Electrochemical Analysis of Ion Channels and Transporters in Pore-Suspending Membranes - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 283

which allow to replace R m,o and C m,o . Based on these considera-
tions, the equivalent circuit shown in Fig. 7B contains only three
free parameters ( R el , R m,c and C m,c ).
If active ion channels are incorporated in pore-suspending
membranes, solely the resistance of the bilayer covering the open
pores, R m,o changes significantly. In this case, approach (2) is al-
ready too elaborate for data analysis and a more simple equivalent
circuit can be applied (approach 2'), which is depicted in Fig. 7 C .
Here, the resistance R a represents the overall resistance at the limit
of low frequencies, which reads:

RR

Re ox m,c

lim Z Ȧ R= R ( )

(3)

a ,o

R RR

Ȧ o 0

m,o ox m,c

Im

lim Z Ȧ ( ) 0

(4)

Ȧ o 0

In the model shown in Fig. 7C , R a is in parallel to a constant
phase element (CPE). The constant phase element was chosen in-
stead of a capacitor to account for the non-ideal capacitive behav-
iour of the system. With the known parameter R ox , R m,c and R m,o
can be calculated from Eq. (3). In Fig. 8 , the results of the two dif-
ferent approaches (2) and (2') are compared.
The fitting results demonstrate that approach (2) (---) and (2')
(—) reflect the course of the impedance data slightly better than
approach 1 (not shown). For approach (1), the parameter R m,c is
three orders of magnitude larger than those determined by ap-
proach (2) and (2'), which is a result of the assumption of an ideal
membrane coverage on the solid area. However, this does not nec-
essarily imply that approaches (2) and (2') are more valid models
than (1). All of them are a compromise to minimize the number of
free parameters in data analysis. From four independent experi-
ments we determined C m,o,sp as 0.75-1.80 μF cm -2 and R m,sp as
(2.3-6.9)·10 3 ȍ cm 2 . The differing area dependent values may re-
flect the error in the porous area, which was not individually de-
termined for each substrate. Furthermore, hemifused vesicles could
still be present, although not resolved in impedance spectra as a
second dispersion. While for approach (2') no information about