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

Authors: Jurij Lah; Mojca Seručnik; Gorazd Vesnaver
Journal: Journal of Nucleic Acids
 (2011)

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## 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.


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## Body

## 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 ΔcP0. 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 (εD260=84600 M−1cm−1, εHP260=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 ofcPex=c̅p2-c̅pD,F versus T thermograms in which the differences between the partial molar heat capacity of the measured oligonucleotide c̅p2 (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, c̅pD,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 cPex(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,cP(T), with the subtracted baseline may be equalized with the oligonucleotide partial molar heat capacity, c̅P2(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(1)ΔH(T1→T2)=∫T1T2c̅p2(T)dT.
Since the enthalpy is the state function, the enthalpy change ΔH(T1→T2) may be expressed also as(2)ΔH(T1→T2)=∫T1Tref(c̅p2(T))FdT+ΔH(Tref)+∫TrefT2(c̅p2(T))UdT,
where (c̅p2(T))F and (c̅p2(T))U are the partial molar heat capacities of the folded and unfolded DNA conformation, respectively, ΔH(Tref)is the enthalpy of unfolding at Tref which can be any temperature between T1 and T2. By choosing Tref=T1/2 where T1/2 is the melting temperature at which a half of oligonucleotide molecules undergo unfolding transition (2) transforms into(3)ΔHT(1/2)cal=∫T1T1/2[c̅p2(T)-(c̅p2(T))F]dT+∫T1/2T2[c̅p2(T)-(c̅p2(T))U]dT,
where ΔHT1/2calis a model-independent enthalpy of transition at T1/2 that can be easily determined by the appropriate integration of the experimental [c̅p2(T)-(c̅p2(T))F] and [c̅p2(T)-(c̅p2(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 (Figure2). 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
(4)HP⟷KHPII⟷KISS;KHPI=[I][HP]KIS=[S][I]
can be expressed at given P and T as(5)H=n1H̅1+n2H̅2=n1H̅1+nHPH̅HP+nIH̅I+nSH̅S,
where KHPI and KIS 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: (6)n2=nHP+nI+nS,nHP in (6) represents the number of moles of the oligonucleotide in the folded hairpin state, nI is the number of moles in the intermediate state, nS is the number of moles in the unfolded single-stranded state and H̅1,H̅2,H̅HP,H̅I, andH̅S are the corresponding partial molar enthalpies of the solvent, solute and folded, intermediate and unfolded oligonucleotide, respectively. By defining the molar fraction,αi, of the solute species, i, as αi=ni/n2 one obtains from (5) that(7)H̅2=αHPH̅HP+αIH̅I+αSH̅S.
Finally, by introducing αHP=1-αI-αS into (7) and taking the temperature derivative of the modified (7) one obtains the model function for the measured DSC signal, cP,ex, expressed as(8)cP,ex=c̅P,2-c̅P,HP=αIΔcP,HPI+dαIdTΔHHPI+αS(ΔcP,HPI+ΔcP,IS)+dαSdT(ΔHHPI+ΔHIS),
in which at any temperature c̅P,2 is the measured cP (with subtracted baseline), c̅P,HPis the partial molar heat capacity of HP extrapolated from low-temperature region over the entire measured temperature interval, ΔHHPI=H̅I-H̅HP (enthalpy of the hairpin to intermediate state transition), ΔHIS=H̅S-H̅I (enthalpy of the intermediate state to unfolded single stranded state transition), ΔcP,HPI=c̅P,I-c̅P,HP and ΔcP,IS=c̅P,S-c̅P,I.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)).
(a)(b)(c)(d)cP,ex can be obtained experimentally simply by subtracting the hairpin c̅P,HPversus T curve extrapolated from low-T region over the entire measured temperature interval from the corresponding measured c̅P,2 versus T curve. The model-based cP,ex, however, can be calculated from the right-hand side term of (8). According to the suggested model (4) the total solute molar concentration, cT, and the fractions αi of the solute species present in the solution can be expressed as cT=[HP]+[I]+[S]and αHP=[HP]/cT, αI=[I]/cT and αS=[S]/cT. Since αHP+αI+αS=1 one obtains from (4) that(9)αS=1(KHPIKIS)-1+KS-1+1,αI=αSKIS.
For the description of the DSC experiment with the model function (8) one needs also the temperature derivatives of αS and αI. By using for each transition, i, the van’t Hoff relation(10)dln⁡KidT=ΔHi0RT2,
one obtains(11)dαSdT=αS2[KHPI-1KIS-1(ΔHHPI0+ΔHIS0)RT2+KIS-1ΔHIS0RT2],dαIdT=KIS-1(dαSdT-αSΔHIS0RT2).
Assuming that for each transition, i, the corresponding ΔcPi0 does not depend on T the standard free energy of that transition, ΔGi(T)0, can be obtained at any T from the integrated form of the Gibbs-Helmholtz relation  as (12)ΔGi(T)0=T[ΔGi(Ti,(1/2))0Ti,1/2+ΔHi(Ti,1/2)0(1T-1Ti,1/2)+ΔcPi0(1-Ti,1/2T-ln⁡TTi,1/2)],
where Ti,1/2 is the temperature at which the αi values sof species participating in transition i are the same. The corresponding equilibrium constant, Ki, is related to ΔGi(T)0 as (13)ΔGi(T)0=-RTln⁡Ki,
and for the suggested mechanism of the hairpin unfolding (4) it can be easily seen that for each suggested monomolecular transition ΔGi(Ti,1/2)0=0. Finally, according to the DSC experiments performed at different oligonucleotide concentrations the ΔHi(T) values appear to be concentration independent thus indicating that one may assume for each transition that ΔHi(T)=ΔHi(T)0 and ΔcPi=ΔcPi0. Using these assumptions and (8)–(13) one can express the model function (14) (14)cP,ex=αIΔcp,HPI0+dαIdTΔHHPI0+αS(Δcp,HPI0+Δcp,IS0)+dαSdT(ΔHHPI0+ΔHIS0),
only in terms of parameters Ti,1/2, ΔHi(Ti,1/2)0, and ΔcP,i0, characteristic for each of the suggested transitions. Their “best fit” values are obtained by fitting the model function (14) to the experimental cP,ex versus T curves. Furthermore, since for each transition, i, the corresponding ΔHi(T)0 and ΔSi(T)0 quantities can be expressed as(15)ΔHi(T)0=ΔHi(Ti,1/2)0+ΔcP,i0(T-Ti,1/2),TΔSi(T)0=ΔHi(T)0-ΔGi(T)0,
the “best fit” parameters Ti,1/2, ΔHi(Ti,1/2)0 and ΔcP,i0 can be used also to obtain the ΔHi(T)0 and ΔSi(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(16)D⟷KDS2S;KDS=[S]2[D],
that can be described in terms of the total oligonucleotide concentration, cT, 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, αS, and the equilibrium constant KDS interrelated as(17)cT=[D]+[S]2;αS=[D]cT;KDS=4αS2cT1-αS.
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(18)cP,ex=c̅P,2-c̅P,D=αSΔcP,DS0+dαSdTΔHDS0,
where c̅P,2 is the measured cP of the sample solution with subtracted baseline, c̅P,D is the heat capacity of the duplex form extrapolated from the low-T region over the whole measured temperature interval, ΔcP,DS0=ΔcP,DS=2c̅PS-c̅PD and ΔHDS0=ΔHDS=2H̅S-H̅D. From the suggested model (16) and (17) it follows that ΔGDS(T1/2)0=-RTln(2cT) and(19)αS=12[-KDS4cT+(KDS4cT)2+KDScT],∂αS∂T=ΔHDS0RT2αS(1-αS)2-αS.
The corresponding expressions for ΔGDS(T)0  ΔHDS(T)0 and TΔSDS(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 ΔHDS(T) and ΔcP,DS are assumed to be independent on the oligonucleotide concentration and thus equal to ΔHDS(T)0, and ΔcP,DS0.Inspection of (18) and (19) shows that the model function (18) is expressed in terms of adjustable parameters, T1/2, ΔHDS(T1/2)0 and ΔcP,DS0 that can be determined by fitting the model function to the experimental cP,ex versus T curve and further used to determine the ΔGDS(T)0, ΔHDS(T)0 and ΔSDS(T)0 values at any T.To obtain a set of the “best fit” adjustable parametersTi,1/2, ΔHi(Ti,1/2)0 and ΔcP,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 ΔcP,i0 quantities do not depend on the added NaCl concentration their values may be determined also from the slopes of the ΔHi(T1/2)0 versus Ti,1/2 curves constructed from the “best fit” ΔHi(T1/2)0 and Ti,1/2 parameters determined at different added salt concentrations [32]. These data can be also used to construct the corresponding Ti,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)).


## 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 (εD260=84600 M−1cm−1, εHP260=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 ofcPex=c̅p2-c̅pD,F versus T thermograms in which the differences between the partial molar heat capacity of the measured oligonucleotide c̅p2 (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, c̅pD,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 cPex(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,cP(T), with the subtracted baseline may be equalized with the oligonucleotide partial molar heat capacity, c̅P2(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(1)ΔH(T1→T2)=∫T1T2c̅p2(T)dT.
Since the enthalpy is the state function, the enthalpy change ΔH(T1→T2) may be expressed also as(2)ΔH(T1→T2)=∫T1Tref(c̅p2(T))FdT+ΔH(Tref)+∫TrefT2(c̅p2(T))UdT,
where (c̅p2(T))F and (c̅p2(T))U are the partial molar heat capacities of the folded and unfolded DNA conformation, respectively, ΔH(Tref)is the enthalpy of unfolding at Tref which can be any temperature between T1 and T2. By choosing Tref=T1/2 where T1/2 is the melting temperature at which a half of oligonucleotide molecules undergo unfolding transition (2) transforms into(3)ΔHT(1/2)cal=∫T1T1/2[c̅p2(T)-(c̅p2(T))F]dT+∫T1/2T2[c̅p2(T)-(c̅p2(T))U]dT,
where ΔHT1/2calis a model-independent enthalpy of transition at T1/2 that can be easily determined by the appropriate integration of the experimental [c̅p2(T)-(c̅p2(T))F] and [c̅p2(T)-(c̅p2(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 (Figure2). 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
(4)HP⟷KHPII⟷KISS;KHPI=[I][HP]KIS=[S][I]
can be expressed at given P and T as(5)H=n1H̅1+n2H̅2=n1H̅1+nHPH̅HP+nIH̅I+nSH̅S,
where KHPI and KIS 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: (6)n2=nHP+nI+nS,nHP in (6) represents the number of moles of the oligonucleotide in the folded hairpin state, nI is the number of moles in the intermediate state, nS is the number of moles in the unfolded single-stranded state and H̅1,H̅2,H̅HP,H̅I, andH̅S are the corresponding partial molar enthalpies of the solvent, solute and folded, intermediate and unfolded oligonucleotide, respectively. By defining the molar fraction,αi, of the solute species, i, as αi=ni/n2 one obtains from (5) that(7)H̅2=αHPH̅HP+αIH̅I+αSH̅S.
Finally, by introducing αHP=1-αI-αS into (7) and taking the temperature derivative of the modified (7) one obtains the model function for the measured DSC signal, cP,ex, expressed as(8)cP,ex=c̅P,2-c̅P,HP=αIΔcP,HPI+dαIdTΔHHPI+αS(ΔcP,HPI+ΔcP,IS)+dαSdT(ΔHHPI+ΔHIS),
in which at any temperature c̅P,2 is the measured cP (with subtracted baseline), c̅P,HPis the partial molar heat capacity of HP extrapolated from low-temperature region over the entire measured temperature interval, ΔHHPI=H̅I-H̅HP (enthalpy of the hairpin to intermediate state transition), ΔHIS=H̅S-H̅I (enthalpy of the intermediate state to unfolded single stranded state transition), ΔcP,HPI=c̅P,I-c̅P,HP and ΔcP,IS=c̅P,S-c̅P,I.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)).
(a)(b)(c)(d)cP,ex can be obtained experimentally simply by subtracting the hairpin c̅P,HPversus T curve extrapolated from low-T region over the entire measured temperature interval from the corresponding measured c̅P,2 versus T curve. The model-based cP,ex, however, can be calculated from the right-hand side term of (8). According to the suggested model (4) the total solute molar concentration, cT, and the fractions αi of the solute species present in the solution can be expressed as cT=[HP]+[I]+[S]and αHP=[HP]/cT, αI=[I]/cT and αS=[S]/cT. Since αHP+αI+αS=1 one obtains from (4) that(9)αS=1(KHPIKIS)-1+KS-1+1,αI=αSKIS.
For the description of the DSC experiment with the model function (8) one needs also the temperature derivatives of αS and αI. By using for each transition, i, the van’t Hoff relation(10)dln⁡KidT=ΔHi0RT2,
one obtains(11)dαSdT=αS2[KHPI-1KIS-1(ΔHHPI0+ΔHIS0)RT2+KIS-1ΔHIS0RT2],dαIdT=KIS-1(dαSdT-αSΔHIS0RT2).
Assuming that for each transition, i, the corresponding ΔcPi0 does not depend on T the standard free energy of that transition, ΔGi(T)0, can be obtained at any T from the integrated form of the Gibbs-Helmholtz relation  as (12)ΔGi(T)0=T[ΔGi(Ti,(1/2))0Ti,1/2+ΔHi(Ti,1/2)0(1T-1Ti,1/2)+ΔcPi0(1-Ti,1/2T-ln⁡TTi,1/2)],
where Ti,1/2 is the temperature at which the αi values sof species participating in transition i are the same. The corresponding equilibrium constant, Ki, is related to ΔGi(T)0 as (13)ΔGi(T)0=-RTln⁡Ki,
and for the suggested mechanism of the hairpin unfolding (4) it can be easily seen that for each suggested monomolecular transition ΔGi(Ti,1/2)0=0. Finally, according to the DSC experiments performed at different oligonucleotide concentrations the ΔHi(T) values appear to be concentration independent thus indicating that one may assume for each transition that ΔHi(T)=ΔHi(T)0 and ΔcPi=ΔcPi0. Using these assumptions and (8)–(13) one can express the model function (14) (14)cP,ex=αIΔcp,HPI0+dαIdTΔHHPI0+αS(Δcp,HPI0+Δcp,IS0)+dαSdT(ΔHHPI0+ΔHIS0),
only in terms of parameters Ti,1/2, ΔHi(Ti,1/2)0, and ΔcP,i0, characteristic for each of the suggested transitions. Their “best fit” values are obtained by fitting the model function (14) to the experimental cP,ex versus T curves. Furthermore, since for each transition, i, the corresponding ΔHi(T)0 and ΔSi(T)0 quantities can be expressed as(15)ΔHi(T)0=ΔHi(Ti,1/2)0+ΔcP,i0(T-Ti,1/2),TΔSi(T)0=ΔHi(T)0-ΔGi(T)0,
the “best fit” parameters Ti,1/2, ΔHi(Ti,1/2)0 and ΔcP,i0 can be used also to obtain the ΔHi(T)0 and ΔSi(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(16)D⟷KDS2S;KDS=[S]2[D],
that can be described in terms of the total oligonucleotide concentration, cT, 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, αS, and the equilibrium constant KDS interrelated as(17)cT=[D]+[S]2;αS=[D]cT;KDS=4αS2cT1-αS.
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(18)cP,ex=c̅P,2-c̅P,D=αSΔcP,DS0+dαSdTΔHDS0,
where c̅P,2 is the measured cP of the sample solution with subtracted baseline, c̅P,D is the heat capacity of the duplex form extrapolated from the low-T region over the whole measured temperature interval, ΔcP,DS0=ΔcP,DS=2c̅PS-c̅PD and ΔHDS0=ΔHDS=2H̅S-H̅D. From the suggested model (16) and (17) it follows that ΔGDS(T1/2)0=-RTln(2cT) and(19)αS=12[-KDS4cT+(KDS4cT)2+KDScT],∂αS∂T=ΔHDS0RT2αS(1-αS)2-αS.
The corresponding expressions for ΔGDS(T)0  ΔHDS(T)0 and TΔSDS(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 ΔHDS(T) and ΔcP,DS are assumed to be independent on the oligonucleotide concentration and thus equal to ΔHDS(T)0, and ΔcP,DS0.Inspection of (18) and (19) shows that the model function (18) is expressed in terms of adjustable parameters, T1/2, ΔHDS(T1/2)0 and ΔcP,DS0 that can be determined by fitting the model function to the experimental cP,ex versus T curve and further used to determine the ΔGDS(T)0, ΔHDS(T)0 and ΔSDS(T)0 values at any T.To obtain a set of the “best fit” adjustable parametersTi,1/2, ΔHi(Ti,1/2)0 and ΔcP,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 ΔcP,i0 quantities do not depend on the added NaCl concentration their values may be determined also from the slopes of the ΔHi(T1/2)0 versus Ti,1/2 curves constructed from the “best fit” ΔHi(T1/2)0 and Ti,1/2 parameters determined at different added salt concentrations [32]. These data can be also used to construct the corresponding Ti,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 Figure2 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 cP 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 Ti,1/2, ΔHi(Ti,1/2)0, and ΔcP,i0 (Table 1). However, analysis of the applied fitting procedure indicates that the parameter ΔcP,IS0 is highly correlated to some other adjustable parameters. Thus, to obtain safe estimate of ΔcP,IS0 another method of its determination has to be used. Assuming that it does not depend on the simple salt concentration ΔcP,IS0 was estimated as a slope of the ΔHIS(T1/2)0 versus TIS,1/2 plot (Figure 3(a)) constructed from the “best fit” parameters determined at different NaCl concentrations (Table 1). This method of determining ΔcP,i0 was justified by a good agreement between the ΔcP,i0 values for other transitions obtained by the described fitting procedure and the ΔcPi0 values determined as the slopes of the corresponding ΔHi(Ti,1/2)0 versus Ti,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 parametersa obtained from fitting the model functions ((14) and (18)) to the duplex (D) and hairpin (HP) DSC thermograms presented in Figure 2.
TransitionT1/2ΔH(T1/2)0ΔH(T1/2)calΔcP0 bΔcP0 cΔnNa+HP → I59.2370.340.9I → S75.0740.370.251.5HP → S117d1110.592.4D → 2S56.571710.250.301.7Error±0.2±2±2±0.05±0.05±0.2aUnits: C°(T1/2), kcalmol-1(∆H(T1/2)0,∆H(T1/2)cal), kcalmol-1K-1(∆cP0); 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 T1/2 curves (Figure 3(a));d the total enthalpy of the of the I→S transition was calculated as ∆HHS(T1/2,IS)0=∆HHI(T1/2,HI)0+∆cPHI0(T1/2,IS-T1/2,HI)+∆HIS(T1/2,IS)0 where T1/2,IS and T1/2,HI are the melting temperatures of the I→S and H→I transitions and ∆HIS(T1/2,IS)0 and ∆HHI(T1/2,HI)0 are the corresponding enthalpies of transition.Estimation of heat capacity changes and number of released Na+ ions: (a) ΔcP,i0 was determined for each transition i as the slope of the ΔHi(Ti,1/2)0 versus Ti,1/2 plot constructed from the model based ΔHi(Ti,1/2)0 and Ti,1/2 values determined at different salt concentrations; (b) the corresponding ln[Na+] versus Ti,1/2 plots from which the ΔnNa+,i values were determined according to (20).
(a)(b)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 experimentalcP,ex(T) versus T curve (ΔHHScal, see (3)) with the corresponding model-based value ΔHHS0 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 releasedNa+ ions, ΔnNa+,i, upon each HP and D transition, expressed per mole of oligonucleotide, may be estimated from [33](20)dTi,1/2dln⁡[Na+]=RTi,1/22ΔHi(Ti,1/2)0ΔnNa+,i,
in which Ti,1/2 is the melting temperature at a given Na+ concentration, [Na+], ΔHi(Ti,1/2)0 is the corresponding enthalpy of transition at Ti,1/2. The ΔnNa+,i values presented in Table 1 were determined from the slopes of the ln[Na+] versus Ti,1/2. plots (Figure 3(b)).At anyT 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=ΔHHS(T)0-ΔHDS(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 ΔΔcP0>0 and ΔΔnNa+>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 ΔΔcP0>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 ΔΔnNa+>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 ΔGT0, ΔHT0, ΔST0, ΔcP0, and ΔnNa+ 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.Table 2
Difference thermodynamic stability parametersa at 25°C exhibiting the influence of the TCTC loop to the unfolding features of the hairpin forming oligonucleotide (HP).
TransitionΔΔG0ΔΔH0TΔΔS0ΔΔcP0ΔΔnNa+(HP → S)-(D → 2S)2.426.624.30.290.7(I → S)-(D → 2S)−0.90.81.7−0.05−0.2Error±3±3±3±0.07±0.3aUnits: kcalmol-1 (ΔΔG0,ΔΔH0,TΔΔS0), kcalmol-1K-1 (ΔΔcP0); for temperature dependence of ΔG0, ΔH0, and TΔS0 see 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.
(a)(b)(c)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.



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*Source: 513910-2011-08-29.xml*