Biology Reference
In-Depth Information
generated from exergonic processes (i.e., binding, de-binding, covalent bond
rearrangements, etc.) catalyzed by the enzyme itself such as the myosin head during
muscle contraction (see (d) (3) in Fig.
11.33
). We will refer to the former as
static
(or
intrinsic
)
conformons
(also called the Klonowski-Klonowska conformons in
[Ji 2000]) and the latter as
dynamic
(or
extrinsic
)
conformons
. These terms were
already employed in Rows (C) and (E) in Table
11.10
and are further discussed in
Sect.
11.4.2
. It is postulated here that the nonzero ground energy levels of the
conformers postulated in Fig.
11.28
result from the presence of one or more
static
conformons
in each conformer.
A functional
conformer
is postulated to carry as many
conformons
as the number
of elementary processes it catalyzes (see Figs.
11.23
,
11.28
), which may be at least
two, namely, binding and de-binding processes. In order for a conformer to carry
out its catalytic act (be it binding, de-binding, or electronic rearrangement, singly or
in combinations), it must satisfy the following two requirements: (a) a conformer
must be thermally activated/excited to reach the transitions state C
{
(as indicated in
Fig.
11.28
) and (b) a conformer must recruit the right set of x out of its n amino acid
residues obeying the conformon equation, Eq.
11.19
.
Satisfying these requirements is tantamount to generating a set of
dynamic
conformons by a conformer within its lifetime.
It is natural to associate with COx the so-called slow protein coordinate, X(t),
that plays a central role in the theory of waiting time distribution of COx proposed
by Prakash and Marcus (2007). COx can be viewed as a system of atoms linked by
covalent bonds, each of which acts as an oscillator with vibrational periods in the
10
14
s range (or vibrational frequencies in the 10
14
/s range), as already indicated.
According to Fourier's theorem (Herbert 1987, pp. 79-92;
http://en.wikipedia.org/
wiki/Fourier_series
)
, it is possible to generate low-frequency collective vibrational
modes by appropriately coupling these high-frequency primary oscillators. Nature
may
slow down
molecular oscillations by increasing the effective mass of
oscillators through compactifying or “chunking” lower-level molecular systems
to higher level ones in steps of about 5 (Ji 1991, pp. 52-56), as exemplified by the
chunking of a DNA double helix into a chromosome (Fig.
2.9
) reducing the linear
size of DNA by a factor of about 10
10
and therefore its effective mass by a factor of
10
30
. This in turn should decrease oscillatory frequency by a factor of (10
30
)
1/2
or
10
15
, since frequency, f, is inversely proportional to the square root of the mass, m,
according to the equation for simple harmonic oscillators,
1
=
2
f
¼
2
ð Þ
1
=
ð Þ
k
=
m
(11.41)
where k is the spring constant. Eq.
11.41
also suggests that the oscillatory frequency
can be reduced by reducing the spring constant, k. Thus, when large domains of a
protein oscillate with respect to one another, the frequency of oscillation can be
reduced not only by increasing effective mass but also by weakening the spring
constant k by, say, changing local electric fields by protonation-deprotonation,
phosphorylation-dephosphorylation,
and
acetylation-deacetylation
reactions
involving critical amino acid residues.
