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.

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 Michaelian approximations, are unable to accurately recapitulate the qualitative signalling responses supported by our detailed models. Strikingly, we show that complex-complete PAR models are capable of new qualitative responses such as one-way switches and a ‘prozone’ effect, depending on the specific PAR-encoding mechanism, which are not supported by Michaelian simplifications. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation is inadequate for predictive models of enzyme-mediated chemical reactions with added regulations such as PAR.

1. Reintroduction projects, which are an important tool in threatened species conservation, are becoming more complex, often involving the translocation of multiple species. Ecological theory predicts that the sequence and timing of reintroductions will play an important role in their success or failure. Following the removal of sheep, goats and feral cats, the Western Australian government is sequentially reintroducing 13 native fauna species to restore the globally important natural and cultural values of Dirk Hartog Island (DHI).2. We use ensembles of ecosystem models to compare 23 alternative reintroduction strategies on DHI, in Western Australia. The reintroduction strategies differ in the order, timing and location of releases on the island. Expert elicitation informed the model structure, allowing for use of different presumed species interaction networks which explicitly incorporated uncertainty in ecosystem dynamics.3. Our model ensembles predict that almost all of the species (~12.5 of 13, on average) will successfully establish in the ecosystem studied, regardless of which reintroduction strategy is undertaken. The project can therefore proceed with greater confidence and flexibility regarding the reintroduction strategy. However, the identity of the at-risk species varies between strategies, and depends on the structure of the species interaction network, which is quite uncertain. The model ensembles also offer insights into why some species fail to establish on DHI, predicting that most unsuccessful reintroductions will be the result of competitive interactions with extant species. Synthesis and applications.Our model ensembles allow for the comparison of outcomes between reintroduction strategies and between different species interaction networks. This framework allows for inclusion of high uncertainty in dynamics. Finally, an ensemble modelling approach also creates a foundation for formal adaptive management as reintroduction projects proceed.

Robust perfect adaptation (RPA) is a ubiquitously observed signalling response across all scales of biological organization. A major class of network architectures that drive RPA in complex networks is the Opposer module—a feedback-regulated network into which specialized integral-computing ‘opposer node(s)’ are embedded. Although ultrasensitivity-generating chemical reactions have long been considered a possible mechanism for such adaptation-conferring opposer nodes, this hypothesis has relied on simplified Michaelian models, which neglect the presence of protein–protein complexes. Here we develop complex-complete models of interlinked covalent-modification cycles with embedded ultrasensitivity, explicitly capturing all molecular interactions and protein complexes. Strikingly, we demonstrate that the presence of protein–protein complexes thwarts the network’s capacity for RPA in any ‘free’ active protein form, conferring RPA capacity instead on the concentration of a larger protein pool consisting of two distinct forms of a single protein. We further show that the presence of enzyme–substrate complexes, even at comparatively low concentrations, play a crucial and previously unrecognized role in controlling the RPA response—significantly reducing the range of network inputs for which RPA can obtain, and imposing greater parametric requirements on the RPA response. These surprising results raise fundamental new questions as to the biochemical requirements for adaptation-conferring Opposer modules within complex cellular networks.