Biology Reference
In-Depth Information
Table 3
Interfering tests on the urea cycle Petri net model
Interfering test
Value of metabolites
Urea cycle defect
NH
4
Citrulline
Argininosuccinate
Ornithine
Arginine
(plasma)
(plasma)
(plasma)
CPS1 blockade
↑↑
↓
↓
↓
↓
Carbamylphosphate
synthase deficiency
OTC blockade
↑
↓
↓
↑
↑
Ornithine transca-
rbamylase deficiency
ASS blockade
↑
↑↑
↓
↓
↓
Argininosuccinate
synthase deficiency
ASL blockade
↑
↑
↑↑
↑
↑
Argininosuccinase
deficiency
↑
↑
↓
↓
↑↑
ARG blockade
Arginase deficiency
Membrane transportation blockade
↑
↑
−
↑↑
↑
HHH syndrome
The values of the model parameters lacking in the literature are verified through numerical experiments
or modifed from several references.
The dynamic behavior of the model system, such as the metabolite fluxes, NH
4
input and urea output
are well described with continuous elements; while control of gene expression are outlined with discrete
ones due to the insufficiency of explicit expression data. Nevertheless, when explicate knowledge about
expression levels of the enzymes are available; it is possible to exploit our model of gene regulatory
network to handle realistic gene expression data with the state equations. The initial values of variables
were assigned and tuned so that the model system behavior would comply maximally with available
experimetnal data on the dynamic characteristics of the system's behavior, based on the following
considerations:
The availability of ammonia or amino acides (denoted as NH
3
) is ingested continuously from plasma
into mitochondria with a stable speed, i.e. the changes of ammonia concentration due to the rate of protein
metabolism are not taken into account. The concentration of nitrogen excreted (urea) in plasma ranges
from 3 mmol/L to 8 mmol/L and thus is regarded to be discharged with a certain rate. The degradation
rates of an enzyme is 0.001 times of its concentration. The places of the main metabolites are directly
linked to the transitions. Reaction rates assigned to these transitions are interpreted with differentail
equations. However, from reality point of view, these transitions involve more than one variable that are
presented in differential functions. In order to get a better understanding of these relationship, serval test
arcs are used, e.g. the test arc between asparate and transition of ASS. There are no real input and output
within these arcs, but the places linked are exploited by the transition firing speed.
In the model, inhibitor arcs are also used to present negative effects of repressors and/or inhibitors
to gene expression. On the biochemical reaction level, negative effects of metabolites are expressed as
enzyme inhibitions that include competitive inhibition, noncompetitive inhibition, irreversible inhibition
and feedback inhibition. Sequentially, the regulation of urea cycle enzyme activities can be brought
in these two ways: First, the gene expression that is regulated by activators and inhibitors controls
the enzyme synthesis, while enzyme synthesis and degradation determine the amount of the enzyme.
Second, the activity of the enzyme can be altered during the metabolic catalysis.
The formalization of the urea cycle model allows the quantitative simulation of metabolic pathways.
Dynamics of the main components on the model regulating the urea cycle are shown in Fig. 8, too.
Moreover, several tests on interfering the fluxes intentionally are conducted and results are observed
(Table 3).
