Abstract
In the presence of rapid buffers the full reaction-diffusion equations
describing Ca$^2+$ transport can be reduced using the rapid buffering
approximation to a single transport equation for Ca$^2+$. Here
we simulate the full and reduced equations, exploring the conditions
necessary for the validity of the rapid buffering approximation for
an isolated Ca$^2+$ channel or a cluster of channels. Using a
point source and performing numerical simulations of different durations,
we quantify the error of the rapid buffering approximation as a function
of buffer and source parameters as well as the time and spatial scale
set by the resolution of confocal microscopic measurements. We carry
out simulations of Ca$^2+$ "sparks" and "puffs," both with and
without the indicator dye Ca$^2+$ Green-1, and find that the
rapid buffering approximation is excellent. These calculations also
show that the traditional calculation of Ca$^2+$ from a fluorescence
signal may grossly underestimate the true value of Ca$^2+$
near a source. Finally, we use the full model to simulate the transient
Ca$^2+$ domain near the pore of an open Ca$^2+$ channel in
a cell dialyzed with millimolar concentrations of 1,2-bis(2-aminophenoxy)ethane-N,N,N,N-tetraacetic
acid or EGTA. In this regime, where the rapid buffering approximation
is poor. Neher's equation for the steady-state Ca$^2+$ profile
is shown to be a reliable approximation adjacent to the pore.
- 8744292
- agents,
- biological,
- biophysics,
- buffers,
- calcium
- calcium,
- channels,
- coloring
- gov't,
- in
- ion
- mathematics,
- models,
- non-p.h.s.,
- non-u.s.
- research
- support,
- transport,
- u.s.
- vitro,
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