Whole Cells - Molecular Theory of the Living Cell - page 426

3. The shapes of the frequency distributions in PDvsF plots are not random
nor normal but resemble surprisingly the blackbody spectrum (see the upper
right-hand panel of Fig. 11.24 ) . As evident in Fig. 12.25 , this visual impression
is validated by the quantitative agreement found between the experimental data
points of PDvsF plots and the theoretical predictions based on the following
equation (referred to as the blackbody radiation-like equation , or BRE) that has
the same form as the Planck's radiation law (see Eq. 11.26 in Sect. 11.3.3 ):

Þ 5

e b =ð Ax þ B Þ

y ¼ a ð Ax þ B =ð 1 Þ (12.26)

where y is frequency, x is the phenotypic distance, and a, b, A, and B are
constants (Ji and So 2009d).
4. The Plank radiation law, Eq. 11.26 , which successfully explained the blackbody
radiation data in 1900 (Nave 2009; Kragh 2000) is of the form:

x 5 e b = x

y ¼ (a = Þ=ð 1 Þ (12.27)

where a and b have the numerical values given in Table 12.10. The concept of
the quantum of action introduced by this equation gave birth to quantum
mechanics which revolutionized physics in the first three decades of the twenti-
eth century. In the last decade of the same century, two experimental techniques
known as the single-molecule enzymological method (Sect. 11.3 ) and DNA
microarrays (Sects. 12.1 and 12.2 ) were invented that have been revolutionizing
experimental biology ever since. Equation 12.27 generalized as Eq. 12.26
(by replacing x with Ax + B) has been found to fit not only the single-molecule
enzymological data of cholesterol oxidase (as shown in Sect. 11.3.3 ) but also
the whole-cell RNA metabolic transitions as shown in Fig. 12.25 . In addition,
Fig. 12.25 includes protein stability data (see Panel f), because they are found to
obey the Universal Principle of Thermal Excitations (UPTE), i.e., Eq. 12.26 ,as
indicated by the solid line. The x-coordinates of the experimental points (open
circles) were the negatives of the D G values read off from Fig. 12.26 , which was
reproduced from Zeldovich et al. (2007b). The solid curve is predicted by the
equation:

sin

A exp hE h 2

P D G ðÞ¼ þ D ð p ð E E min Þ = ð E max E min Þ Þ (12.28)

derived in Zeldovich et al. (2007b), where h and D are, respectively, the mean and
the mean square change of protein stability induced by point mutation. E is the
energy of the native state of a protein, and E max and E min are the maximum and
minimum energies that a protein store upon folding. It is assumed that E can be
replaced by G, which is tantamount to assuming that the volume and entropy
changes accompanying protein folding are relatively insignificant.
The fact that protein stability data fit Eq. 12.26 indicates that thermal
excitations or transitions are implicated in protein stability as well. One possible