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Thermal stability of DNA
Introduction
Materials And Methods
DNA specimens
Equilibrium melting curves
Solvent
van't Hoff enthalpies
Results
Domain stability and Tij in the standard buffer (0.075 M Na+)
Effects of (dA@dT)-tracts
Loop energetics
Transition enthalpies
Dependence on [Na+]
Statistical thermodynamic analysis
Discussion
Acknowledgements
References
Corrigenda
Thermal stability of DNA
ABSTRACT
INTRODUCTION
Differences in energy between stacked G@C and A@T base pairs in polymeric DNAs lead to complex melting profiles (1) that can be observed with high precision by optical methods (2,3). The many sub-transitions in such profiles represent linked temperature standards that provide a high degree of precision for the evaluation of thermodynamic quantities associated with the stability of DNA. We have been involved in carrying out recursive statistical mechanical evaluations of thermodynamic quantities, primarily Tij and [Delta]Hij, for hydrogen bonding and stacking of the 10 neighbor pairs ij in model polymeric sequences. Accurate calorimetric [Delta]Hij have been a special challenge, however, as has been the reconciliation of [Delta]Hij from oligomeric specimens in high counter-ion concentrations (4-7) to enthalpies from polymeric specimens (8-13), indicating a constant transition entropy (8,12,13). Calorimetric enthalpies have been considerably lower in accuracy than Tij (14-19), so that errors in non-calorimetric [Delta]Hij determined from Tij, where [Delta]Hij = Tij@[Delta]S appear small. The magnitudes and order of [Delta]Hij determined in this way differ from calorimetric values, although they lead to better agreement between experimental and calculated curves over the range 50-100°C (17).
Recent results obtained by Chan et al. on an oligomeric specimen with four equi-spaced (dA@dT)-tracts, further complicates the evaluation of thermodynamic quantities (20,21). They find global melting of their specimen to be preceded by a modest two-state transition below 37°C, accompanied by an enthalpic change. These results were interpreted as reflecting a pre-melting structural transition of the (dA@dT)-tracts, from a low-temperature conformational state with bifurcated three-centered hydrogen bonds to a standard B-form at higher temperatures.
This raises questions about (i) the constant entropy assumption; (ii) the applicability of oligomeric [Delta]Hij to polymeric systems; (iii) the nearest neighbor model; (iv) the precise states of melting; (v) experimental errors and (vi) the different ionic strength conditions used in the evaluation of thermodynamic quantities. The goal of these studies was to respond to some of these questions, revisiting the question of DNA stability, with improved values for Tij and [Delta]Hij from helix[lrarr2]coil transition equilibria, including an examination of the dependence of TAA on (dA@dT)-tract lengths. Accuracies of our earlier Tij would undoubtedly have been higher with specimens of greater bias in neighbor frequencies, providing a more sensitive test of thermodynamic additivity. Neighbor-pair stabilities have been measured in this study with model synthetic domains in polymeric specimens, synthesized with biased neighbor pair frequencies and installed in a modified pBR322 plasmid for cloning purposes. The focus has been limited to the dissociation of helix ends and internal domains, since these two classes of structural transition involve the parameter most associated with all five classes that occur during melting (22).
MATERIALS AND METHODS
DNA specimens
Figure 1. Sequence map of the pN/MCS plasmids used in this study. A 54 bp multiple cloning sequence (MCS) containing recognition sequences for 10 restriction enzymes, was installed at the unique NruI locus of pBR322, between two (G+C)-rich domains denoted by the heavy lines. Tandemly repetitive sequences described in Table 1a and b were then inserted at the SmaI locus of the MCS. The principal specimens used in these studies were plasmid DNAs constructed in this laboratory as previously described (23) by established procedures (24). These plasmids contain a repetitive sequence at a site in the plasmid exhibiting favorable energetic characteristics. As shown in Figure 
In the preparation of oligomer repeats, the residues of N-base oligonucleotides were first paired with the residues of complementary overlaps of (N/2)-base oligonucleotides, and then ligated using T4 DNA ligase to generate tandemly repeating duplexes of 100-1000 bp. These duplexes were size fractionated on low-melting agarose, and fragments >200 bp removed from the gel and made blunt with Klenow enzyme. The resulting DNA was ligated into pN/MCS at the SmaI locus of the MCS. In preparation for insertion of the repetitive elements, pN/MCS plasmid was restricted at the unique SmaI site and digested with bacterial alkaline phosphatase to remove the terminal 5[prime] phosphate groups to prevent vector recircularization during the ligation step. The phosphatase was inactivated by the addition of SDS, followed by phenol extraction. Plasmid DNA was then precipitated and ligated to the repetitive DNA at an insert:vector mole ratio of >10:1 using T4 DNA ligase.
Circular recombinant plasmids were introduced into Escherichia coli HB101 or SURE[trade] cells, and transformed cells were selected on agar containing ampicillin. Cells containing plasmid were grown in 1 l of ampicillin-selective LB broth, and amplified by the addition of chloramphenicol. Cells were lysed in alkaline SDS, and the plasmid precipitated from the lysate in isopropanol. Residual contaminates in crude plasmid DNA lead to non-linear baselines in the high resolution melting curves, and could not be removed by any of the convenient filtration procedures that are commercially available. Two successive CsCl gradients were required to achieve a suitable state of purity. The repetitive inserts were checked by double-stranded sequencing over the insert region by the dideoxy chain-termination method (25), as well as by electrophoretic mobility.
Equilibrium melting curves
High resolution derivative melting curves were obtained by the difference-approximation method (26,27), with a modified double-beam ratio-recording spectrophotometer (Cary). The finite difference method involves the approximation of a derivative dAl(nm)/dT by its differential [Delta]Al(nm)/[Delta]T, with analytical reconstruction of the true derivative achieved as previously described (26). Temperatures were ramped at 6°C/h, which has been shown to provide equilibrium melting of most domains. Slower rates lead to a significant increase in thermal degradation, particularly of single-stranded coil regions (28). For this reason, specimens were never re-melted; instead, replicate experiments were always carried out on fresh aliquots of the same or new preparations. The distribution of (G+C) compositions and sizes of domains responsible for sub-transitions were obtained by spectral decomposition of melting curves obtained at 260, 270 and 282 nm, where the ratios of derivative extinction coefficients for A@T and G@C pairs, d[epsis]A@T/d[epsis]G@C, are 4.31, 1.00 and 0.120, respectively (27).
Approximately 1 µg of commercial poly(dA@dT) (Sigma) of mean length >20 000 bp was added to all specimens before melting, to serve as secondary standard of solvent conditions. The complete melting of this synthetic DNA takes place within $0.07°, with melting temperatures given by the relationship:
 |
1 |
Solvent
The solvent consisted of the specified [Na+] in the form of NaCl, plus 0.005 M Na-cacodylate and 0.2 mM Na-EDTA (pH 6.85).
van't Hoff enthalpies
Enthalpies associated with conformational changes in DNA were determined by non-linear regression analysis of first derivative van't Hoff transition equilibria (23) over the entire transition regions of isolated curves for insert sequences, as previously described. The advantage of this method is its high degree of sensitivity, where excellent results can be obtained on <50 µg DNA. The disadvantage is that accurate knowledge of the states of equilibria are determined indirectly, which can be problematic. Denaturation is a complex piecemeal process, with sub-transitions spread over a 15-20° range, emanating from micro-domains of a few base pairs to macro-domains of >500. All have different stabilities and many overlap one another (17), and therefore it can be difficult to determine the states of equilibria for individual transitions. The difficulty can be circumvented, however, by constructing plasmid DNAs, such as the pN/MCS-series described above, that harbor large, discrete domains of sharply-melting oligonucleotide repetitive elements. The equilibrium denaturation of these domains can be isolated from the background contributions of nearby transitions by subtracting denaturation profiles of plasmids without the insert from those that have it (17,23).
RESULTS
Domain stability and Tij in the standard buffer (0.075 M Na+)
Dissociation of DNA takes place in a piecemeal fashion with increasing temperature. Helical segments or domains of variable sizes dissociate in a cooperative fashion by one of five types of sub-transition depending on where the domain occurs (22). Illustrative 270 nm curves of pN/MCS-11 and pN/MCS-12 DNA in the standard buffer are shown in Figure
Figure 2. Illustrative melting curves of pN/MCS11 and pN/MCS12 DNA. These curves were obtained from the derivative of the loss of hypochromicity at 270 nm; in the standard buffer: 0.005 M Na-cacodylate, 0.2 mM Na-EDTA, 0.074 M NaCl, pH 6.85. The insert sequence in these plasmids was [AAGTTGAACAAAT]NAAGTTG, where N = 57 in pN/MCS11 and 16 in pN/MCS12. Curves of pN/MCS11 and pN/MCS12 in Figure Table 1a. Dependence of TM for repetitive insert domains on base sequence, location and size Table 1b. Additional plasmids with repetitive insert domains examined in this study The curves in this figure were obtained from plasmid DNAs linearized at the unique KpnI sequence in the MCS in preparation for melting. The recognition sequence for this enzyme (GGTACC) is immediately adjacent to the insert, which is substantially lower in (G+C) content than the adjacent barrier domain, so that inserts in KpnI-cut plasmids melt from one end of the DNA. The first sub-transitions emanating from both plasmids in Figure The results in Table 1a give clear indications of the level of precision that can be achieved in TM of domains. Tij were derived in this study from a large set of linear algebraic expressions for measured TM of domains, where and where fij represents the fractional neighbor pair frequencies in the domain. Tij were determined by Crout's method for LU matrix decomposition (29). The matrix was filed with 35 linear algebraic equations of the type, together with selected results from our previous study of domains of quasi-random sequence. TM for the synthetic homo- and copolymer duplexes that were included previously (17), but now suspected of adopting unusual non-B structures or of dissociating through mismatched intermediate states, were excluded and replaced instead with 22 equations for the TM of repetitive domains in Table 1a and b. The latter were given greater weight in the matrix since neighbor biases in these sequences are greater. Their TM, sequence assignments and fij are more accurate; greater confidence could be attributed to specific neighbor pairs. Values for Tij in the standard buffer are listed in column six of Table 2, where the average error is ±0.22°. They indicate that TM = 42.145@(G+C) + 63.968, °C, which is in good agreement with equation 8, from a very large collection of TM for natural DNAs accrued over the past 35 years: TM = 41.971@(G+C) + 63.981, °C (19). Table 2a. Nearest stacked and paired neighbour energies Table 2b. Free energy differences between (ij) and the mean for (i,j) A number of pN/MCS plasmids with repetitive inserts with between 0 and 8 AA or TT neighbor pairs were constructed, including a series with 1-6 (dA@dT) pairs in tracts. These appear in Table 1a, where there is a value for the insert mole fraction of AA plus TT nearest neighbors, fAA, listed in column three. A plot of TM for repeat domains against fAA shown in Figure Figure 3. Plot of TM for repeat domains against the mole fraction of AA (TT) neighbor pairs they contain, fAA. The formation of internal loops requires sufficient energy to interrupt the helix; to release stacked residues from cooperative neighbor-pair dispersion forces. Moreover, the restoration of helix from N dissociated coil residues of an internal loop involved in a helix[lrarr2]coil equilibrium is favored by the proximity of loop residues. In consequence, the stability constant sijN, is weighted by a cooperativity parameter, [sigma]c, and loop function for the greater probability of closure: where and where N is the number of residues in the loop domain, D is an empirical stiffness parameter, and [alpha] the loop-closure exponent. Repetitive domains melt as internal loops when the pN/MCS plasmids are linearized by EcoRV, which cuts at position 185, 805 bp away from the insert. The insert is isolated by (G+C)-rich barrier domains on both sides (Fig. Figure 4. Transitions of the sequence [AAGTTGAACAAAAAAT]12AAGTTGA in pN/MCS22 when situated at the end and interior (loop) of the linearized plasmid DNA, are plotted together in this figure. The experimental curves are represented by the continuous traces. Curves represented by open diamonds ([diams]) and squares ([squ]), were calculated for end and loop melting, respectively, by a statistical mechanical routine described in the text. Values for parameters in this routine were taken from Table 2 and the text. The curve represented by open circles ([cir]) was obtained by the van't Hoff cosh equation (22) for two-state transitions, with parameters determined by least-squares regression fit to the experimental loop curve: N = 187 bp, [Delta]HM = 8.33 kcal/mol bp, and TM = 75.34°C.
Figure 5. Plot of [Delta]TM TMloop - TMend against the reciprocal of the loop domain size, 1/N. Experimental results are represented by the open circles, and listed in Table 1a. The dotted line was calculated with the following values in the statistical mechanical routine: [sigma]c = 1.26 × 10-5, D = 1, [alpha] = 1.75. As seen in equation 4, the evaluation of cooperativity and loop parameters requires knowledge of the stability constants, and thereby, of both transition enthalpies and entropies: where ij represents each of the 10 neighbor pairs. Transition enthalpies were determined in this study as described previously (23), by analysis of two-state equilibria associated with the melting of internal domains. The repetitive domains, locked in between two stable (G+C)-rich neighboring domains, are shown to melt in two-state fashion by several criteria when linearization is catalyzed by EcoRV, forcing domains to melt as a closed loop. The example of the two-state transition for the 0.23 (G+C), 200 bp repetitive insert domain in pN/MCS22 is represented by the sharper, higher temperature transition in Figure The overall transition enthalpy for this domain, [Delta]Htotal, was determined by least-squares fit of the three-parameter van't Hoff `cosh' equation to the experimental curve in Figure Average errors of [Delta]Hij determined from transition equilibria are approximately ±5%, larger for domains of high f(G+C). Since errors in Tij are >10-fold smaller than [Delta]Hij, the latter were tested against the [Na+] dependence of Tij, which varies with [Delta]Hij. Determinations of Tij in different [Na+] were carried out to expand the range of applicability of these quantities, as well as confirm values of [Delta]Hij. The effects of [Na+] on stability is given by the Marmur-Schildkraut-Doty equation (30,31): determined from a large collection of measured TM from published and unpublished results acquired over three decades (19). This relationship was determined from the behavior of very large DNAs and large mixtures of DNAs of different overall base compositions [f(G+C)], and is not quantitative for short sequences ([le]4000 bp) of biased neighbor frequency. The Na+ dependence is caused by the ionic strength-independent condensation of Na+ to polyanionic DNAs, which have a particularly high negative charge density relative to the single-stranded products. Na+ are therefore released in large numbers upon melting, Subscripts denote helix (h) and coil (c) states, and DELTA {r bar sub {{N a} sup +}} = {r bar sub {{{N a} sup +} , h}} - {r bar sub {{{N a} sup +} , c}} the number of Na+ counterions released from association with the average-sized cooperatively melting domain. TM of insert domains were measured over the range 0.0344-0.1139 M Na+, and Tij determined as described above for the standard buffer, and plotted against log[Na+]. Values for the slopes, dTij/d log[Na+], and intercepts, T sub {i j} sup {1 . 0 ^ {{M - N a} sup back 20 +}}, for these linear plots are given in columns three and four of Table 2a. Tij increase at different rates with [Na+]. The upshot is that curves of DNAs with domains of different fractional base contents, f(G+C), become more compressed with increasing [Na+]. For example, curves of KpnI-linearized pN/MCS DNA, shown in Figure Figure 6. Illustrative melting curves of pN/MCS DNA (no insert) on a normalizing TM-T scale, at three different sodium ion concentrations. The theoretical expression for the derivative is given by the Manning-Record equation (12,32): where [alpha] is the activity coefficient for Na+; where [Delta][Egr][Lambda][Tgr][Agr] {[pi][sigma][iota] [sigma][upsi][beta] {{[Ngr] [alpha]} [sigma][upsi][pi] +}} = {[pi][sigma][iota] [sigma][upsi][beta] {{{[Ngr] [alpha]} [sigma][upsi][pi] +} , [eta]}} {[pi][sigma][iota] [sigma][upsi][beta] {{{[Ngr] [alpha]} [sigma][upsi][pi] +} , [chi]}} represents the differential ion association parameter for the release (per base) of Na+ bound to helix and coil states, and where [Delta]HM = 0.5[Sigma]fij[Delta]Hij. [Delta]Hij are primarily [Na+]-independent; the effect of [Na+] on DNA stability being entropic (12,33). For the salt concentrations of these experiments, [alpha] [ap] 0.95, while [Delta][Egr][Lambda][Tgr][Agr] {[pi][sigma][iota] [sigma][upsi][beta] {{[Ngr] [alpha]} [sigma][upsi][pi] +}} varies from 0.19 when f(G+C) = 0 to 0.09 when f(G+C) = 1.0 (28). The compression phenomenon arises from this decrease in DELTA {psi sub {{N a} sup +}} with increasing f(G+C). A large collection of calorimetric enthalpies with accompanying TM for dissociation of polymeric DNA specimens, indicate that {{R T} sub M sup 2} / DELTA {H bar sub M} is constant with a value of 55 ± 2 (12). A value of 54 ± 0.2 for {{R T} sub {i j} sup 2} / 0 . 5 DELTA {H sub {i j}}, was obtained over the range 0.03 M < [Na+] < 0.11 M with values of Tij and [Delta]Hij from Table 2a. dTM/d log[Na+] and dTij/d log[Na+] are plotted in Figure Figure 7. Plots of values for the slopes, dTM/dlog[Na+] and dTij/dlog[Na+], for the sodium ion dependence of domain and neighbor-pair melting temperatures, respectively, against TM2(Tij2). Closed circles represent slopes for domains, while open circles represent slopes for Tij. The dotted line was calculated with equation 9, with the following values: [Delta]HM = 0.5@[Delta]Hij = 0.5(52.78@Tij - 9489) and [Delta][Psi]Na+ = -0.0011@Tij + 0.523 over the range 320 < Tij < 410°K. Table 2b lists values for the difference in free energy, [delta][Delta]Gij, between that for (ij) and for the average of like pairs, (i,j), where, The loop parameters were calculated from equations 4 and 6, with values for Tij, [Delta]Sij and [Delta]Hij from Table 2. Results of DELTA {T sub M} = {T sub M sup {l o o p}} - {T sub M sup {e n d}} in Figure Transitions were calculated for the pN/MCS plasmid sequences as previously described (17,22). Curves are represented for the repetitive insert sub-transitions in Figure Figure 8. Two transitions of the 228 bp (A+T)-rich [lambda]-DNA insert sequence (36305-36532) in pN/MCS8 when situated at the end and interior (loop) of the linearized plasmid DNA, at two different sodium ion concentrations, are plotted together in this figure. The four experimental curves are represented by continuous traces. Curves represented by open circles ([cir]) and diamonds ([diams]), were calculated for end and loop melting, respectively, by a statistical mechanical routine with values for parameters from Table 2, and the text. Accurate Tij and [Delta]Hij have been obtained in this study from a systematic analysis of high-resolution melting curves of well-behaved synthetic tandemly repeating sequences over the range 0.034-0.114 M Na+. The polymeric DNA specimens were recombinant plasmids, constructed with repetitive sequence inserts at a site with favorable energetic characteristics and convenient restriction sites for the linearization of plasmids in preparation for melting. Tij differ from those obtained in previous studies (14-18), as is apparent from free energy differences in Table 2b. Standard errors ($0.2°) are significantly less than they were in our previous study (17), although magnitudes of Tij remain in the same order by ij as reported in previous studies, with similar relationships of stacked purines and pyrimidines, [delta][Delta]Gpu@py (-397 cal) > [delta][Delta]Gpu@pu (+30 cal) > [delta][Delta]Gpy@pu (+351 cal), reflecting differences in stacking interactions for purine-pyrimidine, pyrimidine-purine and purine-purine neighbors. Results are consistent with neighbor-pair thermodynamic additivity (35), and the absence of any longer-range energetic factors, despite implications that might be interpreted to the contrary (36). The stability constant for entire domains depends only and quantitatively on the product of stability constants for each individual pair in domains, sijN. Transition enthalpies were determined by analysis of two-state equilibria associated with the melting of internal domains. The repetitive domains, locked in between two stable (G+C)-rich neighboring domains, are shown by several criteria to melt in two-state fashion when linearization is catalyzed by EcoRV, forcing domains to melt as closed loops. Average errors of [Delta]Hij are approximately $5%, slightly larger for domains of high f(G+C). [Delta]Hij were verified from a systematic investigation of variations of Tij with [Na+], which depend inversely on [Delta]Hij (12,32). Verified [Delta]Hij increase with Tij, in close agreement with the empirical function: DELTA {H sub {i j}} = 5 2 . 7 8 cdot {T sub {i j} sup {0 . 0 7 4 5 ^ {{M - N a} sup +}}} - 9 4 8 9, and in parallel with a small increase in [Delta]Sij (Table 2a), which varies with Tij([Na+]). [Delta]Hij increases more-or-less in parallel with the (G+C) content of neighbor pairs, a reflection of increases in neighbor-dependent stacking and hydrogen bonding (37). Small variations in entropy with Tij and f(G+C) appear to reflect variations in residual stacking in the dissociated coil state, and thereby, of variations in base hydration. From a combination of replicate measurements and [Na+]-dependent results, accuracies of [Delta]Hij in Table 2a are approximately $290 cal/mol bp, or $4%, slightly larger for domains of highest f(G+C). Comparisons can be made with the results of an extensive compilation of calorimetric enthalpies and accompanying melting temperatures assembled by Klump (13), for a large number of natural and synthetic DNAs. Calorimetric transition enthalpies and entropies were summarized by the expressions: while the corresponding melting temperatures were fit to the following expression: Substituting 13 into 11 and 12 leads to: Substituting Tij for TM leads to the values for [Delta]Hcal,ij and [Delta]Scal,ij listed in the last two columns of Table 2a. [Delta]Hij and [Delta]Sij are in excellent agreement with [Delta]Hcal,ij and [Delta]Scal,ij, respectively, when the Klump results are presented in this fashion. Although stated that the transition entropy is independent of the sequence (13), values of both [Delta]Sij and [Delta]Scal,ij are seen to increase slightly with Tij([Na+]) and fG+C of the neighbor pair. Neighbor-pair additivity was also observed for (dA@dT)-tracts, where a plot of TM of insert domains against the mole fraction of AA (TT) neighbor pairs they contain, fAA, is linear (r = -0.9997). The absence of curvature or deviation at these higher temperatures suggests (dA@dT)-tracts no longer possess the unique structural features that characterize these tracts at lower temperatures (38-45): large propeller twists of the A@T pair, with three-centered hydrogen bonding and a narrow minor groove with a structural scaffolding provided by (dA@dT)-tract-associated bound water. These results are therefore complementary to those of Chan et al. (20,21), who found that the global melting of an oligomeric specimen with four equi-spaced (dA@dT)-tracts is preceded by a modest transition below 37°C, reflecting a pre-melting structural rearrangement of the tracts from a low temperature conformational state to the standard B-form at higher temperatures. The melting of oligomeric specimens used for measurements of calorimetric [Delta]Hij often occur at <37°C, and therefore could reflect both pre-melting and global contributions. The plot of TM of (dA@dT)-tract-containing domains against fAA extrapolates to 66.81° for the AA (TT) neighbor, in good agreement with that obtained by LU decomposition, 66.77°, but significantly higher than the TM for poly(dA@dT), 65.45°C. The lower TM for the latter reflects the increased access of long (dA@dT)-tracts to greater degrees of pairing freedom during melting, with sliding degeneracy and mismatched loops, (46) and thereby of a larger transition entropy than given in Table 2a for ApA. The energetic effects of loops were determined from pN/MCS plasmids linearized in preparation for melting by EcoRV, which cleaves the DNA 805 bp away from the insert. The insert is isolated by (G+C)-rich barrier domains on both sides (Fig. Statistical mechanical curves computed with this value for the cooperativity parameter, and with Tij([Na+]) and [Delta]Hij in Table 2, are in quantitative agreement with observation: in TM, transition amplitudes, breadths and areas of domain sub-transitions. With accurate values of Tij and [Delta]Hij it is possible to calculate accurate stabilities of different sequences without recourse to actual melting experiments. A program called MELTSIM has been developed for use in the windows operating system for calculating melting curves and denaturation maps of polymeric DNA sequences, and will be made available by anonymous ftp. We gratefully acknowledge Colin McRavey for his excellent assistance in the sequencing of DNAs and for his valuable contributions to discussions and a spirited laboratory environment. We also acknowledge Calvin Mitchell III, for his expert assistance in the development of appropriate statistical methods of analyses. Supported in part by grants from MAES (project no. 08402) and NIH.
a) Mole fraction of (AA + TT) nearest neighbors in the repeat sequence.
b) Circular plasmid DNA linearized by KpnI, immediately adjacent to the repetitive insert domain. Boxed in End-TM denote values for different lengths of the same repetitive sequence, together with the average and standard deviations for all lengths.
c) Circular plasmid DNA linearized by EcoRI, 803 bp away from the repetitive insert domain. Boxed in Loop-TM denote values for replicate measurements, together with the average and standard deviation.
d) Experimental [Delta]TM = TMloop - TMend.
e) Calculated as described in the text.
f) The repeat sequence of this insert was found to be mysteriously corrupted with nine mutations after transformation and amplification in the host cell: three transitions, six transversions and one deletion. The resulting changes in nearest neighbor frequencies led to an increase of 1.4°C in domain TM over that that would have been expected for the prototypic sequence. The calculated TM in column six of this table was determined from the observed (mutated) sequence.
2
3
Effects of (dA@dT)-tracts
Loop energetics
4
5
6
Transition enthalpies
Dependence on [Na+]
7
8
9
10
Statistical thermodynamic analysis
DISCUSSION
11
12
13
14
15
ACKNOWLEDGEMENTS
REFERENCES
CORRIGENDA
See corrigenda in Nucleic Acids Res. (1999) 27
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