INTRODUCTION

TOP ABSTRACT INTRODUCTION RESULTS REFERENCES

It has been known for some time that the main effect of DNA composition on double helix stability is due to the large enthalpic difference (~1000 cal/mol) between the GC and AT base pairs, coming from the extra hydrogen bond in the former. This major energetic difference, however, cannot account for the fine details of DNA differential melting profiles. The next obvious step is to take into account energetic differences between nearest-neighbor (NN) doublets of base pairs, which should arise from different stacking interactions. For DNA there are 10 possible different NN doublets, so that 10 sets of H_ij and S_ij parameters should fully characterize the stability of a particular DNA molecule. The additivity principle, when applied to the NN problem, means that each thermodynamic quantity of a DNA molecule is a linear combination of the corresponding NN quantities, weighted by the frequencies f_ij of the corresponding NN doublets:

(1)

Given the fundamental and practical importance of understanding DNA stability, experimental characterization of H_ij and S_ij has been attempted by many groups over the last 20 years. Measurements of H and S were made by both calorimetry and van't Hoff analysis for a large number of DNA sequences, and the results were fitted to a set of 10 NN parameters as in Eq. 1. Such studies were performed on high polymeric DNA molecules (Blake and Delcourt, 1998; Gotoh and Tagashira, 1981; Vologodskii et al., 1984), oligomers (Doktycz et al., 1992; Santalucia, 1998; Sugimoto et al., 1996), and combinations of the two (Breslauer et al., 1986). As recently summarized by Santalucia (1998), there is a good consensus on G_ij values between most of the studies after conversion to the same temperature, 37°C = 310 K, and ionic strength. This is not true, however, for the individual H_ij and S_ij components of G_ij, as seen in Fig. 1.

View larger version (16K): [in this window] [in a new window]   FIGURE 1   Correlation between thermodynamic melting parameters for the nearest-neighbor doublets (NN) and their melting temperatures Tij. , Polymeric DNA data (Blake and Delcourt, 1998) obtained by van't Hoff analysis of the optical melting profiles. , Oligomeric DNA data from Santalucia (1998) obtained by analysis of Tm dependence versus oligomer strand concentration. , A combination of oligomeric and polymeric DNAs measured by many different methods (Breslauer et al., 1986). , Data for polymeric calf thymus DNA (Gruenwedel, 1974), the melting temperature of which was varied by changing solution ionic strength. In this case the slopes reflect the actual heat capacity change in the course of DNA melting transition, whereas this relationship is indirect for the NN data.

The fitted H_ij and S_ij parameters vary substantially from one study to another, the main difference being between their oligomeric and polymeric values. For example, the polymeric transition entropy appears to be independent of the NN identity and equals S = 24.85 ± 1.74 cal/mol K in I = 0.075 M NaCl (Delcourt and Blake, 1991), while the oligomeric S_ij varies between 19.9 and 27.2 cal/mol K, with an average of 22.4 cal/mol K (Santalucia, 1998). Another important feature is the differential stabilization effect of salt on various base pair doublets, which also appears to depend on DNA length.

This raises doubts regarding many conventional assumptions about DNA melting, such as 1) additivity of NN thermodynamic parameters, i.e., absence of longer range interactions; 2) length independence of DNA melting parameters per base pair; 3) applicability of polyelectrolyte theory in describing salt effects; 4) purely enthalpic difference between NN doublets; and 5) zero heat capacity changes associated with DNA melting. This last assumption is always implicitly made in the data analysis but is rarely discussed. Here we show that if one does not assume constancy of C_p in the melting transition, then the other assumptions can be reconciled with experiment.

	RESULTS

TOP ABSTRACT INTRODUCTION RESULTS REFERENCES

The key point is that there is always, in some sense, a long-range interaction between the base pairs. The transition enthalpy and entropy of a DNA fragment are always measured at the particular melting temperature T_m of this fragment, which is determined by its whole sequence. Therefore, the derived H_ij and S_ij for NN doublets will have thermal contributions dependent on the sequence of the entire fragment. Reported H_ij and S_ij parameters are obtained by averaging thermodynamic data on a set of DNA fragments. It is this averaging that introduces the apparent differences between the polymer and oligomer DNA melting thermodynamics.

To a very good first approximation, the T_m of a DNA fragment is its average over the T_m's of the NN doublets:

(2)

(This relation is strictly true only if S is independent of nearest-neighbor composition. While this has to be assumed when complex optical melting profiles are analyzed, its universal validity has not been demonstrated. However, our analysis herein shows that the assumption is at least self-consistent.) The related thermal contribution to the individual H_ij parameter is then f_ijC_p(T_ij  T⁰), where T⁰ is the standard melting temperature (Rouzina and Bloomfield, 1999). With f_ij  0.1 for a random mixture of nearest neighbors, C_p  100 cal/mol K, and (T_ij  T⁰)  10 K, this thermal contribution amounts to ~100 cal/mol.

On the other hand, melting of polymeric DNA of a given base composition proceeds via cooperative unwinding of large (~200 bp) domains enriched with NN doublets of a particular composition and sequence, the melting temperature T_ij of which strongly correlates with the melting temperature of the whole fragment. In the limiting case of melting of pure fragments containing only one kind of NN, this correlation would be at maximum; i.e., f_ij = 1, T_ij = T_m, and the thermal contribution to H_ij is the largest possible: C_p(T_ij  T⁰). For polymer domains of heterogeneous sequence this correlation is weaker, lying between the random composition case and the pure NN, such that

(3)

where  = f_ij. The corresponding thermal contribution to NN enthalpy of polymeric DNA is C_p(T_ij  T⁰).

We will assume that the differences between various NN doublets are purely enthalpic, so that

(4)

Here S is the NN-type independent entropy change, such as arises from polyelectrolyte effects when the salt concentration is less than 1 M; it is small compared to S⁰ in most situations (Rouzina and Bloomfield, 1999). Thus for I = 0.075 M salt, in which most of experiments analyzed by Blake and Delcourt (1998) were done, S = 1.24 cal/mol K. Then the total enthalpy and entropy of melting for a particular NN doublet melting are

(5)

where the second equality follows from G_ij = 0 at T_ij, and

(6)

These expressions predict much stronger variation of the NN parameters with T_ij than could be expected without the heat capacity change. That is, if C_p = 0, 

(7)

and

(8)

Experimental data for three sets of NN parameters as functions of melting temperature T_ij are presented in Fig. 1, A and B. They can be approximated with the linear functions in Table 1. There is an obvious trend in the first three data sets, which summarize the effects of sequence. While the experimental ranges of variation of H_ij and S_ij among the NN doublets are of similar magnitude for all data sets, the correlations with the melting temperatures T_ij are progressively weaker from polymer through oligomer to mixed polymer-oligomer. The inconsistent signs for the polymer-oligomer parameters are artifacts arising from the poor fit of widely scattered data to linear functions. This poor fit may simply reflect the lack of computational coupling of H and S in the analysis of the calorimetric data as opposed to the computationally coupled, van't Hoff analysis of the optical data. For discussions of this point see Krug et al. (1976), Owczarzy et al. (1997), and Plum et al. (1995).

At the same time, the melting temperatures of the NN doublets and the free energies at 37°C are quite similar for all data sets (Fig. 1 C). This means that even when variations in H_ij and S_ij are not correlated with DNA sequence, they are still correlated with each other because of thermal contributions of ~C_p(T_m  T) (Fig. 2). This implies that the shift of T_m of a fragment is caused in significant part by factors other than change in DNA sequence, such as some variation in solution conditions. For oligomers, such variation could be due to end effects, i.e., energies of ~1 kcal/mol bp associated with helix initiation (Santalucia, 1998) but unrelated to average DNA content.

View larger version (14K): [in this window] [in a new window]   FIGURE 2   Entropy-enthalpy correlation of NN doublet melting from all data sets in Fig. 1 (the symbols have the same meanings). Although H and S each have a range of variation of 100% or more, they are always strongly coupled, supporting the thermal origin of these variations.

When the linear relations in the first three entries in Table 1 are fitted to Eqs. 5 and 6, one obtains self-consistent values with fewer parameters than the constraints in the fit; it is clear that the last data set is close to the situation with C_p = 0, described by Eqs. 7 and 8. The negative C_p value and very large T⁰ are artifacts produced by the very poor linear fit to highly scattered data.

For comparison we also present in Fig. 1 and Table 1 data from a calorimetric study of calf thymus DNA (Gruenwedel, 1974) with T_m varied by salt. We see that variation of the thermodynamic parameters with temperature is even stronger than for polymeric DNAs of different base composition, while the quality of the fits to linear functions is very high. The reason for this is that all of the variation in H and S with temperature comes from the heat capacity contribution (Rouzina and Bloomfield, 1999):

(9)

and

(10)

In Eq. 10 we used Eqs. 8-11 of the accompanying manuscript (Rouzina and Bloomfield, 1999) to relate the relative entropy variation _S to the relative melting temperature shift _S = _H  t_m for the value of _H appropriate to the fixed DNA composition. No averaging over DNA composition was involved. Therefore the actual heat capacity contribution C_p was obtained directly. Comparing Eqs. 9 and 10 to the experimental values in Table 1, we arrive at the values

(11)

The value for H agrees with the 50% CG content of calf thymus DNA (Rouzina and Bloomfield, 1999).

The apparently similar strong dependence of the melting enthalpy on temperature in the cases of NN type or salt variation has two quite different origins. In the case of composition variation, enthalpy varies both directly and because of the indirect, statistically averaged, thermal contribution, i.e.,

(12)

while in the case of salt variation and fixed DNA composition all of the enthalpy variation comes from the thermal contribution:

(13)

Assuming that the value of C_p is 65 cal/mol K, we can estimate that the correlation factor  = 0.40, 0.22, and 0 from top to bottom in Table 2. Thus, as expected, the polymeric data show the largest thermal contribution to thermodynamic parameters, determined by DNA sequence. The two other data sets had progressively less correlation of the thermal contribution with the sequence.

Finally, we want to comment on the ratio

(14)

which is frequently claimed to be a universal constant (Blake and Delcourt, 1998; Privalov et al., 1969; Record et al., 1978). Equation 14 is a general thermodynamic relation, which follows from Eqs. 19 and 35 of the accompanying paper (Rouzina and Bloomfield, 1999). Then using Eq. 34 of that paper, one obtains

(15)

This ratio is independent of salt concentration, and for DNA of base composition X_GC = 0.5 and  = 2.6 it equals ~60. The ratio does not have to be the same for DNAs of different compositions. Nevertheless, in the particular case of the NN parameters given by Blake and Delcourt (1998), we see that with the substitution    = C_p/S⁰ = 26/25  1, the coefficient of X_GC in Eq. 15 is essentially zero, so the ratio is nearly composition-independent with a value of 56, which agrees well with the measured value of 55 ± 2 (Blake and Delcourt, 1998). Once again, there is no need to invoke a variable number of counterions bound, n, to different DNA sequences to explain this observation.