Biology Reference
In-Depth Information
between the autocorrelation functions of waiting times and spectral means utilizing
the concepts of “electrostatic interaction energy” and “solvatochromism.”
The theory of the COx waiting time distribution proposed here based on the
analogy between blackbody radiation and enzymic catalysis
(Ji 2008a) can provide
qualitative molecular mechanistic explanations for all of the observations listed in
Table
11.10
.
Both the Xie and the Marcus groups agree that the waiting time fluctuations of
COx are the result of the conformational fluctuations of the COx molecule. The Xie
group made the assumption that different conformations of the COx molecule
somehow give rise to different waiting times, without proposing any realistic
molecular mechanisms responsible for coupling COx conformational states and
the waiting time variations of its coenzyme, FAD. Given this assumption and the
additional assumption that the Michaelis-Menten mechanisms shown in Schemes
(
11.16
) and (
11.17
) hold for single-molecule enzymes, Xie and his coworkers
derived the
probability distribution function
for waiting times:
Þ
e
k 1t
e
k 2t
p(t)
¼
k
1
k
2
=
k
2
k
1
ð
(11.25)
where p(t) is the probability of observing turnover time t and k
1
(or k_1) and k
2
(or
k_2) are the time-dependent rate constants appearing in Scheme (
11.16
). The fitting
of Eq.
11.25
to measured waiting time distribution is shown in the upper left panel
of Fig.
11.24
(Lu et al. 1998).
Prakash and Marcus (2007) assumed that the
conformations
(i.e., the three-
dimensional structure of a protein that can be altered without breaking or forming
covalent bonds, Sect.
11.3.2
) of a COx molecule, denoted as X(t), can fluctuate on
the milliseconds to seconds timescale, despite the fact that the dynamics of proteins
in general occurs on timescales ranging from tens of femtoseconds (10
15
s) to
seconds (Prakash and Marcus 2007, p. 15984; Kurzynski 1997, Fig. 1). Their
reasoning proceeds as follows:
(a) Fluctuations in X(t)
(b) Fluctuations in the “local electrostatic interaction energy at the active site, E(t)”
(c) Dynamic disorder and fluctuations in spectral means,
where the symbol “ ” reads “leads to” or “causes.” Given these assumptions,
Prakash and Marcus (2007) derived the autocorrelation functions for waiting time
distributions and for spectral mean fluctuations that are similar, in agreement with
observation E (Table
11.10
). However, it should be pointed out that Prakash
and Marcus (2007) did not provide any explanation as to (a) how the slow
conformational fluctuations of COx, namely, X(T), can arise in the first place in
