In this paper we study the chemical reaction of inhibition, determine the appropriate parameter for the application of Tihonov's Theorem, compute explicitly the equations of the center manifold of the system and find sufficient conditions to guarantee that in the phase space the curves which relate the behavior of the complexes to the substrates by means of the tQSSA are asymptotically equivalent to the center manifold of the system. Some numerical results are discussed.

In this paper we study the model of the chemical reaction of fully competitive inhibition and determine the appropriate parameter ∊ (related to the chemical constants of the model), for the application of singular perturbation techniques. We determine the inner and the outer solutions up to the first perturbation order and the uniform expansions. Some numerical results are discussed.

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.

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