Biology Reference
In-Depth Information
formula, Eq.
11.26
, and (b) a nondeterministic (or diachronic) term reflecting the
genetic information embodied in
conformons
(discussed in Sect.
11.3.2
).
The key observations reported by Lu et al. (1998) on cholesterol oxidase (COx)
are as follows:
(A) The rate constant (or turnover time) of a COx molecule is not constant (as
was generally believed prior to the Lu et al. 1998 experiments) but changes after
each cycle of catalysis more or less randomly, ranging from tens of milliseconds
to seconds (Figs.
11.18
,
11.24
). This phenomenon is known as “dynamic
disorder” (Zwanzig 1990) or “dynamic heterogeneity.” The histogram of these
waiting times is
asymmetric
and
rugged
(uneven, zigzag, saw tooth-shaped) as
evident in Figs.
11.18
and
11.24
.The
ruggedness
of the waiting time histogram
(defined as the difference between the measured waiting times and the theoreti-
cal waiting times calculated from a
smooth curve
that best fits the histogram) can
be either due to
experimental error
or , at least in part, to
biological causes
.Lu
et al. (1998) found one
smooth
mathematical function called the probability
distribution function, p(t), i.e., Eq.
11.25
, that fits the waiting time histogram
reasonably well (see the upper left-hand panel in Fig.
11.24
) but cannot model
the ruggedness of the histogram. The conformon-based theory of single-mole-
cule enzymology to be described below can account for both the
smooth
and
rugged
portions of the waiting time histograms.
(B) Increasing the cholesterol concentration by tenfold from 0.2 to 2.0 mM
decreased the longest waiting times measured by tenfold and the mode (i.e.,
the ordinate value under the peak of the distribution curve) of the waiting time
by about fourfold (from 150 to 40 ms).
(C) Pairs of waiting times separated by m turnovers are correlated as long as m is
less than about 10 (see Fig. 3 in Lu et al. 1998). This observation is known as
the “memory effect.”
(D) The spectral mean (i.e., the average wave number or wavelength of the
fluorescence emission of FAD) of a COx molecule fluctuates by about 1.5%
around the mean (see Fig. 5a in Lu et al. 1998).
(E) The autocorrelation function of
waiting times
and that of the
spectral means
are
similar (see Fig. 4a, b in Lu et al. 1998).
The clue to explaining these observations mechanistically was provided by the
unexpected finding that the waiting time distributions of cholesterol oxidase,
Observations A and B, could be modeled using an equation similar in form to
Planck's radiation formula
derived from the blackbody spectrum (see the lower
panel of Fig.
11.24
). A detailed analysis of this finding (as outlined in Table
11.9
below) led me to conclude that the
conformon theory of enzymic catalysis
devel-
oped in Ji (1974a, b, 1979, 2000, 2004a) applies to cholesterol oxidase. In other
words, the single-molecule enzymological data on cholesterol oxidase reported by
Lu et al. (1998) can be accounted for by the conformon theory of molecular
machines as detailed in Table
11.10
. Again, conformons are defined as the
sequence-specific conformational strains of biopolymers (proteins, RNA, and
