Mathematical model of temperature-sensitive plasmid replication.

The copy number of a series of plasmids constructed at Odense University is regulated by the lambda PR/PRM promoters and the temperature-sensitive cI857 repressor. At low temperatures, these plasmids exhibit the low copy number of the parent plasmid R1 (5-6 per cell). At high temperatures, the plasmids exhibit runaway replication, reaching copy numbers of greater than 1,000 per cell. A detailed mathematical model of the temperature-sensitive replication of these plasmids has been developed incorporating three features: replication of the parent plasmid, regulation of the lambda PR/PRM promoters by the cI repressor, and thermal denaturation of the cI857 repressor. Models of the first two of these features have been described by others. We revised and extended those models, described the thermal denaturation of the cI857 repressor, and integrated these features to give a comprehensive model of temperature-sensitive plasmid replication. Model predictions were compared to experimental measurements of both steady-state copy numbers as a function of temperature and the change in copy number following temperature shifts up and down. The model accurately describes the qualitative behavior of the system and gives reasonable quantitative results. This is particularly significant since all the parameter values used in this model were determined independently: that is, there was no adjustment of parameter values to match our experimental data. The regulatory system that gives rise to the temperature-sensitive replication of these plasmids is widely used in biotechnology applications, so the elements of the model related to this regulation should be applicable to a wide variety of systems.