How can we design robust synthetic biological feedback control circuits?

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Francesco Montefusco, Ozgur E. Akman, Declan G. Bates and Orkun S. Soyer

University of Exeter, United Kingdom

Our ability to (re)design biological systems with complex response dynamics requires a better understanding of natural feedback control systems and the evolutionary processes that led to them. Here, we use tools from Control Engineering to investigate a number of possible design strategies for achieving perfect adaptation to perturbations. While integral feedback is well known to achieve robust adaptation, its biological implementation in a synthetic circuit is likely to be highly challenging. Simpler proportional control schemes might be easier to implement, but their ability to provide robust adaptation is limited. Inspired by studies on the molecular basis of osmoregulation, we explore the ability of an ultrasensitive proportional controller to achieve adaptive dynamics, and we discuss different biochemical architectures that can achieve such control. Ultrasensitivity can be biochemically implemented in a straightforward manner through various different mechanisms, including phosphorylation cycles and cooperative binding. Indeed, in the case of osmoregulation, the Hog1/MAPK pathway, which regulates glycerol production to achieve perfect adaptation, is well documented to be capable of high ultrasensitivity, since it employs a phosphorylation cascade. We first analyse the dynamics of a model with two proportional control loops, and show that it does not achieve robust adaptation, since the adaptation requires a careful tuning of the parameters. Addition of an integral control loop with a finite integration window (as would be implemented in any synthetic circuit) does not result in robust perfect adaptation. However, replacing the simple proportional controllers with ultrasensitive controllers results in a fast and robust adaptation to perturbations that does not require high feedback gains and does not produce large overshoots. Our analysis provides much needed insight into how synthetic biological control schemes could be designed using tools and ideas from feedback control theory.