Role of ultrasensitivity in biomolecular circuitry for achieving homeostasis

Living systems have developed control mechanisms for achieving homeostasis. Here, we propose a plausible biological feedback architecture that exploits ultrasensitivity and shows adaptive responses without requiring error detection mechanism (i.e., by measuring an external reference signal and deviation from this). While standard engineering control systems are usually based on error measurements, this is not the case for biological systems. We find that a two-state negative feedback control system, without explicit error measurements, is able to track a reference signal that is implicitly determined by the tunable threshold and slope characterizing the sigmoidal ultrasensitive relationship implemented by the control system. We design different ultrasensitive control functions (ultrasensitive up- or down-regulation, or both) and, by performing sensitivity analysis, show that increasing the sensitivity level of the control allows achieving robust adaptive responses to the effects of parameter variations and step disturbances. Finally, we show that the devised control system architecture without error detection is implemented within the yeast osmoregulatory response network and allows achieving adaptive responses to osmotic stress, by exploiting the ubiquitous ultrasensitive features of the involved biomolecular circuitry.