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.
%0 Journal Article
%1 Smit_1996_2527
%A Smith, G. D.
%A Wagner, J.
%A Keizer, J.
%D 1996
%J Biophys. J.
%K 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,
%N 6
%P 2527--2539
%T Validity of the rapid buffering approximation near a point source
of calcium ions.
%U http://www.pubmedcentral.gov/articlerender.fcgi?tool=pubmed&pubmedid=8744292
%V 70
%X 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.
@article{Smit_1996_2527,
abstract = {In the presence of rapid buffers the full reaction-diffusion equations
describing {C}a$^{2+}$ transport can be reduced using the rapid buffering
approximation to a single transport equation for [{C}a$^{2+}$]. Here
we simulate the full and reduced equations, exploring the conditions
necessary for the validity of the rapid buffering approximation for
an isolated {C}a$^{2+}$ 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 {C}a$^{2+}$ "sparks" and "puffs," both with and
without the indicator dye {C}a$^{2+}$ Green-1, and find that the
rapid buffering approximation is excellent. These calculations also
show that the traditional calculation of [{C}a$^{2+}$] from a fluorescence
signal may grossly underestimate the true value of [{C}a$^{2+}$]
near a source. Finally, we use the full model to simulate the transient
{C}a$^{2+}$ domain near the pore of an open {C}a$^{2+}$ 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 {C}a$^{2+}$ profile
is shown to be a reliable approximation adjacent to the pore.},
added-at = {2009-06-03T11:20:58.000+0200},
author = {Smith, G. D. and Wagner, J. and Keizer, J.},
biburl = {https://www.bibsonomy.org/bibtex/29104bc0a09d51f17ec9e10ad7fd247fe/hake},
description = {The whole bibliography file I use.},
file = {Smit_1996_2527.pdf:Smit_1996_2527.pdf:PDF},
interhash = {0c493eb949a3e7761db6bb1e92aac0a4},
intrahash = {9104bc0a09d51f17ec9e10ad7fd247fe},
journal = {Biophys. J.},
key = 274,
keywords = {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,},
month = Jun,
number = 6,
pages = {2527--2539},
pmid = {8744292},
timestamp = {2009-06-03T11:21:31.000+0200},
title = {Validity of the rapid buffering approximation near a point source
of calcium ions.},
url = {http://www.pubmedcentral.gov/articlerender.fcgi?tool=pubmed&pubmedid=8744292},
volume = 70,
year = 1996
}