Here's why:
1. Restriction enzymes are like molecular scissors that recognize specific DNA sequences (restriction sites) and cut the DNA at those sites.
2. Each restriction enzyme cuts DNA in a specific way, leaving behind either "sticky ends" (short single-stranded overhangs) or "blunt ends" (no overhangs).
3. The goal of genetic engineering is to insert a gene of interest (from the cell DNA) into a plasmid (a small circular piece of DNA).
4. To join these two pieces of DNA, their ends must be compatible. This means they must either both have sticky ends with complementary sequences or both have blunt ends.
5. Cutting both the plasmid and cell DNA with the same restriction enzyme ensures that the resulting fragments will have compatible ends. This allows the gene of interest to be inserted into the plasmid, creating a recombinant plasmid that can then be introduced into a host cell.
In summary: Cutting both the plasmid and cell DNA with the same restriction enzyme creates complementary ends that can be ligated together, allowing the insertion of the gene of interest into the plasmid. This is a fundamental step in many genetic engineering techniques.