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* Departments of Medicine and Physiology and
Neurological Surgery, University of California, San Francisco, California, USA; and
Academic Neurosurgery Unit, St. George’s University of London, Tooting, London, UK
2Correspondence: 1246 Health Sciences East Tower, University of California, San Francisco, CA 94143-0521, USA. E-mail: alan.verkman{at}ucsf.edu
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Key Words: central nervous system • aquaporin 4
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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20% of brain parenchymal volume. The ECS consists of a jelly-like matrix in which neurons, glia, and blood vessels are embedded. Diffusion of small and macromolecule size solutes in the ECS is important for nonsynaptic cell-cell communication, delivery of drugs to cells, elimination of substrates, and extracellular buffering of ions such as K+ and glutamate (1
2
3
4)
. Diffusion in the ECS is altered in a number of central nervous system (CNS) pathologic conditions, such as brain edema, glial scarring, brain tumors, and ischemia (5
6
7)
. ECS volume is thought to change dynamically with neuronal stimulation as occurs during seizure activity and spreading depression.
Most data on diffusion in brain ECS comes from the tetramethylammonium (TMA+) method, which involves pulsed iontophoretic introduction of TMA+ and microelectrode detection of decreasing [TMA+] as it diffuses away from the injection site (8)
. However, this method is largely restricted to measurements in brain slices and provides information only about the diffusion of TMA+ rather than of more biologically relevant molecules. In addition, computation of TMA+ diffusion in the ECS requires complex mathematical deconvolution to account for the nonzero TMA+ permeation into cells (3
, 4)
. To overcome these limitations we developed a cortical surface photobleaching method in which the ECS is stained with membrane-impermeant fluorescent dyes for diffusion measurement by fluorescence recovery after photobleaching (6
, 7
, 9)
. A modification of this approach, which we called "elliptical photobleaching," involves surface illumination and bleaching with an elliptical spot produced by cylindrical optics (9)
. Elliptical photobleaching was applied to measure anisotropic diffusion along white matter tracts in spinal cord to resolve the contributions of ECS geometry vs. extracellular matrix in slowing macromolecular diffusion.
A significant limitation of surface photobleaching methods is the relatively shallow penetration depth of light in tissues, precluding diffusion measurements beyond 150 µm in solid tissues such as brain. We recently developed a microfiberoptic epifluorescence photobleaching (MFEP) method that overcomes this limited light penetration (10)
. Our approach involves introduction, deep in living tissues, of a multimode optical fiber with a tapered shaft and micron-size tip diameter. Fluorescence recovery is measured after the bleaching of a small volume near the tip of the fiberoptic. The use of MFEP for diffusion measurements deep in solid tissues was validated by diffusion measurements in solutions and gels, and modeled to deduce diffusion coefficients from fluorescence recovery data. Using MFEP we reported remarkable slowing of macromolecule diffusion beyond 100–200 µm depth in solid tumors, suggesting a much greater diffusive barrier for drug delivery deep into tumors than previously thought. Here, we report further technical modifications of MFEP involving dual-lumen fluorescent dye introduction and diffusion measurements of fluorescently-labeled macromolecules deep in the brain of living mice.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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in a CD1 genetic background. Protocols were approved by the University of California, San Francisco Committee on Animal Research.
Construction of dual-lumen microfiberoptic
Single, multimode optical fibers, consisting of a 62.5-µm diameter core, were purchased from ThorLaboratories (Newton, NJ, USA). After the distal 4 cm of their cladding was stripped, each fiber was chemically etched by immersion of the fiber tip for 10 min at the interface of 48% aqueous hydrofluoric acid and xylene (Sigma-Aldrich Corp., St. Louis, MO, USA). The fiber tip was then rinsed with distilled water and dried, and the process was repeated several times to create a tapered fiber shaft with a 2- to 5-µm diameter tip, as visualized using a Leica DM 4000B microscope. A very thin coating (10 nm) of aluminum was deposited by rotary sputtering (Evaporated Coatings Inc., Willow Grove, PA, USA) over a length of 7 mm from the tip, excluding the tip itself.
To achieve efficient and standardized dye delivery in deep brain structures, a double-lumen micropipette was fabricated using borosilicate glass microcapillaries. For dye introduction, a single-barrel microcapillary without filament (inner diameter/outer diameter 0.75 mm/1 mm;FHC Inc., Bowdoin, ME, USA) was pulled on a vertical pipette puller (David Kopf Instruments Inc., Tujunga, CA, USA) to a 5-µm diameter tip and a bend of 60° was created 5 mm from the tip (Fig. 1
A). A second pulled microcapillary was created as a guide for the optical fiber. The guide consisted of a 3-mm-long glass microcapillary with tip diameter 100 µm to allow the microfiber to pass freely through the lumen. The dye-introducing and fiber-guide microcapillaries were immobilized with glue on a small glass platform, with the tip of the guide microcapillary positioned 2–2.5 mm proximal to the tip of the dye-introducing microcapillary. This distance was selected to prevent contact of the guide microcapillary with the brain surface to avoid fluid uptake by capillary action.
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Instrumentation for microfiberoptic photobleaching
Bleaching was done using an epifluorescence apparatus as described previously (12)
, with modifications. The first-order beam of an argon ion laser (1 W at 488 nm) was diffracted by an acousto-optic modulator and focused using an x20 objective lens (numerical aperture, 0.25; Zeiss air) onto the back of the optical fiber that contained an FC-type connector (Fig. 1B
). Bleaching was accomplished by increasing laser illumination intensity 3000- to 6000-fold for 0.1–20 ms to reduce fluorescence by 30–40%. The low intensity of the probe beam used for acquisition produced <1% fluorophore bleaching for continuous recordings up to 5 s. Sample fluorescence collected by the optical fiber and objective lens was filtered (490 nm dichroic mirror, 510 nm long-pass filter), detected by a photomultiplier, amplified, and digitized at 14-bit resolution. Fluorescence was sampled continuously over 200 ms before the bleach pulse, at rates of up to 100 Hz for 5 s after bleaching, and at up to 4 Hz (shutter opened for 20 ms per acquisition) for longer times.
Microfiberoptic photobleaching measurements in mouse brain
Mice were anesthetized by i.p. injection of Avertin (2,2,2-tribromoethanol, 125 mg/kg) and immobilized in a mouse stereotactic frame (MyNeuroLab, St. Louis, MO, USA). Additional Avertin was administered as needed to maintain anesthesia. Core temperature was maintained at 37–38°C using a feedback-controlled rectal probe and heating pad. In some experiments water intoxication was produced by i.p. injection of water (10% body weight) together with 1-deamino-8-D-arginine vasopressin (0.4 µg/kg). The skull surface was exposed by a midline scalp incision, and the skin was retracted. In some experiments the temporal muscle was secured with suture to minimize motion artifact from muscle contraction. The intact cortical dura and underlying brain surface were exposed with great care by a craniectomy using a Foredom micromotor drill (MyNeuroLab) with a 1-mm diameter burr and microsurgical instrumentation. The site of the craniectomy was marked using stereotactic coordinates of the brain region to be studied, according to the Paxinos mouse brain map (13)
. The mouse brain in stereotactic coordinates consists of frontal cortex (bregma +1 mm), parietal cortex (bregma –2.06 mm), caudate nucleus (bregma +0 mm), hippocampus (bregma –2.46 mm), and thalamic nucleus (bregma –2.46 mm), with all sites centered 1.2–1.4 mm lateral to midline. In most experiments two overlapping 1-mm diameter burr holes were created to give an approximately rectangular 1.5- x 1-mm space for insertion of the double-barrel microcapillary. In experiments involving topical dye application, a larger, 5-mm diameter craniectomy was made to expose a larger area of dura for dye penetration.
For photobleaching measurements, the tip of the dye-introducing microcapillary of the dual-microcapillary device was inserted gradually into the brain to specified stereotactic coordinates under positive injection pressure to produce a fluid infusion rate of 0.15 µl/min. The site of insertion was specified with high precision using the micropositioning system of the stereotactic frame, taking into account the dimensions of the dual-lumen microcapillary. Artificial cerebrospinal fluid (aCSF) (145 mM NaCl, 4 mM KCl, 1 mM MgCl2, 2.5 mM CaCl2, 1 mM KH2PO4, and 10 mM glucose; pH 7.4) containing FITC-dextran (70 or 500 kDa; 50 mg/ml) or calcein (40 mg/ml) was infused intraparenchymally at a rate of 0.15 µl/min for 15 min using a Hamilton syringe and infusion pump. Measurements were done 20 min or more after dye infusion to allow for fluorescent dye penetration into the brain tissue surrounding the injection site. The optical fiber was mounted on an independent, micron-resolution micromanipulator (World Precision Instruments Inc., Sarasota, FL, USA) for insertion to specified depths (accuracy 5 µm) through the guide microcapillary. After removal of the bone flap, the dura was irrigated continuously with aCSF warmed to 37°C, and body temperature was maintained at 37–38°C. In some control experiments, FITC-dextran was applied topically as described previously (6)
.
Diffusion measurements in solutions and gels
Microfiberoptic photobleaching measurements were made in solutions consisting of aCSF containing 70 kDa FITC-dextran. Measurements were also performed in aCSF-glycerol solutions (0–50% w/v glycerol) and in gelatin gels (2–60 mg/ml gelatin). The microfiber tip was inserted 400 µm into a 200 µl volume of solutions/gels in microcuvettes.
Analysis of microfiberoptic photobleaching data
Recovery curves generally contained a "fast" acquisition (500 data points over 5000 ms) followed by a "slow" acquisition (20–160 data points over 10–80 s, illumination shuttered between collections). At each location, three to nine photobleaching recovery measurements were made, with the fiber tip displaced 5–10 µm in depth to avoid repeat measurements at the exact same location. Each set of three to nine curves from one location was averaged for curve fitting. For most experiments fluorescence recovery data, F(t), were fitted to the equation (14)
: F(t) = (F0 + [R(F – F0) + F0](t/t1/2))[1 + (1/t1/2)]–1, where F is the prebleach fluorescence, F0 is the fluorescence immediately after bleaching, R is the mobile fraction (percentage recovery), and t1/2 is the half-time for recovery. This equation was found empirically to provide a very close fit to the data for determination of t1/2 as the single parameter describing the kinetics of fluorescence recovery. The relative diffusion coefficient in aCSF vs. brain (Do/D) was computed from t1/2 measured in brain vs. aCSF: Do/D = t1/2brain/t1/2aCSF. Determination of Do/D is thus comparative and model/geometry-independent.
Mathematical modeling of diffusion in the ECS
The brain ECS was modeled by construction of a two-dimensional assembly of Voronoi cells in which an ECS for diffusion was created by shrinkage of cellular elements (details provided in Supplemental Material). Positions of seed points were determined by Gaussian-distributed random displacements from an initial uniform distribution. Diffusion in the resultant ECS was simulated as a random walk process. Point particles were placed initially at random positions in the ECS. At each time step, x and y displacements were sampled from normal distributions with zero mean and SD (2Do
t)1/2, where the t is the time interval between successive frames. Trajectories were taken as independent, without particle-particle interactions. Diffusion coefficient and time step were 0.01 µm2/s and 0.01 s, respectively, and the number of total steps was >20,000. For each simulation condition, >350 trajectories were created. The simulation domain size was 10 x 10 µm, and the ECS area fraction was set to 0.14, which corresponds to 20% volume fraction in three dimensions. Simulations were written in Matlab 7.2 (Mathworks Inc. (Natick, MA, USA) and run on a PC. Solute diffusion coefficients were deduced from trajectories by mean-squared displacement analysis. Nonzero molecular size of the diffusing species was modeled by virtual expansion of cells to restrict the accessible x,y coordinates of diffusing molecules and thus simplify the problem of a diffusing molecule of finite size to diffusion of a point-like particle in an ECS of modified dimensions.
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RESULTS |
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A shows fluorescence recovery curves after microfiberoptic photobleaching of aqueous FITC-dextran (70 kDa) made viscous with different concentrations of glycerol. As expected, the fluorescence recovery was slowed with increasing solution viscosity. Recovery curves fitted closely to the semiempirical equation given in the Materials and Methods section with fitted parameter t1/2, the apparent half-time for fluorescence recovery, which is inversely proportional to the diffusion coefficient. FITC-dextran diffusion was slowed 4.5-fold at 50% (vol) glycerol, in agreement with its relative solution viscosity of 4.6.
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Figure 2B
shows fluorescence recovery with the microfiberoptic inserted into gelatin gels of increasing concentration to simulate brain tissue. FITC-dextran was introduced into the gels using the double-lumen device. The microfiberoptic was inserted at a depth of 400 µm in the gels, equivalent to central brain cortex. Recovery curves again fitted well to a single-component diffusion model with 100% fluorescence recovery, with reduced recovery rates (t1/2–1) (Fig. 2B
, inset) with increasing gelatin concentration. FITC-dextran diffusion in saline vs. gels (Do/D) was 4 at a gelatin concentration of 20 mg/ml, similar to the slowing found in brain cortex (see following section). In control studies, fluorescence recovery did not depend on the depth of insertion of the optical fiber (200–800 µm).
FITC-dextran diffusion in brain cortex
Initial experiments using the double-lumen device were done in cerebral cortex. At an insertion depth of 400 µm, fluorescence recovery data fitted well to a single-component diffusion model with Do/D 4.2 and 98% fluorescence recovery (Fig. 2C
). The 4-fold slowing of FITC-dextran diffusion in brain cortex is comparable to our previous data of 3-fold slowing obtained by cortical surface photobleaching (6)
. The lower fold-slowing as measured by surface photobleaching may be related to the relatively higher abundance of white matter tracts in the superficial layers of the cortex. In a control study to exclude the effects of fluid infusion from the double-lumen device, diffusion was compared after loading brain ECS with FITC-dextran using the infusion method vs. topical dye application and diffusion across the intact dura. Do/D measured at a depth of 400 µm did not differ significantly with the two loading methods (Fig. 2D
).
Diffusion was also compared in cortex of wild-type mice vs. mice lacking AQP4, a glial water channel that has been implicated in brain edema, neural signal transduction, and glial cell migration (15)
. Previous cortical surface photobleaching studies showed enhanced diffusion in superficial layers of the cortex in AQP4 null mice (6)
; here we tested whether this difference persists deeper in cortex. Representative original recovery curves are shown in Fig. 3
A and fitted results are summarized in Fig. 3B
. In each case data fitted well to a single-component diffusion model with near 100% fluorescence recovery and depth-independent Do/D. In agreement with the results of Binder et al. (6)
, diffusion was significantly more rapid at all depths in brain cortex in AQP4 null vs. wild-type mice (P<0.001).
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Figure 3C
shows the area of fluorescent dye staining after loading by infusion and a 15-min incubation. As seen by fluorescence imaging of freshly cut brain, the dye was distributed more than 1500 µm away from the infusion site. After dye equilibration, differences in dye distribution could be seen in the various brain regions. However, differences in dye concentration do not affect diffusion measurements because fluorescence recovery after photobleaching is strictly independent of dye concentration.
Molecular diffusion in deep brain structures
As shown in Fig. 4
A, diffusion of 70-kDa FITC-dextran was compared in cerebral cortex, caudate nucleus, hippocampus, and thalamus. FITC-dextran diffusion was also measured in CSF by insertion of the microfiberoptic into the third ventricle. Original recovery data are shown in Fig. 4B
, and Do/D data are summarized in Fig. 4C
. Diffusion in frontal and parietal cortex was slowed 4-fold compared with diffusion in solution, in agreement with prior measurements using comparable size dyes by cortical surface photobleaching (6
, 7)
and integrative optical imaging (16)
. FITC-dextran diffusion in hippocampus was slowed 3.5-fold in the stratum radiatum (depth 1.1 mm) and 5.2-fold in the stratum pyramidale (depth 1.2 mm). The latter result is in accord with the real time iontophoresis studies of McBain et al. (17)
, who reported tortuosity of 1.67–1.83 in the pyramidal layer of hippocampus, higher than values in cerebral cortex (1.51–1.54). In the stratum radiatum of the hippocampus, other studies showed enhanced diffusion relative to cerebral cortex (18
, 19)
, in agreement with the data here. Interestingly, FITC-dextran diffusion was slowed to an even greater extent in the caudate nucleus (7.1-fold) and thalamus (7.4-fold).
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Prior data have shown significant differences in wild-type vs. AQP4 null mice in their response to effectors of brain swelling (20
, 21)
. Figure 4D
shows slowed FITC-dextran diffusion in brain cortex as well as in deep brain structures after hyponatremia produced by acute water intoxication (10% body weight, i.p.), a well-established model of cytotoxic brain edema. Water intoxication caused progressive slowing of FITC-dextran diffusion in the brain cortex of wild-type mice, with less slowing seen in AQP4 null mice. Remarkably, there was 12-fold slowing of FITC-dextran diffusion 10 min after water intoxication at a depth of 400 µm in cortex of wild-type mice, whereas in AQP4 null mice diffusion did not show significant changes. Water intoxication had a reduced effect on ECS diffusion in the hippocampus and caudate nucleus of wild-type mice compared with cortex, and, as found in cortex, in AQP4 null mice water intoxication had little effect on diffusion in hippocampus and caudate nucleus.
Size-dependent solute diffusion in deep brain structures
To investigate the unexpected observation of greater slowing of 70-kDa FITC-dextran in caudate nucleus and thalamus compared with cortex, we compared diffusion of fluorescent probes of different molecular sizes (Fig. 5
A), reasoning that differences in ECS geometry might be manifest as size-dependent diffusion (see Mathematical Model of Molecular Diffusion in Brain ECS section below). The small polar solute calcein (hydrodynamic radius rH 1.4 nm) had similar Do/D in caudate nucleus (3.7±0.8), thalamus (3.9±0.2), and cortex (3.8±0.5) (tortuosities summarized in Fig. 5B
). In contrast, the larger 70 kDa FITC-dextran (rH8 nm) showed significantly slowed diffusion in caudate nucleus (Do/D=7.1±1.6) and thalamus (Do/D=7.4±0.3) compared with cortex (Do/D=4.3±0.2). Remarkably greater regional differences were found for a larger FITC-dextran of molecular size 500 kDa (rH15 nm), with D0/D of 36 ± 6 in caudate nucleus and 34 ± 5 in thalamus, compared with 6.5 ± 0.9 in cortex.
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Mathematical model of molecular diffusion in brain ECS
We developed a mathematical model to account for the unexpected size-dependent molecular diffusion in deep brain structures but not in brain cortex. The brain ECS was generated from Voronoi cell diagrams using cell shrinkage algorithms (see Materials and Methods section and Supplemental Data). We tested two ECS models: 1) "nonheterometric" ECS, in which apposing cell edges were parallel (Fig. 6
A, left), and 2) "heterometric" ECS, in which apposing cell edges were not parallel (Fig. 6A
, right). Other modeling parameters including ECS area fraction (0.14) and cell number (100) were the same for both simulations. Figure 6B
shows an example of a computed particle trajectory as it diffuses through the ECS by a random walk process. Although our experimental data involve three-dimensional (3D) diffusion, we used a simplified two-dimensional model, as has been done previously (see Discussion section), and because modeling of 3D diffusion with any realistic cell geometry is computationally impractical. Also, it has been argued that the major semiquantitative features of ECS modeling should be similar in 2 vs. 3 dimensions (22)
.
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Experimentally measured tortuosity (
exp) is the product of tortuosities from viscous (v) and geometric (g) components, the latter being determined by the model. v was taken as 1.4 from elliptical photobleaching measurements (9)
. Using model parameters specified in the legend to Fig. 6B
for the ECS geometry in Fig. 6A
, g was 1.3–1.4, which is in good agreement with the experimentally measured geometric tortuosity of 1.4. Figure 6C
shows predicted g for the parallel and nonparallel models, as a function of diffusing particle size, along with experimental g. Geometric tortuosity increased greatly with increasing particle size in the case of the nonparallel ECS model as applied to deep brain but was largely unchanged for the parallel ECS as applied to brain cortex, in close agreement with experimental data. The schematic diagrams at the right in Fig. 6C
explain this finding qualitatively. Because a nonzero size particle cannot pass through a gap narrower than its diameter, a nonparallel ECS model predicts a relatively strong dependence of diffusion on particle size. A new hindrance factor produced by nonparallel ECS spacing is thus introduced, which we call "heterometricity." The parallel ECS is termed as a nonheterometric arrangement and the nonparallel ECS as heterometric.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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A central goal of this study was to characterize ECS diffusion in deeper regions of brain in vivo than could be accessed previously. The substantially slowed diffusion of a medium-sized (70 kDa) dextran in caudate nucleus and thalamus contrasts with prior TMA+ measurements showing similar tortuosities of 1.51–1.54 in cortex and neostriatum (23
, 24)
. In agreement with the TMA+ data, we found that diffusion of the small fluorophore calcein, of size similar to TMA+, was comparably slowed in cerebral cortex, thalamus, and caudate nucleus, suggesting that diffusion in the basal ganglia is strongly dependent on the molecular size of the diffusing species. In support of this hypothesis was the finding of greatly reduced diffusion of 500-kDa FITC-dextran in the same deep brain structures, with relatively minor slowing in cortex.
As mentioned in the Results section, the experimentally measured tortuosity of the extracellular space (exp) contains geometric (g) and viscous (v) components. Whereas possible differences in matrix composition in different parts of the brain might account, in part, for the relative slowing of diffusion in deep vs. superficial brain (25
, 26)
, differences in geometry rather than matrix viscosity are likely to account for the size-dependent molecular diffusion in deep brain structures vs. cortex. Size-dependent macromolecular diffusion cannot be conferred without distinct geometric organization, as shown by in vitro studies in which diffusion was measured in solutions containing soluble crowding agents vs. actin matrices (27)
. Also, although the reasoning is somewhat indirect, it has been argued from crowding agent effects that extracellular matrix components have relatively little effect on diffusion (28
, 29)
.
ECS dimensions are clearly major determinants of tortuosity (30
, 31)
; however, available imaging methods are not adequate to provide useful information about the small dimensions of the ECS. Electron microscopy is associated with significant perfusion and fixation artifacts that preclude meaningful preservation of ECS dimensions (18
, 32)
. Cell organization is another determinant of ECS diffusion (30
, 31)
, but despite prominent differences in the cytoarchitecture of the cerebral cortex, experiments show similar diffusion properties in each layer (33
, 34)
. Therefore, measurements of diffusion and mathematical modeling of diffusion data are needed for functional mapping of ECS properties and for deducing the geometric determinants of diffusion.
Prior models have been developed to relate diffusion in the ECS to the geometric organization of the cellular elements in the brain (35
, 36)
. The simplest 3D geometric models with uniformly spaced cubes representing cellular elements yielded of 1.19 (35)
, substantially lower than the experimentally determined of 1.6 or greater. The introduction of elements with more complicated geometry, such as truncated octagonal, rhombicuboctahedral, and tetrahedral geometries, did not increase the predicted further (31)
. Attempting to account for this discrepancy, Rusakov and Kullmann (37)
introduced a role for viscosity in diffusion hindrance as well as a factor retarding the diffusion of large solutes assuming a porous model of the ECS. Another model postulated dead-space microdomains as evenly spaced square cavities in all brain cells (22)
; however, the model required 40% of the ECS to comprise such hypothetical cavities to increase model to that found experimentally; also, the physical nature of such cavities was not defined (36)
. In a more recent 3D model both regular and random arrangements of fluid vesicles were used to model ECS (38)
in an effort to approximate the diverse geometries of nervous cells. Again, these simulations yielded smaller tortuosity values compared with experimental results. The aim of our ECS was also to incorporate more realistic cell shapes, and for the first time we introduced the idea of heterogeneity in ECS dimensions, as well as modeling of size-dependent diffusion. Heterometricity provided a basis for what could be regarded as a size cutoff for diffusing macromolecules. Although the anatomical structures responsible for heterometricity cannot be deduced by electron microscopy, candidate structures include the close approximation of cell membranes at synaptic clefts and at sites of intercellular gap junctions, as well as differences in density of synapses in the deep brain nuclei compared with cerebral cortex. Recent structural data suggested the involvement of AQP4 in cell-cell adhesion (39)
, providing one possible explanation that might contribute to the relative ECS expansion in AQP4 deficiency.
Our results show more rapid diffusion in brain ECS in AQP4 deficiency, indicating relative ECS expansion, as well as regional differences in macromolecular diffusion, particularly for large macromolecules. Newborn rats have an expanded ECS compared with adult rats, which decreases over the first 3 wk of life (33)
as brain AQP4 expression increases to adult levels (40)
. Functionally, diffusion in the ECS is important in ionic buffering, diffusion of nutrients and drugs, and extrasynaptic cell-cell communication. The relative ECS expansion in AQP4 deficiency could account, in part, for the increased seizure threshold and duration in AQP4 null mice (41)
, as well as the impaired reuptake of K+ after neuroexcitation (42)
. An expanded ECS is predicted to slow changes in ECS K+ concentration in response to K+ transport between the intracellular space and the ECS. At this time, the functional significance of regional variations in size-dependent ECS diffusion remains to be established.
In summary, we developed a novel approach to measure macromolecular diffusion in deep brain structures that were previously inaccessible for recordings in vivo. We also introduced a mathematical model that accounted quantitatively for effects of ECS geometry on macromolecular diffusion in deep brain structures. An unexpected slowing of large macromolecules in the thalamus and caudate nucleus led us to propose a novel geometric factor, heterometricity, defined as heterogeneity in ECS dimensions, which substantially hinders macromolecular diffusion in a size-dependent manner.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Received for publication July 26, 2007. Accepted for publication September 20, 2007.
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