Biology Reference
In-Depth Information
3. Directed arcs connecting the places and the transitions represent the relations between corresponding
static elements and active elements. Arc weights
α
and
β
describe the quantities of substances
required before and after a reaction, respectively. In case of modeling a chemical reaction, arc
weights represent quantities given by stoichiometric equations of the reaction itself. Note that the
weight of an arc is omitted if the weight is 1.
Signaling pathways are information cascades of enzyme reactions from transmembrane receptors to
the nucleus DNA, which ultimately regulate intracellular responses such as programmed cellular pro-
liferation, gene expression, differentiation, secretion and apoptosis. For signaling pathways, besides
the catalytic reactions, the information among the molecular interactions such as complex formation,
gathering action, translocation and channel switching need to be modeled according to different types of
interactions as long as the biological facts are known.
Figure 5 shows various molecular interactions of signaling pathways and their correspondence to the
Petri net models. We give explanations about the molecular interactions that appear in the IL-1 signaling
pathway, which is used below to demonstrate our method.
I. A binding reaction induces the formation of homo- or heterodimers and generates a complex
compound. This block shows the ligand-receptor binding interaction and the corresponding Petri
net model that indicates that the transition cannot fire in the absence of ligand although receptors
exist. The number of input places of transitions is two or more while the output place number is
one in the binding reaction. Obviously, we can also expand the conception of association to the
model represented in block I (b), generally representing the simultaneous binding of substrates
S
1
,
...
,
S
n
(
n
1) forming a complex
C
in biological systems.
II. Phosphorylation is a reaction to add a phosphate (PO
2
3
) group to a protein or a small molecule,
and dephosphorylation that is the backward reaction removing phosphate groups from a com-
pound by hydrolysis.
III. Autophosphorylation is a transphosphorylation reaction between receptor subunits frequently
following the binding of a ligand to a receptor with intrinsic protein kinase activity.
IV. Each down-regulated pathway transmits the signals to regulate different down-regulated reac-
tions according to the modification positions on the ligand-receptor complex. The complex often
has many chemical modifications, e.g., phosphorylation and acetylation. Few methods using
Petri nets have been proposed to model this process by using one place (i.e., ligand-receptor
complex) possessing more than one output transitions used to represent the multiple reactions
of modification. These methods are easily understood, but raise an issue that, if the transition of
such a place fires to remove the token(s) from a shared input place at one time, it will disable all
the other transitions of this place simultaneously although the token(s) will return back to the
same input place via a self-loop. To deal with it, we model each distinct active site (modification
position) on the complex as an individual place
C
i
(1
<i<n
) as shown in block IV.
V. Adaptor protein (e.g., Grb2 and SHC1)-mediated association reactions are different from the
binding reaction (see I). The main participator adaptor protein is an accessory protein to main
proteins. These proteins lack the intrinsic enzymatic activities themselves but instead mediate
specific protein-protein interactions driving the formation of protein complexes.
VI. Chemical reactions are the most common reactions in signaling pathways, for which the conver-
sion of substances to products is ordinarily modeled as connecting input places to output places,
both belonging to the same transition.
