Biomedical Engineering Reference
In-Depth Information
pedance of two circuit elements in series is equal to the sum of the
impedances of the single circuit elements. Conversely, the overall
impedance of two circuit elements in parallel is such that its recip-
rocal is equal to the sum of the reciprocals of the single circuit
elements. Consequently, if two circuit elements have appreciably
different impedances, their overall impedance is controlled by the
circuit element of higher impedance if they are in series and by the
circuit element of lower impedance if they are in parallel.
Bearing this in mind, let us consider a biomimetic membrane
consisting of a thiolipid tethered to an electrode surface, with a
lipid monolayer on top of it. As a first approximation, this tethered
bilayer lipid membrane (tBLM) can be regarded as consisting of
three adjacent slabs: the hydrophilic spacer moiety, the lipid bi-
layer moiety, and the aqueous solution bathing the lipid bilayer. A
simple equivalent circuit commonly employed to interpret the im-
pedance spectrum of a tBLM is shown in Fig. 2 ; R : is the re-
sistance of the aqueous electrolyte, R m and C m are the resistance
and capacitance of the lipid bilayer, and C s is the capacitance of
the hydrophilic spacer. As an example, we will consider a tBLM
that makes use of a convenient and widely used thiolipid called
DPTL, first employed by Schiller et al. 1 (see Fig. 1A ). It consists
of a tetraethyleneoxy hydrophilic chain covalently linked at one
end to a lipoic acid residue, for anchoring to the metal via a disul-
fide group, and bound at the other end via ether linkages to two
phytanyl chains. Figure 2 shows the impedance spectrum of a
tBLM consisting of a DPTL monolayer anchored to a mercury
electrode, with a diphytanoylphosphatidylcholine (DPhyPC) mon-
olayer on top of it. This tBLM incorporates gramicidin, a linear
neutral pentadecapeptide that spans lipid bilayers by forming a N-
terminus-to-N-terminus dimer. 2 The elements of the equivalent
circuit are influenced by the movement of K + ions across the lipid
bilayer, induced by the gramicidin channel. The spectrum is dis-
played on a Bode plot, namely a plot of log| Z | and phase angle I
against log f , where | Z | is the magnitude of the impedance.
As already stated, the impedance of circuit elements in series
is determined by the element with the highest impedance; con-
versely, the impedance of circuit elements in parallel is determined
by the element with the lowest impedance. Therefore, at the high-
est frequencies, f= Z/2S, the overall impedance | Z | is determined by
the resistance R : , because the impedance of the C s element,
Search WWH ::




Custom Search