A biomolecular proportional integral controller based on feedback regulations of protein level and activity.

Francis Mairet

doi:10.1098/rsos.171966

Abstract

Homeostasis is the capacity of living organisms to keep internal conditions regulated at a constant level, despite environmental fluctuations. Integral feedback control is known to play a key role in this behaviour. Here, I show that a feedback system involving transcriptional and post-translational regulations of the same executor protein acts as a proportional integral (PI) controller, leading to enhanced transient performances in comparison with a classical integral loop. Such a biomolecular controller—which I call a level and activity-PI controller (LA-PI)—is involved in the regulation of ammonium uptake by Escherichia coli through the transporter AmtB. The PII molecules, which reflect the nitrogen status of the cell, inhibit both the production of AmtB and its activity (via the NtrB-NtrC system and the formation of a complex with GlnK, respectively). Other examples of LA-PI controller include copper and zinc transporters, and the redox regulation in photosynthesis. This scheme has thus emerged through evolution in many biological systems, surely because of the benefits it offers in terms of performances (rapid and perfect adaptation) and economy (protein production according to needs).

Highlights

Through evolution, living organisms have acquired sophisticated regulatory systems that allow them to maintain constant basal activity, even in the presence of perturbations
The present study introduces a regulatory motif based on the coupling in a feedback loop of transcriptional and post-translational regulations of the same executor protein
I propose a feedback control scheme based on the coupling of transcriptional and post-translational regulations acting in the same way on two different time scales

Summary

Introduction

Through evolution, living organisms have acquired sophisticated regulatory systems that allow them to maintain constant basal activity, even in the presence of perturbations (such as intermittent nutrient availability). In cell signalling, perfect adaptation refers to the ability of a system, for any constant stimulus, to always return to the same baseline. The question we should ask is which regulatory motifs can achieve homeostasis or perfect adaptation. Cells adapt to any constant environment [1,2,3]. Yi et al [4] showed that such perfect adaptation results from

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