Algorithm of Melting Temperature

The melting temperature, Tm, is defined as the temperature at which half of the strands are in the double-helical state and half are in the "random-coil" state. The melting temperature of an oligonucleotide is its most critically important value. The most reliable and accurate determination of melting temperature is determined empirically. However, this is cumbersome and not usually necessary. Several useful, handy formulas have been developed to provide the Tm for PCR, Southern and Northern blots, and in situ hybridization.

The main factors affecting Tm are salt concentration, strand concentration, and the presence of denaturants. Other effects such as sequence, length, and hybridization conditions can be important as well.

Empirical Estimation

a) Basic Calculation

The simple estimation of Tm is based on the number of each nucleotide within the sequence.

(Eq.1)

where , , , are the number of the bases A, T(U), G, C in the sequence, respectively.

This equation was developed for short DNA oligos of 14-20 base pairs hybridizing to membrane bound DNA targets in 0.9M NaCl.

For sequences longer than 14 nucleotides, the equation used is

(Eq.2)

b) Algorithm with Salt Adjustment

The equation for DNA oligo shorter than 14 bases is:

(Eq.3)

For DNA oligos longer than 14 nucleotides and pH from 5 to 9, the following formula turns out to be appropriate:

(Eq.4)

Algorithm based on Nearest-Neighbor Thermodynamics

The nearest-neighbor (NN) algorithm for nucleic acids assumes that the stability of a given base pair depends on the identity and orientation of neighboring base pairs. The application of the NN model to nucleic acids was pioneered by Zimm [1] and by Tinoco and coworkers [2]. Subsequently, several experimental and theoretical papers on DNA and RNA NN thermodynamics have appeared [3-4]. There has been disagreement concerning a number of issues, particularly differences between DNA polymer and oligonucleotide NN thermodynamic trends and the salt dependence of nucleic acid denaturation. A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics was shown by SantaLucia[5]. We adopt the algorithm and parameters shown in SantaLucia 1998.

For self-complementary oligonucleotide duplexes, the Tm is calculated from the following thermodynamic equation:

(Eq.5)

where (Kcal/mol) is the sum of the nearest neighbor enthalpy changes for hybrids; is the sum of the nearest neighbor entropy changes(cal/k.mol); R is the Gas Constant (1.987 cal/K.mol); C is the parameter associated with the total oligonucleotide strand concentration. If the strand is self complementary,

(Eq.6)

where is the total molar concentration of strands.

The basic calculation of and is based on NN parameters [Table 1].

A correction of entropy without modification of enthalpy was suggested in SantaLucia 1998 as follows,

(Eq.7)

where is the total entropy with [Na+]=1M; N is the length of the duplex.

It is important to realize that the nearest-neightbor approach has been established on small oligonucleotides. Therefore the use of Eq.5-7 in the non-approximate mode is really accurate only for relatively short sequences (<60bs).

Table 1. Unified oligonucleotide H and S NN parameters in 1 M NaCl

Sequence	H(kcal/mol)	S(cal/k.mol)
AA/TT	7.9	22.2
AT/TA	7.2	20.4
TA/AT	7.2	21.3
CA/GT	8.5	22.7
GT/CA	8.4	22.4
CT/GA	7.8	21.0
GA/CT	8.2	22.2
CG/GC	10.6	27.2
GC/CG	9.8	24.4
GG/CC	8.0	19.9
Init. w/term. G·C	0.1	2.8
Init. w/term. A·T	2.3	4.1
Symmetry correction	0	1.4