Biology Reference
In-Depth Information
C. Calculation of Flux
The di
erential concentration measurement is converted to flux to provide a
direct representation of the number of ions passing through a unit area per unit
time. Calculation of flux enables comparison of Ca
2
þ
transport between di
V
V
erent
cient of Ca
2
þ
, the distance over
V
Y
systems as it takes into account the di
usion coe
which the di
erential concentration measurement was acquired, the surface geom-
etry of the source, and the distance of measurement from the source. It also
provides a value for comparison of Ca
2
þ
flux measured with self-referencing of
CaSMs to other methods for monitoring Ca
2
þ
including intracellular fluorescent
and luminescent ion indicators and radioactive tracer flux studies. For planar
sources where the measuring electrode is relatively close to a large source, such
as a tissue, sheet of cells or large diameter cell, and the di
V
erential concentration
is measured over a small distance ''
D
x'' within the gradient next to the source,
flux (J)is
V
DC
Dx
J ¼D
ð
6
Þ
cient of Ca
2
þ
. By this model, at equilibrium the
flux measured at some distance from the source is the same as the flux at the surface
of the source. According to this equation, e
where ''D'' is the di
V
usion coe
Y
ux, a higher concentration of Ca
2
þ
near the source, is identified by a negative flux.
In order to determine flux at the cell surface for known surface geometries, it is
useful to calculate analyte flow, that is, the quantity of substance (Q) moving per
unit time (
Henriksen et al., 1992
). Flow is the same for all concentric surfaces
surrounding the source surface. Flux at the source surface is the flow divided by the
surface area of the source. Therefore, radially emanating flow from a cylindrical
surface is
Z
¼
Q
2
p
D
ln
b=ðÞ
DðÞ
t
¼
7
Þ
Flow
where ''D'' is the di
cient of the analyte and ''a'' and ''b'' are the radial
distances between the center of the cylinder and the electrode tip at the near and far
poles, respectively. These equations have been adapted from
Crank (1967)
. Ana-
lyte flux at the surface of the cylinder is then determined by dividing by its surface
area 2
p
rl. A caveat of this approach is the assumption that the flow is equal at all
points around the cylinder and along the shaft of the cylinder. An alternative is to
calculate flux per unit length by dividing by 2
p
r (
Henriksen et al., 1992
).
The flow from a spherical source is
V
usion coe
Y
¼
Q
4
p
D
ab
b a
Flow
t
¼
DðÞ
8
Þ
Flux at the cell surface can then be determined by dividing by the spherical surface
area 4
p
r
2
.
