Biomedical Engineering Reference
In-Depth Information
Table 4.31
Predictor ranking by MSE for gene
WNT
5
A
(
x
7
) in melanoma network (Top 10
Predictors Shown)
Rank
1 input
2 inputs
3 inputs
Predictor
MSE
Predictor
MSE
Predictor
MSE
1
x
6
0.096190
x
5
,
x
6
0.063681
x
1
,
x
5
,
x
6
0.051371
2
x
3
0.183881
x
3
,
x
6
0.091656
x
3
,
x
5
,
x
6
0.060039
3
x
2
0.191924
x
1
,
x
6
0.095633
x
2
,
x
5
,
x
6
0.063405
4
x
1
0.294790
x
4
,
x
6
0.095824
x
4
,
x
5
,
x
6
0.063546
5
x
4
0.315267
x
2
,
x
6
0.095870
x
1
,
x
3
,
x
6
0.084099
6
x
5
0.315565
x
3
,
x
5
0.162585
x
3
,
x
4
,
x
6
0.091255
7
x
1
,
x
5
0.171238
x
2
,
x
3
,
x
6
0.091303
8
x
1
,
x
3
0.176896
x
1
,
x
4
,
x
6
0.095274
9
x
2
,
x
3
0.182140
x
1
,
x
2
,
x
6
0.095318
10
x
3
,
x
4
0.182581
x
2
,
x
4
,
x
6
0.095329
Table 4.32
Predictor selection for melanoma network
Gene
Selected Predictor
Zhegalkin function
x
1
PIRIN
x
3
,
x
4
,
x
7
x
4
+
x
3
x
7
−
x
4
x
7
x
2
S
100
P
x
1
,
x
3
x
1
x
3
x
3
RET
1
x
1
,
x
6
,
x
7
x
7
−
x
1
x
7
−
x
6
x
7
+
2
x
1
x
6
x
7
x
4
MART
1
x
1
,
x
2
,
x
7
x
1
−
x
1
x
2
−
x
1
x
7
+
x
1
x
2
x
7
x
5
HADHB
x
1
,
x
4
x
1
+
x
4
−
2
x
1
x
4
x
6
STC
2
x
1
,
x
3
,
x
7
x
7
−
x
1
x
7
−
x
3
x
7
+
x
1
x
3
x
7
x
7
WNT
5
A
x
1
,
x
5
,
x
6
x
1
+
x
6
−
x
1
x
5
−
2
x
1
x
6
−
x
5
x
6
+
2
x
1
x
5
x
6
are shown in Table
4.32
and these results can provide direction for further validation
in lab experiments. In addition, our algorithm also returns the associated Zhegalkin
function along with the selected predictor, also shown in Table
4.32
.
For example, let us examine the predictor selected for WNT5A. In [
17
], the expres-
sion of WNT5A was observed to been associated with the metastasis of melanoma,
so determining the predictors of WNT5A is of great interest for GRN control and
intervention. Our algorithm finds the best predictor (predictor containing Zhelgakin
function with least error) for WNT5A to be (
x
1
,
x
5
,
x
6
), or in other words
PIRIN
,
HADHB
, and
STC2
, the results of which appear consistent with literature [
18
],
[
19
]. From our algorithm, the corresponding Zhegalkin function for WNT5A is
x
1
+
x
6
−
x
1
x
5
−
2
x
1
x
6
−
x
5
x
6
+
2
x
1
x
5
x
6
, which we can convert to the Boolean func-
tion
HADHB
(
PIRIN
STC
2). These findings can be used by biologists to develop
drugs that target
PIRIN
,
HADHB
, and
STC
2 to modify the expression of
WNT
5
A
and
control the metastasis of melanoma (Table
4.24
,
4.25
,
4.26
).
⊕
