Primer Tm Calculator

How primer Tm is calculated

A primer’s melting temperature, Tm, is the temperature at which half of its strands are paired with their complement, and the most accurate way to predict it from the sequence is the nearest-neighbour method: add up the enthalpy and entropy of each pair of neighbouring bases, correct the entropy for salt, then take Tm = ΔH° / (ΔS° + R ln(CT/4)). Here ΔH° is in cal/mol, ΔS° in cal/(mol·K), R is the gas constant, 1.9872 cal/(mol·K), and CT is the total strand concentration in mol/L; the answer comes out in kelvin.

The stacking values are SantaLucia’s 1998 unified parameters, measured in 1 M NaCl. Each end of the duplex adds an initiation term that depends on whether it finishes in an A·T or a G·C pair, and a sequence that is its own reverse complement adds a symmetry term of −1.4 cal/(mol·K) and uses CT in place of CT/4, because it pairs with itself. The salt correction is SantaLucia’s too, ΔS° + 0.368 × (N − 1) × ln[Na⁺] for a primer of N bases with [Na⁺] in mol/L, and magnesium enters through von Ahsen’s sodium equivalent, [Na⁺] + 120 × √([Mg²⁺] − [dNTP]), worked in mM and divided by 1000 before the logarithm is taken.

In von Ahsen and colleagues’ test against 217 perfectly matched duplexes under PCR conditions, nearest-neighbour calculations with this sodium equivalent, plus a DMSO term of 0.75 °C per percent, predicted the Tm with a standard error of 1.76 °C, so treat the tenth of a degree on the headline as arithmetic rather than accuracy. The idea behind the method, that a duplex holds together through each base pair stacking on the next, is easiest to picture in the DNA double helix explorer.

Worked example: the T7 promoter primer

Take the T7 primer, 5′-TAATACGACTCACTATAGGG-3′, at Primer3’s default conditions: 50 nM of strands, 50 mM monovalent salt, 1.5 mM Mg²⁺ and 0.6 mM dNTPs.

• Its 19 stacks and 2 ends sum to ΔH° = −148.8 kcal/mol and ΔS° = −411.2 cal/(mol·K).
• Sodium equivalent: 50 + 120 × √(1.5 − 0.6) = 163.84 mM.
• Salt-corrected entropy: −411.2 + 0.368 × 19 × ln(0.16384) = −423.85 cal/(mol·K).
• Tm = −148,800 / (−423.85 + 1.9872 × ln(1.25 × 10⁻⁸)) = 323.47 K, which is 50.3 °C.

The two counting rules disagree with that and with each other. The Wallace rule gives 2 × 12 + 4 × 8 = 56 °C, and the basic GC formula gives 64.9 + 41 × (8 − 16.4) / 20 = 47.7 °C. Neither knows about the magnesium: set it to zero and the nearest-neighbour Tm falls to 44.6 °C, while both counting rules stay exactly where they were.

Which method is shown when

• Nearest-neighbour is the headline for every sequence from 8 to 60 bases. Above 40 bases it carries a caution, because Kibbe’s OligoCalc paper recommends the method for 8 to 40 bases and Primer3’s own code notes that it becomes less accurate as the sequence grows longer. Primer3 itself designs no primer over 35 bases, a limit its manual ties to the length its melting temperature is valid for.
• The Wallace rule, Tm = 2(A + T) + 4(G + C), is shown at every length and flagged outside 14 to 20 bases, the range it is quoted for.
• The basic GC formula, Tm = 64.9 + 41 × (G + C − 16.4) / N, is shown from 14 bases, the length from which OligoCalc applies it, and reads n/a below that.

Only the first responds to the buffer and the strand concentration. The other two are here because courses teach them and older protocols quote them, and because seeing all three side by side is the quickest way to see how far apart they can be. The ΔG° readout is the free energy of the primer paired with its full complement at 37 °C in the buffer you have set, and the more negative it is, the more stable the duplex.

Salt, magnesium and strand concentration

Cations shield the negative charge on the two phosphate backbones, so the more of them there are, the more stable the duplex and the higher the Tm. With no magnesium, the T7 primer melts at 44.6 °C in 50 mM sodium and at 59.5 °C in 1 M, the concentration the parameters were measured in. Magnesium is far more effective than sodium: 1.5 mM of it with 0.6 mM dNTPs counts as another 114 mM of sodium, because dNTPs bind magnesium and only the excess is free.

Strand concentration enters as a logarithm, so it matters less but never drops out: ten times more strand raises the T7 primer’s Tm by about 3 °C. For PCR, Primer3 uses 50 nM, which its manual describes as an empirically determined concentration of annealing oligo, lower than the 0.5 µM of primer in a typical reaction. Keep 50 nM to compare with Primer3 and with annealing rules written for it. For two oligos annealed at equal concentration, enter the total of both strands, so 1 µM of each is 2000 nM. To bring a resuspended stock down to its working strength, use the dilution calculator, and to measure it, the nucleic acid quantification calculator or, with the oligo’s own extinction coefficient, the Beer-Lambert law calculator.

Common mistakes

• Leaving out the magnesium. A PCR buffer’s Mg²⁺ raises the T7 primer from 44.6 to 50.3 °C here, so a Tm worked out for sodium alone runs low for every primer in the reaction.
• Counting a 5′ tail. A restriction site or adapter added to the 5′ end does not pair with the template in the first cycles. Enter the part that anneals; the tail only pairs once it has been copied into the product. To clone that product, the ligation calculator gives the mass of insert for a vector.
• Comparing Tm values from different tools. Each uses its own parameters, salt correction and default concentrations, so one primer can differ by several degrees between two calculators with nothing wrong in either. Compare primers in one tool at one set of conditions.
• Typing the sequence backwards. The box reads 5′ to 3′. The reverse complement gives exactly the same Tm, because it describes the same duplex, but the reversed sequence does not: the T7 primer written backwards reads 51.9 °C instead of 50.3 °C. The reverse complement calculator turns a sequence round when you need the other strand.
• Trusting the Wallace rule on a long primer. It adds 2 or 4 °C for every base, so any 40-base primer at 50 percent GC comes out at 120 °C, above the boiling point of water.

What this calculator leaves out

• Mismatches, dangling ends and modified bases. The parameters describe a perfectly matched duplex of A, C, G and T. Inosine, locked nucleic acids, phosphorothioates, dyes and quenchers all change the Tm and are not modelled.
• Hairpins and primer dimers. A Tm describes the primer paired with its target and says nothing about whether it folds on itself or pairs with its partner.
• Additives. DMSO and formamide lower the Tm. Published estimates for DMSO run from 0.5 to 0.75 °C per percent, and none is applied here.
• A strand in large excess. For strands at unequal concentrations SantaLucia replaces CT/4 with CA − CB/2, which for a probe or primer that far outnumbers its target is simply the excess strand’s concentration, and that raises the Tm. This tool keeps the equal-strand form that Primer3 uses.
• Other ions and a fuller magnesium model. Only Na⁺, K⁺ and Mg²⁺ are counted, so Tris and other buffer ions are not. Owczarzy and colleagues’ 2008 magnesium correction is more detailed than the sodium equivalent used here.
• RNA and long duplexes. RNA and RNA/DNA hybrids need their own parameters, and a duplex much longer than a primer, such as a PCR product, melts in stages rather than all at once.