Biomedical Engineering Reference
In-Depth Information
to maintain structure—in this case electrons in orbit around its
nucleus. These huge internal fields do not stop us assuming a very
simple ionic model for analysing ionic motion, which we know as
ionic currents and where we use E fields that are tiny, miniscule, by
comparison. What is important is the net field that is present in the
external world.
It also needs to be kept in mind that exposure times for some
cellular effects involve quite lengthy periods. White et al. exposed
protoplasts for around three to four hours before the appearance
of two foci at the poles. Stochastic fluctuations, if significant, exist
oververybriefperiodsandcanbeexpectedtoaverageoutoverlong
periods.
5.7 Electrophoresis of Proteins within the Cell Membrane
Using the
tangential E field results, which were stored in
a file, the diffusion model was tested. Initially, a population check
was made. This ensured that the same number of proteins were
present at the end of a run as at the start. The check was found
accurate to within 10
−
5
particles out of 5
θ
and
φ
10
9
. The mobility and
back-diffusion fluxes were programmed separately and the output
checkedforphysicality.Theresultsweresymmetricin
φ
andshowed
an increasing effect as
θ
increased. Equilibrium was observed only
when back diffusionwas included.
Satisfied that the program was fully working, the complete
program was tested using the results obtained by Poo (1981).
In Poo's experiments, the asymmetry induced upon concanavalin
receptors was tracked in time and exposure levels were varied. To
obtain a comparison the diffusion constant used in the numerical
model was obtained using Eq. (5.4) by assuming a range of cell
radii and assuming an equilibrium time of around 600 seconds.
Figure 5.10 shows the time-varying results for the case of a cell
radius of 100
μ
m. The variation across a range of elevation angles,
corresponding to the north pole down to the equator, is shown.
The results show that asymmetry is foremost at the leading edge
(
×
90
◦
,
0
◦
) but is prominent right along the leading azimuth
θ
=
φ
=
(0
◦
<θ
, 180
◦
,
0
◦
).
φ
=
