Primer Tm Calculator

Tm = ΔH° / (ΔS° + R ln C) - 273.15. ΔH° and ΔS° are the enthalpy and entropy of the primer pairing with its complement, summed over its nearest neighbors; R is 1.987 cal/(K·mol); C is a strand concentration in mol/L. This is Eq. 3 of SantaLucia's 1998 unified nearest-neighbor paper (PNAS 95:1460), and every parameter this calculator uses comes from its Tables 1 and 2.

Worked example. The default is the M13 forward (-20) primer, GTAAAACGACGGCCAGT. Read two bases at a time it has 16 stacks: GT, TA, AA, AA, AA, AC, CG, GA, AC, CG, GG, GC, CC, CA, AG, GT. Each is one of ten Watson-Crick stacks read from one strand or the other, so AC on this strand is the GT/CA stack and CC is GG/CC. Summing Table 2 over the 16, and adding one initiation term for the G·C pair at the 5' end and one for the A·T pair at the 3' end, gives ΔH° = -133.6 kcal/mol and ΔS° = -360.7 cal/(K·mol) in 1 M NaCl. The paper's sodium correction (Eq. 8) adds 0.368 x N x ln[Na+] to the entropy, with N = 16 for a 17-mer: at 50 mM that is -17.6, so ΔS° is -378.3. At 250 nM primer, R ln C = 1.987 x ln(0.00000025) = -30.2. Then Tm = -133,600 / (-378.3 - 30.2) = 327.0 K, or 53.9 °C. The table under the result shows every term.

The paper's own worked example is the free energy of CGTTGA (its Fig. 1): -2.17 - 1.44 - 1.00 - 1.45 - 1.30 + 0.98 + 1.03 = -5.35 kcal/mol at 37 °C. Enter CGTTGA with salt at 1,000 mM and the ΔG°37 row gives -5.35.

Why concentration is in it. Pairing takes two molecules, so a dilute primer finds its partner less often and melts lower. The paper says which C to use: the total strand concentration for a self-complementary oligo, a quarter of it for two complementary strands at equal concentration, and the larger concentration minus half the smaller when they differ. A PCR primer outnumbers its template by orders of magnitude, so the last case reduces to the primer concentration, which is the default here. A tool that assumes equal strands reports lower: for the default primer, 52.8 °C instead of 53.9 °C. Ten times the primer moves the Tm by a few degrees, not tens.

Salt. Sodium shields the negative phosphate backbones from each other, so less of it means a lower Tm: the default primer is 46.5 °C at 10 mM and 60.5 °C at 200 mM. SantaLucia fitted the correction on 26 duplexes between 10 and 300 mM NaCl and reports it predicts their Tm with an average deviation of 2.2 °C. Potassium is treated here as equivalent to sodium, which is an approximation. Magnesium is not modeled at all. PCR buffers contain it, and Owczarzy and colleagues (Biochemistry, 2008) found that under typical PCR conditions magnesium, not the monovalent ions, governs duplex stability; their correction is not included, so for a PCR buffer this calculator's Tm reads low. Compare both primers of a pair here, under the same settings, rather than mixing numbers from different tools.

The rough rules. The Wallace rule, 2 x (A+T) + 4 x (G+C), and the basic GC formula, 64.9 + 41 x (G+C - 16.4) / length, are shown for comparison and labeled as rough. They know only the base count. Rearranging the default primer's 17 bases changes the nearest-neighbor Tm: GCAGTCAGTCAGCAGAA gives 53.1 °C and GGGGGCCCCAAAAAATT 54.1 °C, against 53.9 °C for the original. Both rules give the same answer for all three. Neither responds to salt or concentration at all.

Annealing temperature. A common rule of thumb starts annealing 3 to 5 °C below the lower Tm of the two primers. It is a starting point, not a specification. Polymerase suppliers publish their own Tm tools with rules for their buffers, and their recommendations can differ from this rule; the protocol for the enzyme you are using governs, and a gradient run settles it. This calculator uses the general published method, not any supplier's.

Molecular weight is computed from IUPAC atomic weights: each base as its deoxynucleoside monophosphate less one water, then one water added and one HPO3 removed for the hydroxyl ends of a synthetic oligo. That reproduces the familiar 313.21, 304.20, 289.18 and 329.21 per A, T, C and G and the -61.96 end correction.

The calculation assumes a perfectly matched two-state duplex. Mismatches, dangling ends, hairpins, primer dimers, modified bases and degenerate positions are not modeled.