Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel.

We derive an analytical steady-state solution for the Ca2+ profile near an open Ca2+ channel based on a transport equation which describes the buffered diffusion of Ca2+ in the presence of rapid stationary and mobile Ca2+ buffers (Wagner and Keizer, 1994). This steady-state rapid buffering approximation gives an upper bound on local Ca2+ elevations such as Ca2+ puffs or sparks when conditions for the validity of the rapid buffering approximation are met and is an alternative to approximations that assume that mobile buffers are unsaturable. This result also provides an analytical estimate of the cytosolic Ca2+ domain concentration ([Ca2+]d) near a channel pore and shows the dependence of [Ca2+]d on moderate concentrations of endogenous mobile buffer, Ca2+ indicator dye, and bulk cytosolic Ca2+. Assuming a simple relationship between [Ca2+]d and the lumenal depletion domain of an intracellular Ca2+ channel, lumenal and cytosolic Ca2+ profiles are matched to give an implicit analytical expression for the effect of bulk lumenal Ca2+ on [Ca2+]d.