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active site of an enzyme converting substrate S to product P within the enzyme-
substrate complex (see b and c).
Notice that the substrate is bound through catalytic residues 1, 2, and 3 (see
a
),
while the product is bound through catalytic resides 2, 3, and 4 (see
d
), dictated by
their unique molecular shapes (not shown). Because the conformational changes
necessary to rearrange catalytic residues at the active site when S is converted into
P would be much slower than the electronic transitions accompanying the S to P
conversion (as discussed in Sect.
2.2.3
), it was postulated in (Ji 1974a) that the
conformation of the active site must first change to an intermediate state between
the initial and final states of the enzyme, characterized by the presence of catalytic
resides 1, 2, 3, and 4 (see
b
and
c
), before S can be converted (or, in the quantum
mechanical parlance,
tunnels
) to P at the transition state. This state is denoted as
[ES
EP]* in Process
7.17
. At the transition state, S and P lose their molecular
identities and exist as an intermediate (or a resonance hybrid) between S and P,
which fact is symbolized by the double-headed arrow within the square bracket in
Process
7.17
. The transition state can either return to the initial state regenerating S
or go over (or tunnel) to the final state, leading to the production of P. The height of
the activation free energy barrier (i.e., the difference between the free energy levels
of
a
and
b
) is postulated to be controlled by the genetic information encoded in
the spatial arrangement of the catalytic residues (numbered 1 through 4) in
b
and
c
(Ji 1979) which, of course, would be influenced by the conformational state of the
rest of the enzyme. Therefore, Fig.
7.6
embodies the elements of both
statistical
mechanics
(related to free energy) and
information theory
(related to the geometric
arrangement of the catalytic residues in the active site) and represents a concrete
example of what was referred to as “info-statistical mechanics” in (Ji 2006a). The
proposed mechanism of enzymic catalysis was motivated by the Franck-Condon
principle imported into biology from chemical kinetics in (Ji 1974a), with the
typographical errors therein corrected in Ji (1979) and generalized in (Ji 1991)
into the “
generalized Franck-Condon principle (GFCP)
”or“
the principle of slow
and fast processes (PSFP)”
(see Sect.
2.2.3
).
$
7.2.2 Enzymes as Coincidence Detectors
The molecular mechanism of enzymic catalysis based on PSFP (Fig.
7.4
) can also
be viewed as the process of
coincidence detection
. A coincidence detector is
defined in neurobiology as
a computational unit that fires if the number of input spikes received within a given time
bin,
D
t, equals or exceeds the threshold,
Y
. Mikula and Niebur 2003).
The concept of a
coincidence detector
as applied to an enzyme can be
schematically represented as shown in Fig.
7.7
.
Here, Brownian motions, including the thermally driven fluctuations of the
catalytic residues, are considered to be much slower than the electronic transitions
