How hot can it be?

I'm going to test biotin-tagging of the ends of my big DNA fragments by doing a preliminary tagging with a radioactive (33-P) nucleotide. I need this test because I don't have specific information about the short single-stranded overhangs I expect these fragments to have. I don't know whether most fragments have overhangs, whether 3' and 5' overhangs are equally common, or how long the average overhang is.

But I realized that the unless the overhangs are very long, they will constitute only a tiny fraction of the DNA in such long molecules. So I don't expect much of my 33-P or biotin to be incorporated. I do know the specific activity of the 33-P I'll use (2500 Curie/mmol* **), and this lets me do a back-of-the-envelope calculation of how hot the DNA can get if the tagging reaction works perfectly.

[This is a long but not difficult calculation, relying on the kind of 'dimensional analysis' I learned in Grade 11 Physics class. It has Avogadro's number and Rosie's universal constant (10^18 bp/g) and arithmetic-simplifying assumptions that the average fragment is 75kb long and that a single 33-P nucleotide gets incorporated at each end. This last assumption would be right if 3' and 5' ends were equally common, blunt ends insignificant, and the average overhang about 8 bases.]

The result of this calculation: a perfect labeling reaction could incorporate enough 33-P to give only about 240 dpm per microgram of DNA. This is so low that the 33-P labeling experiment may not be worth doing at all. Using 32-P won't make a big difference, as the standard specific activity of 32-P nucleotides is 3000 Ci/mmol.

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*A Curie is 2.2 x 10^12 dpm (radioactive disintegrations per minute).

** This is close to the theoretical maximum specific activity, with a 33-P as the alpha phosphate of every nucleotide.