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.     

Theory of melting of the triple helix poly (A + 2U) for a 1 : 2 mixture of Poly A to Poly U

The Zimm-Bragg theory is extended to treat the melting of the triple helix poly (A + 2U) for a solution with a 1 : 2 mole ratio of poly A to poly U. Only the case for long chains is considered. For a given set of parameters the theory predicts the fraction of segments in the triple helix, double helix, and random coil states as a function of temperature. Four nucleation parameters are introduced to describe the two order–disorder transitions (poly (A + 2U) ? poly A + 2 poly U and poly (A + U) ? poly A + poly U) and the single order–order transition (poly (A + 2U) ? poly (A + U) + poly U). A relation between the nucleation parameters is obtained which reduces the number of independent parameters to three. A method for determining these parameters from experiment is presented. From the previously published data of Blake, Massoulié and Fresco⁸ for [Na⁺] = 0.04, we find σ_T = 6.0 × 10^?4, σ_D = 1.0 × 10^?3, and σσ* = 1.5 × 10^?3. σ_T and σ_D are the nucleation parameters for nucleating a triple helix and double helix, respectively, from a random coil region. σσ* is the nucleation parameter for nucleating a triple helix from a double helix and a single strand. Melting curves are generated from the theory and compared with the experimental melting curves.     

Helix–coil stability constants for the naturally occurring amino acids in water. XXI. Glutamine parameters from random poly(hydroxypropylglutamine-co-L-glutamine) and poly(hydroxybutylglutamine-co-L-glutamine)

Water-soluble, random copolymers containing L -glutamine and either N⁵-(3-hydroxypropyl)-L -glutamine or N⁵-(4-hydroxybutyl)-L -glutamine were synthesized, fractionated, and characterized. The thermally induced helix–coil transitions of these copolymers were studied in water. A short-range interaction theory was used to deduce the Zimm-Bragg parameters σ and s for the helix–coil transition in poly(L -glutamine) in water from an analysis of the melting curves of the copolymers in the manner described in earlier papers. The computed values of s indicate that L -glutamine is helix-indifferent at low temperature and a helix-destabilizing residue at high temperature in water. At all temperatures in the range of 0–70°C, the glutamine residue promotes helix–coil boundaries since the computed value of σ is large.     

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〉.     

Charge density on native and ultraviolet-irradiated myosin A

The axial ratios (a/b) of native and 60 min. ultraviolet-irradiated myosin A molecules were calculated from previously reported sedimentation and diffusion data; values found were a/b = 74, a = 1880 A., and b = 26 A. for native myosin A; a/b = 104, a = 3280 A., and b = 32 A. for 60 min. ultraviolet-irradiated myosin A. Electrophoretic mobilities gave identical values of 3.2 (±0.1) × 10^?5 cm.²/v.-sec. for both native and 60 min. ultraviolet-irradiated myosin A. From the prior sedimentation and diffusion data, together with newly obtained electrophoretic data, the net charge Z and the charge density σ of native and ultraviolet-irradiated myosin A molecules were calculated from Henry's equation. The following results were obtained: for native myosin A, Z = 160 negative charges per molecule and σ = 22 coulombs/cm.²; for ultraviolet-irradiated myosin A, Z = 312 negative charges per molecule and σ = 20 coulombs/cm.². The results of this study provide an experimental demonstration that, the electrophoretic mobility of charged solute particles is dependent upon the particle charge density and not on the absolute charge of the particle.     

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.     

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.     

Optical activity of polypeptides in the infrared. Predicted CD of the amide I and amide II bands.

The Miyazawa-Blout-Krimm (M-B-K) treatment of polypeptide absorption in the infrared is extended to the calculation of circular dichroism (CD), linear dichroism, and oriented CD for the amide I and amide II transitions. Matrix methods are applied to the α helix and β structures using measured values for the strengths and directions of the transition dipole moments and empirical values from M-B-K for the coupling constants. Relatively small aggregates, a 36-residue helix, and 8-chain × 4-residue β sheets, are large enough to show calculated absorption agreeing with M-B-K results, which are based on infinite lattices. In all cases the predicted CD is an approximately conservative couple. The strongest CD should appear in the α helix, Δε/ε ?± 10^?3 for both transitions. The amide II transition should show moderate CD couples in both β structures, Δε/ε ? (+2 to ?1) × 10^?4. The amide I transitions in β structures should show weak CD couples, Δε/ε = (+3 to ?2) × 10^?5, except that the negative branch in the antiparallel structure may be detectable (Δε/ε ? ?2 × 10^?4) because absorption is very low at its wavelength peak. CD on oriented samples should be enhanced over the unoriented cases, giving values as large as Δε/ε = 3 × 10^?3 because particular directions of observation allow the light to avoid much of the absorption in the sample. If all three structures are considered as helices, then the larger distance of the transition dipoles from the axis in the α helix, and the orientations of the transitions in the different structures, are the factors that, in terms of our previous theoretical work [Snir and Schellman (1973) J. Phys. Chem. 77 , 1653] satisfactorily explain the calculated results. Simple dipole–dipole interaction is calculated to make a substantial contribution to the coupling between groups.     

Thermodynamics and kinetics of the helix-coil transition of oligomers containing GC base pairs

Absorbance-temperature profiles have been determined for the following self-complementary oligonucleotides or equimolar paris of complementary oligonucleotides containing GC base pairs: A₂GCU₂, A₃GCU₃, A₄GCU₄, A₆CG + CGU₆, A₈CG + CGU₈, A₄G₂ + C₂U₄, A₅G₂ + C₂U₅, A₄G₃ + C₃U₄, and A₅G₃ + C₃U₅. In all cases cooperative melting transitions indicate double-helix formation. As was found previously, the stability of GC containing oligomer helices is much higher than that of AU helices of corresponding length. Moreover, helices with the same length and base composition but different sequences also have quite different stabilites. The melting curves were andlyzed using a zipper model and the thermodynamic parameters for the AU pairs determined previously. The effect of single-strand stacking was considered separately. According to this model, the formation of a GC pair from unstacked single strands is associated with an ethalpy change of ?15 kcal/mole. Due to the high degree of single-strand stacking at room temperature the enthalpy change for the formation of GC pairs from unstacked single strands is only ?5 to ?6 kcal/mole. (The corresponding parameters for AU pairs are ?10.7 kcal/mole and ?5 to ?6 kcal/mole.) The sequence dependence of helix stability seems to be primarily entropic since no differences in ΔH were seen among the sequence isomers. The kinetics of helix formation was investigated for the same molecules using the temperature jump technique. Recombination of strands is second order with rate constants in the range of 10⁵ to 10⁷M^?1 sec^?1 depending on the chain length and the nucleotide sequence. Within a series of oligomers of a given type, the rates of recombination decrease with increasing chain length. Oligomers with the sequence A_nGCU_n recombine six to eight times slower than the other oligomers of corresponding chain length. The experimental enthalpies of activation of 6 to 9 kcal/mole suggest a nucleation length of one or two GC base pairs. The helix dissociation process has rate constants between 0.5 and 500 sec^?1 and enthalpies of activation of 25 to 50 kcal/mole. An increase of chain length within a given nucleotide series leads to decreased rates of dissociation and increased enthalpies of activation. An investigation of the effect of ionic strength on A_nGCU_n helix formation showed that the rates of recombination increase considerably with increased ionic strength.     

Fine structure of DNA melting curves.

Theoretical calculations predict that the differential melting curves for random polynucleotide sequences having lengths up to several tens of thousands of base pairs have a clear-cut fine structure. This structure appears in the form of multiple narrow peaks 0.3–0.4°C wide on the bell shaped main curve. The differential melting curves have different shapes for different specific sequences. The theory also predicts the disappearance of the fine structure when the length of the sequence increases and when circular, covalently closed DNA is considered instead of the open structure. The predictions of the theory were confirmed by the measurements of differential melting curves for open and covalently closed circular forms of DNA for PM2 phage (N = 10⁴ base pairs) and also for other phage DNA's of different length: T7 (N = 3.8 × 10⁴); S_D (N = 9.2 × 10⁴); T2 (N = 17 × 10⁴). It was shown that the effect of fine structure results mainly from the cooperative melting out of DNA regions 300–500 base pairs long.     

Conformational studies on copolymers of L-lysine and L-leucine: circular dichroism and potentiometric titration studies

Conformational aspects of a series of copolymers of L -Leucine and L -leucine [poly-(Lys^xLeu^y)] containing 0 to 0.41 mole fraction L -leucine have been studied by circular dichroism (CD) and potentiometric titration in 0.05M KF solution. CD studies on the α-helical conformation showed a dependence of the magnitude of the CD ellipticity band at 222 nm on copolymer composition; the [θ]₂₂₂ decreasing with higher leucine contents. This was interpreted as the result of an increase of the hydrophobicity of the environment of the amide group due to the presence of the leucyl residues. Values of the Zimm-Rice parameter, σ, for the copolymers were obtained from the potentiometric titrations and used to fit theoretical curves to the experimental data. Using the variation of σ with polymer composition, a value of σ for the leucyl residue was estimated to be 6.3 × 10^?2, assuming independence of σ on the amino acid sequence in the copolymer. The free energy change for the conversion of one mole residue from uncharged helix to uncharged coil, ΔG_hc°, was also obtained from the titration data for each copolymer up to a leucine mole fraction of 0.16; a value of 385 cal mole^?1 was estimated for ΔG_hc° for a leucyl residue. These values for σ and ΔG_hc° are compared with other values in the literature for various amino acid residues obtained from titration and melting curve data.     

Influence of base-pair changes and cooperativity parameters on the melting curves of short DNAs

Theoretical melting curves were calculated for four DNA restriction fragments, 157–257 base pairs (bp), and a series of hypothetical block DNAs with sequences d(C_2xA_xC_2x). d(C_2xT_xG_2x), 5 ? x ? 40. These DNAs provided a mixture of A·T/G·C sequence distributions with which to investigate the effects of parameters and base-pair changes on the melting of short DNAs. The sensitivity of DNA melting curves to changes in internal loop melting parameters σ and κ was examined. As Expected, theoretical melting curves of short DNAs with a quasirandom base-pair sequence vary little with changes in internal loop parameters. End melting dominates the transition behaviour of these moleucles. This was also observed for the block DNAs up to x = 22. Beyond this length, melting curves are highly sensitive to the internal loop parameters. Sensitivity is also predicted for a 157-bp fragment with a block distribution of A·T and G·C pairs. These results indicate that accurate evaluation of internal loop parameters is possible with short DNAs (100–200 bp) containing a G·C/A·T/G·C block distribution with at least 22 bp in each block. Duplex-to-single-strands dissociation parameters were reevaluated form experimental melting curve data of eight DNA fragments using a least squares fit approach. This analysis confirmed parameter values previously found with a simplified dissociation model. A Priori predictions are made on the effects of base-pair changes on the melting curves of three characterized DNA restriction fragments. Single base-pair changes are predicted to induce small but measurable changes in the melting curves. The characteristics of the altered melting curves depend on the location of the base-pair change.     

Cooperative lengths of DNA during melting

The mean cooperative length of domains of DNA, determined from the variance in (G + C) content in derivative melting curves of large bacterial DNAs, varies from 230 base pairs (bp) for (A ? T)-rich domains to 580 bp for (G ? C) domains. These values correspond to values for the cooperativity parameter of 2(±2) × 10^?5 and 3(±2) × 10^?6, respectively, and to +7.2 and +9.6 kcal for the free energy of helix interruption in those regions.     

Solution properties of synthetic polypeptides. VI. Helix-coil transition of poly-N5-(3-hydroxypropyl)-L-glutamine

A new procedure for evaluating u and σ characterizing σ-helix-forming polypeptides in solution was derived from Nagai's theory for the helix–coil transition of such polymers. Here u is the activity for helix formation from random coil, and σ is the helix initiation parameter. The necessary data are the helical content f_N at fixed solvent and temperature as a function of N, where N is the degree of polymerization of the polypeptide sample. Such data were obtained from ORD measurements on a number of fractionated samples of poly-N⁵-(3-hydroxypropyl)-L -glutamine (PHPG) in mixtures of water and methanol covering the complete range of composition and at various termperatures (5–40°C). When analyzed in terms of the proposed procedure, they yielded values of σ which were in the range (3.2 ± 0.6) × 10^?4, substantially independent of solvent composition and temperature. These values were much larger than those obtained recently for σ of poly(β-benzyl-L -aspartate) in m-cresol and in a mixture of chloroform and DCA. The data for [η] and s₀ (limiting sedimentation coefficient) as functions of molecular weight indicated that the molecular shape of PHPG in pure methanol is essentially rodlike, whereas that in pure water is not entirely randomly coiled but rather may be regarded as an interrupted helix. These indications were consistent with the results from ORD measurements. When plotted against the corresponding values of f_N, the values of [η] and [s₀] for PHPG in mixtures of water and methanol of various compositions and temperatures formed smooth composite curves, and we attributed these phenomena to the fact that σ of PHPG was nearly constant under these solvent conditions. Here [s₀] stands for a reduced limiting sedimentation coefficient which is equal to the inverse friction factor of the solute molecule.     

A calorimetric study of a polymer–monomer complex formed by polyuridylic acid 3′,5′-cyclic AMP

The existence of a soluble complex formed by polyuridylic acid (poly (U)) and 3′,5′-cyclic AMP (cAMP) is demonstrated by u.v. extinction vs. temperature curves, optical rotation, equilibrium dialysis, and reaction calorimetry. The complex hasthe stoichiometry of 2 poly (U)-cAMP and its formation is accompanied by an enthalpy change of ?13.0 kcal/mole of base triplet. The introuction of an empirical factor α in the equations given by Damle² and Crothers² leads to the evolution of a ΔH value of ?13.4 keal/mole. The parameter α is considered as a correction factor for the concentration dependence of the binding process. There is no relation between α and the reduction of monomer activity due to self-association of monomers. The study of the binding process at several temperatures showed that the cooperativity parameter, σ, is independent of temperature and its value of 6.5 × 10^?3 is in good agreement with σ = 5 × 10^?3 for the poly (U)·poly(A) system.³     

Helix-coil transition of poly-gamma-N-carbobenzoxy-L-alpha, gamma-diaminobutyrate and poly-delta-N-carbobenzoxy-L-ornithine

The helix–coil transition of poly-γ-N-carbobenzoxy-L -α,γ-diaminobutyrate (PCLB) and poly-δ-N-carbobenzoxy-L -ornithine (PCLO) in chloroform–dichloroacetic acid mixtures was followed by optical rotatory dispersion. PCLB displays a “normal” temperature-induced transition, but PCLO an “inverse” one. The thermodynamic parameters for helix formation of the two polymers were determined using the Zimm-Bragg theory. The enthalpy for adding an amide residue to a helical region, ΔH, and the initiation factor σ were ΔH = ?180 cal/mole and σ = 9.2 × 10^?5 for PCLB and ΔH = +490 cal/mole and σ = 1.9 × 10^?5 for PCLO.     

Effects of calcium and manganese ions on the helix–coil transition of DNA

The thermal denaturation method was employed to study the effect of Ca²⁺ and Mn²⁺ ions on the DNA helix–coil transition parameters at Na⁺ concentrations of 10^?3–10^?1M. At low ion concentrations, thermal stability increases, the melting range passes through a maximum, and the denaturation curves become asymmetric. These changes are quantitatively similar for Mn²⁺ and Ca²⁺ ions. With a further increase in the concentration of bivalent ions, the conformational transition temperatures pass through a maximum, and the melting range first tends to saturation and then rapidly decreases to 1–2°C. The Mn²⁺ concentrations, at which the above effects occur, are an order of magnitude lower than the Ca²⁺ concentrations. Comparison of experimental results and calculation in terms of the ligand theory permitted estimation of binding constants characterizing association between Mn²⁺ and Ca²⁺ ions and bases of native and denatured DNA. We show that, unlike the interaction with phosphates, bivalent ion–DNA base binding is weakly dependent on monovalent ion concentration in the solution.     

On the possibility of true phase transition in heterogeneous DNA during thermal denaturation under conditions close to equal stability of A+T and G+C pairs

The DNA helix–coil transition has been studied in the presence of high concentrations of manganese ions (about 10^?3M), which corresponds to the conditions close to equal stability of the A+T and G+C pairs, at the ionic strengths of 10^?1, 10^?2, and 1.6 × 10^?3M Na⁺. With the Mn²⁺ ion effect, the transition range is significantly reduced to not more than 0.2°C at 1.2 × 10^?3M Mn²⁺ and 1.6 × 10^?3M Na⁺. The melting curves display a sharp kink at the end of the helix–coil transition, which is interpreted as an indication of the second-order phase transition. It is shown that the melting curves obtained can be approximated by a simple analytical expression 1 – θ = exp[–a(t_c - t)], where θ is the DNA helix fraction, t_c is the phase transition temperature, and a is an empirical parameter characterizing the breadth of the melting range and responsible for the magnitude of a jump of the helicity derivative with respect to the temperature at the phase transition point.     

Triple helix–coil transition of covalently bridged collagenlike peptides

The thermal triple helix–coil transition of covalently bridged collagenlike peptides with repeating sequences of (Ala-Gly-Pro)_n, n = 5–15, was studied optically. The peptides were soluble in water/acetic acid (99:1) and were found to form triple-helical structures in this solvent system beginning with n = 8. The thermodynamic analysis of the transition equilibrium curves for n = 9–13 yielded the parameters ΔH°_s = ?7.0 kJ per tripeptide unit, ΔS°_s = ?23.1 J deg^?1 mol^?1 per tripeptide unit for the coil-to-helix transition, and the apparent nucleation parameter σ ? 5 × 10^?2. It was suggested through double-jump temperature experiments that the rate-limiting step during refolding is not only influenced by the difficulties of nucleation, but also by cis–trans isomerization of the Gly-Pro peptide bond.     

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.