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.     

Solvent dependence of the helix-coil transition of poly-gamma-benzyl-L-glutamate. A PMR study

The coil to helix conformational transitions undergone by poly-γ-benzyl-_L-glutamate in solutions of haloacetic acids and various cosolvents were studied by means of proton magnetic resonance. The results indicate a very small solvent dependence of the α-CH Helix–coil chemical shift difference. The helical stabilities of PBLG in different solvent mixtures were interpreted in terms of modifications of the “solvent structure.”     

Osmotically induced helix-coil transition in poly(glutamic acid)

Protein folding and conformational changes are influenced by protein-water interactions and, as such, the energetics of protein function are necessarily linked to water activity. Here, we have chosen the helix-coil transition in poly(glutamic acid) as a model system to investigate the importance of hydration to protein structure by using the osmotic stress method combined with circular dichroism spectroscopy. Osmotic stress is applied using poly(ethylene glycol), molecular weight of 400, as the osmolyte. The energetics of the helix-coil transition under applied osmotic stress allows us to calculate the change in the number of preferentially included water molecules per residue accompanying the thermally induced conformational change. We find that osmotic stress raises the helix-coil transition temperature by favoring the more compact α-helical state over the more hydrated coil state. The contribution of other forces to α-helix stability also are explored by varying pH and studying a random copolymer, poly(glutamic acid-r-alanine). In this article, we clearly show the influence of osmotic pressure on the peptide folding equilibrium. Our results suggest that to study protein folding in vitro, the osmotic pressure, in addition to pH and salt concentration, should be controlled to better approximate the crowded environment inside cells.     

Enthalpy of helix-coil transition of DNA: dependence on Na+ concentration and GC-content

The enthalpy of helix-coil transition of DNA (delta H) is determined from the experiments on DNA melting with ligands by means of absolutely general formula, which contains only values directly known from the experiment (M.D. Frank-Kamenetskii, and A.T. Karapetian, Mol. Biol. USSR 6, 621 (1972)) with the combination of the "area" method (P.O. Vardevanian, et al., Biophysica 28, 130 (1983)). The experimentally obtained data show that delta H depends on both concentration of Na+ in solution and GC-content of DNA and is of high accuracy.     

Calculation of kinetic curves for the helix-coil transition of polypeptides

Methods for calculating the rate of cooperative transitions on a linear lattice, for which the helix–coil transition of polypeptides is an example, are reported. The problem is to determine the kinetic characteristics of the transition given the rate constants for a set of elementary steps: in this case, the transformations of individual segments between the helix and coil states. The most straightforward method is to store the state of a long lattice (in which helix and coil segments are represented by 1′s and 0′s) in a computer and to use random-number techniques to generate its behavior as a function of time. This is, in principle, a solution to the problem, but it requires very large amounts of computer time. We have devised a matrix iteration procedure which allows much faster computation while reproducing the results of the random-number method accurately. In this procedure the computer operates repeatedly with a transition probability matrix on a vector which represents the time-dependent state of a finite group of units. The choice of a finite group neglects kinetic correlations between the state changes of units inside and outside the group, but comparison with the random-number method indicates that these correlations are not important. Thus it is possible to generate the kinetic behavior of the model under essentially any conditions, for either relaxation or large perturbations. Examination of these calculated curves suggests a simple and quite generally applicable solution to the inverse problem—that of evaluating the rate constants from kinetic curves. The initial slope is well defined in almost every case, and since an analytic equation can be written relating this to the rate constants, these can be obtained directly from the initial rate. This latter is therefore the most convenient single measure of transition rate.     

A carbon-13 magnetic resonance study of the helix-coil transition in polyuridylic acid

The temperature-dependent conformations of poly(U) in 0.5M CsC1 have been studied by carbon-13 nuclear magnetic resonance. The transition from random coil to an ordered structure results in broadening of lines in the ¹³C spectra, due to intramolecular ¹H–¹³C dipolar interactions and restricted motions in the ordered state. Changes in the chemical shifts suggest that the bases are interacting below the transition temperature. The random coil form shows conformation preferences for internal rotation about C4′–C5′, C5′–O5′, and C3′–O 3′ bonds. The statistical randomness of the coil arises mainly because of flexibility about O–P bonds. The results are analyzed in conjunction with theoretical calculations and light-scattering data.     

Kinetics of the helix-coil transition in DNA

The kinetics of the helix-coil transition have been investigated for T2 and T7 phage DNA in a formamide-water-salt mixed solvent using a slow temperature perturbation technique (applicable to kinetic processes with rate constants ? 3 min^?1). In this solvent degradation of the DNA is effectively suppressed. Complex kinetic curves are observed by absorbance and viscosity measurements for the response to denaturing perturbations in the transition region. Analysis of the decay curves indicates that the denaturation reaction in this time range can be treated as a first-order reaction with a variable first-order rate parameter, k, the derivative of the logarithm of the absorbance or viscosity change with respect to time. In the approach to denaturation equilibrium in the transition region, the rate parameter is determined only by the instantaneous extent of denaturation of the molecules. Near equilibrium, the rate parameter assumes a constant value characteristic of the equilibrium state. In this region, where the denaturation reaction proceeds as a simple first-order process, both the decay of absorbance (reflected local conformational change) and the decay of solution viscosity (reflecting macromolecular conformational change) are characterized by the same constant value of k. In 83% formamide, 0.3M Na⁺, the rate parameter k for T2 DNA decreases from an extrapolated value of 2.0 min^?1 at 0% denaturation to 0.11 min^?1 at 90% denaturation. Rate parameters determined for T7 DNA at the same counterion concentration and fraction of denaturation are approximately five times as large as those cited for T2 DNA, indicating an inverse proportionality of rate constant to molecular length. On the other hand, simple first-order kinetic responses with constant k are obtained for renaturing perturbations within the transition, indicating that the mechanism of rewinding differs, in most cases, from that of unwinding. Only in the limit of very small perturbations about a given equilibrium position are the rate constants k obtained from denaturing and renaturing perturbations equal. For perturbations of finite size, it appears possible that an intramolecular initiation or nucleation event may precede rewinding and limit the rate of this reaction. The rate parameters again are approximately inversely proportional to molecular weight. The one exception to the first-power dependence on molecular weight appears when temperature jumps are made upward into the post-transition region. Here the molecular-weight dependence is second power, but complications arising from the different strand-separation properties of T2 and T7 DNA's make interpretation difficult. The previously used model of friction-limited unwinding appears to fit all the observations except for the molecular-weight dependence.     

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.     

Pressure dependence of the helix–coil transition temperature of poly[d(G-C)]

The Pressure Dependence of the Helix-Coil Transition Temperature (T_m) of Poly[d(G-C)] was studied as a function of sodium ion concentration in phosphate buffer. The molar volume change of the transition (ΔV) was calculated using the Clapeyron equation and calorimetrically determined enthalpies. The ΔV of the transition increased from +4.80 (±0.56) to +6.03 (±0.76) mL mol^?1 as the sodium ion concentration changed from 0.052 to 1.0M. The van't Hoff enthalpy of the transition calculated from the half-width of the differentiated transition displayed negligible pressure dependence: however, the value of this parameter decreased with increasing sodium ion concentration, indicating a decrease in the size of the cooperative unit. The volume change of the transition exhibits the largest magnitude of any double-stranded DNA polymer measured using this technique. For poly[d(G-C)] the magnitude of the change in ΔV with sodium ion concentration (0.94 ± 0.05 mL mol^?1) is approximately one-half that observed for either poly[d(A-T)] or poly (dA)·poly(dT). The ΔV values are interpreted as arising from changes in the hydration of the polymer due to the release of counterions and changes in the stacking of the bases of the coil form. As a consequence of solvent electrostriction, the release of counterions makes a net negative contribution to the total ΔV, implying that disruption of the slacking interactions contributes a positive volume change to the total ΔV. The larger magnitude of the ΔV compared with that of other double-stranded polymers may be due in part to the high helix-coil transition temperature of poly[d(G-C)], which will attenuate the contribution of electrostriction to the total volume change. The data in addition show that in the absence of other cellular components, the covalent structure of DNA is stabile under conditions of temperature and pressure more extreme than those experienced by any known organism. © 1995 John Wiley & Sons, Inc.     

Thermodynamics of oligo (A) N -2poly(U) from the dependence of the temperature of the helix-coil transition on oligomer concentration

On the basis of elementary two-state, ideal solution thermocynamics, a modified expression for the melting of oligo. polynucleotide helices is derived which is applicable to variations in T_m^N and/or oligomer concentration, C_m with oligomer length, N: ((I)) ΔH_r is the enthalpy per helix residue, i.e., per base-pair or base-triplet, V_r^f is the thermodynamic “available” or “reaction” volume, in liters/mole of helical residues; and n is the number of polynucleotide strands, e.g., n = 2 for oligo (A)_N·2 poly(U)∞. Some earlier treatments have engendered confusion in the interpretation of the “reaction volume,” but with the derivation herein, the entropic origin and physical significance of V_r^f is unequivocal. The following approximation was arrived at for the reduction expected in the configurational entropy, ΔS_r^{conf, ∞}, for (A)∞·2(U)∞, when the poly(A), strand is substituted for by an equivalent strand of contiguous oligo(A)_N,′s: ((II)) This adjustment of ΔS_r^{conf, ∞} represents the source of the coefficient to 1/T_m^∞ in expression (I). The expectation that ΔS_r^{conf, N} < ΔS_r^{conf, ∞} is due to the effect of releasing normal internucleotide configurational restrictions every Nth residue in one-third of the strands of the (A)_N·2(U)∞ helix. Although the reduction in ΔS_r^{conf, ∞} (II) may seem small (i.e., only 5.5% for the tetramer), its effect on the magnitude of V_r^f in expression (I) is exponential. Thus, without these considerations the quantitative applicability of earlier expressions is questionable. By examining the variation in T_m^N with c_m for a single N, all assumptions, required for evaluating V_r^f or the entropic effects of discontinuities in the (A)_N strand are avoided in the determination of a reliable enthalpy. We have therefore examined the system ((III)) and obtained a ΔH_r = 12.58 ± 0.08 kcal per mole (A)·2(U) base-triplets between 5 and 2.5°C. That this value for ΔH_r is in such excellent agreement with all calorimetric values reported for (A)∞·2(U)∞ suggests that the enthalpy for reaction(III) is not significantly affected by disconnections in the backbone of (A)₄·2(U)∞. From (I), V_r^f = 6.0 × 10^?4 1/mole or 1 Å ³per helical residue. ΔH_r°, corrected for residual single-strand stacking in (A)₄, is in excellent agreement with that found earlier for (A)₁·2(U)∞. A residual heat capacity of 90 kcal(±20) per mole (A)·2(U) base-triplets per °C is deduced from the decrease of ΔH_r° with temperature.     

Photochemical covalent binding of urocanic acid to polynucleic acids

Photolysis of E-[ring-2-14C]urocanic acid (UA) with native or denatured calf thymus DNA leads to covalent binding of the radiolabel to the nucleic acid. A similar observation is made upon photolysis of the labeled UA with the polyribonucleotides, in which case a strong preference is observed for binding to poly[U]. DNA or poly[U], which had been reacted with UA and purified by dialysis and multiple precipitations, releases UA upon further irradiation with 254 nm light (as expected for cyclobutane adducts). Quantum efficiencies for binding of the UA to native DNA have been measured at 308 and 266 nm and are 0.30 x 10(-5) and 1.3 x 10(-4), respectively, at comparable reactant concentrations. The large increase at the shorter wavelength (where DNA absorption is more competitive) is taken as evidence for the primary role of a DNA excited state in initiating the binding reaction(s).     

Magnesium ion effect on the helix-coil transition of DNA

The effect of magnesium ions on the parameters of the DNA helix-coil transition has been studied for the concentration range 10^?6–10^?1M at the ionic strengths of 10^?3M Na⁺. Special attention has been given to the region of low ion concentrations and to the effect of polyvalent metallic impurities present in DNA. It has been shown that binding with Mg⁺⁺ increases the DNA stability, the effect being observed mainly in the concentration range 10^?6–10^?4M. At[Mg⁺⁺]>10^?2M the thermal stability of DNA starts to decrease. The melting range extends to concentrations ～10^?5M and then decreases to 7–8°C at the ion content of 10^?3M. Asymmetry of the melting curves is observed at low ionic strengths ([Na⁺] = 10^?3M) and [Mg⁺⁺] ? 10^?5M. The results, analyzed in terms of the statistical thermodynamic theory of double-stranded homopolymers melting in the presence of ligands, suggest that the effects observed might be due to the ion redistribution from denatured to native DNA. An experimental DNA–Mg⁺⁺ phase diagram has been obtained which is in good agreement with the theory. It has been shown that thermal denaturation of the system may be an efficient method for determining the ion-binding constants for both native and denatured DNA.     

Solvation model dependency of helix-coil transition in polyalanine

Helix-coil transitions in polyalanine molecules of length 10 are studied by multi-canonical Monte Carlo simulations. The solvation effects are included by either a distance-dependent dielectric permittivity or by a term that is proportional to the solvent-accessible surface area of the peptide. We found a strong dependence of the characteristics of the helix-coil transition from the details of the solvation model.     

Theoretical study for volume changes associated with the helix-coil transition of peptides.

We calculate the partial molar volumes and their changes associated with the coil(extended)-to-helix transition of two types of peptide, glycine-oligomer and glutamic acid-oligomer, in aqueous solutions by using the Kirkwood-Buff solution theory coupled with the three-dimensional reference interaction site model (3D-RISM) theory. The volume changes associated with the transition are small and positive. The volume is analyzed by decomposing it into five contributions following the procedure proposed by Chalikian and Breslauer: the ideal volume, the van der Waals volume, the void volume, the thermal volume, and the interaction volume. The ideal volumes and the van der Waals volumes do not change appreciably upon the transition. In the both cases of glycine-peptide and glutamic acid-peptide, the changes in the void volumes are positive, while those in the thermal volumes are negative, and tend to balance those in the void volumes. The change in the interaction volume of glycine-peptide does not significantly contribute, while that of glutamic acid-peptide makes a negative contribution.     

Exploring the helix-coil transition via all-atom equilibrium ensemble simulations

The ensemble folding of two 21-residue alpha-helical peptides has been studied using all-atom simulations under several variants of the AMBER potential in explicit solvent using a global distributed computing network. Our extensive sampling, orders of magnitude greater than the experimental folding time, results in complete convergence to ensemble equilibrium. This allows for a quantitative assessment of these potentials, including a new variant of the AMBER-99 force field, denoted AMBER-99 phi, which shows improved agreement with experimental kinetic and thermodynamic measurements. From bulk analysis of the simulated AMBER-99 phi equilibrium, we find that the folding landscape is pseudo-two-state, with complexity arising from the broad, shallow character of the "native" and "unfolded" regions of the phase space. Each of these macrostates allows for configurational diffusion among a diverse ensemble of conformational microstates with greatly varying helical content and molecular size. Indeed, the observed structural dynamics are better represented as a conformational diffusion than as a simple exponential process, and equilibrium transition rates spanning several orders of magnitude are reported. After multiple nucleation steps, on average, helix formation proceeds via a kinetic "alignment" phase in which two or more short, low-entropy helical segments form a more ideal, single-helix structure.     

Changes in the polyelectrolyte-amphiphile interaction due to helix-coil transition induced by specific counterions or variations in temperature

For the system κ-carrageenan/amitriptyline it is shown that the degree of binding of amitriptyline is closely related to the carrageenan conformation as regulated by the counterions (Na⁺ or K⁺). The adsorption becomes much more pronounced when the carrageenan molecule is in the helix form (counterion K⁺) than when it has a coil conformation (counterion Na⁺). Furthermore, for the helical state the adsorption becomes strongly cooperative. It is also shown experimentally that the release from the adsorbed state has a conversion temperature at about 42°C (helix-coil transition). The effect is also related to the linear charge density. For κ-carrageenan with a higher charge density the adsorption is strong and cooperative both in the presence of Na⁺ and K⁺ ions. © 1996 John Wiley & Sons, Inc.