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where k's are rate constants. A similar mechanism, Scheme (
11.17
), was proposed
for the on-time distribution.
O
2
!
E-FADH
d
þ
E-FAD
O
2
!
E-FAD
f
þ
H
2
O
2
(11.17)
e
Schemes (
11.16
) and (
11.17
) do not obey the
Principle of Microscopic Revers-
from
e
to
f
are not symmetric as demanded by PMR. An alternative mechanism that
obeys PMR is proposed in Fig.
11.19
. Since this mechanism is based on the
generalized Franck-Condon principle discussed in Sect.
2.2.3
, we may refer to the
mechanisms proposed in Fig.
11.19
as the
Franck-Condon mechanism
of the action
of cholesterol oxidase. The Franck-Condon mechanism entails expanding the
number of the states involved in one cycle of the enzymatic turnover from the
original 6 to a total of 16, as explained in the legend to Fig.
11.19a
, b. The unique
features of the Franck-Condon mechanism are:
1. The enzyme can exist in two states - the ground state (see
a, h, i
and
p
) and the
thermally
activated/excited
state (see
b, g, j
and
o
).
2. The enzyme binds its substrate or product only when in a thermally activated/
excited state (see
c, f, k,
and
n
).
It should be noted that “energized state” is
synonymous with “thermally activated/excited state stabilized by ligand bind-
ing.” Without such ligand-induced stabilization, thermally activated/excited
states are thought to relax rapidly back to ground states.
3. In the Franck-Condon state, the distinction between
substrate
and
product
disappears due to the highly unusual microenvironment of the enzyme active
site prevailing in this state. This is tantamount to asserting that
d
m
at the Franck-Condon state, within the Heisenberg uncertainty principle
(Reynolds and Lumry 1966; Ji 1974a).
¼
e,
and
l
¼
The Franck-Condon mechanism proposed in Fig.
11.19
provides a novel set of
explanations for the single-molecule fluorescence data reported by Lu et al. (1998).
Their data are reproduced in Fig.
11.20
with a particular attention given to the
variations in the amplitudes of the fluorescence fluctuations recorded in Fig. 1b of
their paper. The features of their data that are of special interest are summarized in
Table
11.6
along with the corresponding explanations offered by the Franck-
Condon mechanism shown in Fig.
11.19
.
One of the most significant outcomes of analyzing the single-molecule fluores-
cence data measured by Lu et al. (1998) as shown in Table
11.6
is that there may
exist two high-energy states - one relatively long-lasting after stabilization by
ligand binding (denoted by the superscript
*
) and capable of performing external
work and the other short-lived (denoted by the superscript
{
). Thus we will refer to
the former as the
energized state
distinct from the Franck-Condon state. Since
energized states are characterized by their
stored energy
in the sense of McClare
(1971, 1974) (see also Sect.
2.1.4
), the enzymes in energized states are capable of
