Acta Chim. Slov. 2007, 54, 445–451
445
Scientific paper
Stability of a Short DNA Duplex as a Function
of Temperature: the Effect of ?Cp
and Added Salt Concentration†
Igor Drobnak, Mojca Seru~nik, Jurij Lah* and Gorazd Vesnaver*
University of Ljubljana, Faculty of Chemistry and Chemical Technology, A{ker~eva 5, 1000 Ljubljana, Slovenia.
* Corresponding author: Jurij Lah, phone: +386 1 2419 414, fax: +386 1 2419 425, e-mail: jurij.lah@fkkt.uni-lj.si; Gorazd Vesnaver, phone: +386 1 2419 402, fax: +386 1 2419 425, e-mail: gorazd.vesnaver@fkkt.uni-lj.si;
Received: 16-04-2007
†Dedicated to Prof. Dr. Jo`e [kerjanc on the occasion of his 70th birthday
Abstract
Recently, it has been shown that ?cp effects accompanying the helix-to-coil transitions of DNA duplexes are not negligible. To find out if this is the case also with a short model (5’-CGAATTCG-3’)2 duplex we studied its thermal unfolding by high sensitivity differential scanning calorimetry (DSC) at 0, 0.1, 0.3 and 1 M added NaCl. We succesfully described the measured DSC thermograms by the model function that is based on the two-state approximation of the unfolding process and contains three adjustable parameters: T1/2 – the melting temperature, ?H(T ) – enthalpy of unfolding at T1/2 and ?cp – the change of heat capacity upon DNA unfolding. These ?H(T ) values are1/i2n good agreement with those obtained by the straightforward integration of the DSC thermograms. Fro1m/2 the available experimental data a ?H(T ) versus T1/2 plot was constructed and ?cp was obtained as a slope of the observed linear relationship. We believe that e1/x2cellent agreement between this ?cp and the one obtained as adjustable parameter from fitting the experimental DSC thermograms strongly supports our suggestion that ?cp accompanying unfolding of DNA is independent of temperature an added salt concentration and may be accurately determined from the described fitting procedure. Analysis of our results shows that even for short DNA duplexes the errors in the nearest-neighbor estimates of ?G(25 °C), ?H(25 °C) and
AS
(25 °C)
of unfolding based on the Ac = 0 assumption may be significant. It also shows that the experimental T1/2 versus ln[Na+] slope depends on the salt concentration and agrees reasonably well with the one predicted by the electrostatic polyelectrolyte theory.
Keywords: DNA, thermodynamics, differential scanning calorimetry, heat capacity, stability.
1. Introduction
Temperature induced melting of DNA duplexes is the process of separating the two strands wound in a double helix into two single strands. Characteristically, such phase transitions are accompanied by a relatively small transition free energy, ?G(T), that results from the compensation of a large transition enthalpy, ?H(T), and large transition entropy, ?S(T).1–4 In such transition studies the heat capacity change, ?cp(T), that also accompanies the melting processes has been typically overlooked. Only recently,5–9 with the employment of the last generation of high-sensitivity differential scanning calorimetry (DSC) instruments in DNA melting studies, it has become increasingly clear that DNA thermal transitions may be associated with a significant change in cp(T). This means that quantitative knowledge of ?cp(T) is required to compare ?G(T), ?H(T)
and ?S(T) of transition of nucleic acids at some common reference temperature. Empirically, ?cp(T) is thought to arise mainly from solvent effects that accompany the exposure of non-polar10–13 and/or aromatic surfaces upon unfolding. Since net base stacking is greater in the folded duplex than in the unfolded single strands14 one would expect duplex unfolding to be accompanied by a ?cp(T) that corresponds to increased amount of unstacked bases and consequently to increased hydration of aromatic surfaces. Despite the potential for such “hydration” heat capacity to provide a key to understanding solute – solvent interactions there is as yet no general model for ?cp(T) that can be applied to macromolecular transitions. Currently, the only successful models that describe ?cp(T) resulting from molecular conformational transitions are those for proteins and are based on the accompanying changes in solvent-accessible surface areas. These models employ
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Acta Chim. Slov. 2007, 54, 445–451
empirical formulas that have been parameterized using model compound (peptides, amino acid fragments) transfer and protein unfolding thermodynamic data.10–13,15 Unfortunately, there are no data for corresponding nucleic acid model compounds i.e. bases, sugars and fragments of phosphate backbone. Thus the only approach used to date for obtaining reliable ?cp(T) for nucleic acid unfolding has been its direct measurement by DSC.
The polyelectrolyte nature of DNA adds further complexity to its behavior in solution. A dense atmosphere of condensed counterions around the polyanionic DNA backbone has a major impact on the thermodynamics of unfolding. Experimental and theoretical studies show that the temperature at the midpoint of the thermally induced duplex-to-single-strands transitions (melting temperature, T1/2) strongly depends on the concentrations and charges of cations in the solution.5,6,8,9,16,17 They also show that upon unfolding a substantial amount of the condensed counterions is released because the extent of coun-terion binding to DNA in the duplex form is larger than in the single-stranded form.18–21 By contrast, as recent analysis of ?cp(T) of DNA melting suggests,8 the electrostatic effects arising from the DNA’s polyelectrolyte nature cannot account significantly for the observed ?cp(T) values. This further means that ?cp(T) is not expected to depend on the added salt concentration.
The primary goal of our study was to investigate whether the ?cp(T) effects accompanying the helix-to-coil transitions of short DNA duplexes are as important as those observed with longer double helical oligonu-cleotides.7 To see to what extent these ?cp(T) values affect the temperature dependence of the corresponding transition quantities ?G(T), ?H(T) and ?S(T) we studied the thermally induced unfolding of the (5’-CGAATTCG-3’)2 duplex at different concentrations of NaCl by employing DSC. Using these data we also tried to find out whether the observed ?cp(T) exhibits any significant dependence on temperature or added salt concentration.
2. Experimental
Materials. Oligonucleotide 5’-CGAATTCG-3’ was purchased from Invitrogen Co., Germany. Its concentrations in buffer solutions were determined at 25 °C spec-trophotometrically in the Cary Bio 100 UV-spectropho-tometer. For the extinction coefficient of its duplex form we used the value ?260 = 143600 M–1 cm–1 that was determined from the nearest-neighbor data of Cantor et al.22 The buffer solutions used in all experiments consisted of 10 mM phosphate buffer, 1 mM Na2EDTA and 0, 0.1, 0.3 or 1 M NaCl. All solutions were adjusted to pH = 7.0.
Differential scanning calorimetry (DSC). DSC measurements were performed with a Nano-II DSC calorimeter (CSC, UT). Thermal denaturation of the (5’-CGAATTCG-3’)2 duplex in buffer solutions with different added NaCl concentrations was monitored be-
tween 5 and 95 °C. A heating rate of 1 °C min–1 was used. Essentially the same results were obtained
also at the heating rate of 0.25 °C min–1. The unfolding
–– of DNA was monitored in terms of (cp2(T) – cp 2(T)) versus T thermograms in which the differences betAween the
– raw signal, corrected for the buffer contribution, cp2(T),
and the corresponding heat capacity of the native duplex
– state, cp 2(T), are normalized for the duplex concentration (FigA 3a).
3. Analysis of DSC Data
The thermally induced duplex to single strands transition that appears to be an all-or-none process
(1)
may be described in terms of the total duplex concentration, ctot, and the fraction of duplex molecules that undergo transition into single strands, a(T). Experimentally this transition can be followed by DSC. At very low ctot values used in DSC experiments the measured c (T) (baseline subtracted) can be equalized with the DNA partial molar heat capacity, – 2 T). Thus, the overall heat effect, AH(T _>T), that accompanies the transition of DNA from its native duplex state at T1 (a(T) = 0) to its denatured single stranded state at T2 (a(T) = 11) can be expressed as
(2)
Since enthalpy is a state function eq. 2 can be expressed as
(3)
and by choosing Tref = T1/2 where T1/2 is the melting temperature (?= 1/2) one obtains that the molar enthalpy of
transition at T
KCal
 ^H (T 1/2 )
is
(4)
Evidently, ?HC(Ta l  ) can be determined from the
(T     )
measured DSC thermo1g/2ram simply by integration of the
––                 ––
experimental (cp2(T) – cp 2(T)) and (cp2(T) – 2cp (T))curves
over the corresponding Atemperature intervalsA and thus, may be considered as a model-independent quantity.
Moreover, the corresponding ?ccpa(lT) at given T is defined
– as a difference between the post-transitional (2cp (T)) and
–                                        A
the pre-transitional (cp 2(T)) baselines extrapolated to that
T (Fig. 3). According tAo the measured DSC thermogram
the ?ccp a(lT) for the (5’-CGAATTCG-3’)2 duplex appears to
be independent of temperature (Fig. 3).
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447
For   the   temperature   dependent   equilibrium described by eq. 1 the partial molar enthalpy of DNA,
in which the quantities ?G°(T), ?G(°T   ), ?H°(T), ?H°
1/2
(T     ) 1/2
H2(T), is defined as
(5)
where n2 and n1 are the total numbers of moles of the
DNA duplex and solvent, respectively. When expressed in
terms of the corresponding partial molar enthalpies of the
––
double stranded and single stranded state, HA (T) and HA(T), – H2(T) takes the form:                                   2
(6)
By taking the temperature derivative of eq. 6 at constant p, n1 and n2 one obtains
cmt)   cpJ,tn + a(T)"cMr) + ""(n
I 5T J
(7)
–– where ?cp(T) = (2cp(T) – cp 2(T), ?H(T) = (2HA(T) – HA (T)), the subscript 2 denotes DNAA at a given thermal equi2librium and the subscripts A2 and A refer to its corresponding duplex and single-stranded state, respectively. Since ?cp(T) and ?H(T) appear to be independent of the DNA concentration, which means that ?cp(T) = ?c°p(T) and ?H(T) = ?H°(T), eq. 7 becomes
(8)
and can be considered as the model function for the measured DSC thermogram.
A detailed description of the thermal duplex-to-single-strands equilibrium (eq. 1) includes the following relations
(doaj)        =AH;,T}atTt(\-am) {  ÔT   J           RT-      l-a„.
~AG,
(9)
AG(",, = 7"
rm  +Aff(T"4r  71,J+M' 'V    r ,
?S°(T) and ?c°p refer to the duplex-to-single-strands transitions that occur between their standard states at T or T1/2 and ?c°p is assumed to be independent of temperature. Inspection of eqs 1, 8 and 9 shows that the model function (eq. 8) contains only three adjustable parameters: T1/2,
?H°(T   ) and ?c°p. They can be determined by fitting the
–– mode1l/2 function to the experimental (cp2(T) – cp 2(T)) versus
T curve and used to calculate the ?G°(T), ?H°(TA) and ?S°(T) values at any other T (eq. 9). To obtain the “best fit” values of the three adjustable parameters at each of the added NaCl concentrations the non-linear Levenberg-Marquardt regression procedure was used. Inspection of these results shows that T1/2 increases with increasing added salt concentration. Since the enthalpies of transition appear to be salt-independent quantities (Fig. 2b) ?c°p may be calculated simply as the slope of the ?H°(T ) versus T1/2 curve constructed from the “best fit” ?H1(°T/2 ) and T1/2 values determined at different NaCl concen1/t2rations (Fig 3b). Using these data we also obtained the experimental dependence of T1/2 on the concentration of Na+ ions (Fig 4) from which the amount of Na+ ions released upon the unfolding of the DNA duplex at a given salt concentration was estimated.
4. Results and Discussion
The results of DSC melting experiments performed on duplex solutions in phosphate buffer and 0, 0.1, 0.3 and 1 M NaCl are presented in Fig. 1. Good agreement between the model dependent quantities (c„ m - cn m) (eq
—                 —                                                                                P?(  )           PA.'}'-   '
8), (#2m – Ha (t)) (eq 6) and am obtained from the “best fit” model parameters T1/2, AH?T ) and Ac° with the corresponding non-model values obtained directly from the measured DSC thermograms (Fig. 1) indicates that the observed transition may be considered as a two state transition. The two-state description of the (5’-CGAATTCG-3’)2 unfolding process may be justified also in the usual, less strict, way by the observed good agreement of the model dependent and model independent AH
(T    ) 1/2
values
(Table 1). Moreover, the ?H°(T ) value determined in 1 M NaCl (Fig. 2b) is close to the c1/o2rresponding transition enthalpy, ?H°(25 °C), calculated at 25 °C using the nearest neighbor approach.23 Since the nearest neighbor data reported at 25 °C were obtained from the experimental data at the corresponding melting temperatures assuming that ?c°p = 0 the observed agreement, in fact, supports the credibility of our results.
By using the “best fit” values of the adjustable parameters T1/2, ?H°(T ) and ?c°p and eq. 9 the characteristic thermodynamic qu1/a2 ntities of duplex-to-single-strands transitions ?G°(T), ?H°(T) and ?S°(T), were determined as functions of temperature and salt concentration (Fig. 2). They appear to be moderately temperature-dependent and ?G°(T) versus T curve exhibits a slightly curved shape typi-
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Acta Chim. Slov. 2007, 54, 445–451
Figure 1. Thermal unfolding of the (5’-CGAATTCG-3’)2 duplex followed by DSC thermograms measured at several concentrations of added NaCl_and presented as: (a) (è (T - è (T)) as a function of T, (b) (H2(T - HA (T)) as a function of T and (c) a(T as a function of T. Full lines represent graphs of the best fitted model functions (eq. 8), (eq. 6) and (eq. 9) while points represent the corresponding experimental values (experimental a(T = AH(T/AH(total)).
cal of the processes that are accompanied by ?c°p > 0.24–26 In the measured temperature interval the highest duplex stability (the highest ?G°(T) value) is observed at the highest salt concentration. The comparison of ?G°(25 °C), ?H°(25 °C) and ?S°(25 °C) determined in 1M NaCl with the corresponding nearest-neighbor (n.n.) data23 shows that the errors in the nearest-neighbor estimates that result from the ?c°p = 0 assumption are significant even for short DNA duplexes like (5’-CGAATTCG-3’)2: ??G°(25 °C) = ?G°(25 °C) (exp) – ?G°(25 °C) (n.n.) = –1.2 kcal/mol and the corresponding ??H°(25 °C) = –7.2 kcal/mol and ??S°(25 °C) = –20.5 cal/mol K.
As shown in Fig. 2b the enthalpy of transition, ?H°(T), appears within the experimental error to be independent of salt concentration. This observation strongly supports the use of the already mentioned alternative method of determining ?c°p according to which ?c°p is obtained as the (??H°(T )/?T1/2) slope of the measured linear dependence of ?H1°/( 2T ) on T1/2 (Fig. 3b). Inspection of data in Table 1 reveals t1h/2at the ?c°p obtained from both methods is almost identical and agrees rather well with the model independent estimate of ?c°p obtained by the extrapolation method (Fig. 3a). Its value of 27 ± 5 cal (mol of base pairs)–1 K–1 also agrees well with ?c°p values reported by Tihomirova et al.7 for a number of 13-mer duplexes.
We believe that for the observed two state transition the ?c°p value obtained from fitting the DSC thermogram is more reliable than the one determined in the most frequent manner, that is by subtracting the pre-transitional DSC baseline from the post-transitional one. Namely, the described fitting procedure involves a large number of experimental points while subtraction of the two baselines is always problematic due to their unsafe extrapolation over the measured temperature interval.
Fig. 4 presents the salt dependence of the melting temperature, T1/2 determined from the corresponding DSC thermograms. The values of T1/2 increase with increasing salt concentration, a result that reflects the well known salt-effect on the stability of nucleic acids.27 Temperature induced helix-to-coil transitions of DNA in solution, in the absence or presence of added salt, have been described in terms of the counterion condensation polyelectrolyte theory of Manning and Record18,28,29 which takes into account only electrostatic polyion-counterion interactions and predicts that
flj;i/1,/Sln[Na+] = 0.9-(Ä7'I/AHJi(i))-A«N
(10)
Table 1. Thermodynamic parameters of (5’-CGAATTCG-3’)2 duplex unfolding at [NaCl] = 0.1 M. T1/2 /°C
AH™   Vkcal mol 1
(Ty2 )
Ac°/kcal mol 1 K 1
a Number of released Na+ ions per base pair.
A           a
Na+
		cal	fit	cal	fit	slope	
value	45.7	54.8	56.5	0.24	0.22	0.21	0.20
error	±0.2	±1.5	±0.5	±0.06	±0.03	±0.03	±0.02
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Figure 2. Thermodynamics of thermally induced helix-to-coil transition of the (5’-CGAATTCG-3’)2 duplex at different NaCl concentrations. ?G°(T), ?H°(T) and T ?S°(T)of transition presented as a function of temperature were obtained at each NaCl concentration from eq. 9 using the corresponding “best fit” adjustable parameters T1/2, ?H°      and ?c°.
where AH'1 ) is the enthalpy of the helix-to-coil transition of the (5 -CGAATTCG-3’)2 duplex at T1/2, the 0.9 is a correction factor that takes care of the conversion of the mean ionic activity to ionic concentration and A«Na+ is the number of Na+ ions released upon unfolding of a single duplex molecule. A fit of a second order polynomial function to the experimental T1/2 versus ln[Na+] curves has allowed us to estimate the slopes in order to calculate the release of the counterions (eq. 10, Fig. 4). The value of A«Na+ = 0.2 counterions/base pair obtained at 0.1 M NaCl (Table 1) is in a reasonably good agreement with the A«Na+ values reported to accompany unfolding of some other
Figure 3. Determination of ?c°p that results from the unfolding of
–– the (5’-CGAATTCG-3’)2 duplex: (a) (cp2(T) – cp 2(T)) versus T DSC
thermogram measured at 1.0 M NaCl (points) Adescribed with the corresponding best fit model function (full line) expressed in terms of T1/2, ?H°(T ) and ?c°p. Another way of determining ?c°p is by subtracting the p1/r2e-transitional from the post-transitional baseline ?c°p (cal). (b) ?c°p is obtained as the slope of the ?H°(T ) versus T1/2 curve constructed from the ?H°(T ) and T1/2 values 1d/2etermined at different NaCl concentrations.     1/2
oligonucleotide duplexes.16,17 In the counterion condensation theory the fraction of the counterions bound to a DNA duplex and its single strands can be expressed in terms of their linear charge densities. The theory predicts that for polymeric DNA (B form) the fraction of phosphates neutralized by the monovalent counterions bound to the double-helical DNA and its single strands,?H and ?C, are ?H = 0.88 and ?C = 0.71. For short DNA oligomers it has been shown, however, that due to the reduced counterion condensation at the ends of the molecules these oligomers exhibit a reduced counterion binding as compared with polymers of the same linear charge density. According to Record and Lohman the average fractions of condensed counterions for 8-mer DNA dou-
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450                                                               Acta Chim. Slov.
ble- and single-stranded form are Y„     = 0.72 and Wn
 H(av)                                  C(av)
= 0.67, respectively, which means that upon unfolding of the double helix only 0.1 of counterions/base pair will be released.17,28 Relatively good agreement of this theoretical value with the one determined from our experimental T1/2 versus ln[Na+] slopes (Fig. 4, eq. 10) is consistent with a general observation that the electrostatic counterion condensation polyelectrolyte theory can successfully describe a very limited number of physico-chemical phenomena that occur in solutions containing DNA. These include for example the unfolding of DNA with accompanying AnNa+ or ligand binding to DNA with accompanying salt dependence of the binding constant. By contrast, numerous studies that involve energetics of conformational transitions or ligand binding to DNA have shown that electrostatic effects and thus electrostatic polyelectrolyte theories alone cannot account for the observed behavior of thermodynamic quantities.27,30,31 This is the case also with the present study which shows that only the release of Na+ counterions upon unfolding of the (5’-CGAATTCG-3’)2 duplex can be explained in terms of electrostatics while the stability parameters AG°( T ), AH°T), AS°( T ) and Ac° seem to be determined mainly by non-coulombic interactions such as hydrogen bonding, van der Waals interactions and hydrophobic hydration.
Figure 4. The helix-to-coil transition of the (5’-CGAATTCG-3’) duplex: the dependence of T1/2 on the added NaCl concentration.
5. Acknowledgment
This work was supported by the Ministry of Higher Education, Science and Technology and by the Agency for Research of Republic of Slovenia through the Grants No. P1-0201 and J1-6653.
2007, 54, 445–451
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Povzetek
V zadnjem ~asu se je pokazalo, da efekti Ac , ki spremljajo razvitje dvojnih vija~nic DNA, niso zanemarljivi. Da bi odgovorili na vpra{anje ali velja ta ugotovitev tudi za kratke DNA oligomere, smo {tudirali toplotno inducirano razvitje dupleksa (5’-CGAATTCG-3’)2 v vodnih raztopinah ob dodatku 0, 0,1, 0,3 in 1 M NaCl, pri ~emer smo uporabili visoko ob~utljivo diferencno dinami~no kalorimetrijo (DSC). Izmerjene DSC termograme smo uspe{no opisali z modelno funkcijo osnovano na enostopenjskem modelu procesa razvitja, ki vsebuje tri prilagodljive parametere: T1/2 - temperaturo polovice prehoda, AH(T ) - entalpijo razvitja pri T1/2 in Ac - spremembo toplotne kapacitete DNA, ki spremlja njeno razvitje. Tako dolo~ene vrednosti AH(T ) se dobro ujemajo z ustreznimi vrednostmi, ki jih dobimo z neposredno integracijo DSC termogramov. S pomo~jo eksperimentalnih podatkov smo konstruirali AH(T ) - T1/2 diagram in dolo~ili Ac kot naklon dobljene linearne odvisnosti. Menimo, da odli~no ujemanje obeh Ac vrednosti potrjuje upravi-cenost na{e postavke, da Ac razvitja DNA ni odvisna od temperature ali koncentracije dodane soli in jo lahko zato zanesljivo dolo~imo s pomo~jo popisovanja eksperimentalnih DSC termogramov z ustrezno modelno funkcijo. Analiza na{ih rezultatov poka`e, da ocene AG( T ), AH(T ) in AS(T) razvitja dvojne vijacnice, osnovane na »nearest-neighbor« pribli`ku in predpostavki, da je Ac = 0, lahko celo za kratke oligomere DNA vodijo do znatnih napak. Poka`e tudi, da eksperimentalno dolo~ena odvisnost T1/2 od ln[Na+] ni linearna, a se kljub temu dokaj dobro ujema z napovedjo elek-trostatske teorije raztopin polielektrolitov.
Drobnak et al.:   Stability of a Short DNA Duplex as a Function of Temperature: ...