Biology Reference
In-Depth Information
Fig. 4. Petri net model of a simple enzyme catalyzed biochemical reaction (Michaelis-Menten reaction).
substrate concentration dependence found in many allosteric enzymes. In the first case, we can introduce
a general function
v
=
K
app
S
to meet the lack of unknown parameters, where
K
app
is the apparent
rate constant. As we know the Michaelis-Menten equation is only valid when the concentrations of
substrate and enzyme meet the precondition that [E] is not less than 0.001[S]. Considering the effect of
enzyme concentration on the reaction rate in case the enzyme is sensitively regulated, i.e., the enzyme
concentration is a variable of the model, the Michaelis-Menten equation can be written as
·
S
K
m
+
S
=
·
k
cat
S
K
m
+
S
·
E
·
v
max
v
=
,
where
k
cat
is known as turnover number. When there is more than one substrate involved in an enzymatic
reaction, and its kinetic type is unknown, one gets processes more complicated than we discussed in the
previous section. As the Michaelis-Menten equation is obviously invalid at this time, we simply apply
the following function:
n
S
i
k
mi
+
S
i
.
v
=
v
max
·
i
−
1
For instance, given a two-substrate biochemical reaction,
S
2
(
K
m
1
+
S
1
)
·
(
K
m
2
+
S
2
)
v
max
·
S
1
·
v
=
.
Fortunately, if a two or more substrate biochemical reaction is already determined as one of the ki-
netic types such as competitive kinetics, Ping-Pong kinetics, etc.
and available in the literature, the
corresponding function is recommended to employ.
Model of Genetic regulatory networks
Although metabolic reactions determine anabolism and catabolism, the regulation of metabolism is
mainly based on the regulation of gene expression because this determines whether a protein is present
to carry out its particular metabolic reaction. Gene regulatory networks are the on-off switches and
rheostats of a cell operating at the gene level. Based on interactions between genes and proteins and
reactions of genes and proteins, they dynamically orchestrate the level of expression for each gene in the
genome by controlling whether and how vigorously that gene will be transcribed into RNA. Each RNA
transcript then functions as the template for synthesis of a specific protein by the process of translation.
