70
3 Fundamentals of DET-Type Bioelectrocatalysis
the electrochemically active center is located at r as from the center of the enzyme
(Fig. 3.4, (A)). By assuming the random orientation of the enzyme at a planar electrode, the electrode reaction center in the enzyme rotates in the range between r −
r as and r + r as with a probability density function (f ) given by [73, 74]
f =
1
2r as
.
(3.16)
Substitution of Eq. (3.14) into Eq. (3.12) gives the steady-state DET current by
the enzymes located at z = d − (r − r as ):
i s,z=d−(r −r as ) =
i
lim
s
1 +
1
K
E
+
k c
k o
max K
E
1−α exp(−β(z+r −r as ))
,
(3.17)
with
i
lim
s
= ±n S F Ak c E .
(3.18)
The integration of the current gives the total current by the whole enzymes on the
electrode as follows for oxidation of S:
Fig. 3.4 Schematic model
of an adsorbed enzyme on
(A) planar and (B) spherical
mesoporous-electrodes
(Reproduced from Ref. [67],
Copyright (2016) with
permission from The
American Chemical Society)
A
B
Electrode
Active site
d
r as
Enzyme
r
Electrode
R p
d
Center of Enzyme
Center of pore
z
z
x
r − r as
0