Plasmid propagation depends on origin of replication, a cis-acting DNA element recognized by host replication machinery. Ori contains AT-rich duplex unwinding element, DnaA boxes, and binding sites for host initiation factors that recruit helicase, primase, and DNA polymerase III holoenzyme for autonomous bidirectional replication independent of chromosomal replication. Without functional origin, plasmid cannot duplicate and is lost during cell division. LacZ, promoter, and reporter genes control phenotype or expression but do not confer replication ability. Copy number is also regulated by elements within ori region.
Ref:
NCERT Biology Class XII Principles on Klenow fill-in labeling, Lehninger Chapter 9 DNA cloning techniques, and Molecular Cloning by Sambrook Chapter 10 documenting end-labeling of cohesive termini.