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 ap proximation to a single transport equation for [Ca2+]. Here we simulat e the full and reduced equations, exploring the conditions necessary f or the validity of the rapid buffering approximation for an isolated C a2+ channel or a cluster of channels. Using a point source and perform ing numerical simulations of different durations, we quantify the erro r of the rapid buffering approximation as a function of buffer and sou rce parameters as well as the time and spatial scale set by the resolu tion of confocal microscopic measurements. We carry out simulations of Ca2+ ''sparks'' and ''puffs,'' both with and without the indicator dy e Ca2+ Green-1, and find that the rapid buffering approximation is exc ellent. These calculations also show that the traditional calculation of [Ca2+] from a fluorescence signal may grossly underestimate the tru e value of [Ca2+] near a source. Finally, we use the full model to sim ulate the transient Ca2+ domain near the pore of an open Ca2+ channel in a cell dialyzed with millimolar concentrations of 1,2-bis(2-aminoph enoxy)ethane-N, N, N, N-tetraacetic acid or EGTA. In this regime, wher e the rapid buffering approximation is poor, Neher's equation for the steady-state Ca2+ profile is shown to be a reliable approximation adja cent to the pore.