Biology Reference
In-Depth Information
Fig. 1. Basic elements of HPN, HDN, and HFPN.
from/going out the continuous transition. In contrast, the definition of HDN does not allow to transfer
different amount through these two types of arcs. However, HDN has the following firing feature of
continuous transition which HPN does not have; “the speed of continuous transition of HDN can be
given as a function of values in the places”.
From the above discussion, we can know that each of HPN and HDN has its own feature for the firing
mechanism of continuous transition. As a matter of fact, both of these features of HPN and HDN are
essentially required for modeling common biological reactions. (See the example of Fig. 6 in which four
monomers compose one tetramer.)
This motivated us to propose hybrid functional Petri net (HFPN) [Matsuno
et al.,
2003b] which includes
both of these features of HPN and HDN. Moreover, HFPN has the third feature for arcs, that is, a function
of values of the places can be assigned to any arc. This feature was originated from the idea in the paper
[Hofestadt and Thelen, 1998] which was introduced in order to realize the calculation of dynamic
biological catalytic process on Petri net based biological pathway modeling. In fact, these three features
are realized in HFPN by introducing a new type transition called a
functional continuous transition
which allows us to assign any functions to arcs and transitions for controlling the speed/condition of
consumption/production/firing. An example to use the functional continuous transition is given in the
beginning of section “HFPN modeling of the
lac
operon gene regulatory mechanism and glycolytic
pathway”.
Usage of discrete and continuous elements
Biological pathways essentially consist of discrete parts such as a genetic switch control and con-
tinuous parts such as a metabolic reaction. These discrete and continuous parts can be represented by
discrete elements (discrete place and discrete transition) and continuous elements (continuous place and
continuous transition) of HFPN.
For example, a control system turning on or off the gene expression with operator site can be represented
by discrete elements. That is, if the discrete place has a token, the protein necessary for activating the
operator site has bound to the operator, that means the gene expression turn on. In addition, using the
delay concept of the discrete transition, wean easily describe the transcription which happens after a
certain time.
On the other hand, biological phenomenon such as transcription, translation, and enzymic and
metabolic reactions have been treated as events whose conditions change continuously. By model-
ing the transcription and the translation with continuous elements in the following way, expression levels
of mRNA and proteins can be simulated. Continuous places are used for storing concentrations of mRNA
and protein. Reaction speeds of transcription and translation are assigned at parameters of continuous
