Mathematical model of negative control of E-coli bacteria

A mathematical model for the negative control of the lac operon is presented. This model consists of coupled nonlinear differential equations representing the dynamic behaviors of the repressor-inducer components of negative control components of the system. To eliminate the dependency of the magnitude on the system of units of measurements, a dimensionless derivation for the operon system was employed to produce singularly perturbed models with fast and slow time-scale models. The fast model represents the dynamical behavior of the operator. Whereas the slow model represents the dynamical behaviors of the inducer and the repressor. It is shown that by applying the singular perturbation theory we can study the approximate behavior of the free operator by solving one equation instead of three coupled nonlinear differential equations. The behavior of the system can be described as a rapid on-off switch of structural gene transcription. This is consistent with the requirement of the bacterial cell to quickly respond to nutrient fluctuations