Asymptotics and numerical analysis for enzymatic auxiliary reactions

In this paper we study the mathematical model of auxiliary (or coupled) reactions, a mechanism which describes several chemical reactions. In order to apply singular perturbation techniques, we determine an appropriate perturbation parameter ǫ (which is related to the kinetic constants and initial conditions of the model), the inner and outer solutions and the matched expansions of the solutions, up to the first order in ǫ, in the total quasi-steady-state approximation (tQSSA) framework. The contribution of these expansions can be useful for the estimation of the kinetic parameters of the reaction by means of the interpolation of experimental data with the explicit approximations of the solutions. Some numerical results are discussed, showing the high reliability of the tQSSA with respect to the standard QSSA.