What is the difference between single digestion and double digestion when discussing restriction enzymes?
Single digest: one restriction enzyme only
Double digest: two restriction enzymes
NOTE: in this answer, for RE's (Restriction Enzymes) read Endonucleases....
RE's are highly specific for the DNA-sequence they splice: it is almost invariably a predetermined Palindromic sequence.
For instance, Hin DIII will only make a cut in the sequence:
The amount of bases in this palindorme is 6.
I'm not going into statistical analysis, but it is safe to assume this will result in less cuts than for instance the activity of Sau3A:
If you have an amount of (total nuclear) DNA, say, from a human for "fingerprinting", digesting (splicing, or cutting) it with Sau3A might not lead to the desired result: you will get too many small fragments resulting in an unintelligible "smear" across your Electrophoresis Gel slab.
Cutting with Hin DIII will result in a few large bands that can be tell-tale, but you would like to have more certainty.
So, cutting with TWO different restriction enzymes, like a mixture of Hin DIII (5'
You can run into trouble with this however: DNA is fairly inert and robust, but RE's are not. Since they are extracted from different organisms (bacteria), each RE will have its own optimum environment within the Host Cell. Therefore, each RE will have it's own optimum buffer-mixture (think of pH if nothing else) , and therein lies the problem....
Although in the laboratory it has been found that most RE's are fairly happy with TRIS-based buffers (Tris-HydroxyMethyl AminoMethane), such as TBE (Tris/Borate/EDTA), each RE will need tweaking of the chosen buffer for optimum activity. Other factors, such as temperature, can also have an influence.
So, if the two RE's are compatible bufferwise you might do a double digest in one go, but depending on the compatibility of your two RE's of choice, you might need to do it in two phases: stop the reaction of the first digest (heat-shock), purify the DNA-digest, then do the second digest...
But as by the time of writing over 3000 RE's have been identified, and more than 600 are commercially available, it is not for me to give you an exhaustive list of combinations.
In the 80's we got most of our RE's from either Bethesda labs (USA), New England Biolabs (USA) or Boehringer Ingelheim (Germany), and they might give you a list of compatible RE's and their buffers for double digestion.