Biology Reference
In-Depth Information
Fig. 4. Extension of the model of Reddy
et al.
[9].
definition.
An algorithm for the examination of the limitation of Petrinets was presented.
However,
using self-modified Petrinets the detection of limitation is an unsolvable problem [23].
The capacity value is important for the detection of bottlenecks. The definition of capacities permits
fixing an interval for each metabolite, which represents the normal scope of this concentration. Moreover,
the detection of bottlenecks can be reduced to the reachability problem. Using small Petrinets the
reachability graph can be constructed in practice, which permits calculating all bottlenecks.
Biochemical networks represent a set of biochemical reactions which are highly connected. To
analyze metabolic pathways, all activated biochemical reactions are of importance. However,
death
and
liveliness
of transitions and configurations must be considered.
A transition is called
death
,ifitcan
never be enabled.
Otherwise the transition is called
liveliness
.
The detection of
death
and
liveliness
depends on the reachability problem.
APPLICATIONS
Description of the model
The formalization of Reddy
et al.
[9] does not permit modeling the kinetic effects of biochemical
reactions. However, our extension allows a flexible modeling process. Therefore, we have to consider
the following aspects:
-
actual arrow weight depends on the actual configuration,
-
inhibitor metabolites reduce the concentration of the metabolites,
-
a transition can also be activated without inhibitors and activators,
-
for the detection of bottlenecks and critical configurations we define concentration borders for every
place which will be tested after the firing of each transition.
The extension of our model will be demonstrated in Fig. 4.
Activators and inhibitors will be used regarding the actual configuration.
The arrow weight is no
longer a constant description.
In our example F and H design the concentration of the activator and
