DNA ligase is used to create a phosphodiester bond between the 5' phosphate and 3' hydroxyl groups of DNA. Most commonly, one needs to insert a DNA sequence of interest into a plasmid. Ideally, you can cut the DNA and vector with the same restriction enzyme. Then you can add both DNA sequences, the cut insert and vector sequence, and ligate them together to form a circular vector using DNA ligase. T4 DNA ligase is the most commonly used DNA ligase for molecular biology techniques.
Endy:DNA ligation using T4 DNA ligase -- Using T4 DNA Ligase
Knight:DNA ligation using NEB Quick Ligation Kit -- 5min ligation.
Knight:TOPO TA cloning -- For PCR products.
Silver:Ligation -- A protocol using the Roche Kit.
BE.109:DNA ligation -- A ligation protocol for classroom use in a laboratory class taught at MIT. Uses T4 DNA ligase but has interesting tips and tricks.
- If you are having trouble with your ligation, NEB offers FAQ's (Quick Ligation T4 DNA ligase) to help.
- Prior to the ligation, some heat their DNA slightly (maybe ~37°C) to melt any sticky ends which may have annealed improperly at low temperatures.
- Tom Knight has read that ligase can inhibit transformation. By heat-inactivating the ligase, this inhibition can be avoided. However, according to the NEB FAQ, heat-inactivation of PEG (which is present in the ligation reaction) also inhibits transformation, therefore a spin-column purification is recommended prior to transformation if you are having problems.
- Treating PCR products with proteinase K prior to restriction digest dramatically improves the efficiency of subsequent ligation reactions. 
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