Ultrasensitivity in Phosphorylation-Dephosphorylation Cycles with Little Substrate

Abstract

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. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with phosphosites, we find an upper bound of the Hill number of , and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells.

Large-scale functional analysis of the roles of phosphorylation in yeast metabolic pathways

“…Furthermore, we used a nutritionally complex medium that favors glycolytic metabolism and exponential growth, which may not be representative of natural environments where more kinases and phosphatases may be essential (55). Moreover, phosphorylation of metabolic enzymes may be more crucial in mediating dynamic transitions between two steady states, but less important for maintaining steady-state metabolism (56,57).…”

Crosstalk and Ultrasensitivity in Protein Degradation Pathways

“…by "overexpressing" the protein, which would correspond to increasing in this model). The steady-state responses of PTM cycles in vivo may thus be quite different from the standard predictions that have been made in the absence of any consideration of protein turnover (7)(8)(9)(10)(11)(12).…”

“…This phenomenon, known as "0 th -order ultrasensitivity", has had profound implications for understanding how biochemical networks can exhibit switch-like behavior. Despite decades of progress in understanding 0 th -order ultrasensitivity and other aspects of PTM function (7)(8)(9)(10)(11)(12), to there have been few attempts to systematically characterize the general behavior of PTM cycles that drive protein degradation.…”

When More Is Less: Dual Phosphorylation Protects Signaling Off State against Overexpression

“…Many studies focused on the stimulus-response relationship of a kinase that is activated by multisite phosphorylation. The profile can be graded, biphasic, switch like, or bistable depending on a multitude of factors like the order (11) and/or processitivity (12,13) of multisite phosphorylation, competition effects between modifying enzymes (5), or the sequestration of components within enzyme-substrate complexes (14)(15)(16)(17). Some of the effects of competition and sequestration have been shown experimentally in vivo.…”