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Nucleic Acid Thermodynamics

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UNAFold A site for predicting how a given nucleic acid will fold.

The Thermodynamics of DNA Structural Motifs

Nearest-neighbor method

One problem in nucleic acid thermodynamics is to determine the thermodynamic parameters for forming double-stranded nucleic acid AB from single-stranded nucleic acids A and B.

AB ↔ A + B

The equilibrium constant for this reaction is $K=\ln {\frac {[A][B]}{[AB]}}$. According to thermodynamics, the relation between free energy, ΔG, and K is ΔG° = -RTln K, where R is the ideal gas law constant, and T is the kelvin temperature of the reaction. This gives, for the nucleic acid system,

$\Delta G^{\circ }=-RT\ln {\frac {[A][B]}{[AB]}}$.

The melting temperature, T_m, occurs when half of the double-stranded nucleic acid has dissociated. If no additional nucleic acids are present, then [A], [B], and [AB] will be equal, and equal to half the initial concentration of double-stranded nucleic acid, [AB]_initial. This gives an expression for the melting point of a nucleic acid duplex of

$T_{m}={\frac {-\Delta G^{\circ }}{R\ln {\frac {[AB]_{initial}}{2}}}}$.

Because ΔG° = ΔH° -TΔS°, T_m is also given by

$T_{m}={\frac {\Delta H^{\circ }}{\Delta S^{\circ }+R\ln {\frac {[AB]_{initial}}{2}}}}$.

This equation is based on the assumption that only two states are involved in melting: the double stranded state and the random-coil state. However, nucleic acids may melt several intermediate states. To account for such complicated behavior, the methods of statistical mechanics must be used.

Nearest-neighbor method

Some of these parameters can be determined using the nearest-neighbor method. The interaction between bases on different strands depends somewhat on the neighboring bases. Instead of treating a DNA helix as a string of interactions between base pairs, the nearest-neighbor model treats a DNA helix as a string of interactions between 'neighboring' base pairs. So, for example, the DNA shown below has nearest-neighbor interactions indicated by the arrows.

    ↓ ↓ ↓ ↓ ↓

5' C-G-T-T-G-A 3'

3' G-C-A-A-C-T 5'

The free energy of forming this DNA from the individual strands, ΔG°, is represented (at 37°C) as

ΔG°₃₇(predicted) = ΔG°₃₇(CG initiation) + ΔG°₃₇(CG/GC) + ΔG°₃₇(GT/CA) + ΔG°₃₇(TT/AA) + ΔG°₃₇(TG/AC) + ΔG°₃₇(GA/CT)

The first term represents the free energy of the first base pair, CG, in the absence of a nearest neighbor. The second term includes both the free energy of formation of the second base pair, GC, and stacking interaction between this base pair and the previous base pair. The remaining terms are similarly defined. In general, the free energy of forming a nucleic acid duplex is

$\Delta G_{37}^{\circ }(total)=\Delta G_{37}^{\circ }(initiation)+\sum _{i=1}^{10}n_{i}\Delta G_{37}^{\circ }(i)$.

Each ΔG° term has enthalpic, ΔH°, and entropic, ΔS°, parameters, so the change in free energy is also given by

$\Delta G^{\circ }(total)=\Delta H_{total}^{\circ }+T\Delta S_{total}^{\circ }$.

Values of ΔH° and ΔS° have been determined for the ten possible pairs of interactions. These are given in Table 1, along with the value of ΔG° calculated at 37°C. Using these values, the value of ΔG₃₇° for the DNA helix shown above is calculated to be -22.4 kJ/mol. The experimental value is -21.8 kJ/mol.

Table 1. Nearest-neighbor parameters for DNA/DNA duplexes in 1 M NaCl.

Nearest-neighbor sequence (5'-3'/3'-5')	$\Delta H$° kJ/mol	$\Delta S$° J/(mol·K)	$\Delta G$°37 kJ/(mol·K)
AA/TT	-33.1	-92.9	-4.26
AT/TA	-30.1	-85.4	-3.67
TA/AT	-30.1	-89.1	-2.50
CA/GT	-35.6	-95.0	-6.12
GT/CA	-35.1	-93.7	-6.09
CT/GA	-32.6	-87.9	-5.40
GA/CT	-34.3	-92.9	-5.51
CG/GC	-44.4	-113.8	-9.07
GC/CG	-41.0	-102.1	-9.36
GG/CC	-33.5	-83.3	-7.66
Terminal A-T base pair	9.6	17.2	4.31
Terminal G-C base pair	0.4	-11.7	4.05

The parameters associated with the ten groups of neighbors shown in table 1 are determined from melting points of short oligonucleotide duplexes. Curiously, it works out that only eight of the ten groups are independent. A more realistic way of modeling the behavior of nucleic acids would seem to be to have parameters that depend on the neighboring groups on both sides of a nucleotide, giving a table with entries like "TCG/AGC". However, this would involve around 64 groups; the number of experiments needed to get reliable data for so many groups would be considerable. Because the results from the nearest neighbor method agrees reasonably well with experiment, the extra effort to develop a different model may not be justifiable.