Biomedical Engineering Reference
In-Depth Information
to
c
∂
2
[
Ca
]
J
diffusion
=
(
D
Ca
+
h
M
D
M
+
h
E
D
E
)
∂
x
2
(3.5)
2
E
h
M
D
M
h
E
D
E
K
E
,
eq
+[
Ca
]
−
K
M
,
eq
+[
Ca
]
+
[
Ca
]
·
E
[
Ca
]
with
[
B
l
,
total
]
K
l
,
eq
h
l
=
2
,
with
l
=
M
,
E
(3.6)
(
K
l
,
eq
+[
Ca
])
where
K
l
,
eq
,
D
l
are the calcium disassociation constant and diffusion constant for
species
l
E
for mobile and exogenous buffers respectively [23, 53]. The buffer-
ing factor scales the flux to account for the calcium binding effect of the buffers. The
first term in the square brackets represents the diffusive transport of calcium. The
last term in the square brackets represents the uptake of calcium by mobile buffers as
free calcium moves down its concentration gradient and is a non-diffusive term. The
approach assumes that the sum of the concentrations of bound and unbound buffer at
any given point in space remains constant. Other equilibrium approaches for approx-
imating buffering have been suggested by Zhou and Neher [56] and are evaluated for
accuracy, i.e., under what conditions they can be used, by Smith [46]. These have
not been discussed here for brevity, but the reader should seek the sources mentioned
for more details.
The principles described above can be applied to models for neurons. Neher [37]
developed an equation for the effective diffusion constant based on these principles
that can be used to calculate the diffusion profile of a calcium flux release from a
channel. This profile would fall off more sharply in the presence of calcium buffers.
With this, the distance between a release site and channel activated by calcium can
be calculated by determining the concentration of an exogenous buffer with known
calcium dissociation constant, such as BAPTA, at which the activation of the calcium
sensitive signal is abolished upon stimulation. For example, in chick dorsal root gan-
glion cells, calcium enters via voltage gated calcium channels. This method suggests
that calcium-activated chloride channels are 50-400 nm distant and the ryanodine
receptors are 600 nm distant [55].
While the buffering of the charges of the cellular membranes can be approximated
by the rapid buffering approximations above, this fails to account for the effect of
the electrical charges on diffusion of charged particles. For this purpose, a model of
electrodiffusion based on the Nernst-Planck electrodiffusion equations can be used.
This approach has been used to describe diffusion in membrane-restricted spaces
such as the cardiac diadic junction by Soeller and Cannell [48].
=
M
,
3.2.1
Intracellular calcium stores
The main intracellular calcium store is the endoplasmic reticulum (ER). This is
known as the sarcoplasmic reticulum (SR) in muscle cells. The major calcium han-
dling components in the ER are the calcium release channels, the calcium uptake
pumps, and the calcium buffers in the ER lumen.
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