Biomedical Engineering Reference
In-Depth Information
1000
synth
p53
100
10
1
5
10
15
20
25
30
35
# of IO pairs
Fig. 3.3
Plot of # of mean solutions vs # of gene expressions observations (IO pairs)
Table 3.4
Attractor cycles and states for
p
53 network [
ATM
,
p
53,
Wip
1,
Mdm
2]
dna
_
dsb
Attractor Cycle
0
(0000)
1
(1000)
→
(1100)
→
(1110)
→
(0110)
→
(0111)
→
(0011)
→
(0001)
expression observations is needed to reduce the size of the solution space and keep the
computation tractable. An
ad
vantage is that our method is inherently parallelizable.
By cofactoring
2
on
x
and
x
, where
x
is a variable of
S
, we can partition
S
into 2
problems,
S
x
and
S
x
. Each of these can run in parallel on separate machines. In
general, we may partition
S
into 2
k
partitions (by using
k
variables) and run each
partition in parallel.
3.4.3
Function and BN Results for p53
We validate our SAT algorithm using the
p53
network. Let us assume that we have
the attractor states as input to our algorithm. Using attractor states is a reasonable
assumption since in the long run, a BN would transition to these attractor states, thus
these states are most likely to be measured in practice. From the logic function of
the
p53
network, we observe 2 attractor cycles containing 8 attractor states in total.
We define the state space as [
ATM
,
p
53,
Wip
1,
Mdm
2] and the attractor cycles are a
singleton cycle if
dna
_
dsb
=
0 and a 7 state cycle if
dna
_
dsb
=
1 as shown Table
3.4
.
2
The
cofactor
of
S
(
x
1
,
...x
i
...x
n
) wrt
x
i
is
S
x
i
(
x
1
,
...x
i
...x
n
)
=
S
(
x
1
,
...x
i
=
1
...x
n
)
