Ligation Calculator
insert ng = ratio × vector ng × insert length ÷ vector length. The ligation calculator turns a molar ratio into the nanograms you actually pipette.
Insert mass
- Insert to add 3 × 50 ng × 750 bp ÷ 3,000 bp. The insert is 25% of the vector's length, so 3:1 by molecules is 0.75:1 by mass.
- 37.5 ng
- The formula Moles of DNA are mass ÷ (length × mass per base pair). Write that for the insert and the vector, set their ratio to the target, and the mass per base pair cancels. That is why it does not appear here.
- insert ng = ratio × vector ng × (insert bp ÷ vector bp)
- Vector 50 ng × 1000 ÷ (3,000 bp × 661.9 g/mol per bp). A linear molecule has two ends, so ends are twice the molecules.
- 25.2 fmol of molecules, 50.4 fmol of ends
- Insert 37.5 ng × 1000 ÷ (750 bp × 661.9 g/mol per bp). The ratio of insert to vector here is 3.00, as asked.
- 75.5 fmol of molecules, 151 fmol of ends
- Total DNA in the ligation Vector plus insert. Check it against the range your ligase's protocol gives for the reaction volume.
- 87.5 ng
- To pipette 50 ng ÷ 50 ng/µL; 37.5 ng ÷ 20 ng/µL. Volumes under about 0.5 µL are hard to pipette accurately; dilute the stock and pipette more of it instead.
- 1.00 µL of vector, 1.88 µL of insert
| Insert:vector | Insert mass | Insert | Insert ends |
|---|---|---|---|
| 1:1 | 12.5 ng | 25.2 fmol | 50.4 fmol |
| 2:1 | 25.0 ng | 50.4 fmol | 101 fmol |
| 3:1 | 37.5 ng | 75.5 fmol | 151 fmol |
| 5:1 | 62.5 ng | 126 fmol | 252 fmol |
| 7:1 | 87.5 ng | 176 fmol | 353 fmol |
| 10:1 | 125 ng | 252 fmol | 504 fmol |
- The ratio is of molecules, not of masses. Mixing equal nanograms of a 750 bp insert and a 3 kb vector is already a 4:1 molar excess of insert.
- Lengths are of the fragments that go into the tube: the vector after it is cut open, the insert after digestion. For a PCR product, include the primer tails.
- This is the arithmetic of the setup only. It does not model end compatibility, dephosphorylation of the vector, ligase activity or transformation efficiency, which decide whether the ligation works.
How the Ligation Calculator works
The formula:
insert (ng) = insert:vector ratio × vector (ng) × insert length (bp) ÷ vector length (bp)
A worked example, the one above: 50 ng of a 3,000 bp linearized vector, a 750 bp insert, and a 3:1 molar ratio. The insert is a quarter the length of the vector, so a molecule of it weighs a quarter as much. Three of them per vector molecule is 3 × 50 × 750 ÷ 3,000 = 37.5 ng of insert.
Why molar, not mass. Ligation joins ends, one insert end to one vector end, so what matters is how many molecules of each are in the tube. A nanogram of a short fragment contains many more molecules than a nanogram of a long one. In the example, 37.5 ng of insert is less mass than the 50 ng of vector, yet it is three times as many molecules. Getting this backwards, and adding insert by mass, is the most common reason a ratio is far off what was intended.
Where the mass per base pair went. The number of moles in a mass of DNA is mass ÷ (length × mass per base pair). Write that for both fragments, set the insert-to-vector ratio, and the mass per base pair is on both sides, so it cancels. The insert mass depends only on the two lengths, the vector mass and the ratio. The mass per base pair matters only for the absolute amounts in pmol, which the page also gives.
The mass per base pair used for those. Rather than adopt one of the round figures in circulation (650 and 660 g/mol are both common), it is computed here from the IUPAC atomic weights. Each nucleotide in a chain is its monophosphate less one water: dA 313.21, dC 289.18, dG 329.21 and dT 304.20 g/mol as the free acid. An A-T pair is 617.41 and a G-C pair 618.39, an average of 617.9 g/mol. DNA in a buffer carries a sodium ion on each phosphate in place of the proton, adding 21.98 g/mol per nucleotide, so the sodium salt is 661.9 g/mol per base pair. The difference between any of these is a few percent of the pmol figure and none of the insert mass.
pmol of ends. A linear double-stranded fragment has two ends, so pmol of ends is twice pmol of molecules. Some protocols specify the amount of DNA ends per reaction rather than nanograms, which is why both are shown. In the example the vector is 25.2 fmol of molecules and 50.4 fmol of ends.
Choosing the ratio. 3:1 insert:vector is a common starting point. Many protocols suggest trying a few ratios side by side, and the table above gives the insert mass for each. An excess of insert drives the vector toward carrying one; too large an excess raises the chance of several inserts in one vector. For an equimolar ligation, enter 1.
What the page does not model: whether the ends are compatible, whether the vector was dephosphorylated, the ligase, the buffer, the temperature or the transformation. It sets up the arithmetic of the tube.
Ligation Calculator FAQ
How do I calculate insert to vector ratio for ligation?
Insert ng = ratio × vector ng × insert bp ÷ vector bp. For 50 ng of a 3,000 bp vector, a 750 bp insert and a 3:1 ratio: 3 × 50 × 750 ÷ 3,000 = 37.5 ng of insert.
Is the 3:1 ratio by mass or by moles?
By moles: molecules of insert per molecule of vector. A mass ratio would give very different numbers of molecules whenever the two fragments differ in length, which they nearly always do.
What mass per base pair should I use, 650 or 660?
For the insert mass it does not matter: the figure cancels. For pmol, the sodium salt of dsDNA computed from IUPAC atomic weights is 661.9 g/mol per base pair and the free acid 617.9. 650 and 660 are round figures within a few percent of the sodium salt.
How do I convert ng of DNA to pmol?
pmol = ng × 1,000 ÷ (length in bp × mass per bp). 50 ng of a 3,000 bp fragment at 661.9 g/mol per bp is 50,000 ÷ 1,985,589 = 0.0252 pmol, or 25.2 fmol. Double it for pmol of ends.