Conformational energetics of stable and metastable states formed by DNA triplet repeat oligonucleotides: Implications for triplet expansion diseases

Abstract

We have embedded the hexameric triplet repeats (CAG)₆ and (CTG)₆ between two (GC)₃ domains to produce two 30-mer hairpins with the sequences d[(GC)₃(CAG)₆(GC)₃] and d[(GC)₃(CTG)₆(GC)₃]. This construct reduces the conformational space available to these repetitive DNA sequences. We find that the (CAG)₆ and (CTG)₆ repeats form stable, ordered, single-stranded structures. These structures are stabilized at 62°C by an average enthalpy per base of 1.38 kcal·mol⁻¹ for the CAG triplet and 2.87 kcal·mol⁻¹ for the CTG triplet, while being entropically destabilized by 3.50 cal·K⁻¹·mol⁻¹ for the CAG triplet and 7.6 cal·K⁻¹·mol⁻¹ for the CTG triplet. Remarkably, these values correspond, respectively, to 1/3 (for CAG) and 2/3 (for CTG) of the enthalpy and entropy per base values associated with Watson–Crick base pairs. We show that the presence of the loop structure kinetically inhibits duplex formation from the two complementary 30-mer hairpins, even though the duplex is the thermodynamically more stable state. Duplex formation, however, does occur at elevated temperatures. We propose that this thermally induced formation of a more stable duplex results from thermal disruption of the single-stranded order, thereby allowing the complementary domains to associate (perhaps via “kissing hairpins”). Our melting profiles show that, once duplex formation has occurred, the hairpin intermediate state cannot be reformed, consistent with our interpretation of kinetically trapped hairpin structures. The duplex formed by the two complementary oligonucleotides does not have any unusual optical or thermodynamic properties. By contrast, the very stable structures formed by the individual single-stranded triplet repeat sequences are thermally and thermodynamically unusual. We discuss this stable, triplet repeat, single-stranded structure and its interconversion with duplex in terms of triplet expansion diseases.

A variety of debilitating human diseases with non-Mendelian inheritance patterns have been traced to highly repetitive DNA sequences. Sequence analysis has shown the disease state to be associated with expansion of repetitive sequences of three nucleotides, most commonly (CAG)_n/(CTG)_n, and (CCG)_n/(CGG)_n repeats, copied beyond a critical threshold value. Consequently, these diseases collectively are referred to as triplet expansion diseases (1–4). Even in healthy subjects, three nucleotide repeat domains in chromosomes are highly variable in length but generally do not exceed the threshold value of ≈30 repeats. Various triplet expansion diseases differ in the phenotype of the disease, the location of the expanded DNA domain, and whether the expanded domain is found within gene introns, gene exons, or upstream/downstream of genes in putative regulatory regions (5). The one common feature among the different diseases is that the affected repetitive DNA segment has expanded beyond the repeat number found in the healthy population.

Proposed mechanisms for DNA expansion assume that the structure and dynamics of the repetitive DNA segments themselves play critical roles in the development of the disease (4–7). This assumption is based on the observation that cloned triplet repeat sequences also expand and contract within bacterial hosts (8–13). It has been suggested that the relevant DNA sequences either have unusual properties in the duplex state or adopt unusually stable alternative secondary structures involving single-stranded domains, which alter the course of the “normal” cellular DNA chemistry (14). Initial structural and some thermodynamic studies of model poly/oligonucleotides have indeed indicated that single strands consisting of repeated copies of (CAG)_n, (CTG)_n, and (CCG)_n are able to adopt extensive secondary structures (14–28); however, conformational heterogeneity and/or kinetically trapped metastable states have precluded the determination of reliable thermodynamic data for this important class of DNA sequences (15, 29–33). The absence of reliable thermodynamic data prevents a rational evaluation of the different models and precludes theoretical predictions as to which sequences may be prone to assume structures that may lead to the disease state (34).

To alleviate this shortcoming, we have designed a series of oligonucleotide model systems in which two triplet repeat sequences, (CAG)₆ and (CTG)₆, are embedded between alternating (GC)₃ sequences, thereby, in principle, allowing formation of stable stem/loop (hairpin) structures, as shown in Scheme . The stem portion of the hairpin consists of alternating GC base pairs, which act as a duplex clamp. The loop region contains the single-stranded triplet repeat sequence. The stem restricts the conformational space of the triplet repeat sequences with respect to slipped and misaligned structures and perhaps also prevents the formation of multiple kinetically trapped intermediates. The triplet repeat sequences are free to adopt whatever structure they prefer within the constraints imposed by the hairpin stem. The sequences chosen for this purpose, X[CAG]₆X and X[CTG]₆X, are complementary to each other, such that our constructs allow us to investigate the thermodynamics of each triplet repeat sequence in isolation and also when combined to form the corresponding duplex, as shown in Scheme . We show below that each of the triplet repeat sequences significantly adds to the overall thermodynamic stability of the hairpins; that the duplex is structurally and thermodynamically indistinguishable from canonical B form DNA; and that formation of the duplex is inhibited at low temperatures (presumably due to loop structure), even though the duplex is the thermodynamically most stable state.

Scheme 1.

Proposed model for the interaction of the two complementary triplet repeat oligonucleotides.

Materials and Methods

Materials.

Oligonucletides were synthesized and purified as previously described (35, 36). Concentrations were determined optically in 10 mM Na cacodylate, pH 7.0, buffer by using a Varian 300 UV/Vis spectrophotometer. Extinction coefficients at 260 nm were determined by phosphate assay (37, 38) in denaturing conditions (80 or 90°C) and were found to be = 280,000 M⁻¹⋅cm⁻¹ (90°C); = 308,000 M⁻¹⋅cm⁻¹ (90°C); = 249,670 M⁻¹⋅cm⁻¹ (80°C), where X = (GC)₃. Oligomer stocks were dialyzed extensively against at least two changes of buffer (10 mM Na cacodylate/1 mM Na₂EDTA/Y mM NaCl) of the desired ionic strength.

UV Absorption Measurements.

Temperature-dependent UV absorption measurements were conducted and analyzed as previously described by using an Aviv (Lakewood, NJ) DS14 UV/VIS spectrophotometer equipped with a five-cell thermoelectric cell holder (35, 39–41). Unless otherwise indicated, oligonucleotide concentrations were always 1 μM in single strand or duplex.

Circular Dichroism (CD) Spectroscopy.

CD spectra as a function of temperature were recorded by using an Aviv DS61 Spectropolarimeter equipped with a thermoelectric cell holder in a 1-mm path length cell. After subtraction of buffer scans, sample scans were normalized for concentration (42), by using the software provided. Concentrations were 16 μM in single strand and 8 μM in duplex.

Calorimetry.

Excess heat capacity measurements were performed by using a NanoDSCII differential scanning calorimeter (DSC) (CSC, Provo, UT) with nominal cell volumes of 0.3 ml. Dialyzed samples of nominal concentration 50 μM (single strands) or 25 μM (duplex) were placed in the sample cell, whereas the appropriate buffer was placed in the reference cell. Samples were scanned repeatedly at a constant scan rate of 1°C/min in the temperature range 0–105°C. After buffer subtraction, the excess heat capacity data were normalized for DNA concentration and analyzed as previously described (41, 43, 44). ΔC_p values were determined from the difference in the pre- and post-transition baseline extrapolated to the T_m of the transition.

Results and Discussion

The X[CAG]₆X and X[CTG]₆X Oligonucleotides Form Stable Hairpins.

By design, we expect the ordered structure for each triplet repeat 30-mer molecule to be a hairpin with a stem of six alternating purine/pyrimidine GC base pairs and a large loop domain comprised of the triplet repeat sequence (Scheme ). Although a variety of alternative structural models of intermolecular dimers with bulges also are feasible, the observed lack of concentration dependence of the T_m (not shown) for each 30 mer is consistent with these oligonucleotides adopting monomolecular hairpin structures (41). Hairpin formation also is supported by the moderate dependence of the T_m on the ionic strength (Table 1) characteristic of such secondary structures (45, 46). Taken together with the optical melting curve measurements presented below, we interpret the data as indicative of the formation of hairpin structures, consistent with our design objective.

Table 1.

Thermodynamic data for oligonucleotide order–disorder processes in 100 mM Na⁺/10 mM cacodylate/1 mM EDTA, pH 6.8, buffer

Oligomer	Tm	ΔH	ΔS	ΔCp	ΔH	dTm/ dlog[Na+]
X[TTT]6X	62.6	42.3	125.9	410	50.7	ND
X[CAG]6X	80.9	86.5	244.3	1,050	75.1	11.26
X[CTG]6X	81.5	110.2	310.7	850	101.4	11.79
X[CAG]6X and X[CTG]6X	70.7	−66.7	−193.9	ND	(−199.5)	0.13
	89.2	247.2	682.2	ND	273.4	15.05
X[CAG]6X⋅X[CTG]6X	89.3	278.7	768.9	1,470	244.6	15.99

 ND, not determined.

^*°C, estimated error is ±0.2°C.

^† kcal·mol⁻¹, estimated error is ±5%.

^‡ cal·mol⁻¹·K⁻¹, estimated error is ±5%.

^§ cal·mol⁻¹·K⁻¹, estimated error is ±15%.

^¶ Free energies (ΔG) at any temperature can be calculated from the data in columns 2–5 by using the equation: ΔG^T = ΔH^Tm − TΔS^Tm − ΔC_p(T_m − T) + TΔC_pln(T_m/T).

^∥ °C, estimated error is ±0.5°C.

Optical Evidence.

We observe clear differences in the CD spectra for each triplet repeat containing oligonucleotide (X[CAG]₆X and X[CTG]₆X) at low (0°C) and high (95°C) temperatures (Fig. 4A, which is published as supporting information on the PNAS web site, www.pnas.org). Such temperature-dependent differences suggest that these two molecules adopt ordered structures at low temperature (e.g., hairpins), which are disrupted at higher temperatures. Further, we observe substantial differences in the CD spectra of the two triplet repeat containing oligonucleotides when compared with the spectrum of X[TTT]₆X, in which the triplet repeat sequences are replaced entirely by thymidine residues. This observation suggests significant differences in the ordered low-temperature structures of the two triplet repeat-containing molecules relative to the molecule with the [TTT]₆ domain. Because the [TTT]₆ sequence is assumed to exhibit minimal order (47–49), we ascribe the order apparent in the low-temperature CD spectrum of X[TTT]₆X to its terminal (GC)₃ stem region. We therefore propose that the temperature-dependent differences in CD spectra observed between the two triplet repeat-containing molecules and our control hairpin X[TTT]₆X are due to contributions from order in the single-stranded, looped, triplet repeat sequences, as well as to differences in the intrinsic optical properties of the nucleotide bases. Sharp transitions observed near 80°C in the corresponding optical melting curves (Fig. 4B, which is published as supporting information on the PNAS web site) for X[CAG]₆X and X[CTG]₆X, as compared with the broad transition at 62°C for the X[TTT]₆X hairpin, also are consistent with the presence of stabilizing ordered structures in both triplet repeat containing loops. NMR studies will provide additional insight into the detailed structure of the loop order we observe here.

Calorimetric Studies.

Calorimetrically measured excess heat capacity curves for the X[CAG]₆X (red) and X[CTG]₆X (blue) triplet-containing hairpins and the control X[TTT]₆X hairpin (green) are shown in Fig. 1. The corresponding thermodynamic parameters are listed in Table 1. The measured thermodynamic parameters for the proposed hairpin structures refer to the combined contributions from the duplex stem domain and from the nominally single-stranded triplet repeat loop domain. To isolate the thermodynamic contribution of order in the triplet repeat loop regions of these hairpins, we have compared these hairpins to the similarly constructed hairpin, X[TTT]₆X. Implicit in the choice of X[TTT]₆X as a thermodynamic reference is the assumption that the all-T loop resembles, more than any other base combination, an unstructured loop (47, 49–54). In support of this assumption, we note that the measured enthalpy for X[TTT]₆X is in good agreement with the enthalpy predicted by nearest-neighbor data (55, 56) for the hairpin stem. This observation suggests that an all-T loop exhibits no enthalpically stabilized structure. We recognize that this dissection of the thermodynamic parameters is imperfect due to the differences inherent in the junction between the conserved stem and the variable loop regions, including the possibility that the stem may be extended by one GC base pair in the X[CAG]₆X and X[CTG]₆X hairpins. In practice, any junction effects are subsumed into the loop contribution in our analysis.

Fig 1.

Excess heat capacity vs. temperature profiles (DSC melting curves) of X[CAG]₆X (red), X[CTG]₆X (blue), and X[TTT]₆X (green) in 100 mM Na⁺ buffer.

The Triplet Repeat Loop Sequences Strongly Stabilize the Hairpin Structures.

Thermal stability.

Inspection of Fig. 1 and Table 1 reveals that the presence of the [CAG]₆ and [CTG]₆ triplet repeat loop domains results in an increase in thermal stability of the hairpins relative to the X[TTT]₆X hairpin by 18.3 and 18.9°C, respectively. This increase in T_m is due to the apparent increase in order in the triplet repeat loop domains relative to the unstructured [TTT]₆ loop. These data are consistent with suggestions that triplet repeat sequences can adopt extensive secondary structures (14–28); however, these data alone do not imply anything about the nature of that order.

Thermodynamic stability.

Our DSC measurements reveal that, in addition to an increase in thermal stability (T_m), the presence of either triplet repeat sequence also results in an increase in the thermodynamic stability (ΔG) of the hairpins relative to the X[TTT]₆X reference hairpin. Inspection of the data in Table 1 reveals that the observed increases in the stabilities of the two hairpins with triplet repeat loops result from highly favorable enthalpic and partially compensating unfavorable entropic contributions. Because the heat capacity changes associated with the order–disorder transitions of each hairpin are not identical, it is important to compare enthalpy and entropy data at a common reference temperature (57–59). To avoid long extrapolations, we select the T_m of the X[TTT]₆X as the thermodynamic reference temperature (62.6°C) for this comparison. These data, which can be derived directly from the data in Table 1, are summarized in Tables 2 and 3, which are published as supporting information on the PNAS web site. Although the T_m values for the two triplet repeat containing hairpins are nearly identical, the enthalpy and entropy changes associated with their order–disorder transitions are markedly different, an important feature that would be missed if one simply compared thermal stabilities (T_m values). As expected for favorably ordered domains, the triplet repeat loops enthalpically stabilize the hairpins by ΔΔH_cal = 24.9 kcal⋅mol⁻¹ for the [CAG]₆ domain (67.2–42.3) and by ΔΔH_cal = 51.7 kcal⋅mol⁻¹ for the [CTG]₆ domain (94.0–42.3), relative to the enthalpic stabilization imparted to the X[TTT]₆X hairpin by the [TTT]₆ loop. Also as expected for ordered domains, the triplet repeat loops entropically destabilize the hairpins by ΔΔS_cal = 63.1 cal⋅mol⁻¹⋅K⁻¹ for the [CAG]₆ domain (189.0–125.9) and by ΔΔS_cal = 138.0 cal⋅mol⁻¹⋅K⁻¹ for the [CTG]₆ domain (263.9–125.9), relative to the entropic destabilization imparted to the X[TTT]₆X hairpin by the [TTT]₆ loop. Because the [TTT]₆ loop is assumed to be highly disordered, its entropic contribution likely represents only loop configurational entropy (50). Thus, the large entropic and enthalpic impacts of the [CAG]₆ and [CTG]₆ loops argue strongly for significant order in the triplet repeat sequences in their single-stranded states. The magnitudes of these loop impacts are remarkably large, representing ≈1/3 for [CAG]₆ and 2/3 for [CTG]₆ of the total enthalpy and entropy values expected for the corresponding Watson–Crick base pairs (55, 56). These results demonstrate that single-stranded triplet repeat regions can exhibit unusual stability, with the energetic nature of this order depending on the specific triplet repeat sequence. We use the term “triplet repeat structure” as a generic description for the structures adopted by all triplet repeat sequences in their single-stranded state. It is assumed that this term does not necessarily refer to a unique secondary structure but rather to an ensemble of structures adopted by triplet repeat DNA sequences in solution, without all such sequences necessarily adopting the same ensemble of secondary structures.

Taken together, our data demonstrate that the X[CAG]₆X and X[CTG]₆X oligonucleotides form stable hairpin structures with significant order in the triplet repeat loop domains. We consider our approach using constrained hairpin structures to derive thermodynamic data for the highly repetitive triplet repeat sequences superior to traditional studies of unconstrained model oligonucleotides. In unconstrained systems, highly repetitive sequences are known to adopt a wide range of secondary structures, including slipped DNA structures, inter- and intramolecular foldback structures, and others (7, 29, 30). Traditional approaches therefore result, at best, in thermodynamic data that are averaged over an often poorly defined distribution of populations. The likelihood of significantly populated alternative conformations is greatly diminished by the combined hairpin/loop approach used here.

Hairpin–Hairpin Interactions.

The X[CAG]₆X and X[CTG]₆X hairpins do not interact at low temperature.

CD spectra imply that the X[CAG]₆X and X[CTG]₆X hairpins do not interact at low temperature, despite having 18-base looped domains that are complementary to each other. The CD spectrum of an equimolar mixture of X[CAG]₆X and X[CTG]₆X at low temperature (before heating) is essentially identical to the calculated spectrum for noninteracting oligonucleotides obtained by summing weighted CD spectra of X[CAG]₆X and X[CTG]₆X (Fig. 5A, which is published as supporting information on the PNAS web site). These spectra differ significantly from the CD spectrum of the corresponding X[CAG]₆X⋅X[CTG]₆X duplex. These observations suggest that the two hairpins do not interact with each other at 0°C. In fact, we find such noninteracting behavior persists even up to ≈60°C.

The X[CAG]₆X and X[CTG]₆X hairpins do interact at elevated temperatures (>60°C) below the global hairpin melting temperature, to form a duplex.

Because the 18-base triplet repeat loop domains in X[CAG]₆X and X[CTG]₆X are complementary to one another, one might expect loop–loop interactions to occur. Once formed, such an initiation complex, a “kissing hairpin”-like structure (60–64), is expected to “zip up” to form the fully paired duplex, even at low temperatures, as cartooned in Scheme . Indeed, we observe such duplex formation from two hairpins with complementary looped regions when we mix X[TTT]₆X with X[AAA]₆X (unpublished results). The observation here that a duplex does not form on mixing of X[CAG]₆X and X[CTG]₆X at temperatures below 60°C suggests that the triplet repeat loops adopt structures that inhibit formation of a viable initiation complex. However, the proposed single-stranded loop structure can be thermally disrupted to form a duplex at a temperature below that required to globally melt the hairpins. We propose that this disruption of local structure allows the complementary looped sequences to associate into a bimolecular “initiation complex” (perhaps a “kissing hairpin”), from which the duplex state can grow. Preliminary kinetic experiments (unpublished observations) are consistent with this cascade of events, as cartooned in Scheme .

Optical evidence of hairpin–hairpin interactions.

Our temperature-dependent CD spectra (Fig. 5B, which is published as supporting information on the PNAS web site) reveal that the X[CAG]₆X and X[CTG]₆X hairpins interact to form a duplex after heating to 70°C, with an optical signature that differs from that calculated for noninteracting hairpins at 70°C. This observation suggests that, after heating to 70°C, the two oligomers interact and adopt a conformation different from that assumed before heating. We propose that the heating process induces formation of the X[CAG]₆X⋅X[CTG]₆X duplex from the complementary oligonucleotides. This behavior suggests that the order in the triplet repeat loop, the presumptive origin of inhibition of duplex formation, is disrupted at elevated temperature.

In Fig. 2, we present temperature-dependent optical data consistent with the proposition that the two complementary oligonucleotides X[CAG]₆X and X[CTG]₆X (red curve) form a duplex at elevated temperature. At temperatures up to ≈60°C, the measured absorbance of the 1:1 mixture of X[CAG]₆X and X[CTG]₆X is identical to that calculated by addition of the separate melting curves (dashed black curve) for a 1:1 noninteracting hairpin mixture. This observation is consistent with no interactions between the hairpins below 60°C. At higher temperatures, the measured absorbance decreases (red curve), a hypochromic effect, which reflects an increase in order within the DNA consistent with duplex formation. At even higher temperatures, the absorbance increases, a hyperchromic effect, due to the disruption of the duplex. Reheating the same sample results in a curve in which only the duplex to single-strand transition is observed (blue curve). Because the isolated hairpin structures do not reform on cooling, we conclude that the duplex state is the thermodynamically more stable state at low temperature. This conclusion means that the isolated hairpins, when present together, represent a kinetically trapped state.

Fig 2.

Absorbance vs. temperature profiles (UV-melting curves) of a 1:1 mixture of X[CAG]₆X with X[CTG]₆X in 100 mM Na⁺ buffer. The red curve is observed on heating for the first time; the blue curve is observed in all subsequent heating cycles. The dashed black line represents the calculated melting curve expected for noninteracting hairpins. Note the unusual hypochromic (negative) absorbance change above 60°C in the red curve indicating the formation of the X[CAG]₆X⋅X[CTG]₆X duplex.

The duplex-to-disordered single-strand transition depends on DNA concentration and ionic strength. The hairpin to disordered single-strand transitions are concentration independent, while also depending on ionic strength, albeit to a lesser degree than the duplex. By contrast, we find the observed hypochromic transition (duplex formation) to be nearly independent of DNA concentration and ionic strength. Taken together, these observations suggest that the hypochromic transition is dominated by a monomolecular process in which the average charge density of the molecules does not change significantly. Because the formation of duplex is by definition a bimolecular process, and therefore concentration dependent, we conclude that monomolecular processes preliminary to duplex formation overwhelm the contribution of strand association to the duplex formation process.

Based on the CD- and temperature-dependent optical data presented above, we propose the series of thermally induced transitions shown in Scheme between the noninteracting hairpins, the duplex, and the disordered single strands. In addition, we infer one or more intermediate states in the transition between the isolated hairpins and the duplex. In this scheme, we propose as a working model that the initiation complex for duplex formation is a “kissing hairpin” (60, 62). More direct structural and kinetic studies will be required to evaluate this proposed state, as well as to define in detail the nature of the surprisingly stable single-stranded triplet repeat looped structure.

At elevated temperatures, the X[CTG]₆X and X[CAG]₆X oligonucleotides form an optically and thermodynamically “normal” Watson–Crick duplex.

As noted above, a duplex is formed from the complementary oligonucleotides X[CTG]₆X and X[CAG]₆X by heating to 95°C and slow cooling to 0°C. The CD spectrum of the resultant X[CTG]₆X⋅X[CAG]₆X duplex (Fig. 5 A and B) is consistent with that observed for normal, Watson–Crick base-paired B form DNA (65). No anomalies in the shape or position of the spectrum are apparent, thereby implying an absence of any unusual duplex structure imparted by the triplet repeat sequence.

Calorimetric characterization of the X[CTG]₆X⋅X[CAG]₆X duplex also reveals nothing unusual. The calorimetrically determined enthalpy change for disruption of the X[CTG]₆X⋅X[CAG]₆X duplex, 278.7 kcal⋅mol⁻¹, is in good agreement with estimates derived from nearest-neighbor data based on polymers, 262.0 kcal⋅mol⁻¹, (55) and a combination of polymers and oligonucleotides, 273.3 kcal⋅mol⁻¹ (56). The measured entropy change of 769 cal⋅mol⁻¹⋅K⁻¹ and the heat capacity change of 1470 cal⋅mol⁻¹⋅K⁻¹ also are in agreement with values expected for a duplex of 80% GC (57–59). Consequently, by all thermodynamic measures, the X[CTG]₆X⋅X[CAG]₆X duplex behaves like a conventional Watson–Crick duplex and does not show any unusual properties that could be attributed specifically to the triplet repeat sequences. In short, this triplet repeat-containing duplex does not exhibit any anomalous optical or thermodynamic properties. As a result, the unusual properties of the single-stranded triplet repeat domains we report here represent reasonable candidates in efforts to define a biophysical basis for the biological origins of triplet repeat diseases.

Our calorimetric data produce a closed thermodynamic cycle consistent with the proposed model.

We applied calorimetric methods to characterize the individual and overall thermodynamics of the processes we have proposed above. Table 1 lists the thermodynamic data obtained from the first and second calorimetric heating scans for an equimolar mixture of X[CAG]₆X and X[CTG]₆X. These transition curves are shown in Fig. 3. The first calorimetric heating scan of an equimolar mixture of the two hairpins (red) shows an unusual exothermic (negative) transition, which we assign to the thermally induced duplex formation from the kinetically trapped hairpin starting states. The subsequent endothermic (positive) transition in the red curve corresponds to the more conventional duplex melting event. The second heating scan (blue) shows only the positive duplex melting transition, which we used above to establish the thermodynamic parameters for the duplex. Significantly, the DSC experiment permits measurement of the enthalpy changes untainted by the kinetics of the processes and the non-two-state nature of the duplex to single-strand transition. The near superposition of the only transition in the second scan with the second transition in the first scan is consistent with its assignment to duplex melting.

Fig 3.

Excess heat capacity vs. temperature profiles (DSC-melting curves) of a 1:1 mixture of X[CAG]₆X with X[CTG]₆X in 100 mM Na⁺ buffer. The red curve is observed on heating for the first time; the blue curve is observed in all subsequent heating cycles. The dashed black line represents the calculated melting curve expected for noninteracting hairpins. Note the unusual exothermic (negative) heat capacity change above 60°C in the red curve indicating the formation of the X[CAG]₆X⋅X[CTG]₆X duplex.

We again define a convenient reference temperature to evaluate the thermodynamic parameters for the transitions observed in Fig. 3. To avoid the need for a value for the heat capacity change associated with the exothermic (negative) transition of the first DSC scan (which we cannot directly measure due to peak overlap), we select the T_m for that transition as the reference temperature (57–59). Scheme shows a schematic representation of the processes for interconversion of the three equilibrium thermodynamic states that we define in our model of the interactions of the X[CAG]₆X and X[CTG]₆X oligonucleotides: the isolated hairpins, the duplex, and the unstructured single strands (coils). The corresponding enthalpy and entropy values for the different transitions at our reference temperature of 70.7°C are shown in Scheme and are listed in Table 4, which is published as supporting information on the PNAS web site. The critical feature, which allows us to close the thermodynamic cycle depicted in Scheme , is that we independently measure the hairpin-to-coil transition enthalpies of each isolated hairpin without interference from any competing hairpin/duplex equilibrium (dashed black curve, Fig. 3). Applying Hess's law to the cycle, we see that A−B = C, where A, B, and C represent the enthalpy changes associated with these transitions. Thus, from the separately measured DSC data for disruption of the two hairpin ordered structures (dashed black) and the DSC of the duplex-to-coil transition (blue curve), we calculate the enthalpy change associated with the transition of the hairpins to the duplex. We find A − B = (75.8 + 100.9) − 251.3 = −74.6 kcal⋅mol⁻¹, in very good agreement with the measured exothermic transition in the first DSC scan (−66.7 kcal⋅mol⁻¹), which we assign to the transition from the isolated hairpins to the duplex. An analogous cycle in terms of entropy also closes, with A − B = (213.6 + 284.3) − 691.3 = −193.4 cal⋅mol⁻¹⋅K⁻¹ for the calculated value and −193.9 cal⋅mol⁻¹⋅K⁻¹ for the measured value.

Scheme 2.

Proposed model for the thermodynamic cycle observed for the triplet repeat oligonucleotides. Pathway A is determined only for the hairpins in isolation, which is indicated by the dashed arrows. The equilibrium for pathway B is shifted so far onto the side of the duplex that the reverse reaction (duplex to hairpin) is never observed, as indicated by the crossed arrow.

The critical observation here is that the isolated hairpins are kinetically trapped in an ordered state from which a significant activation barrier has to be overcome before duplex formation can occur, even though the duplex is the most thermodynamically stable state. In the next section, we discuss the implications of our observations within the context of current models of the biology associated with triplet repeat sequences and the onset of the disease state.

Biological Implications

Our experimental results demonstrate that the triplet repeat sequences CAG and CTG may adopt very stable, ordered, single-stranded structures. By contrast, the duplex formed by the (CAG)₆ and (CTG)₆ repeat sequences appears quite ordinary by every structural and thermodynamic measure evaluated herein. Although the duplex is the thermodynamically favored state for the studied oligonucleotides, our results also demonstrate that the transition through which the ordered single-stranded states form a duplex is kinetically inhibited. The ordered single-stranded triplet repeat structures represent metastable intermediate states (local energy minima), which once formed, persist in the absence of heating.

Given the hypothesis that DNA structure and dynamics are at least in part responsible for the development of the disease state in triplet repeat diseases (4–7), our experimental results favor models that involve, even if only transiently, single-stranded structure as part of the mechanism. Our results clearly suggest that, when in the duplex state, triplet repeat DNA behaves like conventional duplex DNA and is unlikely to be involved with the development of the disease state. Although it will not occur spontaneously from the duplex state, conditions for the formation of ordered single-stranded triplet repeat structure may exist during the course of normal cellular DNA chemistry (replication, transcription, etc.), when the duplex partially dissociates locally into single-stranded domains. The influence of proteins on the formation of ordered single strands remains to be assessed. However, our data suggest that, once formed, ordered, single-stranded triplet repeat structures can represent local minima. Errors in the passage of the replication fork through the triplet repeat domain (10, 67, 68), faulty repair processes (69, 70), or some other yet-to-be-determined mechanism may lead to expansion of triplet repeat DNA when such single-stranded ordered states are populated. Because the onset of the expansion of the triplet repeat domain may depend on such metastable states, the lifetime as well as the relative thermodynamic stability of the ordered structure must be considered in the regulation of events that allow expansion to occur. This interplay between the thermodynamic stability and the lifetime of the single-stranded structures also should determine the observed threshold values for the onset of the disease state.

Abbreviations

• CD, circular dichroism

• DSC, differential scanning calorimeter