Validity of the rapid buffering approximation near a point source of calcium ions.
In the presence of rapid buffers the full reaction-diffusion equations describing Ca2+ transport can be reduced using the rapid buffering approximation to a single transport equation for [Ca2+]. Here we simulate the full and reduced equations, exploring the conditions necessary for the validity of the rapid buffering approximation for an isolated Ca2+ 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 Ca2+ "sparks" and "puffs," both with and without the indicator dye Ca2+ Green-1, and find that the rapid buffering approximation is excellent. These calculations also show that the traditional calculation of [Ca2+] from a fluorescence signal may grossly underestimate the true value of [Ca2+] near a source. Finally, we use the full model to simulate the transient Ca2+ domain near the pore of an open Ca2+ 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 Ca2+ profile is shown to be a reliable approximation adjacent to the pore.
Smith
G D
GD
Institute of Theoretical Dynamics, University of California, Davis 95616, USA.
Wagner
J
J
Keizer
J
J
D055592:Biophysical Phenomena; D001703:Biophysics; D002021:Buffers; D002118:Calcium / Q000737:chemistry / Q000378:metabolism*; D015220:Calcium Channels / Q000378:metabolism; D004396:Coloring Agents; D066298:In Vitro Techniques; D017136:Ion Transport; D008433:Mathematics; D008954:Models, Biological
D002021:Buffers; D015220:Calcium Channels; D004396:Coloring Agents; D002118:Calcium