Biology Reference
In-Depth Information
4. As pointed out by Huynen and van Nimwegen (1998), the exponent
g
of the
power law underlying the GFS distribution increases with genome size N. From
their Fig. 2, the following equation was obtained:
g ¼
:
:
0
94 log N
4
38
(14.33)
For the convenience of future discussions, it may be convenient to refer to
Eq. 14.31 as the
Huynen-van Nimwegen (HN) equation
and
g
as the Huynen-van
Nimwegen (HN) exponent, Fig.
14.6
from which this equation derives as the
Huynen-van Nimwegen
(HN)
plot,
and
the
individual
curves
in
the
Huynen-Nimwegen plot as
Huynen-van Nimwegen (HN) curves.
The molecular model of evolution proposed by Zeldovich et al. (2007a, 2008), to
be referred to as the
Zeldovich-Shakhnovich model
for brevity, is based on the
following six assumptions:
(a)
An organism can be treated as a set of genes
.
(b)
The genetic code transforms genes into amino acid sequences of proteins
.
(c)
The lattice protein folding model transforms the amino acid sequence of a
protein into its native conformation, that is, the most stable conformation, or the
conformation with the lowest Gibbs free energy of folding
.
(d)
The probability P
alive
that an organism is alive is proportional to the probabil-
ity P
nat
(i)
that protein i is in its native conformation
:
min
i
P
nat
ðiÞ
P
alive
(14.34)
where the symbol min
i
indicates the least stable of all the proteins, each labeled
with the index, i, with i
¼
1 through N, the number of proteins in the genome
.
(e)
Therefore,
the dead rate, d, of an organism is negatively related to the
probability
P
nat
ðiÞ
Þ
d
¼
d
0
ð
1
(14.35)
where d
0
is the original dead rate of an organism before undergoing genetic
mutations
.
(f)
The probability P
nat
of the native state of the least stable protein in the genome
is postulated to be inferable from the amino acid sequence of the protein using
the 3
3 lattice model with the Miyazawa-Jernigan potential (Miyazawa and
Jernigan
1996
):
3
!
X
M
e
ðE
0
=TÞ
=
e
ðE i=TÞ
e
ðDE=TÞ
Þ
P
nat
¼
1
=ð
1
þ
(14.36)
i
¼
0
where E_0 (or E
0
) is the energy of the ground-state conformation of a protein,
E_i(or E
i
) is the energy of the ith conformation of the protein, M
¼
103,346 is
