On plasmid incompatibility

In this paper is presented a brief review of the current state of information on plasmid incompatibility followed by a detailed mathematical model dealing with incompatibility between autonomous homogenic plasmids and based on the assumption that the intracellular plasmid copy pool is randomized with respect to assortment during cell division. Two cases are considered: one in which each plasmid copy replicates once in each generation of cell growth (regular replication) and one in which plasmids are chosen at random for replication from a common pool, irrespective of their replication history (random replication). In both cases, it is assumed that the partition of plasmid copies to daughter cells at cell division is regular—existing plasmid copies are divided equally among the two daughter cells (equipartition). In the case of regular replication coupled with equipartition, it is shown that the survival of heteroplasmid cells (cells containing at least one copy of each of two incompatible plasmids) during exponential growth in a nonselective medium is given by H = H₀[1 − 1/(2N − 1)]ⁿ, where H₀ and H are the numbers of heteroplasmid cells after 0 and n generations of growth, respectively, and N is the plasmid copy number in newborn cells. In the second case, (random replication-equipartition), it is shown that the survival of the heteroplasmid population during exponential growth under nonselective conditions is given by H = H₀[(N − 1)(2N + 1)/(2N − 1)(N + 1)ⁿ. Sample calculations are presented to show that segregation is more rapid in the latter than in the former case. Finally, some of the plasmid-linked genetic determinants that might be expected to affect the expression of incompatibility between nonisogenic plasmids are briefly considered. These determinants include recognition specificity for replication origins, recognition specificity, specific activity of copy number control systems, and recognition specificity of partition systems.