Qualitative Behavior of a Metabolic Pathway with Hybrid Feedback
Abstract
We study the qualitative behavior of a model to represent local regulation in a
metabolic network. The model is based on the end-product control structure introduced in [A.
Goelzer, F. Bekkal Brikci, I. Martin-Verstraete et al., BMC Syst Biol 2 (2008), pp. 1{18]. In this
class of regulation, the metabolite eector is the end-product of a metabolic pathway. We suppose
the input to the pathway to switch between zero and a positive value according to the concentration
of the metabolite eector. Considering the switched system as a dierential inclusion, we prove that
it converges to a globally uniformly asymptotically stable equilibrium point, reaches the sliding mode
or oscillates around the sliding mode depending on the positive value of the input. Finally, we show
that in any case the solution of the switched system is the limit of solutions of equation sequences
with smooth or piecewise linear inputs.