Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Six enzymes cut DNA and leave sticky ends. Their sites, with the cut in the top strand marked by a caret, are shown.
BamHI: G^GATCC. BglII: A^GATCT. EcoRI: G^AATTC. SalI: G^TCGAC. XhoI: C^TCGAG. HindIII: A^AGCTT.
A vector needs an origin of replication, a selectable marker and cloning sites, few of them and best of all one for the enzyme in use. DNA ligase joins ends that fit. Copies of the gene in a culture copies of the plasmid in one cell the number of cells.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Six enzymes and their sites.
Plan. Work out the overhang of each enzyme. Ends fit if they leave the same overhang, because these sites are palindromic.
Step 1. BamHI and BglII both leave the overhang GATC. SalI and XhoI both leave TCGA. EcoRI leaves AATT. HindIII leaves AGCT.
Step 2. (a) The pairs that fit: BamHI with BglII, and SalI with XhoI. EcoRI and HindIII fit only themselves.
Step 3. (b) The ends of BamHI and BglII fit, so ligase can join the DNA and the vector. The joint has the sequence AGATCC or GGATCT, which is neither the site of BamHI nor the site of BglII. So neither enzyme will cut the joint again.
Answer: (a) BamHI with BglII, and SalI with XhoI. (b) Yes, it can be joined, and the joint is not cut again by either enzyme.
Watch out. Fitting ends are not the same as the same enzyme.
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