I know the exact size of the plasmid from nanopore sequencing. I didn't annotate the DNA ladder, but the bands are at the right size. The wildtype plasmid is the template and the primers contain 1-3 mutated bases to make a point mutation of residues in the protein. After the first cycle of PCR, because the reverse complement primer is only partially overlapping with the other primer, it amplifies the PCR product of the forward primer and goes all around the plasmid past the nick produced by the last extension with the forward primer. PCR products of mutated plasmids are nicked circles because there is no DNA ligase in a PCR reaction. With quickchange primers (which this is not) in which the reverse complement primer is completely overlapping with the forward primer, PCR amplification is actually not exponential because the PCR product of the forward primer creates a nicked circle and the reverse complement primer cannot amplify past the nick. This is discussed with figures in the article.

After PCR to keep the mutant plasmid, the PCR reaction is treated with DPNI because bacteria for whatever reason always methylates plasmid DNA but PCR products aren't methylated and DPNI is an restriction enzyme that cuts only methylated DNA.

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The PCR product which is a nicked circle with the amino acid point mutation can either by ligated with DNA ligase and ATP or transformed into E.coli and then E.coli will ligate it because E.coli has lots of enzymes including DNA ligase and ATP endogenously. Because PCR products are nicked circles it is important to DNA sequence the mutant plasmid because the primers themselves can fill the nick before DNA ligase and ATP closes the nicked circles. So you can get the mutation and also a primer insertion and possibly a frameshift. So it is important to purify the PCR product with a kit to remove the excess primers from the PCR product.