I haven't done a P1 transduction (or any E. coli genetics) for 20 years. But I'm being sent E. coli strains carrying chromosomal lacZ fusions and will need to move these fusions into different genetic backgrounds. This is stuff I did in grad school and I'm delighted to be doing it again.
P1 is a phage (bacteria virus). Particles of phage inject their DNA into E. coli cells, where the DNA is replicated and instructs the cell to make lots of phage proteins. Then the phage proteins self-assemble into phage particles that each fill themselves with a phage DNA, and other phage-encoded proteins cause the cell to lyse (burst open), freeing the new phage to go infect more cells.
What makes P1 useful for strain construction is its tendency to make the mistake of filling itself with a fragment of E. coli DNA rather than P1 DNA. The particles that do this still go on to inject their DNA into new cells, but this DNA (of course) doesn't make new phage or burst the cell. Instead it often recombines with the chromosome of this cell. If the original cell (the 'donor') and the new cell (the 'recipient') had different versions (alleles) of a gene, the donor cell's allele will sometimes get recombined into the recipient cell. The fragment of DNA that's transferred is about 100 genes long, so even big differences (presence or absence of whole genes) can be transferred.
Say strain A has an gene that I want to put into strain B. I first replicate P1 with strain A as host. This produces about 5 ml of a phage 'lysate', usually containing about 10^10 Pi phage per ml. Most of these are normal but some have DNA from strain A. I then infect strain B with these phage, using fewer phage than I have bacteria (I think), so most bacteria get infected by only a single phage. Most of these are infected by normal phage, and go on to lyse and release new phage. To prevent these phage from killing other cell, after the first cells have had time to inject their DNA into their hosts (10 minutes?) I add some citrate, which binds up the calcium the phage need to attach to new cells. Then I put the strain B cells onto agar plates with medium that only cells with the strain A gene can grow on, and I leave them in the incubator overnight. If I haven't messed up, the next day the plates will have lots of strain B colonies with the desired gene.
Lovely pure genetics. No enzymes, no PCR, no kits, and the cells do all the work.
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