Biology Reference
In-Depth Information
In other words, what is measured from the blackbody is what it absorbs from its
environment, but what is measured from the COx molecule is not what it absorbs
from its environment but what
that absorbed energy helps the enzyme molecule to
accomplish (e.g., a
b transition in Fig.
11.19
), namely, the removal of the
fluorescence from its coenzyme, FAD, by catalyzing its reduction to the non-
fluorescent FADH
2
. It is important to point out that the heat absorbed by an enzyme
cannot perform any molecular work, including catalysis,
since no thermal energy
can drive any work under isothermal conditions
, according to the Second Law of
Second Law as formulated by McClare in 1971 (see Statement 2.5 in Chap.
2
), an
enzyme can utilize thermal energy if it can be paid back or returned to its environ-
ment within its turnover time, leading to the following generalization:
!
An enzyme can utilize thermal energy to facilitate catalysis without violating the Second
Law, if the chemical reaction being catalyzed can release heat to the environment within the
times shorter than
t
, the turnover time of the enzyme. (11.39)
We may refer to Statement 11.39 as the
First Law of Enzymic Catalysis
,to
emphasize the fundamental role that thermal energy, as manifested in molecular
motions (or Brownian motions), plays in enzymic catalysis, the foundational
process of the phenomenon of life.
The blackbody spectrum measures all the thermal photons absorbed by the
blackbody wall, but the waiting time distribution of COx measures only a small
fraction of the thermal photons absorbed by the COx molecule that helps COx to
reach its transition state, C
{
. This difference is visualized in Fig.
11.28
in terms of
the
multiple levels
(labeled E
1
though E
5
) of thermal excitations for blackbody
radiation on the one hand and the
fixed level
of thermally activated transition state in
the COx molecule labeled C
{
that triggers catalytic event on the other.
The reason that Planck's radiation formula, Eq.
11.26
, can account for the
waiting time distribution of COx, in the form of Eq.
11.27
with X(w) set to zero,
is probably because of the mechanistic isomorphism between blackbody radiation
and enzymic catalysis as indicated by the similar distributions of the upward arrows
in the two panels in Fig.
11.28
: A set of arrows starting from a common ground state
reaching different activated states on the one hand and a similar set of arrows
starting from different ground states arriving at the common activated state, C
{
,on
the other. The rationale for invoking different ground states for the thermal activa-
tion in COx is given in (6) below. Due to the varying levels of conformational
energy associated with C
i,
the thermal energies required for C
i
to reach the common
transition state, C
{
, differs as indicated by the varying lengths of the upward arrows
in the right-hand panel of Fig.
11.28
.
6. It is well known that a protein molecule contains many internal mechanical (i.e.,
conformational) strains variously referred to as “mobile defects” (Lumry 1974;
Lumry and Gregory 1986), “frustrations” (Anderson 1983, 1987), or conformons
(Green and Ji 1972a, b; Ji 1974b, 2000) as already indicated in Sect.
11.3.2
.
The number and locations of these mechanical strains within an enzyme proba-
bly vary from one conformer to another (Fig.
11.21
). The conformers of a protein
