Ricerc@Sapienza

In this paper we study the mathematical model of the Goldbeter--Koshland switch, or
futile cycle, which is a mechanism that describes several chemical reactions, in particular the so-called
phosphorylation-dephosphorylation cycle. We determine the appropriate perturbation parameter epsilon
(related to the kinetic constants and initial conditions of the model) for the application of singular
perturbation techniques. We also determine the inner and outer solutions and the corresponding
uniform expansions, up to the first order in epsilon , beyond the total quasi-steady state approximation
(tQSSA). These expansions, in particular the inner ones, can be useful for the estimation of the kinetic
parameters of the reaction by means of the interpolation of experimental data. Some numerical results
are discussed. Moreover, in a study case, we determine the center manifold of the system and show
that, at zero order, it is asymptotically equivalent to the tQSSA of the system.