Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Zero-order ultrasensitivity is a well-known mechanism to generate sigmoidal curves in phosphorylation cycles, but one of its key assumptions often implies that the substrate is more abundant than the modifying enzymes. However, in endogenous conditions, the situation is often the opposite - there are more enzymes than substrate. Yet, ultrasensitivity has been experimentally reported in this regime.

In this talk, I will introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than the numbers of substrates. The model combines concerted allosteric transitions of the substrate with two-stage binding of the enzymes: the enzymes bind first to a docking site on the substrate and only then to the substrate's phosphosites. This constraint provides an intuitive explanation for the appearance of ultrasensitivity in the system. Ultrasensitivity is generated because the kinase can bind to the fully phosphorylated form of the substrate (at its docking site) and sequester the substrate away from the phosphatase and, similarly, the phosphatase can bind to the fully dephosphorylated form of the substrate and sequester the substrate away from the kinase. The Hill number of the response, a measure of the degree of ultrasensitivity, can be calculated analytically. The number of kinase-phosphatase competitions, which reflects the number of phosphosites, determines the upper bound of the Hill number.

This model is in accordance with recent experimental observations and, given its generality, the mechanism presented here may be common and often underlay decision-making circuits in eukaryotic cells.