Physics - Molecular Theory of the Living Cell - page 51

Renormalization

Interacton 1 + Interaction 2 Emergenton

'Chunking'

Fig. 2.8 A schematic representation of the definition of renormalization. Interactons are defined
as material entities or processes that interact with one another physically or chemically to produce
new entities or processes called emergentons . The process of interaction between interactons
leading to the production of an emergenton is here defined as “renormalization,” which is deemed
equivalent to the concept of “chunking” used in computer science (Hofstadter 1980)

In the vicinity of the critical point we need to stop viewing atoms separately. Rather, they
should be considered communities that act in unison. Atoms must be replaced by boxes of
atoms such that within each box all atoms behave as one.
For the purpose of biological applications, we will define “renormalization” as
the process of grouping or “chunking” (Hofstadter 1980, pp. 285-309) two or more
entities or processes (to be called interactons ) into one unit of action (to be called
emergentons ), leading to the emergence of new properties not possessed by indi-
vidual interactons . We may represent this idea schematically as shown in Fig. 2.8 .
One of the simplest examples of renormalization as defined in Fig. 2.8 is
provided by the chemical reaction occurring in a test tube between two reactants,
A and B, to form product C:

A+B ! C (2.57)

Using the language of “renormalization,” Reaction 2.57 can be described as
“A and B combining to form a new unit called C which exhibits some emergent
properties.”
The speed of Reaction 2.57 is determined by the concentrations of A and B, the
properties of the agents mediating the reactions (e.g., enzymes), and the physical
conditions of the reactor (e.g., pressure, temperature, surface characteristics of
reactor walls).
Most chemical reactions essential for maintaining the living state of the cell do
not occur without being catalyzed by enzymes. That is, they have too high activa-
tion energy barriers to be overcome through thermal collisions alone (Ji 1974b,
1991, 2004a). This can be represented schematically as:

E

A+B ! C (2.58)

where E stands for the enzyme catalyzing the reaction. Since A and B combining to
form C can be described as a renormalization (or chunking ) process and since this
process does not occur without E, we can refer toE as the renormalizer (or a chunkase ).
That is, all enzymes are renormalizers or chunkases consistent with the definition of
renormalization or chunking given in Fig. 2.8 . Also, since renormalization leads to the
emergence of novel properties, we can state that:
Enzymes provide the physical mechanisms for the emergence of new properties in
the cell. (2.59)