Principles and Mechanisms of Biological Evolution - Molecular Theory of the Living Cell - page 498

of thermodynamics, would it be too far-fetched to infer that there may be a new law
of thermodynamics that is associated with D I that controls, selects, and organizes
spontaneous processes in nature? Such a conjectured law is referred to as the Fourth
Law of thermodynamics, or the Principle of Organization in Table 14.9 .This
Fourth Law seems consistent with the classification scheme of the thermodynamic
laws given in Fig. 2.2 and with the two laws described in Table 4.1 , namely, the
Laws of Requisite Variety and Requisite Information.

14.7 The Zeldovich-Shakhnovich and the MTLC
(Molecular Theory of the Living Cell or the Bhopalator)
Models of Evolution: From Sequences to Species

Unlike the past models of biological evolution that are based on phenomenological
population genetics, the newly emerging microscopic/molecular models of evolu-
tion increasingly utilize the genome-wide molecular information provided by the
thermodynamic stabilities of proteins (e.g., Fig. 12.26 ) (Koomin et al. 2002;
Zeldovich et al. 2007a, b; Zeldovich and Shakhnovich 2008) and comparative
genomic data such as shown in Fig. 14.6 . For example, the microscopic physical
model of evolution proposed by Zeldovich et al. (2007a, b, 2008) quantitatively
accounts for not only the protein stability distribution in Fig. 12.26 (see the solid
curve) but also the power-law behavior of the frequency distribution of gene family
sizes (Fig. 14.6 ).
The gene family size (GFS) distribution curves in Fig. 14.6 can be characterized
in terms of four numbers: N ¼ the number of the genes in the genome of an

organism; n i ¼ the number of genes in the ith gene family, a gene family being

defined as a set of genes sharing some common features such as nucleotide
sequences, protein folds, and/or functions; f i ¼

the frequency of the occurrence

of the ith gene family size in a genome; m ¼ the number of gene families in a

genome. These numbers are related as follows:

X

m

N ¼ f i n i ¼ AUC (14.31)

i ¼ 1

where AUC is the area under the curve of GFS distribution.
Figure 14.6 contains the following valuable features that may shed important
light on the fundamental mechanisms underlying cell structures and functions
driving both evolution and development:

1. The distributions of gene family sizes (GFSs) obey a power law

P(S) ¼ cS g (14.32)