Abstract This paper describes the working principles of an algorithm for boundedness analysis of open Chemical Reaction Networks endowed
with mass-action kinetics. Such models can be thought of both as a special class of compartmental syste…
Abstract
This paper describes the working principles of an algorithm for boundedness analysis of open Chemical Reaction Networks endowed
with mass-action kinetics. Such models can be thought of both as a special class of compartmental systems or a particular
type of continuous Petri Nets, in which the firing rates of transitions are not constant or preassigned, but expressed as
a function of the continuous marking of the network (function which in chemistry is referred to as the “kinetics”). The algorithm
can be applied to a broad class of such open networks, and returns, as an outcome, a classification of the possible dynamical
behaviors that are compatible with the network structure, by classifying each variable either as bounded, converging to 0
or diverging to ∞. This can be viewed as a qualitative study of Input–Output Stability for chemical networks, or more precisely,
as a classification of its possible I–O instability patterns. Our goal is to analyze the system irrespectively of values of
kinetic parameters. More precisely, we attempt to analyze it simultaneously for all possible values. Remarkably, tests on
non-trivial examples (one of which is discussed in this paper) showed that, as the kinetic constants of the network are varied,
all the compatible behaviors could be observed in simulations. Finally, we discuss and illustrate how the results relate to
previous works on the qualitative dynamics of closed reaction networks.
- Content Type Journal Article
- Pages 751-774
- DOI 10.1007/s11047-009-9163-7
- Authors
- David Angeli, Dipartimento di Sistemi e Informatica, University of Florence, Florence, Italy