There are a number of different ways to calculate the melting temperature (T_m) of an oligo. All of these methods will give different results. Please note that these calculations are theoretical. Optimum T_m values must be determined empirically.

For details on each of the calculations performed below please see the notes below, "Theoretical T_m of Oligos".

Theoretical T_m of Oligos

There are several formulas for calculating melting temperatures (T_m). In all cases these calculations will give you a good starting point for determining appropriate annealing temperatures for PCR, RT-PCR, hybridization and primer extension procedures. However, a precise optimum annealing temperature must be determined empirically. 

Basic T_m Calculations

The simplest formula is as follows (1):

This formula is valid for oligos <14 bases and assumes that the reaction is carried out in the presence of 50mM monovalent cations. For longer oligos, the formula below is used:

Where N is the length of the primer.

For example, Promega’s T7 Promoter Primer (TAATACGACTCACTATAGGG) is a 20mer composed of 5 T’s, 7 A’s, 4 C’s, and 4 G’s. Thus, its melting temperature is calculated:

Salt-Adjusted T_m Calculations

Another commonly used formula takes into account the salt concentration of the reaction (1–4). This formula has several variations, but all of them are essentially as follows:

Where N is the number of nucleotides in the oligo. Note that PCR is typically performed in the presence of ~50mM monovalent cations.

81.5°C + 16.6°C  x  (log₁₀[0.05])  +  0.41°C x (40)  –  675/20  =  42.5°C

 

Base-Stacking T_m Calculations

The most sophisticated T_m calculations take into account the exact sequence and base stacking parameters, not just the base composition (1,5,6).

The equation used is:

Where:

• ΔH is the enthalpy of base stacking interactions adjusted for helix initiation factors (6,7).
• ΔS is the entropy of base stacking adjusted for helix initiation factors (6,7) and for the contributions of salts^(a) to the entropy of the system (6).
• R is the universal gas constant (1.987Cal/°C*Mol)

This equation, as implemented above, is valid if the following assumptions are met:

• The primer is not self complementary. For self-complementary oligos, the denominator of the equation becomes ΔS + R ln([primer]/4)
• The primer concentration is much greater than the target concentration^(b). If the concentrations are almost equal, the denominator of the equation becomes  ΔS + R ln([primer] – [target]/2)
• The primer is an "oligo" rather than a long polymer. The salt effects on polymers is significantly different from those on oligos. For a complete discussion, see reference 6.

For a complete discussion of the parameters involved in base-stacking calculations of T_m, see references 5, 6 and 8.

Use of the base-stacking calculations yields a T_m of 56°C for Promega’s T7 Primer when magnesium contributions are taken into account (and 47°C when they are not). 

It is apparent that all three methods give similar, but different, values for primer T_m. In most cases any one of the formulas will yield an adequate approximation of the actual T_m of the oligo but for best results the optimum annealing temperature will need to be determined empirically using the theoretically calculated T_m as a starting point.

Molecular weight of single stranded DNA

The molecular weight of a specific segment of DNA is equal to the sum of the molecular weights of each of the nucleotides. For a know sequence, this is calculated as the sum of the molecular weights of each nucleotide monophosphate (adjusted for the phosphodiester bond)^c:

Molecular weight^d = (329.2 * number of G's) + (313.2 * number of A's) + (304.2 * number of T's) + (289.2 * number of C's) 
This molecular weight is adjusted by -78 for an assumed missing 5' phosphate group (PO₃) which is replaced by a single hydrogen and +17 for a 3′ hydroxyl . This must be adjusted by +78 if a 5′ phosphate is present. 

Notes

^(a)We have found that most melting temperature calculations do not take into account the effects of magnesium on helix stability. Therefore, most empirical guidelines used to design experiments will not apply when the magnesium effects are included. We have included the option to consider magnesium in the equation if it is desirable but have not included it in the default setting. Including magnesium will generally raise the theoretical melting temperature by about 5–8°C for oligonucleotides in a 1.5mM Mg²⁺ solution (8,9).

^(b)The concentrations of the primer and the target sequence will change dramatically during PCR*, but generally this will not make a significant difference to the calculated T_m. A standard 50µl reaction may contain 0.1µg of human genomic DNA as a template and is 0.5µM for each primer. This reaction would be approximately 2 femtomolar (2 x 10^–15M) for each single copy target. At the end of 30 cycles, this same reaction may produce about 0.5µg of a specific 1kb amplimer that gives a final concentration of 15nM. In this case the primer concentration will not change significantly and thus will remain much greater than the target concentration (6,8).

(c)The molecular weight of the each nucleotide used in calculations was decreased by 1 in Sepetember, 2003 to correct an error. 

^(d)The molecular weights of dNMP's are 18 greater than those shown in this equation because dNMP's have 3′-hydroxyl groups and 5'- hydrogens that are lost during polymerization.

References

1. Rychlik, W. and Rhoads, R.E. (1989) Nucl. Acids Res. 17, 8543.
2. PCR Core Systems Technical Bulletin #TB254, Promega Corporation.
3. Sambrook, J., Fritsch, E.F. and Maniatis, T. (1989) Molecular Cloning: A Laboratory Manual, Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY.
4. Mueller, P.R. et al. (1993) In: Current Protocols in Molecular Biology 15.5, Greene Publishing Associates, Inc. and John Wiley and Sons, New York.
5. Borer P.N. et al. (1974) J. Mol. Biol. 86, 843.
6. SantaLucia, J. (1998) Proc. Nat. Acad. Sci. USA 95, 1460.
7. Allawi, H.T. and SantaLucia, J. Jr. (1997) Biochemistry 36, 10581.
8. von Ahsen N. et al. (1999) Clin. Chem. 45, 2094.
9. Nakano S. et al. (1999) Nucl. Acids Res. 27, 2957.

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