides with longer chain lengths showed, under the experimental conditions, hysteresis in the transition range depending on the direction of the successive temperature changes. The detailed thermodynamic analysis of the optical transition curves was only possible for the two small peptides α1CB2 and α1CB4. We observed a higher stability of α1CB2 relative to α1CB4 (α1CB2 has higher imino acid content), accompanied with increased values of both denaturation enthalpy and entropy. Further, we observed a linear relationship between the calorimetrically determined denaturation enthalpy of all the CNBr peptides and their imino acid content. Although this behavior is qualitatively in accordance with the observation of Privalov and Tiktopulo on various kinds of native collagen, the CNBr peptides showed much lower values of the thermodynamic parameters ΔH⁰ and ΔS⁰ and differed also in the rate of their change with imino acid content. These differences are interpreted as being caused by misalignment in the helical form of the CNBr peptides resulting in a rupture of the specific interactions in the native form.     

Kauzmann's paradox and the glass transition

Kauzmann showed that the entropy of a liquid decreases rapidly on cooling towards the kinetic glass transition temperature and extrapolates to unreasonable values at lower temperature. The temperature where the extrapolated liquid entropy meets the crystal entropy is now called the Kauzmann temperature. Thermodynamics, with Planck's statement of the third law, shows that the entropy of a liquid cannot be less than the entropy of a glass with the same enthalpy. This is the thermodynamic condition violated by the Kauzmann extrapolation and it suggests a thermodynamic glass transition. Simulations show that, for the simple models studied and regardless of how the liquid entropy is extrapolated, the Kauzmann temperature cannot be reached because the entropy of glasses with the same enthalpy as the liquid is greater than that of the crystal.     

Enthalpy changes in the helix-coil transition of poly(gamma-benzyl L-glutamate)

The helix-coil transition temperature T_c of poly(γ-benzyl L -glutamate) in binary solvent mixtures of dichloroacetic acid and 1,4-dichlorobutane, 1-chlorooctane, or 1-chlorododecane have been measured. A treatment is presented with which the transition enthalpy can be calculated from the observed dependence of T_c on solvent composition. Results are compared with previously obtained calorimetric data. The underlying assumptions of the calculation are discussed.     

Enthalpy distribution for the alpha-helix/random coil transition in a model peptide: a study of two-state behavior.

We use heat capacity data of Taylor et al. to calculate the enthalpy distribution of a model peptide using the moments/maximum-entropy method. The peptide was designed with small covalent loops at both ends of the molecule to nucleate alpha-helix thus giving a system that would be expected to show a helix-coil transition that is very close to being two state. If we subtract a background contribution from the heat capacity data, then the enthalpy distribution we obtain shows two distinct peaks representing helix and coil. The difference in the peak enthalpy values agrees closely with the DeltaH obtained from the two-state analysis. On the other hand, if we use the complete heat capacity without subtracting background we then obtain an enthalpy distribution that has only a single peak at all temperatures. We show that this result can be consistent with the existence of two states, helix and coil, but only if the range of variation of the enthalpy of each species is so large as to make the notion of a species fairly meaningless.     

Theory of helix-coil transition on DNA-ligand complexes: the effect to two types of interaction of ligand on the parameters of transition

The effect of ligand interacting with native DNA by two types on the parameters of helix-coil transition in homopolymers is considered using the most probable distribution method (Yu.S. Lazurkin et al., Biopolymers 1970). It is shown that at a small relative concentration of ligand the melting enthalpy (delta H) of DNA may be obtained from the universal formula which contains only values directly known from the experiments. It is shown that the formula for the change of melting temperature and width of melting range depending on the total ligand concentration in solution is converted into the corresponding formulae which are defined for the case when only one type of interaction of ligand and DNA is considered.     

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.     

Effects of mutations on the thermodynamics of a protein folding reaction: implications for the mechanism of formation of the intermediate and transition states

We have measured changes in heat capacity, entropy, and enthalpy for each step in the folding reaction of CD2.d1 and evaluated the effects of core mutations on these properties. All wild-type and mutant forms fold through a rapidly formed intermediate state that precedes the rate-limiting transition state. Mutations have a pronounced effect on the enthalpy of both the intermediate and folded states, but in all cases a compensatory change in entropy results in a small net free-energy change. While the enthalpy change in the folded state can be attributed to a loss of van der Waals interactions, it has already been shown that changes in the stability of the intermediate are dominated by changes in secondary structure propensity [Lorch et al. (1999) Biochemistry 38, 1377-1385]. It follows that the thermodynamic basis of beta-propensity is enthalpic in origin. The effects of mutations on the enthalpy and entropy of the transition state are smaller than on the ground states. This relative insensitivity to mutation is discussed in the light of theories concerning the nature of the rate-limiting barrier in folding reactions.     

Thermodynamics of the acid transition in blue copper proteins

The thermodynamic parameters of the conformational transition occurring at low pH (acid transition, AT) in blue copper proteins, involving protonation and detachment from the Cu(I) ion of one histidine ligand, have been determined electrochemically for spinach and cucumber plastocyanins, Rhus vernicifera stellacyanin, cucumber basic protein (CBP), and Paracoccus versutus amicyanin. These data were obtained from direct protein electrochemistry experiments carried out at varying pH and temperature. For all species but CBP, the overall conformational change turns out to be exothermic. The entropy change is remarkably species-dependent. In particular, we found that (i) the balance of bond breaking/formation favors the acid transition in plastocyanins, which show remarkably negative DeltaH degrees '(AT) values, and (ii) the transition enthalpy turns out to be much less negative (or even positive) for the two phytocyanins (stellacyanin and CBP): for these species, the transition turns out to be observable thanks to the favorable (positive) entropy change. Thus, it is apparent that the thermodynamic "driving force" for this transition is enthalpic for the plastocyanins and entropic for the phytocyanins. Amicyanin is an intermediate case in which both enthalpic and entropic terms favor the transition. Under the assumption that the transition entropy originates from solvent reorganization effects, which are known to involve compensative enthalpy and entropy changes, the free energy change of the transition would also correspond to the enthalpy change due to bond breaking/formation in the first coordination sphere of the metal and in its immediate environment. Indeed, this term turns out to be very similar for the proteins investigated, in line with the conservation of the Cu(I)-His bond strengths in these species, except for amicyanin, for which the greater exothermicity of the transition can be ascribed to peculiar features of the active site.     

Thermodynamic parameters are sequence-dependent for the supercoil-induced B to Z transition in recombinant plasmids

The entropy and enthalpy changes which contribute to the thermodynamics of the B to Z transition were determined for three recombinant plasmids containing a (dC-dG)16 tract and for a plasmid containing a pair of (dT-dG)20 regions. For each base pair which adopts a left-handed conformation in the plasmids with (dC-dG)16 sequences, the delta HBZ and delta SBZ are -2.1 kcal/mol bp and -8.8 cal/K-mol bp, respectively. In the plasmid containing the (dT-dG)20 tracts, however, the delta HBZ and delta SBZ values are 0.58 kcal/mol bp and -0.76 cal/K-mol bp, respectively. Also, these determinations show that for each B-Z junction that forms in the plasmids containing the (dC-dG), the enthalpy and entropy changes are 24 kcal/mol junction and 65 cal/K-mol junction, whereas for the (dT-dG) plasmid, the enthalpy and entropy changes are -1.8 kcal/mol junction and -22 cal/K-mol junction, respectively. Those values for the enthalpy and entropy changes for the formation of a BZ junction in (dC-dG) and (dT-dG) plasmids suggest that the properties and possibly the structures of the junctions are different. Calculations using the enthalpy and entropy changes determined in this study reveal that the B to Z transition in plasmids containing (dC-dG) blocks are more temperature-dependent than the transitions in plasmids with (dT-dG) blocks. Surprisingly, at temperatures above 60 degrees C, calculations indicate that the B to Z transitions in (dT-dG) plasmids should be energetically favored over that transition in (dC-dG) plasmids.     

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.