Biomedical Engineering Reference
In-Depth Information
Table 4.5
Linear predictor ranking by MSE for gene
Rb
(
x
2
) in mutated network (Top 10 predictors
shown), correct predictor is
x
1
,
x
4
,
x
5
,
x
9
Rank
1 input
2 inputs
3 inputs
4 inputs
Predictor
MSE
Predictor
MSE
Predictor
MSE
Predictor
MSE
1
x
1
0.1626
x
1
,
x
4
0.0676
x
1
,
x
4
,
x
9
0.0501
x
1
,
x
4
,
x
8
,
x
9
0.0365
2
x
8
0.2268
x
1
,
x
3
0.0952
x
1
,
x
3
,
x
4
0.0512
x
1
,
x
4
,
x
6
,
x
9
0.0377
3
x
7
0.2323
x
1
,
x
6
0.1030
x
1
,
x
4
,
x
5
0.0561
x
1
,
x
3
,
x
4
,
x
8
0.0385
4
x
3
0.2398
x
1
,
x
9
0.1037
x
3
,
x
4
,
x
7
0.0592
x
1
,
x
3
,
x
4
,
x
9
0.0397
5
x
6
0.2425
x
3
,
x
4
0.1058
x
1
,
x
4
,
x
6
0.0623
x
1
,
x
4
,
x
5
,
x
6
0.0405
6
x
4
0.2482
x
5
,
x
6
0.1062
x
3
,
x
4
,
x
5
0.0626
x
1
,
x
4
,
x
5
,
x
9
0.0415
7
x
5
0.2517
x
1
,
x
8
0.1083
x
1
,
x
4
,
x
7
0.0660
x
1
,
x
4
,
x
5
,
x
8
0.0445
8
x
9
0.2572
x
1
,
x
7
0.1086
x
3
,
x
4
,
x
9
0.0698
x
1
,
x
3
,
x
4
,
x
5
0.0446
9
x
1
,
x
5
0.1111
x
1
,
x
3
,
x
5
0.0705
x
1
,
x
4
,
x
7
,
x
9
0.0450
10
x
4
,
x
7
0.1251
x
3
,
x
4
,
x
8
0.0710
x
1
,
x
3
,
x
4
,
x
6
0.0454
states. Each pair of current and next state forms a minterm (row) in the table. Since
there are
n
=
9 genes in the mutated network, the state transition table contains
2
9
512 rows. We randomly sample
m
rows from this table and convert the binary
values of each gene to a continuous value. The conversion process takes a binary
value (0,1) and uniformly and randomly perturbs the value up to
p
, resulting in a
continuous value ([0,
p
], [1
=
p
, 1]). The value of
p
can be from 0 to 0.5 and is
proportional to the number of occurrences of either binary value for a gene in the set
of rows. For example, if a gene
x
i
has the value 1 occurring 75 % in the set of rows,
p
−
0
.
375, and as such the 1 value is perturbed from [0.625,1] for
gene
x
i
. Hence, each gene will have a different perturbation that is dependent on the
occurrences of the binary values 1 and 0 in the the input set.
As an additional constraint, we limit our algorithm to search on predictors with 4
or less inputs. In general, this is a reasonable assumption as most genes have been
observed to have relatively few inputs in practice. We individually select genes
x
2
to
x
9
as the target gene and then apply our method on the mutated network to determine
predictor rankings for each of these 8 genes. We exclude gene
CycD
(
x
1
)asitisan
extracellular signal, and thus not predicted by any genes in the mutated cell-cycle
network.
For the mutated mammal network, Table
4.5
through
4.12
(linear representation)
and Table
4.13
through
4.20
(sigmoid representation) lists the top 10 predictors for
genes
x
2
through
x
9
respectively as determined by our algorithm. Gene CycD (
x
1
)
not included as this gene is controlled by an extracellular signal and as such is not
regulated by any of the other 8 genes in the network. For each target gene, the correct
(actual) predictor is listed in the table captions. Each table shows predictors for a
specific target gene and is organized as follows. The '1 input' column lists the 1 input
predictors ranked by their associated MSE from lowest MSE to highest MSE. The
top ranked 1 input predictor has the lowest MSE and therefore is the best fitting 1
input predictor. Similarly, the '2 input' column lists the 2 input predictors ranked
by MSE. And so on for the '3 input' column and '4 input' columns. For example,
Table
4.12
lists the predictors for
CycB
(
x
9
). In the 1 input column, the best (lowest
=
(0
.
75)
∗
(0
.
5)
=
