On the Role of Ultrasensitivity in Biomolecular Control Systems

Abstract — One of the most important design parameters in synthetic biological circuits is the gain of the system. In many naturally occurring biological control systems, however, the precise role of the gain in ensuring accurate control is unclear. In this study, we employ control theory to explore the role of gain in osmoregulation. It has been well-documented that the upstream signalling pathways involved in this system implement high levels of ultrasensitivity, however, the role of such high gain in producing the observed perfect adaptation is not clear. Indeed, it has been argued that a simple integral feedback controller can explain osmoadaptation without the need for high gain. Here, we extend a recently developed proportional controller model for this system with the implementation of ultrasenstivity. We evaluate the performance of the resulting two controllers under different biological assumptions and allowing different levels of gain. We find that a proportional controller implementing ultrasensitivity allows more precise and faster adaptation of cell volume following an osmo-shock. Such an input-output relationship can be tuned as a filter, where the proportional controller couldn’t, and thereby allowing re-sponses to signals above a certain threshold. Our results provide insights on the potential role of gain in biological systems, and should be of interest to synthetic biologists attempting to design biomolecular control systems. I