Biology Reference
In-Depth Information
We may refer to (2a) above as the “passive symmetry-breaking” mechanism, and
(2b) as the “active symmetry breaking” mechanism. The cosmological (excluding
biological) symmetry breakings may belong to the category of
passive symmetry
breakings
, but living systems may utilize both
passive
and
active symmetry breakings
.
These terms are related to the active and passive complexities discussed in Sect.
5.2.3
.
An example of “active symmetry breakings” in morphogenesis is provided by
the cell migration leading to germband expansion (Zallen 2006, Zallen and
Wieschaus 2004) and an example of “passive symmetry breakings” is given by
rosette formation among non-migrating cells in the germband of
Drosophila
(Zallen 2006). It seems possible that passively broken symmetry can be reversed,
if some active mechanisms can intervene. This would mean that normal morpho-
genetic processes can implicate many active and passive symmetry-breaking pro-
cesses organized in space and time, driven by free energy dissipation under the
control of genetic information encoded in proteins, DNA, and RNA.
The cosmological symmetry breakings shown in Fig.
15.12
may have their
counterparts in
biological symmetry breakings
exemplified by the development of
a multicellular organism from a single fertilized egg cell. Biological symmetry
breakings can be represented diagrammatically as bifurcation trees such as the
inverted tree (Fig.
7.8
) or the TRAL model (Fig.
15.8
). If there are n cells in an adult
organism, it will take (log n/log 2) generations of cell divisions for a fertilized egg
cell to become an adult organism. Since there are about 10
13
cells in the adult
human body, it will take about 40 generations (10
13
~2
40
) of cell divisions for a
fertilized egg (see the node labeled 1 in Fig.
7.7
or the center node in Fig.
15.8
)to
mature into an adult human being with all its complexities. Figure
7.7
, when rotated
by 90
anticlockwise, resembles Fig.
15.12
in that the complexity (or order) of the
system increases from left to right. If this comparison is valid, the Universe at the
time of the Big Bang would be akin to a fertilized egg perhaps with superstrings
acting as a “cosmological DNA” (Ji 1991).
Figure
7.7
was used to represent the postulate that enzymes can be viewed as
branching (i.e., the nodes labeled 16-31) can be thought to represent Brownian
particles or thermally fluctuating physicochemical processes, and the nodes at the
next level (i.e., the nodes labeled 8-15) represent coincidence-detecting events.
The leaves in Fig.
7.7
can be thought of as molecular events (e.g., enzymic
reactions) which affect the next higher level (e.g., gene expression) which in turn
affect the next higher level (e.g., cell divisions) and so on until the root (e.g., an
embryo) is reached. Interpreted in this manner, Fig.
7.7
can be viewed as the
mechanism for coupling genotype and phenotype, or microscale events and macro-
scale events, without any thermal gradients and hence as a system of dissipative
symmetry breakings. In other words, these nodes are events (requiring x, y, z, and
t to be specified and hence 4-dimensional in nature) that occurs if and only if two or
more lower-level events occur more or less synchronously, that is, within a certain
time window or bin,
D
t, with intensities equal to or greater than the threshold,
Y
