Biology Reference
In-Depth Information
Fig. 1. Elements of VON++.
Fig. 2. Presentation of transition rate in continuous systems.
Fig. 3. Presentation of intermediate reaction rate.
The discrete transition is the active element in discrete event Petri nets. Transition can fire if all
places connected with input arcs contain equal or more tokens than the input arcs specify. It can be
assigned with a delay time. The continuous transition differs from the traditional the discrete transition;
its activity is not comparable with the abrupt firing of discrete transition. The firing speed assigned to
a continuous transition describes its firing behavior. It can be a constant or a function, i.e. transport of
tokens according to
v
(
t
)
, in Fig. 1,
v
(
t
)=
1.
The rates of bioprocesses are not defined within a Petri net, they should be specified separately. In
automated control systems represented by Petri nets, execution of transitions usually depends on the
presence of a specific number of tokens in all staring places. However, in most chemical and biological
systems the rate of a process (transition) is defined by the mass action law. The change of tokens
(or concentration) is proportional to the number of tokens (or concentration) in all starting places as
expressed in the Fig. 2.
V
is the rate of firing of the transition;
k
is a constant (called a rate coefficient
in chemical kinetics);
m
3
,
m
4
are the concentration of place
S
1
and place
S
2
. Coefficient
k
varies
with temperature, pressure, solvent, and other factors. As a result,
v
will become a function of several
variables. Figure 3 indicates how token number (or concentration) of reaction intermediate
P
1
changes.
Traditionally, kinetics has been taught in biochemistry courses in terms of the steady-state kinetics.
This corresponds to a detailed study of the local properties of individual enzymes. However, one can go
further and create kinetic models of the whole pathway. Such models are composed of coupled ordinary
differential (for time courses) or algebraic (for steady states) equations. These equations are non-linear
