Biomedical Engineering Reference
In-Depth Information
analysis, a cell of radius 20
μ
m was examined, corresponding to the
average of the cell sizes used by White etal. (1990).
Results are shown in Fig. 5.9a-c. In Fig. 5.9a, the total magnitude
of the E field at the membrane mid-point (
r
=
R
+
d
/2) is shown
across the upper-half membrane surface induced by a normalised
external E field of strength 1 V m
−
1
. Corresponding to this result,
Fig. 5.9b shows the induced
component at these mid-membrane
points, while Fig. 5.9c shows the same induced
θ
θ
component just
outside the membrane inthe extracellular region.
Examination of the results shows that the radial component is
maximal, just under 6,000 V m
−
1
(per unit incident field), at the
leadingedgeonthemid-planeandattheoppositepointofthisplane
ontheotherside,whilegoingtozeroatbothpoles.Correspondingly,
the
θ
and
φ
components (
φ
not shown) act in opposite fashion,
reaching a maximum at the poles and zero around the equatorial
plane. Their total magnitude, however, just outside the membrane
in the extracellular region, is reduced from the 6,000 V m
−
1
of the
radial component, being, as expected, at the maximum, about 1.5
times the incident field. Interestingly, the tangential field inside the
membrane isabout0.5 times the extracellular tangentialfield.
At this point, a word or two is required to discuss the size of
the E field strengths we have just presented and how these relate to
the endogenous membrane E fields, which are huge by comparison.
First, assuming two elementary electric charges to be separated by
a distance of 5 nm, the corresponding Coulomb E field is calculated
to be 5.8
10
7
Vm
−
1
. The potential across this distance is then
287 mV, which is of similar order to measured transmembrane
potentials of around 80-100 mV (Plonsey and Barr, 1988). It can
readily be seen that the huge E fields across a lipid bilayer tend
to dominate the structure in which many lipids are located next to
each other. Having no tangential components, the result is a regular
latticeofverystrongopposinglipids.Thelatticeexiststomaintaina
structural interface between intracellular and extracellular regions
and also creates an environment in which the surface can maintain
a concentration gradient of ionsdiffusingacross it.
Do the small tangential components have any physical signifi-
cance? We answer this by analogy. Examining the atomic structure
of an ion, we see that similar, even larger, Coulomb forces are used
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