Protein-protein complexes can undermine ultrasensitivity-dependent biological adaptation

Robust Perfect Adaptation (RPA) is a ubiquitously-observed signalling response across all scales of biological organisation. A major class of network architectures that drive RPA in complex networks is the Opposer module - a feedback-regulated network into which specialised 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, and which are now widely acknowledged to make inaccurate predictions of signalling responses. 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 networks 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. Furthermore, compared to predictions by simplified models, the parametric requirements for RPA in this protein pool are much more severe, and RPA generally obtains over a narrower range of input stimuli. These surprising results raise fundamental new questions as to the biochemical requirements for adaptation-conferring Opposer modules within complex cellular networks.