Biology Reference
In-Depth Information
Process of gene regulatory networks is not restricted to the level of transcription, but also may be carried
out at the levels of translation [Pyronnet
et al.
, 1996], splicing [Yao
et al.
, 1996], posttranslational protein
degradation [Hochstrasser, 1996], active membrane transport [Weissmuller and Bisch, 1993], and other
processes. In addition, such networks often include dynamic feedback loops that provide for further
regulation of network architecture and output.
Building complete kinetic models of genetic regulatory systems requires detailed knowledge on reac-
tion mechanisms, often, the following steps
ad hoc
are considered:
1. The gene (DNA) is transcribed into RNA by the enzyme RNA polymerase.
2. RNA transcripts are subjected to post-transcriptional modification and control: rRNA transcript
cut into appropriate size classes and initial assembly in nuclear organizer; tRNA transcript folds
into shape; mRNA transcripts are modified, noncoding sequences (introns) removed from interior
of transcript; in eukaryotes, all RNA types must move to the cytoplasm via the nuclear membrane
pores.
3. Then mRNA molecules are translated by ribosomes (rRNA
+
ribosomal proteins) that match the
3-base codons of the mRNA to the 3-base anticodons of the appropriate tRNA molecules.
4. Finally, newly synthesized proteins are often modified after translation (post-translation) before
carrying out its function, which may be transporting oxygen, catalyzing reactions or responding
to extracellular signals, or even directly or indirectly binding to DNA to perform transcriptional
regulation and thus forming a closed feedback loop of gene regulation.
However, at present time, the information of the bioprocesses from genes to the gene-encoded products
is still unclear or unavailable. So far, we can regard the unknown part as a black box of transition (one
transition that can be visualized as the representation of a part of Petri net) and simplify the whole
procedure as a higher level of abstraction (Fig. 5):
This modification does not involve changing the structure of the complete net and any modification
to this subnet is reflected in the behavior of the original transition. Therefore, Petri net models are
extensible and ways of plug-in concept, they can be extended without significant deviation from the
existing structure.
As to model gene regulatory networks quantitatively, the state equations of the following form are
used to model bioprocesses such as activation of proteins, binding of proteins to genes, binding of RNA
polymerase and so on.
If
state
[
i
]
(
condition
), then
dstate
[
i
]
dt
=
state
[
i
]
(
consequence
)
For example, the concentration of the gene product is
state
[
i
]
. The condition contains regulatory terms
for this gene and describes whether the gene is being expressed or not. It depends on the state of the cell,
and may contain models for promoters, enhancers, other proteins, nucleic acid, etc. The consequence
then describes the result of condition changing, here, the rate of gene expression.
So the differential mass balances describing the concentration of mRNA and of the encoded protein
can be given as:
If
(
∃
(Gene, transcriptional factor(s), RNA nucleotides, binding of RNA polymerase, etc.)
not
(Repressors, etc.))
Then
d
[
mRNA
]]
dt
(transcription is initiated and mRNA is produced,
=[
mRNA
](
GPC, mRNA
)=
k
is
[
GPC
]
−
k
d
[
mRNA
]
)
If
(Modified mRNA, tRNA, initiation factor(s), amino acid, binding of ribosome, etc.)
Then
(the gene-encoded protein is synthesized,
d
[
[P]
dt
=[
P
](
P, mRNA
)=
k
tl
[
mRNA
]
−
k
d
[
P
]
−
k
r
[
P
]
)
Where
k
ts
and
k
tl
are the rates of transcription and translation respectively,
k
d
is the rate of degradation
