Kinetics of diffusion in a spherical cell. II. Solute buffering included

This paper on diffusion kinetics in neurons presents an analysis of diffusion in the presence of solute buffering. Computational rather than theoretical methods are usually necessary since buffering generally precludes an analytical solution to the diffusion equations. As in the companion paper, our methods are illustrated in the context of calcium diffusion in a spherical cell. However, the same methods can be applied to the spread of any second messenger and other geometries. Analytical or computational predictions of the time course of diffusion and buffering may help guide further experiments and simulations. For example, simulations of calcium diffusion in a model of the bullfrog sympathetic ganglion cell show that buffering at depths greater than 5-6 microns is almost instantaneous compared to diffusion from sources at the cell membrane. Since buffering complicates the design of multicompartmental models, we demonstrate that a few compartments designed on the basis of diffusion alone (Carnevale and Rosenthal, 1992) may be a satisfactory framework for a model that includes bimolecular buffering. An analytical solution may be possible if the buffering reaction can be linearized. We describe a method for linearizing bimolecular saturating buffering, i.e., approximating it by a unimolecular non-saturating process that immobilizes solute. The analytical solution for the linearized reactive diffusion problem fits a non-linear model of calcium movement in the bullfrog sympathetic ganglion cell quite well after a few milliseconds.