Ricerc@Sapienza

Because of the unavoidable intrinsic noise affecting biochemical processes, astochastic approach is usually preferred whenever a deterministic model givestoo rough information or, worse, may lead to erroneous qualitative behaviorsand/or quantitatively wrong results. In this work we focus on the chemicalmaster equation (CME)-based method which provides an accurate stochasticdescription of complex biochemical reaction networks in terms of the probabilitydistribution of the underlying chemical populations.

We summarize some recent results concerning the study of the asymptotic properties of four important enzyme reactions, which are ubiquitous in every
intracellular enzyme reaction network. Mainly following the fundamental ideas by Nayfeh, after ad hoc adimensionalizations, we apply classical singular perturbation
techniques in order to determine the matched expansions of the solutions, in terms of a suitable parameter, up to the first order. We show some numerical results, for
the different mechanisms and different parameter values.

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