Biology Reference
In-Depth Information
of specific reaction steps on reaction networks. For instance, it is known that hyperammonemia is a
hereditary disease concerning the urea cycle, resulting from an enzyme deficiency. Ornithine transcar-
bamylase (OTC), a deficiency of an X-linked enzyme disorder of urea synthesis, leads to a disease
whose clinical manifestations include lethargy, coma, and cerebral edema. The identification of sites in
a metabolic pathway that result in such diseases, caused by inborn errors in metabolism, would be useful
so that the relevant enzyme or metabolite could be substituted or suitably modified. In addition, simu-
lating the related complex metabolic networks will additionally help to understand the impact of various
factors (e.g. enzyme insufficiency, metabolic blockade, drugs effects, etc.) on metabolic systems. This
is particularly useful in the pharmaceutical industry for designing site-directed drugs to target mutant
enzymes.
In order to understand the molecular logic of the cell, methods of modeling and simulation are of im-
portance. Different models are available in the literature, commonly falling into two different categories:
the descriptive models (discrete approaches) and the analytical models (differential equations). Tradi-
tionally, metabolic pathways are regarded as coherent sets of enzymatic reactions and can be interpreted
as relational graphs. Each node represents a metabolite and each edge represents a biochemical reaction
that is catalyzed by a specific enzyme. Kohn and Letzkus [1983] expanded the graph theory by a specific
function that allowed the modeling of dynamic processes. Then, the first application of Petri net on
modeling metabolic pathways was introduced by Reddy
et al.
[1993]. In contrast to naive graphs, Petri
net is a graphically oriented language of design, specification, simulation and verification of systems. It
offers a formal way to represent the structure of a discrete event system, simulate its behavior, and draw
certain types of general conclusions on the properties of the system. Ordinary Petri net models do not
have such functions as quantitative aspects, so there are some extension of Petri nets that can support
dynamic change, task migration, superimposition of various levels of activities and the notion of mode
of operations. Various extensions of PNs, such as (Stochastic) Timed PNs [Wang, 1998; Wang, 1999],
Colored PNs [Kurt, 1997], Predicate/Transition Nets [Genrich, 1987] and Hybrid PN [David and Alla,
1992], allow for qualitative and/or quantitative analyses of resource utilization, effect of failures, and
throughput rate. Hofestaedt and Thelen [1998] also presented an extension formalization, a self-modified
Petri net, which allows the quantitative modeling of regulatory biochemical networks. During the last
years some more papers appeared [Genrich
et al.
, 2001; Goss and Peccoud, 1999; Hofestaedt
et al.
,
2000a; Matsuno
et al.
, 2000; Matsuno
et al.
, 2001], indicating that the Petri net methodology seems to
be useful in modeling and simulation of metabolism. We are motivated to exploit the methodology of
Petri net to model gene regulated metabolic networks in the cell, explain the importance of sustaining
core research, and identify promising opportunities for future research.
HYBRID PETRI NETS
We suppose that readers have some background knowledge of Petri nets, otherwise, they are strongly
referred to read W. Reisig's Petri Nets: An Introduction [Reisig, 1985] or some basic reference topics
at Petri nets world at
http://www.daimi.au.dk/PetriNets/
where a large amount of investigations on Petri
nets have been compiled in the literature, and various applications have chosen Peti nets as their control
models due to the intuitively understandable graphical notation of Petri nets. Herewith a brief description
of hybrid Petri nets is presented as the following context.
Definition 1:
A hybrid Petri net is a six tuple
Q
=
(
P
,
T
,
Pre
,
Post
,
h
,
M
) such that:
P
=
{
P
1
,
P
2
,
...
,
P
n
}
is a finite, not empty, set of places;
