Biology Reference
In-Depth Information
holding
n
-weight such as homotrimers or -tetramers.
VIII. Translocation refers to the movement of molecules, substances or ions across cell membranes
or via the bloodstream in biology. Figure 5 shows the nuclear translocation within a cell. A
transition is modeled to indicate the movement action of substances before and after.
IX. Intracellular signal pathways are largely carried out by second messenger molecules. Ca
2+
acts
as a second messenger molecule inside the cell. Usually the concentration of free Ca
2+
within
the cell is very low; it is stored inside of organelles, mostly the endoplasmic reticulum. In order
to become active, Ca
2+
has to be released from the organelles into the cytosol. Two transitions
t
o
and
t
c
are introduced to denote channel activity of “open” and “close”, respectively.
t
o
is
enabled when input place holds up token(s) after the association of organelles and substances,
whereas
t
c
is enabled as long as some stop mechanisms shut off the channel.
X. This is the opposite of I. Dissociation process is a general process in which complexes and
molecules separate or split into smaller molecules or ions. The number of input places of
transitions is one while the output place number is two or more.
XI. Since an enzyme itself plays a role as catalyst in biological pathways and there occurs no
consumption in biochemical reactions, the reaction is modeled as a transition, where the enzyme
is modeled as an enzyme place that has a self-loop with the same arc-weight. That is, once an
enzyme place is occupied by a token, the token will return to the place again to keep the firable
state, if the transition has fired.
XII. A source transition represents an activity to provide substances that will take part in the reactions.
A sink transition denotes small and natural degradation of a substance.
XIII. Internalization is a phenomenon to decrease the number of receptors on the surface of a cell
membrane, due to be exposed to corresponding biological agents such as ligands for a long time.
As a result of decreasing the number of receptors, responsiveness to the ligands is decreased. The
internalization is modeled by an output transition connected with a place denoting the receptor
via a normal arc.
IL-1 induced signaling pathway
In this paper, we use the example of the IL-1 induced signaling pathway (see Fig. 6) to demonstrate
our proposed method. IL-1 is a proinflammatory cytokine, and plays an important role in regulating
the mechanism of inflammation. The IL-1 signaling pathway is composed of the NF-
κ
B (nuclear
transcription factor-
κ
B) pathway and the MAPK (mitogen activated protein kinase) pathway [13]. We
construct the IL-1 signaling pathway by using our modeling method. Figure 7 illustrates the Petri net
model of the IL-1 signaling pathway.
DETERMINING FIRING DELAY TIME OF TRANSITIONS
As shown in Fig. 7, the Petri net model without firing delay time of transitions is constructed. This
model describes the structural information of connection relationships. The next task is to validate
the model by means of simulation, i.e., to investigate whether the constructed model is consistent with
biological facts obtained from biological experiments and scientific publications. Unfortunately, such
reliable data describing detailed reactions are not reported in most cases. It thus leads us to develop a
general methodology to determine the delay time of the transitions representing reaction rates.
