Biology Reference
In-Depth Information
Macroscopic Machines
(Rigidity)
Thermal barrier
(Boltzmann barrier)
Molecular Machines
(Thermal Fluctuations)
Size
Quantum barrier
(Heisenberg barrier)
Quons
(Quantum Mechanical Tunneling)
Fig. 11.26 The importance of the size of particles or material systems in determining their
physical properties under physiological conditions. Macroscopic machines (e.g., computer) must
be large enough to resist the thermal fluctuations of their component parts (to avoid short
circuiting) but molecular machines (e.g., enzymes) must be (1) small enough to undergo thermal
fluctuations under physiological conditions and yet (2) large enough to prevent, when necessary,
the quantummechanical tunneling of quons (e.g., electrons, protons, etc.) at their active sites. Thus
molecular machines
can be said to be separated from macroscopic machines by what has been
referred to as the
thermal (or Boltzmann) barrier
(Ji 1991, pp. 29-35) and from quons by what may
be referred to as the
quantum
(or
Heisenberg
)
barrier
wave-particle duality and the quantum mechanical tunneling, including molecules,
atoms, and subatomic particles). This idea is diagrammatically represented as
shown in Fig.
11.26
.
5. Having discussed the meaning of the nondeterministic term of Eq.
11.27
in some
detail, we are now ready to tackle the meaning of the deterministic term of the
equation, which will reveal, among other things, the fundamental role of
thermal
fluctuations
in enzymic catalysis. As already pointed out, Eq.
11.27
with X(w)
set to 0 fits the waiting time distribution fairly well, at least as well as Eq.
11.25
derived by Lu et al. (1998). To quantitatively compare the capabilities of
Eqs.
11.25
and
11.27
to fit the experimentally measured waiting time distribu-
tion, the following quantity was defined as a measure of the
deviation of the
theoretical predictions from measured data
called DTE (
Deviation of Theory
from Experiment)
:
1
=
2
2
DTE
¼ððð
ð
Calculated w
Measured w
Þ=
Measured w
Þ
Þ
Þ
100
(11.37)
DTE represents the absolute value of the deviation of the theoretically
predicted w from the measured w expressed as a fraction of the measured w.
Figure
11.27
shows the results of applying Eq.
11.37
to Eqs.
11.25
and
11.27
.
The average DTE values are about the same for these two equations but the standard
deviations and the coefficients of variations are about twice as large for Eq.
11.25
as
