The plasmid pUC19 is a circle of 2,686 bp. EcoRI cuts it once, after base 396, and HindIII cuts it once, after base 447. What fragments does each enzyme give alone, and what do the two give together? Which bands would a standard agarose gel show?
1
One enzyme alone
A circle cut once opens into one linear piece with all 2,686 bp. EcoRI alone and HindIII alone each give a single 2,686 bp fragment, not two pieces. Why not two? A circle has no ends, so the first cut only opens it.
2
Find the short fragment
With both enzymes the circle is cut twice and gives two fragments. The first lies between the two cuts.
447−396=51
3
Find the long fragment
The rest of the circle is the other fragment.
2686−51=2635
4
Check it by the wraparound
The long fragment also runs from the HindIII cut past the end of the numbering to the EcoRI cut, L−clast+cfirst. The two ways agree.
2686−447+396=2635
5
Check the total
Two fragments of a 2,686 bp circle must add back to 2,686.
51+2635=2686
6
Predict the gel
Each single digest shows one band at 2,686 bp. The double digest shows a band at 2,635 bp, only a little below it. The 51 bp piece is below the roughly 100 bp at which agarose separates well. It also carries only 51/2686, about 2%, of the DNA, so its band is faint at best. A polyacrylamide gel separates pieces that small.
Result
Each enzyme alone opens the circle into one 2,686 bp fragment. Together they cut it into 51 bp and 2,635 bp, which add to 2,686. A standard agarose gel shows the 2,635 bp band clearly, while the 51 bp piece is too small to separate well and too faint to see easily.
Your turn
1. One like the example
A 4,000 bp plasmid has one site for enzyme A, after base 300, and one for enzyme B, after base 1,200. What fragments does the double digest give?
Show the answer and explanation
900 bp and 3,100 bp.
The short fragment lies between the cuts, 1,200−300=900. The long one wraps around, 4,000−1,200+300=3,100. Together they make 4,000.
1200−300=9004000−1200+300=3100900+3100=4000
2. A variation
A 5,000 bp plasmid is cut at 500,2,000 and 4,200 bp. Find the fragments.
Show the answer and explanation
Three fragments, 1,500,2,200 and 1,300 bp.
A circle cut three times gives three fragments. Two lie between neighboring cuts, 2,000−500=1,500 and 4,200−2,000=2,200. The third wraps around, 5,000−4,200+500=1,300. They add to 5,000.
A 3,000 bp plasmid gives one 3,000 bp band with enzyme A alone and one with enzyme B alone. Together they give 800 and 2,200 bp. A cuts after base 100. Where can B cut?
Show the answer and explanation
After base 900 or after base 2,300.
The 800 bp fragment lies between the two cuts, so B is 800 bp from A on one side or the other. One side gives 100+800=900. The other wraps around, 100−800+3,000=2,300. A third enzyme, or the sequence, decides between them.
100+800=900100−800+3000=2300
Keep exploring
pUC19 opens in Restriction digest & gel with the EcoRI cut at 396 and the HindIII cut at 447. Delete one cut to see a single 2686 bp fragment. The arithmetic opens in Math from 447−396=51.
