Mathematical analysis of binary activation of a cell cycle kinase which down-regulates its own inhibitor

In mammalian cells, the heterodimeric kinase cyclin E/CDK2 (EK2) mediates c ell cycle progress from G1 phase into S phase. The protein p27(kip1) (p27) binds to and inhibits EK2; but EK2 can phosphorylate p27, and that leads to the deactivation of p27, presumably liberating more EK2 and forming a posi tive-feedback loop. It has been proposed that this positive-feedback loop g ives rise to binary (all-or-none) release of EK2 from its inactive complex with p27. Binary release suggests a bistable biochemical system in which a stable steady state with low EK2 activity is extinguished in a saddle-node bifurcation, causing the system to shift abruptly to a stable steady state with high EK2 activity. Two mathematical models are discussed, one in which free EK2 deactivates p27 in the EK2-p27 inhibitory complex as well as free p27, and one in which the rate of EK2-catalyzed deactivation of free p27 h as saturable kinetics with respect to free p27. In general, if inhibitory b inding is approximately in equilibrium, bistability requires that there be a potential unstable steady state where the reaction order of p27 deactivat ion is greater with respect to EK2 than with respect to p27. (C) 1999 Elsev ier Science B.V. All rights reserved.