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temperature; h is the Planck constant; and R is the gas constant. Since
D
H
{
¼
D
E
{
+P
D
V
{
, where P is the pressure and
D
V
{
is the activation volume of COx,
D
H
{
¼ D
E
{
if
D
V
{
is zero, which is generally assumed to be true, thus transforming
Eq.
11.46
to
11.47
:
z
=
R
z
=
RT
e
D
S
e
D
E
w
¼
1
=
k
¼
(h
=
k
B
T)
ð
Þð
Þ
(11.47)
Equation (
11.47
) is equivalent to Eq.
2
in Ji (1974a, p. 420), based on which the
following postulate was made in Ji (1974a, pp. 434-435):
...
the enzyme can control the rate of chemical reactions by affecting either
D
E
{
or
D
S
{
.The
enzyme can alter the magnitude of
D
E
{
by changing the curvature of the potential energy
hypersurface of the substrate, which it does by undergoing appropriate conformational
transitions
. I now postulate that the catalytic negentropy stored in the enzyme can regulate
the rate of enzymic reactions by modulating the magnitude of
D
S
{
. I regard the enzyme as a
negentropy reservoir from which the substrate can borrow negentropy (i.e., negative entropy)
reaction, the negentropy withdrawn from the enzyme can be returned to the protein, so that no
net changes in the negentropy content of the enzyme may result. Although the vast kinetic
energies stored in the enzyme cannot be localized on the substrate as a means of catalysis,
because of the second law, I believe that the transfer of negentropy from the enzyme to the
substrate can be invoked for the purpose of catalysis without violating the second law. The
molecular mechanism of negentropy transfer from the enzyme to the substrate may be
identified with the ordering of the catalytic groups in the reaction cavity in the Franck-
Condon state and the disordering of structures elsewhere in the enzyme. (11.48)
The
negentropy transfer
from domain A to domain B, the active site, in an
enzyme to reach the transition state can affect
D
S
{
(and hence alter the associated
waiting time, w; see Eq.
11.46
) in three ways” (a)
positively
, increasing
D
S
{
; (b)
negatively
, decreasing
D
S
{
; and (c)
neutrally
, having no effect on
D
S
{
. Although
some negentropy transfer from A to B may not affect
D
S
{
and associated w, it can
still affect the probability, p(w), of the occurrence of w, again in three ways - (d)
positively
, increasing p(w); (e)
negatively
, decreasing p(w); and (f)
neutrally
,
having no effect on p(w) - depending on the amino acid sequence of the
conformons involved, as illustrated in Column (5) in Table
11.11
.
The term “negentropy” should be interpreted with caution. This term is para-
doxical in the sense that when defined as “negative entropy change (NEC),”
negentropy signifies or is associated with “order” and “information,” but, when
defined as “negative entropy (NE),” it violates the Third Law of thermodynamics,
according to which entropy of a thermodynamic system can never be less than zero
(or negative). This situation was referred to as the
Schr
...
odinger's paradox
in Sect.
Therefore the phrase “negentropy reservoir” appearing in Statement 11.48 can
be interpreted as those regions or domains of an enzyme serving as storage sites
for negentropy in the form of
ordered
or
low-entropy conformational structures.
The key message of Statement 11.48 is that an enzyme can utilize the negentropy
stored in one region of an enzyme to organize the catalytic residues at the active site
to reach the transition state, and this process can be viewed as a form of
negentropy
€
