Biology Reference
In-Depth Information
Table 1
Stationary states for the full regulatory network of
A. thaliana
flower mor-
phogenesis (see Fig. 7)
EMF1
TFL1
LFY
AP1
AG
LUG
UFO
AP3
PI
SUP
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
?
0
0
0
0
1
0
1
1
1
0
?
1
0
0
0
0
0
1
1
0
?
1
0
0
0
0
0
0
0
?
?
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
?
0
0
0
0
0
1
1
1
1
0
Symbol '?' allows for both 0 and 1.
Table 2
Stationary states from Table 1 (only genuine ones)
EMF1
TFL1
LFY
AP1
AG
LUG
UFO
AP3
PI
SUP
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2. As the flower morphogenesis begins the expression of genes
LFY
and
AP1
can be observed. The
latter is also active in sepal cells of the flower.
3. Next, the genes
LUG
and
UFO
come to play, but their activity is only a part of the process and is
not observed in the differentiated cells.
4. As the activity of the above mentioned genes fades away, the new genes responsible for the flower
type -
AG
,
AP3
and
PI
- become active.
5. At the end of the process the gene
SUP
is briefly active.
The genes can be divided into two groups, the genes that are temporary (
LFY
,
LUG
,
UFO
and
SUP
)
and genes that are an essential part of the final equilibria (
EMF1
,
TFL1
,
AP1
,
AG
,
PI
and
AP3
). This
classification allows one to distinguish between genuine and false
stationary states
, as it is unlikely for
temporary genes to be observed in genuine stationary states.
The straightforward approach
Table 1 shows the stationary states found for the Petri net from Fig. 7. For this type of network one
can find the stationary states either manually, or automatically using our translation to the Presburger
formulae, as described in Sections “Logical description of stationary states” and “Petri nets with bounds”.
Table 2 shows only those states from Table 1 that are considered biologically significant (see the beginning
of this Section).
The identified stationary states can be easily attributed to the ones observed in the different flower
cells (compare with Mendoza
et al.
, 1999). The stationary state [0000100110] represents activities
B
and
C
(expression of genes
AG
,
AP3
and
PI
), and is observed in the
stamen
cells. The stationary state
[0000100000] represents activity
C
(only gene
AG
is expressed) and is observed in the
carpel
cells.
[1100000000] is the last known stationary state, which is found in non-flowering cells. The stationary
state [1100000110] was never observed in reality, however it might be of biological significance as
mentioned in the beginning of the section “Stationary state analysis” (see also Mendoza
et al.
, 1999).
