Theoretical rate of plasmid loss

[David Womble]

In article <ant.20.30AB1611 at molbiol.uct.ac.za> you wrote:
: Can anyone point me in the direction of a Ref. for calculating  what 
: percentage of a population of cells will loose their plasmids given that the 
: plasmids have no stability region (ie: plasmids are randomly partitioned to 
: each daughter). I wish to be able to plot a graph of generation vs. 
: percentage of population that still contain a plasmid given that no 
: selection has been used since generation 0. I would also like to be able to 
: repeat the calculation assuming that the plasmids ARE platitioned (ie: 
: thatthe plasmid has a par function)

: In nushell: If I have a plasmid of copy number n and I grow it for z 
: generations without selction what proportion of the population will retain 
: the plasmid.

At least 2 forces are at work in this situation.  First is the rate
that plasmid-free cells are segregated per cell per generation.  If
one makes the assumption that plasmids are distributed randomly, then 
for any given cell this will be a function of the standard binomial 
distribution based on the number of independently segregating plasmid
molecules present in the cell at the time of cell division.  Also 
contributing to this factor will be the distribution of plasmid 
copy numbers within the population of cells, since some cells will have
more and some fewer plasmid copies.  The simplest distribution is
the normal Gausian distribution, but this will depend on the biology
of the plasmid replication control mechanism and its ability to 
correct for deviations from the mean.

The second force is the differential rates of growth of plasmid-free
and plasmid-containing cells, sinice this will contribute significantly
to the observed population shift over a period of many generations.
This may even be the primary contributor to the shift if the rate of
production of plasmid-free cells is low.  This can be analyzed by 
the standard genetic methods of mutation and population shift.

For references that discuss the plasmid biology in both practical and
theoretical terms, see:

Austin & Nordstrom (1990) Partition-mediated incompatibility of 
bacterial plasmids.  Cell 60:351-354.

Nordstrom & Austin (1989) Mechanisms that contribute to the stable
segregation of plasmids.  Annu. Rev. Genet. 23:37-69.

Womble & Rownd (1986) Regulation of IncFII plasmid DNA replication; A
quantitative model for control of plasmid NR1 replication in the
bacterial cell division cycle.  J. Mol. Biol. 192:529-548.


--
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

--
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