Influence of a Hairpin Loop on the Thermodynamic Stability of a DNA Oligomer

Abstract

DSC was used to evaluate the mechanism of the thermally induced unfolding of the single-stranded hairpin HP = 5′-CGGAATTCCGTCTCCGGAATTCCG-3′ and its core duplex D (5′-CGGAATTCCG-3′)₂. The DSC melting experiments performed at several salt concentrations were successfully described for HP and D in terms of a three-state transition model HP↔I (intermediate state) ↔ S (unfolded single-stranded state) and two state transition model D↔2S, respectively. Comparison of the model-based thermodynamic parameters obtained for each HP and D transition shows that in unfolding of HP only the HP↔I transition is affected by the TCTC loop. This observation suggests that in the intermediate state its TCTC loop part exhibits significantly more flexible structure than in the folded state while its duplex part remains pretty much unchanged.

1. Introduction

Hairpin loops are a common form of nucleic acid secondary structure and are crucial for tertiary structure and function [1]. They are known to play a key role in a number of biological processes such as gene expressions, DNA recombination, and DNA transposition [2–4]. In RNA molecules hairpins act as nucleation sites for RNA folding into final conformations [5–7] and play a critical role in RNA-protein recognition and gene regulation [8, 9]. Furthermore, due to the specificity of probe/target hybridization determined as a match-versus-mismatch discrimination, hairpin DNA oligomer probes have become an important tool in modern biotechnology and diagnostics [10, 11]. The thermodynamics and kinetics of hairpin formation, hairpin binding to complementary nucleic acids, and hairpin-ligand associations have been studied extensively [12–21]. There is no doubt that studies of hairpin-to-coil transitions and hairpin-ligand binding affinity and specificity have greatly enhanced our understanding of structural features and function of the naturally occurring nucleic acids [22, 23]. However, despite extensive biophysical research on the systems involving hairpin structures that produced a number of high-quality explanations and evaluations on properties and behavior of nucleic acids containing hairpin formations, there are still many unresolved questions.

As pointed out by Marky et al. [24] the most suitable hairpin molecules for studying the thermodynamics of their conformational transitions and ligand binding are the single-stranded hairpin molecules. They form stable partially paired duplexes that tend to melt in simple monomolecular transitions. Furthermore, their conformational stability and ligand binding properties are easily compared with those of the corresponding core duplexes. In this way one can evaluate the contributions of the loops to the thermal stability of the hairpins. Despite the simple structure of single-stranded hairpins it is not clear whether their monomolecular folding/unfolding transitions occur in a two-state or multistate manner. Measurements of their thermally induced unfolding transitions followed by UV, CD, and/or fluorescence spectroscopy as a rule result in sigmoidal melting curves suggesting that they may be considered as two-state processes. The same conclusion can be reached also on the basis of DSC measurements performed on the same sample solutions in the older generation of less sensitive DSC instruments (e.g., Microcal MC-2) which resulted in single-peak DSC thermograms. Recent measurements of conformational transitions of DNA quadruplex structures have shown, however, that the sigmoidal shape of UV or CD melting curves may be misleading. Namely, the DSC measurements performed on samples for which sigmoidal UV and CD melting curves were observed using the DSC of the latest generation (CSC, Microcal) resulted in thermograms containing two or three well-distinguished peaks thus indicating that the observed DNA melting process occurs in a multi-state manner [25, 26]. Furthermore, recent T-jump experiments performed on small hairpin molecules have produced a direct evidence that their unfolding transitions involve intermediate structures and thus cannot be considered as two-state processes [19, 27–29].

In our DSC study of the unfolding mechanism and stability of the 5′-CGGAATTCCGTCTCCGGAATTCCG-3′ hairpin we performed the DSC melting experiments on the hairpin and its core duplex, (5′-CGGAATTCCG-3′)₂ (see Figure 1), at several salt concentrations using an extremely sensitive microcalorimeter (CSC). To see to what extent the TCTC loop affects the hairpin unfolding process we attempted to describe for each oligonucleotide the measured DSC thermograms in terms of the simplest possible unfolding model. We derived the corresponding model functions and by fitting them to the experimental data we tested the appropriateness of the suggested models and obtained for each transition the characteristic thermodynamic quantities of transition ΔG_(T)⁰, ΔH_(T)⁰, ΔS_(T)⁰, and Δc_P⁰. By comparing these values determined for the hairpin and the core duplex we tried to estimate the contribution of the TCTC loop to the stability of the hairpin.

Figure 1.

Schematic presentation of the model oligonucleotides: hairpin (HP), duplex (D).

2. Materials and Methods

2.1. Materials

Self-complementary oligonucleotide 5′-CGGAATTCCG-3′ and oligonucleotide 5′-CGGAATTCCGTCTCCGGAATTCCG-3′ that in solution at room temperature form a duplex (D) and a single-stranded hairpin structure (HP), respectively, were purchased HPLC pure from Invitrogen Co., Germany and used without any further purification. Their concentrations in buffer solution (10 mM phosphate buffer and 1 mM Na₂EDTA adjusted to pH = 7.0)) in the presence of 100 mM NaCl were determined at 25°C spectrophotometrically in the Cary Bio 100 UV-spectrophotometer. The molar extinction coefficients were determined using the nearest neighbor data of Cantor et al. [30] for single-stranded DNA at 25°C and the absorbance at 260 nm of thermally unfolded oligonucleotide extrapolated back to 25°C (ε_D260 = 84600 M⁻¹cm⁻¹, ε_HP260 = 216000 M⁻¹cm⁻¹). The phosphate buffer solutions used in all experiment contained 0, 0.1, 0.3, or 1.0 M NaCl.

Differential scanning calorimetry (DSC). Thermally induced unfolding of duplex (D) and hairpin (H) in buffer solutions with different added NaCl concentrations was followed between 5 and 95°C in a Nano-II DSC calorimeter (CSC; UT) at the heating rate of 1°C/min and essentially the same results were obtained from several test-experiments performed at the heating rate of 0.25°C/min. The thermally induced unfolding of both oligonucleotides was monitored in terms of $c_{P_{\text{ex}}}={\bar{c}}_{p_2}-{\bar{c}}_{p_{D,F}}$ versus T thermograms in which the differences between the partial molar heat capacity of the measured oligonucleotide ${\bar{c}}_{p_2}$ (raw signals corrected for the solvent contributions) and the partial molar heat capacities of the corresponding folded states extrapolated from low temperatures over the whole measured temperature interval, ${\bar{c}}_{p_{D,F}}$, are normalized for the duplex or hairpin concentration. The total enthalpy of unfolding, ΔH_(T)^cal  ,was obtained from the measured thermograms as the area under the c_Pex(T) versus T curve.

2.2. Analysis of the DSC Thermograms

The thermally induced conformational transitions can be experimentally followed in a model-independent way only by DSC. At relatively low concentrations used in DSC experiments the measured solute-normalized heat capacity of the sample solution, c_P(T), with the subtracted baseline may be equalized with the oligonucleotide partial molar heat capacity, ${\bar{c}}_{P_2(T)}$. Thus, the overall heat effect that accompanies the measured conformational transition from its initial folded state at the temperature T₁ to its final unfolded state at T₂ can be expressed as

$$\mathrm{\Delta }{H}_{\left(T_1\to T_2\right)}=\underset{T_1}{\overset{T_2}{{\displaystyle \int }}}{\bar{c}}_{p_2\left(T\right)}dT.$$ (1)

Since the enthalpy is the state function, the enthalpy change ΔH_(T1→T2) may be expressed also as

$$\begin{array}{cc}\hfill \mathrm{\Delta }{H}_{\left(T_1\to T_2\right)}& =\underset{T_1}{\overset{T_{\text{ref}}}{{\displaystyle \int }}}{\left({\bar{c}}_{p_2\left(T\right)}\right)}_{F}dT+{\mathrm{\Delta }H}_{\left(T_{\text{ref}}\right)}\hfill \\ \hfill & \hspace{1em}+\underset{T_{\text{ref}}}{\overset{T_2}{{\displaystyle \int }}}{\left({\bar{c}}_{p_2\left(T\right)}\right)}_{U}dT,\hfill \end{array}$$ (2)

where ${({\bar{c}}_{p_2(T)})}_F$ and ${({\bar{c}}_{p_2(T)})}_U$ are the partial molar heat capacities of the folded and unfolded DNA conformation, respectively, ΔH_(Tref)  is the enthalpy of unfolding at T_ref which can be any temperature between T₁ and T₂. By choosing T_ref = T_1/2 where T_1/2 is the melting temperature at which a half of oligonucleotide molecules undergo unfolding transition (2) transforms into

$$\begin{array}{cc}\hfill \mathrm{\Delta }{H}_{T_{\left(1/2\right)}}^{\text{cal}}& =\underset{T_1}{\overset{T_{1/2}}{{\displaystyle \int }}}\left[{\bar{c}}_{p_2\left(T\right)}-{\left({\bar{c}}_{p_2\left(T\right)}\right)}_F\right]dT\hfill \\ \hfill & \hspace{1em}+\underset{T_{1/2}}{\overset{T_2}{{\displaystyle \int }}}\left[{\bar{c}}_{p_2\left(T\right)}-{\left({\bar{c}}_{p_2\left(T\right)}\right)}_U\right]dT,\hfill \end{array}$$ (3)

where ΔH_T1/2^cal  is a model-independent enthalpy of transition at T_1/2 that can be easily determined by the appropriate integration of the experimental $[{\bar{c}}_{p_2(T)}-{({\bar{c}}_{p_2(T)})}_F]$ and $[{\bar{c}}_{p_2(T)}-{({\bar{c}}_{p_2(T)})}_U]$ curves as presented in (3).

According to the DSC thermograms of the measured hairpin (HP), its thermally induced unfolding involves at least two conformational transitions (Figure 2). Thus, the simplest suggested model to describe the observed thermal behavior would consist of two consecutive monomolecular transitions: HP (hairpin) ↔ I (intermediate state) ↔ S (unfolded single-stranded state). The enthalpy, H, of a solution containing an HP sample characterized by the suggested thermal unfolding

$$\text{HP}\stackrel{K_{\text{HPI}}}{⟷}\mathbf{I}\stackrel{K_{\text{IS}}}{⟷}\text{S};\hspace{1em}\hspace{1em}{K}_{\text{HPI}}=\frac{\left[\text{I}\right]}{\left[\text{HP}\right]}\hspace{1em}\hspace{1em}{K}_{\text{IS}}=\frac{\left[\text{S}\right]}{\left[\text{I}\right]}$$ (4)

can be expressed at given P and T as

Figure 2.

DSC thermograms and their model analysis: hairpin (HP) unfolding characterized in terms of a three-state model HP ↔ I ↔ S (a) and the corresponding fractions of species (b); duplex (D) unfolding characterized in terms of a two-state model D ↔ 2S (c) and the corresponding fractions of species (d). In panels (a) and (c) symbols represent experimental data points while lines of the same color correspond to the best-fit model functions ((14) and (18)).

$$H=n_1{\bar{H}}_1+n_2{\bar{H}}_2=n_1{\bar{H}}_1+n_{\text{HP}}{\bar{H}}_{\text{HP}}+n_{\text{I}}{\bar{H}}_{\text{I}}+n_{\text{S}}{\bar{H}}_{\text{S}},$$ (5)

where K_HPI and K_IS are the corresponding equilibrium constants, the quantities in brackets are the equilibrium molar concentrations of HP, I, and S, n₁ is the number of moles of solvent, and n₂ is the number of moles of solute (oligonucleotide) that can be further expressed as:

$$n_2=n_{\text{HP}}+n_{\text{I}}+n_{\text{S}},$$ (6)

n _HP in (6) represents the number of moles of the oligonucleotide in the folded hairpin state, n_I is the number of moles in the intermediate state, n_S is the number of moles in the unfolded single-stranded state and ${\bar{H}}_1,\mathrm{\hspace{0.17em}\hspace{0.17em}}{\bar{H}}_2,\mathrm{\hspace{0.17em}\hspace{0.17em}}{\bar{H}}_{\text{HP}},\mathrm{\hspace{0.17em}\hspace{0.17em}}{\bar{H}}_{\text{I}}$, and$\mathrm{\hspace{0.17em}\hspace{0.17em}}{\bar{H}}_{\text{S}}$ are the corresponding partial molar enthalpies of the solvent, solute and folded, intermediate and unfolded oligonucleotide, respectively. By defining the molar fraction,  α_i, of the solute species, i, as α_i = n_i/n₂ one obtains from (5) that

$${\bar{H}}_2={\alpha }_{\text{HP}}{\bar{H}}_{\text{HP}}+{\alpha }_I{\bar{H}}_I+{\alpha }_{\text{S}}{\bar{H}}_{\text{S}}.$$ (7)

Finally, by introducing α_HP = 1 − α_I − α_S into (7) and taking the temperature derivative of the modified (7) one obtains the model function for the measured DSC signal, c_P,ex, expressed as

$$\begin{array}{cc}\hfill c_{P,\text{ex}}& ={\bar{c}}_{P,2}-\mathrm{\hspace{0.17em}\hspace{0.17em}}{\bar{c}}_{P,\text{HP}}\hfill \\ \hfill & ={\alpha }_{\text{I}}\mathrm{\Delta }{c}_{P,\text{HPI}}+\frac{d{\alpha }_{\text{I}}}{dT}\mathrm{\Delta }{H}_{\text{HPI}}+{\alpha }_{\text{S}}\left(\mathrm{\Delta }{c}_{P,\text{HPI}}+\mathrm{\Delta }{c}_{P,\text{IS}}\right)\hfill \\ \hfill & \hspace{1em}+\frac{d{\alpha }_{\text{S}}}{dT}\left(\mathrm{\Delta }{H}_{\text{HPI}}+\mathrm{\Delta }{H}_{\text{IS}}\right),\hfill \end{array}$$ (8)

in which at any temperature ${\bar{c}}_{P,2}$ is the measured c_P (with subtracted baseline), ${\bar{c}}_{P,\text{HP}}\mathrm{\hspace{0.17em}\hspace{0.17em}}$is the partial molar heat capacity of HP extrapolated from low-temperature region over the entire measured temperature interval, $\Delta H_{\text{HPI}}={\bar{H}}_{\text{I}}-{\bar{H}}_{\text{HP}}$ (enthalpy of the hairpin to intermediate state transition), $\Delta H_{\text{IS}}={\bar{H}}_{\text{S}}-{\bar{H}}_{\text{I}}$ (enthalpy of the intermediate state to unfolded single stranded state transition), $\Delta c_{P,\text{HPI}}={\bar{c}}_{P,\text{I}}-{\bar{c}}_{P,\text{HP}}$ and $\Delta c_{P,\text{IS}}={\bar{c}}_{P,\text{S}}-{\bar{c}}_{P,\text{I}}$.

c _P,ex can be obtained experimentally simply by subtracting the hairpin ${\bar{c}}_{P,\text{HP}}\mathrm{\hspace{0.17em}\hspace{0.17em}}$versus T curve extrapolated from low-T region over the entire measured temperature interval from the corresponding measured ${\bar{c}}_{P,2}$ versus T curve. The model-based c_P,ex, however, can be calculated from the right-hand side term of (8). According to the suggested model (4) the total solute molar concentration, c_T, and the fractions α_i of the solute species present in the solution can be expressed as c_T = [HP] + [I] + [S]  and α_HP = [HP]/c_T, α_I = [I]/c_T and α_S = [S]/c_T. Since α_HP + α_I + α_S = 1 one obtains from (4) that

$${\alpha }_{\text{S}}=\frac{1}{{\left(K_{\text{HPI}}{K}_{\text{IS}}\right)}^{-1}+K_{\text{S}}^{-1}+1},\hspace{1em}\hspace{1em}{\alpha }_{\text{I}}=\frac{{\alpha }_{\text{S}}}{K_{\text{IS}}}.$$ (9)

For the description of the DSC experiment with the model function (8) one needs also the temperature derivatives of α_S and α_I. By using for each transition, i, the van't Hoff relation

$$\frac{d\ln \hspace{0.17em}{K}_i}{dT}=\frac{\mathrm{\Delta }{H}_i^0}{R{T}^2},$$ (10)

one obtains

$$\begin{array}{cc}\hfill \frac{d{\alpha }_{\text{S}}}{dT}& ={\alpha }_{\text{S}}^2\left[K_{\text{HPI}}^{-1}{K}_{\text{IS}}^{-1}\frac{\left(\mathrm{\Delta }{H}_{\text{HPI}}^0+\mathrm{\Delta }{H}_{\text{IS}}^0\right)}{R{T}^2}+K_{\text{IS}}^{-1}\frac{\mathrm{\Delta }{H}_{\text{IS}}^0}{R{T}^2}\right],\hfill \\ \hfill \frac{d{\alpha }_{\text{I}}}{dT}& =K_{\text{IS}}^{-1}\left(\frac{d{\alpha }_{\text{S}}}{dT}-{\alpha }_S\frac{\mathrm{\Delta }{H}_{\text{IS}}^0}{R{T}^2}\right).\hfill \end{array}$$ (11)

Assuming that for each transition, i, the corresponding Δc_Pi⁰ does not depend on T the standard free energy of that transition, ΔG_i(T)⁰, can be obtained at any T from the integrated form of the Gibbs-Helmholtz relation as

$$\begin{array}{cc}\hfill \mathrm{\Delta }{G}_{i\left(T\right)}^0& =T[\frac{\mathrm{\Delta }{G}_{i\left(T_{i,\left(1/2\right)}\right)}^0}{T_{i,1/2}}+\mathrm{\Delta }{H}_{i\left(T_{i,1/2}\right)}^0\left(\frac{1}{T}-\frac{1}{T_{i,1/2}}\right)\hfill \\ \hfill & \hspace{1em}\hspace{0.5em}\hspace{0.5em}+\mathrm{\Delta }{c}_{P_i}^0\left(1-\frac{T_{i,1/2}}{T}-\ln \hspace{0.17em}\frac{T}{T_{i,1/2}}\right)],\hfill \end{array}$$ (12)

where T_i,1/2 is the temperature at which the α_i values sof species participating in transition i are the same. The corresponding equilibrium constant, K_i, is related to ΔG_i(T)⁰ as

$$\mathrm{\Delta }{G}_{i\left(T\right)}^0=-RT\ln \hspace{0.17em}{K}_i,$$ (13)

and for the suggested mechanism of the hairpin unfolding (4) it can be easily seen that for each suggested monomolecular transition ΔG_i(Ti,1/2)⁰ = 0. Finally, according to the DSC experiments performed at different oligonucleotide concentrations the ΔH_i(T) values appear to be concentration independent thus indicating that one may assume for each transition that ΔH_i(T) = ΔH_i(T)⁰ and Δc_Pi = Δc_Pi⁰. Using these assumptions and (8)–(13) one can express the model function (14)

$$\begin{array}{cc}\hfill c_{P,\text{ex}}& =\mathrm{\hspace{0.17em}\hspace{0.17em}}{\alpha }_{\text{I}}\mathrm{\Delta }{c}_{p,\text{HPI}}^0+\frac{d{\alpha }_{\text{I}}}{dT}\mathrm{\Delta }{H}_{\text{HPI}}^0+{\alpha }_{\text{S}}\left(\mathrm{\Delta }{c}_{p,\text{HPI}}^0+\mathrm{\Delta }{c}_{p,\text{IS}}^0\right)\hfill \\ \hfill & \hspace{1em}+\frac{d{\alpha }_{\text{S}}}{dT}\left(\mathrm{\Delta }{H}_{\text{HPI}}^0+\mathrm{\Delta }{H}_{\text{IS}}^0\right),\hfill \end{array}$$ (14)

only in terms of parameters T_i,1/2, ΔH_i(Ti,1/2)⁰, and Δc_P,i⁰, characteristic for each of the suggested transitions. Their “best fit” values are obtained by fitting the model function (14) to the experimental c_P,ex versus T curves. Furthermore, since for each transition, i, the corresponding ΔH_i(T)⁰ and ΔS_i(T)⁰ quantities can be expressed as

$$\begin{array}{c}\mathrm{\Delta }{H}_{i\left(T\right)}^0=\mathrm{\Delta }{H}_{i\left(T_{i,1/2}\right)}^0+\mathrm{\Delta }{c}_{P,i}^0\left(T-T_{i,1/2}\right),\\ T\mathrm{\Delta }{S}_{i\left(T\right)}^0=\mathrm{\Delta }{H}_{i\left(T\right)}^0-\mathrm{\Delta }{G}_{i\left(T\right)}^0,\end{array}$$ (15)

the “best fit” parameters T_i,1/2, ΔH_i(Ti,1/2)⁰ and Δc_P,i⁰ can be used also to obtain the ΔH_i(T)⁰ and ΔS_i(T)⁰ values at any T.

In contrast to HP unfolding, the measured thermally induced duplex (D) to single strand (S) transition appears to be a simpler, all-or-none process

$$D\stackrel{K_{\text{DS}}}{⟷}2\text{S};\hspace{1em}\hspace{1em}{K}_{\text{DS}}=\frac{{\left[\text{S}\right]}^2}{\left[\text{D}\right]},$$ (16)

that can be described in terms of the total oligonucleotide concentration, c_T, the concentrations of the duplex form [D] and the single strands [S], the fraction of duplex molecules that undergo the unfolding transition at a given temperature, α_S, and the equilibrium constant K_DS interrelated as

$$c_T=\left[\text{D}\right]+\frac{\left[\text{S}\right]}{2};\hspace{1em}\hspace{1em}{\alpha }_{\text{S}}=\frac{\left[\text{D}\right]}{c_T};\hspace{1em}\hspace{1em}{K}_{\text{DS}}=\frac{4{{\alpha }_{\text{S}}}^2{c}_T}{1-{\alpha }_{\text{S}}}.$$ (17)

A similar, though much simpler derivation of the model function than the one presented for unfolding of the hairpin structure (14) leads for the suggested D ↔ 2S transition to

$$c_{P,\text{ex}}={\bar{c}}_{P,2}-{\bar{c}}_{P,\text{D}}={\alpha }_{\text{S}}\mathrm{\Delta }{c}_{P,\text{DS}}^0+\frac{d{\alpha }_{\text{S}}}{dT}\mathrm{\Delta }{H}_{\text{DS}}^0,$$ (18)

where ${\bar{c}}_{P,2}$ is the measured c_P of the sample solution with subtracted baseline, ${\bar{c}}_{P,\text{D}}$ is the heat capacity of the duplex form extrapolated from the low-T region over the whole measured temperature interval, $\Delta c_{P,\text{DS}}^0=\Delta c_{P,\text{DS}}=2{\bar{c}}_{P_{\text{S}}}-{\bar{c}}_{P_{\text{D}}}$ and $\Delta H_{\text{DS}}^0=\Delta H_{\text{DS}}^{}=2{\bar{H}}_{\text{S}}-{\bar{H}}_{\text{D}}$. From the suggested model (16) and (17) it follows that ΔG_DS(T1/2)⁰ = −RTln (2c_T) and

$$\begin{array}{c}{\alpha }_{\text{S}}=\frac{1}{2}\left[-\frac{K_{\text{DS}}}{4c_T}+\sqrt{{\left(\frac{K_{\text{DS}}}{4c_T}\right)}^2+\frac{K_{\text{DS}}}{c_T}}\right],\\ \frac{\partial {\alpha }_{\text{S}}}{\partial T}=\frac{\mathrm{\Delta }{H}_{\text{DS}}^0}{R{T}^2}\mathrm{\hspace{0.17em}\hspace{0.17em}}\frac{{\alpha }_{\text{S}}\left(1-{\alpha }_{\text{S}}\right)}{2-{\alpha }_{\text{S}}}.\end{array}$$ (19)

The corresponding expressions for ΔG_DS(T)⁰  ΔH_DS(T)⁰ and TΔS_DS(T)⁰ are the same as those shown for each transition in the suggested hairpin unfolding mechanism (12), (13) and (15). Similarly, in deriving (18) the ΔH_DS(T) and Δc_P,DS are assumed to be independent on the oligonucleotide concentration and thus equal to ΔH_DS(T)⁰, and Δc_P,DS⁰.

Inspection of (18) and (19) shows that the model function (18) is expressed in terms of adjustable parameters, T_1/2, ΔH_DS(T1/2)⁰ and Δc_P,DS⁰ that can be determined by fitting the model function to the experimental c_P,ex versus T curve and further used to determine the ΔG_DS(T)⁰, ΔH_DS(T)⁰ and ΔS_DS(T)⁰ values at any T.

To obtain a set of the “best fit” adjustable parameters T_i,1/2, ΔH_i(Ti,1/2)⁰ and Δc_P,i⁰ describing the hairpin and duplex thermal unfolding at each of the added salt concentrations the iterative nonlinear Levenberg-Marquardt χ² regression procedure was used [31]. Furthermore, assuming that for the observed transitions the accompanying Δc_P,i⁰ quantities do not depend on the added NaCl concentration their values may be determined also from the slopes of the ΔH_i(T1/2)⁰ versus T_i,1/2 curves constructed from the “best fit” ΔH_i(T1/2)⁰ and T_i,1/2 parameters determined at different added salt concentrations [32]. These data can be also used to construct the corresponding T_i,1/2 versus ln [Na⁺] plots from which the amount of the Na⁺ ions released upon thermal unfolding of the hairpin or duplex structure can be estimated (see discussion, (20)).

3. Results and Discussion

According to the measured DSC thermograms presented in Figure 2 the thermally induced unfolding of the hairpin HP consists of at least two conformational transitions while the one observed for the duplex D occurs in a simpler “all or none” manner. In addition, UV melting experiments (not shown) resulted for HP in biphasic melting curves that exhibit transitions independent on HP concentration (monomolecular transitions) while for D monophasic melting curves dependent on D concentration (nonmonomolecular transition) were observed. Moreover, excellent repeatability of the consecutive measured heating and cooling c_P versus T curves and the observed independence of the measured DSC peaks on the applied heating rate (several test experiments) clearly shows that the studied thermal unfolding events may be considered as reversible processes. Model analysis of the measured thermograms shows that the hairpin thermal unfolding can be well described in terms of a three state model involving H (hairpin) ⟷I (intermediate state) ⟷S (unfolded single-stranded structure) transitions and the corresponding model function (14) characterized for each of the suggested transitions with the corresponding “best fit” adjustable parameters T_i,1/2, ΔH_i(Ti,1/2)⁰, and Δc_P,i⁰ (Table 1). However, analysis of the applied fitting procedure indicates that the parameter Δc_P,IS⁰ is highly correlated to some other adjustable parameters. Thus, to obtain safe estimate of Δc_P,IS⁰ another method of its determination has to be used. Assuming that it does not depend on the simple salt concentration Δc_P,IS⁰ was estimated as a slope of the ΔH_IS(T1/2)⁰ versus T_IS,1/2 plot (Figure 3(a)) constructed from the “best fit” parameters determined at different NaCl concentrations (Table 1). This method of determining Δc_P,i⁰ was justified by a good agreement between the Δc_P,i⁰ values for other transitions obtained by the described fitting procedure and the Δc_Pi⁰ values determined as the slopes of the corresponding ΔH_i(Ti,1/2)⁰ versus T_i,1/2 plots (Table 1). By using the parameters presented in Table 1 one can calculate for the duplex and hairpin solutions the relative populations of the model-predicted species in the measured temperature interval and at all added salt concentrations (Figure 2). Evidently, the thermal stability of the folded state of the measured duplex and the hairpin is substantially enhanced by increasing the added salt concentration. At low salt concentrations, however, a small fraction of the hairpin molecules undergoes transition into the intermediate state already at physiological temperatures.

Table 1.

Thermodynamic parameters^a obtained from fitting the model functions ((14) and (18)) to the duplex (D) and hairpin (HP) DSC thermograms presented in Figure 2.

Transition	T1/2	ΔH(T1/2)0	ΔH(T1/2)cal	ΔcP0 b	ΔcP0 c	ΔnNa+
HP → I	59.2	37			0.34	0.9
I → S	75.0	74		0.37	0.25	1.5
HP → S		117d	111		0.59	2.4
D → 2S	56.5	71	71	0.25	0.30	1.7
Error	±0.2	±2	±2	±0.05	±0.05	±0.2

^aUnits: °C(T_1/2), kcal  mol⁻¹(∆H_(T1/2)⁰, ∆H_(T1/2)^cal), kcal  mol⁻¹  K⁻¹  (∆c_P⁰); unless stated otherwise the values are those obtained at [Na⁺] = 0.13M;

^bobtained from fitting the model function;

^cobtained as the slope of ∆H_(T1/2)⁰ versus T_1/2 curves (Figure 3(a));

^d the total enthalpy of the of the I → S transition was calculated as ∆H_HS(T1/2,IS)⁰ = ∆H_HI(T1/2,HI)⁰ + ∆c_PHI⁰(T_1/2,IS − T_1/2,HI) + ∆H_IS(T1/2,IS)⁰ where T_1/2,IS and T_1/2,HI are the melting temperatures of the I → S and H → I transitions and ∆H_IS(T1/2,IS)⁰ and ∆H_HI(T1/2,HI)⁰ are the corresponding enthalpies of transition.

Figure 3.

Estimation of heat capacity changes and number of released Na⁺ ions: (a) Δc_P,i⁰ was determined for each transition i as the slope of the ΔH_i(Ti,1/2)⁰ versus T_i,1/2 plot constructed from the model based ΔH_i(Ti,1/2)⁰ and T_i,1/2 values determined at different salt concentrations; (b) the corresponding ln [Na⁺] versus T_i,1/2 plots from which the Δn_Na⁺,i values were determined according to (20).

A standard way of testing the quality of a suggested model is to compare the enthalpy of unfolding determined at a given temperature directly by an appropriate integration of the experimental c_P,ex(T) versus T curve (ΔH_HS^cal, see (3)) with the corresponding model-based value ΔH_HS⁰ calculated at the same temperature using the reported “best fit” adjustable parameters. As shown in Table 1 a good agreement was obtained which clearly supports the appropriateness of the suggested H⟷I⟷  S unfolding model.

It is well known that DNA unfolding is accompanied by release of counterions. The number of the released Na⁺ ions, Δn_Na⁺,i, upon each HP and D transition, expressed per mole of oligonucleotide, may be estimated from [33]

$$\frac{d{T}_{i,1/2}}{d\ln \hspace{0.17em}\left[{\text{Na}}^{+}\right]}=\frac{R{T}_{i,1/2}^2}{\mathrm{\Delta }{H}_{i\left(T_{i,1/2}\right)}^0\mathrm{\hspace{0.17em}\hspace{0.17em}}}\mathrm{\Delta }{n}_{{\text{Na}}^{+},i},$$ (20)

in which T_{i, 1/2} is the melting temperature at a given Na⁺ concentration, [Na⁺], ΔH_i(Ti,1/2)⁰ is the corresponding enthalpy of transition at T_{i, 1/2}. The Δn_Na⁺,i values presented in Table 1 were determined from the slopes of the ln [Na⁺] versus T_{i, 1/2}. plots (Figure 3(b)).

At any T in the measured range of physiological temperatures the difference between the given property characterizing the total unfolding of the hairpin H and the duplex D (for ex. ΔΔH_(T)⁰ = ΔH_HS(T)⁰ − ΔH_DS(T)⁰) reflects the contribution of the TCTC loop to that property relative to the core duplex (Figure 4, Table 2). Thus, the observed ΔΔH_(T)⁰ > 0 indicates a favorable energy contribution of the TCTC loop to the stability of the hairpin that results, very likely, from the increased number of stacking interactions (in the first place from those occurring at the core duplex-loop connections) [34]. The corresponding ΔΔS_(T)⁰ > 0 is consistent with the highly positive ΔΔH_(T)⁰ indicating that the unfavorable entropy contribution of the TCTC loop to the hairpin stability arises largely from a substantial disruption of the loop structure accompanying the unfolding of the hairpin. The observed ΔΔc_P⁰ > 0 and ΔΔn_Na⁺ > 0 show, however, that the loop contributions to ΔΔH_(T)⁰and ΔΔS_(T)⁰ may be, to a certain extent, determined also by hydration [35] and electrostatic interactions. The ΔΔc_P⁰ > 0 suggests that within the folded hairpin conformation, not only the core duplex but also the TCTC loop are less exposed to water than in the unfolded state. In addition, the observed ΔΔn_Na⁺ > 0 may be ascribed to a decrease in the surface charge density accompanying the unfolding of the oligonucleotide which is significantly more pronounced in the case of hairpin unfolding. Comparison of the ΔΔ values for ΔG_T⁰, ΔH_T⁰, ΔS_T⁰, Δc_P⁰, and Δn_Na⁺ quantities determined for the HP → I and I → S transitions of the hairpin with the corresponding ΔΔ values determined for the D → 2S transition of the duplex shows that the ΔΔ values for the I → S and D → 2S transitions are very close (Figure 4, Table 2). Evidently, one may speculate that in the hairpin structure only the HP → I transition is influenced by the TCTC loop. In other words, it seems that the observed HP → I transition reflects mainly the changes in the TCTC conformation. Thus, the intermediate state I may be considered as a state in which the core duplex remains more or less unchanged while the TCTC loop occurs as a more flexible structure characterized by the additional stacking interactions and the freedom of the neighboring water molecules and ions similar to the one in the unfolded state.

Figure 4.

Thermodynamics of hairpin and duplex unfolding: standard Gibbs free energy (a), standard enthalpy (b), and the corresponding entropy contribution (c) presented for each model predicted hairpin (I → S, HP → S) and duplex (D → 2S) transitions as functions of temperature at [Na⁺] = 0.13M.

Table 2.

Difference thermodynamic stability parameters^a at 25°C exhibiting the influence of the TCTC loop to the unfolding features of the hairpin forming oligonucleotide (HP).

Transition	ΔΔG0	ΔΔH0	TΔΔS0	ΔΔcP0	ΔΔnNa+
(HP → S)-(D → 2S)	2.4	26.6	24.3	0.29	0.7
(I → S)-(D → 2S)	−0.9	0.8	1.7	−0.05	−0.2
Error	±3	±3	±3	±0.07	±0.3

^aUnits: kcal  mol⁻¹ (ΔΔG⁰, ΔΔH⁰, TΔΔS⁰), kcal  mol⁻¹K⁻¹ (ΔΔc_P⁰); for temperature dependence of ΔG⁰, ΔH⁰, and TΔS⁰ see Figure 4.

To the best of our knowledge this is the first time that a three-state unfolding of a simple hairpin structure, observed by DSC, has been reported and characterized thermodynamically. We believe that the main reason for this is that in most studies of thermal unfolding of hairpins too high starting temperatures have been chosen and therefore the low-temperature transitions have been overlooked.