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A 'phagemid' or 'phasmid' is a type of cloning vector developed as a co-infection of the M13 helper phage and plasmids to produce a smaller version of the virus.
an example is PRS314 which is of 4.78 kb size. Phagemids contain an ori for double stranded replication as well as an ori for single stranded replication, mostly not comprising the entire phagemid (i.e., only a small part of the phagemid is copied as a single strand).
They find their application at phage displays.
A phagemid is different from a closely related cloning vector called a cosmid. While a cosmid can enter a host cell very effectively, almost all of the viral genes have been removed to make room for exogenous DNA, therefore the virus cannot replicate itself. In a phagemid, however, an origin of replication is present. This means that in the presence of a 'helper' virus such as f1, the rest of the genes to replicate viral proteins are present, therefore more virus particles can be created using the host cell's resources.