Anisotropic and heterogeneous diffusion in the turtle cerebellum: implications for volume transmission

Abstract

1. Measurements of extracellular diffusion properties were made in three orthogonal axes of the molecular and granular layers of the isolated turtle cerebellum with the use of iontophoresis of tetramethylammonium (TMA+) combined with ion-selective microelectrodes. 2. Diffusion in the extracellular space of the molecular layer was anisotropic, that is, there was a different value for the tortuosity factor, lambda i, associated with each axis of that layer. The x- and y-axes lay in the plane parallel to the pial surface of this lissencephalic cerebellum with the x-axis in the direction of the parallel fibers. The z-axis was perpendicular this plane. The tortuosity values were lambda x = 1.44 +/- 0.01, lambda y = 1.95 +/- 0.02, and lambda z = 1.58 +/- 0.01 (mean +/- SE). By contrast, the granular layer was isotropic with a single tortuosity value, lambda Gr = 1.77 +/- 0.01. 3. These data confirm the applicability of appropriately extended Fickian equations to describe diffusion in anisotropic porous media, including brain tissue. 4. Heterogeneity between the molecular and granular layer was revealed by a striking difference in extracellular volume fraction, alpha, for each layer. In the molecular layer alpha = 0.31 +/- 0.01, whereas in the granular layer alpha = 0.22 +/- 0.01. 5. Volume fraction and tortuosity affected the time course and amplitude of extracellular TMA+ concentration after iontophoresis. This was modeled by the use of the average parameters determined experimentally, and the nonspherical pattern of diffusion in the molecular layer was compared with the spherical distribution in the granular layer and agarose gel by computing isoconcentration ellipsoids. 6. One functional consequence of these results was demonstrated by measuring local changes in [K+]o and [Ca2+]o after microiontophoresis of a cerebellar transmitter, glutamate. The ratios of ion shifts in the x- and y-axes in the granular layer were close to unity, with a ratio of 1.04 +/- 0.08 for the rise in [K+]o and 1.03 +/- 0.17 for the decrease in [Ca2+]o. In contrast, ion shifts in the molecular layer had an x:y ratio of 1.44 +/- 0.14 for the rise in [K+]o and 2.10 +/- 0.42 for the decrease in [Ca2+]o. 7. These data demonstrate that the structure of cellular aggregates can channel the migration of substances in the extracellular microenvironment, and this could be a mechanism for volume transmission of chemical signals. For example, the preferred diffusion direction of glutamate along the parallel fibers would help constrain an incoming excitatory stimulus to stay "on-beam."