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Key points Extracellular space (ECS) rapid volume pulsation (RVP) accompanying epileptiform activity is described for the first time. Such RVP occurs robustly in several in vitro and in vivo mouse models of epileptiform activity. In the in vitro 4-aminopyridine model of epileptiform activity, RVP depends on the activity of the electrogenic Na+ /HCO3 - cotransporter (NBCe1). NBCe1 pharmacological inhibition suppresses RVP and epileptiform activity. Inhibition of changes in ECS volume may represent a useful target in epilepsy patients who are resistant to current treatments. Abstract The extracellular space (ECS) of the brain shrinks persistently by approximately 35% during epileptic seizures. Here we report the discovery of rapid volume pulsation (RVP), further transient drops in ECS volume which accompany events of epileptiform activity. These transient ECS contractions were observed in multiple mouse models of epileptiform activity both in vivo (Bicuculline Methiodide model) and in vitro (Hyaluronan synthase 3 knock-out, Picrotoxin, Bicuculline, and 4-Aminopyridine models). By using the probe transients quantification (PTQ) method we show that individual pulses of RVP shrank the ECS by almost 15% in vivo. In the 4-Aminopyridine in vitro model, the individual pulses of RVP shrank the ECS by more than 4%, and these transient changes were superimposed on a persistent ECS shrinkage of 36% measured with the real-time iontophoretic method. In this in vitro model, we investigated several channels and transporters that may be required for the generation of RVP and epileptiform activity. Pharmacological blockages of Na+ /K+ /2Cl- cotransporter type 1 (NKCC1), K+ /Cl- cotransporter (KCC2), the water channel Aquaporin-4 (AQP4) and inwardly-rectifying potassium channel 4.1 (Kir4.1) were ineffective in halting the RVP and the epileptiform activity. In contrast, pharmacological blockade of the electrogenic Na+ /HCO3 - cotransporter (NBCe1) by 4,4'-diisothiocyano-2,2'-stilbenedisulfonic acid (DIDS) eliminated both the RVP and the persistent ECS shrinkage. Importantly, this blocker also stopped the epileptiform activity. These results demonstrate that RVP is closely associated with epileptiform activity across several models of epileptiform activity and therefore the underlying mechanism could potentially represent a novel target for epilepsy management and treatment. This article is protected by copyright. All rights reserved.

Brain extracellular space is the narrow microenvironment that surrounds every cell of the central nervous system. It contains a solution that closely resembles cerebrospinal fluid with the addition of extracellular matrix molecules. The space provides a reservoir for ions essential to the electrical activity of neurons and forms an intercellular chemical communication channel. Attempts to reveal the size and structure of the extracellular space using electron microscopy have had limited success; however, a biophysical approach based on diffusion of selected probe molecules has proved useful. A point-source paradigm, realized in the real-time iontophoresis method using tetramethylammonium, as well as earlier radiotracer methods, have shown that the extracellular space occupies ∼20% of brain tissue and small molecules have an effective diffusion coefficient that is two-fifths that in a free solution. Monte Carlo modeling indicates that geometrical constraints, including dead-space microdomains, contribute to the hindrance to diffusion. Imaging the spread of macromolecules shows them increasingly hindered as a function of size and suggests that the gaps between cells are predominantly ∼40 nm with wider local expansions that may represent dead-spaces. Diffusion measurements also characterize interactions of ions and proteins with the chondroitin and heparan sulfate components of the extracellular matrix; however, the many roles of the matrix are only starting to become apparent. The existence and magnitude of bulk flow and the so-called glymphatic system are topics of current interest and controversy. The extracellular space is an exciting area for research that will be propelled by emerging technologies.

Diet influences dopamine transmission in motor- and reward-related basal ganglia circuitry. In part, this reflects diet-dependent regulation of circulating and brain insulin levels. Activation of striatal insulin receptors amplifies axonal dopamine release in brain slices, and regulates food preference in vivo. The effect of insulin on dopamine release is indirect, and requires striatal cholinergic interneurons that express insulin receptors. However, insulin also acts directly on dopamine axons to increase dopamine uptake by promoting dopamine transporter (DAT) surface expression, counteracting enhanced dopamine release. Here we determined the functional consequences of acute insulin exposure and chronic diet-induced changes in insulin on DAT activity after evoked dopamine release in striatal slices from adult ad-libitum fed (AL) rats and mice, and food-restricted (FR) or high-fat/high-sugar obesogenic (OB) diet rats. Uptake kinetics were assessed by fitting evoked dopamine transients to the Michaelis-Menten equation and extracting C(peak) and V(max). Insulin (30 nM) increased both parameters in the caudate putamen and nucleus accumbens core of AL rats in an insulin receptor- and PI3-kinase-dependent manner. A pure effect of insulin on uptake was unmasked using mice lacking striatal acetylcholine, in which increased V(max) caused a decrease in C(peak). Diet also influenced V(max), which was lower in FR versus AL. The effects of insulin on C(peak) and V(max) were amplified by FR but blunted by OB, consistent with opposite consequences of these diets on insulin levels and insulin receptor sensitivity. Overall, these data reveal acute and chronic effects of insulin and diet on dopamine release and uptake that will influence brain reward pathways.

This review describes the basic concepts and protocol to perform the real-time iontophoresis (RTI) method, the gold-standard to explore and quantify the extracellular space (ECS) of the living brain. The ECS surrounds all brain cells and contains both interstitial fluid and extracellular matrix. The transport of many substances required for brain activity, including neurotransmitters, hormones, and nutrients, occurs by diffusion through the ECS. Changes in the volume and geometry of this space occur during normal brain processes, like sleep, and pathological conditions, like ischemia. However, the structure and regulation of brain ECS, particularly in diseased states, remains largely unexplored. The RTI method measures two physical parameters of living brain: volume fraction and tortuosity. Volume fraction is the proportion of tissue volume occupied by ECS. Tortuosity is a measure of the relative hindrance a substance encounters when diffusing through a brain region as compared to a medium with no obstructions. In RTI, an inert molecule is pulsed from a source microelectrode into the brain ECS. As molecules diffuse away from this source, the changing concentration of the ion is measured over time using an ion-selective microelectrode positioned roughly 100 µm away. From the resulting diffusion curve, both volume fraction and tortuosity can be calculated. This technique has been used in brain slices from multiple species (including humans) and in vivo to study acute and chronic changes to ECS. Unlike other methods, RTI can be used to examine both reversible and irreversible changes to the brain ECS in real time.

The concentration of extracellular calcium plays a critical role in synaptic transmission and neuronal excitability as well as other physiological processes. The time course and extent of local fluctuations in the concentration of this ion largely depend on its effective diffusion coefficient (D*) and it has been speculated that fixed negative charges on chondroitin sulphate proteoglycans (CSPGs) and other components of the extracellular matrix may influence calcium diffusion because it is a divalent cation. In this study we used ion-selective microelectrodes combined with pressure ejection or iontophoresis of ions from a micropipette to quantify diffusion characteristics of neocortex and hippocampus in rat brain slices. We show that D* for calcium is less than the value predicted from the behaviour of the monovalent cation tetramethylammonium (TMA), a commonly used diffusion probe, but D* for calcium increases in both brain regions after the slices are treated with chondroitinase ABC, an enzyme that predominantly cleaves chondroitin sulphate glycans. These results suggest that CSPGs do play a role in determining the local diffusion properties of calcium in brain tissue, most likely through electrostatic interactions mediating rapid equilibrium binding. In contrast, chondroitinase ABC does not affect either the TMA diffusion or the extracellular volume fraction, indicating that the enzyme does not alter the structure of the extracellular space and that the diffusion of small monovalent cations is not affected by CSPGs in the normal brain ionic milieu. Both calcium and CSPGs are known to have many distinct roles in brain physiology, including brain repair, and our study suggests they may be functionally coupled through calcium diffusion properties.

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding, or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix, and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is approximately 20% and the tortuosity is approximately 1.6 (i.e., free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge, and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases, and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties is valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain.

Brain diffusion properties are at present most commonly evaluated by magnetic resonance (MR) diffusion imaging. MR cannot easily distinguish between the extracellular and intracellular signal components, but the older technique of real-time iontophoresis (RTI) detects exclusively extracellular diffusion. Interpretation of the MR results would therefore benefit from auxiliary RTI measurements. This requires a molecular probe detectable by both techniques. Our aim was to specify a minimum set of requirements that such a diffusion probe should fulfill and apply it to two candidate probes: the cation tetramethylammonium (TMA+), used routinely in the RTI experiments, and the anion hexafluoroantimonate ( SbF 6 − ). Desirable characteristics of a molecular diffusion probe include predictable diffusion properties, stability, minimum interaction with cellular physiology, very slow penetration into the cells, and sufficiently strong and selective MR and RTI signals. These properties were evaluated using preparations of rat neocortical slices under normal and ischemic conditions, as well as solutions and agarose gel. While both molecules can be detected by MR and RTI, neither proved an ideal candidate. TMA+ was very stable but it penetrated into the cells and accumulated there within tens of minutes. SbF 6 − did not enter the cells as readily but it was not stable, particularly in ischemic tissue and at higher temperatures. Its presence also resulted in a decreased extracellular volume. These probe properties help to interpret previously published MR data on TMA+ diffusion and might play a role in other diffusion experiments obtained with them.

Aquaporin-4 (AQP4) is the major water channel expressed at fluid–tissue barriers throughout the brain and plays a crucial role in cerebral water balance. To assess whether these channels influence brain extracellular space (ECS) under resting physiological conditions, we used the established real-time iontophoresis method with tetramethylammonium (TMA+) to measure three diffusion parameters: ECS volume fraction (α), tortuosity (λ), and TMA+loss (k′).In vivomeasurements were performed in the somatosensory cortex of AQP4-deficient (AQP4−/−) mice and wild-type controls with matched age. Mice lacking AQP4 showed a 28% increase in α (0.23 ± 0.007 vs 0.18 ± 0.003) with no differences in λ (1.62 ± 0.04 vs 1.61 ± 0.02) andk′(0.0045 ± 0.0001 vs 0.0031 ± 0.0009 s−1). Additional recordings in brain slices showed similarly elevated α in AQP4−/−mice, and no differences in λ andk′between the two genotypes. This is the first direct comparison of ECS properties in adult mice lacking AQP4 water channels with wild-type animals and demonstrates a significant enlargement of the volume fraction but no difference in hindrance to TMA+diffusion, expressed as tortuosity. These findings provide direct evidence for involvement of AQP4 in modulation of the ECS volume fraction and provide a basis for future modeling of water and ion transport in the CNS.

Epidermal growth factor (EGF) stimulates proliferation, process outgrowth, and survival in the CNS. Understanding the actions of EGF necessitates characterizing its distribution in brain tissue following drug delivery or release from cellular sources. We used the integrative optical imaging (IOI) method to measure diffusion of fluorescently labeled EGF (6,600 Mr; 4 μg/ml) in the presence of excess unlabeled EGF (90 μg/ml) to compete off specific receptor binding and reveal the “true” EGF diffusion coefficient following injection in rat brain slices (400 μm). The effective diffusion coefficient was 5.18 ± 0.16 × 10−7(SE) cm2/s ( n = 22) in rat somatosensory cortex and the free diffusion coefficient, determined in dilute agarose gel, was 16.6 ± 0.12 × 10−7cm2/s ( n = 27). Tortuosity (λ), a parameter representing the hindrance imposed on EGF by the convoluted brain extracellular space (ECS), was 1.8, the lowest yet measured by IOI for a protein in brain. Control experiments with fluorescent dextran of similar molecular weight and tetramethylammonium confirmed EGF did not affect local ECS structure. We conclude that transport of smaller growth factors such as EGF through brain ECS is less hindered than that of larger proteins (>10,000 Mr, e.g., nerve growth factor) where typically λ > 2.1. Modeling was used to predict that low λ will allow EGF sources in the brain to be further from target cells and still elicit a biological response. High λ values for larger growth factors imply more constrained local biological effects than with smaller proteins such as EGF.

A new method was developed to extract diffusion parameters in brain tissue using a sinusoidal iontophoretic point source of tetramethylammonium operated at different frequencies. The resulting steady state oscillating extracellular concentration of this probe molecule was continuously monitored using an ion-selective microelectrode located about 100 microm from the source. Because the probe molecules must diffuse through the extracellular space (ECS), the oscillating concentration at the recording location will develop a phase lag and an amplitude attenuation relative to the sinusoidal source. These two components of the signal can be analyzed to determine the tortuosity factor lambda and the ECS volume fraction alpha. The method also measures the nonspecific clearance rate constant kappa. In brain slices this reflects washout of diffusing molecules. Values of alpha (0.18+/-0.05) and lambda (1.67+/-0.08) obtained from this frequency method in rat cortical slices were similar to those obtained by the real-time iontophoretic method employing a square pulse source. The relative merits of the frequency method compared to the pulse method are discussed.

Dual-probe microdialysis was used to study interstitial diffusion in the rat brain. A radiolabelled tracer, (3H]mannitol, was continuously infused at different concentrations via a probe acutely implanted into the striatum of an anaesthetized male rat or into a dilute agar gel. Samples were collected by a second probe placed 1 mm away from the first, and the recovered [3H]mannitol was measured by liquid scintillation counting. In the striatum, the delivery of [3H]mannitol was counteracted by its removal from the extracellular space by passive uptake into cells and clearance into the microcirculation, causing the diffusion profile to approach quasi steady-state levels within 2 h. Diffusion data from brain and agar were analysed using a mathematical model. The apparent (effective) diffusion coefficient for [3H]mannitol was D* = 2.9 x 10(-6) cm2/s, the effective volume fraction alpha* = 0.30 and the clearance rate constant kappa= 2.3 x 10(-5)/s. A tortuosity, lambda = 1.81, and penetration distance r = 4.2 mm, were calculated. We conclude that, using dual-probe microdialysis, parameters reflecting geometric and dynamic tissue properties may be obtained using appropriate mathematical analysis. Quantitative dual-probe microdialysis will be valuable in characterizing interstitial diffusion and the clearance processes underpinning volume transmission in the brain.

In this paper, we further develop the general theory of microdialysis by extending the linear model of Bungay et al. to provide a theoretical basis for in vitro and in vivo microdialysis. Specifically, we considered the effect of active clearance processes on in vivo microdialysis, and thereby elaborated the theory of Benveniste et al. to endogenous compounds. We examined the use of steady state tissue diffusion resistance with negligible clearance processes to interpret microdialysis data. The influence of the tissue properties on the in vitro and in vivo recoveries in dual-probe microdialysis was analyzed and we simulated the effect of the operating parameters on dual probe microdialysis performance. We estimated that the minimum clearance rate constant detectable by microdialysis in a quasi-steady state is about 5.5 × 10−5 s−1. This minimum rate constant establishes a criterion, below which inhibition of the active clearance processes does not show detectable influences on the microdialysis extraction efficiency.

Water compartmentalization was studied in a thick-slice (1000 μm) model of ischemia by combining water-content measurements with extracellular diffusion analysis. Thick slices bathed in artificial cerebrospinal fluid continually gained water. Total tissue water content was increased by 67% after 6 hours of the incubation. Diffusion measurements using the tetramethylammonium method showed that the extracellular space, typically occupying 20% of brain tissue in vivo, was decreased to 10% at 30 minutes and 15% at 6 hours in both deep and superficial layers of thick slices. Quantification of water compartmentalization revealed that water moved initially from the extracellular space into the cells. Later, however, both compartments gained water. The initial cell swelling was accompanied by dramatic shifts in potassium. An initial rise of extracellular potassium to about 50 mmol/L was measured with a potassium-selective microelectrode positioned in the center of the thick slice; the concentration decreased slowly afterwards. Potassium content analysis revealed a 63% loss of tissue potassium within two hours of the incubation. In thick slices, ionic shifts, water redistribution, and a loss of synaptic transmission occur in both deep and superficial layers, indicating the spread of ischemic conditions even to areas with an unrestricted supply of nutrients.

It has long been assumed that one important mechanism for the dissipation of local potassium gradients in the brain extracellular space is the so-called spatial buffer, generally associated with glial cells. To date, however, there has been no analytical description of the characteristic patterns of K+ clearance mediated by such a mechanism. This study reanalyzed a mathematical model of Gardner-Medwin (1983, J. Physiol. (Lond.). 335:393–426) that had previously been solved numerically. Under suitable approximations, the transient solutions for the potassium concentrations and the corresponding membrane potentials of glial cells in a finite, parallel domain were derived. The analytic results were substantiated by numerical simulations of a detailed two-compartment model. This simulation explored the dependence of spatial buffer current and extracellular K+ on the distribution of inward rectifier K+ channels in the glial endfoot and nonendfoot membranes, the glial geometric length, and the effect of passive KCl uptake. Regarding the glial cells as an equivalent leaky cable, the analyses indicated that a maximum endfoot current occurs when the glial geometric length is equal to the corresponding electrotonic space constant. Consequently, a long glial process is unsuitable for spatial buffering, unless the axial space constant can match the length of the process. Finally, this study discussed whether the spatial buffer mechanism is able to efficiently transport K+ over distances of more than several glial space constants.

The initiation of focal interictal epileptiform activity (FIEA) has been shown to depend on the activation of a sufficiently large volume of brain tissue. We estimated the size of this 'critical volume' for the convulsant pentylenetetrazol (PTZ) by analyzing the diffusion following its microinjection into rat motor cortex. PTZ concentration was monitored 100-200 microm away from the injection site with a PTZ-sensitive microelectrode. Diffusion analysis in 0.3% agar yielded the free diffusion coefficient D (8.50 +/- 0.15 X 10(-6) cm2 x s(-1) at 37 degrees C, median +/- S.E.M.). In brain tissue, diffusion was modified by extracellular volume fraction (alpha), tortuosity (lambda = (D/ADC)1/2; ADC = apparent diffusion coefficient) and non-specific uptake (k'). Using a value of 0.2 for alpha from previous studies, we found values of lambda = 1.61 +/- 0.01, k' = 3.37 +/- 0.15 X 10(-3) s(-1) and an injected volume U of 5.16 +/- 0.45 X 10(-10) l for pulses without FIEA, and lambda = 1.95 +/- 0.06, k' = 6.24 +/- 1.73 X 10(-3) s(-1) and U = 7.40 +/- 0.66 X 10(-10) l for pulses with FIEA. From the calculated concentration distribution of PTZ during FIEA we estimated a threshold concentration of about 1.77 mM PTZ and a volume with a radius of about 219 microm in which this concentration had to be exceeded. Since this critical volume was comparable in size to foci elicited by penicillin or electric stimuli in previous studies, it is concluded that it is determined by intrinsic tissue properties rather than by the convulsive agent being used.

1. An in vitro slice model of ischemia was used to study changes in extracellular potassium concentration and diffusion properties in the stratum pyramidale of CA1 and CA3 regions of the hippocampus and in the cortex of the rat. Slices were submerged in artificial cerebrospinal fluid, and ischemia was induced by removing oxygen and glucose until anoxic depolarization occurred. 2. Extracellular potassium concentration was measured with a valinomycin-based ion-selective microelectrode. The bathing medium contained 5 mM potassium, and in vitro ischemia caused the potassium concentration to rise to 45 mM in CA1, 12 mM in CA3, and 32 mM in cortex. 3. Extracellular volume fraction and tortuosity were determined during normoxic conditions and in vitro ischemia by measuring the diffusion of tetramethylammonium. This cation was iontophoretically released into the extracellular space and its concentration as a function of time determined with an ion-selective microelectrode approximately 100 microns away from the source. 4. During normoxia the volume fraction was 0.14, 0.20, and 0.18, and tortuosity was 1.50, 1.57, and 1.62 in CA1, CA3, and cortex, respectively. These data confirm that the volume fraction of CA1 is smaller than in the two other regions. 5. During ischemia the volume fraction decreased to 0.05, 0.17, and 0.09 in CA1, CA3, and cortex, respectively. Only in CA3 did the tortuosity change significantly by increasing to 1.75. Because of limitations in the time resolution of the diffusion method, the changes in volume fraction and tortuosity during the anoxic depolarization phase of ischemia may have been underestimated.(ABSTRACT TRUNCATED AT 250 WORDS)

This paper describes the theory of an integrative optical imaging system and its application to the analysis of the diffusion of 3-, 10-, 40-, and 70-kDa fluorescent dextran molecules in agarose gel and brain extracellular microenvironment. The method uses a precisely defined source of fluorescent molecules pressure ejected from a micropipette, and a detailed theory of the intensity contributions from out-of-focus molecules in a three-dimensional medium to a two-dimensional image. Dextrans tagged with either tetramethylrhodamine or Texas Red were ejected into 0.3% agarose gel or rat cortical slices maintained in a perfused chamber at 34 degrees C and imaged using a compound epifluorescent microscope with a 10 x water-immersion objective. About 20 images were taken at 2-10-s intervals, recorded with a cooled CCD camera, then transferred to a 486 PC for quantitative analysis. The diffusion coefficient in agarose gel, D, and the apparent diffusion coefficient, D*, in brain tissue were determined by fitting an integral expression relating the measured two-dimensional image intensity to the theoretical three-dimensional dextran concentration. The measurements in dilute agarose gel provided a reference value of D and validated the method. Values of the tortuosity, lambda = (D/D*)1/2, for the 3- and 10-kDa dextrans were 1.70 and 1.63, respectively, which were consistent with previous values derived from tetramethylammonium measurements in cortex. Tortuosities for the 40- and 70-kDa dextrans had significantly larger values of 2.16 and 2.25, respectively. This suggests that the extracellular space may have local constrictions that hinder the diffusion of molecules above a critical size that lies in the range of many neurotrophic compounds.

The diffusion of valproate (VPA) and trans -2-en-valproate were studied in agar gel and in the cerebral cortex of the rat using pressure microejection and VPA-selective microelectrodes. From the agar measurements a free diffusion coefficient for VPA of6.52×10 −6 cm 2 ·s −1 and for trans -2-en-VPA of5.25×10 −6 cm 2 ·s −1 for 37°C was determined. The tortuosity value in the cortex was 1.92 for VPA and 1.67 for trans -2-en-VPA. The tortuosity values suggest that VPA and trans -2-en-VPA diffuse mainly in the extracellular space of the brain.

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."

Extracellular space volume fraction, tortuosity and nonspecific uptake of tetramethylammonium--three diffusion parameters of brain tissue--were measured in gray matter of the somatosensory neocortex and subcortical white matter of the rat during postnatal development. The three parameters were determined from concentration-time profiles of tetramethylammonium in postnatal days 2-120 in vivo. Tetramethylammonium concentration was measured with ion-selective microelectrodes positioned 130-200 microns from an iontophoretic source. Data were correlated with cytoarchitectonic structure and average thickness of the regions in 0-90-day-old rats using rapidly frozen tissue. Extracellular space volume fraction was largest in the newborn rats and diminished with age. In two-to three-day-old animals, volume fraction (mean +/- S.E.) was 0.36 +/- 0.04 in layers III and IV, 0.38 +/- 0.02 in layer V, 0.41 +/- 0.01 in layer VI and 0.46 +/- 0.01 in white matter. The earliest decrease in volume fraction was found in layers V and VI at postnatal days 6-7 followed by a decrease in layer III and IV at postnatal days 8-9 and in white matter at postnatal days 10-11. A further dramatic reduction in volume fraction occurred in all cortical layers and especially in the white matter between postnatal days 10 and 21. There was no further decrease in volume fraction between postnatal day 21 and adults (90-120 days old). The adult volume fraction values were: layer II, 0.19 +/- 0.002; III, 0.20 +/- 0.004; IV, 0.21 +/- 0.003; V, 0.22 +/- 0.003; VI, 0.23 +/- 0.007; white matter, 0.20 +/- 0.008. Values of tortuosity ranged between 1.51 and 1.65, nonspecific cellular uptake varied from 3.3 x 10(-3)/s to 6.3 x 10(-3)/s. The variations in each parameter were not statistically significant at any age. These data represent the first characterization of diffusion parameters in a developing brain. They confirm previous histological indications of a relatively large extracellular volume fraction during early postnatal development. The constancy of the tortuosity shows that diffusion of small molecules is no more hindered in the developing brain than in the adult. The large extracellular space volume fraction of the neonatal brain could significantly dilute ions, metabolites and neuroactive substances released from cells, relative to release in adults, and may be a factor in preventing anoxia, seizure and spreading depression in young animals. The diffusion characteristics could also play an important role in the developmental process itself.

Dopamine reaches targets in the outer retina of the clawed frog (Xenopus laevis) by diffusion from a network of dopaminergic cells and processes located predominantly at the junction of inner nuclear and inner plexiform layers. We obtained values for the steady-state release, uptake, and extracellular concentration of dopamine in the retina by a combination of HPLC (with electrochemical detection), scintillation spectroscopy, and fast-scan cyclic voltammetry. Vitreal concentrations of dopamine varied from 564 +/- 109 nM in light-adapted eyes near the time of subjective dawn to 156 +/- 12 nM in dark-adapted eyes. The data are consistent with a simple model for steady-state dopamine diffusion from an appropriately sited thin-sheet source. This model was used to generate a profile of extracellular dopamine concentration as a function of retinal depth. The model predicted an increase in the dopamine concentration from the vitreous to the layer of dopaminergic cells, remaining constant from that layer to the distal tips of the photoreceptors. This prediction was borne out by comparing fast-scan voltammetric measures of dopamine at the distal tips of the receptors with the vitreal concentrations determined by HPLC using electrochemical detection.

An external electric field applied parallel to longitudinal axis of neurons selectively depolarizes either end and thereby activates voltage-sensitive conductance changes in a large population of neurons. Here, we characterized such population responses in the in vitro turtle cerebellum. The responses were recorded and analyzed using a multimodal approach: the magnetic evoked field was measured using a Superconducting Quantum Interference Device (SQUID) magnetometer, and concurrently the electric field potentials were recorded. Laminar profile and current-source density analysis were used to uncover the pattern of activation due to the applied electric field. Intracellular recording provided further information for identifying the elements producing the observed responses. Finally, pharmacological manipulations confirmed the nature of the conductance changes. Our results show that it is possible to activate a defined cell population of the cerebellum by an applied field and obtain a magnetic response of the order of 0.5–2 pT. A field applied from the dorsal to the ventral side of cerebellum produced tetrodotoxin-sensitive population spikes. This component was followed by a kynurenic acid (KYNA)-sensitive postsynaptic response, most likely comprised of Ca(2+)-mediated action potentials occurring at the proximal pole of the Purkinje cell dendrites and evoked by climbing fiber inputs. The applied electric field directed from the ventral to the dorsal side of cerebellum gave rise to a complex of responses that was made up of a KYNA-sensitive component (presumably synaptically activated) and an Mn(2+)-sensitive but KYNA-insensitive component (probably due to a directly activated calcium conductance change). This study provides insights into the effects of electric and magnetic fields applied to the nervous tissue of experimental animal and human studies.

1. Diffusion properties of submerged, superfused slices from the rat neostriatum were measured by quantitative analysis of concentration-time profiles of tetramethylammonium (TMA+) introduced by iontophoresis. TMA+ was sensed at an ion-selective microelectrode (ISM) positioned 100-150 microns from the source pipette. Slice viability was assessed from the extracellular field potentials evoked by intrastriatal electrical stimulation. 2. Under normoxic conditions the extracellular volume fraction (alpha) was 0.21 (range 0.18-0.24), and the tortuosity (lambda) was 1.54, in slices with good field potentials. In slices with poor field potentials, alpha was 0.09-0.16. Extraction of correct alpha and lambda in the slice required evaluation of nonspecific uptake, k', which was 1 x 10(-2) s-1. 3. Slices were made hypoxic by superfusing physiological saline equilibrated with 95% N2-5% CO2 for 10-30 min. Synaptic components of field potentials were inhibited after 3-4 min in hypoxic media. In some experiments extracellular K+ concentration [( K+]o) was monitored with ISMs. During hypoxia, [K+]o rose from an average baseline of 5.1 mM to 7-10 mM. After reoxygenation, [K+]o transiently fell below the original level. 4. The average value for alpha during hypoxia was 0.13 (a 38% decrease), which was significantly different from control (P less than 0.001) and increased progressively during hypoxic exposure. In contrast, tortuosity and k' were unchanged by this treatment. 5. These data represent the first characterization of the diffusion properties of the rat striatal slice and of changes in extracellular volume fraction during hypoxia in a brain slice preparation.(ABSTRACT TRUNCATED AT 250 WORDS)

The intercellular spaces between neurons and glia contain an amorphous, negatively charged extracellular matrix (ECM) with the potential to shape and regulate the distribution of many diffusing ions, proteins and drugs. However, little evidence exists for direct regulation of extracellular diffusion by the ECM in living tissue. Here, we demonstrate macromolecule sequestration by an ECM component in vivo , using quantitative diffusion measurements from integrative optical imaging. Diffusion measurements in free solution, supported by confocal imaging and binding assays with cultured cells, were used to characterize the properties of a fluorescently labeled protein, lactoferrin (Lf), and its association with heparin and heparan sulfate in vitro. In vivo diffusion measurements were then performed through an open cranial window over rat somatosensory cortex to measure effective diffusion coefficients ( D *) under different conditions, revealing that D * for Lf was reduced ≈60% by binding to heparan sulfate proteoglycans, a prominent component of the ECM and cell surfaces in brain. Finally, we describe a method for quantifying heparan sulfate binding site density from data for Lf and the structurally similar protein transferrin, allowing us to predict a low micromolar concentration of these binding sites in neocortex, the first estimate in living tissue. Our results have significance for many tissues, because heparan sulfate is synthesized by almost every type of cell in the body. Quantifying ECM effects on diffusion will also aid in the modeling and design of drug delivery strategies for growth factors and viral vectors, some of which are likely to interact with heparan sulfate.

Diffusion within the extracellular space (ECS) of the brain is necessary for chemical signaling and for neurons and glia to access nutrients and therapeutics; however, the width of the ECS in living tissue remains unknown. We used integrative optical imaging to show that dextrans and water-soluble quantum dots with Stokes–Einstein diameters as large as 35 nm diffuse within the ECS of adult rat neocortex in vivo . Modeling the ECS as fluid-filled “pores” predicts a normal width of 38–64 nm, at least 2-fold greater than estimates from EM of fixed tissue. ECS width falls below 10 nm after terminal ischemia, a likely explanation for the small ECS visualized in electron micrographs. Our results will improve modeling of neurotransmitter spread after spillover and ectopic release and establish size limits for diffusion of drug delivery vectors such as viruses, liposomes, and nanoparticles in brain ECS.

During ischemia, the transport of molecules in the extracellular space (ECS) is obstructed in comparison with healthy brain tissue, but the cause is unknown. Extracellular tortuosity (λ), normally 1.6, increases to 1.9 in ischemic thick brain slices (1000 μm), but drops to 1.5 when 70,000Mrdextran (dex70) is added to the tissue as a background macromolecule. We hypothesized that the ischemic increase in λ arises from diffusion delays in newly formed dead-space microdomains of the ECS. Accordingly, λ decreases when dead-space diffusion is eliminated by trapping dex70 in these microdomains. We tested our hypothesis by analyzing the diffusion of several molecules in neocortical slices. First we showed that diffusion of fluorescent dex70 in thick slices declined over time, indicating the entrapment of background macromolecules. Next, we measured diffusion of tetramethylammonium (TMA+) (74Mr) to show that the reduction of λ depended on the size of the background macromolecule. The synthetic polymer, 40,000Mrpolyvinylpyrrolidone, reduced λ in thick slices, whereas 10,000Mrdextran did not. The dex70 was also effective in normoxic slices (400 μm) after hypoosmotic stress altered the ECS to mimic ischemia. Finally, the dex70 effect was confirmed independently of TMA+using fluorescent 3000Mrdextran as a diffusion marker in thick slices: λ decreased from 3.29 to 2.44. Taken together, these data support our hypothesis and offer a novel explanation for the origin of the large λ observed in ischemic brain. A semiquantitative model of dead-space diffusion corroborates this new interpretation of λ

Spreading depression (SD) and ischemia are different pathophysiological events but have similar characteristics. This study investigated whether similarity exists in the light scattering (LS) properties during SD and ischemia in rat neocortical slices. SD was induced by injection of K+ while ischemia was simulated by removing oxygen and glucose. LS was simultaneously recorded with changes in extracellular direct current (DC) potential and extracellular space (ECS) volume. LS was measured using a photon counting fiber optic system and the ECS volume change was determined by measuring the ECS concentration of tetramethylammonium (TMA+). Slices maintained in normal artificial cerebrospinal fluid (ACSF) showed a consistent LS increase during SD, but exhibited two different LS behaviors during 6 min of ischemia. In eight slices, LS decreased and remained so until the end of the ischemic challenge. In another 10 slices, LS diminished initially but, after 2 min, suddenly reversed sign, accompanied by a rapid negative shift in extracellular DC potential. When 50 or 91% of Cl− in the ACSF was replaced by membrane-permeable propionate, LS retained its increase during SD, but always showed the sudden LS reversal during ischemia. In contrast, when Cl− was substituted with membrane-impermeant methylsulfate, the SD-induced LS increase was replaced by an LS decrease, and the sudden LS reversal during ischemia was absent. While the LS signal showed different characteristics during SD and ischemia, the DC potential always presented negative shifts and the ECS volume always exhibited similar decreases. These results suggest that the polarity of the LS signal is determined by the competition of at least two factors: cell swelling and anion influx.

Somatodendritic release of dopamine (DA) in midbrain is, at least in part, nonsynaptic; moreover, midbrain DA receptors are predominantly extrasynaptic. Thus somatodendritic DA mediates volume transmission, with an efficacy regulated by the diffusion and uptake characteristics of the local extracellular microenvironment. Here, we quantitatively evaluated diffusion and uptake in substantia nigra pars compacta (SNc) and reticulata (SNr), ventral tegmental area (VTA), and cerebral cortex in guinea pig brain slices. The geometric parameters that govern diffusion, extracellular volume fraction (α) and tortuosity (λ), together with linear uptake ( k′), were determined for tetramethylammonium (TMA+), and for DA, using point-source diffusion combined with ion-selective and carbon-fiber microelectrodes. TMA+-diffusion measurements revealed a large α of 30% in SNc, SNr, and VTA, which was significantly higher than the 22% in cortex. Values for λ and k′ for TMA+ were similar among regions. Point-source DA-diffusion curves fitted theory well with linear uptake, with significantly higher values of k′ for DA in SNc and VTA (0.08–0.09 s− 1) than in SNr (0.006 s− 1), where DA processes are sparser. Inhibition of DA uptake by GBR-12909 caused a greater decrease in k′ in SNc than in VTA. In addition, DA uptake was slightly decreased by the norepinephrine transport inhibitor, desipramine in both regions, although this was statistically significant only in VTA. We used these data to model the radius of influence of DA in midbrain. Simulated release from a 20-vesicle point source produced DA concentrations sufficient for receptor activation up to 20 μm away with a DA half-life at this distance of several hundred milliseconds. Most importantly, this model showed that diffusion rather than uptake was the most important determinant of DA time course in midbrain, which contrasts strikingly with the striatum where uptake dominates. The issues considered here, while specific for DA in midbrain, illustrate fundamental biophysical properties relevant for all extracellular communication.

An unexpected decrease of extracellular space (ECS) tortuosity was recently reported in thick (1000 μm) ischemic slices using radiotracers. The current study shows that the tortuosity in thick slices from rat neocortex can increase or decrease depending on experimental conditions, whereas ECS volume fraction remains diminished to approximately 10%. Using diffusion of tetramethylammonium, it was found that tortuosity rose from a normoxic value of 1.66 to 1.99 in thick slices. However, tortuosity dropped to 1.54 when dextran (70,000 molecular weight) was added to the bathing medium. The current results show that dextran enhances diffusion in thick ischemic slices without increasing the size of the ECS.

Volume transmission depends on the migration of informational substances through brain extracellular space (ECS) and almost always involves diffusion; basic concepts of diffusion are outlined from both the microscopic viewpoint based on random walks and the macroscopic viewpoint based on the solution of equations embodying Fick's Laws. In a complex medium like the brain, diffusing molecules are constrained by the local volume fraction of the ECS and tortuosity, a measure of the hindrance imposed by cellular obstacles. Molecules can also experience varying degrees of uptake or clearance. Bulk flow and the extracellular matrix may also play a role. Examples of recent work on diffusion of tetramethylammonium (molecular weight, 74) in brain slices, using iontophoretic application and ion-selective microelectrodes, are reviewed. In slices, the volume fraction is about 20% and tortuosity about 1.6, both similar to values found in the intact brain. Using integrative optical imaging, results obtained with dextrans and albumins up to a molecular weight of 70,000 are summarized, for such large molecules the tortuosity is about 2.3. Experiments using synthetic long-chain PHPMA polymers up to 1,000,000 molecular weight show that these molecules also diffuse in the ECS but with a tortuosity of about 1.6. Studies with osmotic challenge show that volume fraction and tortuosity do not vary together as expected when the size of the ECS changes; a model is presented that explains the osmotic-challenge on the basis of changes in cell shape. Finally, new analytical insights are provided into the complex movement of potassium in the brain.

The structure of brain extracellular space resembles foam. Diffusing molecules execute random movements that cause their collision with membranes and affect their concentration distribution. By measuring this distribution, the volume fraction (alpha) and the tortuosity (lambda) can be estimated. The volume fraction indicates the relative amount of extracellular space and tortuosity is a measure of hindrance of cellular obstructions. Diffusion measurements with molecules500 Mr show that alpha approximately 0.2 and lambda approximately 1.6, although some brain regions are anisotropic. Moleculesor =3000 Mr show more hindrance, but molecules of 70000 Mr can move through the extracellular space. During stimulation, and in pathophysiological states, alpha and lambda change, for example in severe ischemia alpha = 0.04 and lambda = 2.2. These data support the feasibility of extrasynaptic or volume transmission in the extracellular space.

The apparent diffusion coefficient, D*, was measured in rat cortical slices and compared to the free diffusion coefficient, D, for three negatively charged proteins, lactalbumin (mol. wt = 14,500), ovalbumin (45,000) and bovine serum albumin (66,000). The temporal evolution of the spatial distribution of albumin molecules labeled with the Texas Red fluorophore was determined using integrative optical imaging at intervals after a brief pressure injection from a micropipette in slices of adult rat cerebral cortex and dilute agarose gel. Diffusion coefficients were obtained by fitting appropriate equations to the data. In slices at 34 degrees C, the values of D* (10(-7) cm2/s, mean +/- S.E.M.) for lactalbumin, ovalbumin and bovine serum albumin were 2.37 +/- 0.10, 1.60 +/- 0.08 and 1.63 +/- 0.07, respectively. In agarose gel, values of D (10(-7) cm2/s) were 11.87 +/- 0.20, 10.02 +/- 0.25 and 8.29 +/- 0.17, respectively. From these data the tortuosity factors, (D/D*)0.5, were calculated, with 2.24 obtained for lactalbumin, 2.50 for ovalbumin and 2.26 for bovine serum albumin. Previous optical measurements using dextrans with mol. wts of 40,000 and 70,000 gave tortuosities of 2.16 and 2.25, but in contrast previous determinations with ion-selective microelectrodes using the small cation tetramethylammonium (mol. wt = 74.1) give tortuosities of about 1.6. The results show that proteins as large as bovine serum albumin diffuse through brain extracellular space but are more hindered than smaller molecules. A simple model compared the differences in diffusion properties of bovine serum albumin, dopamine and nitric oxide in brain tissue and discussed the implications for volume transmission of chemical information between cells. The results are also relevant to the behavior of diffusible factors in brain development and the delivery of therapeutic agents.

1. Water compartmentalization in the turtle cerebellum subject to media of different osmolalities was quantified by combining extracellular diffusion analysis with wet weight and dry weight measurements. The diffusion analysis also determined the tortuosity of the extracellular space. 2. Isolated cerebella were immersed in normal, oxygenated physiological saline (302 mosmol kg-1), hypotonic saline (238 mosmol kg-1) and a series of hypertonic salines (up to 668 mosmol kg-1). The osmolality was varied by altering the NaCl content. 3. Extracellular volume fraction and tortuosity of the granular layer of the cerebellum were determined from measurements of ionophoretically induced diffusion profiles of tetramethylammonium, using ion-selective microelectrodes. The volume fraction was 0.22 in normal saline, 0.12 in hypotonic medium and 0.60 in the most hypertonic medium. Tortuosity was 1.70 in the normal saline, 1.79 in the hypotonic and 1.50 in the most hypertonic saline. 4. The water content, defined as (wet weight-dry weight)/wet weight, of a typical isolated cerebellum (including granular, Purkinje cell and molecular layers) was 82.9%. It increased to 85.2% in hypotonic saline and decreased to 80.1% in the most hypertonic saline. 5. Measurements of extracellular volume fraction and water content were combined to show that hypotonic solutions caused water to move from the extracellular to the intracellular compartment while hypertonic solutions caused water to move from the intracellular to extracellular compartment, with only a relatively small changes in total water in both cases. 6. These results suggest the use of the isolated turtle cerebellum as a model system for studying light scattering or diffusion-weighted magnetic resonance imaging.

Ca2+ diffusion in brain extracellular space (ECS) regulates local Ca2+ concentration and influences synaptic transmission and neuronal excitability. Ca2+ diffusion is controlled by ECS geometry and extracellular matrix, a major component of which is chondroitin sulfate (CS). Previous experiments (Hrabetova et al., J. Physiol. 2009, 587:4029) show that Ca2+ movement is reduced when interacting with CS, however the process still obeys the diffusion equation. This implies that Ca2+-CS interaction can be modeled as a fast equilibrium bimolecular reaction (FEBR; Nicholson et al. Comput. Visual Sci., 2012, 10.1007/s00791-012-0185-9). The FEBR would provide an alternative to solving the Poisson-Boltzmann equation for electrostatic interactions between negatively charged CS and mobile cations.Our objectives were 1) to test whether the FEBR model describes previous experimental data, 2) if so, to determine the dissociation constant Kd, (ratio between backward and forward rate constants), 3) to explore the effect of background Ca2+ and/or Na+ on Ca2+ diffusion and 4) use a Monte Carlo simulator (MCell; www.mcell.org) to verify results.We developed analytical expressions for the Ca2+ effective diffusion coefficient in the presence of CS and compared results to experimental data with different background Ca2+ and CS concentrations (Magdelenat et al., Biopolymers, 1974, 13:1535; Maroudas et al., Biophys. Chem., 1988, 32:257). This validated the FEBR approach and provided estimates of Kd (0.01 to 0.1 mM) in agreement with literature data. Kd values were resolved into forward and backward rate constants using the Damkohler formula and the results further tested with MCell. Finally, we extended the work to include additional background Na+.We conclude that the FEBR model captures the main features of Ca2+ diffusion in CS matrix and can be extended to interactions involving multiple cations. Supported by NIH/NINDS grant R01-NS-28642.

Texas Red-labelled dextran with a mol. wt of 3000 g mol-1, a marker for the extracellular space, was injected unilaterally into the neostriatum of adult rats (0.3-30 micrograms microliter-1) and its distribution evaluated 1 min to 5 h later. Diffusion in the neuropil was observed with clearance starting after 30 min. After 10-15 min strong labelling along the myelinated fibre bundles was observed in the entire neostriatum. After about 20 min the labelling along the fibres reached into the corpus callosum and the overlaying deep layers of the cerebral cortex. A marked cellular uptake and accumulation of labelled dextran was found in putative perivascular pericytes. Thus, in the living brain preferential extracellular fluid pathways for diffusion exist, especially along fibre bundles, which allow the exchange of chemical signals between two distant regions. These may represent extracellular fluid pathways for volume transmission.

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.

1. We determined the origin of the apparent tissue conductivity (sigma 2) of the turtle cerebellum in vitro. 2. Application of a current with a known current density (J) along the longitudinal axis of a conductivity cell produced an electric field in the cerebellum suspended in the cell. The measured electric field (E) perpendicular to the cerebellar surface indicated a significant inhomogeneity in sigma a (= J/E) with a major discontinuity between the molecular layer (0.25 +/- 0.05 S/m, mean +/- SD) and granular layers (0.15 +/- 0.03 S/m) (n = 39). 3. This inhomogeneity was more pronounced after anoxic depolarization. The value of sigma a decreased to 0.11 +/- 0.03 and 0.040 +/- 0.008 S/m in the molecular and granular layers, respectively. The ratio of sigma a S in the two layers increased from 1.67 in the normoxic condition to 2.75 after anoxic depolarization. 4. This difference in sigma a across the two layers was present within the range of frequencies (DC to 10 kHz) studied where the phase of sigma a was small (less than +/- 2 degrees) and therefore sigma a was ohmic. 5. The inhomogeneity in sigma a was in part due to an inhomogeneity in the extracellular conductivity (sigma e) as determined from the extracellular diffusion of ionophoresed tetramethylammonium. Like sigma a, the value of sigma e was also higher in the molecular layer (0.165 S/m) than in the granular layer (0.097 S/m). The inhomogeneity in sigma e was due to a smaller tortuosity and a larger extracellular volume fraction in the molecular layer compared with the granular layer. 6. sigma a was, however, consistently higher, by approximately 50%, than sigma e. A core conductor model of the cerebellum indicated that these discrepancies between sigma a and sigma e were attributable to additional conductivity produced by a passage of the longitudinal applied current through the intracellular space of Purkinje cells and ependymal glial cells, with the glial compartment playing the dominant role. Cells with a long process and a short space constant such as the ependymal glia evidently enhance the effective “extracellular” conductivity by serving as intracellular conduits for the applied current. The result implies that the effective sigma e may be larger than sigma e for neuronally generated currents in the turtle cerebellum because the space constant for Purkinje cells is several times greater than that for the ependymal glia and consequently Purkinje cell-generated currents travel over a long distance relative to the space constant of glial cells.(ABSTRACT TRUNCATED AT 400 WORDS)

Fast-scan cyclic voltammetry with carbon fibre microelectrodes was used to detect endogenous dopamine (DA) and 5-hydroxytryptamine (5-HT) release from three distinct regions of guinea-pig mid-brain in vitro: rostral and caudal substantia nigra (SN) and the ventral tegmental area (VTA). Previous electrophysiological studies have demonstrated that cells of the caudal SN and the VTA have similar characteristics, whereas cells in the rostral SN have distinctly different properties. In the present study, we confirmed that each region has tyrosine hydroxylase-positive neurons and determined, using high-performance liquid chromatography, that DA levels were similar in rostral and caudal SN, but lower in SN than in VTA. In each region, application of veratrine, which was shown by intracellular recordings to have a reversible depolarising action, evoked a signal attributable to DA and distinguishable from that of 5-HT. Release signals were monitored every 250 ms with a spatial resolution of less than 50 microns.l DA release was calcium-dependent and was not detectable in a catecholamine-poor area such as the cerebellum, or in mid-brain tissue pre-treated with reserpine. Within the normal mid-brain, the amount of DA released was correlated with tissue content in that it was higher in the VTA than in either region of SN. It is concluded that DA released from somato-dendritic parts of mid-brain neurons exhibits site-specific variation. This is the first report of direct monitoring of DA and 5-HT release from these regions with in situ electrodes and demonstrates the utility of fast-scan cyclic voltammetry to investigate the mechanisms and possible non-classical functions of somato-dendritic DA release.

A major source of diffusion anisotropy in the central nervous system is the presence of oriented fibers (e. g. corpus callosum; cerbellar molecular layer). The diffusion properties may be explored experimentally using a point-source paradigm based on tetramethylammonium (TMA; Sykova & Nicholson, Physiol. Rev. 2008, 88, 1277). To better understand such results the MCell Monte Carlo program (www.mcell.psc.edu) was used to model diffusion from a point source in bundles of rectangular fibers with extracellular volume fractions (α) ranging from 0.02 - 0.8.The simulation employed 64 rectangular rods each of 0.6 x 0.6 μm in cross-section with surfaces that reflected the particles. Rods were spaced appropriately to obtain the required α and the length of each rod was chosen to make the rods into a cubic ensemble. A population of 250,000 point particles was released into the center of the ensemble with free diffusion coefficient (D) equal to that for TMA and the simulations run with a time-step of 10 ns for 1 ms. These parameters ensured that the particles remained within the ensemble.It was found that the component of the effective diffusion tensor, D∗, aligned with the direction of the bundles was equal to D so the tortuosity (λ = (D/D∗)1/2) was unity in this axis. For the two symmetrical components of D∗ in the orthogonal axes, λ was a function of α that could be accurately describe by an expression derived by Bell & Crank (J. Chem. Soc. Faraday Trans., 2, 1974, 70, 1259). These results are compared to those already obtained for an assembly of cubes (Tao & Nicholson, J. Theoret. Biol. 2004, 229, 59). Supported by NIH/NINDS Grant R01-NS-28642.

The construction and application of liquid-membrane ion-selective microelectrodes (ISM) are described. Recommendations are provided for the selection of appropriate cocktails containing neutral carriers to form the liquid membrane to sense K+, Ca2+, H+ and Na+. The use of charged carriers to sense Cl- and the cation tetramethylammonium (TMA+) is discussed. A detailed protocol is given for constructing double-barreled electrodes (ion-sensor and reference barrel) with tips of 1 micron diameter or more for extracellular ion measurements. The primary results obtained with ISMs in the brain cell microenvironment are briefly surveyed. The theoretical basis for measuring diffusion properties of extracellular space is described. Such measurements enable the estimation of volume fraction (proportion of tissue that is extracellular space) and tortuosity (hindrance of diffusion due to cellular obstructions). A method is given for using TMA+ ISMs in combination with iontophoresis or pressure ejection of TMA+ from a nearby micropipette to measure diffusion properties.

In the context of this paper we shall discuss methods of measuring the diffusion of small molecules through the extracellular space of the brain. The study of such diffusion properties has relevance to the transport of metabolites, the spread of neuromodulators and the application of drugs to the brain. The extracellular space (ECS) is a component of the brain cell microenvironment (Schmitt and Samson 1969, Nicholson 1980, Cserr 1986). The movement of neuromodulators and neuroactive substances through this environment - so-called volume transmission - has been the topic of a recent symposium (Fuxe and Agnati 1991).

The tetramethylammonium (TMA+) method for measuring the volume fraction and tortuosity of brain extracellular space is presented in detail. The temporal and spatial distribution of TMA+ in the extracellular space following iontophoresis or pressure microinjection is described by suitable equations and illustrated with graphs. By fitting the equations to the concentration versus time data obtained from measurements with ion-selective micropipettes, the volume fraction and tortuosity can be measured. In addition, the concentration-dependent uptake of TMA+ can be estimated from the given equations. The final section of the paper derives simple numerical estimates of TMA+ loss from the extracellular space by this mechanism.Key words: extracellular space, volume fraction, tortuosity, uptake, tetramethylammonium.

The tissue volume required to produce a penicillin-induced interictal discharge in the local EEG was estimated. A pair of microelectrodes were lowered into the motor cortex of anaesthetised and artificially ventilated rats. One double-barrelled electrode was used to release tetramethylammonium (TMA+) by iontophoresis or to pressure eject a solution containing penicillin (PEN-) and TMA+ concentration. The extracellular distribution of PEN- was defined using diffusion analysis of the TMA+. From these data the spatial distribution of PEN- was estimated at the times of first interictal spikes in the EEG. The critical mass of active nerve cells was calculated from the threshold concentration of PEN- needed to elicit paroxysmal depolarisation shifts in neocortical slices and found to lie within a tissue sphere with a radius of ca. 150 microns.

1. Regulation of brain extracellular and intracellular water content, regarded as volume, and electrolytes in response to 90 min of hypernatremia has been studied in the cerebral cortex of rats under urethane anaesthetic. 2. Total tissue electrolytes and water were partitioned between extracellular and intracellular compartments based on measurements made in two series of experiments. In one, tissue samples were collected and analysed for total water, Na+, K+ and Cl-. In the other, tissue extracellular volume fraction, [Na+] and [K+] were measured in situ using ion-selective microelectrodes. 3. Osmotically induced water loss from cerebral cortex was less than that predicted for ideal osmotic behaviour, revealing a degree of volume regulation, and this regulation was associated with net tissue uptake of Na+, Cl- and K+. 4. Total water content was 3.77 g H2O (g dry weight)-1 in control cortex and this decreased by 7% after 30 min of hypernatremia and then remained relatively stable at this value. Control extracellular water content, based on an extracellular volume fraction of 0.18, was 0.88 g H2O (g dry weight)-1. Control intracellular water content, estimated as the difference between total and extracellular water contents, was 2.89 g H2O (g dry weight)-1. After 30 min of hypernatremia, extracellular water content decreased by an average of 27% but intracellular water did not change. This indicates selective regulation of cell volume. By 90 min the extracellular water content had decreased by 47% and the loss in extracellular water content appeared to be accompanied by a roughly equivalent increase in intracellular water content. The intracellular volume increase, however, was not statistically significant. The tortuosity of the extracellular space averaged 1.57 and increased to 1.65 during the hypernatremia. 5. Brain extracellular fluid and plasma [Na+] were roughly equal in control tissue. Both increased by 30 mu equiv (g H2O)-1 as a result of the hypernatremia, although extracellular [Na+] lagged behind the plasma value during much of the first 60 min of hypernatremia. Extracellular [K+] was homeostatically regulated at 3 mu equiv (g H2O)-1 independent of changes in plasma electrolytes. 6. Estimates of extracellular and intracellular ion content (mu equiv (g dry weight)-1) indicate that extracellular Na+, Cl- and K+ content decreased during hypernatremia, by 32, 21 and 42% respectively, whereas intracellular ion content increased by 100, 169 and 5% respectively. 7. It is concluded that during acute hypernatremia the extracellular space decreases in volume through the loss of water and electrolytes while the intracellular compartment maintains its water content and gains electrolytes.(ABSTRACT TRUNCATED AT 400 WORDS)

Mung bean plants (Wilczek) accumulate increasingly greater amounts of buffer-extractable copper in both their shoots and roots when grown in liquid medium containing greater than 2 micrograms per milliliter copper (31.4 micromolar) as cupric sulfate. This increase in soluble copper is accompanied by an increase in the relative amount of low molecular weight (7,000 to 20,000) macromolecular-bound copper and a decrease in the relative amount of high molecular weight (greater than 20,000) copper. The major low molecular weight copper protein has been isolated from copper-intoxicated mung bean plants by a combination of ammonium sulfate fractionation, gel filtration, and ion exchange chromatography. It was identified as mung bean plastocyanin on the basis of its molecular weight, optical behavior, and amino acid composition. No evidence was found for a low molecular weight copper-binding protein corresponding to mammalian thionein or chelatin.