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wherein the vertices are objects and directed edges (or arrows) are morphisms with
the characteristics that all directed paths in the network with the same endpoints
lead to the same result by the operation called “composition” usually denoted by the
symbol
h. I
find it necessary to introduce another kind of composition to be denoted by the
symbol ^ such that A^B
. Thus if the diagram in Fig. 12.33 commutes, it follows that g
f
¼
k
¼
C indicates that A and B are the complementary aspects
of C. The commutativity diagram in Fig. 12.33 embodies two major principles
discussed in this topic, namely, complementarity and supplementarity, first
introduced into physics by N. Bohr (1958) and discussed in detail in Sect. 2.3.1 .
These principles are represented as two different compositions of morphisms as
shown in Eqs. 12.50 and 12.51.
Hence we can characterize the commutativity diagram in Fig. 12.33 by the
following statement:
The C 2 category is complementarity/supplementarity dual . (12.52)
Based on Statement 12.52, we may refer to the C 2 category as the complemen-
tarity/supplimentarity dual category . The physical interpretations of the five
morphisms appearing in the C 2 commutativity diagram are indicated in the legend
to Fig. 12.33 . These interpretations may be subject to improvements as our knowl-
edge progresses.
12.17 Signal Transduction
Living cells constantly communicate with their environment using molecules as
information carriers. The molecules carrying environmental information are called
the primary messengers, and most primary messengers cannot enter the cell interior
due to the impermeable cell membrane, except steroids that are lipid-soluble and
hence can penetrate the hydrophobic barrier provided by the cell membrane. Thus,
in order for the extracellular information to be transmitted to the interior of the cell,
the information carried by primary messengers must be transferred to, or trans-
duced into, secondary messengers catalyzed by receptors embedded in the cell
membrane (see Table 12.14 ). This is phenomenon is known as signal transduction .
Barbieri (2003, p. 108) recognizes three distinct mechanisms of signal transduction
across the cell membrane as explained in the legend to Fig. 12.34 .Whatiscommonto
all these mechanisms of transmembrane signal transduction is the role played by
membrane receptors which act asmolecular machines that “translate” first messengers
to second messengers (see Table 12.14 ). As can be seen in the second and the fifth
columns of Table 12.14 , there is no structural relation (or similarity) between first and
second messengers (compare, for example, acetylcholine and cAMP, the first and
second messengers for G-protein coupled receptors). In other words, the relation
between first and second messengers are arbitrary from the point of view of chemistry
and physics but fixed and constant (or absolute ) from the point of view of semiotics or
communications theory in that the information carried by first messengers are reliably
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