Biology Reference
In-Depth Information
Since one of the unique features of all networks is the emergence of a new
property beyond the properties of individual nodes, it may be claimed that:
The
raison d'eˆtre
of a network is its
emergent
property.
(2.60)
That is, there is an inseparable connection between
networks
and
emergences
in
the sense that no emergence is possible without a network. Therefore, we may refer
to Statement 2.60 as the Emergent Definition of Networks (EDN).
Emergence has become a topic of great theoretical and philosophical interests in
recent years (Laughlin 2005; Clayton and Davies 2006; Reid 2007), and the concept
of network is even more widely discussed in natural, computer, and human sciences
(Barabasi 2002; Sporns 2011). However, to the best of my knowledge, not much
attention has been given so far to formulating possible
mechanisms
connecting
networks to their emergent properties. One of the major aims of this topic is to
suggest that “renormalization” as defined in Fig.
2.8
can serve as a universal
mechanism of emergence in all networks in physics, chemistry, biology, and
beyond. For a related discussion, readers are referred to Cao and Schweber (1993).
2.4.2
“Chunk-and-Control” (C & C) Principle
As indicated in Fig.
2.8
, the concepts of renormalization and chunking can be
viewed as essentially equivalent in content, the only difference being that the
former emerged in physics and the latter in computer science independently. The
main point of this section is to suggest that the principle of renormalization or
chunking has also been in operation in the living cell since eukaryotes emerged on
this planet over 1.5 billion years ago.
Computer scientists have discovered the utility of the
divide and conquer
(D &
C) strategy in software programming in which they break down a large and
complex problem into two or more smaller sub-problems repeatedly until the sub-
problems become easy enough to be solved directly. Cells apparently utilize a
similar strategy on the molecular level. For example, when cells divide they must
control the behaviors of all the DNA molecules (46 of them in the human genome,
each 10
7
base-pair long) in the nucleus so that they are reproduced and divided into
two identical sets. To accomplish this gigantuan task, cells appear to chunk the
DNA components into increasingly larger units as shown in Fig.
2.9
, first into
nucleosmes which are “strung” together into 11 nm-diameter “beads-on-a-string”
form. This is wound into a 30 nm chromatin fiber (also known as solenoid) with six
nucleosomes per turn, which is further condensed into 300 nm looped domain, 50
turns per loop. The next stage of condensation or chunking is “miniband,” each
containing 18 loops. Finally these minibands are stacked together to form the
metaphase
chromosomes with
the
cross-sectional
diameter
of
about
10
6
m. Thus, the cross-section diameter of a DNA double helix (or DNA
duplex) (2
1.4
10
9
m) has increased by a factor of about 10
3
, resulting in a 10
9
-fold
compaction of DNA volume. Since this compaction has taken place in five steps,
