Mathematical Model of the SOS Response Regulation of an Excision Repair Deficient Mutant ofEscherichia coliafter Ultraviolet Light Irradiation

A mathematical model for the development of the SOS signal in nucleotide-excision repair deficientEscherichia colicells subjected to ultraviolet light irradiation is proposed, in which regions of single-stranded DNA (gaps) are created during replication of a damaged chromosome when the strand elongation stops at pyrimidine dimers. The concentration of single-straded DNA of gaps as a function of time is obtained. The model for the interaction of the LexA and RecA proteins, a well-established key event in SOS regulation, is presented, resulting in a system of differential equations for the concentration of LexA, RecA and activated RecA proteins. The simulated LexA protein kinetic curves agree with experimental data for two excision repair deficient mutants:uvrA6anddnaC28 uvrB(del), which is also a temperature-sensitive DNA replication initiation mutant. It is shown that the model can be used to quantitatively describe the kinetics of SOS reponse through the amount of the SOS signal (concentration of single-stranded DNA) in a cell as a function of time.