Determination of melting temperature and temperature melting range for DNA with multi-peak differential melting curves

Many factors that change the temperature position and interval of the DNA helix–coil transition often also alter the shape of multi-peak differential melting curves (DMCs). For DNAs with a multi-peak DMC, there is no agreement on the most useful definition for the melting temperature, T_m, and temperature melting width, ΔT, of the entire DNA transition. Changes in T_m and ΔT can reflect unstable variation of the shape of the DMC as well as alterations in DNA thermal stability and heterogeneity. Here, experiments and computer modeling for DNA multi-peak DMCs varying under different factors allowed testing of several methods of defining T_m and ΔT. Indeed, some of the methods give unreasonable “jagged” T_m and ΔT dependences on varying relative concentration of DNA chemical modifications (r_b), [Na⁺], and GC content. At the same time, T_m determined as the helix–coil transition average temperature, and ΔT, which is proportional to the average absolute temperature deviation from this temperature, are suitable to characterize multi-peak DMCs. They give smoothly varying theoretical and experimental dependences of T_m and ΔT on r_b, [Na⁺], and GC content. For multi-peak DMCs, T_m value determined in this way is the closest to the thermodynamic melting temperature (the helix–coil transition enthalpy/entropy ratio).     

Melting studies of short DNA hairpins: Influence of loop sequence and adjoining base pair identity on hairpin thermodynamic stability

Spectroscopic and calorimetric melting studies of 28 DNA hairpins were performed. These hairpins form by intramolecular folding of 16 base self‐complementary DNA oligomer sequences. Sequence design dictated that the hairpin structures have a six base pair duplex linked by a four base loop and that the first five base pairs in the stem are the same in every molecule. Only loop sequence and identity of the duplex base pair closing the loop vary for the set of hairpins. For these DNA samples, melting studies were carried out to investigate effects of the variables on hairpin stability. Stability of the 28 oligomers was ascertained from their temperature‐induced melting transitions in buffered 115 mM Na⁺ solvent, monitored by ultraviolet absorbance and differential scanning calorimetry (DSC). Experiments revealed the melting temperatures of these molecules range from 32.4 to 60.5°C and are concentration independent over strand concentrations of 0.5 to 260 μM; thus, as expected for hairpins, the melting transitions are apparently unimolecular. Model independent thermodynamic transition parameters, ΔH_cal, ΔS_cal, and ΔG_cal, were determined from DSC measurements. Model dependent transition parameters, ΔH_vH, ΔS_vH, and ΔG_vH were estimated from a van't Hoff (two‐state) analysis of optical melting transitions. Results of these studies reveal a significant sequence dependence to DNA hairpin stability. Thermodynamic parameters evaluated by either procedure reveal the transition enthalpy, ΔH_cal (ΔH_vH) can differ by as much as 20 kcal/mol depending on sequence. Similarly, values of the transition entropy ΔS_cal (ΔS_vH) can differ by as much as 60 cal/Kmol (eu) for different molecules. Differences in free energies ΔG_cal (ΔG_vH) are as large as 4 kcal/mol for hairpins with different sequences. Comparisons between the model independent calorimetric values and the thermodynamic parameters evaluated assuming a two‐state model reveal that 10 of the 28 hairpins display non‐two‐state melting behavior. The database of sequence‐dependent melting free energies obtained for the hairpins was employed to extract a set of n‐n (nearest‐neighbor) sequence dependent loop parameters that were able to reproduce the input data within error (with only two exceptions). Surprisingly, this suggests that the thermodynamic stability of the DNA hairpins can in large part be reasonably represented in terms of sums of appropriate nearest‐neighbor loop sequence parameters. © 1999 John Wiley & Sons, Inc. Biopoly 50: 425–442, 1999     

Thermodynamics of the B to Z transition in poly(dGdC)

The thermodynamics of the B to Z transition in poly(dGdC) was examined by differential scanning calorimetry, temperature-dependent absorbance spectroscopy, and CD spectroscopy. In a buffer containing 1 mM Na cacodylate, 1 mM MgCl₂, pH 6.3, the B to Z transition is centered at 76.4°C, and is characterized by ΔH_cal = 2.02 kcal (mol base pair)^?1 and a cooperative unit of 150 base pairs (bp). The t_m of this transition is independent of both polynucleotide and Mg²⁺ concentrations. A second transition, with ΔH_cal = 2.90 cal (mol bp)^?1, follows the B to Z conversion, the t_m of which is dependent upon both the polynucleotide and the Mg²⁺ concentrations. Turbidity changes are concomitant with the second transition, indicative of DNA aggregation. CD spectra recorded at a temperature above the second transition are similar to those reported for ψ(–)-DNA. Both the B to Z transition and the aggregation reaction are fully and rapidly reversible in calorimetric experiments. The helix to coil transition under these solution conditions is centered at 126°C, and is characterized by ΔH_cal = 12.4 kcal (mol bp)^?1 and a cooperative unit of 290 bp. In 5 mM MgCl₂, a single transition is seen centered at 75.5°C, characterized by ΔH_cal = 2.82 kcal (mol bp)^?1 and a cooperative unit of 430 bp. This transition is not readily reversible in calorimetric experiments. Changes in turbidity are coincident with the transition, and CD spectra at a temperature just above the transition are characteristic of ψ(–)-DNA. A transition at 124.9°C is seen under these solution conditions, with ΔH_cal = 10.0 kcal (mol bp)^?1 and which requires a complex three-step reaction mechanism to approximate the experimental excess heat capacity curve. Our results provide a direct measure of the thermodynamics of the B to Z transition, and indicate that Z-DNA is an intermediate in the formation of the ψ-(–) aggregate under these solution conditions.     

Influencing factors of dsDNA dye (high-resolution) melting curves and improved genotype call based on thermodynamic considerations

High-resolution melting of dsDNA using suitable dyes is a simple and cost-effective alternative for mutation scanning. Analytical variation can result from salt and template concentration (C_T). To overcome this problem the van’t Hoff transition enthalpy ΔH_vH from dsDNA melting curves was estimated and used for robust genotype calling or mutation scanning. Model calculations show the effect of salt, C_T, and temperature resolution on (1) T_m, (2) difference plots, (3) melting peaks, and (4) calculated ΔH_vH. Using the LightCycler480, the influence of dye (ResoLight) and scanning speed was assessed. The model calculations show that only ΔH_vH is not influenced by salt and C_T. Higher amplicon enthalpy ameliorates the ability to discriminate mutations. Temperature resolution is important for peak- but not for curve-based genotyping. ResoLight increases T_m by 3.4 °C, while lowering ΔH_vH. Using a 4-bp deletion in a 200-bp amplicon as a model, the miscalling rate improved substantially, when using ΔH_vH instead of difference plots. Melting curves of duplex DNA are influenced by dye and salt and less so by duplex concentrations. As predicted from theory, ΔH_vH is a robust measure for mutation detection in two-state melting. The influence of dyes on enthalpy is of general impact for PCR assays.     

Dynamics of molecular organization in agarose sulphate

Nongelling solutions of structurally regular chain segments of agarose sulphate show disorder–order and order–disorder transitions (as monitored by the temperature dependence of optical rotation) that are closely similar to the conformational changes that accompany the sol–gel and gel–sol transitions of the unsegmented polymer. The transition midpoint temperature (T_m) for formation of the ordered structure on cooling is ～25 K lower than T_m for melting. Salt-induced conformational ordering, monitored by polarimetric stopped-flow, occurs on a millisecond time scale, and follows the dynamics expected for the process 2 coil ? helix. The equilibrium constant for helix growth (s) was calculated as a function of temperature from the calorimetric enthalpy change for helix formation (ΔH_cal = ?3.0 ± 0.3 kJ per mole of disaccharide pairs in the ordered state), measured by differential scanning calorimetry. The temperature dependence of the nucleation rate constant (k_nuc), calculated from the observed second-order rate constant (k_obs) by the relationship k_obs = k_nuc(1 ? 1/s) gave the following activation parameters for nucleation of the ordered structure of agarose sulphate (1 mg mL^?1; 0.5M Me₄NCl or KCl): ΔH* = 112 ± 5 kJ mol^?1; ΔS* = 262 ± 20 J mol^?1 K^?1; ΔG*₂₉₈ = 34 ± 6 kJ mol^?1; (k_nuc)₂₉₈ = (7.5 ± 0.5) × 10⁶ dm³ mol^?1 s^?1. The endpoint of the fast relaxation process corresponds to the metastable optical rotation values observed on cooling from the fully disordered form. Subsequent slow relaxation to the true equilibrium values (i.e., coincident with those observed on heating from the fully ordered state) was monitored by conventional optical rotation measurements over several weeks and follows second-order kinetics, with rate constants of (2.25 ± 0.07) × 10^?4 and (3.10 ± 0.10) × 10^?4 dm³ mol^?1 s^?1 at 293.7 and 296.2 K, respectively. This relaxation is attributed to the sequential aggregation processes helix + helix → dimer, helix + dimer → trimer, etc., with depletion of isolated helix driving the much faster coil–helix equilibrium to completion. Light-scattering measurements above and below the temperature range of the conformational transitions indicate an average aggregate size of 2–3 helices.     

Calorimetric measurement of enthalpy change in the isothermal helix-coil transition of poly(L-ornithine) in aqueous solution.

The enthalpy change associated with the isothermal pH-induced uncharged coil-to-helix transition ΔH_h° in poly(L -ornithine) in 0.1 N KCl has been determnined calorimetrically to be ?1530 ± 210 and ?1270 ± 530 cal/mol at 10° and 25°C, respectively. Titration data provided information about the state of charge of the polymer in the calorimetric experiments, and optical rotatory dispersion data about its conformation. In order to compute ΔH_h°, the observed calorimetric heat was corrected for the heat of breaking the sample cell, the heat of dilution of HCl, the heat of neutralization of the OH^? ion, and the heat of ionization of the δ-amino group in the random coil. The latter was obtained from similar calorimetric measurements on poly(D ,L -ornithine). Since it was discovered that poly(L -ornithine) undergoes chain cleavage at high pH, the calorimetric measurements were carried out under conditions where no degradation occurred. From the thermally induced uncharged helix–coil transition curve for poly(L -ornithine) at pH 11.68 in 0.1 N KCl in the 0°–40°C region, the transition temperature T_tr and the quantity (?θ_h/?T)_Ttr have been obtained. From these values, together with the measured values of ΔH_h°, the changes in the standard free energy ΔG_h° and entropy ΔG_h°, associated with the uncharged coil-to-helix transition at 10°C have been calculated to be ?33 cal/mol and ?5.3 cal/mol deg, respectively. The value of the Zimm–Bragg helix–coil stability constant σ has been calculated to be 1.4 × 10^?2 and the value of s calculated to be 1.06 at 10°C, and between 0.60 and 0.92 at 25°C.     

Application of modified ising model to the helix-coil transition of DNA molecules

Equilibrium properties of heterogeneous DNA near the melting temperature T_m are investigated using the grand partition function. The present approach gives exact and analytical solutions. The algebraic expressions enhance a more thorough understanding of the correlation among many observed equilibrium phenomena. The following quantities have been examined: melting temperature T_m, transition width W, partial melting curves θ_AT and θ_GC, mean length of a helical segment h, and correlation length γ.     

Thermodynamics of the helix-coil transition in polypeptides in mixed organic solvents: the influence of inert solvent and side chain

The thermally induced coil–helix transition of poly(γ-benzyl-L -glutamate) (PBLG) and poly(γ-methyl-L -glutamate) (PMLG) in binary solvent mixtures was investigated by calorimetric and optical rotatory dispersion (ORD) measurements. Dichloroacetic acid was the common active solvent, and the inert solvent was one of the chlorinated hydrocarbons, such as chloroform, 1,3-dichloropropane, 1-chlorobutane, or 1-chlorooctane. The thermodynamic parameters characterizing the intramolecular polypeptide and polypeptide–solvent interactions were calculated using the Karasz and Gajnos theoretical model [(1973) J. Phys. Chem. 77 , 1139–1145]. It was found that the enthalpy (ΔH₁) and entropy (ΔS₁) of helix stabilization in the absence of the active solvent depend on the inert solvent, but only in the case of PBLG. This is explained by the additional helix stabilization achieved by the stacking of the benzyl groups. The stacking is more pronounced in less polar chlorinated hydrocarbons with longer aliphatic chains. The results obtained indicate that the maximum helix stability is reached in chlorinated hydrocarbons with 12 C atoms. In the case PMLG, with an aliphatic ester side group, ΔH₁ and ΔS₁ are independent of the inert solvent. The ORD measurements were used to determine the maximum fraction of helicity attained at constant solvent composition and the transition temperature, T_c, at the point where f_H = 0.5. It was found that, for the same solvent composition, T_c was higher than the temperature of the midpoint of the calorimetric peak. This is explained by the fact that the maximum fraction of helicity is less than unity. The finite transition width was taken into account by calculating the phase boundaries for different fractions of helicity using the value of σ estimated from the calorimetric and van't Hoff enthalpies in the usual manner.     

Correlation between percentage guanine-cytosine content and melting temperature of deoxyribonucleic acid

An explicit relation between the percentage (G + C)-content X_GC, and the melting temperature (T_m) of a natural DNA, is derived froma a statistical mechanics calculation with due consideration given to the base pair bonding and stacking interactions. The well-known Marmur-Doty empirical formula, linearly relating these two quantities, can now be understood in terms of the fundamental processes. We also propose a simpler experimental procedure for the determination of X_GC. It is similar to the melting temperature method, but we take only one reading at a prescribed temperature of any natural DNA in addition to the two normalization readings. It should be more sensitive for DNAs having X_GC ranging from 35 to 65%.     

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.     

Determination of DNA base compositions from melting profiles in dilute buffers

Equations were determined for the dependency of the melting temperature (T_m) of DNA upon the logarithm of the sodium ion concentration, for four DNA samples of widely different base compositions (θ_GC). The slopes of these T_m versus log M equations wore found to decrease with increasing θ_{G C}of the samples. An empirical equation relating T_m, log M (Na⁺) and θ_{G C} was derived, which also accounts for differences in T_m versus log M slopes. Data from the literature for some synthetic polynucleotides and for the crab(Cancer pagarus) satellite poly AT are discussed in relation to the above finding. The changes in T_m versus log M slopes with θ_{G C} are interpreted in terms of changes in the thermodynamic parameters ΔS and ΔH with base composition.     

Slow relaxational processes in the melting of linear biopolymers: A theory and its application to nucleic acids

We treat the problem of the mean time of complete separation of complementary chains of a duplex containing N base pairs. A combination of analytical and computer methods is used to obtain the exact solution in the form of a compact expression. This expression is used to analyze the limits of application of the equilibrium theory of helix–coil transition in oligo- and polynucleotides. It also allows the melting behavior of a biopolymer to be predicted when its melting is nonequilibrium. In the case of oligonucleotides for which the equilibrium melting takes place at a high value of the stability constant s, the general expression turns into the equation of Craig, Crothers, and Doty, used by them to determine the rate constant k_f of the growth of a helical region from temperature-jump experiments. For the case of fragmented DNA with N ～ 10², the melting process is shown to be completely nonequilibrium, and as a result, the observed melting temperature should be higher than that for the equilibrium. A simple equation is obtained that makes possible calculation of the real, “kinetic” melting temperature T_k. As N increases, the observed melting temperature should approach the equilibrium value, T_m. This analysis has explained quantitatively the peculiar chain-length dependence of the experimentally observed shift in the DNA melting temperature during fragmentation. A thorough analysis is given of the nonequilibrium effects in the melting process of long DNA molecules (N ? 10³). The main conclusion is that even in the presence of profound hysteresis phenomena, the melting profile observed on heating may differ only slightly from the equilibrium profile.     

Solution properties of synthetic polypeptides. XII. Enthalpy changes accompanying helix-coil transition of polypeptide

For helix-coil transitions of polypeptide in binary mixtures consisting of helix-forming solvent and coil solvent, the transition enthalpy ΔH(T,x) has been found to depend significantly on temperature (T) and solvent composition (x). For such systems, calorimetric measurements may yield some averages of ΔH(T,x) which are no longer amenable to direct comparison with ΔH itself. Theoretical equations relating calorimetric data to ΔH(T,x) are derived and tested favorably with experimental data. It is demonstrated that the transition enthaply from heat capacity measurements is approximately equal to ΔH_cfm, while those from heat of dilution and heat of solution measurements are equal to ΔH_c. Here ΔH_c denotes the value of ΔH at the transition point and f_m represents the maximum helical content attained in a thermally induced transition. The discrepancies among calorimetric data are also discussed.     

Helix-coil dynamics of a Z-helix hairpin

The helix–coil transition of a Z-helix hairpin formed from d(C-G)₅T₄(C-G)₅ has been characterized by equilibrium melting and temperature jump experiments in 5M NaClO₄ and 10 mM Na₂HPO₄, pH 7.0. The melting curve can be represented by a simple all-or-none transition with a midpoint at 81.6 ± 0.4°C and an enthalpy change of 287 ± 15 kJ/mole. The temperature jump relaxation can be described by single exponentials at a reasonable accuracy. Amplitudes measured as a function of temperature provide equilibrium parameters consistent with those derived from equilibrium melting curves. The rate constants of Z-helix formation are found in the range from 1800 s^?1 at 70°C to 800 s^?1 at 90°C and are associated with an activation enthalpy of ?(50 ± 10) kJ/mole, whereas the rate constants of helix dissociation are found in the range from 200 s^?1 at 70°C to 4500 s^?1 at 90°C with an activation enthalpy +235 kJ/mole. These parameters are consistent with a requirement of 3–4 base pairs for helix nucleation. Apparently nucleation occurs in the Z-helix conformation, because a separate slow step corresponding to a B to Z transition has not been observed. In summary, the dynamics of the Z-helix–coil transition is very similar to that of previously investigated right-handed double helices.     

High-throughput thermal stability assessment of DNA hairpins based on high resolution melting

On the basis of high-resolution melting, a high-throughput approach to measure melting temperatures (T_ms) of short DNA hairpins was developed. With this method, T_ms of thousands of triloop, tetraloop, and pentaloop hairpins involving various loop sequences and various closing base pairs (cbp) were obtained in hours. The stability of triloop hairpins decreased with the change of cbp (5′–3′) in the order of c-g > g-c > t-a ≥ a-t, showing that the cbp of 5′-Pyr-Pur-3′ (Pyr = pyrimidine, Pur = purine) contributed more stability than 5′-Pur-Pyr-3′. For tetraloop hairpins, GNNA, GNAB, and CNNG (N = A, G, C, or T; B = G, C, or T) were found to be highly stable irrespective of the cbp type. TNNA was also stable in both g-c and a-t families, while CGNA only in the c-g family. Pentaloop hairpins of cTGNAGg, cGNYNAg (Y = T or C) and cCGNNAg were exceptionally stable motifs. In most cases, pyrimidine-rich loops were more favorable to stabilize the whole structure than purine-rich ones. The present approach showed a good performance in assessing the thermal stability of large amounts of DNA hairpins comprehensively. These data are useful to understand the sequence dependence of the stability of DNA secondary structures and promising to improve the structure simulation by consummating basic databases.     

Melting curves, denaturation maps, and genetic map of phiX174: their relations and applications.

In this paper we analyze theoretically the observable details of the differential melting curves (DMC) and the denaturation maps (DM) of a DNA. With the help of a mathematical model, we explore their implications, their relation with each other and with the genetic map of the molecule, and discuss possible future applications. ?X174 is used as the example, since its sequence and genetic map are available. We find that each gene section of ?X174 has a characteristic DMC. A reconstruction scheme to get the DMC of a whole piece from those of its constituent genes is shown to be fairly successuful. The relations between the melting curve and the denaturation maps are clarified. We observe that nearly always, the beginning and end of a gene melt at lower temperatures. The sharp features in the DM indicate that despite the long-range cooperative interactions, the DM do reflect the local sequence effect. Denaturation maps (theoretical) of ?X174 and SV40 are presented. From available data of other authors, we estimate that the dependence of the melting temperature t_m on GC, the fraction of (G+C)-content, and on x, the ionic concentration in fractions of the standard saline citrate solution, can be expressed as t_m(x, GC) = -5.2 (log x)GC + 18.4 log x + 41.0GC + 69.4. The first two coefficients are less certain.     

Target concentration dependence of DNA melting temperature on oligonucleotide microarrays

The design of microarrays is currently based on studies focusing on DNA hybridization reaction in bulk solution. However, the presence of a surface to which the probe strand is attached can make the solution‐based approximations invalid, resulting in sub‐optimum hybridization conditions. To determine the effect of surfaces on DNA duplex formation, the authors studied the dependence of DNA melting temperature (T_m) on target concentration. An automated system was developed to capture the melting profiles of a 25‐mer perfect‐match probe–target pair initially hybridized at 23°C. Target concentrations ranged from 0.0165 to 15 nM with different probe amounts (0.03–0.82 pmol on a surface area of 10¹⁸ Ų), a constant probe density (5 × 10¹² molecules/cm²) and spacer length (15 dT). The authors found that T_m for duplexes anchored to a surface is lower than in‐solution, and this difference increases with increasing target concentration. In a representative set, a target concentration increase from 0.5 to 15 nM with 0.82 pmol of probe on the surface resulted in a T_m decrease of 6°C when compared with a 4°C increase in solution. At very low target concentrations, a multi‐melting process was observed in low temperature domains of the curves. This was attributed to the presence of truncated or mismatch probes. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Ligand-induced melting reaction of specific-sequence DNA molecules

An algorithm for the calculation of ligand-induced helix–coil transitions of macromolecules of any specific sequence was derived. The probabilities of each residue to be in helix and ligand-free, helix and ligand-bound, coil and ligand-free, and coil and ligand-bound states can be calculated by extending the recursion relation formula proposed by D. Poland [(1974) Biopolymers 13 , 1859–1871]. Calculations using hypothetical DNAs having block heterogeneities for melting reactions showed that cooperative binding specific to single strands weakens the effect of the heterogeneity. Fine structures in the melting profiles or cooperatively melting regions, which have so far been found in thermal melting experiments, were predicted to exist in ligand-induced melting reactions for natural DNA fragments.     

High‐resolution calorimetric and optical melting profiles of DNA plasmids: Resolving contributions from intrinsic melting domains and specifically designed inserts

We demonstrate that differential scanning calorimetry (DSC) can be used to yield high‐resolution melting profiles for DNA plasmids that agree in all major features with the corresponding plasmid melting profiles derived using more traditional optical techniques. We further demonstrate that by combining information derived from both calorimetric and optical melting profiles one can glean insights that are unavailable from either melting curve alone. By using both optical and calorimetric observables, we show how one can resolve, identify, and measure the thermodynamic properties of particular sequences/domains of interest within a plasmid. We also show that complementary DSC and optical melting studies on plasmids with and without specifically designed inserts can provide fundamental advantages over the corresponding melting studies on other model system constructs for thermodynamically characterizing nucleic acid sequences/structures. © 1999 John Wiley & Sons, Inc. Biopoly 50: 303–318, 1999