Plasmid segregation and accumulation

The segregation of plasmids in a bacterial population is investigated. Hereby, a dynamical model is formulated in terms of a size-structured population using a hyperbolic partial differential equation incorporating non-local terms (the fragmentation equation). For a large class of parameter functions this PDE can be re-written as an infinite system of ordinary differential equations for the moments of its solution. We investigate the influence of different plasmid production modes, kinetic parameters, and plasmid segregation modes on the equilibrium plasmid distribution. In particular, at small plasmid numbers the distribution is strongly influenced by the production mode, while the kinetic parameters (cell growth rate resp. basic plasmid reproduction rate) influence the distribution mainly at large plasmid numbers. The plasmid transmission characteristics only gradually influence the distribution, but may become of importance for biologically relevant cases. We compare the theoretical findings with experimental results.