Nonequilibrium Thermodynamics and Nonlinear Kinetics in a Cellular Signaling Switch

We develop a rigorous nonequilibrium thermodynamics for an open system of nonlinear biochemical reactions responsible for cell signal processing. We show that the quality of the biological switch consisting of a phosphorylation-dephosphorylation cycle, such as those in protein kinase cascade, is controlled by the available intracellular free energy from the adenosine triphosphate (ATP) hydrolysis in vivo: ΔG=k_BTln⁡([ATP]/K_eq[ADP]), where K_eq is the equilibrium constant. The model reveals the correlation between the performance of the switch and the level of ΔG. The result demonstrates the importance of nonequilibrium thermodynamics in analyzing biological information processing, provides its energetic cost, establishes an interplay between signal transduction and energy metabolism in cells, and suggests a biological function for phosphoenergetics in the ubiquitous phosphorylation signaling.