Ultrasensitive Regulation in the Tryptophan System in Escherichia coli Provides Effective Noise Mitigation

The tryptophan system in Escherichia coli maintains intracellular concentration of tryptophan in a narrow band regardless of the nutritional status and uncertainty in its environment. The system is characterized by three distinct regulations namely, genetic regulation, mRNA attenuation and enzyme inhibition, that use the tryptophan concentration as a feedback signal. It has been shown previously, that the multiple feedback loop design is responsible for rapid synthesis of tryptophan when faced with starvation. It is well known that a design with rapid response to external signals also implies poorer noise mitigation properties. This work investigates the design elements that limit the adverse impact of the multiple feedback loop architecture on noise propagation in the tryptophan system using a frequency response analysis. Specifically, we use sinusoidal input describing functions to approximate the transfer characteristics of the ultrasensitive regulators and then obtain the frequency response of the closed-loop feedback system. The study suggests that the tryptophan system of E. coli has evolved to simultaneously satisfy the two properties of rapid response and noise mitigation. Particularly, the multiple feedback loop is responsible for the rapid response, while the nonlinear regulation provides effective noise mitigation.