Diffusion of flexible random-coil dextran polymers measured in anisotropic brain extracellular space by integrative optical imaging

Abstract

There are a limited number of methods available to quantify the extracellular diffusion of macromolecules in an anisotropic brain region, e.g., an area containing numerous aligned fibers where diffusion is faster along the fibers than across. We applied the integrative optical imaging method to measure diffusion of the fluorophore Alexa Fluor 488 (molecular weight (MW) 547) and fluorophore-labeled flexible random-coil dextran polymers (dex3, MW 3000; dex75, MW 75,000; dex282, MW 282,000; dex525, MW 525,000) in the extracellular space (ECS) of the anisotropic molecular layer of the isolated turtle cerebellum. For all molecules, two-dimensional images acquired an elliptical shape with major and minor axes oriented along and across, respectively, the unmyelinated parallel fibers. The effective diffusion coefficients, D*(major) and D*(minor), decreased with molecular size. The diffusion anisotropy ratio (DAR = D*(major)/D*(minor)) increased for Alexa Fluor 488 through dex75 but then unexpectedly reached a plateau. We argue that dex282 and dex525 approach the ECS width and deform to diffuse. In support of this concept, scaling theory shows the diffusion behavior of dex282 and dex525 to be consistent with transition to a reptation regime, and estimates the average ECS width at approximately 31 nm. These findings have implications for the interstitial transport of molecules and drugs, and for modeling neurotransmitter diffusion during ectopic release and spillover.

FIGURE 1

Anisotropic extracellular diffusion measured with the IOI method. (a) Schematic of turtle cerebellum (ML, molecular layer; PCL, Purkinje cell layer; GL, granular layer; PF, parallel fiber; PC, Purkinje cell; and GC, granular cell). Diffusion measurements were done in the horizontal plane (x,y) of the ML. (b) A time sequence of two-dimensional images (scale bar 100 μm) of three-dimensional diffusion cloud was captured by the charge-coupled device (CCD) camera; panel shows a single image at t = 6 s. Dashed lines show the major and the minor axes of elliptical diffusion cloud. (c) The intensity profiles along major (solid line) and minor (not shown) axes were extracted and fitted with an appropriate theoretical model (dashed line). The lower 10% of the curves were not used in the fitting.

FIGURE 2

Estimation of the DAR from simulations: radii ratio method. (a) Injection volume diameter d was set at 100 μm (spherical injection volume 0.1 nL with volume fraction 0.30). Two sets of and were used. The radii ratio stabilizes faster for the larger (b) The values of and were set at 2.12 × 10⁻⁶ cm² s⁻¹ and 1.44 × 10⁻⁶ cm² s⁻¹, respectively. Three different spherical injection volumes, with diameters d = 2, 100, 200 μm, were used. The radii ratio stabilizes faster for a small injection.

FIGURE 3

Estimation of the DAR from simulations: radii ratio method versus method. Several elliptical injections with R_major/R_minor equal to 2.00, 1.22, 1.00, and 0.5 at t = 0 s were simulated and analyzed. It took >150 s to obtain the value of DAR with radii ratio method. By contrast, the method (inset) can quantify the DAR at any time point after the injection from as few as two subsequent images (in practice, the whole series is analyzed). See text for details.

FIGURE 4

Diffusion of AF in agarose gel and ML of isolated turtle cerebellum. (a) Sequence of images taken after the injection of AF in agarose gel (scale bar 100 μm). The first image taken shortly after the injection is labeled as t = 0 s here and elsewhere. (b) Sequence of images taken in the ML (scale bar 100 μm). Extracted elliptical contours are shown below the images. (c) Fluorescence intensity profiles (black) extracted at t = 30 s along major and minor axes are superimposed with theoretical curves (blue, major; red, minor). (d) Theoretical curves obtained along major and minor axes at times as in panel b are shown superimposed to emphasize the differences in the shape between major and minor axes. (e) After a spherical injection, the DAR estimate gradually increased and stabilized at ∼ 20 s in anisotropic ML (circles). In isotropic dilute agarose gel, the DAR estimate remained <1.1 (triangles). (f) The values of and were estimated from the γ²/4 versus time curves. In anisotropic ML, the values of and were 24.5 × 10⁻⁷ cm² s⁻¹ and 16.7 × 10⁻⁷ cm² s⁻¹, respectively, at 25°C. In isotropic dilute agarose gel, the values of (43.3 × 10⁻⁷ cm² s⁻¹) and (41.4 × 10⁻⁷ cm² s⁻¹) obtained at 25°C were similar as indicated by overlapping γ²/4 versus time curves (crosses, data; lines, linear regression).

FIGURE 5

Anisotropic diffusion of dextran polymers in ML of isolated turtle cerebellum. Images and intensity profiles (green) superimposed with theoretical curves (orange) for dex75 (a) and dex525 (b) are shown (scale bar 100 μm). (c) The γ²/4 versus time curves (circles, dex75; crosses, dex525; lines, linear regression) yielded and values 1.39 × 10⁻⁷ cm² s⁻¹ and 0.88 × 10⁻⁷ cm² s⁻¹, respectively, for dex75 at 25.5°C, and 0.14 × 10⁻⁷ cm² s⁻¹ and 0.08 × 10⁻⁷ cm² s⁻¹, respectively, for dex525 at 24°C. Linear regression lines for dex75 are steeper indicating higher values of and For dex525, data obtained for t < 200 s (dashed vertical line) show nonlinearity and were excluded from the analysis.

FIGURE 6

Summary of DAR values measured with AF and dextran polymers. The DAR for a group of dex75, dex282, and dex525 is significantly larger (asterisks) than for AF and dex3 (see text for details). Dotted line shows the plateau at DAR = 1.78.

FIGURE 7

Application of scaling theory to the experimental data. Diffusion coefficients of AF and dextran polymers are plotted as a function of molecular weight in agarose gel (solid line) and the ML of isolated turtle cerebellum (dashed line, major axis; dotted line, minor axis). Scaling exponents are shown. In the agarose gel, scaling exponent obtained for all molecules agrees with Zimm's prediction. In the ML, diffusion of AF, dex3, and dex75 in the ML also is consistent with Zimm's prediction. In contrast, diffusion behavior of two largest dextran polymers (dex282 and dex525) is consistent with a reptation regime. The intersections of two different regimes estimate the average size of ECS at 31 nm (see text for details).