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Enthalpy-Entropy Compensation in DNA Melting Thermodynamics

1995; Elsevier BV; Volume: 270; Issue: 2 Linguagem: Inglês

10.1074/jbc.270.2.746

1083-351X

John Petruska, Myron F. Goodman,

Advanced biosensing and bioanalysis techniques

We investigate enthalpy-entropy compensation for melting of nearest-neighbor doublets in DNA. Based on data for 10 normal doublets and for doublets containing a mispaired or analog base, the correlation of ΔS° with ΔH° follows a rectangular hyperbola. Doublet melting temperature relates linearly to ΔH° by Tm = To +ΔH°/a, where To ≈ 273 K and a ≈ 80 cal/mol-K. Thus Tm is proportional to ΔH°+ aTo rather than to ΔH° alone as previously thought by assuming ΔS° to be constant. The term aTo ≈ 21.8 kcal/mol may reflect a constant enthalpy change in solvent accompanying the DNA enthalpy change for doublet melting and is roughly equivalent to breaking four H-bonds between water molecules for each melted doublet. The solvent entropy change (aTo /Tm ) declines with increasing Tm , while the DNA entropy change (ΔH°/Tm ) rises, so the combined DNA + solvent entropy change stays constant at 80 cal/K/mol of doublet. If such constancy in DNA + solvent entropy changes also holds for enzyme clefts as “solvent,” then free energy differences for competing correct and incorrect base pairs in polymerase clefts may be as large as enthalpy differences and possibly sufficient to account for DNA polymerase accuracy. The hyperbolic relationship between ΔS° and ΔH° observed in 1 M salt can be used to evaluate ΔH° and ΔS° from Tm at lower, physiologically relevant, salt concentrations. We investigate enthalpy-entropy compensation for melting of nearest-neighbor doublets in DNA. Based on data for 10 normal doublets and for doublets containing a mispaired or analog base, the correlation of ΔS° with ΔH° follows a rectangular hyperbola. Doublet melting temperature relates linearly to ΔH° by Tm = To +ΔH°/a, where To ≈ 273 K and a ≈ 80 cal/mol-K. Thus Tm is proportional to ΔH°+ aTo rather than to ΔH° alone as previously thought by assuming ΔS° to be constant. The term aTo ≈ 21.8 kcal/mol may reflect a constant enthalpy change in solvent accompanying the DNA enthalpy change for doublet melting and is roughly equivalent to breaking four H-bonds between water molecules for each melted doublet. The solvent entropy change (aTo /Tm ) declines with increasing Tm , while the DNA entropy change (ΔH°/Tm ) rises, so the combined DNA + solvent entropy change stays constant at 80 cal/K/mol of doublet. If such constancy in DNA + solvent entropy changes also holds for enzyme clefts as “solvent,” then free energy differences for competing correct and incorrect base pairs in polymerase clefts may be as large as enthalpy differences and possibly sufficient to account for DNA polymerase accuracy. The hyperbolic relationship between ΔS° and ΔH° observed in 1 M salt can be used to evaluate ΔH° and ΔS° from Tm at lower, physiologically relevant, salt concentrations. INTRODUCTIONThermal denaturation studies of DNA have revealed that the melting temperature, Tm , 1The abbreviations used are: Tmelting temperature of DNA duplex or individual doublets of base pairsbpbase pair(s). of a DNA double helix depends on strand length(1Martin F.H. Uhlenbeck O.C. Doty P. J. Mol. Biol. 1971; 57: 201-215Crossref PubMed Scopus (150) Google Scholar, 2Porschke D. Biopolymers. 1971; 10: 1989-2013Crossref Scopus (96) Google Scholar, 3Blake R.D. Biopolymers. 1987; 26: 1063-1074Crossref PubMed Scopus (22) Google Scholar), strand concentration (4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar, 5Marky L.A. Breslauer K.J. Biopolymers. 1987; 26: 1601-1620Crossref PubMed Scopus (1097) Google Scholar, 6Marky L.A. Kallenbach N. McDonough A. Seeman N.C. Breslauer K.J. Biopolymers. 1987; 26: 1621-1634Crossref PubMed Scopus (93) Google Scholar, 7Gaffney B.L. Jones R.A. Biochemistry. 1989; 28: 5881-5889Crossref PubMed Scopus (123) Google Scholar), base sequence(8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar, 9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar, 10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar), and ionic strength of added salt (8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar, 9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar, 10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar, 11Marmur J. Doty P. J. Mol. Biol. 1962; 5: 109-118Crossref PubMed Scopus (2992) Google Scholar). Such studies indicate that double helix stability can be predicted in terms of the standard free energy change, ΔG° = ΔH° - TΔS°, if one knows the standard enthalpy and entropy changes (ΔH° and ΔS°) for the melting of each nearest-neighbor doublet of base pairs in DNA(9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar). Normal B-form helical DNA, with Watson-Crick base pairs stabilized by nearest-neighbor base stacking, has 10 possible kinds of nearest-neighbor doublets. For the melting of each doublet, ΔH° and ΔS° have been evaluated experimentally in 1 M NaCl but only Tm (ΔH°/ΔS°) has been measured at lower salt concentrations. In this paper we provide a formula to describe the relationship between ΔH° and ΔS° measured in 1 M salt and show how standard enthalpy and entropy changes may be evaluated from Tm at lower salt concentrations to predict B-DNA stability under more physiologically relevant conditions.The focal point of this work pertains to “enthalpy-entropy compensation,” the strong correlation between enthalpy and entropy changes observed for molecular association/dissociation reactions in aqueous solution and attributed to water's influence as solvent (12Lumry R. Rajender S. Biopolymers. 1970; 9: 1125-1227Crossref PubMed Scopus (1118) Google Scholar, 13Breslauer K.J. Remeta D.P. Chou W.-Y. Ferrante R. Curry J. Zaunczkowski D. Snyder J.G. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1987; 84: 8922-8926Crossref PubMed Scopus (247) Google Scholar, 14Petruska J. Goodman M.F. Boosalis M.S. Sowers L.C. Cheong C. Tinoco Jr., I. Proc. Natl. Acad. Sci. U. S. A. 1988; 85: 6252-6256Crossref PubMed Scopus (285) Google Scholar). For the melting of DNA doublets, we find that ΔS° correlates with ΔH° in the manner of a rectangular hyperbola. The hyperbolic curve that we obtain by fitting normal doublet data (4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar, 9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar) also applies to the melting of doublets containing base mispairs (4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar, 7Gaffney B.L. Jones R.A. Biochemistry. 1989; 28: 5881-5889Crossref PubMed Scopus (123) Google Scholar) and the base analog O6-methylguanine(7Gaffney B.L. Jones R.A. Biochemistry. 1989; 28: 5881-5889Crossref PubMed Scopus (123) Google Scholar).EXPERIMENTAL PROCEDURESExpressing DNA Melting Temperature as an Average of Doublet Tm ValuesThe formula used to describe the melting temperature of a DNA double helix in terms of nearest-neighbor doublets has been derived previously by assuming that ΔS, the entropy change upon melting, is the same for all doublets. If ΔS is constant, then each doublet has a melting temperature in degrees Kelvin (Tm = ΔH/ΔS) directly proportional to ΔH, the enthalpy change upon melting. This supposition was made originally by Gotoh and Tagashira (8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar) and more recently by Delcourt and Blake(10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar), to evaluate doublet melting temperatures and enthalpy changes from Tm measurements on duplexes of known base sequence. The reasoning is as follows.A DNA duplex with n base pairs (bp), having the first bp stacked on the second, the second on the third, etc., has n-1 doublets of stacked bp contributing to duplex stability. For each doublet (MN) there is a characteristic enthalpy change upon melting (ΔHMN ) that depends on the stacking interaction between nearest neighbors M and N. The average enthalpy change per mole of doublet in the duplex is given by ΔH=∑ΔHMNfMN(Eq. 1) where fMN is the mole fraction of doublet MN and ∑ is the sum for all MN types in the duplex. In terms of the two strands in the duplex, MN means MN/M′N′, i.e. base sequence 5′-MN-3′ on one strand paired with complementary base sequence 3′-M′N′-5′ on the opposite strand. Since the two strands are antiparallel, MN/M′N′ is equivalent to N′M′/NM, so there are 10 distinct MN types arising from the 16 possible nearest-neighbor base sequences in normal DNA.Corresponding to ΔH given by, the average entropy change per mole of doublet is ΔS = ΔH/Tm, where Tm is the duplex melting temperature in degrees Kelvin. If all doublets have the same entropy change, i.e. ΔSMN = ΔHMN /TMN = c, then the duplex Tm value is an average of doublet Tm values, Tm=∑TMNfMN(Eq. 2) where TMN = ΔHMN /c is the Tm value for doublet MN. This formula applies to DNA duplexes that are long enough so that end effects are negligible, and Tm is practically independent of strand concentration. In the case of short duplexes, the sum in is multiplied by a factor less than 1, about (n-1)/n, to account for the decrease in Tm with decreasing n because of end effects(1Martin F.H. Uhlenbeck O.C. Doty P. J. Mol. Biol. 1971; 57: 201-215Crossref PubMed Scopus (150) Google Scholar, 2Porschke D. Biopolymers. 1971; 10: 1989-2013Crossref Scopus (96) Google Scholar), and another term is required to describe Tm dependence on strand concentration(4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar).Measurements of DNA Melting Temperatures at Various Salt Concentrations-has been used to describe DNA melting temperatures in terms of doublet Tm values, for duplexes of length 100 bp or greater, in salt solutions of low ionic strength, μ = 0.020 M(8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar) and 0.075 M(10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar). In such low concentrations of salt, long duplexes have melting temperatures sufficiently below the boiling point of water to be measured accurately. By a least-squares fit to duplex Tm values obtained for a wide range of known base sequences, self-consistent TMN values have have been determined for all normal MN doublets in 0.020 and 0.075 M NaCl. The corresponding “constant” doublet entropy change (ΔSMN = c) at these NaCl concentrations were estimated to be c = 24 cal/mol-K and 25 cal/mol-K, respectively, for the purpose of evaluating ΔHMN = cTMN for each doublet(8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar, 10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar).In salt solutions of 1 M or above, Tm for long DNA duplexes may exceed the boiling point of water and so cannot be measured directly, but short duplexes of 10 bp or less have Tm values low enough to be measured accurately over a wide range of total strand concentration (Ct). Tinoco and co-workers (4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar) have shown that the equilibrium constant (Keq ) for duplex dissociation at Tm has the value Ct/4 ideally, so the corresponding standard free energy change is ΔGo=-RTlnKeq=RTmln(4/Ct)=ΔHo-TmΔS∞(Eq. 3) For each short (7-10 bp) duplex examined, a van't Hoff plot of Rln(4/Ct) versus 1/Tm was found to give a straight line with slope and intercept yielding ΔH° and ΔS° values for the duplex(4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar, 7Gaffney B.L. Jones R.A. Biochemistry. 1989; 28: 5881-5889Crossref PubMed Scopus (123) Google Scholar, 14Petruska J. Goodman M.F. Boosalis M.S. Sowers L.C. Cheong C. Tinoco Jr., I. Proc. Natl. Acad. Sci. U. S. A. 1988; 85: 6252-6256Crossref PubMed Scopus (285) Google Scholar). This experimental (van't Hoff) method of measuring ΔH° and ΔS° has been confirmed by Breslauer and co-workers (9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar) using calorimetry. A systematic replacement of one bp by another in short duplexes enabled Breslauer and co-workers to evaluate ΔH°MN and ΔS°MN for each normal doublet in 1 M NaCl (Table 1).Tabled 1Effect of Increasing DNA Strand LengthAs duplexes are made longer, their enthalpy and entropy changes increase with the number of doublets and the contribution from Ct becomes less significant. This effect can be seen by dividing by Tm and by n-1, to obtain for an average doublet, ΔH°/Tm = ΔS°+ R[ln(4/Ct)]/(n-1). For long duplexes, with n = 100-1000 and Ct = 10-5-10-6M, the term R[ln(4/Ct)]/(n-1) is only 0.03 to 0.3 cal/mol-K, which is negligible compared to ΔS° of 20-25 cal/mol-K for the average doublet. Thus, doublet Tm values obtained from long duplexes of 100 bp or more at μ = 0.020 M(8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar) and 0.075 M(10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar) are essentially equivalent to ΔH°/ΔS° for the doublets at these two ionic strengths.RESULTSFormulation of Enthalpy-Entropy Compensation Enthalpy-Entropy Compensation Fits a Rectangular HyperbolaTable 1 shows the ΔH° and ΔS° values obtained for normal DNA doublets by applying van't Hoff analysis and calorimetry to short duplexes in 1 M NaCl(4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar, 9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar). Clearly ΔS° is not constant but varies with ΔH°. A plot of ΔS° versus ΔH°, including doublets containing base mispairs, indicates a correlation (Fig. 1a) similar to the enthalpy-entropy compensation attributed to the influence of water as solvent in protein interactions (12Lumry R. Rajender S. Biopolymers. 1970; 9: 1125-1227Crossref PubMed Scopus (1118) Google Scholar) and drug-DNA binding(13Breslauer K.J. Remeta D.P. Chou W.-Y. Ferrante R. Curry J. Zaunczkowski D. Snyder J.G. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1987; 84: 8922-8926Crossref PubMed Scopus (247) Google Scholar).Figure 1:Enthalpy-entropy compensation found for DNA melting in salt solutions of 1 and 0.1 M ionic strength. In a, the standard entropy change, ΔS°, evaluated for melting in 1 M NaCl, is shown plotted against the corresponding enthalpy change, ΔH°, for each nearest-neighbor doublet of base pairs in normal DNA (9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar) and for doublet combinations containing normal pairs and mispairs(4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar). Eight of the 10 normal doublets are represented by solid circles (•) and two by open circles (○). The latter are doublets TG/AC and GA/CT, whose values (9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar) appear anomalous by comparison with results for doublet combinations(4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar), (TG/AC + GT/CA)/2 and (GA/CT + AG/TC)/2, represented by solid squares ( ■ ). Doublet combinations containing a mispair (TX/AY + XT/YA)/2 are represented by open squares (□). The solid curve is the rectangular hyperbola, described by, fitted by nonlinear regression to the eight solid circles and two solid squares. The dashed line is a linear least-squares fit to the same normal doublet data. In b is shown a similar plot for melting in 0.1 M NaCl, using ΔS° and ΔH° obtained for internal doublet combinations, (TX/AY + XT/YA)/2, where X/Y is a normal base pair ( ■ ), a mismatched base pair (□), or a pair containing the base analogue, O6-methyl G (▵). Each doublet combination is evaluated from triplet (TXT/AYA) in the center of the 9-bp duplex(7Gaffney B.L. Jones R.A. Biochemistry. 1989; 28: 5881-5889Crossref PubMed Scopus (123) Google Scholar), (GTTTXTTTG/CAAAYAAAC), as described in text. The solid curve and dashed line are the same as shown in a.View Large Image Figure ViewerDownload Hi-res image Download (PPT)These results raise an interesting question: how can enthalpy-entropy compensation be formulated, consistent with the observation that Tm relates to doublets in the simple manner(8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar, 10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar) described by? A straight-line approximation of ΔS° versus ΔH°, shown by the dashed line in Fig. 1a, is unsatisfactory because the line intersects the ΔS° axis at a positive value. The value of ΔS° cannot remain positive when ΔH° becomes negative because Tm = ΔH°/ΔS° would then become negative on the Kelvin scale, which is physically impossible.A satisfactory fit to the data is obtained with a rectangular hyperbola (Fig. 1, solid line). An analytic expression for the hyperbolic curve is generated simply by introducing a constant(To) in the linear relationship between Tm and ΔH°, Tm=To+ΔHoa(Eq. 4) Substitution of ΔH°/ΔS° for Tm in and solving for ΔS° results in the enthalpy-entropy compensation formula, ΔSo=aΔHoaTo+ΔHo(Eq. 5) This expression for ΔS° versus ΔH° has the form of a rectangular hyperbola passing through the origin (ΔH° = 0, ΔS° = 0). Near the origin, where ΔH° is much less than aTo, ΔS° is close to ΔH°/To, since the initial slope is 1/To. However, as ΔH° increases, the slope decreases continuously as ΔS° approaches a. With ΔH° related to doublets by and ΔS° described by, Tm = ΔH°/ΔS° remains related to doublets as in, Tm=To+ΔHoa=∑TMNfMN(Eq. 6) where TMN = To+ (ΔH°MN /a) is the Tm value for doublet MN, with ΔH°MN being its standard enthalpy change upon melting.The constant To may reflect the influence of solvent on DNA melting. If Tm were simply proportional to ΔH°, then at ΔH° = 0, the melting temperature would be 0 K, as expected for melting in vacuum. The presence of solvent may provide a resistance to DNA melting, so that as ΔH° approaches 0, the melting temperature approaches To > 0 K. Thus, Tm in degrees Kelvin is proportional to ΔH°+ aTo rather than to ΔH° alone, and instead of the DNA entropy change, ΔS° = ΔH°/Tm, being constant for all doublets, we now have the DNA + solvent entropy change, (ΔH°+ aTo)/Tm, equal to the constant a. The higher To is above 0 K, the higher a is above ΔS° = ΔH°/Tm. The constants a and To can be evaluated by fitting to the experimental data (Fig. 1) and, as shown below, To is within experimental error the same as the melting temperature of ice.Evaluation of Enthalpy-Entropy Compensation ConstantsTo evaluate To and a in, we make use of the ΔH° and ΔS° calorimetric values assigned to the 10 normal doublets in 1 M NaCl (9Breslauer K.J. Frank R. Blocker H. Marky L.A. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 3746-3750Crossref PubMed Scopus (1545) Google Scholar) and also van't Hoff measurements for two of the doublets, TG/AC and GA/CT (see Table 1). The plot of ΔS° versus ΔH° (Fig. 1a) shows eight points (solid circles) falling on a smooth curve or straight line while two (open circles) fall slightly below this trend. We do not use the two low points in fitting because van't Hoff measurements (4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar) for the same two doublets combined with their reverse counterparts (TG/AC + GT/CA)/2 and (GA/CT + AG/TC)/2 yielded higher points (solid squares) in much better agreement with the trend. Using the latter two points instead, we provide the alternative assignments shown in brackets in Table 1.The solid curve in Fig. 1a is the hyperbola described by fitted by nonlinear regression to the 10 points represented by the (eight) solid circles and (two) solid squares. For comparison, a dashed straight line showing the result of a linear least-squares fit to the same 10 points is also presented. By comparing the hyperbolic curve and straight line (Fig. 1a) with additional points (open squares) obtained for various X/Y mispairs (4Aboul-ela F. Koh D. Tinoco I.J. Martin F.H. Nucleic Acids Res. 1985; 13: 4811-4825Crossref PubMed Scopus (411) Google Scholar) in the doublet combination, (TX/AY + XT/YA)/2, we see that the curve successfully predicts the trend of mispair data whereas the straight line does not.The hyperbolic curve fitted by nonlinear regression yields To = 275 K and a = 81 cal/mol-K. Similar results, To = 273 ± 13 K and a = 79 ± 9 cal/mol-K, are obtained by rearranging to give linear expressions, ΔH°/ΔS°versus ΔH° and ΔH° versus ΔH°/ΔS°, to which linear regression is applied as in the Hanes-Woolf method of fitting the rectangular hyperbola in Michaelis-Menten enzyme kinetics(15Segel I.H. Enzyme Kinetics. John Wiley and Sons, Inc., New York1975Google Scholar).Thus for normal DNA doublets in 1 M NaCl, we find To is close to 273 K (ice melting point) and a is about 80 cal/mol-K, with an uncertainty of ±15 degrees and ±10 cal/mol-K, respectively. Within this margin of error, the same constant values may be expected to hold at lower salt concentrations also, since the melting point of ice differs by less than 5 degrees between 0 and 1 M NaCl. As shown in Fig. 1b, this expectation is supported by measurements in 0.1 M NaCl (7Gaffney B.L. Jones R.A. Biochemistry. 1989; 28: 5881-5889Crossref PubMed Scopus (123) Google Scholar) for doublet combinations of type, (TX/AY + XT/YA)/2, where X/Y includes normal pairs, mispairs, and also pairs and mispairs with the base analog, O6-methyl G.Analysis of Salt Effects on Doublet Thermodynamic Values Thermodynamic Evaluations for Base Pairs and Mispairs at Lower Salt ConcentrationGaffney and Jones(7Gaffney B.L. Jones R.A. Biochemistry. 1989; 28: 5881-5889Crossref PubMed Scopus (123) Google Scholar), using the van't Hoff method based on, have obtained thermodynamic data in 0.1 M NaCl for short (9 bp) duplexes containing various internal base pairs or mispairs (X/Y) at the center, including the base analog, O6-methyl G. We have analyzed their data to evaluate ΔH° and ΔS° for various doublet combinations at the center of the duplex. We start by calculating ΔS° for each 9 bp duplex, using the reported ΔH° and Tmax measurements at 10 -4M strand concentration; Tmax being a melting temperature, slightly different from Tm, measured at the maximum slope of the melting curve instead of the midpoint. To obtain ΔS°, we take ΔH°/Tmax measured at Ct = 10 -4M and subtract 20.1 cal/mol-K; the latter being a constant correction factor, consisting of 1.8 cal/mol-K (correction for the difference between Tmax and Tm) and 18.3 cal/mol-K (value of RlnCt). The formula, ΔS° = (ΔH°/Tmax) - 20.1 cal/mol-K, is applied to each duplex, D = GGTTXTTGG/CCAAYAACC. From the measured ΔH°(D) and calculated ΔS°(D), we subtract estimates of ΔH° and ΔS° for D with internal triplet Tr deleted, ΔH°(D-Tr) = 55 (±1) kcal/mol and ΔS°(D-Tr) = 166 (±2) cal/mol-K, to obtain ΔH°(Tr) and ΔS°(Tr) for the internal triplet, Tr = TXT/AYA. The values, ΔH°(Tr)/2 and ΔS°(Tr)/2, are then assigned to the doublet combinations, (TX/AY + XT/YA)/2.Fig. 1b shows a plot of ΔS° versus ΔH° for the melting of these doublet combinations in comparison with the same (solid) hyperbolic curve and (dashed) straight line drawn in Fig. 1a. The data are consistent with a hyperbola describing enthalpy-entropy compensation and not a straight line. Since the data fall on or near the same curve as in Fig. 1a, they indicate that the same compensation constants evaluated for normal DNA doublets in 1 M NaCl also hold at 0.1 M NaCl. Furthermore, since the doublet combinations include O6-methyl G (open triangles) along with normal base pairs (solid squares) and mispairs (open squares), it appears that To≈ 273 K and a ≈ 80 cal/mol-K apply even when DNA bases are chemically modified.Evaluation of TmDependence on Salt ConcentrationThe last column in Table 1 shows the melting temperature calculated for each normal doublet of base pairs in 1.0 M NaCl by applying and to ΔH° and ΔS°, including the alternative assignments given in brackets. The Tm value shown in each case is the average (± deviation from average) of two calculated results, one being Tm = To+ΔH°/a and the other being the mean of Tm = aTo/(ΔS°-a) and Tm = ΔH°/ΔS°. Although these two calculations are obviously not independent, they do serve to provide an internal consistency check of ΔH° and ΔS°, since one selects ΔH° and the other emphasizes ΔS°. The deviation from average of the two results indicates the degree of uncertainty in the Tm values predicted.For the majority of doublets, the predicted Tm values (Table 1) are above 100°C, as one might expect by extrapolation from lower salt concentrations(10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar). Additionally, the uncertainty (± deviation from average) is acceptable for all the original assignments, except for the two doublets TG/AC and GA/CT, shown as open circles falling below the curve in Fig. 1a. The alternative assignments (Table 1, in brackets) reduce the uncertainty from ± 21° and ± 15° to much lower values (± 6° and ± 5°, respectively), close to those found for the other doublets.Table 2 shows a comparison of our calculated Tm values at μ = 1 M with experimental results obtained at two lower ionic strengths, μ = 0.02 M(8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar) and 0.075 M(10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar). The calculated and experimental results are consistent in showing that seven of the 10 normal doublets have a large Tm dependence on μ, while three have only a small dependence. Since duplex Tm values tend to show a linear dependence on logμ, the following linear formula has been suggested(16Blake R.D. Delcourt S.G. Biopolymers. 1990; 29: 393-405Crossref PubMed Scopus (16) Google Scholar), Tm=T1.0+Slogμ(Eq. 7) Tabled 1where T1.0 is the Tm value at μ = 1.0 and S is a characteristic slope for each doublet, in degrees/unit change in logμ.According to, if one evaluates ΔTm/Δlogμ, using the Tm difference (ΔTm) between any two μ values (μ1 and μ2, with Δlogμ = logμ1 - logμ2), one should find an approximately constant S value for each doublet. The last column in Table 2 shows the average value of S = ΔTm/Δlogμ (± deviation from average) calculated from corresponding Tm and logμ differences between each pair of preceding columns. As seen in Table 2(last column), seven of the 10 normal DNA doublets have similarly large S values, ranging from 42 to 25 degrees/unit change in logμ, while the other three have much smaller values (7 or less).The three doublets with small S all have base G in position 1 of the doublet, namely GT/CA, GA/CT, and GC/CG. In contrast, all the doublets with G in position 2, namely CG/GC, GG/CC, TG/AC, and AG/TC, have some of the largest S values. CG/GC has the highest value of T1.0 ( ~ 149°C) and largest value of S ( ~ 42) of all normal doublets. Its reverse counterpart GC/CG has the second highest T1.0 ( ~ 139°C) but smallest S ( ~ 0). These results suggest that CG/GC is the most stable of all doublets at 1 M ionic strength or above, while GC/CG is the most stable at lower ionic strengths.DISCUSSIONThe hyperbolic variation of ΔS° with ΔH° observed experimentally (Fig. 1, a and b) indicates a significant enthalpy-entropy compensation in DNA melting thermodynamics. This behavior shows that Tm = ΔH°/ΔS° is not proportional to ΔH°, as previously suggested(8Gotoh O. Tagashira Y. Biopolymers. 1981; 20: 1033-1042Crossref Scopus (229) Google Scholar, 10Delcourt S.G. Blake R.D. J. Biol. Chem. 1991; 266: 15160-15169Abstract Full Text PDF PubMed Google Scholar), but may be linearly related to ΔH°, as described by. This equation includes a melting temperature constant, To, which is introduced as a parameter to represent the complex and poorly understood influence of solvent on DNA stability.The inclusion of To leads to an expression for enthalpy-entropy compensation in the form of a rectangular hyperbola,. The hyperbolic curve obtained by fitting experimental data for normal doublets in 1 M NaCl (Fig. 1a) indicates that To is close to the melting temperature of ice. The same hyperbolic curve, with no further adjustment of the two parameters (To and a) appears to hold reasonably well for mispaired doublets in 1 M NaCl (Fig. 1a) and for both normal and mispaired double