In one of these alleles, delta M15, an 'in frame' deletion of a short N-terminal domain of the enzyme produces a protein lacking beta-galactosidase activity.

The other allele - referred to as the alpha complementing fragment - encodes the N-terminal domain deleted from delta M15 but lacks the bulk of the beta-galactosidase C-terminal domain.
The alpha complementing fragment also lacks detectable beta-galactosidase activity.

While neither the delta M15 allele nor the alpha complementing fragment has detectable beta-galactosidase activity, when the two alleles are present in the same cell they exhibit complementation (hence the name - alpha complementing fragment) and combine to form a functional enzyme.

X-gal - a galactose derivative that, when hydrolysed by beta-galactosidase, produces a blue precipitate in the cell.

Since neither X-gal nor the blue precipitate is toxic to the cell, the assay can be used simultaneously with positive selection based on antibiotic resistance.

While the lacZ coding sequence is far too large to use in a plasmid vector
(the vector would be too large to transform efficiently even without a foreign DNA insert)
the alpha complementing fragment is an appropriate small size.

In addition to the small size of the alpha complementing fragment, the polypeptide product is remarkably tolerent to changes in its amino acid sequence.
This characteristic made it possible to engineer clusters of desirable restriction enzyme recognition sites into the alpha complementing fragment coding region.
(see class handout of pUC and pBluescript vectors for details of polylinker sequence)

Insertion of foreign DNA fragements into this polylinker (or multiple cloning site (MCS) results in insertional inactivation of the alpha complementing fragment.

Host cells containing the plasmid vector alone will be antibiotic resistant (positive selection discussed previously) and will exhibit alpha complementation of the host lacZ delta M15 allele (colony is blue).

Host cells containing recombinant plasimids
(vector + insert) will be antibiotic resistant but will lack beta-galactosidase activity (colony is white).