Ricerc@Sapienza

The goal of this paper is to accurately describe the metastable dynamics of the solutions to the hyperbolic relaxation of the Cahn–Hilliard equation in a bounded interval of the real line, subject to homogeneous Neumann boundary conditions. We prove the existence of an approximately invariant manifoldM0 for such boundary value problem, that is we construct a narrow channel containing M0 and satisfying the following property: a solution starting from the channel evolves very slowly and leaves the channel only after an exponentially long time.

We show some recent results related to the application of singular perturbation techniques in the framework
of the so-called total quasi-steady-state approximation (tQSSA) for the approximation of some important enzyme reactions:
the fully competitive inhibition, the Goldbeter-Koshland cycle, the double phosphorylation mechanism. We determine the
uniform expansions up to the first order in terms of appropriate perturbation parameters, related to the initial conditions and
to the kinetic parameters characterizing the reactions.

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

The complex intracellular signal transduction networks can be decomposed into simpler moduli, where fundamental reactions, like the Goldbeter-Koshland
switch (which models, for example, the phosphorylation-dephosphorylation cycle) (1; 2), the competitive inhibition (3) and the double phosphorylation mechanism

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