Ligation Calculator

How much insert a ligation needs

The insert mass for a ligation is the insert:vector molar ratio times the vector mass times the insert length divided by the vector length: insert ng = ratio × vector ng × insert bp ÷ vector bp. So 50 ng of a 3000 bp vector at 3:1 needs 3 × 50 × 500 ÷ 3000 = 25 ng of a 500 bp insert.

The ratio counts molecules, not nanograms. A molecule of double-stranded DNA weighs its length times an average mass per base pair, about 650 g/mol, and because that average is the same for the insert and the vector it cancels, leaving only the ratio of the two lengths. A short insert therefore needs far less mass than the vector for the same number of molecules, and at 3:1 an insert a third of the vector’s length needs exactly the vector’s mass: 50 ng of a 1000 bp insert for 50 ng of a 3000 bp vector. Addgene points out that what really matters is the number of DNA ends available to join, but every linear fragment has two ends however long it is, so counting molecules gives the same ratio.

Using the calculator

Enter the mass of cut vector you plan to use, the lengths of the linearised vector and of the insert in base pairs, and the ratio as one number: 3 for 3:1. The insert mass appears in the answer field. Any field can be the unknown, so you can solve for the ratio to check a ligation you have already set up, or for the vector mass when the insert is the piece in short supply.

Under the answer are the vector and insert in pmol, the total DNA going into the reaction, and the insert mass at 1:1, which times any ratio gives the mass for that ratio. To turn a mass into a volume, divide it by the concentration of the stock, which the nucleic acid quantification calculator works out from an A260 reading.

Worked example: a 500 bp PCR product at 3:1

Promega’s pGEM-T manual asks how much of a 0.5 kb PCR product to add to 50 ng of its 3.0 kb vector for a 3:1 insert:vector ratio.

• Length ratio: 500 bp ÷ 3000 bp = 0.1667, so one insert molecule weighs a sixth of one vector molecule.
• Insert mass: 3 × 50 ng × 0.1667 = 25 ng.
• At 1:1 the same insert would be 50 ng × 0.1667 = 8.33 ng, the 8.3 ng the manual gives.
• In moles, at 650 g/mol per base pair, the vector is 50 ng ÷ (3000 × 650 g/mol) = 0.0256 pmol and the insert 0.0769 pmol, three times as much.

The reaction then holds 75 ng of DNA. If the PCR product is at 12.5 ng/µL, the 25 ng is 2 µL. A much smaller volume is hard to pipette accurately, so dilute a concentrated prep first: C1V1 = C2V2 holds for ng/µL exactly as it does in the molar units of the dilution calculator.

Choosing a ratio

3:1 insert to vector is the usual starting point. It is the ratio in NEB’s T4 DNA ligase protocol, and Addgene calls it usually sufficient when the insert is smaller than the vector. If a ligation gives few colonies, NEB’s troubleshooting guide suggests trying ratios from 1:1 to 10:1, going to 20:1 only for short adaptors, while Promega reports ratios from 1:8 to 8:1 working with its pGEM-T vectors and suggests 1:3 to 3:1 as starting points. The calculator shows a caution above 10:1 and below 1:1.

Check which way round a protocol writes the ratio. NEB’s T4 DNA ligase protocol puts the vector first, as 1:3 vector to insert, and Promega’s pGEM-T manual puts the insert first, as 3:1 insert:vector, and both mean three insert molecules for every vector molecule. This calculator takes the insert:vector form, so both are entered as 3.

What this does not cover

The calculation assumes every molecule you weighed can take part. It cannot see how much of the vector was actually cut, whether the ends are compatible, or whether at least one of the two pieces carries a 5′ phosphate for the ligase to join, which NEB’s troubleshooting guide asks you to check. Any of these changes the effective ratio without changing a single nanogram.

It also leaves the rest of the reaction to the kit. NEB’s T4 DNA ligase protocol builds 20 µL from 2 µL of 10X buffer, the DNA, water and 1 µL of ligase, and Promega’s pGEM-T protocol builds 10 µL around 5 µL of its 2X buffer. NEB also suggests keeping total DNA under 10 ng/µL, which is 200 ng in a 20 µL reaction, so the total under the result is worth a glance.

The pmol figures use 650 g/mol per base pair. Published values run from about 607 to 660 g/mol per base pair, depending on the source and on whether the counter-ions are counted, so another calculator’s pmol can differ by up to about 7 percent. The insert mass does not change at all, because the same figure cancels from both sides of the ratio.

Common mistakes

• Setting up equal masses and calling it 1:1. Equal nanograms are equal numbers of molecules only when the pieces are the same length. 50 ng of a 500 bp insert with 50 ng of a 3 kb vector is 6:1.
• Entering the ratio the wrong way round. 1:3 insert to vector in place of 3:1 puts in a ninth of the insert you meant. NEB’s 1:3 vector to insert is 3 here.
• Mixing kb and bp. The lengths only enter as a ratio, so both in kb still gives the right mass, but one in kb and the other in bp is out by a factor of 1000. The calculator warns about a vector under 1000 bp.
• Using the uncut plasmid length. The vector length is what goes into the tube. Cutting a 1.5 kb fragment out of a 6 kb plasmid leaves a 4.5 kb backbone, and entering 6000 bp gives a quarter less insert than the ratio needs.
• Trusting an A260 reading on a PCR product. Leftover primers and nucleotides absorb at 260 nm too, so the insert is overstated and the real ratio comes out lower than planned. Promega suggests estimating a PCR product against mass standards on a gel or with a fluorescent assay.

Converting units first? Use the mass conversion table.