Ultrasensitivity and bistability in covalent modification cycles with positive autoregulation

Switch-like behaviours in biochemical networks are of fundamental significance in biological signal processing, and exist as two distinct types: ultra-sensitivity and bistability. Here we propose two new models of a reversible covalent-modification cycle with positive autoregulation (PAR) - a motif structure that is thought to be capable of both ultrasensitivity and bistability in different parameter regimes. These new models appeal to a modelling framework that we call complex complete, which accounts fully for the molecular complexities of the underlying signalling mechanisms. Each of the two new models encodes a specific molecular mechanism for PAR. We demonstrate that the modelling simplifications for PAR models that have been used in previous work, which rely on a Michaelian approximation for the enzyme-mediated reactions, are unable to accurately recapitulate the qualitative signalling responses supported by our full complex-complete models. Strikingly, we show that the parameter regimes in which ultrasensitivity and bistability obtain in the complex-complete framework contradict the predictions made by the Michaelian simplification. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation may be inadequate for predictive models of enzyme-mediated chemical reactions with added regulations.