Biomedical Engineering Reference
In-Depth Information
Table 2.4
Melanoma network predictor set selection
PIRIN
S100P
RET1
MART1
HADHB
STC2
WNT5A
x
1
x
2
x
3
x
4
x
5
x
6
x
7
A
Predictor set
1357
2137
3146
4357
5124
6124
7124
Resolution ratio
2.57
1.41
1.34
1.30
1.41
1.66
1.31
B
Predictor set
1357
2137
3146
4137
5134
6137
7126
Resolution score
1.78
1.77
1.84
1.97
1.99
1.98
2.56
AB
Predictor set
1357
2367
3146
4137
5137
6357
7124
Weighted sum
2.06
1.57
1.75
1.61
1.45
1.39
1.88
The final predictor set is present in a small number of attractor cycle orderings.
For example, the final predictor set selected by methods A, B, and AB are found
in respectively 8, 4, and 6 attractor cycle orderings out of the total 5040 possible
orderings. Hence the algorithm will enable us to generate a few deterministic
GRNs.
Some predictors are common among the predictor sets between the three methods.
For example, all three methods select
f
1
={
x
3
,
x
5
,
x
7
}
(
PIRIN
predicted by
RET1, HADHB, WNT5A
) as well as
f
3
. We can conclude this
predictor is highly likely to be a final predictor in the GRN. Also, a majority
of the predictors selected by the three method share common input genes. For
example, the predictor selected by all methods for gene
x
2
(
S100P
) contain 2
common genes
={
x
1
,
x
4
,
x
6
}
(
RET1, WNT5A
), indicating these 2 genes are likely to be
contained in the final predictor of
f
2
. Similarly
f
7
has two common genes
x
1
and
x
2
for all methods.
{
x
3
,
x
7
}
Using the above results, biologists can target their research on gene regulation
and control, focusing on the gene relationships determined by the predictor set
results.
2.6
Chapter Summary
Determining the predictor set for a gene regulatory network is important in many
applications, particularly inference and control of the GRN which we discuss in sub-
sequent chapters. In this research, we formulate gene predictor set inference as an
instance of Boolean satisfiability. In our approach, we determine all possible order-
ings of attractor state data, generate the CNF encapsulating predictor and biological
constraints, and apply a highly-efficient and modified SAT solver to find candidate
predictor sets. The SAT results are analyzed using three selection methods to produce
the final predictor set. We have tested our algorithm on attractor state data from a
melanoma study, and determined the predictor sets for this GRN.
The results of this research, however, only reveals the predictor set (topology) of
the GRN. Our next step is to determine the gene regulating function (logic) of the
genes in the GRN to fully define the BN. In the next chapter, we describe a logic
synthesis method for determine gene functions for a GRN using a SAT-based logic
synthesis approach.
