LCS & GBML Central

Hybrid Petri net (HPN) is an extension of the Petri net formalism, which enables us to handle continuous information in addition
to discrete information. Firstly, this paper demonstrates how biological pathways can be modeled by the integration of discrete
and continuous elements, with an example of the λ phage genetic switch system including induction and retroregulation mechanisms.
Although HPN allows intuitive modeling of biological pathways, some fundamental biological processes such as complex formation
cannot be represented with HPN. Thus, this paper next provides the formal definition of hybrid functional Petri net with extension
(HFPNe), which has high potential for modeling various kinds of biological processes. Cell Illustrator is a software tool
developed on the basis of the definition of HFPNe. Hypothesis creation by Cell Illustrator is demonstrated with the example
of the cyanobacterial circadian gene clock system. Finally, our ongoing tasks, which include the development of a computational
platform for systems biology, are presented.

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.