Physics - Molecular Theory of the Living Cell - page 56

Table 2.14 Three major classes of renormalizable networks in biology
Renormalizable
network Node Network Network of networks Emergent properties
1. Cells Atoms Molecules System of molecules Self-reproduction (cell cycle)
2. Organisms a Molecules Cells System of cells Development (ontogeny)
3. Populations Cells Organisms System of organisms Evolution (phylogeny)
a Organisms can be either multicellular or unicellular. In other words, the term “organism” can
signify either an independent organism or a part of an organism, depending on the context of the
discourse
2.4.3 Living Systems as Renormalizable Networks
of SOWAWN Machines
It has been known for over one and a half centuries that all living systems are
composed of networks (i.e., systems) of cells. Since the development of biochem-
istry in the early decades of the twentieth century, cells have in turn been known to
be composed of networks of biopolymers (e.g., DNA, RNA, proteins,
carbohydrates) and small molecular and submolecular entities (e.g., ATP, glucose,
metal ions) that are transformed and organized in space and time. Based on these
observations alone, it appears logical to conclude that living systems are examples
of networks of networks - i.e., networks in which individual nodes can in turn act as
networks at a lower level of organization (or a higher level of resolution). The
phenomenon of a network acting as a unit to constitute a node in a higher-order (or
higher-level) network represents “renormalization” as defined in Fig. 2.8 . In addi-
tion, networks are renormalizable in that a network can act as a node of a larger
network or accept as its node's smaller networks. Therefore, a renormalizable
network can act as any one of the following - (a) a network, (b), a node, and (c)
a network of networks - depending on the level of resolution at which it is viewed.
The concept of a renormalizable network can be applied to at least three distinct
levels in biology, as shown in Table 2.14 . It is here postulated that, at each level of
the networks, a new property emerges that is unique to that level (see the last
column in Table 2.14 ). The emergent property of a renormalizable network is in
turn thought to result from a unique set of mechanisms of interactions operating
among its component nodes (or interactons ) and it is such mechanisms that
implement renormalization.
As evident in Table 2.14 , the renormalizable network theory (RNT) described
here is a general molecular theory that can be applied to all living systems, ranging
from unicellular to multicellular organisms and their populations. The RNT
described in this topic combines the molecular theories of enzymic catalysis
formulated in 1974 (Ji 1974a, 1979), the concept of renormalization imported
from condensed matter physics (Cao and Schweber 1993; Stauffer and Aharony