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Theoretical plasmid partitioning

David Womble dwomble at cmb.biosci.wayne.edu
Fri Nov 24 20:31:51 EST 1995

```David J. States (states at ibc.wustl.edu) wrote:

: For copy number N, on average N/2 will be partitioned to each
: daughter cell following cell division. If the plasmids segeragate
: independently, the distribution will be a binomial distribution, and
: the odds of a daughter not getting any plasmids is (1/2)**N.
: So after X generations, the fraction, f, of the population positive
: for the plasmid will be:

: f = ( 1 - (1/2)**N )**X

Perhaps not quite that simple...for average copy number N, there would
most likely be a distribution of copy numbers around that mean in the
population of cells in culture.  It would probably be those cells in
which the copy number was lower than average which contributed most
to the early production of plasmid-free cells.  After that, the
difference in growth rates (plasmid-free cells often grow a little
faster) which is the major contributor to the population shift.

: > b) if daughter plasmids are partitioned equally between both
: > daughter cells.

: This is a trivial case.  If the copy number is > 1 and daughters
: are paritioned equally, or if the copy number is 1 and the plasmid
: co-replicates with the genome, then all progeny will carry the plasmid.
: If the copy number is equal to 1 and the plasmids don't co-replicate
: then there is a question of if they replicate at all.  If the plasmids
: don't divide, they get diluted out as 1/(2**X) as the host population
: expands exponentially.

Perhaps not so trivial, in particular since it seems most likely that
the partition systems we know about so far might segregate at least
1 plasmid copy to each daughter (if at least 2 copies are present)
with the remainder, if any, distributed at random.  This will
contribute to the distribution of plasmid copies within the population
of cells in culture.  That distribution will be corrected back
toward the mean regulated copy number by the plasmid's replication
control mechanism.  The rate of correction will depend on the
biology of the particular plasmid.

Based on that biology, one needs to calculate the probablility of a
cell existing in the population with only one plasmid copy present at
the time of cell division.  This will be non-zero for almost all
plasmids we know about, and that will be the rate of production of
plasmid free cells in this situation.  This assumes that the partition
mechanism itself is 100 % efficient, which might not be the case.  I
know of no plasmid for which the partition efficiency has actually
been measured.

--
David D. Womble
Center for Molecular Medicine and     Phone:  313-577-2374
Genetics, Wayne State University      Fax:    313-577-6200
5047 Gullen Mall, Detroit, MI 48202   E-mail: dwomble at cmb.biosci.wayne.edu

```