Computing core reactions of uncertain polynomial kinetic systems

Abstract

Kinetic systems form a wide nonlinear system class with good descriptive power that can efficiently be used for the dynamical modeling of non-negative models emerging not only in (bio)chemistry but in other important scientific and engineering fields as well. The directed graph structure assigned to kinetic models give us important information about the qualitative dynamical properties of the system. In this paper we extend the previous results for computing structurally invariant directed edges (called core reactions) for uncertain kinetic polynomial models, where the uncertainty is represented as a multi-dimensional interval in the space of monomial coefficients. We show that the computation can be put into the framework of linear programming. Using illustrative examples we demonstrate the properties of the computed structures and the potential application of the method in the support of structural identification of biochemical networks.