Theoretical plasmid partitioning

[David J. States]

Anthony Smith wrote:
> Can anyone point me to a reference on theoretical plasmid 
> partitioning...
> Given that a plasmid of copy number N is grown without selection 
> for X generations, what percentage of the population will retain 
> the plasmid:
> a) if daughter plasmids are partitioned randomly in both 
> daughter cells.

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

> 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.

David States