Thermodynamics of Oligonucleotide Duplex Melting

Research: Science and Education edited by

Advanced Chemistry Classroom and Laboratory

Joseph J. BelBruno Dartmouth College Hanover, NH 03755

Thermodynamics of Oligonucleotide Duplex Melting

Sherrie Schreiber-Gosche and Robert A. Edwards* Department of Biological Sciences, University of Calgary, Calgary, AB T2N 1N4, Canada; *[email protected]

C

T

A

C

G

G

A A

T

G

B

T

A

A

G

C

T

T

C

G

A

C

G

G

T

A

C

C ...

... A

C

G

T

A

T

G

C

T

A

C

G

A

G

T

C

A

T

G

C

G

T

G

C

T

A

A

C

T A

G

...

C

...

T

A

C

T

C

A

G

C

G

644

G

C

(1)

where the variables have their standard definitions. The fraction of duplex melted is usually measured spectroscopically, so that Keq values have been determined as a function of temperature (9, 10). This provides the data for van’t Hoff plots, that allows the standard enthalpy and entropy to be calculated (9, 10). From the ΔH° and ΔS° of melting for a large number of oligonucleotides, it has been possible to use nearest-neighbor analysis to derive ΔH° and ΔS° values for all possible base-stacking interactions (3, 11–14). Any oligonucleotide duplex can then be treated as a combination of nearest neighbors to get ΔH° and ΔS° values, from which the Tm can be predicted. From biochemistry courses and texts, most students develop an ingrained habit of thinking that the energetics and hence, the melting temperatures for oligonucleotides are determined solely by the difference in the number of hydrogen bonds between GC and AT base pairs. This misconception arises from the fact that hydrogen bonding between bases determines the specificity of duplex formation and from the strong correlation between Tm and (G + C) base content (15). However, it is often not appreciated that melting of the duplex does not abolish hydrogen bonds to the bases, since after disassociation the bases are hydrogen bonded to water. Further, students commonly think of single-

T

G

ΔG ° = − RT ln K eq

A

A

C

T

A

T

Calculating melting temperatures for oligonucleotide duplexes provides an instructive exercise in the application of thermodynamics to biochemistry. Hybridized complementary oligonucleotide sequences are important in a number of molecular biology applications, including polymerase chain reaction (PCR) primers, nucleotide probes, gene arrays, silencing RNA, and single nucleotide polymorphisms. Melting temperatures are important parameters used in designing experimental conditions for these applications. A number of empirical equations based on (G + C) base content, duplex length, and the salt concentration have been used to estimate the melting temperatures of oligonucleotide duplexes (1, 2). However, melting temperatures are more accurately calculated with a thermodynamic approach that takes into account the concentration of the oligonucleotide (2–4). This approach has been discussed briefly in some textbooks (5, 6) and has been incorporated into online calculators (7, 8). Since biochemistry has become a more integral part of the curriculum for chemistry majors, an in-depth treatment of this topic can also be used in physical chemistry classes. The melting temperature, Tm, of an oligonucleotide duplex is defined as the temperature at which 50% of the duplex is dissociated. A student laboratory exercise describing how Tm can be determined has been published (9). By assuming that there is a two-state equilibrium that is maintained throughout the melting process, the Tm can be related to the standard Gibbs energy for the dissociation as

Figure 1. Diagrammatic representations of the melting of short oligonucleotide chains for the three cases described in the text: (A) a non-self-complementary duplex; (B) a self-complementary duplex; and (C) a probe or primer at a higher concentration than the concentration of its hybridization site.

stranded oligonucleotides as rigid linear structures, rather than as flexible molecules with unstacked bases as is illustrated in Figure 1. Therefore, this topic helps students to focus on the losses of hydrophobic interactions and of π−π interactions that occur

Journal of Chemical Education • Vol. 86 No. 5 May 2009 • www.JCE.DivCHED.org • © Division of Chemical Education

Research: Science and Education

when bases become unstacked, as an important determinant of melting temperature (11, 16). Because 25 °C is often called a “standard temperature” in introductory chemistry courses, it is necessary to explain to students that standard Gibbs energies can be calculated and related to Keq at any temperature of interest. Temperatures of interest include Tm and Tm − 5 °C, because a temperature about 5 °C less than Tm is often used to attain conditions in which most of the oligonucleotide primer is annealed to the template. The thermodynamic approach also helps students appreciate that the melting temperature for a primer depends upon the concentration of oligonucleotide used. Melting temperatures are often rapidly approximated at the bench from the number of A and T bases, NAT, and G and C bases, NCG, in one of the strands according to (1, 2)

Tm = 2 NAT + 4 NGC

(2)

Although this equation is easy to use, it is not accurate (2). The thermodynamic approach equips students to calculate more accurate Tm values by explicitly taking into account the dependence of Tm on duplex concentration, as is required for modern primer design (4). This approach also provides a more rigorous framework for understanding the influence of mismatches on melting temperature, which is needed for site-directed mutagenesis or dealing with the possibility of incorrect annealing. Melting Equilibrium The thermodynamic approach involves two steps. First, data from a nearest-neighbor analysis are used to obtain the standard entropy and standard enthalpy of the stacking interactions between base pairs in the duplex. Then, the melting temperature is obtained as the midpoint where the duplex, composed of strands X and Y, is 50% dissociated in the equilibrium (9, 10)

X⋅Y

X+Y

(3)

The Keq for dissociation is related to the total oligonucleotide strand concentration (i.e., Ctot) (6, 12). The concept of Ctot is easily understood if it is thought of as the sum of the single strand concentrations at a high temperature where the duplex is completely dissociated:

C tot = [ X]tot + [Y]tot

(4)

However, it is important to remember that the thermodynamic data have been obtained under initial conditions consisting of a duplex that has been heated to separate, with no extra single stands (neither X nor Y) being present. Under these conditions, the total strand concentration is twice the initial duplex concentration. The relationship between Keq and Ctot is conceptually different in three common cases, which are diagrammed in Figure 1: (i) melting of non-self-complementary duplexes, (ii) melting of self-complementary duplexes (i.e., palindromes), and (iii) melting of a probe or primer that is at much higher concentration than the concentration of its complementary hybridization site. These three cases are important because some of the thermodynamic measurements have utilized a self-complementary strand,

in which the strand base pairs with itself; however, others have utilized non-self-complementary duplexes. In addition, many applications for melting temperatures utilize the melting temperature of a probe or primer that is at much higher concentration than the concentration of its complementary hybridization site on large DNA molecules. The relationships between concentrations, between Keq and Ctot, and between the melting temperature and Ctot are tabulated for each of these three cases in Table 1. Students can be expected to rationalize the origin of any of the concentration relationships and be able to obtain from the concentration relationships the relationship between Keq and Ctot for each of the cases. The equations for Tm in terms of ΔH°, ΔS°, and Keq in Table 1 can be obtained by substituting ΔH° − T ΔS° for standard Gibbs energy into eq 1 and isolating the temperature to obtain

T =

ΔH ° ΔS ° − R ln K eq

(5)

Substituting one half for the fraction dissociated (i.e., f = ½) and the relevant equations for Keq in terms of Ctot into eq 5 leads to the tabulated equations for Tm. Base Stacking The notation that is used for stacking interactions consists of specifying the bases that are stacked as nearest neighbors next to each other, for example, an AG stacking interaction with an adenine base stacked on a guanine base as shown on the upper left of Figure 2. For a single oligonucleotide strand, taking into account direction, there are 16 possible nearest neighbors (e.g., AA, AT, AC, AG, and so forth; where the first base is closer to the 5′-end of the oligonucleotide). The disruption of each of these base-stacking interactions contributes a unique quantity to the standard enthalpy and entropy of melting. Note that the energetics are similar, but not identical, for nearest-neighbor couplets with a different order (e.g., the energetics of AG stacking is not identical to GA energetics). Although there is some inconsistency in the notation used for the direction of the second strand (3), most authors use a notation in which the strands are shown antiparallel (e.g., AG/TC means 5′-AG-3′ base paired with 3′-TC-5′ to produce an A stacked on a G and a C stacked on a T). Simplified Stacking Method For double-stranded duplexes, there are only 10 unique stacking interactions for Watson–Crick base pairing, because the order on one of the strands dictates the order on the complementary strand so that 6 stacking interactions are redundant. (e.g., AG/TC = CT/GA). Superficially it might seem as though each double-stranded stacking interaction would have a redundant partner, however, this is not the case, and it is a useful exercise for students to consider the 16 possibilities and find those that do have partners. For teaching purposes, it is possible to simplify this to consider only three general sets of stacking interactions: (i) A or T stacked on an A or T, (ii) C or G stacked on a C or G, and (iii) all other interactions. This three-set simplification ignores direction and is amenable to hand calculations (see below).

© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 86 No. 5 May 2009 • Journal of Chemical Education

645

Research: Science and Education Table 1. Relationships Between Concentrations and Equilibrium Constants for Each of the Three Cases of Duplex Melting Description of Case and Equilibrium

Relationships Between Concentrations at Any Temperature4,5

f = Case 1 Non-self-complementary duplex oligonucleotide.1

[ X]

C tot =

f = Case 2 Self-complementary duplex oligonucleotide.2

+ [Y ] + 2 [ X⋅Y ]

[ X] 2 [ X⋅ X ]inital [ X]

C tot =

fraction dissociated: f = 1/2

[ X ]m

=

K eq = 2f 2

f = Case 3 Oligonucleotide at high concentration hybridized to DNA at low concentration.3

[ X ]tot

+ 2 [ X⋅X ]

[Y ]tot

X+Y

=

[Y ]tot

K eq = f

[Y ]

ΔH ° C tot 4

[ X ]m

= 2 [ X⋅X ]m

K eq = C tot ΔH ° ΔS ° − R ln C tot


[ X ]tot

C tot ≈

[ X⋅Y ]m

ΔS ° − R ln

Tm =

C tot 1− f

[Y ] [Y ]tot >>

=

C tot 4

K eq =

Tm =

[Y ]m


C tot = 2 [ X⋅X ]initial

2X

X⋅Y

[ X⋅Y ]initial

C tot 2 (1 − f )

K eq = f 2

X⋅X

[Y ]

=

C tot = 2 [ X⋅Y ]initial

X+Y

X⋅Y

[ X] X⋅Y [ ]initial

Relationships at the Melting Temperature (Tm).6–8

≈

>

[ X⋅Y ]

[X]

+ [ X⋅Y ]

C tot 1− f

[Y ]m

=

[ X⋅Y ]m

K eq = C tot Tm =

ΔH ° ΔS ° − R ln C tot

1For

case 1 the initial conditions consist of a duplex with no extra X or Y present. case 2 the strand is base paired with itself to produce a palindrome. 3For case 3 a primer strand (X) is paired with DNA (Y) on the first few rounds of PCR. Unbound single-stranded primer is also present. 4The fraction of the duplex that is melted (dissociated) is f. 5For case 3 the relevant DNA concentration (i.e., [Y] ) is the concentration of DNA strands that contain the sequence complementary to the primer tot (i.e., the concentration of hybridization sites). 6The subscript “m” is used to refer to the melting temperature (where half of the duplex is dissociated into single-stranded form(s)) and concentrations at that temperature. 7ΔHº and ΔSº in this article are for melting (i.e., the forward direct is dissociation of strands). Standard enthalpy and entropy are often tabulated for the reverse of melting (i.e., the formation of duplex). 2For

Tm = 8The

Δ rH ° Δ r S ° + R ln

C tot 4

or

Tm =

Δ rH ° Δ r S ° + R ln C tot

derivations of the equations for Tm follow from

Δ G ° (T ) = −R T ln K eq = Δ H ° − T ΔS ° where ΔHº and ΔSº can be treated as independent of temperature. Both ΔHº and ΔSº depend on temperature through ΔCp, but the values of ΔCp for oligonucleotide melting are not large (4, 14). Further, the small ΔCp dependent temperature contributions of enthalpy to ΔGº and of entropy to ΔGº are about equal in magnitude and opposite in sign, and therefore cancel each other out.

646



four AA, AT, TA, and TT base stackings ⇒ NAA = 4 oligonucleotide: 5′-CTTTCATGTCCGCAT-3∙ three CC, CG, GC, and GG base stackings ⇒ NCC = 3 Figure 3. Illustration of the stacking interactions on an oligonucleotide: NAA is the number of occurrences in the single strand of AA, AT, TA, and TT stacking interactions; NCC is the number of occurrences in the single strand of CC, CG, GC, and GG stacking interactions; and Nother is the number of occurrences in the single strand of AC, AG, TC, TG, CA, CT, GA, and CT stacking interactions. The complementary stand would have the same number of stacking interactions of each type (not shown).

Figure 2. Diagram highlighting the difference between base-pairing and base-stacking interactions. The structure has been expanded slightly to show the regions where base-stacking interactions will occur. The hydrogen bonds come from base pairing, whereas the stacking interactions arise from the bases being on top of one another. Note that slight variations in the energetics of the stacking interactions occur between various base-pair combinations (not shown).

Counting such interactions along an oligonucleotide sequence helps students to more clearly delineate between base pairing and base stacking, because they observe stacking interactions on couplets that do not base pair (e.g., AA, AG, etc.). Calculating the Standard Enthalpies, Entropies, and Melting Temperatures Empirical values for the ΔH° and ΔS° of each nearestneighbor base-stacking interaction have been derived by fitting the experimental standard enthalpies and entropies for many oligonucleotides as the sum of individual ΔH° and ΔS° nearestneighbor components (3, 11–14). SantaLucia has presented, in a consistent format, the empirical ΔG° values derived from diverse sets of oligonucleotides by several investigators for the 10 different stacking interactions (14). These parameters are relatively consistent with each other and the widely used unified set of ΔH° and ΔS° parameters adequately describes oligomer and polymer thermodynamics (14). Usually these are tabulated for base-stacking formation (i.e., the reverse of melting as two strands come together). An entropy of “initiation” is also pres-

ent, which accounts for the order arising from the association of two strands to form one complex. Empirical corrections have also been derived for end effects, which essentially account for base pairs at the ends that have only one nearest neighbor. In the unified set of parameters compiled by SantaLucia the end effects are included in the initiation parameters (14). Finally, for palindrome duplexes a symmetry correction is required to account for the decrease in order when a duplex with end-to-end symmetry is changed into two single strands that do not individually have end-to-end symmetry. There are many tables of published values for the experimental thermodynamic parameters for oligonucleotide duplexes (3, 4, 11–13, 17), so the predicted values of examples chosen for students can be compared to experimental values. Examples may even be drawn from an oligonucleotide primer or probe that is used for a particular experiment within the student’s range of experience. A sample is shown in Figure 3 and Table 2 that includes the averaged parameters for the generalized equations. Thus, for example, an A base stacked on top of another A or a T base will contribute 7.6 kcal/mol to the standard enthalpy. In the simplified calculations of Table 2, there are enthalpy and entropy corrections for the ends. The negative enthalpy correction is present because the bases at the ends do not have neighbors on both sides and thus are not held as firmly in place as the other bases. As a result, the end base may be transiently unstacked more often than an internal base, so there is slightly less favorable interaction between an end base and its neighbor. The standard entropy correction is also dominated by entropy from the transient unstacking of end bases. Since the end bases are already transiently unstacked in the double-stranded form, the negative entropy correction adjusts the positive entropy of dissociation to be smaller for the end bases than for internal bases. The positive contribution to entropy from the separation of strands is buried in the entropy correction for the ends. A comparison between the accuracy of calculating Tm by the various methods is shown in Table 3 for a set of duplexes that has the length range, NaCl concentration, and oligonucleotide concentrations that actually might be used for PCR. Because the empirical parameters for ΔH° and ΔS° apply to 1.0 M NaCl, it is necessary to correct for the experimental salt concentrations.


647

Research: Science and Education Table 2. Simplified Calculation Method Applied to the Oligonucleotide in Figure 3 with an Oligonucleotide Concentration of 2.0 µM Parameter Calculated Nother

Equations and Calculated Values N other =

(N

Comments

− 1) − N AA − N CC

Nother, NAA, and NCC are defined in the caption to Figure 3. N is the number of bases in one strand.

= 15 − 1 − 4 − 3 = 7 7..6 NAA + 8.2 Nother + 9.1NCC − 2 (1.2)

Δ H° = ΔHº

7.6 (4 ) + 8.2 (7 ) + 9.1(3) − 2.4

=

= +112.7

kcal mol

kcal mol

kcal mol

The enthalpies (in kcal/mol) for base-stacking interactions of each type are listed below.1

ΔS ° = 21.5 NAA + 22.1 Nother + 22.8 N CC + 1.4 δsym − 2 (0.7) ΔSº

=

21.5 ( 4)

+

22.1(7 )

cal = +307.7 mol K Tm =

Tm

+ 22.8 (3) − 2 (0.7)

cal mol K cal mol K

δsym = 0 for this case; but δsym = 1 for palindromes. The entropies (cal/mol) for base-stacking interactions of each type are listed below.2

ΔH ° ΔS ° − 1.987

cal C ln tot mol K 4

cal m ol = cal cal 2 × 10 − 6 307.7 − 1.987 ln mol K mol K 4 112.7 × 103

Tm calculated for 1.0 M NaCl. From experiment on this Oligo Tm = 62.8 ºC at 2.0 µM in 1.02 M NaCl (17).

= 334.9 K = 61.7 °C 1ΔHº AA = 7.6 kcal/mol, 2ΔSº AA = 21.5 cal/(mol

ΔHºother = 8.2 kcal/mol, ΔHºCC = 9.1 kcal/mol. K), ΔS ºother = 22.1 cal/(mol K), ΔSºCC = 22.8 cal/(mol K).

Table 3. Root Mean Square Deviation between Predicted and Experimental Melting Temperatures Calculation Method

Bench2

Von Ahsen, et al.3

SantaLucia4

Owczarzy et al.5

Simplified Stacking6

15-mers, 20-mers, and 25-mers (N = 180)1

7.5 ºC

2.3 ºC

1.6 ºC

2.0 ºC

1.7 ºC

1T was predicted for the 15-mers, 20-mers, and 25-mers from Table 2 of Owczarzy et al. (17) in 69, 119, and 220 mM NaCl at C m tot = 2.0 µM and compared to the experimental Tm values. 2T = 2N m AT + 4NGC referred to as the “bench method” (1, 2). 3Equation 12 from Von Ahsen et al. (2) based on GC base content, length, and salt correction. 4SantaLucia (14) as implemented by the HYTHERTM server (8). 5SantaLucia (14) method with Owczarzy et al. (17) salt correction. 6Simplified stacking method described above with SantaLucia salt correction (14).

The root mean squared deviation (RMSD) for the more accurate methods is approximately the same as has been obtained by others on larger sets of oligonucleotides of more variable length (2–4). The results of our comparison show that the simple bench method (1, 2) is inaccurate. Von Ahsen et al. (2) have developed a fairly accurate method of predicting Tm values based on the length, (G + C) base content, and salt concentration, but the method of SantaLucia (14) is more accurate. This method is

648

made readily available on the HYTHERTM server. In fact, the HYTHERTM server is known to be one of the most accurate of the available servers (4, 8, 18). Correcting to the low salt corrections using the method of Owczarzy (17) gives slightly less accurate results. However, the simplified stacking method described in this article gave predictions that were nearly as accurate as those obtained by SantaLucia (14), and yet these calculations are simple enough to be done by hand. Therefore,


Research: Science and Education Table 4. Calculating the Percentage of Primer That Will Be Annealed to a Template DNA When the Temperature Is 5 °C below the Tm for the Primer CAGCCTCGTTCGCACAGCCC at 0.5 µM Parameter Calculated

Equations and calculated values kcal mol cal ΔS° = +454.31 mol K

Comments

ΔH° = +164.4

Entropy, Enthalpy, and Tm

From the HYTHERTM server for this sequence at 0.5 mM with 1 nM complementary strand and 69 mM NaCl.

Tm = 67..1 °C = 340.25 K ΔG ° = +164.4 ΔG º

− 335.25 K 454.31 = 12100

Keq

Fraction of template unbound

kcal mol

K eq = exp −

cal mol K

ΔGº calculated at 62.1 ºC, which is 5 °C below the Tm.

cal at 62.1 °C mol

ΔG ° RT

= 1.30 × 10 −8

f C tot 1− f Therefore: f = 0.0253

K eq =

we suggest the use of this simplified method for instructional purposes. When discussing the accuracy of the predictions, it is useful to have students consider the 95% confidence limits that can be applied to any oligonucleotide of interest. Thus, approximate confidence limits (i.e., 2×RMSD) for the predicted Tm of an oligonucleotide with a length of 15–25 bases would be about ±3 °C for the most accurate calculations, but the basic bench calculations are much less accurate with confidence limits of ±15 °C. Confidence limits provide a foundation for the student to understand how imprecise knowledge of the melting temperatures may contribute to the observation that PCR reactions often do not work as expected. It is common practice to modify the concentrations of various salts to overcome problems with PCR. One basis for this procedure is that the changes in the salt concentration result in changes to the Tm, which may improve the annealing to the template. Students can qualitatively rationalize why increasing the concentrations of salt increases the Tm by considering the effect of changing the salt concentration on the repulsion between strands and the hydrophobic effect. Counter ions help to neutralize repulsion between the phosphate groups on the two strands of a duplex and the strength of the hydrophobic interaction between stacked bases would be expected to increase at higher ionic strength (15, 19–21). Thus, melting temperatures depend on both the nature and the concentrations of the salt present. Empirical equations for salt corrections have been worked out (2, 3, 14, 17) and equations to correct Tm for Mg 2+ and nucleotide triphosphate concentrations are also available

mol L

Keq at 62.1 ºC.

Therefore 97% of the primer will be annealed when temperature is 5 ºC less than Tm.

(2). Students can use the empirical entropies and enthalpies to predict the melting temperature of an oligonucleotide duplex of interest and then correct to specified conditions. The salt correction of SantaLucia (14) adds a correction term, which is dependent on ln[Na+], to the standard entropy calculated from the unified parameters (or the simplified method) Salt correction:

(

ΔS ° = Δ S °1 + 0. 368

cal mol K

) (N

(

)

− 1) ln [ Na+] M (6)

where ΔS°1 is the predicted value at 1 M NaCl and N is the number of bases. Primer concentration is usually not treated as an adjustable parameter for PCR optimization. However, students can explore the dependence of Tm on primer concentration by calculating Tm of any primer at several concentrations to show that a tenfold change in concentration leads to a change of several degrees in the melting temperature. Since it is common to use a temperature 5 °C less than the melting temperature for annealing a primer to DNA, it is instructive for students to calculate the percentage of primer that would be annealed at the lower temperature (see example in Table 4). This calculation illustrates that at 5 °C below Tm most of the primer (about 97%) would be bound to the template, thus providing a starting point for the DNA polymerase. After polymerization the duplex that has formed is much longer and thus high temperatures (above 90 °C) are used to melt them in preparation for the next PCR cycle.


649


Conclusions The logic and calculations involved in predicting the melting temperatures of oligonucleotide duplexes provide an opportunity for students to apply thermodynamic analysis to an important biochemical problem that is useful for a number of molecular biology applications. The major objectives of this article were to (i) explain how the equilibrium constant for the process of melting (dissociation of strands) can be expressed in terms of the total strand concentration for three conceptually different cases, (ii) emphasize that the disruption of base stacking is the important consideration in obtaining the standard enthalpy and entropy for the melting, and (iii) present a simplified method of calculating the standard enthalpy and entropy that is manually tractable. By being able to do simplified calculations students will understand the analysis well enough so that the servers that calculate melting temperatures are not just black boxes. For advanced students, further development of this topic can be pursued in terms of three-state equilibrium for mismatched sequences (22, 23), primer design (4), or counterion condensation theory (17, 19). Acknowledgments We would like to thank Wayne Gosche of Sosa Original Graphics Inc. for preparing Figures 1 and 2. We would also like to thank Isabelle Barrette-Ng of the University of Calgary for proofreading the article. Literature Cited 1. Meinkoth, J.; Wahl, G. Anal. Biochem. 1984, 138, 267–284. 2. Von Ahsen, N.; Wittwer, C. T.; Schütz, E. Clin. Chem. 2001, 47, 1956–1961. 3. Owczarzy, R.; Vallone, P. M.; Gallo, F. J.; Paner, T. M.; Lane, M. J.; Benight, A. S. Biopolymers 1998, 44, 217–239. 4. Chavali, S.; Mahajan, A.; Tabassum, R.; Maiti, S.; Bharadwaj, D. Bioinformatics 2005, 21, 3918–3925. 5. Tinoco, I., Jr.; Sauer, K.; Wang, J. C.; Puglisi, J. D. Physical Chem-

650

istry: Principles and Application in Biological Sciences; Prentice Hall: Englewood Cliffs, NJ, 2002. 6. Hammes, G. G. Thermodynamics and Kinetics for the Biological Sciences; John Wiley and Sons: Hoboken, NJ, 2000. 7. Kibbe, W. A. Nucleic Acids Res. 2007, 35, W43–W46. 8. Peyret, N.; SantaLucia, J., Jr. HYTHERTM version 1.0. http:// ozone3.chem.wayne.edu/loginpage.html (accessed Feb 2009). 9. Howard, K. P. J. Chem. Educ. 2000, 77, 1469–1471. 10. Martin, F. H.; Uhlenbeck, O. C., Doty, P. J. Mol. Biol. 1971, 57, 201–215. 11. Breslauer, K. J.; Frank, R.; Blocker, H.; Marky, L. A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 3746–3750. 12. SantaLucia, J., Jr.; Allawi, H. T.; Seneviratne, P. A. Biochemistry 1996, 35, 3555–3562. 13. Sugimoto, N.; Nakano, S.-I.; Yoneyama, M.; Honda, K.-I. Nucleic Acids Res. 1996, 24, 4501–4505. 14. SantaLucia Jr., J. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 1460–1465. 15. Marmur, J.; Doty, P. J. Mol. Biol. 1962, 5, 109–118. 16. Yakovchuk, P.; Protozanova, E.; Frank-Kamenentskii, M. D. Nucleic Acids Res. 2006, 34, 564–574. 17. Owczarzy, R.; You, Y.; Moreira, B. G.; Manthey, J. A.; Huang, L.; Behlke, M. A.; Walder, J. A. Biochemistry 2004, 43, 3537–3554. 18. Panjkovich, A.; Melo, F. Bioinformatics 2005, 21, 711–722. 19. Tan, Z.-J.; Chen S.-J. Biophys. J. 2006, 90, 1175–1190. 20. Friedman, R. A.; Honig B. Biophys. J. 1995, 69, 1528–1535. 21. Dill, K. A.; Truskett, T. M.; Vlachy, V.; Hribar-Lee, B. Annu. Rev. Biophys. Biomol. Struct. 2005, 34, 173–199. 22. Allawi, H. T.; SantaLucia, J., Jr. Biochemistry 1997, 36, 10581–10594. 23. Peyret, N; Seneviratne, P. A.; Allawi, H. T.; SantaLucia, J., Jr. Biochemistry 1999, 38, 3468–3477.

Supporting JCE Online Material

http://www.jce.divched.org/Journal/Issues/2009/May/abs644.html Abstract and keywords Full text (PDF) Links to cited URL and JCE article


Thermodynamics of Oligonucleotide Duplex Melting

Recommend Documents