Biology Reference
In-Depth Information
Fig. 11.25 The thermal excitation of ground-state and the relaxation of the transition-state
conformations of an enzyme during a catalytic cycle. C
i
and C
j
are the ith and jth conformational
states (or conformers), respectively, and C
{
is the
common
transition state of the enzyme
(Fig.
11.28
). The symbols t
ie
and t
jr
stand for, respectively, “the ith excitation time” or the time
required for the conformational transition from C
i
to C
{
and “the jth relaxation time” or the time
taken for the conformational transition from C
{
to C
j
activation) to reach the common transition state, C
{
(see Fig.
11.28
). After
catalysis, C
{
must relax, in the time span of t
jr
(r standing for relaxation), back to
agroundstate,C
j
, where j can be equal to or different from C
i
(see Fig.
11.25
).
If the lifetime t
i
of C
i
is longer than the sum of t
ie
and t
jr
,i.e.,
t
i
¼
a
t
ie
þ
t
jr
(11.30)
where
a
is a positive constant greater than unity, there is a high probability
that C
{
will relax back to C
i
or to C
j
where j is in the neighborhood of i. This
would provide one possible mechanism to account for the “memory effect,”
Observation C, in Table
11.10
, the observation that long waiting times are
likely to be followed by long waiting times and short waiting times are likely
to be followed by short waiting times, since C
{
is more likely to relax back to
C
i
than to C
j
.
4. Assumption (a) in (2) is experimentally testable. If this assumption is proven to
be invalid, the waiting time distribution of Lu et al. (1998) can be completely
accounted for
deterministically
, i.e., based on the laws of physics (see Row 3,
Table
4.1
), either by Eqs.
11.25
or
11.27
with X(w) set to zero. If Assumption (a)
is proven to be valid, then the waiting time distribution of Lu et al. (1998) cannot
be completely accounted for based on the laws of physics alone (i.e., in terms of
synchronic
laws alone as defined in Table
4.1
) but entails invoking additional
history of living systems. In other words, if Assumption (a) can be validated by
further experiments, it would be possible to conclude that the waiting time
distribution of Lu et al. (1998) embodies two orthogonal sets of regularities
Eq.
11.27
, it may be possible to make the following statements:
Biological Phenomena
¼
Synchronic Laws
þ
Diachronic Rules
(11.31)
Biological phenomena embody synchronic laws and diachronic rules that are orthogonal to
each other. (11.32)
Evidently, Eq.
11.31
and Statement 11.32 combine both
inexorable
laws of
physics and the
arbitrary
rules of biological evolution, reminiscent of the theory
