Nucleic Acid Thermodynamics - Thermodynamics of The Two-state Model

Thermodynamics of The Two-state Model

Several formulas are used to calculate T_m values. Some formulas are more accurate in predicting melting temperatures of DNA duplexes . For DNA oligonucleotides, i.e. short sequences of DNA, the thermodynamics of hybridization can be accurately described as a two-state process. In this approximation one neglects to possibility of intermediate partial binding states in the formation of a double strand state from two single stranded oligonucleotides. Under this assumption one can elegantly describe 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 . According to the Van´t Hoff equation, 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,

.

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

.

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

.

The terms ΔH° and ΔS° are usually given for the association and not the dissociation reaction (see the nearest-neighbor method for example). This formula then turns into:

, where _total < _total.

As mentioned, 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 via several intermediate states. To account for such complicated behavior, the methods of statistical mechanics must be used, which is especially relevant for long sequences.