Biology Reference
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view of the rapid oscillatory motions of peptide bonds, and (b) how X(t) mediates
the reduction of FAD to FADH
2
, which probably takes place on the femtosecond
timescale, thus implicating the coupling between two events whose time constants
differ by a factor of about 10
10
. In contrast, the theory based on (a) the analogy
between blackbody radiation and enzymic catalysis and (b) the generalized Franck-
these questions (see D and E in Table
11.10
and (5) below).
2. In 2008, I noticed the similarity between the waiting time distribution of COx
enzymic activity reported by Lu et al. (1998) and the blackbody spectrum (see the
upper two panels in Fig.
11.24
). (
http://www.nationmaster.com/encyclopedia/
Planck%27 s-law-of-blackbody-radiation
)
. The similarity between the histogram
given on the upper left-hand corner and the blackbody spectrum measured at
4,500 K shown in the upper right-hand corner of Fig.
11.24
is particularly
striking. This observation motivated me to use Planck's radiation formula
(Nave 2009), Eq.
11.26
, generalized in the form of Eq.
11.27
(with the X(w)
term set to zero), to model the waiting time distribution of Lu et al. (1998),
leading to the result shown in the lower portion of Fig.
11.24
(see the smooth
curve marked with squares).
The Planck radiation formula which successfully accounted for the blackbody
spectrum in 1900 is given in Eq.
11.26
(Nave 2009):
=
5
e
hc
=l
k
B
T
u
l;
ð Þ¼
T
8
p
hc
=l
1
Þ
(11.26)
where u(
l
, T) is the
spectral energy density
, i.e., the intensity of radiation emitted or
absorbed at wavelength
l
by the blackbody wall when heated to T K; h is the Planck
constant; c is the speed of light; and k
B
is the Boltzmann constant.
The equation derived in Ji (2008b) on the basis of the analogy between black-
body radiation and enzymic catalysis is given in Eq.
11.27
:
=
aw
5
e
b
=
w
pw
ðÞ¼
1
þ
Xw
ðÞ
(11.27)
where p(w) is the frequency (or probability) of the occurrence of waiting time w, a
and b are constants with numerical values of 3.5
10
5
and 2
10
2
, respectively,
and X(w) is a
nondeterministic
function of w.
It should be noted that Eq.
11.26
, which is based on the Bose-Einstein statistics,
reduces to Eq.
11.28
, known as the Wien's law (Kragh 2000), which is based on the
Boltzmann statistics, if the exponential term is much greater than unity:
e
hc
=l
k
B
T
5
u
l;
ð Þ¼
T
8
p
hc
=l
(11.28)
0and
the e
b/w
term is much greater than unity, but calculations showed that the exponential
term was not much greater than 1 and hence Eq.
11.27
could not be simplified.
As explained by Kragh (2000), the Wien's law fitted the short-wavelength portion
Equation
11.27
can also be reduced to a form similar to Eq.
11.28
,ifX(w)
¼
