I have digested my DNA with NotI enzyme and put it in the −20 °C freezer without heat inactivating it. Can restriction enzymes work at −20 °C? Should I expect STAR activity?
Enzymes have temperature optima based on the organism they were isolated from. So I would predict the there is virtually no activity at −20 °C. Another consideration is that the reactions are likely to be frozen solid, so that would limit diffusion, and also slow it down. But the real question is: what are you afraid of? Just the star activity? Even if there were star activity, would that adversely affect your experiments?
While there is unlikely to be any activity when the enzyme is frozen, there are better methods to prevent star activity.
1: If you are running the reaction in a PCR machine, you can program the machine prior to the digest to heat up to 65 degrees for 10 minutes after the intended digestion timeframe to heat inactivate NotI. Since NotI is a heat-labile enzyme, this prevents star activity by denaturing it.
2: You can use NotI-HF, which has been engineered by NEB to greatly reduce the amount of star activity and can therefore be left incubating at 37°C overnight.
3: You can gel purify or perform a "PCR purification" on your digested DNA samples, this also removes any protein present and therefore prevents star activity.