Biology - Molecular Theory of the Living Cell - page 108

information/energy complementarity. I assume that any organization has a purpose
or equivalently that systems of material components organize themselves (i.e., self-
organize) to accomplish a purpose or a goal, the final cause of Aristotle.

4.14 The Quantization as a Prelude to Organization

Quantization (or discretization) may be essential for any organization, since organi-
zation entails selection and selection in turn requires the existence of discrete entities
to choose from. In Sects. 11.3.3 and 12.12 , experimental evidence is presented that
indicates that biological processes such as single-molecule enzymic activities (Lu
et al. 1998; Ji 2008b), whole-cell RNA metabolism (Ji and So 2009d), and protein
folding (Ji 2012) are quantized because they all obey mathematical equations similar
in form to the blackbody radiation equation (see Table 4.6 ) that was discovered by
M. Planck in physics in 1900 which led to the emergence of quantum mechanics two
and a half decades later (Herbert 1987; Kragh 2000; Nave 2009).
To make the blackbody radiation data fit a mathematical equation, Planck had to
assume that the product of energy and time called “action” is quantized in the unit later
called the Planck constant, h , which has the numerical value of 6.625 10 27 erg s.

This quantity seems too small to have any measurable effects on biological processes
which occur in the background of thermal fluctuations involving energies in the order
of kT, where k is the Boltzmann constant, 1.381

10 16 erg/degree and T is the
absolute temperature. The numerical value of kT is 4.127 10 14 ergs at room

298 K, which is 13 orders of 10 greater than h . Thus, it appears
reasonable to assume that biological processes are quantized in the unit of k rather than
in the unit of h as in physics, which leads me to suggest that
The Boltzmann constant k is to biology what the Planck constant h is to physics.

temperature, T ¼

(4.36)

Thus, by combining the evidence for the quantization of biological processes
provided by Table 4.6 and Statement 4.36, it appears logical to conclude that

Biological processes at the molecular and cellular levels are quantized in the unit of the
Boltzmann constant k. (4.37)
Statement 4.37 may be referred to as the “Boltzmann Quantization of Biological
Processes” (BQBP). If Statement 4.37 turns out to be true, we will have two types of
quantizations in nature - (1) the Planck quantization in the unit of h and (2) the
Boltzmann quantization in the unit of k. These two types of quantizations are
compared in Table 4.7 , the fifth row of which suggests the final cause of the two
types of quantizations, and the last row suggests that the Planck quantization is to
Boltzmann quantization what atoms are to quantum dots (more on this in Sect. 4.15 ).
The relation between the Planck quantization and the Boltzmann quantization
postulated in Row 5 may be summarized as in Statement 4.38 and schematically
represented in Fig. 4.9 :
Quantization precedes organization.

(4.38)