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2. The two-dimensional network of mRNA molecules (denoted by dots) centered
on the
p53-coding mRNA
acting as the hub (see 2 on Plane B, the RNA Space)
3. The two-dimensional network of proteins (denoted by dots) centered on the
p53
protein acting as the hub (see 3 on Plane C, the Protein Space)
4. The two-dimensional network of chemical reactions (denoted as dots in Plane D
or the Chemical Space) catalyzed by one or more proteins (e.g., see the inverted
circular cone labeled 17 that connects the Protein Space and the Chemical
Reaction Space)
5. The network of
functions
(denoted as dots) associated with one or more proteins
including the p53-mediated functions (see 5 on Plane E or the Function Space)
6. Stacking of the above five two-dimensional networks into a three-dimensional
network at each time point, t, to form “hypernetworks” or “supernetworks”
ThegraycircularconesinFig.
9.2
, both straight and curved, represent the bio-
chemical analog of “renormalization” in condensed matter physics (Sect.
2.4
)(Domb
1996) and hence may be referred to as “renormalization cones.” A renormalization
cone can be viewed as a geometric representation of a group of biological entities
(be they genes, RNA, proteins, or chemical reactions) located on the base of the cone
acting as a unit to catalyze a process (represented by the apex of the cone).
Most of the dots in each plane in Fig.
9.2
are probably linked to form networks, one
of which is explicitly shown as a small network in the Gene Space (see 10). The best
known example of such in-plane networks is the protein-protein interaction network
known as the protein interactome (Ito et al. 2001; Stumpf et al. 2008; Suter et al. 2008).
There are two kinds of links (depicted as straight lines) in Fig.
9.2
- the
horizontal
links belonging to a plane (e.g., network 10) and
vertical
links spanning
two or more spaces (see lines labeled 6, 7, 8, and 9). All the points in one space
should be connected to their counter parts in adjacent spaces via vertical lines,
if one gene codes for one RNA (see line 6), which in turn codes for one protein
(line 7), which catalyzes one reaction (line 8). It is well known that a group of about
50 proteins acts as a unit to catalyze the transcription process in eukaryotes (which
is indicated by Cone labeled 14), and another group of a similar size catalyzes
translation (see Cone 13). As indicated above, such a process of grouping of a set of
proteins into a functional unit (called a SOWAWN machine or a hyperstructure) is
reminiscent of “renormalization” in statistical mechanics (Sect.
2.4.4
) (Fisher 1998;
Barabasi 2002; Domb 1996). Abundant experimental data indicate that some
RNA molecules participate in regulating not only transcription and translation,
as represented by Cones labeled 11 and 12, but also transcript degradation
(not shown) (Mattick 2003, 2004; Hannon and Rossi 2004) are represented by
Cones labeled 11 and 12. As indicated by Cones 15 and 16, chemical reactions can
influence the rates of transcription and translation, for example,
directly
by covalently
modifying DNA and RNA or
indirectly
by changing the pH, metal ion concentrations,
or membrane potentials of the microenvironment inside the cell. Thus, Cones 15
and 16 can provide molecular mechanisms for epigenetic phenomena which are
emerging as important topics in both developmental and evolutionary biology
(West-Eberhard 1998; 2003; Riddihough and Zahn 2010; Bonasio et al. 2010).
