Emergence and Enhancement of Ultrasensitivity through Posttranslational Modulation of Protein Stability

Signal amplification in biomolecular networks converts a linear input to a steeply sigmoid output and is central to a number of cellular functions including proliferation, differentiation, homeostasis, adaptation, and biological rhythms. One canonical signal amplifying motif is zero-order ultrasensitivity that is mediated through the posttranslational modification (PTM) cycle of signaling proteins. The functionality of this signaling motif has been examined conventionally by supposing that the total amount of the protein substrates remains constant, as by the classical Koshland-Goldbeter model. However, covalent modification of signaling proteins often results in changes in their stability, which affects the abundance of the protein substrates. Here, we use mathematical models to explore the signal amplification properties in such scenarios and report some novel aspects. Our analyses indicate that PTM-induced protein stabilization brings the enzymes closer to saturation. As a result, ultrasensitivity may emerge or is greatly enhanced, with a steeper sigmoidal response, higher magnitude, and generally longer response time. In cases where PTM destabilizes the protein, ultrasensitivity can be regained through changes in the activities of the involved enzymes or from increased protein synthesis. Importantly, ultrasensitivity is not limited to modified or unmodified protein substrates-when protein turnover is considered, the total free protein substrate can also exhibit ultrasensitivity under several conditions. When full enzymatic reactions are used instead of Michaelis-Menten kinetics for the modeling, the total free protein substrate can even exhibit nonmonotonic dose-response patterns. It is conceivable that cells use inducible protein stabilization as a strategy in the signaling network to boost signal amplification while saving energy by keeping the protein substrate levels low at basal conditions.