Biology Reference
In-Depth Information
Brownian Motions
(
Thermal fluctuations)
Ordered
Motions
(
Catalysis
)
Coincidence
Detector
Chemical Reactions
(Free energy source)
Fig. 7.7 Enzymic catalysis viewed as a
coincidence-detecting event
involving the synchrony
between the substrate-binding event and the event of complementary conformational alignment of
catalytic residues at the binding site
involved in chemical bond-breaking or bond-forming processes within substrates,
the heart of the catalytic process. Only when right Brownian motions of the
catalytic residues
coincide
with the presence of the right substrates at the active
site of an enzyme is the catalysis postulated to occur. Hence, catalysis can be
thought of as a form of
ordered motions
of enzymes as a whole, and the free energy
cost for rectifying the random Brownian motions to ordered motions is borne by the
free energy-releasing chemical reaction whose occurrence is postulated to be
synchronous with the ordered motions and/or by the free energy of substrate
binding partially stored in enzymes as conformational strains. The latter mechanism
is similar to what is referred to as the
Circe effect
by Jencks (1975).
In another sense, enzymes can be viewed as
selectors of Brownian motions
enabled
or driven by chemical reactions that they catalyze
coincidentally
, the selecting actions
involving a small subset of the
conformers
of the catalytic residues that are accessible
through thermal fluctuations of an enzyme. Conformers are conformational isomers,
not to be confused with conformons, which are conformational strains localized in
sequence-specific sites within a conformer. Conformers are a
geometric
concept,
whereas conformons are both a
geometric
and
energetic concept.
The rate of the occurrence of such coincident events can be estimated from the
equation derived by Mikula and Nieber (2003):
p
j
t
X
m
1
D
m
j
mj
N
out
ð
p
;
m
; y;
q
¼
0
Þ¼
ð
1
p
Þ
(7.18)
j¼
0
where
N
out
¼
the output rate, firings per minute;
p
¼
the probability of a spike
occurring within a time bin
D
t; m
¼
the number of input spike trains, each having
n time bins;
the threshold number of spikes that must be exceeded by the
summed input spikes before the coincidence detector fires or is activated;
q
Y ¼
¼
the
correlation coefficient between spike trains 1,
...
,
m
; and
j
¼
the number of
coincident spike trains.
Although Eq.
7.18
was derived based on the neuron as a model of a coincidence
detector, I am assuming that the Mikula-Niebur equation can be applied to
enzymes
(as suggested in Fig.
7.7
) and
protein complexes
in general. Equation
7.18
can also
be extended to
assemblies of neurons
in the brain to represent an increased neuronal
synchrony associated with perception (Woelbern et al. 2002; Anderson et al. 2006;
Averbeck and Lee 2004).
