A Non-Equilibrium Steady-State Theory of Phosphorylation-Dephosphorylation Switch in Cellular Signalling

We present a mathematical theory for a biochemical switch system, which can be either the phosphorylation-dephosphorylation cycle (PdPC) reactions catalyzed by a kinase and a phosphatase, or GTPase cycles catalyzed by a guanine exchange factor (GEF) and a GTPase activating protein (GAP). The theory is based on the recently developed open-system nonequilibrium thermodynamics, the chemical master equation, and the traditional enzyme kinetics. We show how ultrasensitivity, as a new form of cooperativity, arisies in an open system, and the role of cellular energy in the functioning of switches. We also investigate PdPC/GTPase systems with feedbacks and how it leads to various nonlinear bifurcations.