Insert:vector molar ratio in ligation and cloning

A 3:1 ligation means three insert molecules for every vector molecule — a ratio of molecules, not of nanograms. Because a shorter fragment packs more molecules per nanogram, you have to convert the ratio into a mass.

Molecules, then mass

Ligation efficiency depends on how often an insert end meets a vector end, so the useful ratio is molar. But you pipette mass. For DNA, mass is proportional to length × number of molecules, so to hold a molar ratio you scale the mass by the length ratio:

insert mass = vector mass × (insert length ÷ vector length) × molar ratio

A worked example

50 ng of a 5,000 bp vector, a 1,000 bp insert, at a 3:1 insert:vector molar ratio: 50 × (1,000 ÷ 5,000) × 3 = 30 ng of insert. Notice the insert is one-fifth the length of the vector, so even at three times the molar amount it is still less mass than the vector. Drop to a 1:1 ratio and you would use just 10 ng.

Choosing a ratio

A 3:1 insert:vector molar ratio is a common starting point for cohesive (sticky-end) ligations; blunt-end ligations often use higher ratios because they are less efficient. There is no universal best value — set up a small range (say 1:1 to 5:1) against a fixed amount of vector and see which gives the most colonies. The same molar reasoning applies to Gibson and other assembly reactions.