Thermodynamic and Kinetic Analysis of Sensitivity Amplification in Biological Signal Transduction

Based on a thermodynamic analysis of the kinetic model for the protein phosphorylation-dephosphorylation cycle, we study the ATP (or GTP) energy utilization of this ubiquitous biological signal transduction process. It is shown that the free energy from hydrolysis inside cells, $\Delta G$ (phosphorylation potential), controls the amplification and sensitivity of the switch-like cellular module; the response coefficient of the sensitivity amplification approaches the optimal 1 and the Hill coefficient increases with increasing $\Delta G$. We discover that zero-order ultrasensitivity is mathematically equivalent to allosteric cooperativity. Furthermore, we show that the high amplification in ultrasensitivity is mechanistically related to the proofreading kinetics for protein biosynthesis. Both utilize multiple kinetic cycles in time to gain temporal cooperativity, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein.