Analysis of a cell cycle model for Escherichia coli

Ribosome and protein synthesis, DNA replication and cell division in Escherichia coli cells are described by a mathematical model that integrates previous descriptions in quantitative terms and proposes a new formalization to relate ribosome net synthesis to cell growth. The model assumes a cell size control of DNA replication and therefore is structurally divided into two subsystems: the first, whose state variables are ribosomes and protein, and the second, which is activated when the protein level reaches a threshold and which is comprised of DNA replication and cell division. The dynamics of the entire system is set only by the first subsystem: the values of its parameters determine whether the cells will be in a resting condition or will grow exponentially and in the latter case the resulting duplication time, while the structure and the parameter values of the second subsystem determine the size and the composition of the cell and the timing of DNA replication during the cycle. Relationships are derived that allow a simple determination of the time of initiation and of termination of DNA replication and the number of chromosome origins involved in any possible cell cycle as well as the macromolecular levels at the beginning of a cycle and on the average in a population of cells in balanced exponential growth.