Measuring thermodynamic preferences to form non-native conformations in nucleic acids using ultraviolet melting

Significance Thermodynamic preferences of nucleic acids to adopt non-native conformations are crucial for understanding how they function but prove difficult to measure experimentally. As a result, little is known about how these thermodynamic preferences vary with sequence and structural contexts, physiological conditions, and chemical modifications. Here, we show that modifications stabilizing non-native conformations and rendering them the major state, in conjunction with melting experiments, enable facile measurements of thermodynamic preferences to form various nonnative conformations in DNA and RNA. Delta-melt provided rare insights into the cooperativity of forming tandem Hoogsteen base pairs and revealed large and distinct sequence-specific preferences to form G-C+ and A-T Hoogsteen and A-T base open conformations in DNA, which may contribute to sequence-specific DNA biochemistry.

. UV-melting curves. UV melting curves (black points) used to estimate thermodynamic preferences for (a) A-T and (b) G-C + Hoogsteen bp formation, (c) A-T base opening, (d) N 6methylamino rotation in N 6 -methyl adenine (m 6 A), (e) cooperative formation of A-T/G-C + Hoogsteen bps and (f) sequence-dependent formation of G-C + Hoogsteen bps. Fits of the data to a two-state model are shown in blue lines (Methods). The modification used to measure the thermodynamic preferences is indicated in parentheses. The name of the constructs (secondary structures in Fig.  S4 and S13) and buffer conditions are highlighted above the melts. A260 refers to the absorbance at 260nm. HS denotes high salt (> 25mM NaCl, Methods). The UV melting data for scaf2_AGG m1GC and scaf2_TGG m1GC are not shown above as they were not used to determine thermodynamic preferences, as they displayed non-two-state melting behavior (Fig. S3, Methods). All data were collected on a Perkin-Elmer UV-Vis spectrophotometer (Methods). Figure S2. UV-melting curves. UV melting curves (black points) used to estimate thermodynamic preferences for (a, b and c) A-T Hoogsteen bp formation, (d) A-T base opening, and (e and f) sequence-dependent formation of A-T Hoogsteen bps and base opened states, respectively. Fits of the data to a two-state model are shown in blue lines (Methods). The modification used to measure the thermodynamic preferences is indicated in parentheses. The name of the constructs (secondary structures in Fig. S4 and S13) and buffer conditions are highlighted above the melts. A260 refers to the absorbance at 260nm. HS denotes high salt (> 25mM NaCl, Methods). The UV melting data for scaf2_AAG AT , scaf2_AAG m1AT , scaf2_AAG Am3T , scaf2_CAC AT , scaf2_GAC AT , scaf2_TAG AT , scaf2_TAG m1AT , scaf2_AAA Am3T and scaf2_GAG Am3T are not shown above as they were not used to determine thermodynamic preferences, as they displayed non-two-state melting behavior (Fig. S3, Methods). All data were collected on a Cary-100 UV-Vis spectrophotometer (Methods).  Fig. S4 and S13) and buffer conditions are highlighted above the melts. A260 refers to the absorbance at 260nm. HS denotes high salt (> 25mM NaCl, Methods). Figure S4. Representative NMR spectra of the DNA and RNA constructs used for NMR measurements. (a) DNA constructs used for imino proton exchange measurements. (b) Representative 1 H 1D spectra of the imino region of A6-DNA and G-DNA. Spectra for TBP-DNA have been reported previously (1). (c) Isotope labeled DNA and RNA constructs used for R1ρ and CEST measurements. Solid and dashed lines denote stable and labile Watson-Crick bps respectively. (d) Representative 2D [ 13 C/ 15 N, 1 H] HSQC spectra of the isotope labeled DNA and RNA constructs. HS refers to high salt (> 25mM NaCl, Methods). Squares in panels a and c denote sites at which A-T base opening and A-T/G-C + Hoogsteen bps were monitored using imino proton exchange and R1ρ/CEST, respectively. 13 C, 15 N uniformly labeled (A, C, T and G) nucleotides are denoted in bold while atom-specifically 13 C/ 15 N nucleotides are indicated using outlines. All other nucleotides are unlabeled. m 1 A, m 1 G, and m 6 A denote N 1 -methyl adenine, N 1 -methyl guanine and N 6 -methyl adenine, respectively. All nucleotides in DNA and RNA have deoxyribose and ribose sugars respectively, apart from rA/rG in DNA, which have a ribose sugar. The A and U nucleotides in hpGGACU m6A6 (m 6 A6 C2,C8 lb) are site-specifically 13 C labeled at C2 and C8, and 15 N labeled at N3, respectively.
Spectra for A6-RNA m6A16 (m 6 A16 C2,C8 lb), hpGGACU m6A6 (m 6 A6 C2,C8 lb) and hpGGACU m6A6 (m 6 A6 C10 lb) were reported in another study (2). 6 -methyl adenine (m 6 A). HS refers to high salt (> 25mM NaCl, Methods). Secondary structures and labeling schemes for the constructs used for the above measurements are provided in Fig. S4, and Table S3. RF powers for R1ρ and CEST are color-coded. Two-state individual/shared fits (Table S5, Methods) of the data to the Bloch-McConnell equations are shown as solid lines. Error bars for the R1ρ and CEST data were obtained using a Monte-Carlo based approach as described in the Methods. Error bars for the CEST intensities are smaller than the data points.

Figure S6. Degeneracy analysis evaluating how well the population of the minor state (pi)
is determined using the R1ρ or CEST data. Shown is the normalized reduced  2 (  2 ) as a function of fixing pi to different values when fitting R1ρ or CEST profiles probing (a) A-T and (b, d) G-C + Hoogsteen bp formation and (d) methylamino rotation in N 6 -methyl adenine (m 6 A). HS refers to high salt (> 25mM NaCl, Methods). The absolute r 2 values obtained from fitting the R1ρ or CEST profiles were normalized such that r 2 = 1 for the best fit. The values of pi obtained from free fitting the R1ρ or CEST profiles are indicated using a dashed line. Differences in the shapes of the r 2 profiles for different data sets could be related to the differences in experimental error (Methods) or sampling of the data points in the measurements (Fig. S5, Table S4). Figure S7. Testing delta-melt on G-C + Hoogsteen bps using the N 1 -methylguanosine mimic. (a) In duplex DNA, G-C Watson-Crick bps exist in dynamic equilibrium with a minor G-C + Hoogsteen bp. Population of the minor Hoogsteen bp was obtained as described previously (3). m 1 G (red) biases the Watson-Crick to Hoogsteen equilibrium of G-C bps towards the Hoogsteen conformation via loss of a hydrogen bond donor (G-N1), and due to steric clashes (curved black dashes) (4). G-C + Hoogsteen bps have been proposed to contribute to DNA recognition by proteins such as TBP (5) and to DNA damage induction (6). (b) Duplexes used in UV melting experiments with and without m 1 G substitution (indicated in bold). (c) Correlation plot between G melt  (i) obtained from melting experiments on m 1 G-C/G-C bp containing DNA (Fig. S1, Table  S1) and G conf  (i) measured using NMR for formation of G-C + Hoogsteen bps ( Fig. S4-S6, Tables S3-S5). Points are color-coded according to the duplexes in panel b. A total of seven points were used for comparison, corresponding to two different tri-nucleotide sequence contexts (5'-TGG-3'/5'-TGC-3') embedded in three different duplexes, at two positional contexts. Error bars for NMR and delta-melt measurements were obtained using a Monte-Carlo scheme, and by propagating the uncertainties from UV melts, respectively, as described in Methods. Shown are the Pearson's correlation coefficient (r) and root mean square error (RMSE)(Methods). Blue shaded region denotes the estimate of the error of linear regression obtained using Monte-Carlo simulations, while open symbols denote data derived from weak RD profiles (Methods).    (a) Duplexes used to examine cooperativity of Hoogsteen bp formation using delta-melt. m 1 A and m 1 G (red) denote N 1 -methyl adenine and guanine respectively. All nucleotides are unlabeled. (b) Overlay of 1 H 1D spectra of the imino region of the duplexes with single and tandem N 1 -methylated purines. (c) 2D [ 13 C, 1 H] HSQC spectra of the aromatic region of DNA constructs with tandem N 1methylated purines. The downfield shifted m 1 A + -C8 resonance characteristic of a syn conformation of m 1 A + in an m 1 A + -T Hoogsteen bp is indicated (7). HS corresponds to high salt (> 25 mM NaCl, Methods). In addition to NaCl, the buffers used for NMR measurements contained 15 mM sodium phosphate, 0.1 mM EDTA in a 90% H2O:10% D2O mixture. * denotes tentative or unknown assignments. Figure S12. NMR measurements probing cooperative formation of Hoogsteen bps. Shown in panels a, b and c are the duplexes with and without preformed Hoogsteen bps induced by N 1methyl adenine/guanine (m 1 A + /m 1 G) (left) along with off-resonance R1ρ relaxation dispersion profiles for the indicated nuclei (right). Sites which were probed for Hoogsteen bp formation using NMR are indicated with a box on the duplex. RF powers for R1ρ profiles are color-coded. Twostate individual/shared fits (Table S5, Materials and Methods) of the data to the Bloch-McConnell equations is shown as solid lines. Error bars for the R1ρ data were obtained from a Monte-Carlo based approach as described in the Materials and Methods. (d) Comparison of the population of the transient Hoogsteen bp (pi) obtained from NMR measurements in panels a, b and c, for samples with and without preformed Hoogsteen bps. Error bars for pi were obtained using a Monte-Carlo scheme as described in Methods. 'x' denotes a flat R1ρ profile from which pi could not be obtained. (e) Chemical structure of echinomycin (top) and structure of echinomycin bound DNA (bottom, PDB ID: 1XVN). Watson-Crick and Hoogsteen bps in the echinomycin-DNA complex are shown in gray and red, respectively, while echinomycin is shown using blue sticks. Also shown is the secondary structure of echinomycin bound DNA, with echinomycin indicated using blue dashed lines. (f and h) Secondary structures of the duplexes used for NMR measurements in the presence of bound echinomycin (blue dashes). (g and i) Overlay of the imino region of the 1 H 1D spectra (g, left) and 1 H 1D imino SOFAST spectra (i, left), and overlay of the aromatic region of the 2D [ 13 C, 1 H] HSQC spectra (right). The E12DNA-WC echinomycin complex shows NMR signatures (red circles) of cooperative formation of tandem A11-T6/A7-T10/A9-T8 Hoogsteen bps at low temperature (10 °C), that are absent at high temperature (25 °C). * denotes tentative or unknown assignments. R1ρ measurements in panels a, b and c were performed in a buffer containing 15 mM sodium phosphate, 25 mM sodium chloride, 0.1 mM EDTA at pH 5.4 (at 25 ºC in 100% D2O for panels a and b, and at 10 ºC 90% H2O:10% D2O for panel c). Echinomycin measurements were performed in a 90% H2O:10% D2O buffer containing 15 mM sodium phosphate, 125 mM sodium chloride, 0.1 mM EDTA, at the indicated pH. Figure S13. Measuring sequence-dependent thermodynamic preferences for Hoogsteen bp formation and base opening using delta-melt. (a, d, g) Duplexes used in the UV melting experiments for measuring sequence-dependent thermodynamic preferences. m 1 G, m 1 A and m 3 T (red) denote N 1 -methyl guanine, N 1 -methyl adenine, and N 3 -methyl thymine, respectively. All nucleotides are unlabeled and have deoxyribose sugars. (b, e, h) Bar plots of the energy for melting (G melt,25 C  at 25 °C) of wild-type Watson-Crick A-T/G-C/A-T (b, e and h, left) and modified m 1 A + -T/m 1 G-C + /A-m 3 T (b, e and h, right) bp containing duplexes as a function of sequence. (c, f, i) Bar plot of the thermodynamic propensity (G delta−melt,25 C  ( ) at 25 °C) for the formation of A-T (c) and G-C + (f) Hoogsteen, and A-T base opened states (i) obtained using delta-melt as a function of sequence. Buffer conditions are given in Tables S1-S2. Error bars for G melt  and G delta− melt  (i) were obtained by propagating the error in UV melting measurements as described in Methods. * denotes samples for which the melts were non-two-state, preventing extraction of melting energetics (Methods, Fig. S3). Figure S14. 1 H 1D spectra of the constructs used to measure sequence-dependent thermodynamic propensities to form Hoogsteen bps. Shown are overlays of the imino region of the 1 H 1D spectra of the DNA duplexes used for measuring sequence-dependent thermodynamic preferences for formation of (a) A-T and (b) G-C + Hoogsteen bps. Secondary structures of the constructs are given in Fig. S13 a, d. All measurements were done at pH 5.4 in a buffer containing 15mM sodium phosphate, 150mM NaCl and 0.1mM EDTA at 10 C. All the Watson-Crick G-C base pair containing constructs (panel b, black) display the number of imino peaks expected for duplex formation with expected secondary structures (Fig. S13d). The m 1 A + -T base pair containing constructs have proton signals around 9-11 ppm which correspond to T19-H3 and m 1 A6 + -H6a/b in an m 1 A6 + -T19 Hoogsteen bp. The m 1 G-C base pair containing constructs have proton signals around 9-11 ppm which correspond to downfield shifted amino protons for protonated cytosine, as expected for the formation of an m 1 G-C + Hoogsteen base pair. The lack of Hoogsteen bp signatures for scaf2_AAA m1AT , scaf2_CAA m1AT , scaf2_AAC m1AT , scaf2_CAC m1AT , scaf2_AAT m1AT , scaf2_CAT m1AT , scaf2_CGC m1GC , scaf2_GGC m1GC and scaf2_TGC m1GC could be due to exchange broadening. Figure S15. Thermodynamic preferences for formation of minor conformational states from delta-melt. Correlation plots (left) between the sequence-dependent thermodynamic preferences for A-T (a) and G-C + Hoogsteen (b) bp formation, and A-T base opening (c), and the melting energetics for corresponding unmodified (A-T/G-C/A-T) and modified (m 1 A + -T/m 1 G-C + /A-m 3 T) duplexes used in delta-melt (left). The Pearson correlation coefficient (r) is indicated in inset. Plots (right) of the thermodynamic preferences for A-T (a) and G-C + Hoogsteen (b) bp formation, and A-T base opening (c), as a function of sequence (5' to 3' direction). '_' corresponds to either the A/T/C/G bases. Error bars for the conformational preferences and melting energies were obtained by propagating the error in melting energies, and by performing multiple UV melting experiments, respectively, as described in Methods. Figure S16. Comparison of the entropy and enthalpy of conformational changes in nucleic acids from delta-melt and NMR. Shown in panels a, b and c are the secondary structure of the construct used for NMR measurements with the position of interest enclosed by a box, temperaturedependence of the NMR derived free energies for the conformational change, and comparison of the enthalpy and entropy values obtained from NMR and that obtained from UV melting measurements (Methods). Shown in panel d is a correlation plot of the enthalpy and entropy values for base opening in TBP DNA obtained using imino proton exchange NMR measurements in Chen et al. (1), and UV melting measurements in this study. Black lines denotes y=x. Error bars for the thermodynamic parameters obtained from NMR and UV melting experiments were obtained as described in Methods. Blue shaded regions in panels a, b and c denote the estimate of error of linear regression obtained as described in Methods. Buffer conditions for panels a, b and c are summarized in Tables S1 and S3. [NaCl] denotes the concentration of sodium chloride used in the buffer, Ct denotes the concentration of the double stranded/hairpin species at the start of the melting measurement, Tm is the melting temperature, H melt  and S melt  denote the enthalpy and entropy of unfolding, respectively, G melt,25 C  denotes the free energy of unfolding at 25 C. The modification used to measure the thermodynamic preferences is indicated in parentheses. m 1 A, m 1 G, m 3 T, m 6 2A, m 6 A, denote N 1 -methyl adenine, N 1 -methyl guanine, N 3 -methyl thymine, N 6,6 -dimethyl adenine and N 6methyl adenine, respectively. * indicates melts conducted in 90% H2O:10% D2O solvent. Secondary structures of samples are given in Fig. 3b, 4b, 5b, 6b and 7b, and Fig. S7b, S13a, S13d and S13g. Buffer compositions for each sample are indicated under the 'Buffer preparation' section of the methods. Errors for thermodynamic quantities were obtained based on multiple UV melting experiments, as described in Methods.
Melting parameters for scaf2_AGG m1GC and scaf2_TGG m1GC are not reported as these samples show deviations from 2-state melting behavior (Methods, Fig. S3). [NaCl] denotes the concentration of sodium and magnesium chloride used in the buffers, respectively, Ct denotes the concentration of the double stranded/hairpin species at the start of the melting measurement, Tm is the melting temperature, H melt  and S melt  denote the enthalpy and entropy of unfolding, respectively, G melt,25 C  denotes the free energy of unfolding at 25 C and m 6 A denotes N 6 -methyl adenine. The modification used to measure the thermodynamic preferences is indicated in parentheses. m 1 A, rA, rC, rT, m 1 G, m 3 T, m 6 2A, m 6 A, denote N 1 -methyl adenine, N 1 -methyl guanine, ribo adenine, ribo cytosine, ribo thymidine, N 3 -methyl thymine, N 6,6dimethyl adenine and N 6 -methyl adenine, respectively. * indicates melts conducted in 90% H2O:10% D2O solvent. Secondary structures of samples are given in Fig. 3b, 4b and 5b, and Fig. S13a, S13d and S13g. Buffer compositions for each sample are indicated under the 'Buffer preparation' section of the methods. Errors for thermodynamic quantities were obtained based on multiple UV melting experiments, as described in Methods. The melting parameters for scaf2_AAA Am3T , scaf2_AAG AT , scaf2_AAG m1AT , scaf2_AAG Am3T , scaf2_CAC AT , scaf2_GAC AT , scaf2_GAG Am3T , scaf2_TAG AT and scaf2_TAG m1AT are not reported as they show deviations from two-state melting behavior (Methods, Fig. S3). [NaCl] denotes the concentration of sodium chloride used in the buffers, respectively, H2O:D2O denotes the ratio of H2O and D2O in the buffer. rA, m 1 G, rG, m 6 A, m 1 A denote ribo adenosine, N 1methyl guanine, ribo guanine, N 6 -methyl adenine, N 1 -methyl adenosine, respectively. Secondary structures of the constructs are given in Fig. S4.             pi denotes the population of the i th minor conformation, kex the exchange rate (sum of forward and backward rate constants) between the major and i th minor conformation, i-Major = i -Major, where i and Major are the Larmor frequencies of the spin in the i th minor conformation and the major conformation, R1 and R2 are the longitudinal and transverse spin relaxation rate constants, respectively, and m 6 A denotes N 6 -methyl adenine. * denotes data for which  was fixed during fitting (Methods). Errors in the exchange parameters were obtained using a Monte-Carlo scheme as described in Methods.  0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.1, 0.2, 0.3, 0.5, 0.7, 1.0, 1.3, 1.6 0.002, 0.004, 0.006, 0.008, 0.01, 0.015, 0.02, 0.025, 0.03, 0.04, 0.05, 0.1,  0.2, 0.3, 0.5, 0.7, 1.0, 1.3   0.1   0.0, 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.008, 0.01, 0.015, 0.02, 0.03,  0.04, 0.05, 0.1, 0.2  Kinetic parameters obtained from imino proton exchange experiments.
[NH3] denotes the effective ammonia concentration in the buffer, R1w and R1n are the longitudinal relaxation rate constants of water and the thymine imino proton, respectively, E denotes the efficiency of inversion of the shaped pulse in the NMR experiment (Methods) and kex denotes the exchange rate of the thymine imino proton with water. Errors for R1n and kex were set to be equal to the standard error of the fit and were computed as described in Methods. Secondary structures of the constructs are given in Fig. S4. Errors of the exchange parameters were computed using a Monte-Carlo based approach as described in Methods. Buffer used for the measurements was composed of 10 mM sodium phosphate, 100 mM sodium chloride, 1 mM EDTA and 1 mM triethanolamine (TEOA) in 95% H2O:5% D2O. Sequence context refers to the context numbers in Fig. 9b in the main text. Secondary structure of samples are given in Fig. S4. Nuclei denotes the atoms on which R1 experiments were performed and [NaCl] denotes the concentration of sodium chloride used in the buffer for the measurements.

Discussion S1: Extracting melting energetics from UV melting experiments
In a typical UV melting experiment, a nucleic acid sample at a given concentration is slowly heated in a controlled manner to ensure the different conformational states are at equilibrium throughout the process (8). During the experiment, the absorbance of the sample, typically at 260 nm (A260), is recorded to obtain a melting curve (Fig. S17a). The baseline at low temperatures in the melting curve reflects temperature-dependent changes in the extinction coefficient of the folded (duplex/hairpin) species. Following the lower baseline, the melting curve (Fig. S17a) has a sigmoidal part during which the folded species gradually transitions into the unfolded singlestranded species. The baseline at high temperatures (Fig. S17a) then reflects temperaturedependent changes in the extinction coefficient of the unfolded single-stranded species.
The melting curves can be fit to a two-state model assuming only folded and unfolded single-stranded species are present in solution by least-squares minimization, to obtain the enthalpy (H melt  ) and entropy (S melt  ), and consequently the free energy (G melt ) of melting, in addition to the extinction coefficients for the unfolded single-stranded and folded species (9,10). It is important to note that accurate extraction of thermodynamic parameters from this 'curve fitting' approach requires well defined lower and upper baselines (~10-15 C) (8). Indeed, samples for which we do not have well defined baselines (for example, A6-DNA m1A16 at pH 6.8, A6-DNA m1G10 at pH 6.8, data for A-T base opening in Fig. S1) do have relatively larger error bars in the delta-melt correlation plots (Fig. 3c, S7c and 5c). Deviations from fitting to a two-state model ( Fig.  S3 and S17b) can indicate presence of alternative species in solution such as intra or intermolecularly folded single-strands (11)(12)(13). As an independent test of the two-state model to fit the data for nucleic acid duplexes, UV melting experiments typically are also performed as a function of sample concentration (Fig.  S17c) (8,14,15). The variation of the melting temperature (Tm) of the duplex sample, the temperature at which melting is half complete, with sample concentration can also be fit to obtain H melt  and S melt  . For duplex samples that melt in a two-state manner, the H melt  and S melt  values obtained from curve fitting at a given concentration or through concentration-dependent Tm measurements typically agree to within 15% (8,9,16).
Here it is important to note that agreement between the concentration-dependent and curve fitting approaches is a necessary but insufficient condition for two-state melting for duplexes (17). Validity of a two-state melting approximation can only be completely ascertained by supplementing melting curves with information from other techniques such as calorimetry, which can independently measure melting thermodynamics (16,18,19), or NMR (13,20,21) and analytical centrifugation (22,23), which can monitor structural changes during melting. In this study, we used the curve fitting approach to extract thermodynamic parameters for all samples, given its simplicity and high throughput, and the fact that two-state melting behavior has been independently validated for some of the duplexes in this study using NMR (A2-DNA and A6-DNA) (24).
Lastly, it should also be noted that fitting of the data using both curve fitting or concentration-dependent measurements as described above typically assumes a temperature invariant enthalpy and entropy of melting i.e., a heat capacity change of zero during melting (9,16). However, nucleic acid melting is well known to have a non-zero heat capacity change, which is generally attributed to the temperature-dependent unstacking when forming the single-stranded species (9,25,26). Interestingly, studies from the Turner lab have shown that the errors in H melt  and S melt  obtained by neglecting heat capacity changes mutually cancel one another, resulting in G melt  values that are most accurate near the sample Tm (15,25), even for samples that do not melt in a two-state manner (11,27). In other studies, they have also shown that the errors in G melt  on account of assuming a heat capacity of zero that accumulate on moving away from the Tm cancel one other when taking the difference in G melt  between two samples, resulting in accurate values for G melt  between two samples (27). Thus, even though our curve fitting based melting experiments cannot completely rule out non two-state behavior for samples for which the fit to the data is good, it is not expected to significantly affect the G melt  values and the delta-melt correlations.

Discussion S2: Offsets ( ) from delta-melt experiments
The offset c(i) is the difference in energetic cost to modify the single-stranded (ss) versus the i th minor conformational state i(WT), typically with a methyl group in the cases studied here. In this way, c(i) carries interesting information concerning the difference in thermodynamic reactivity between the single-stranded and the minor conformation. This could for example find utility in understanding reactivities of nucleic acids structures to chemical probing reagents (28) or in defining the damage susceptibility of different nucleic acid conformations. Note that the c(i) provides no information regarding kinetics, which could be important for the above processes.
Interestingly, for m 1 A + -T bps, c(i) ~0.3 kcal/mol (Fig. 3c), suggesting that the free energy of N 1 -methylation of a single-stranded adenine, and an adenine in an A-T Hoogsteen bp are similar to each other. This supports findings from a recent study indicating that the A-T Hoogsteen bps increase the susceptibility of A-N1 to alkylation damage relative to Watson-Crick bps (29). Similar results are obtained for G-C + Hoogsteen bps, with c(i) ~-0.1 kcal/mol (Fig. S7c), suggesting that the free energy of N 1 -methylation of a single-stranded guanine, and a guanine in a G-C + Hoogsteen bp are similar to each other.
Interestingly, for C-T mismatches c(i) ~ -0.6 kcal/mol (Fig. 4c) is slightly negative, suggesting that it is more energetically favorable to replace an A to a C in single-stranded DNA, relative to an A-T Hoogsteen bp in duplex DNA, while that for T-T mismatches c(i) ~-0.2 kcal/mol (Fig. 4d) is close to zero, suggesting that A to T substitutions in A-T Hoogsteen bps and singlestrands are iso-energetic.
For A-T base opening, c(i) ~2.4 kcal/mol (Fig. 5c), suggesting that the free energy of N 3methylation of T in an open A-T bp is much more favorable than the methylation of T when it is single-stranded, presumably due to favorable stacking interactions of the methyl within the context of the open bp in the duplex.
However, we cannot rule out that the large magnitude of c(i) arises from over-estimation of the base catalyst accessibility factor . Although is typically assumed to be 1 when interpreting imino proton exchange data (30), if was truly a smaller number than one, it would lead to a reduction in ΔG conf ○ (i) measured by NMR imino exchange, leading to a decrease in c(i)(Methods). Thus, given that m 1 A + , m 1 G and m 3 T occur naturally as forms of damage (31), delta-melt provides insights into the relative thermodynamic preferences of single-versus double-stranded DNA to undergo damage.
For isomerization of the m 6 A N 6 -methyl amino group, c(i) ~ 0.7 kcal/mol (Fig. 6c), implying that N 6 -methylation of syn m 6 A in single-strand RNA is less thermodynamically favorable relative to N 6 -methylation of an m 6 A(syn)-U bp in duplex RNA, potentially due to stacking interactions of the methyl in the duplex context.

Discussion S3: Rationalizing sequence-dependent stabilities of Watson-Crick and Hoogsteen bps obtained from delta-melt with prior literature
The delta-melt data (Fig. 8b, Fig. S15) suggests that sequence-dependencies of the energies of the A-T Watson-Crick and G-C + Hoogsteen bps dominate variations in the thermodynamic preferences for formation of A-T and G-C + Hoogsteen bps, respectively. This is in contrast to earlier observations by Alvey et al suggesting that preferences for both A-T and G-C + Hoogsteen bp formation are dominated by variations in the stability of the Watson-Crick bps. This observation was based on an inverse correlation of the thermodynamic propensities for forming Hoogsteen bps with the stability of the Watson-Crick bp computed using nearest neighbor thermodynamic parameters.
This discrepancy with Alvey et al for the results for G-C + Hoogsteen bps can be rationalized based on the observation that the preferences in the prior study were averaged over different trinucleotide steps to compute an averaged preference for a dinucleotide step, while such averaging was not performed in this case, and because of differences in buffer conditions between nearest neighbor measurements and those used in this study.

Discussion S4: Correlating cancer signatures with thermodynamic preferences from deltamelt
Analysis of cancer genomes has shown that it is possible to decompose the set of all mutations in a cancerous genome into contributions from distinct mutational fingerprints or signatures, which are proposed to arise from different mutational processes acting on DNA (32). For many of these signatures, the underlying causative biological processes remain unknown.
Interestingly, we found a good correlation between the probabilities for formation of A-T Hoogsteen bps obtained from the thermodynamic preferences measured using delta-melt (Fig. 8b,  Methods), and probabilities of T>A mutations corresponding to signature 17A (SBS17A, Fig. S18b, Methods), whose etiology is unknown, though it has been proposed that it could arise from 5-fluorouracil exposure (33) and/or oxidative damage to DNA (34). Transient A-T Hoogsteen bps which expose the Watson-Crick face of adenine to the solvent could be damaged by a damaging agent, resulting in a DNA lesion (Fig. S18c). If left unrepaired, this lesion can be replicated by translesion synthesis polymerases such as pol iota, which can misincorporate an adenine opposite the lesion, leading to a T>A mutation (Fig. S18c). Thus, the extent of this mutation that occurs would be proportional to the amount of lesion formed, which in turn would be proportional to the population of the transient Hoogsteen bp, resulting in the correlation we observe (Fig. S18b). Indeed, it has been shown that pol iota can misincorporate A opposite lesions on the Watson-Crick face such as m 1 A + (35) in-vitro, leading to a T>A mutation. Additional experiments are required to test this hypothesis for the origin of T>A mutations in Signature 17A. As a control, a weaker correlation is observed for T>A mutations in Signature 8 (SBS8), whose etiology is also unknown (Fig. S18b). (i) values from delta-melt show that in some cases, the agreement is better than others (Fig. S16). This could be due to systematic errors in estimation of enthalpies and entropies in UV melting measurements due to the assumption of a heat capacity of zero i.e., neglecting the temperature-dependence of the enthalpy and entropy (15). These errors are compensatory in nature such that estimate of free energies from UV melting is accurate (15). Nevertheless, we cannot rule out that deviations in enthalpies and entropies from delta-melt and

Unlabeled oligonucleotides
In what follows we use "lb" inside a bracket following the construct name to refer to specific duplexes (see Fig. S4) in which one or both strands are isotopically labeled, and isotopically labeled hairpins. For example, A6-DNA m1A16 (s2lb), is a version of the A6-DNA m1A16 duplex with a specific labelling scheme defined in Fig. S4. Constructs without "lb" in the name are unlabeled. Secondary structures and labeling schemes of all constructs used for NMR measurements are given in Fig.  S4.
The m 1 G and m 3 T modified strands in the scaf2 series of DNA duplexes and in the A2-DNA m1G10 and A6-DNA m3T6 duplexes, the rNTP modified single-strands in the A6-DNA rA16 , A6-DNA rC16 , A6-DNA rT16 duplexes, and the unlabeled RNA single-strands in A6-RNA m6A16 (m 6 A16 C2,C8 lb), A6-RNA m6A16 , A6-RNA m62A16 , dsGGACU m6A6 and dsGGACU m62A6 were synthesized in-house using a MerMade 6 Oligo Synthesizer. Standard RNA phosphoramidites (nac-rA, n-ac-rG, n-ac-rC, rU, rT, rm 6 A and rm 6 2A, Chemgenes) and DNA phosphoramidites (n-ibu-G, n-bz-A, n-ac-C, T, m 3 T and n,n-dmf-m 1 G, Chemgenes), and columns (1000 Å from Bioautomation) were used with a coupling time of 6-12 min (RNA) and 1 min (DNA), with the final 5′-dimethoxy trityl (DMT) group retained during synthesis. The oligonucleotides were cleaved from the supports (1 μmol) using ∼1 ml of AMA (1:1 ratio of ammonium hydroxide and methylamine) for 30 min and deprotected at room temperature for 2 hours. The m 1 G and m 3 T containing DNA samples were then purified using Glen-Pak DNA cartridges and ethanol precipitated, while all the other samples were dried under airflow to obtain oligonucleotide crystals. They were then dissolved in 115 μl DMSO, 60 μl TEA and 75 μl TEA.3HF and heated at 65°C for 2.5 h for 2′-O deprotection. The samples were then neutralized using 1.75 ml of Glen-Pak RNA quenching buffer, loaded onto Glen-Pak RNA cartridges for purification and were subsequently ethanol precipitated. The rG modified single-strand comprising the A6-DNA rG10 duplex used for UV melting measurements was synthesized above as described for the rA modified single-strand in A6-DNA rA16 , while that comprising the A6-DNA rG10 (s1lb) duplex used for NMR measurements was purchased from IDT.
The m 1 A + modified strands in the scaf2 series of DNA duplexes were also synthesized in house using a Mermade-6 Oligo Synthesizer. UltraMild DNA phosphoramidites (T, n-pac-C, ntbpac-G, n-pac-A, n-fmoc-m 1 A) and Ultramild Cap A (Glen Research), and columns (1000 Å from Bioautomation) were used with a coupling time of 1 min, with the final 5′-dimethoxy trityl (DMT) group retained during synthesis. The powdered supports were then incubated with ~2 mL of concentrated NH4OH for 1 hour and room temperature for cleavage of oligonucleotides from the support. The supports were spun down and the supernatant was collected in separate tubes. The remaining support was washed with ~0.5 mL of concentrated NH4OH, which was pooled together with the supernatant post spinning down, to result in a net volume of ~2 mL of the cleaved oligo in NH4OH. The oligonucleotides were then heated for 18 hours at 37 C for base deprotection. The oligo solutions were then dried under air flow to bring the volume to ~1mL following which they were purified with Glen Pak DNA cartridges and ethanol precipitated. 13 C/ 15 N-labeled oligonucleotides Uniformly 13 C/ 15 N isotope labeled DNA strands comprising duplexes A6-DNA(ulb), A6-DNA(s1lb), A6-DNA(s2lb), A6-DNA m1A16 (s2lb), A6-DNA m1G10 (s1lb), A6-DNA rG10 (s1lb) and AcDNA(ulb), and residue-type (G and T or C and A labeled on either strand) DNA strands comprising duplexes A2-DNA(ulb) and A2-DNA(s2lb) were synthesized using an in vitro primer extension approach (39) with a template DNA (IDT), Klenow fragment DNA polymerase (New England Biolabs), uniformly 13 C, 15 N-labeled deoxynucleotide triphosphates (dNTPs, Silantes) and/or unlabeled dNTPs (Thermo Fisher Scientific). The reaction mixture was centrifuged to remove excess pyrophosphate, and then subsequently concentrated to 1.5 mL using a 3 kDa molecular weight cutoff centrifugal concentrator (Millipore Sigma). 1.5 mL of a formamide based loading dye was then added to the reaction mixture, which was then heated at 95 °C for 5 min for denaturation. The mixture was then loaded onto a denaturing gel (20% 29:1 polyacrylamide/8M urea in TBE buffer) for resolution of the target oligonucleotide from other nucleic acid species. Gel bands corresponding to the pure target single-strands were identified by UV-shadowing and subject to electroelution (Whatman, GE Healthcare, in TAE buffer) followed by ethanol precipitation. Careful optimization of the NTP concentrations, in particular ATP, and that of Mg 2+ during primer extension was seen to be necessary to avoid spurious NTP addition to form dangling ends in the resulting oligonucleotides.
Resonance assignments for A6-DNA, A6-DNA m1A16 , A6-DNA m1G10 , A6-DNA rA16 , A6-DNA rG10 , A2-DNA, AcDNA, hpGGACU m6A6 , G-DNA, TAR, E12DNA-HG and E12DNA-WC were obtained from prior studies (43)(44)(45)(46)(47)(48) (Fig. S4). Assignments for A6-RNA m6A16 will be published in a subsequent study (2). These studies also show that the constructs fold into their expected secondary structures as given in Fig. S4. Note that the C1'-H1' assignments for T5 and T6 were incorrectly swapped in assignments of A6-DNA, and consequently in those of A6-DNA m1A16 , A6-DNA m1G10 , A6-DNA rA16 , A6-DNA m1rA16 , A6-DNA rG10 , A6-DNA m1rG10 in prior studies (4,43,44,(49)(50)(51). Nevertheless, the conclusions of these prior studies are not affected by the assignment swap. The assignment swap has been corrected in the assignments in this study and in the BMRB entries 30254 and 30255. Resonance assignments for A6-DNA m3T9 were obtained using 2D [ 1 H, 1 GC and scaf2_TGC GC were easily obtained since they were site-specifically labeled. All the NMR spectra were processed using NMRpipe (52) and analyzed using SPARKY (T. D. Goddard and D. G. Kneller, SPARKY 3, University of California, San Francisco). 13 C/ 15 N R1ρ relaxation dispersion Off-resonance 13 C/ 15 N R1ρ relaxation dispersion (RD) experiments were implemented using a 1D selective excitation scheme as described in prior studies (50,53,54). The spin-lock power (ω1/2π) used ranged from 100 to 1000 Hz, while the offsets used ranged from 10 and 3.5 times the spin-lock power for 13 C and 15 N experiments, respectively (Table S4). For each resonance, six to ten delay times were selected during the relaxation period with maximum duration up to 60 ms and 150 ms for 13 C and 15 N, respectively. The experimental conditions for all the 13 C/ 15 N R1ρ RD experiments (temperature, magnetic field, solvent) are summarized in Table S3.

Analysis of R1ρ data
The R1ρ data was analyzed as described previously (55). Briefly, 1D peak intensities as a function of delay times extracted using NMRPipe (52) were fitted to a mono-exponential decay to obtain the R1ρ value for the different spin-lock power and offset combinations. The error in R1ρ was estimated using a Monte Carlo procedure as described previously (56). Exchange parameters of interest, such as the population of the i th minor conformation (pi), the exchange rate between the major and i th minor conformation (kex = k1 + k-1, in which k1 and k-1 are the forward and backward rate constants, respectively), the chemical shift difference between the i th minor and the major conformations (Δωi-Major = ωi -ωMajor, in which ωi and ωMajor are the chemical shifts of the nucleus in the i th minor and the major conformations, respectively) were then extracted by fitting the R1ρ data for a given nucleus to a two-state exchange model using the Bloch-McConnell equations. The validity of a two-state model to analyze the R1ρ data for Hoogsteen bp formation and N 6 -methyl amino rotation has been extensively validated based on prior studies (2-4, 43, 44, 50, 51). Owing to the presence of an equilibration delay (5 ms) in the pulse sequences (50,53), initial magnetization at the start of the Bloch-McConnell simulations was assumed to be equilibrated between the major and minor conformations. Combined fits of the R1ρ data for multiple nuclei were performed by sharing pi and kex. Owing to the weak nature of the RD profiles (see below) for G6-C1' and C8 in scaf2_TGC GC at pH 5.4 150mM NaCl (high salt, >25mM, HS) and 40 C, the values of i-Major obtained when fitting both data sets with shared pi and kex were seen to deviate significantly from values determined under low salt (25 mM, 30 C) conditions, where RD profiles were stronger and more well defined (Fig. S5). Thus, the high salt data set at 40 C was fit while fixing i-Major for G6-C1' and G6-C8 to the values obtained from RD measurements under low salt (25 mM, 30 C) conditions (Table S5).
affect the extracted exchange parameters for most of the RD profiles measured in this study as they are strong (fitted Rex values of > ~4 s -1 ), and given the small magnitude of the passive chemical shift changes (i-Major < ~0.5 ppm). Nevertheless, nuclei for which the RD profiles are intrinsically weak, with fitted Rex values of < ~4 s -1 (G10-C1' in A6-DNA at pH 6.8 25 C, A16-C8 in A2-DNA at pH 6.8 25 C, and G6-C1' and G6-C8 in scaf2_TGC GC at pH 5.4HS 30 C and 40 C) are likely to be influenced to a greater extent by such passive exchange contributions relative to nuclei with stronger RD profiles. These passive contributions could also cause deviations from the true exchange parameters for the active exchange when fitting the data assuming a two-state model. However, given the weak nature of the RD profiles, it is difficult to robustly fit them to a three-state exchange model to extract exchange parameters for both the active and passive exchange. Thus, we have fit these weak RD profiles (G10-C1' in A6-DNA at pH 6.8 25 C, A16-C8 in A2-DNA at pH 6.8 25 C, and G6-C1' and G6-C8 in scaf2_TGC GC at pH 5.4HS 30 C and 40 C) assuming a twostate exchange model and suggest that the fitted exchange parameters be interpreted with caution, and have highlighted these weak data sets using open symbols and * in Fig. 3c, 4c, 4d, S7c, and Fig. 9b.
The uncertainty in the exchange parameters was obtained using a Monte-Carlo scheme as described previously (58). All the fitting parameters have been summarized in Table S5. The sensitivity of the fit to the R1ρ data to changes in pi was examined by computing the reduced χ 2 while fixing pi to a range of different values (Fig. S6). Off-resonance R1ρ profiles ( Fig. 9b and Fig.  S5) were generated by plotting (R2 + Rex) = (R1ρ -R1cos 2 )/sin 2 , where  is the angle between the effective field of the observed resonance and the z-axis, as a function of OBS = OBS -RF, in which OBS is the Larmor frequency of the observed resonance and RF is the angular frequency of the applied spin-lock. Errors in (R2 + Rex) were determined by propagating the error in R1ρ obtained as described above.
Alignment of initial magnetization during the Bloch-McConnell fitting was performed based on the kex/i-Major ratio as described previously (56). Interestingly, RD profiles for A21-C1' in A6-DNA at 25C and 30 C, G10-C1' in A6-DNA at pH 6.8 25 C, and G6-C1' and C8 in scaf2_TGC GC pH 5.4HS 30 C and 40 C could be better fit with a highly populated ES on the order of a few percent in slow exchange, while assuming alignment along the ground state effective field. Nevertheless, these highly populated solutions were excluded based on the lower populations measured previously for a wide range of sequence contexts in DNA (in the case of A21-C1' in A6-DNA at 25 and 30 C)(3), and alternative measurements at pH 5.4 (in the case of G10-C1' in A6-DNA at pH 6.8 25 C) and at low salt (G6-C1' and C8 in scaf2_TGC GC pH 5.4 30 and 40 C) wherein the exchange parameters were robust (Fig. S6). Thus, the alignment of magnetization for A21-C1' in A6-DNA at 25 and 30 C, G6-C1' and C8 in scaf2_TGC GC pH 5.4HS 30 C and 40 C was fixed to be along the effective field of the population averaged state when plotting the reduced χ 2 profiles as a function of pi (Fig. S6). 13 C CEST 13 C CEST experiments on the aromatic C8/C2 and C1' carbons were carried out using a pulse sequence employing a selective excitation scheme in a 1D manner, as described previously (24,59,60). The 13 C CEST experiments on the methyl carbon in hpGGACU m6A6 (m 6 A6 C10 lb) were carried out in a 2D mode using a pulse sequence derived from prior 13 C CEST pulse sequences (2,59,61).
The spin-lock power ranged from 10 to 70 Hz and from 10 to 50 Hz, respectively. The list of spin-lock power offset combinations used for CEST experiments can be found in Table S4. A relaxation time of 200 ms was used for all CEST experiments. The experimental conditions for all the 13 C/ 15 N CEST experiments (temperature, magnetic field, solvent) have been summarized in Table S3.

Analysis of CEST data
The analysis of CEST data was performed as described previously (24,60). Briefly, 1D peak intensities were obtained in a manner similar to that for R1ρ. All intensities at a given radiofrequency (RF) power were normalized by the average of the intensities over the triplicate CEST measurements with zero relaxation delay using the same RF power, to obtain normalized CEST profiles. Normalized CEST profiles were plotted as a function of offset  = RF -OBS, in which OBS is the Larmor frequency of the observed resonance and RF is the angular frequency of the applied spin-lock (Fig. S5). The error in the intensity for each RF power was obtained as the standard deviation of triplicate experiments with zero relaxation delay and same RF power. Exchange parameters of interest (pi, kex, Δωi-Major) were then extracted by fitting the normalized CEST profiles to a two-state exchange model using the Bloch-McConnell equations. Combined fits of the CEST data for multiple nuclei were performed by sharing pi and kex.
Treatment of spin-lock inhomogeneity and alignment of the initial magnetization during CEST fitting was performed as described previously (60). Only GS magnetization was considered to be present at the start of the relaxation delay during CEST fitting for the C2/C8/C1' and imino nitrogen spins, owing to the absence of the equilibration delay in the pulse sequence. GS and ES magnetization was considered to be equilibrated while fitting the methyl CEST data on hpGGACU m6A6 (m 6 A6 C10 lb) as the pulse sequence employs hard pulses to excite spins (2). The sensitivity of the fit to the CEST data to changes in pi was examined by computing the reduced χ 2 while fixing pi to a range of different values (Fig. S6). All the fitting parameters from CEST experiments have been summarized in Table S5. The errors of all the fitting parameters were estimated using 100 Monte Carlo iterations as described previously (24).

Imino 1 H exchange
The kinetics of base opening were determined using a combination of experiments including a saturation recovery experiment to measure water proton R1 (R1w) and a magnetization transfer experiment to measure the exchange rate of the imino proton with water, as described previously (36). The relaxation delay times for measuring water proton R1 were 0.0, 0.4, 0.8, 1.  Table S6.

Analysis of imino 1 H exchange data
The net exchange rate (kex) between imino and water protons can be measured by fitting the 1D imino 1 H peak volume at each delay time (t) in the magnetization transfer experiment to Equation 2 shown below, where W(t) is the imino 1 H peak volume as a function of relaxation delay time t, W0 is the initial imino 1 H peak volume at zero delay, W(t)/W0 is the normalized peak volume, E is the efficiency of the pulse for inverting water, R1n represents the summation of imino 1 H R1 and kex. In the above equation, R1w and E are fixed parameters while kex and R1 are fitting parameters. The error of all the fitting parameters was set to be equal to the standard fitting error, obtained as the square root of the diagonal elements of the covariance matrix of the fitting parameters. We also examined the sensitivity of the fitting to changes in the fitting parameter kex by fixing kex to a range of values and plotting the residual sum of squares (RSS) as a function of kex (Fig. S9b). All the fitting parameters have been summarized in Table S7. The efficiency of the inversion pulse was computed as follows, E = 1 − W inv W eq (4) where Winv and Weq are the peak volumes of the water proton with and without applying the inversion pulse in the magnetization exchange experiment (with zero relaxation delay and no water suppression), respectively.
To obtain the population pi of the base open state, the net kex between imino proton and water was measured in the presence of different effective ammonia concentrations (20 mM, 40 mM, 100 mM and 150 mM), and the inverse of kex ( =1/kex) was linearly fit to the inverse of the effective ammonia concentration using Equation 5, where 0 is the inverse of the base opening rate (lifetime of the closed state), is the base catalyst accessibility factor which is generally assumed to be 1 (62), [NH3] is the effective ammonia concentration, Kdiss is the bp dissociation constant defined by, diss = i 1 − i (6) and kB is the rate constant for exchange catalysis which is given by, B = coll 1 + 10 pK a Nu −pK a NH3 (7) where kcoll is the bi-molecular collision rate constant between the imino proton and ammonia in the open state, and pK a Nu and pK a NH3 are the pKa for the imino proton in the open state and ammonia, respectively. Under the conditions used in our study kB is equal to 2.5x10 8 M -1 s -1 at 25 °C (62).
Given the errors obtained for kex based on the covariance matrix as described above, Monte-Carlo simulations were performed to compute the errors in Kdiss. In particular, 1/kex at each ammonia concentration was sampled from a gaussian with mean equal to the average fit 1/kex value and standard deviation equal to the error in 1/kex. The sampling was repeated for all ammonia concentrations for a given iteration, and the variation of 1/kex vs. 1/[NH3] was fit to compute a Kdiss value. The procedure was repeated for 10,000 iterations and the mean and standard deviation of the resultant Kdiss distribution were set to be equal to the mean and error of the fitted Kdiss. The region spanned by the family of straight lines thus obtained is colored blue in Fig. S9c. The error in pi was determined by propagating the error in Kdiss (Table S8).
To benchmark our implementation of the imino 1 H exchange measurements in this study, we compared our measurements on T6 in G-DNA at 25 °C to a prior study (62) and obtained a consistent free energy for opening (Table S8). pi values for T3, T5, T16, T17, T18, T19 and T21 in TBP-DNA at 15 °C were obtained from a prior study (1).
The melting temperature (Tm) and standard enthalpy change of melting (H melt,WT ○ or H melt,Mod ○ (i)), respectively, were obtained by fitting the absorbance at 260 nm (A260) from the optical melting experiment to a two-state all-or-none model using Equation 8, A 260 = ((( melt * T) + melt ) * melt ) + ((( fold * T) + fold ) × (1 − melt )) (8) where melt , melt , fold and fold are coefficients describing the temperature-dependence of the extinction coefficients for the melted and folded species, respectively, and pmelt is the population of the melted duplex/hairpin species. pmelt for a WT duplex and hairpin are given by the following expressions (analogous expressions can also be written for melting of the modified nucleic acid Mod by replacing WT by Mod), respectively, where Tm is the melting temperature (K), T is the temperature (K), and R is the gas constant (kcal/mol/K). It should be noted that pmelt is commonly denoted by the symbol  in the literature (9,63). where CT is total concentration of the duplex/hairpin. Using the obtained enthalpies and entropies, the free energy of melting was then computed as follows, For UV melting profiles of scaf2_AGG m1GC , scaf2_TGG m1GC , scaf2_AAG AT , scaf2_AAG m1AT , scaf2_AAG Am3T , scaf2_CAC AT , scaf2_GAC AT , scaf2_TAG AT , scaf2_TAG m1AT , scaf2_AAA Am3T and scaf2_GAG Am3T (Fig. S3), minor and reproducible deviations from two-state fits were observed in the lower/upper baselines which could potentially arise from the existence of multiple folded species in equilibrium with each other (11,64). Due to the lack of knowledge about alternative folded species for the above samples, we have chosen not to fit the UV curves for them. Understanding the conformational dynamics that gives rise to such minor deviations and how that affects the interpretation of the melting data will be the subject of future studies.  (27) The Coopmelt term was determined using delta-melt by using duplexes containing N 1methylated purines at tandem bps, and their singly methylated counterparts (Fig. S11a). Errors in Coopmelt were obtained by propagating the errors in ΔΔG melt ○ (i) values obtained as described above.
True estimation of Hoogsteen cooperativity requires knowledge of Coopoffset. However, if we assume the offset term of double Hoogsteen c(HG1 + 2) and triple Hoogsteen c(HG1 + 2 + 3) is small, in a manner analogous to single Hoogsteen ( Fig. 3c and S7c, Discussion S2), or that the offset for tandem Hoogsteen is the sum of offsets for single Hoogsteen bps, we will approximately have ΔG coop ○ ~ Coop melt (28) Our measurements (Fig. 7, Appendix S7) indicate that Hoogsteen base pairs form cooperatively in DNA. It is important to consider the influence of cooperativity while interpreting the delta-melt measurements for measuring energetics of Hoogsteen base pair formation. Here, it is important to note that delta-melt assumes that the modification mimics the minor conformation of the wild-type molecule both at the base pair of interest, and includes conformational changes (such as flipping to Hoogsteen) of the neighboring base pairs required to accommodate the base pair of interest. Thus, the energetics for Hoogsteen bp formation obtained from delta-melt also include contributions to change the conformations of the neighbors to accommodate formation of the Hoogsteen bp. The values obtained for Hoogsteen cooperativity (Fig. 7, Appendix S7) indicate that the populations of paired species in which the bps neighboring the N 1 -methylation site are Hoogsteen are <10% of that of the species in which they are Watson-Crick during the course of the melts, suggesting that their contributions to the melting curves are likely to be small. Thus, in practice, the energetics obtained from delta-melt correspond to the flipping of a given base pair to Hoogsteen, while its neighbors are Watson-Crick.