Calculation of melting curves for DNA

A method is reported for calculating the melting curve of a DNA molecule of random base sequence, including in the formalism the dependence of the free energy of base pair formation on the size of a denatured section. Some explicit results are shown for a “typical” base sequence, in particular the probability of helix formation at individual base pairs in several different regions of the molecule and the amount of melting from the end of the chain. Particular attention is drawn to the variation of local melting behavior from one region of the molecule to another. It is found that sections rich in AT melt at relatively low temperatures with a fairly broad transition curve, whereas regions rich in GC pairs melt at higher temperatures (as expected) with a very abrupt, local transition curve. To account qualitatively for the results one may divide melting into two kinds of processes: (a) the nucleation and growth of denatured regions, and (b) the merging together of two denatured sections at the expense of the intervening helix. The first of these processes dominates in the first stages of melting, and leads to rather broad local melting curves, whereas the second process predominates in the later stages, and occurs, in a particular part of the molecule, over a very narrow temperature range. It is estimated that the average length of a helix plus adjacent coil section at the midpoint of the transition is approximately 600 base pairs. Since transition curves which measure the local melting behavior reflect local compositions fluctuations, these curves contain information about the broad outlines of base sequence in the molecule. Some suggestions are made concerning experiments by which this potential information source could be exploited. In particular, it is pointed out that one might hope to map AT or GC rich regions at particular genetic loci in a biologically active DNA molecule. Values of the relevant parameters found earlier for the transition of homopolymers produce melting curves for a DNA of random base sequence which are in good agreement with the experimental transition curve for T2 phage DNA. Hence the present theoretical picture of the melting of polynucleotides is at least internally self-consistent.     

Monitoring of fluorescence during DNA melting as a method for discrimination and detection of PCR products in variety identification

DNA melting curves of genotype-specific PCR fragments were used to differentiate between species and amongst varieties of cereals. Melting curves were generated by ramping the temperature of PCR fragments through their dissociation temperature in the presence of a double-stranded DNA binding dye. Genotypes were discriminated by differences in the position and shape of the melting curve which is a function of the fragment's sequence, length and GC content. Amplification of 5S ribosomal RNA genes generated species-specific fragments for six of the major cereal crops. Of the 15 possible pairwise comparisons, 13 distinctions could be reliably made using melting curve position data. Wheat varieties were identified by the melting profiles of PCR products generated using microsatellite primers. DNA melting curve analysis was conveniently coupled with capillary-PCR using a LightCycler instrument to provide a rapid method of genotyping in cereals.     

Sequence and temperature effect on hydrogen bond disruption in DNA determined by a statistical analysis

We use the modified self-consistent phonon approximation theory to calculate temperature dependent interbase hydrogen bond disruption profiles for a number of six base pair repeating sequence infinite B-DNA polymers with various guanine-cytosine/adenine-thymine ratios. For comparison we also include results we have obtained in our earlier work on several B-DNA homopolymers, copolymers and a four-base-pair repeating sequence polymer. Our theory gives a statistical estimate of thermal fluctuational disruption probability of individual hydrogen bonds in individual base pairs in DNA as a function of temperature. The calculated probabilities show no sequence dependence at premelting temperatures, in agreement with proton exchange measurements. These probabilities however become very sensitive to base sequence at temperatures close to the observed melting temperatures. Multi-phasic critical transitions are found in which a portion of base pairs are disrupted at temperatures below the final disruption temperature. These transitions include localized as well as non-localized base pair opening. The localized transitions involve disruption of a few base-pairs at every other location without large scale base unstacking, and they may not appear in the observed UV curves with current resolution. On the other hand the overall disruption behavior is consistent with observations. The midpoint transition temperatures are close to the observed melting temperatures and these temperatures show the observed linear dependence on guanine-cytosine content. Our calculations indicate that our theory can be used effectively to calculate H-bond disruption behavior of different DNA sequences. Received: 20 February 1996 / Accepted: 2 May 1996     

Studies of DNA dumbbells. VI. Analysis of optical melting curves of dumbbells with a sixteen-base pair duplex stem and end-loops of variable size and sequence

Optical melting curves of 22 DNA dumbbells with the 16-base pair duplex sequence 5′-G-C-A-T-C-A-T-C-G-A-T-G-A-T-G-C-3′ linked on both ends by single-strand loops of A_t or C_t sequences (˛ = 2, 3, 4, 6, 8, 10, 14), T_t sequences (˛ = 2, 3, 4, 6, 8, 10), and G_t sequences (t = 2, 4) were measured in phosphate buffered solvents containing 30, 70, and 120 mM Na⁺. For dumbbells with loops comprised of at least three nucleotides, stability is inversely proportional to end-loop size. Dumbbells with loops comprised of only two nucleotide bases generally have lower stabilities than dumbbells with three base nucleotide loops. Experimental melting curves were analyzed in terms of the numerically exact (multistate) statistical thermodynamic model of DNA dumbbell melting previously described (T. M. Paner, M. Amaratunga & A. S. Benight (1992), Biopolymers 32, 881). Theoretically calculated melting curves were fitted to experimental curves by simultaneously adjusting model parameters representing statistical weights of intramolecular hairpin loop and single-strand circle states. The systematically determined empirical parameters provided evaluations of the energetics of hairpin loop formation as a function of loop size, sequence, and salt environment. Values of the free energies of hairpin loop formation ΔG_loop(n > t) and single-strand circles, ΔG_cir(N) as a function of end-loop size, t = 2-14, circle size, N = 32 + 2_t, and loop sequence were obtained. These quantities were found to depend on end-loop size but not loop sequence. Their empirically determined values also varied with solvent ionic strength. Analytical expressions for the partition function Q(T) of the dumbbells were evaluated using the empirically evaluated best-fit loop parameters. From Q(T), the melting transition enthalpy ΔH, entropy ΔS, and free energy ΔG, were evaluated for the dumbbells as a function of end-loop size, sequence, and [Na⁺]. Since the multistate analysis is based on the numerically exact model, and considers a statistically significant number of theoretically possible partially melted states, it does not require prior assumptions regarding the nature of the melting transition, i.e., whether or not it occurs in a two-state manner. For comparison with the multistate analysis, thermodynamic transition parameters were also evaluated directly from experimental melting curves assuming a two-state transition and using the graphical van't Hoff analysis. Comparisons between results of the multistate and two-state analyses suggested dumbbells with loops comprised of six or fewer residues melted in a two-state manner, while the melting processes for dumbbells with larger end-loops deviate from two-state behavior.Dependence of thermodynamic parameters on[Na⁺] as a function of loop size suggests single-strand end-loops have different counterion binding properties than the melted circle. Results are compared with those obtained in an earlier study of dumbbells with the slightly different stem sequence 5'-G-C-A-T-A-G-A-T-G-A-G-A-A-T-G-C-3' linked on the ends by T loops (˛ = 2,3,4,6,8,10,14).© 1996 John Wiley &Sons, Inc.     

A cooperative self-consistent microscopic theory of thermally induced melting of a repeat sequence DNA polymer

We attempt to extend the modified self-consistent phonon theory to describe thermal fluctuational base-pair opening of repeat sequence DNA polymers in the helix–coil transition region as well as in the premelting region. A microscopic base-pair open state is introduced and the effect of this open state is taken into account self-consistently in a mean field system that models the DNA polymer. Our analysis indicates the structure of this open state changes with temperature in such a manner that on average a base pair opens and unstacks with its neighbors more completely as temperature increases. We apply this theory to a homopolymer—poly(dG) · poly(dC) to evaluate the base-pair opening probability in a temperature range from 273 to 366.5 K. At 366.5 K the system undergoes cooperative melting. Our calculated base-pair opening probabilities are in general agreement with several experimental estimates at room temperature. The calculated probabilities show typical melting curve behavior at temperatures close to the observed melting temperature. The cooperative modified self-consistent phonon approximation approach becomes a viable microscopic theory of melting. © 1993 John Wiley & Sons, Inc.     

Thermodynamic description of oligonucleotide self-association in DNA concatamer structures

A scheme of equilibrium formation of concatamers by two different oligonucleotides has been considered. It is shown that in the general case, the dependence of the concentration of oligonucleotide components on temperature cannot be found in analytical form. Therefore, it is impossible to find the thermodynamic parameters of concatamer formation (ΔH ⁰, ΔS ⁰) and melting temperatures by analyzing the profiles of thermal denaturation of oligonucleotide complexes. An algorithm for numerical solution of implicit dependences has been developed. A number of approaches are considered that simplify the analysis of heat denaturation curves for concatamer complexes. It is shown that the dependence of the efficiency of concatamerization on temperature can be described analytically when duplex fragments have close stability and there is no cooperativity at the oligonucleotide junction. In this case, the dependence of melting temperature on thermodynamic parameters and oligonucleotide concentration has the same form as in the case of the duplex structure formed by a pair of non-self-complementary oligonucleotides. The ability of various model approaches to describe the experimental curves of concatamer heat denaturation is evaluated. For concatamer structures used as signal amplifiers in DNA hybridization analysis, a function is introduced that shows the relative contribution of a concatamer of given length to the magnitude of signal amplification. The dependence of the maximum of this function on the concentration of oligonucleotides, the thermodynamic characteristics of their complexes, and temperature has been determined. It is shown by the gel retardation assay that the function of the length distribution of concatamers qualitatively correlates with the experimental dependences.     

Phase transitions, Kauzmann curves, and inverse melting

Walter Kauzmann's classic 1948 review of liquid supercooling and glass formation drew attention to the temperatures at which (by extrapolation) enthalpies and entropies of liquid and crystal phases would appear to become equal. In the temperature-pressure (T, p) plane, the collection of such 'Kauzmann temperatures' generate characteristic curves. The present study examines the connection of those Kauzmann loci to equilibrium inverse melting phenomena, i.e. cases where isobaric heating causes freezing of the liquid. Such cases are associated with local minima or maxima in the melting curve p(m)(T), and we point out the possible relevance of melting curve maxima to the thermodynamics of protein folding. Both equal-enthalpy and equal-entropy Kauzmann curves must pass through melting curve extrema. Three thermodynamic identities have been obtained to describe the vicinity of these points; they involve, respectively, the slopes of the two Kauzmann curves, and the second temperature derivative of the melting pressure. The second of these three equations is formally identical to the first Ehrenfest relation for second-order phase transitions, but carries no phase-transition implication. For purposes of specific numerical illustration, the inverse-melting behavior displayed by (3)He at low temperature has been analyzed in detail.     

Simultaneous mutation scanning and genotyping by high-resolution DNA melting analysis

This protocol permits the simultaneous mutation scanning and genotyping of PCR products by high-resolution DNA melting analysis. This is achieved using asymmetric PCR performed in the presence of a saturating fluorescent DNA dye and unlabeled oligonucleotide probes. Fluorescent melting curves of both PCR amplicons and amplicon-probe duplexes are analyzed. The shape of the PCR amplicon melting transition reveals the presence of heterozygotes, whereas specific genotyping is enabled by melting of the unlabeled probe-amplicon duplex. Unbiased hierarchal clustering of melting transitions automatically groups different sequence variants; this allows common variants to be easily recognized and genotyped. This technique may be used in both laboratory research and clinical settings to study single-nucleotide polymorphisms and small insertions and deletions, and to diagnose associated genetic disorders. High-resolution melting analysis accomplishes simultaneous gene scanning and mutation genotyping in a fraction of the time required when using traditional methods, while maintaining a closed-tube environment. The PCR requires <30 min (capillaries) or 1.5 h (96- or 384-well plates) and melting acquisition takes 1-2 min per capillary or 5 min per plate.     

Analysis of thermal melting curves

T(m) is defined as Temperature of melting or, more accurately, as temperature of midtransition. This term is often used for nucleic acids (DNA and RNA, oligonucleotides and polynucleotides). A thermal denaturation experiment determines the stability of the secondary structure of a DNA or RNA and aids in the choice of the sequences for antisense oligomers or PCR primers. Beyond a simple numerical value (the T(m)), a thermal denaturation experiment, in which the folded fraction of a structure is plotted vs. temperature, yields important thermodynamic information. We present the classic problems encountered during these experiments and try to demonstrate that a number of useful pieces of information can be extracted from these experimental curves.     

Thermodynamic differences among homologous thermophilic and mesophilic proteins.

Here, we analyze the thermodynamic parameters and their correlations in families containing homologous thermophilic and mesophilic proteins which show reversible two-state folding <--> unfolding transitions between the native and the denatured states. For the proteins in these families, the melting temperatures correlate with the maximal protein stability change (between the native and the denatured states) as well as with the enthalpic and entropic changes at the melting temperature. In contrast, the heat capacity change is uncorrelated with the melting temperature. These and additional results illustrate that higher melting temperatures are largely obtained via an upshift and broadening of the protein stability curves. Both thermophilic and mesophilic proteins are maximally stable around room temperature. However, the maximal stabilities of thermophilic proteins are considerably greater than those of their mesophilic homologues. At the living temperatures of their respective source organisms, homologous thermophilic and mesophilic proteins have similar stabilities. The protein stability at the living temperature of the source organism does not correlate with the living temperature of the protein. We tie thermodynamic observations to microscopics via the hydrophobic effect and a two-state model of the water structure. We conclude that, to achieve higher stability and greater resistance to high and low temperatures, specific interactions, particularly electrostatic, should be engineered into the protein. The effect of these specific interactions is largely reflected in an increased enthalpy change at the melting temperature.     

Differentiation of Staphylococcus spp. by high-resolution melting analysis

High-resolution melting analysis (HRMA) is a fast (post-PCR) high-throughput method to scan for sequence variations in a target gene. The aim of this study was to test the potential of HRMA to distinguish particular bacterial species of the Staphylococcus genus even when using a broad-range PCR within the 16S rRNA gene where sequence differences are minimal. Genomic DNA samples isolated from 12 reference staphylococcal strains (Staphylococcus aureus, Staphylococcus capitis, Staphylococcus caprae, Staphylococcus epidermidis, Staphylococcus haemolyticus, Staphylococcus hominis, Staphylococcus intermedius, Staphylococcus saprophyticus, Staphylococcus sciuri, Staphylococcus simulans, Staphylococcus warneri, and Staphylococcus xylosus) were subjected to a real-time PCR amplification of the 16S rRNA gene in the presence of fluorescent dye EvaGreen?, followed by HRMA. Melting profiles were used as molecular fingerprints for bacterial species differentiation. HRMA of S. saprophyticus and S. xylosus resulted in undistinguishable profiles because of their identical sequences in the analyzed 16S rRNA region. The remaining reference strains were fully differentiated either directly or via high-resolution plots obtained by heteroduplex formation between coamplified PCR products of the tested staphylococcal strain and phylogenetically unrelated strain.     

Single nucleotide polymorphism genotyping using allele-specific PCR and fluorescence melting curves

We present a PCR method for identification of single nucleotide polymorphisms (SNPs), using allele-specific primers designed for selective amplification of each allele. Matching the SNP at the 3' end of the forward or reverse primer, and additionally incorporating a 3' mismatch to prevent amplification of the incorrect allele, results in selectivity of the allele-specific primers. DNA melting analysis with fluorescent SYBR Green affords detection of the PCR products. By incorporating a GC-rich sequence into one of the two allele-specific primers to increase the melting temperature, both alleles can be measured simultaneously at their respective melting temperatures. Applying the DNA melting analysis to SNPs in ApoE and ABCA1 yielded results identical to those obtained with other genotyping methods. This provides a cost-effective, high-throughput method for amplification and scoring of SNPs.     

Temperature effects on DNA chip experiments from surface plasmon resonance imaging: isotherms and melting curves

We present an analysis of hybridization experiments on a DNA chip studied by surface plasmon resonance imaging. The reaction constants at various temperatures and for different probe lengths are obtained from Langmuir isotherms and hybridization kinetics. The melting curves from temperature scans are also obtained without any labeling of the targets. The effects of the probe length on the hybridization thermodynamics, deduced from the temperature dependence of the reaction constants as well as from the melting curves, suggest dispersion in the length of the hybridization segments of the probes accessible to the targets. Those are, however, sufficient to suggest efficient point mutation detection from temperature scans.     

Speed-up of DNA melting algorithm with complete nearest neighbor properties

We describe an optimized algorithm, which is faster and more accurate compared to previously described algorithms, for computing the statistical mechanics of denaturation of nucleic acid sequences according to the classical Poland-Scheraga type of model. Nearest neighbor thermodynamics has been included in a complete and general way, by rigorously treating nearest neighbor interactions, helix end interactions, and isolated base-pairs. This avoids the simplifications of previous approaches and achieves full generality and controllability with respect to thermodynamic modeling. The algorithm computes subchain partition functions by recursion, from which various quantitative aspects of the melting process are easily derived, for example the base-pairing probability profiles. The algorithm represents an optimization with respect to algorithmic complexity of the partition function algorithm of Yeramian et al. (Biopolymers 1990, 30, 481-497): we reduce the computation time for a base-pairing probability profile from O(N2) to O(N), where N is the sequence length. This speed-up comes in addition to the speed-up due to a multiexponential approximation of the loop entropy factor as introduced by Fixman and Freire22 and applied by Yeramian et al. The speed-up, however, is independent of the multiexponential approximation and reduces time from O(N3) to O(N2) in the exact case. A method for representing very large numbers is described, which avoids numerical overflow in the partition functions for genomic length sequences. In addition to calculating the standard base-pairing probability profiles, we propose to use the algorithm to calculate various other probabilities (loops, helices, tails) for a more direct view of the melting regions and their positions and sizes. This can provide a better understanding of the physics of denaturation and the biology of genomes.     

Estimation of melting curves from enzymatic activity-temperature profiles

Measuring the reversible thermal unfolding of enzymes is valuable for quantifying the effects of environmental factors on the thermodynamic stability of proteins. The thermal unfolding behavior of enzymes is typically studied using calorimetry or optical techniques such as circular dichroism, fluorescence, or light scattering. These techniques often have practical limitations and usually require the protein to be electrophoretically pure. An alternative technique for analyzing the thermodynamic stability of enzymes is to estimate the melting curve from temperature-activity data. This technique does not require electrophoretically pure enzyme, provided the sample does not have competing enzymatic activities or proteins which can affect enzyme stability (e.g., proteases). Moreover, small amounts of contaminant proteins should not affect the results as long as enzymatic assays are performed at low protein concentrations where nonspecific protein-protein interactions are negligible. To illustrate this technique, the melting curve for beta-galactosidase from Escherichia coli in the presence of 1 mM EDTA, and the shift caused by adding 1 mM Mg(+2), were calculated from activity-temperature data. Melting temperatures predicted from activity-temperature data compared closely with those obtained using other techniques. Application of this analysis to multisubstrate enzymes is illustrated by estimating the melting profiles for partially purified hydrogenases from several thermophilic Methanococcii. Limitations and important considerations for estimating melting profiles from activity-temperature data are discussed. (c) 1993 John Wiley & Sons, Inc.     

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).     

Effects of a hairpin polyamide on DNA melting: comparison with distamycin and Hoechst 33258

We have used DNase I footprinting and fluorescence melting studies to study the interaction of the hairpin polyamide Im-Py-Py-Py-(R)H2Ngamma-Im-Py-Py-Py-beta-Dp with its preferred binding sites (5'-WGWWCW; W=A or T) and other sequences. DNase I footprinting confirmed that the ligand binds to the sequence AGAACA at nanomolar concentrations and that changing the terminal A to G causes a dramatic decrease in affinity, while there was no interaction with the reverse sequence WCWWGW. Fluorescence melting studies with 11-mer duplexes showed that the polyamide had very different effects on the forward (TGWWCT) and reverse (TCTAGT) sequences. At low concentrations, the polyamide produced biphasic melting curves with TGATCT, TGTACT and TGAACT, suggesting a strong interaction. In contrast, the melting profiles with TCTAGT were always monophasic and showed much smaller concentration dependent changes in Tm. The polyamide also showed weak binding to the sequence TGATCT when one of the central AT pairs was replaced with an AC mismatch. These melting profiles were compared with those produced by the AT-selective minor groove binding agents distamycin and Hoechst 33258 at the same sites and at similar sequences containing A5 and (AT)3, which are expected to bind distamycin in the 1:1 and 2:1 modes, respectively. These ligands produced simple monophasic melting curves in which the Tm steadily increased as the ligand concentration was raised.     

A thermodynamic comparison of mesophilic and thermophilic ribonucleases H

The mechanisms by which thermophilic proteins attain their increased thermostability remain unclear, as usually the sequence and structure of these proteins are very similar to those of their mesophilic homologues. To gain insight into the basis of thermostability, we have determined protein stability curves describing the temperature dependence of the free energy of unfolding for two ribonucleases H, one from the mesophile Escherichia coli and one from the thermophile Thermus thermophilus. The circular dichroism signal was monitored as a function of temperature and guanidinium chloride concentration, and the resulting free energies of unfolding were fit to the Gibbs-Helmholtz equation to obtain a set of thermodynamic parameters for these proteins. Although the maximal stabilities for these proteins occur at similar temperatures, the heat capacity of unfolding for T. thermophilus RNase H is lower, resulting in a smaller temperature dependence of the free energy of unfolding and therefore a higher thermal melting temperature. In addition, the stabilities of these proteins are similar at the optimal growth temperatures for their respective organisms, suggesting that a balance of thermodynamic stability and flexibility is important for function.     

Distinguishing Anuran species by high‐resolution melting analysis of the COI barcode (COI‐HRM)

Taxonomic identification can be difficult when two or more species appear morphologically similar. DNA barcoding based on the sequence of the mitochondrial cytochrome c oxidase 1 gene (COI) is now widely used in identifying animal species. High‐resolution melting analysis (HRM) provides an alternative method for detecting sequence variations among amplicons without having to perform DNA sequencing. The purpose of this study was to determine whether HRM of the COI barcode can be used to distinguish animal species. Using anurans as a model, we found distinct COI melting profiles among three congeners of both Lithobates spp. and Hyla spp. Sequence variations within species shifted the melting temperature of one or more melting domains slightly but do not affect the distinctness of the melting profiles for each species. An NMDS ordination plot comparing melting peak profiles among eight Anuran species showed overlapping profiles for Lithobates sphenocephala and Gastrophryne carolinensis. The COI amplicon for both species contained two melting domains with melting temperatures that were similar between the two species. The two species belong to two different families, highlighting the fact that COI melting profiles do not reveal phylogenetic relationships but simply reflect DNA sequence differences among stretches of DNA within amplicons. This study suggests that high‐resolution melting analysis of COI barcodes (COI‐HRM) may be useful as a simple and rapid method to distinguish animal species that appear morphologically similar.