There are two algorithms for melting temperature calculation:

• Rough
• Primer 3

Rough

The melting temperature is calculated as follows. For sequences of length 15 or longer:

For shorter sequences:

Here "nA", "nT", "nC", "nG" denote the number of the corresponding nucleotide.

Primer 3

This calculation algorithm is borrowed from the Primer3 package. The algorithm uses the nearest-neighbor (NN) model or the formula from Bolton and McCarthy, PNAS 84:1390 (1962) (as presented in Sambrook, Fritsch and Maniatis, Molecular Cloning, p 11.46 (1989, CSHL Press)). The algorithm has the following parameters:

• DNA concentration (nanomolar) - a value to use as nanomolar concentration of each annealing oligo over the course the PCR. This parameter corresponds to 'c' in equation (ii) of the paper [SantaLucia (1998) A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proc Natl Acad Sci 95:1460-1465 http://www.pnas.org/content/95/4/1460.full.pdf+html], where a suitable value (for a lower initial concentration of template) is "empirically determined".
• Monovalent concentration (millimolar) - the millimolar concentration of monovalent salt cations (usually KCl) in the PCR.
• Divalent concentration (millimolar) - the millimolar concentration of divalent salt cations (usually MgCl^(2+)) in the PCR.
• DNTP concentration (millimolar) - the millimolar concentration of the sum of all deoxyribonucleotide triphosphates. A reaction mix containing 0.2 mM ATP, 0.2 mM CTP, 0.2 mM GTP and 0.2 mM TTP would have this value equals to 0.8.
• DMSO concentration (%) - the concentration of DMSO in percent.

• DMSO factor - The melting temperature of primers can be approximately corrected for DMSO:
  

  Tm = Tm(without DMSO) + DMSO factor * DMSO concentration

• Formamide concentration (mol/l) - The concentration of formamide in mol/l. The melting temperature of primers can be approximately corrected for formamide:

  Tm = Tm(without formamide) + (0.453 * GC% / 100 - 2.88)  * Formamide concentration

• NN Max Length - the maximum sequence length for using the nearest neighbor model. For sequences longer than this, algorithm uses the "GC%" formula from Bolton and McCarthy, PNAS 84:1390 (1962):

  Tm = 81.5 - DMSO concentration * DMSO factor + 0.453 * (GC% - 2.88) * Formamide concentration + 16.6 * log10(Monovalent concentration / 1000) + 0.41 * GC% - 600 / Length

• Thermodynamic table - specifies the thermodynamic table for the melting temperature calculation:
  
  • Breslauer - method for Tm calculations from the paper[Rychlik W, Spencer WJ and Rhoads RE (1990) "Optimization of the annealing temperature for DNA amplification in vitro", Nucleic Acids Res 18:6409-12 http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=2243783]. and the thermodynamic parameters from the paper[Breslauer KJ, Frank R, Bl�cker H and Marky LA(1986) "Predicting DNA duplex stability from the base sequence" Proc Natl Acad Sci 83:4746-50 http://dx.doi.org/10.1073/pnas.83.11.3746]
  • SantaLucia - method for Tm calculations and the thermodynamic parameters from [SantaLucia JR (1998) "A unified view of polymer, dumbbell and oligonucleotide DNA nearest-neighbor thermodynamics", Proc Natl Acad Sci 95:1460-65 http://dx.doi.org/10.1073/pnas.95.4.1460]
• Salt Correction Formula - specifies the salt correction formula for the melting temperature calculation:
  • Schildkraut - [Schildkraut, C, and Lifson, S(1965) "Dependence of the melting temperature of DNA on salt concentration", Biopolymers 3:195-208 (not available on-line)]
  • SantaLucia - [SantaLucia JR(1998) "A unified view of polymer, dumbbell and oligonucleotide DNA nearest - neighbor thermodynamics", Proc Natl Acad Sci 95:1460-65 http://dx.doi.org/10.1073/pnas.95.4.1460]
  • Owczarzy - [Owczarzy, R., Moreira, B.G., You, Y., Behlke, M.A., and Walder, J.A. (2008) "Predicting stability of DNA duplexes in solutions containing magnesium and monovalent cations", Biochemistry 47 : 5336 - 53 http://dx.doi.org/10.1021/bi702363u]