text: Modeling by Dushek et al. proposes a possible mechanism for ultrasensitivity outside of the zero-order regime. For the case of membrane-bound enzymes acting on membrane-bound substrates with multiple enzymatic sites (such as tyrosine-phosphorylated receptors like the T-Cell receptor), ultrasensitive responses could be seen, crucially dependent on three factors: 
  1) limited diffusion in the membrane,
  2) multiple binding sites on the substrate, and
  3) brief enzymatic inactivation following catalysis.
  Under these particular conditions, although the enzyme may be in excess of the substrate (first-order regime), the enzyme is effectively locally saturated with substrate due to the multiple binding sites, leading to switch-like responses. This mechanism of ultrasensitivity is independent of enzyme concentration, however the signal is significantly enhanced depending on the number of binding sites on the substrate.  Both conditional factors (limited diffusion and inactivation) are physiologically plausible, but have yet to be experimentally confirmed. Dushek's modeling found increasing Hill cooperativity numbers with more substrate sites (phosphorylation sites), and with greater steric/diffusional hindrance between enzyme and substrate. This mechanism of ultrasensitivity based on local enzyme saturation arises partly from passive properties of slow membrane diffusion, and therefore may be generally applicable.