Exploiting Ultrasensitivity for Biomolecular Implementation of a Control System without Error Detection

The application of engineering principles to understand and design biological systems is a powerful approach in systems and synthetic biology, respectively. In these fields, feedback control is widely used for achieving a better understanding of biological homeostasis. Ultrasensitivity, a common feature of biomolecular circuitry, has been recently exploited for explaining the adaptive response dynamics observed in the yeast osmoregulatory response network. Here, we find that a generic control system working without error detection and implementing such ultrasensitive nonlinear dynamics allows achieving tunable adaptive responses: the system is able to track a reference signal that is not imposed externally, but it is determined by tunable threshold and slope characterizing the sigmoidal signal-response relationship of the controller. In particular, we show how the system exhibits adaptive dynamics by working around the point of high sensitivity of the sigmoidal response of the ultrasensitive controller. By performing a sensitivity analysis by changes of the nominal parameter values of the control system, we also show a good level of robust performance in terms of adaptation. Therefore, our analysis provides insights into how biology can measure a reference state and deviations from this (i.e. error) by exploiting the ultrasensitive response observed in many different biomolecular systems.