Modelling Neuronal Calcium Dynamics - Computational Neuroscience: A Comprehensive Approach - page 86

and calcium activated potassium channels is modeled along with the endogenous
mobile buffer calbindin. Also, the calbindin captures calcium microseconds after it
enters the cells and carries it away from the channel mouth. This in effect, causes
calcium to quickly reach a steady state level near one or more open channels. Fur-
thermore, it restricts the area in which calcium is elevated, i.e., it causes calcium
to fall off more steeply as the distance from the channel increases. It also showed
that a calcium binding molecule with a calcium dissociation constant and diffusional
properties similar to calbindin is necessary to simulate the experimental results.

3.3.2 Cross-talk between channels

Another area in which local domains of calcium is important is the communication
or cross-talk between ion channels ( Figure 3.5) . In such situations, ion channels are
located in close proximity so that calcium entry through one channel causes high
local calcium concentrations that can act on other nearby channels of the same or
different types. Sometimes this will occur in a subspace bounded by cell membranes
and organelles, and other times not. The calcium concentration in the local domains
can easily be 100 times that of the bulk cytoplasm. In Figure 3.5, calcium-activated
chloride channels are located in close proximity to voltage gated calcium channels.
The ryanodine receptors in the ER are located at some slightly further distance. Un-
der highly buffered, low level activation of the voltage gated channels might activate
the chloride channels but not the ryanodine receptors as observed by Ward and co-
workers [55].
This has been modeled extensively in the area of excitation-contraction (EC) cou-
pling in cardiac cells on the cellular level [24]. In EC coupling, opening of voltage-
gated L-type calcium channels in the cell membrane allows calcium entry that trig-
gers release from internal stores via the ryanodine receptor. This process is termed
calcium-induced calcium release. In this system, the L-type calcium channel and the
ryanodine receptors are situated in a membrane restricted subspace with only 12-15
nm between the membranes containing the two types of channels. In these cellular
models, the domain is treated as a small compartment that contains ion channels and
buffers, and communicates with the bulk cytoplasm. The group behavior of these
ion channels is modeled, which smooths the rapid changes of calcium fluxes due to
channel opening. In these models, since the time scale of calcium dynamics is much
slower than the kinetics of the buffers, the rapid buffering approximation should be
used.
Another approach is to model the details of this compartment in cardiac cells [39,
48]. These models also contain ion channels and buffers, and also communicate
with the bulk myoplasm. However, they are generally stochastic to simulate ion
channel dynamics and do not include whole cell calcium dynamics. Since a small
number of channels is modeled, there are rapid changes in the calcium fluxes. This
results in large time dependent changes in calcium requiring a small time step. This
necessitates that the buffering equations be solved dynamically rather than with a
steady-state approximation.
Calcium induced calcium release has also been observed in neurons [1, 22, 55].