Biology Reference
In-Depth Information
Table 20.1 The
interaction matrix
of the Nrf2 signaling pathway constructed from Fig.
20.1
(or
Fig. 4 of Surh 2003). The interaction between the ith and jth nodes is positive (+1, i.e., enhanced),
negative (
576
possible interactions, only 25 directed interactions have been found experimentally, thus the Nrf2
signaling pathway carries log
2
(576/25)
1, i.e., inhibited), or nonexistent (0, i.e., has no effect). Out of the 24
24
¼
4.5 bits of Shannon/Hartely information (see Sect.
4.3
for the definition of the Shannon and Hartley informations). Please note that some of the
assignments of +1,
¼
1 or 0 (especially involving nodes 7, 8, 9, and 10) are ambiguous and
admit other possibilities
12345678 9 101112131415161718192021222324
1 0000000+1 0 0+10 0 0 00 0 0 000000
2 0000000+1 0 0 00 0 0 00 0 0 000000
3 0000000+1 0 0 00 0 0 00 0 0 000000
4 0000000+1 0 0 00 0 0 00 0 0 000000
5 0000000 0
1
1000 000 00000000
6 0000000+1 0 0 00 0 0 00 0 0 000000
7 0000000 0 0 0 00 0 0 00 0 0 000000
8 0000000 0 0 0 00 0 0+10 0 0 000000
9 0000000+1 0 0 00 0 0 00 0 0 000000
100000000 0+1 0 00 0 0 00 0 0 000000
110000000 0 0 0 00 0 +1 00 0 0 000000
120000000 0 0 0 00 0 0+10 0 0 000000
130000000 0
0000 000 00000000
140000000 0 0 0 00 0 0 00 0+1 000000
150000000 0 0 0 00 0 0 00 0 0+100000
160000000 0 0 0 00 0 0+10 0 0+100000
170000000 0 0 0 00 0 +1 00 0+1+100000
180000000 0 0 0 00 0 +1 00 +1 0 000000
190000000 0 0 0 00 0 0+10 +1 0 000000
200000000 0 0 0 00 0 0 00 0 0 000000
210000000 0 0 0 00 0 0 00 0 0 000000
220000000 0 0 0 00 0 0 00 0 0 000000
230000000 0 0 0 00 0 0 00 0 0 000000
240000000 0 0 0 00 0 0 00 0 0 000000
of the Nrf2 pathways 1, 2, 3,4, 5, 6,
...
, 39, and 40 are, respectively, 0.3, 0, 0.4, 0,
0.1 0.2,
, 0, 0, and 0. The corresponding probabilities under experimental
condition 2 are 1, 0, 0, 0, 0, 0,
...
, 0, and 0, meaning that only pathway 1 is
...
activated under this condition.
Once the
question-and-answer matrix
is determined, all the apparatus-elicited
answers can be mapped onto the 2
40
-dimensional hypercube discussed in Sect.
entropy
can be estimated using the coordinate values of each answer and Eq.
5.23
.
These entropies were calculated for the rows labeled 1, 2, and 3 in Table
20.2
.
As can be seen, Apparatus-elicited answer 1 is least certain, while apparatus-
elicited answers 2 and 2
40
are both much more certain than Answers 1 and 3.
The above method of calculating the Kosko entropy associated with any toxico-
logical statement or knowledge can be summarized as shown in Table
20.3
.