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Ligation Calculator (Vector:Insert Ratio)

Calculate how much insert to add to a ligation for a chosen insert-to-vector molar ratio, or work out the ratio you have from the masses, with picomoles and pipetting volumes.

Formula

minsert=r×mvector×LinsertLvectorm_{\text{insert}} = r \times m_{\text{vector}} \times \dfrac{L_{\text{insert}}}{L_{\text{vector}}}
pmol=m (ng)×1000L (bp)×650\mathrm{pmol} = \dfrac{m\,(\mathrm{ng})\times 1000}{L\,(\mathrm{bp})\times 650}
r=pmolinsertpmolvectorr = \dfrac{\mathrm{pmol}_{\text{insert}}}{\mathrm{pmol}_{\text{vector}}}
rr
insert-to-vector molar ratio, for example 3 for 3 : 1
LL
length of each fragment in base pairs

How it works

A ligation joins ends, and what matters is the number of ends of each molecule, not their mass. A short insert has many more molecules per nanogram than a long vector, so equal masses are very unequal in molar terms. The calculation converts to picomoles with the average weight of 650 g/mol per base pair, then sets the molar ratio you want.

Ratios from 1 : 1 to 10 : 1 are used. A common start for a single insert is about 3 : 1, and larger ratios are used for short inserts or blunt ends. The best value depends on the ends, the insert and the ligase, so treat the result as a starting point.

Worked example

50 ng of a 3,000 bp vector and a 1,000 bp insert at a 3 : 1 insert-to-vector molar ratio.

  1. Vector = 50 × 1000 / (3000 × 650) = 0.0256 pmol.
  2. Insert = 3 × 50 × 1000 / 3000 = 50 ng, which is 50 × 1000 / (1000 × 650) = 0.0769 pmol.

Add 50 ng of insert: 0.0769 pmol, exactly three times the vector's 0.0256 pmol.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Double-stranded fragments at 650 g/mol per base pair.
  • The concentrations are accurate. A spectrophotometer overstates DNA that contains RNA or contaminants.
  • The vector is fully digested and, if needed, dephosphorylated, so that it cannot close on itself.

Common mistakes

  • Using masses rather than moles, which gives a huge molar excess of a short insert and many multiple-insert products.
  • Forgetting that the length used is the length of the fragment with the ends as cut, not of the final plasmid.
  • Dropping a ligation with too little DNA in the reaction. Follow the ligase supplier's range of total DNA.

Related tools

Restriction Digest PredictorFragment sizes for a single or multiple enzyme digestOpen calculatorPlasmid Size CalculatorSize of a recombinant plasmid after cloningOpen calculatorTransformation Efficiency CalculatorColony-forming units per microgram of DNAOpen calculatorDNA and RNA Molarity CalculatorConvert ng/µL to nM, pmol per µg and molecules per µLOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.