Electrochemical Analysis of Ion Channels and Transporters in Pore-Suspending Membranes - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 305

front of the bilayer. 22,82 Not only is the membrane conductance a
function of the ion concentration in solution, 22 as demonstrated in
the previous Section, but also ı W :

RTK 1

ı (7)

W

22

c

zF 2 D

w

ı W is determined by the diffusion coefficient D w of ions in the
aqueous medium and the partition coefficient K of ions between
the lipid and aqueous phase. The other parameters in Eq. (7) are
denoted as usual. The plots in Fig. 14 B indeed show a linear be-
haviour of ı W ( c -1 ). However, the linear regressions do not cross
the origin. The slopes s were determined to be s Li = 44.2 kȍ s -0.5
mM, s Na = 32.8 kȍ s -0.5 mM, and s K = 29.2 kȍ s -0.5 mM. With
D Li < D Na < D K , 83 the values for s are expected to follow the trend
s Li > s Na > s K , which agrees with the finding. The second parameter
K , however, also determines the slope but cannot be readily de-
fined as it depends on the bilayer itself. Assuming that K is similar
for Li + , Na + and K + , the ratio m I / m J of the ions I + and J + reflects the
ratio of their diffusion coefficients D J 0.5 /D I 0.5 . Table 1 shows a
comparison of the experimentally determined and theoretical ratios
of diffusion constants. 83 The main deviation from theory is the ob-
servation that the linear regressions do not cross the origin, i.e.,
ı W,0 0. ı W,0 appears to be independent of the cation with an aver-
age ı W,0 = (6800 ± 500) kȍ s -0.5 . This value implies that even at
high ion concentrations, the mass transport cannot be neglected,
which might be attributed to the fact that the alkali cations were
only added from the cis compartment of the cell, resulting in an
ion gradient across the bilayer. The ion gradient causes an electro-
chemical potential driving the ion transport across the bilayer,
which is not included in our model.
It is worth noting that the mass transport phenomena cannot
be readily investigated in case of SSMs, 22 as the impedance data of
gramicidin-doped SSMs at low frequencies are hampered by the
capacitance of the underlying gold electrode. This became also
obvious in a study of Vallejo and Gervasi 84 on gramicidin-
containing SSMs. To account for mass transport, they introduced a
Warburg impedance in their electrical model, but did not extract
ı W -values that reflect the expected trend, when varying the mono-