Biology Reference
In-Depth Information
Table 20.2 The question-and-answer matrix for the Nrf2 signaling pathway, each cell being filled
with the fit (i.e., fuzzy bit) or the probability values (ranging from 0 to 1) derived from the
experimental data on the Nrf2 signaling pathway depicted in Fig.
20.1
. Each question requires an
answer consisting of 40 fits ranging from 0 (
Yes), inclusive. The elements of the
matrix not explicitly shown and symbolized as dots can be assumed to be zero
No) to 1 (
¼
¼
Possible binary questions
Apparatus-elicited answers
123456.
.
. 90
Kosko entropy, S
K
1
0.3 0 0.4 0
0.1 0.2 .
.
. 0
0
0.872
2
0.9 0 0
0
0
0.1 .
.
. 0
0
0.00262
3
0.4 0 0.1 0.2 0
0.2 .
.
. 0
0.1 0.816
.
.
.
2
40
10
12
1.10
0
0 0
0
0.9 0
0.1 0
0.00262
¼
Table 20.3 The five-step procedure for calculating the Kosko entropy as a measure of the
uncertainty
associated with a toxicological knowledge, statement, or mechanism
Step Procedure
1
Summarize the preexisting knowledge of interest in the form of a pathway such as the Nrf2
signaling pathway (Fig.
20.1
)
Construct the interaction matrix (e.g., Table
20.1
) based on that pathway
2
3
Construct the question-and-answer matrix (e.g., Table
20.2
)
4
Fill in the appropriate boxes in the question-and-answer matrix based on the experimental
observations (also called the apparatus-elicited answers) available
5
Calculate the Kosko entropies for all apparatus-elicited answers (also called mechanisms)
based on the numerical coordinates given in the question-and-answer matrix, using the
Pythagorean equation, Eq.
5.23
This five-step procedure for calculating the
Kosko entropy
associated with any
toxicological statement represents or defines the content of the
Toxicological
Uncertainty Principle
. As such, the same procedure can be applied to any toxico-
logical statement, including those concerning the mechanisms underlying the liver
toxicity of acetaminophen (also called paracetamol or Tylenol
®
), for example.
Over the past four decades, we have accumulated a massive amount of informa-
tion about how
Tylenol
®
in excessive doses can injure the liver (Ryder and
Beckingham 2001; Larson et al. 2005) and how chronic and acute alcohol ingestions
may aggravate or protect against, respectively, the drug toxicity (McClain et al.
1980; Prescott 2000). Acetaminophen is the most widely used over-the-counter
analgesic and found in nearly 200 medications such as
Excedrin
,
Midol
,
NyQuil
,
and
Sudafed
. Despite the long history of research, both basic and clinical, on the
mechanisms responsible for acetaminophen hepatotoxicity, our knowledge about
these mechanisms is still uncertain and may remain so even if much more detailed
investigations are to be carried out in the future in this field. Parallel to further
research along the traditional line, it may be helpful for the further progress in
acetaminophen toxicology to introduce the Toxicological Uncertainty Principle as
embodied in the Kosko entropy (see Table
20.2
). That is, it may be necessary to
