©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Enthalpy-Entropy Compensation in DNA Melting Thermodynamics (*)

(Received for publication, August 19, 1994; and in revised form, November 7, 1994)

John Petruska Myron F. Goodman

From the Department of Biological Sciences, University of Southern California, Los Angeles, California 90089-1340

ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
FOOTNOTES
ACKNOWLEDGEMENTS
REFERENCES

ABSTRACT

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 DeltaS° with DeltaH° follows a rectangular hyperbola. Doublet melting temperature relates linearly to DeltaH° by T = T + DeltaH°/a , where T approx 273 K and a approx 80 cal/mol-K. Thus T is proportional to DeltaH° + aT rather than to DeltaH° alone as previously thought by assuming DeltaS° to be constant. The term aT approx 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 (aT/T) declines with increasing T, while the DNA entropy change (DeltaH°/T) 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 DeltaS° and DeltaH° observed in 1 M salt can be used to evaluate DeltaH° and DeltaS° from T at lower, physiologically relevant, salt concentrations.


INTRODUCTION

Thermal denaturation studies of DNA have revealed that the melting temperature, T, (^1)of a DNA double helix depends on strand length(1, 2, 3) , strand concentration (4, 5, 6, 7) , base sequence(8, 9, 10) , and ionic strength of added salt (8, 9, 10, 11) . Such studies indicate that double helix stability can be predicted in terms of the standard free energy change, DeltaG° = DeltaH° - TDeltaS°, if one knows the standard enthalpy and entropy changes (DeltaH° and DeltaS°) for the melting of each nearest-neighbor doublet of base pairs in DNA(9) . 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, DeltaH° and DeltaS° have been evaluated experimentally in 1 M NaCl but only T(DeltaH°/DeltaS°) has been measured at lower salt concentrations. In this paper we provide a formula to describe the relationship between DeltaH° and DeltaS° measured in 1 M salt and show how standard enthalpy and entropy changes may be evaluated from T 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 (12, 13, 14) . For the melting of DNA doublets, we find that DeltaS° correlates with DeltaH° in the manner of a rectangular hyperbola. The hyperbolic curve that we obtain by fitting normal doublet data (4, 9) also applies to the melting of doublets containing base mispairs (4, 7) and the base analog O^6-methylguanine(7) .


EXPERIMENTAL PROCEDURES

Expressing DNA Melting Temperature as an Average of Doublet T(m) Values

The 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 DeltaS, the entropy change upon melting, is the same for all doublets. If DeltaS is constant, then each doublet has a melting temperature in degrees Kelvin (T(m) = DeltaH/DeltaS) directly proportional to DeltaH, the enthalpy change upon melting. This supposition was made originally by Gotoh and Tagashira (8) and more recently by Delcourt and Blake(10) , to evaluate doublet melting temperatures and enthalpy changes from T(m) 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 (DeltaH) 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

where f 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 DeltaH given by , the average entropy change per mole of doublet is DeltaS = DeltaH/T(m), where T(m) is the duplex melting temperature in degrees Kelvin. If all doublets have the same entropy change, i.e. DeltaS = DeltaH/T = c, then the duplex T(m) value is an average of doublet T(m) values,

where T = DeltaH/c is the T(m) value for doublet MN. This formula applies to DNA duplexes that are long enough so that end effects are negligible, and T(m) 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 T(m) with decreasing n because of end effects(1, 2) , and another term is required to describe T(m) dependence on strand concentration(4) .

Measurements of DNA Melting Temperatures at Various Salt Concentrations-has been used to describe DNA melting temperatures in terms of doublet T(m) values, for duplexes of length 100 bp or greater, in salt solutions of low ionic strength, µ = 0.020 M(8) and 0.075 M(10) . 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 T(m) values obtained for a wide range of known base sequences, self-consistent T values have have been determined for all normal MN doublets in 0.020 and 0.075 M NaCl. The corresponding ``constant'' doublet entropy change (DeltaS = 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 DeltaH = cT for each doublet(8, 10) .

In salt solutions of 1 M or above, T(m) 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 T(m) values low enough to be measured accurately over a wide range of total strand concentration (C(t)). Tinoco and co-workers (4) have shown that the equilibrium constant (K) for duplex dissociation at T(m) has the value C(t)/4 ideally, so the corresponding standard free energy change is

For each short (7-10 bp) duplex examined, a van't Hoff plot of Rln(4/C(t)) versus 1/T(m) was found to give a straight line with slope and intercept yielding DeltaH° and DeltaS° values for the duplex(4, 7, 14) . This experimental (van't Hoff) method of measuring DeltaH° and DeltaS° has been confirmed by Breslauer and co-workers (9) using calorimetry. A systematic replacement of one bp by another in short duplexes enabled Breslauer and co-workers to evaluate DeltaH° and DeltaS° for each normal doublet in 1 M NaCl (Table 1).



Effect of Increasing DNA Strand Length

As duplexes are made longer, their enthalpy and entropy changes increase with the number of doublets and the contribution from C(t) becomes less significant. This effect can be seen by dividing by T(m) and by n-1, to obtain for an average doublet, DeltaH°/T(m) = DeltaS° + R[ln(4/C(t))]/(n-1). For long duplexes, with n = 100-1000 and C(t) = 10-10M, the term R[ln(4/C(t))]/(n-1) is only 0.03 to 0.3 cal/mol-K, which is negligible compared to DeltaS° of 20-25 cal/mol-K for the average doublet. Thus, doublet T(m) values obtained from long duplexes of 100 bp or more at µ = 0.020 M(8) and 0.075 M(10) are essentially equivalent to DeltaH°/DeltaS° for the doublets at these two ionic strengths.


RESULTS

Formulation of Enthalpy-Entropy Compensation

Enthalpy-Entropy Compensation Fits a Rectangular Hyperbola

Table 1shows the DeltaH° and DeltaS° values obtained for normal DNA doublets by applying van't Hoff analysis and calorimetry to short duplexes in 1 M NaCl(4, 9) . Clearly DeltaS° is not constant but varies with DeltaH°. A plot of DeltaS° versus DeltaH°, 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 (12) and drug-DNA binding(13) .


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, DeltaS°, evaluated for melting in 1 M NaCl, is shown plotted against the corresponding enthalpy change, DeltaH°, for each nearest-neighbor doublet of base pairs in normal DNA (9) and for doublet combinations containing normal pairs and mispairs(4) . Eight of the 10 normal doublets are represented by solid circles (bullet) and two by open circles (circle). The latter are doublets TG/AC and GA/CT, whose values (9) appear anomalous by comparison with results for doublet combinations(4) , (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 (box). 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 DeltaS° and DeltaH° obtained for internal doublet combinations, (TX/AY + XT/YA)/2, where X/Y is a normal base pair (), a mismatched base pair (box), or a pair containing the base analogue, O^6-methyl G (up triangle). Each doublet combination is evaluated from triplet (TXT/AYA) in the center of the 9-bp duplex(7) , (GTTTXTTTG/CAAAYAAAC), as described in text. The solid curve and dashed line are the same as shown in a.



These results raise an interesting question: how can enthalpy-entropy compensation be formulated, consistent with the observation that T(m) relates to doublets in the simple manner(8, 10) described by ? A straight-line approximation of DeltaS° versus DeltaH°, shown by the dashed line in Fig. 1a, is unsatisfactory because the line intersects the DeltaS° axis at a positive value. The value of DeltaS° cannot remain positive when DeltaH° becomes negative because T(m) = DeltaH°/DeltaS° 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(T(o)) in the linear relationship between T(m) and DeltaH°,

Substitution of DeltaH°/DeltaS° for T(m) in and solving for DeltaS° results in the enthalpy-entropy compensation formula,

This expression for DeltaS° versus DeltaH° has the form of a rectangular hyperbola passing through the origin (DeltaH° = 0, DeltaS° = 0). Near the origin, where DeltaH° is much less than aT(o), DeltaS° is close to DeltaH°/T(o), since the initial slope is 1/T(o). However, as DeltaH° increases, the slope decreases continuously as DeltaS° approaches a. With DeltaH° related to doublets by and DeltaS° described by , T(m) = DeltaH°/DeltaS° remains related to doublets as in ,

where T = T(o) + (DeltaH°/a) is the T(m) value for doublet MN, with DeltaH° being its standard enthalpy change upon melting.

The constant T(o) may reflect the influence of solvent on DNA melting. If T(m) were simply proportional to DeltaH°, then at DeltaH° = 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 DeltaH° approaches 0, the melting temperature approaches T(o) > 0 K. Thus, T(m) in degrees Kelvin is proportional to DeltaH° + aT(o) rather than to DeltaH° alone, and instead of the DNA entropy change, DeltaS° = DeltaH°/T(m), being constant for all doublets, we now have the DNA + solvent entropy change, (DeltaH° + aT(o))/T(m), equal to the constant a. The higher T(o) is above 0 K, the higher a is above DeltaS° = DeltaH°/T(m). The constants a and T(o) can be evaluated by fitting to the experimental data (Fig. 1) and, as shown below, T(o) is within experimental error the same as the melting temperature of ice.

Evaluation of Enthalpy-Entropy Compensation Constants

To evaluate T(o) and a in , we make use of the DeltaH° and DeltaS° calorimetric values assigned to the 10 normal doublets in 1 M NaCl (9) and also van't Hoff measurements for two of the doublets, TG/AC and GA/CT (see Table 1). The plot of DeltaS° versus DeltaH° (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 (4) 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 (4) 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 T(o) = 275 K and a = 81 cal/mol-K. Similar results, T(o) = 273 ± 13 K and a = 79 ± 9 cal/mol-K, are obtained by rearranging to give linear expressions, DeltaH°/DeltaS°versus DeltaH° and DeltaH° versus DeltaH°/DeltaS°, to which linear regression is applied as in the Hanes-Woolf method of fitting the rectangular hyperbola in Michaelis-Menten enzyme kinetics(15) .

Thus for normal DNA doublets in 1 M NaCl, we find T(o) 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 (7) 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, O^6-methyl G.

Analysis of Salt Effects on Doublet Thermodynamic Values

Thermodynamic Evaluations for Base Pairs and Mispairs at Lower Salt Concentration

Gaffney and Jones(7) , 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, O^6-methyl G. We have analyzed their data to evaluate DeltaH° and DeltaS° for various doublet combinations at the center of the duplex. We start by calculating DeltaS° for each 9 bp duplex, using the reported DeltaH° and T(max) measurements at 10M strand concentration; T(max) being a melting temperature, slightly different from T(m), measured at the maximum slope of the melting curve instead of the midpoint. To obtain DeltaS°, we take DeltaH°/T(max) measured at C(t) = 10M 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 T(max) and T(m)) and 18.3 cal/mol-K (value of RlnC(t)). The formula, DeltaS° = (DeltaH°/T(max)) - 20.1 cal/mol-K, is applied to each duplex, D = GGTTXTTGG/CCAAYAACC. From the measured DeltaH°(D) and calculated DeltaS°(D), we subtract estimates of DeltaH° and DeltaS° for D with internal triplet Tr deleted, DeltaH°(D-Tr) = 55 (±1) kcal/mol and DeltaS°(D-Tr) = 166 (±2) cal/mol-K, to obtain DeltaH°(Tr) and DeltaS°(Tr) for the internal triplet, Tr = TXT/AYA. The values, DeltaH°(Tr)/2 and DeltaS°(Tr)/2, are then assigned to the doublet combinations, (TX/AY + XT/YA)/2.

Fig. 1b shows a plot of DeltaS° versus DeltaH° 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 O^6-methyl G (open triangles) along with normal base pairs (solid squares) and mispairs (open squares), it appears that T(o) approx 273 K and a approx 80 cal/mol-K apply even when DNA bases are chemically modified.

Evaluation of T(m)Dependence on Salt Concentration

The last column in Table 1shows the melting temperature calculated for each normal doublet of base pairs in 1.0 M NaCl by applying and to DeltaH° and DeltaS°, including the alternative assignments given in brackets. The T(m) value shown in each case is the average (± deviation from average) of two calculated results, one being T(m) = T(o) + DeltaH°/a and the other being the mean of T(m) = aT(o)/(DeltaS°-a) and T(m) = DeltaH°/DeltaS°. Although these two calculations are obviously not independent, they do serve to provide an internal consistency check of DeltaH° and DeltaS°, since one selects DeltaH° and the other emphasizes DeltaS°. The deviation from average of the two results indicates the degree of uncertainty in the T(m) values predicted.

For the majority of doublets, the predicted T(m) values (Table 1) are above 100 °C, as one might expect by extrapolation from lower salt concentrations(10) . 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 2shows a comparison of our calculated T(m) values at µ = 1 M with experimental results obtained at two lower ionic strengths, µ = 0.02 M(8) and 0.075 M(10) . The calculated and experimental results are consistent in showing that seven of the 10 normal doublets have a large T(m) dependence on µ, while three have only a small dependence. Since duplex T(m) values tend to show a linear dependence on logµ, the following linear formula has been suggested(16) ,



where T is the T(m) 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 DeltaT(m)/Deltalogµ, using the T(m) difference (DeltaT(m)) between any two µ values (µ(1) and µ(2), with Deltalogµ = logµ(1) - logµ(2)), one should find an approximately constant S value for each doublet. The last column in Table 2shows the average value of S = DeltaT(m)/Deltalogµ (± deviation from average) calculated from corresponding T(m) 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 T (149 °C) and largest value of S (42) of all normal doublets. Its reverse counterpart GC/CG has the second highest T (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.


DISCUSSION

The hyperbolic variation of DeltaS° with DeltaH° observed experimentally (Fig. 1, a and b) indicates a significant enthalpy-entropy compensation in DNA melting thermodynamics. This behavior shows that T(m) = DeltaH°/DeltaS° is not proportional to DeltaH°, as previously suggested(8, 10) , but may be linearly related to DeltaH°, as described by . This equation includes a melting temperature constant, T(o), which is introduced as a parameter to represent the complex and poorly understood influence of solvent on DNA stability.

The inclusion of T(o) 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 T(o) is close to the melting temperature of ice. The same hyperbolic curve, with no further adjustment of the two parameters (T(o) and a) appears to hold reasonably well for mispaired doublets in 1 M NaCl (Fig. 1a) and for both normal and mispaired doublets, including the base analog O^6-methyl G in 0.1 M NaCl (Fig. 1b). Thus, the constants evaluated by fitting data at 1 M ionic strength, T(o) = 273 ± 15 K and a = 80 ± 10 cal/mol-K, appear to hold at lower ionic strengths as well.

Interpretation of Enthalpy-Entropy Compensation Constants T(o) and a

Our analysis of thermal melting and calorometric data has established the following points: (i) DeltaS° is not a constant for DNA doublets but instead varies in a manner resembling enthalpy-entropy compensation; (ii) the variation of DeltaS° with DeltaH° can be described to a good approximation by a rectangular hyperbola (Fig. 1, a and b), defined by two constants, T(o) and a; (iii) the constant T(o) is close to ice melting temperature; (iv) the constant a is much larger than DeltaS° and could be the combined DNA + solvent entropy change for doublet melting.

In the case of protein denaturation, enthalpy-entropy compensation is attributed to interactions with surrounding water molecules(12) . However, the detailed interactions between water and proteins are not well understood. In the absence of an adequate theory to account for enthalpy-entropy compensation, we can only speculate on the nature of the interactions between water and DNA that might provide new insight into the phenomenon.

The finding that T(o) approx 273 K implies that DeltaH° for the melting of DNA doublets is approximately proportional to T(m) evaluated in degrees Celsius, as seen from , instead of being proportional to T(m) evaluated in degrees Kelvin,

The corresponding entropy change for doublet melting, DeltaS° = DeltaH°/T(m), is not constant, but is proportional to the ratio of T(m)(°C) to T(m)(K), as seen from ,

Since T(m)(K) = 273 + T(m)(°C), a plot of DeltaS° against T(m)(°C) should also yield a rectangular hyperbola, like the plot of DeltaS° versus DeltaH° described by (solid curves in Fig. 1, a and b).

According to , DeltaH° is the difference between aT(m) and aT(o). What do these empirical terms represent? We suggest that aT(o) represents an enthalpy change in solvent (water) accompanying the DNA enthalpy change DeltaH° for doublet melting. According to this interpretation, aT(m) = DeltaH°+ aT(o) is the combined DNA + solvent enthalpy change for each doublet, with a = (DeltaH° + aT(o) )/T(m) being the combined DNA + solvent entropy change for doublet melting. The constancy of the parameter a implies that T(m) approaches T(o) when DeltaH° approaches 0, and that as DeltaH° increases, the DNA entropy change (DeltaS° = DeltaH°/T(m)) increases by the same amount as solvent entropy change (aT(o)/T(m)) decreases, so that their sum stays constant at the value a for each doublet.

The large value of a (80 cal/mol-K) indicates that the solvent enthalpy change, aT(o) = 21.8 kcalmol, is considerably larger than any DeltaH° value found for normal doublets (Table 1). The implication is that the change in solvent enthalpy is always greater than the change in DNA enthalpy when DNA melting occurs, and also that the solvent entropy change (aT(o)/T(m)) exceeds the DNA entropy change (DeltaH°/T(m)).

The magnitude of aT(o) is large enough to require that at least four H-bonds between water molecules be broken, per DNA doublet, when melting occurs. This estimate is made by considering the melting of ``Watson-Crick'' DNA, WbulletC W + C, as being accompanied by the breakage of H-bonds between H(2)O molecules,

where m is the number of water H-bonds broken for each DNA (WbulletC) unit melted. Since about 5 kcal/mol is required to break an H-bond between water molecules(17) , m must be at least 21.8/5 = 4.3/melted doublet. The number could be larger, depending on the strength of H-bonding between H(2)0 and dissociated W and C (right-hand side of ).

Interpretation of Ionic Strength Effects

Thermodynamic models of DNA interactions with salt ions (18, 19) suggest that S in , i.e. the slope of T(m) relative to the logarithm of the ionic strength, may be proportional to the amount of counterion (Na) released upon duplex melting. For an S value around 20°, about 0.4 of a counterion is expected to be released per melted base pair or base-stacking interaction. If the release of counterion and S are proportional, then CG/GC, the doublet with the largest S (Table 2), releases approximately 1 counterion upon disruption of its stacking interaction while its reverse counterpart GC/CG releases 0. Since the two doublets have the same bases and the same sugar-phosphate backbone for counterion binding, what factor might be responsible for this difference?

Doublet GC/CG is known to have the highest intrinsic base stacking energy in B-DNA because it has a large, attractive electrostatic base-stacking component(8) . The intrinsic base stacking energy of CG/GC is considerably lower because it has a repulsive electrostatic component. Calculations of electrostatic interactions versus twist angle (20) indicate that the electrostatic attraction in GC/CG promotes a large twist angle, around 40°, while the repulsion in CG/GC promotes a small twist angle, around 25°, compared to the average 36° angle between stacked base pairs in B-DNA.

The favorable alignment of oppositely charged atoms in the stacked base pairs of GC/CG may be sufficiently stable in B-form duplex as not to attract salt ions, whereas the unfavorable alignment in CG/GC may attract salt ions to counteract repulsions between atoms of like charge. Such differences in ion attraction might be the reason why GC/CG stability shows almost no dependence on salt concentration, while CG/GC stability rises dramatically, as indicated by S = 1° and 42°, respectively (Table 2).

Relevance to DNA Replication Fidelity

DNA polymerases have high accuracy characterized by low misinsertion efficiencies, around 10 to 10(21) , indicating large differences in free energy (about 5-8 kcal/mol) between right and wrong base pairs in polymerase active sites(22, 23) . However, measurements of DeltaG° = DeltaH° - TDeltaS° for DNA melting indicate only small DeltaG° differences (DeltaDeltaG° approx 0.2 to 3 kcal/mol) between correct and incorrect base pairs at room temperature (14) . The differences are small because of enthalpy-entropy compensation. Because DeltaS° correlates with DeltaH°, the value of DeltaDeltaG° = DeltaDeltaH° - TDeltaDeltaS° is small compared to DeltaDeltaH°(14) . Values of DeltaDeltaG° for base pair differences can be an order of magnitude less than DeltaDeltaH° and generally are much too small to account for DNA polymerase fidelity(14) .

Having described enthalpy-entropy compensation and evaluated the influence of solvent, by , we now see that free energy differences for DNA + solvent may be as large as differences in DeltaH°. The DNA + solvent change in enthalpy for doublet melting is DeltaH = DeltaH°+ aT(o), while the corresponding change in entropy is DeltaS = a. Thus, for DNA + solvent at temperature T, the free energy change for doublet melting is DeltaG = DeltaH° + a(T(o) - T). Since a and T(o) are constant, then differences in DeltaG may equal differences in DeltaH° at constant T. In other words, the magnitude of DeltaDeltaG for DNA + solvent may equal DeltaDeltaH° for DNA and be sufficient to account for DNA polymerase accuracy.

The above finding provides an unexpected source of free energy that a polymerase might exploit. The result, DeltaDeltaG equals DeltaDeltaH, while not applicable to DNA alone, is found to apply to DNA in combination with solvent, with water as solvent. Perhaps, it also applies to enzyme as ``solvent.'' Possibly, as we have suggested previously, the geometric constraints placed on substrate and template bases in the polymerase active cleft can suppress DeltaDeltaS sufficiently to make DeltaDeltaG equal DeltaDeltaH(21) . To the extent that dNTP and template bases confront one another in a lower dielectric medium that tends to exclude water, DeltaDeltaH values between correct and incorrect base pairs may be even larger than in water(24) . Thus it seems likely that the enzyme active site can exploit the large differences in enthalpy between matched and mismatched base pairs to achieve high nucleotide insertion fidelity(14) . Replication and repair polymerases and reverse transcriptases exhibit different levels of insertional accuracy perhaps by placing different constraints on bound dNTP and DNA, and by achieving different levels of water exclusion.


FOOTNOTES

*
This work was supported by National Institutes of Health Grants GM21422 and AG11398. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked ``advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

(^1)
The abbreviations used are: T, melting temperature of DNA duplex or individual doublets of base pairs; bp, base pair(s).


ACKNOWLEDGEMENTS

We thank Dr. Linda B. Bloom and Steven Creighton for providing constructive comments and valuable aid in the analysis of data by computer.


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