On Multiple Regulatory Mechanisms in the Tryptophan Operon System in Escherichia coli: In silico Study of Perturbation Dynamics

Living organisms often exist in uncertain environments where changes are the norm. Cellular systems therefore require resilient regulatory mechanisms for timely and stable adaptation. Among various regulation motifs, multiple feedback control emerges as a common theme. The tryptophan operon system in Escherichia coli regulates the production ofintracellular tryptophan using an apparatus of three feedback mechanisms: repression, attenuation and enzyme inhibition; each provides essentially the same function but operates in distinctly different ways. Here we aim to understand the roles of each loop by studying transient dynamics of the system to perturbations of different types; to reveal the underlying relationships between individual control mechanisms and macroscopic behaviour. We develop an S-systems approximation of an existing model for the system and characterise transient dynamics by introducing two measurable quantities: maximum disturbance (MD) and recovery time (RT). Our simulation results showed that combined regulation using all three feedback mechanisms significantly increases system stability, broadening the range of kinetic parameters for stable behaviour. Enzyme inhibition was shown to directly control the disturbance level in system variables after perturbations. Attenuation, on the other hand, was found to speed up system recovery whereas repression lengthens recovery time. The method developed in this paper and the defined transient dynamics measurements can be applied to other cellular systems.