General theoretical approach to the thermodynamic and kinetic properties of cooperative intramolecular transformations of linear biopolymers

A general method to calculate experimentally accessible thermodynamic and kinetic quantities for any type of cooperative transitions is developed. Special attention has been directed to transition curves and mean relaxation times. The procedure is applied to the most general case of nearest-neighbor cooperativity by using the linear Ising model and the matrix method of evaluation. The various potential types of end effects arid the resulting chain length dependences are discussed in detail. The significance of the theory with respect to the helix-coil transition of polypeptides as well as to the polyproline I-II transition is indicated.     

Volume and enthalpy profiles of CO rebinding to horse heart myoglobin

Carbon monoxide binding to myoglobin was characterized using the photothermal beam deflection method. The volume and enthalpy changes coupled to CO dissociation were found to be 9.3+/-0.8 mL x mol(-1) and 7.4+/-2.8 kcal x mol(-1), respectively. The corresponding values observed for CO rebinding have the same magnitude but opposite sign: Delta V=-8.6+/-0.9 mL x mol(-1) and Delta H=-5.8+/-2.9 kcal x mol(-1). Ligand rebinding occurs as a single conformational step with a rate constant of 5 x 10(5) M(-1) s(-1) and with activation enthalpy of 7.1+/-0.8 kcal x mol(-1) and activation entropy of -22.4+/-2.8 cal x mol(-1) K(-1). Activation parameters for the ligand binding correspond to the activation parameters previously obtained using the transient absorption methods. Hence, at room temperature the CO binding to Mb can be described as a two-state model and the observed volume contraction occurs during CO-Fe bond formation. Comparing these results with CO dissociation reactions, for which two discrete intermediates were characterized, indicates differences in mechanism by which the protein modulates ligand association and dissociation.     

The nature of stacking interations in polynucleotides. Molecular states in Oligo- and polyribocytidylic acids by relaxation analysis.

The dynamics of the helix-coil transition of single-stranded poly(C) (polyribocytidylate) and CpC (cytidyly(3'-5')cytosine) was investigated by an improved cable temperature-jump technique. The single-strand relaxation was characterized by following the ultraviolet (uv) absorbance changes at 248 and 280 nm. Poly(C) and CpC showed single relaxation processes with amplitudes corresponding to those expected from equilibrium melting curves. The relaxation time contants in the range of 25-100 ns were independent of the nucleotide concentration, but strongly dependent upon temperature. Using thermodynanic parameters obtained from circular dichroism (CD) and uv absorbance melting curves, the following rate constants k (at 20 degrees C, 1.05 M ionic strength, pH 7) and activation enthalpies EA were calculated for poly (C): helix formation kR = 1.11 X 10(-7) s-1 (EAR = 2.6 kcal); helix dissociation kD = 2.1 X 10(6) s-1 (EAD = 11.9 kcal). The rate constants obtained for CpC were higher by a factor of about 2 in kR and 12 in kD, whereas the activation enthalpies closely corresponded to those found for the polymer. In addition to the single-stranded helix-coil relaxation, poly(C) and CpC exhibit a relaxation process with a time constant below 25 ns and maximum amplitudes at wavelengths lambda greater than or equal to 285 nm. The same process is found in cytidine and is attributed to hydration equilibria. The hydration reaction can be considered to be in equilibrium during the entire time range of the helix-coil transition and thus the data obtained for the helix-coil transition can be described by a simple two-state model. The rate parameters indicate the existence of relatively high energy barriers in the helix-coil transition and provide strong evidence evidence against an oscillating dimer model. If there is an ensemble of substates for one of the states (as may be expected for the coil form), the energy difference between the populated substates is small compared with the energy difference between the major conformational states.     

Study of poly-L-lysine conformations in aqueous methanol solution by using polarized Raman techniques.

Raman polarization measurements of the amide I band are reported in ionized poly-L-lysine dissolved in aqueous methanol. The observed changes with methanol concentration, attributed to changes in coil conformation and to the helix-coil transition, represent a novel method of measuring polymer conformation. Polarization measurements as a function of temperature yield values of the energy differences between rotational isomeric states in the coil. deltaH, of 8.8 +/- 0.7, 10.4 +/- 1.1 and 10.8 +/- 1.5 kJ/mol at methanol concentrations (v/v) of 85, 80 and 70% respectively. The stabilization energy of the helix is estimated at 9.3 kJ/mol.     

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.     

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.     

Melting of oligodeoxynucleotides with various structures

Effects of DNA fragments end structures on their melting profiles were studied experimentally and theoretically. We examined melting of hairpins and dumbbells obtained from 62-bp-long linear DNA duplex which is a perfect palindromic sequence. To fit theoretical melting profile to experimental ones additional theoretical parameters were incorporated into the standard statistical mechanical helix-coil transition theory. From comparison theoretical and experimental melting profiles theoretical parameters connected with end-structure effects were evaluated. Analysis revealed the stabilization effect of the hairpin loops and helix ends with respect to DNA duplex melting. Both type of ends make melting these oligodeoxynucleotides more cooperative than predicted by the standard helix-coil transition theory. At low ionic strength ([Na+] less than 0.04 M) this effect becomes so pronounced that melting of the DNA duplexes 30-40 bp-long conforms to the two state model. From the analysis experimental data obtained for dumbbell structures loop-weighting factor for single-stranded loop consisting of 132 nucleotides was determined. This parameter decreases 10 times with the ionic strength decreasing by an order of magnitude from 0.2 to 0.02 M Na+.     

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.     

B-A and B-Z transitions in deoxyoligoduplexes containing 4- and 5- methylcytosine

Self-complementary oligodeoxynucleotides: GGACCCGGGTCC, GGA4mCCCGGGTCC, GGA5mCCCGGGTCC, CGCGCGCG, CG4mCGCGCG, CG5mCGCGCG were synthetized to study the contribution of methyl groups into the energetics of the three known cooperative transitions in DNA: helix-coil, B-A and B-Z With the use of circular dichroism and absorbtion methods the profiles of the above transitions were obtained by variation of temperature (helix-coil), trifluoroethanol fraction (B-A), NaCl and trifluorethanol contents (B-Z). On the basis of the transition widths and shifts of the transition points due to the methylations the energetics of the methyl groups was estimated. 5mC stabilizes the B form relatively the A form by 0.33 kcal/mol; while 4mC by 0.5 kcal/mol. In the B-Z transition 5 mC stabilizes the Z form by 0.28 kcal/mol relatively the B form; 4mC stabilizes also the Z form although by 0.14 kcal/mol only. Thus, these naturally occurring modifications could modulate substantially the ability of a DNA piece to shift into the A or Z form.     

Thermodynamics of unfolding of beta-trypsin at pH 2.8

The unfolding equilibrium of beta-trypsin induced by thermal and chemical denaturation was thermodynamically characterized. Thermal unfolding equilibria were monitored using UV absorption and both far- and near-UV CD spectroscopy, while fluorescence was used to monitor urea-induced transitions. Thermal and urea transition curves are reversible and cooperative and both sets of data can be reasonably fitted using a two-state model for the unfolding of this protein. Plots of the fraction denatured, calculated from thermal denaturation curves at different wavelengths, versus temperature are coincident. In addition, the ratio of the enthalpy of denaturation obtained by scanning calorimetry to the van't Hoff enthalpy is close to unity, which supports the two-state model. Considering the differences in experimental approaches, the value for the stability of beta-trypsin estimated from spectroscopic data (deltaGu = 6.0 +/- 0.2 kcal/mol) is in reasonable agreement with the value calculated from urea titration curves (deltaGUH2O = 5.5 +/- 0.3 kcal/mol) at pH 2.8 and 300 degrees K.     

Effect of N4-methylcytosine and 5-methylcytosine on the stability of the DNA helix

The thermodynamic parameters (delta H, delta S) of the helix-coil transition of self-complementary oligonucleotides d(CGCGCGCG), d(CG5mCGCGCG), d(CG4mCGCGCG), d(GGACCCGGGTCC), d(GGA5mCCCGGGTCC), and d(GGA4mCCCGGGTCC) were determined. The substitution of 4mC for C was found to decrease the melting temperature of the oligonucleotides. The destabilization effect of the two substitutions is equivalent to the change of A.T for G.C pair. The free energy decrease of the helix-coil transition due to the introduction of two 4mC into an octanucleotide was estimated to be 1,24 kcal/mol.     

Macromolecular binding equilibria in the lac repressor system: studies using high-pressure fluorescence spectroscopy

High hydrostatic pressure coupled with fluorescence polarization has been used to investigate protein subunit interactions and protein-operator association in lac repressor labeled with a long-lived fluorescent probe. On the basis of observation of a concentration-dependent sigmoidal decrease in the dansyl fluorescence polarization, we conclude that application of high hydrostatic pressure results in dissociation of the lac repressor tetramer. The 2-fold decrease in the rotational relaxation time and the high-pressure plateau are consistent with a tetramer to dimer transition. The volume change for tetramer dissociation to dimer is -82 +/- 5 mL/mol. The dissociation constant calculated from the data taken at 4.5 degrees C is 4.3 +/- 1.3 nM. The tetramer dissociation constant increases by a factor of 3 when the temperature is raised from 4.5 to 21 degrees C. A very small effect of inducer binding on the subunit dissociation is observed at 4.5 degrees C; the Kd increases from 4.5 to 7.1 nM. At 21 degrees C, however, inducer binding stabilizes the tetramer by approximately 0.8 kcal/mol. Pressure-induced monomer formation is indicated by the curves obtained upon raising the pH to 9.2. The addition of IPTG shifts the pressure transition to only slightly higher pressures at this pH, indicating that the stabilization of the tetramer by inducer is not as marked as that observed at pH 7.1. From the decrease in the polarization of the dansyl repressor-operator complexes, we also conclude that the application of pressure results their dissociation and that the volume change is large in absolute value (approximately 200 mL/mol). The lac repressor-operator complex is more readily dissociated upon the application of pressure than the tetramer alone, indicating that operator binding destabilizes the lac repressor tetramer.     

Volume changes of the molten globule transitions of horse heart ferricytochrome c: a thermodynamic cycle.

Volume changes among the unfolded (U), native (N), and molten globule (MG) conformations of horse heart ferricytochrome c have been measured. U to N (pH 2 to pH 7) was determined in the absence of added salt to be -136 +/- 5 mL/mol protein. U to MG (pH 2, no added salt to pH 2, 0.5 M KCl) yielded + 100 +/- 6 mL/mol. MG to N was broken into two steps, N to NClx at pH 7 by addition of buffered KCl to buffered protein lacking added salt (NClx = N interacting with an unknown number, X, of chloride ions), and MG to NClx by jumping MG at pH 2 in 0.5 M KCl to pH7 at the same salt concentration. The delta V of N to NClx was -30.9 +/- 1.4 mL/mol protein, whereas MG to NClx entailed a delta V of -235 +/- 6 mL/mol. Within experimental error, the results add up to zero for a complete thermodynamic cycle. We believe this to be the first volumetric cycle to have been measured for the conformational transitions of a protein. The results are discussed in terms of hydration contributions from deprotonation of the protein, other hydration effects, and the formation and/or enlargement of packing defects in the protein's tertiary structure during the steps of folding.     

Reversible unfolding of bovine odorant binding protein induced by guanidinium hydrochloride at neutral pH

An analysis of the unfolding and refolding curves at equilibrium of dimeric bovine odorant binding protein (bOBP) has been performed. Unfolding induced by guanidinium chloride (GdnHCl) is completely reversible as far as structure and ligand binding capacity are concerned. The transition curves, as obtained by fluorescence and ellipticity measurements, are very similar and have the same protein concentration-independent midpoint (C1/2 approximately 2.6 M). This result implies a sequential, rather than a concerted, unfolding mechanism, with the involvement of an intermediate. However, since it has not been detected, this intermediate must be present in small amounts or have the same optical properties of either native or denatured protein. The thermodynamic best fit parameters, obtained according to a simple two-state model, are: deltaG degrees un,w = 5.0 +/- 0.6 kcal mol(-1), m = 1.9 +/- 0.2 kcal mol(-1) M(-1) and C1/2 = 2.6 +/- 0.1 M. The presence of the ligand dihydromyrcenol has a stabilising effect against unfolding by GdnHCl, with an extrapolated deltaG degrees un,w of 22.2 +/- 0.9 kcal mol(-1), a cooperative index of 3.2 +/- 0.3 and a midpoint of 4.6 +/- 0.4 M. The refolding curves, recorded after 24 h from dilution of denaturant are not yet at equilibrium: they show an apparently lower midpoint (C1/2 = 2.2 M), but tend to overlap the unfolding curve after several days. In contrast to chromatographic unfolding data, which fail to reveal the presence of folded intermediates, chromatographic refolding data as a function of time clearly show a rapid formation of folded monomers, followed by a slower step leading to folded dimers. Therefore, according to this result, we believe that the preferential unfolding/refolding mechanism is one in which dimer dissociation occurs before unfolding rather than the reverse.     

Melting of Oligodeoxynucleotides with Various Structures

Abstract

Effects of DNA fragments end structures on their melting profiles were studied experimentally and theoretically. We examined melting of hairpins and dumbbells obtained from 62- bp-long linear DNA duplex which is a perfect palindromic sequence. To fit theoretical melting profile to experimental ones additional theoretical parameters were incorporated into the standard statistical mechanical helix-coil transition theory. From comparison theoretical and experimental melting profiles theoretical parameters connected with end- structure effects were evaluated. Analysis revealed the stabilization effect of the hairpin loops and helix ends with respect to DNA duplex melting. Both type of ends make melting these oligodeoxynucleotides more cooperative than predicted by the standard helix-coil transition theory. At low ionic strength ([Na⁺] < 0.04 M) this effect becomes so pronounced that melting of the DNA duplexes 30–40 bp-long conforms to the two state model.

From the analysis experimental data obtained for dumbbell structures loop-weighting factor for single-stranded loop consisting of 132 nucleotides was determined. This parameter decreases 10 times with the ionic strength decreasing by an order of magnitude from 0.2 to 0.02 M Na⁺.     

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.     

Stability of recombinant Lys25-ribonuclease T1

The conformational stability of recombinant Lys25-ribonuclease T1 has been determined by differential scanning microcalorimetry (DSC), UV-monitored thermal denaturation measurements, and isothermal Gdn.HCl unfolding studies. Although rather different extrapolation procedures are involved in calculating the Gibbs free energy of stabilization, there is fair agreement between the delta G degrees values derived from the three different experimental techniques at pH 5, theta = 25 degrees C: DSC, 46.6 +/- 2.1 kJ/mol; UV melting curves, 48.7 +/- 5 kJ/mol; Gdn.HCl transition curves, 40.8 +/- 1.5 kJ/mol. Thermal unfolding of the enzyme is a reversible process, and the ratio of the van't Hoff and calorimetric enthalpy, delta HvH/delta Hcal, is 0.97 +/- 0.06. This result strongly suggests that the unfolding equilibrium of Lys25-ribonuclease T1 is adequately described by a simple two-state model. Upon unfolding the heat capacity increases by delta Cp degrees = 5.1 +/- 0.5 kJ/(mol.K). Similar values have been found for the unfolding of other small proteins. Surprisingly, this denaturational heat capacity change practically vanishes in the presence of moderate NaCl concentrations. The molecular origin of this effect is not clear; it is not observed to the same extent in the unfolding of bovine pancreatic ribonuclease A, which was employed in control experiments. NaCl stabilizes Lys25-ribonuclease T1. The transition temperature varies with NaCl activity in a manner that suggests two limiting binding equilibria to be operative. Below approximately 0.2 M NaCl activity unfolding is associated with dissociation of about one ion, whereas above that concentration about four ions are released in the unfolding reaction.(ABSTRACT TRUNCATED AT 250 WORDS)     

Improved thermodynamic parameters and helix initiation factor to predict stability of DNA duplexes.

To improve the previous DNA/DNA nearest-neighbor parameters, thermodynamic parameters (deltaH degrees, deltaS degrees and deltaG degrees) of 50 DNA/DNA duplexes were measured. Enthalpy change of a helix initiation factor is also considered though the parameters reported recently did not contain the factor. A helix initiation factor for DNA/DNA duplex determined here was the same as that of RNA/RNA duplex (deltaG degrees(37) = 3.4 kcal/mol). The improved nearest-neighbor parameters reproduced not only these 50 experimental values used here but also 15 other experimental values obtained in different studies. Comparing deltaG degrees(37) values of DNA/DNA nearest-neighbor parameters obtained here with those of RNA/RNA and RNA/DNA, RNA/RNA duplex was generally the most stable of the three kinds of duplexes with the same nearest-neighbor sequences. Which is more stable between DNA/DNA and RNA/DNA duplexes is sequence dependent.     

Kinetic studies on the helix-coil transition of fluorescent labeled poly(-L-lysine) by the temperature-jump technique

Fluorescent dansyl labels were covalently attached to poly (L-lysine) (poly(Lys)) with a degree of polymerization of 300 to 600. The degree of labeling was 0.01 to 0.085 (mol label to mol amino acid residues). From the decay of the anisotropy of fluorescence it was concluded that the labels were highly mobile both in the coiled and helical state. A decrease of fluorescence intensity accompanied the helix-coil transition. Identical pH induced transition curves were measured by circular dichroism and fluorescence. The midpoint of the transition was at pH 10.2. The kinetics of the transition were studied by temperature-jump relaxation using fluorescence detection. A single relaxation phase was observed. The relaxation time tau exhibited a distorted bell shaped dependence on the degree of helicity f with a maximum value tau(max) = 15 micros at f = 0.3 and 20 degrees C. It was independent of polymer concentration and of the degree of labeling. A rate constant of helix propagation kF = 10(7) s(-1) was calculated from tau(max) and published values of the nucleation parameter sigma. The activation energy was 16 kJ mol . The observed rate constant is comparable to that of poly(L-glutamic acid) but two orders of magnitude smaller than that found for polyamino acids with nonionizable side chains.     

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.