Principles and Mechanisms of Biological Evolution - Molecular Theory of the Living Cell - page 501

the total number of accessible conformations, T is the absolute temperature, and
DE is the sum of the energy differences between the ith and ground state
conformations of the protein with i running from 1 to M .
The Zeldovich-Shakhnovich model based on these assumptions plus the second-
ary constraints (explained below) has been simulated on a computer, resulting in a
set of novel findings, including (1) the emergence of “dominating protein sequences
(DPSs)” reminiscent of Andersons's finding (Sect. 13.1 ), (2) the exponential popu-
lation growth following the appearance of DPSs, and (3) the power-law distributions
of protein family sizes (which are directly related to gene family sizes through the
genetic code) (see Fig. 4a, b in Zeldovich and Shakhnovich 2008), and (4) the
asymmetric distribution of protein stability data (see the solid curve in Fig. 12.31 ) .
The secondary constraints implemented in the computer simulation of the
Zeldovich-Shakhnovich model include: (1) random mutations of a nucleotide in
a randomly selected gene with constant rate m per unit time per DNA length (with
no mutation allowed for stop codons to ensure constant length of protein
sequences), (2) duplication of randomly selected genes within an organism's
genome with constant rate u, and (3) birth of an organism via duplication of an
already existing organism with constant rate b.
Although the Zeldovich-Shakhnovich model provides what appears to be the
first successful microscopic mechanism (connecting nucleotide sequences to organ-
ismic properties) to account for Observation ( 1 ) above (Zeldovich et al. 2007a), it
does not explain Observations ( 2 )-( 4 ). To account for these observations, it is here
suggested that at least two laws - the Law of Requisite Variety (LRV) (see Sect.
5.3.2 ) and the Principle of Rule-Governed Creativity (RGC) (see Sects. 6.1.4 and
12.10 ), and two new concepts, that is, active versus passive complexities (Sect.
5.2.3 ) and equilibrium structures (equilibrons) versus dissipative structures
(dissipatons) (Sect. 3.1.5 ) , needs to be utilized as detailed below:
Observation (1) The key point of the model proposed by Huynen and van
Nimwegen (1998) to account for the power law distribution of gene family sizes
is that “all the genes within a family are affected in the same (or at least a similar)
way by the environment.” That is, “gene families have to behave in a coherent
fashion within the genome; that is, the probabilities of duplication of genes within a
gene family are not independent of each other.” In the following discussion, I will
refer to this feature of the Huynen-van Nimwegen model as the Huynen-van
Nimwegen constraint (HVC). In the Zeldovich-Shakhnovich model (Zeldovich
et al. 2007a, b; Zeldovich and Shakhnovich 2008), HVC is implemented by what
is called the “weakest link,” which Zeldovich et al. postulated to be the lowest free
energy conformation of the least stable of the proteins in a genome, the probability
of which was calculated using Eq. 14.35. Another possibility suggested by the
molecular theory of the living cell proposed in this topic is that HVC is satisfied
by a gene family, X, acting as a dissipaton (i.e., IDSs; see Sect. 12.5 ) carrying out
a critical cell function Y under environmental condition Z. Function Y of an
organism is said to be critical under environment Z, if inhibiting or removing Y
leads to the demise of the organism under Z. “Critical” in this sense is synonymous