Introduction.

Thermodynamics of DNA Duplex Denaturing

Objective: The purpose of this lab is to evaluate thermodynamics of double helical DNA and determine: 

• the dominant forces of interaction in DNA from its melting curve and 
• the thermodynamic parameters of the single strand to helix transition >
• compare thermodynamic properties of DNA duplex of different sequences

You will measure thermodynamic properties (DH°, DS°, and DG°) of short DNA duplexes by melting the ordered native structure (duplex or double helix) into the disordered, denatured state (single strands) while monitoring the transition using ultraviolet (UV) spectrophotometry.

Deoxyribonucleic acid (DNA) is a polymer that is normally a double stranded macromolecule. Two polynucleotide chains (strands) are held together by weak forces and form a DNA molecule. The monomer units of DNA are nucleotides, each of which consists of a 5-carbon sugar (deoxyribose), a nitrogen containing base attached to the sugar, and a phosphate group. There are four different types of nucleotides found in DNA, differing only in the nitrogenous base. The four nucleotides are given one letter abbreviations as shorthand for the four bases:

• A is for adenine (purine)
• G is for guanine (purine)
• C is for cytosine (pyrimidine)
• T is for thymine (pyrimidine)

Using these abbreviations one can easily describe any nucleotide sequence, which is also called the primary structure. All genetic information is stored in the primary sequence. The sequence is written in the direction from 5'-end to the 3'- end of sugar phosphate backbone, e.g. 5'-ACCGGTTA-3'OH, or simply, ACCGGTTA (which is different from the opposite sequence, ATTGGCCA). In the native form, each strand is coupled into a duplex or double helix with its complementary strand. In this secondary structure:

• the two complimentary polynuceotide strands form a helical spiral, winding around a helix axis
• the sugar-phosphate backbones of the two DNA strands are antiparallel (5'-->3'/ 3'-->5') and usually are coiled in a right-handed spiral 
• the bases of the individual nucleotides are on the inside of the helix, stacked on top of each other like the steps of a spiral staircase
• stabilizing the double helix is base pairing between T-A and between C-G by hydrogen bonds and base stacking

Additional information on DNA can be found in numerous internet sites.^1-3 

Melting of DNA

Two strands of a DNA molecule  can be dissociate  into single polydeoxyribonucleotide strands (the process is also called denaturing or melting) by heat or urea. It proceeds because of breaking the hydrogen bonds between complementary bases and disrupting the base stacking. Knowing how denaturation proceeds is important for understanding DNA replication and manipulation with DNA in laboratory. Denaturation of DNA can be caused by a number of physical factors such as change in salt concentration, pH or other factors, but importantly for this application, denaturation of DNA can be started by increasing temperature. Melting of DNA by heat is a standard method for preparing "single-stranded DNA" (ssDNA).

The denaturation of DNA occurs over a narrow temperature range and causes a number of physical changes. For instance, the buoyant density of the system increases, the viscosity decreases, the optical rotation becomes more negative and, most importantly for this application, the ultraviolet absorption at 260 nm increases. The simplest characterization of DNA denaturing is via melting temperature, T_m, the temperature at which half the melting has taken place. The T_m depends on DNA length, sequence, ionic environment, pH, etc. Because GC pairs consist of three  hydrogen bonds, while AT pairs only have two, the temperature at which a particular DNA molecule "melts" usually will increase with higher percentage of GC pairs.  The relationship between melting temperature (T_m) and GC content for long DNA can be simplified to:

            T_m = 69^o + 0.41(%G+C)                                                         (1)

This equation empasizes that GC pairs are more stable than AT pairs but it oversimplifises the phenomenon. As the ordered regions of stacked base pairs in the DNA duplex are disrupted, the UV absorbance increases. This difference in absorbance between the duplex and single strand states is due to an effect called hypochromicity. Hypochromicity (means "less color") is the result of  nearest neighbor base pair interactions. When the DNA is in the duplex state (dsDNA), interactions between base pairs decrease the UV absorbance relative to that of single strands. When the DNA is in the single strand state the interactions are much weaker, due to the decreased proximity, and the UV absorbance is higher than that in the duplex state. On denaturation, the absorbance of the strands more closely approaches that of the free bases and an increase of up to 40% in the UV absorbance is observed. The profile of UV absorbance versus temperature is called a melting curve; the midpoint of the transition is defined as the melting temperature, T_m. The  dependence of the melting transition, T_m, on the strand concentration can be analyzed to yield quantitative thermodynamic data including DH°, DS°, DG° for the transition from duplex to single strand DNA. Alternatively, one can get this information by analyzing the whole melting curve.

Thermodynamic analyses of this type are done extensively in biochemistry research labs, particularly those involved in nucleic acid structure determination. In addition to providing important information about the conformational properties of either DNA or RNA sequences (mismatched base pairs and loops have distinct effects on melting properties), thermodynamic data for DNA are also important for several basic biochemical applications. For example, information about the T_m can be used to determine the minimum length of a oligonucleotide probe needed to form a stable double helix with a target gene at a particular temperature.

Thermodynamic Analysis of Small Oligomers

Assuming a two-state model, in which denaturing has no intermediate states ("all-or-none"), the steep part of the melting curve reflects the double strand (dsDNA ) to single strand equilibrium (ssDNA₁ + ssDNA₂ )

             ssDNA₁ + ssDNA₂   <--> dsDNA                                              (2)

The two-state model approximates well short (less than 12 base pairs) DNA duplexes. The association constant at the midpoint (when half of the DNA is single stranded and the other half is helical) is K₅₀ = 4/[C], where [C] is the sum of the concentrations of the two single strands which are non-self-complementary. (For self-complementary strands, K₅₀ = 1/[C])  Since, for any process at equilibrium, DG^o = -RT lnK and DG^o = DH^o - TDS^o, we have  

            DH^o - TDS^o = -RT lnK                                                   (3)

where R = 1.987 cal·K^-1mole^-1. At the midpoint, T = T_m and K = K₅₀ = 4/[C].  Therefore, for non-self-complementary strands,

            DH^o - T_mDS^o = -RT_m ln(4/[C])                                       (4) 

After rearranging terms, we get 

            1/T_m = R ln[C] /DH^o + (DS^o – R ln4)/DH^o                      (5)

For self-complementary strands, the equation transforms into:

          1/T_m = R ln[C] /DH^o + DS^o/DH^o                                       (5') 

From the concentration dependence of the melting temperature, the standard enthalpy and entropy can be determined using so-called van’t Hoff plot of 1/T_m versus ln[C].  The standard free energy of duplex formation, DG^o, at any temperature can then be determined. 

Information on DH°, DS°, DG° can be also determined from a single melting curve. Indeed, equation for equilibrium in reaction (2) can be expressed via the degree of hybridization:

 as follows:

Similarly for self-complementary strands, it transforms into:

Upon denaturing (melting) value of a changes from 1 to 0. Its temperature dependence is related to the temperature dependence of K and to DH°, DS°, in accordance with Eq.(3). You will use the software supplied with Cary 100 spectrophotometer⁴ to analyze a(T) and calculate DH°, DS° for your DNA.  

Nearest Neighbor Model. (You will need it for extra credit analysis)

Measuring thermodynamic properties of every imaginable sequence is not very productive. Scientists cannot feel comfortable with a subject until they can predict the result before the measurement. The thermodynamics of nucleic acids has been studied by many research laboratories. It was found that satisfactory results can be achieved with the nearest-neighbor (NN) model.^5-8  This NN model assumes that stability of a DNA duplex depends on the identity and orientation of neighboring base pairs. If we only consider Watson-Crick DNA duplexes, ten different nearest-neighbor interactions are possible in any duplex structure.  These interactions are AA/TT, AT/TA, TA/AT, CA/GT, GT/CA, CT/GA, GA/CT, CG/GC, GC/CG, and GG/CC.  Here the slash, /, separates strands in antiparallel orientation (e.g., AC/TG means 5’-AC-3’ paired with 5’-TG-3’).  The stability of a DNA duplex can be predicted from its primary sequence if the relative stability, DG^o, of each DNA nearest- neighbor interaction is known. Different groups arrived at slightly different NN sets of parameters (see Table1) by choosing different treatment of the duplex endings. The total free energy change of a DNA helix from its individual strands is given by:        

where DG^o(i) = DH^o(i) - TDS^o(i) are the stand free energy changes for the ten possible Watson-Crick NNs, n_i is the number of occurrences of each type of NN, i, and DG^o(sym) equals +0.43 kcal/mol if the duplex is self-complementary and zero if it is not self-complementary. To account for differences between duplexes with terminal AT versus terminal GC pairs, two initiation parameters are introduced.  

Table 1. DHº (kcal/mol) and DSº (cal/K·mol) for nearest neighbor calculation. All values refer to forming duplex at 1M NaCl, 25^oC, and pH = 7.0.

The melting temperature and the relative stability of the DNA duplex also depend on the ionic strength and pH. Qualitatively, T_m and DG^o should increase with the [Na⁺] concentration because cations electrostatically shield the anionic phosphates groups of the nucleotides and minimize their repultion. SantaLucia⁶ suggested a simple formula to accommodate the salt correction assuming that it is independent of sequence but dependent on the oligonucleotide length⁹:      

where DG^o (oligomer, [Na⁺]) is the DG^o for an oligonucleotide duplex dissolved in a given sodium concentration, DG^o (unified oligomer, 1M NaCl) is the DG^o predicted from the unified NN parameters at 1M NaCl, and N is the total number of phosphates in the duplex divided by 2.  The solution was buffered at a pH of 7 for the published NN values.

From inspecting Table 1 and Figure on the left, one can see that hydrogen bonding alone is not sufficient for explaining stability of DNA duplex. Stacking interaction has a significant contribution. It is clearly seen in comparing enthalpy for sequences that differ only in their order and, as a result, in the overlap between bases.      

For example, compare GC/GC, CG/CG and GG/CC duplexes. The former has the greatest overlap and the largest stacking energy. Similar observation can be correlated among other duplexes, e.g.  TA/TA, AA/TT and AT/AT duplexes.

CC_vs_GC_vs_CG TA_vs_AA_vs_AT

References.

1. DNA structure tutorial at U. Arizona.  
2. Exploring DNA from the Laboratory of Molecular Biology, Cambridge, UK.
3. DNA Structure from Tulane University.
4. Thermal application for Cary 100
5. Breslauer, K. J.; Frank, R.; Blocker, H., Marky, L. A. Proc. Natl. Acad. Sci. USA 1986, 83, 3746-3750.
6. SantaLucia, J. Jr. Proc. Natl Acad. Sci. USA 1998, 95, 1460-1465.
7. Allawi, H. T.; SantaLucia, J., Jr. Biochemistry 1997, 36, 10581-10594.
8. Sugimoto, N.; Bajabo, S.; Yoneyama, M.; Honda, K. Nucleic Acids. Res. 1996, 24, 4501-4505.
9. Record. M. T., Jr.; Lohman, T. M. Biopolymers 1978, 17, 159-166.

Last updated 03/12/09.