A mathematical model of the incompatibility of plasmids using a mechanism of master replication

A mathematical model of incompatibility for plasmids that use master-replication was worked out. Formulas for calculating the segregation velocity of two incompatible plasmids and for determining the number of cell generations (l gamma), necessary to achieve a gamma-share of polyplasmid cells are given. It is shown that l gamma strives to -8 lg gamma with the increase of the copy number N, i.e. it does not depend on N. This is the main distinction of model presented from those by Novick at al. and Ishii et al., who consider the mechanisms of regular and random replication. For these mechanisms l gamma increases proportional to N. So, at N greater than 30, the difference between l gamma, calculated for the master-replication and the random replication exceeds 10. This allows to determine the mechanism of replication used by the plasmid by measuring the velosity of incompatible plasmids segregation.