The melting temperature, T_{m}, of an oligonucleotide is its most critically important value. The most reliable and accurate determination of melting temperature is determined empirically^{1}, however, this is cumbersome and not usually necessary.

Several useful, handy formulas have been developed to provide the T_{m} for PCR, Southern and Northern blots, and* in situ hybridization*.

The main factors affecting T_{m} are salt concentration, strand concentration, and the presence of denaturants (such as formamide or DMSO). Other effects such as sequence, length, and hybridization conditions can be important as well.

## Definitions

T_{m} - The temperature at which 50% of the oligonucleotide and its perfect complement are in duplex.

T_{d} - The temperature at a particular salt concentration, and total strand concentration at which 50% of an oligo and its perfect filter-bound complement are in duplex.

## Equations

The simplest equation for T_{d} is the Wallace rule^{2}:

(1) T_{d} = 2°C(A+T) + 4°C(G+C)

T_{d} is a filter-based calculation where A, G, C, and T are the number of occurrences of each nucleotide. This equation was developed for short DNA oligos of 14-20 base pairs hybridizing to membrane bound DNA targets in 0.9M NaCl.

The melting temperature for the sequence TGCTCA is, 2(1+2) + 4(1+2) = 18°C. The nature of the immobilized target strand provides a net decrease in the T_{m} observed when both target and probe are free in solution. The magnitude of the decrease is approximately 7-8°C.

Another familiar equation^{3} for DNA which is valid for oligos longer than 50 nucleotides from pH 5 to 9 is:

(2) T_{m} = 81.5 + 16.6 log M + 41(XG+XC) - 500/L - 0.62F

Where M is the molar concentration of monovalent cations, XG and XC are the mole fractions of G and C in the oligo, L is the length of the shortest strand in the duplex, and F is the molar concentration of formamide.

This is a far more useful equation to most researchers, as it includes adjustments for salt (although the equation is < when M=0) and formamide , the two most common agents for changing hybridization temperatures.

Thus, at M = 0.9, and F = 0, T_{m} = 81.5+16.6(log(0.9))+41(.17+.33)-500/6-0.62(0)=17.9° C. Similar equations apply for RNA.^{4}

## Theoretical

Several studies have derived accurate equations for T_{m} using thermodynamic basis sets for nearest neighbor interactions.^{5} The equation for DNA and RNA is:

Where ΔH (Kcal/mol) is the sum of the nearest neighbor enthalpy changes for hybrids, A is a small, but important constant containing corrections for helix initiation, ΔS (eu) is the sum of the nearest neighbor entropy changes, R is the Gas Constant (1.987 cal deg^{-1} mol^{-1}) and C_{t} is the total molar concentration of strands. If the strand is self complementary, C_{t }/4 is replaced by C_{t}.

ΔH and ΔS values for nearest neighbor interactions of DNA and RNA are shown in Table 1. Please note that this equation includes a factor to adjust for salt concentration.

For example, our sample sequence would result in the following expression assuming 200 nM strand concentration at 900 mM NaCl:

1000*(-5.8-11.1-7.8-5.6-5.8)

---------------------------------------------------------- - 273.15 + 16.6log(0.9)

[(-10.8)+(-12.9-26.7-20.8-13.5-12.9)+(1.987)ln[(2.0E^{-7})/4]]

Therefore: T_{m} = 1.725°C

Notice the considerable difference between the results of equations (1) and (3) in this case. This shows how much of an effect sequence can have on the T_{m}.

## Comparisons

So which value do we use? Remember that Equation 1 was derived for 14-20mers used in membrane hybridizations and may be expected to have a limited range of applicability - an important point, as this equation is used by almost all researchers for oligos used for PCR as well as blots. Equation 3 is certainly more appropriate in this case. On the other hand, Equation 3 becomes inappropriate for oligos longer than a 50-mer. For long oligos, equation 2 is probably the best choice. The best equation for a particular researcher will depend on the oligo and the type of experiment involved.

Solution based amplification strategies can use the Wallace rule for convenience, but one should add 8° C to the result to convert T_{d} to T_{m}. Accuracy will also be compromised if the salt concentration varies much from 0.9 M. Researchers doing Southern, Northern or other filter hybridizations can use equation (1) as is. As with any theoretical approach, the results of these equations should be used with caution. Many experiments involve reagents or conditions that invalidate the results of these equations. Sometimes only an empirical approach provides a satisfactory answer. For instance, in situ hybridizations provide sufficiently different environments from case to case that anomalous results may occur.

Counter ion identity, solvation effects, conjugated groups (biotin, digoxigenin, alkaline phosphatase, fluorescent dyes, etc.), and impurities may also affect the T_{m}. In these cases, theoretical equations are inaccurate, but still provide a useful estimate to begin development.

## Conclusions

At Sigma, all oligo T_{m} are calculated using the nearest neighbor method with values of 50 mM for cation concentration and 0.5 micromolar for the strand concentration.^{6} For individuals, it may make more sense to use the less complicated equations. Whichever equations one uses, one will obtain accurate results as long as one remembers to correct for salt or formamide concentration and to observe the limits of applicability of each equation.

## Materials

## References

- The common way to determine the actual melting point is to use a thermostatted cell in a UV spectrophotometer. If temperature is plotted vs. absorbance, an S-shaped curve with two plateaus will be observed. The absorbance reading halfway between the plateaus corresponds to T
_{m}.
- Wallace, R.B.; Shaffer, J.; Murphy, R.F.; Bonner, J.; Hirose, T.; Itakura, K.
*Nucleic Acids Res.* 6, 3543 (1979).
- Howley, P.M; Israel, M.F.; law, M-F.; Martin,M.A.
*J. Biol. Chem.* 254, 4876.
- The equations for RNA are:

T_{m} = 79.8 + 18.5 log M + 58.4 (XG+XC) + 11.8(XG+XC)2 - 820/L - 0.35F

And for DNA-RNA hybrids:

T_{m} = 79.8 + 18.5 log M + 58.4 (XG+XC) + 11.8(XG+XC)2 - 820/L - 0.50F

These equations are derived for oligo-immobilized target hybrids. In general, one can say that RNA-RNA hybrids are highest in stability, then RNA-DNA, and then DNA-DNA.
- For DNA see: Breslauer, K.J.; Frank, R.; Blšcker, H.; Marky, L.A. Proc. Natl. Acad. Sci. USA 83, 3746-3750(1986). For RNA see: Freier, S.M.; Kierzek, R.; Jaeger, J.A.; Sugimoto, N.; Caruthers, M.H.; Neilson, T.; Turner, D.H.
*Proc. Natl. Acad. Sci.* 83, 9373-9377 (1986).
- These values have been found to be the most appropriate for PCR. Rychlik, W.; Spencer, W.J.; Rhoads, R.E. (1990)
*Nucl. Acids Res.* 18(21), 6409-6412.