Interaction between diffusion and Michaelis-Menten uptake of dopamine after iontophoresis in striatum.

A quantitative description of the behavior of a neurotransmitter in the brain extracellular microenvironment requires an understanding of the relative importance of diffusion versus uptake processes. This paper models the behavior of dopamine released from a small iontophoresis electrode and its voltammetric detection by a carbon fiber sensor 100 microns away as a basis for developing a new paradigm for measuring dopamine kinetics in intact rat neostriatum. The diffusion equation incorporating uptake, characterized by a maximum velocity Vmax and a Michaelis-Menten constant Km, was transformed to an integral equation and solved numerically for the dopamine concentration, C. Analytical solutions were derived for limiting cases of a steady-state free-boundary problem when C >> Km and the linear time-dependent problem when C << Km. These solutions were compared with complete numerical solutions, both for normal uptake (Vmax = 0.2 or 0.8 microM s-1; Km = 0.15 microM), and in the presence of the uptake blocker nomifensine (Km = 6 microM). The results suggest that an experimental strategy for the quantitative analysis of dopamine, and other compounds, in living tissue is to fit a family of concentration versus time curves generated with different iontophoretic current strengths and recorded with a microsensor, to the numerical solution of the diffusion-uptake equation.