Small delay, big waves: a minimal delayed negative feedback model captures Escherichia coli single cell SOS kinetics

Abstract

Background: How exactly does an organism coordinate its responses to differing environmental conditions, especially when several responses and physiological priorities are potentially conflicting? Recently, single cell results have been published on the kinetics of the bacterial SOS response. Based on these, we construct a relatively simple mathematical model for the regulatory control of the mutagenic elements of the Escherichia coliDNA repair system. Methods: We employ one first order delay differential equation for the dynamics of the activation level of mutagenic gene repair and one first order ordinary differential equation for the dynamics of the level of DNA damage. After manual adjustment of parameters, our model qualitatively reproduces the UV dose dependent RecA expression peak occurrence, peak amplitude and peak timing. Parameter noise captures qualitatively the fluctuations observed in the experimental data. Quantitative agreement is achieved for timing of the three response peaks for different doses of UV. Conclusions: A delayed negative feedback is likely to play a primary role in the regulation of the E. coli mutagenic gene repair. The model presented in this paper is an example of how a delayed regulatory mechanism establishes control over a critical organismic response with negative secondary effects.