Biology Reference
In-Depth Information
Fig. 1. Elements of hybrid (functional) Petri net.
notions in mathematics, physics and computer science which are irrelevant to biology/medicine. (2)
Allow users to represent biopathways intuitively and understand/manage easily details of the represen-
tation and simulation mechanism; otherwise, users could not have confidence that the understanding and
knowledge in their minds coincides with the object represented with the software tools.
From these criteria, in this paper, we firstly define a novel notion of Petri net called
hybrid functional
Petri net
(HFPN) by extending the notions of hybrid Petri net [5] and functional Petri net [6] so that the
notion will be suited for modeling biopathways.
Then, we introduce a software tool,
Genomic Object Net
(GON), for representing and simulating
biopathways, which we have developed by employing the architecture of HFPN. GON has an editor
and a simulator of HFPN with a graphical user interface (GUI) which shall resolve the matters (1) and
(2). In order to demonstrate the effectiveness of GON for representing and simulating biopathways, we
will present two HFPN models: the circadian rhythm of
Drosophila
as an example of a gene regulatory
mechanism and apoptosis induced by Fas ligand as an example of signal transduction.
HYBRID FUNCTIONAL PETRI NET
Ordinary differential equations (ODEs) are widely accepted to express biological phenomena such as
biochemical reactions. But in this approach, it is rather difficult to observe the whole system intuitively
such as a picture if the system constitutes a large network of cascades. Although the discrete Petri net
model allows very intuitive graphical representation, the mechanism of ODEs cannot be directly realized
because the discrete Petri net model deals with only integers as the contents of places. For sophisticated
dynamic systems in which control mechanisms of genes and chemical reactions with enzymes are
concurrently performed, it is more reasonable to use real numbers for representing the amounts of some
objects, e.g. the concentrations of a protein, mRNA, complex of proteins, metabolites, etc.
The hybrid Petri net model (HPN) [5] has been introduced as an extension of the discrete Petri net
model so that it can handle real numbers in a continuous way and it allows us to express explicitly the
relationship between continuous values and discrete values while keeping the good characteristics of
discrete Petri net soundly. Drath [7, 8] has also enhanced this notion to define the hybrid dynamic net
model (HDN) for modeling more complex systems.
In HPN/HDN model, two kinds of places and transitions are used,
discrete/continuous places
and
discrete/continuous transitions
. A discrete place and a discrete transition are the same notions as used
in the discrete Petri net model. A continuous place holds a nonnegative real number as its content.
A continuous transition fires continuously in the HPN/HDN model and its firing speed is given as a
function of values in the places in the model. For graphical notations, discrete transition, discrete place,
continuous transition and continuous place are drawn as shown in Fig. 1.
