Extrasynaptic transmission and the diffusion parameters of the extracellular space

Extrasynaptic volume transmission, mediated by the diffusion of neuroactive substances in the extracellular space (ECS), plays an important role in short- and long-distance communication between nerve cells. The ability of a substance to reach extrasynaptic high-affinity receptors via diffusion depends on the ECS diffusion parameters, ECS volume fraction alpha (alpha=ECS volume/total tissue volume) and tortuosity lambda (lambda2=free/apparent diffusion coefficient), which reflects the presence of diffusion barriers represented by, e.g., fine astrocytic processes or extracellular matrix molecules. These barriers channel the migration of molecules in the ECS, so that diffusion may be facilitated in a certain direction, i.e. anisotropic. The diffusion parameters alpha and lambda differ in various brain regions, and diffusion in the CNS is therefore inhomogeneous. Changes in diffusion parameters have been found in many physiological and pathological states, such as development and aging, neuronal activity, lactation, ischemia, brain injury, degenerative diseases, tumor growth and others, in which cell swelling, glial remodeling and extracellular matrix changes are key factors influencing diffusion. Changes in ECS volume, tortuosity and anisotropy significantly affect the accumulation and diffusion of neuroactive substances and thus extrasynaptic transmission, neuron-glia communication, mediator "spillover" and synaptic crosstalk as well as, cell migration. The various changes occurring during pathological states can be important for diagnosis, drug delivery and treatment.     

A model of effective diffusion and tortuosity in the extracellular space of the brain

Tortuosity of the extracellular space describes hindrance posed to the diffusion process by a geometrically complex medium in comparison to an environment free of any obstacles. Calculating tortuosity in biologically relevant geometries is difficult. Yet this parameter has proved very important for many processes in the brain, ranging from ischemia and osmotic stress to delivery of nutrients and drugs. It is also significant for interpretation of the diffusion-weighted magnetic resonance data. We use a volume-averaging procedure to obtain a general expression for tortuosity in a complex environment. A simple approximation then leads to tortuosity estimates in a number of two-dimensional (2D) and three-dimensional (3D) geometries characterized by narrow pathways between the cellular elements. It also explains the counterintuitive fact of lower diffusion hindrance in a 3D environment. Comparison with Monte Carlo numerical simulations shows that the model gives reasonable tortuosity estimates for a number of regular and randomized 2D and 3D geometries. Importantly, it is shown that addition of dead-end pores increases tortuosity in proportion to the square root of enlarged total extracellular volume fraction. This conclusion is further supported by the previously described tortuosity decrease in ischemic brain slices where dead-end pores were partially occluded by large macromolecules introduced into the extracellular space.     

Extracellular space diffusion and extrasynaptic transmission

The diffusion of neuroactive substances in the extracellular space (ECS) plays an important role in short- and long-distance communication between nerve cells and is the underlying mechanism of extrasynaptic (volume) transmission. The diffusion properties of the ECS are described by three parameters: 1. ECS volume fraction alpha (alpha=ECS volume/total tissue volume), 2. tortuosity lambda (lambda2=free/apparent diffusion coefficient), reflecting the presence of diffusion barriers represented by, e.g., fine neuronal and glial processes or extracellular matrix molecules and 3. nonspecific uptake k'. These diffusion parameters differ in various brain regions, and diffusion in the CNS is therefore inhomogeneous. Moreover, diffusion barriers may channel the migration of molecules in the ECS, so that diffusion is facilitated in a certain direction, i.e. diffusion in certain brain regions is anisotropic. Changes in the diffusion parameters have been found in many physiological and pathological states in which cell swelling, glial remodeling and extracellular matrix changes are key factors influencing diffusion. Changes in ECS volume, tortuosity and anisotropy significantly affect the accumulation and diffusion of neuroactive substances in the CNS and thus extrasynaptic transmission, neuron-glia communication, transmitter "spillover" and synaptic cross-talk as well as cell migration, drug delivery and treatment.     

Determination of Brain Interstitial Concentrations by Microdialysis

Microdialysis is an extensively used technique for the study of solutes in brain interstitial space. The method is based on collection of substances by diffusion across a dialysis membrane positioned in the brain. The outflow concentration reflects the interstitial concentration of the substance of interest, but the relationship between these two entities is at present unclear. So far, most evaluations have been based solely on calibrations in saline. This procedure is misleading, because the ease by which molecules in saline diffuse into the probe is different from that of tissue. We describe here a mathematical analysis of mass transport into the dialysis probe in tissue based on diffusion equations in complex media. The main finding is that diffusion characteristics of a given substance have to be included in the formula. These include the tortuosity factor (lambda) and the extracellular volume fraction (alpha). We have substantiated this by studies in a well-defined complex medium (red blood cell suspensions) as well as in brain. We conclude that the traditional calculation procedure results in interstitial concentrations that are too low by a factor of lambda 2/alpha for a given compound.     

Calcium diffusion in the brain cell microenvironment

A review of some of the literature on Ca2+ diffusion in free media and a variety of nervous tissues is presented. In the majority of tissue studies the apparent diffusion coefficient of Ca2+ is three to nine times smaller than that in a free aqueous medium. The methodology of using pressure microejection and Ca2+ ion-selective microelectrodes to measure Ca2+ diffusion is discussed. Our ongoing studies of Ca2+ diffusion in the cerebral cortex of the rat, using these methods, also confirm that Ca2+ diffusion is mainly influenced by the tortuosity of the tissue rather than other factors such as binding to extracellular charge sites or uptake.     

Diffusion properties of the brain in health and disease

Extrasynaptic transmission between neurons and communication between neurons and glia are mediated by the diffusion of neuroactive substances in the extracellular space (ECS)--volume transmission. Diffusion in the CNS is inhomogeneous and often not uniform in all directions (anisotropic). Ionic changes and amino acid release result in cellular (particularly glial) swelling, compensated for by ECS shrinkage and a decrease in the apparent diffusion coefficients of neuroactive substances or water (ADCW). The diffusion parameters of the CNS in adult mammals (including humans), ECS volume fraction alpha (alpha = ECS volume/total tissue volume; normally 0.20-0.25) and tortuosity lambda (lambda2 = D/ADC; normally 1.5-1.6), hinder the diffusion of neuroactive substances and water. A significant decrease in ECS volume and an increase in diffusion barriers (tortuosity) and anisoptropy have been observed during stimulation, lactation or learning deficits during aging, due to structural changes such as astrogliosis, the re-arrangement of astrocytic processes and a loss of extracellular matrix. Decreases in the apparent diffusion coefficient of tetramethylammonium (ADCTMA) and ADCW due to astrogliosis and increased proteoglycan expression were found in the brain after injury and in grafts of fetal tissue. Tenascin-R and tenascin C-deficient mice also showed significant changes in ADCTMA and ADCW, suggesting an important role for extracellular matrix molecules in ECS diffusion. Changes in ECS volume, tortuosity and anisotropy significantly affect neuron-glia communication, the spatial relation of glial processes towards synapses, the efficacy of glutamate or GABA 'spillover' and synaptic crosstalk, the migration of cells, the action of hormones and the toxic effects of neuroactive substances and can be important for diagnosis, drug delivery and new treatment strategies.     

Contribution of dead-space microdomains to tortuosity of brain extracellular space

The extracellular space (ECS) of the brain is a major channel for intercellular communication, nutrient and metabolite trafficking, and drug delivery. The dominant transport mechanism is diffusion, which is governed by two structural parameters, tortuosity and volume fraction. Tortuosity (lambda) represents the hindrance imposed on the diffusing molecules by the tissue in comparison with an obstacle-free medium, while volume fraction (alpha) is the proportion of tissue volume occupied by the ECS. Diffusion of small ECS markers can be exploited to measure lambda and alpha. In healthy brain tissue, lambda is about 1.6 but increases to 1.9-2.0 in pathologies that involve cellular swelling. Previously it was thought that lambda could be explained by the circumnavigation of diffusing molecules around cells. Numerical models of assemblies of convex cells, however, give an upper limit of about 1.23 for lambda. Therefore, additional factors must be responsible for lambda in brain. In principle, two mechanisms could account for the measured value: a more complex ECS geometry or an extracellular macromolecular matrix. Here we review recent work in ischemic tissue suggesting concave geometrical formations, dead-space microdomains, as a major determinant of extracellular tortuosity. A theoretical model of lambda based on diffusion dwell times supports this hypothesis and predicts that, in ischemia, dead spaces occupy approximately 60% of ECS volume fraction leaving only approximately 40% for well-connected channels. It is further proposed that dead spaces are present in healthy brain tissue where they constitute about 40% of alpha. The presence of dead-space microdomains in the ECS implies microscopic heterogeneity of extracellular channels with fundamental implications for molecular transport in brain.     

Changes in extracellular space volume and geometry induced by cortical spreading depression in immature and adult rats

Changes in extracellular space (ECS) diffusion parameters, DC potentials and extracellular potassium concentration were studied during single and repeated cortical spreading depressions (SD) in 13-15 (P13-15), 21 (P21) and 90-day-old (adult) Wistar rats. The real-time iontophoretic method using tetramethylammonium (TMA+)-selective microelectrodes was employed to measure three ECS parameters in the somatosensory cortex: the ECS volume fraction alpha (alpha = ECS volume/total tissue volume), ECS tortuosity lambda (increase in diffusion path length) and the nonspecific TMA+ uptake k'. SD was elicited by needle prick. SD was significantly longer at P13-15 than at P21 and in adults. During SD, alpha in all age groups decreased from 0.21-0.23 to 0.05-0.09; lambda increased from 1.55-1.65 to 1.95-2.07. Ten minutes after SD, alpha (in adults) and lambda (all age groups) increased compared to controls. This increase persisted even 1 hour after SD. When SD was repeated at 1 hour intervals, both alpha and lambda showed a gradual cumulative increase with SD repetition. Our study also shows that cortical SD is, as early as P13, accompanied by severe ECS shrinkage and increased diffusion path length (tortuosity) with values similar to adults, followed by a long-lasting increase in ECS volume and tortuosity when compared to pre-SD values.     

Three-dimensional modeling of the brain's ECS by minimum configurational energy packing of fluid vesicles

The extracellular space of the brain is the heterogeneous porous medium formed by the spaces between the brain cells. Diffusion in this interstitial space is the mechanism by which glucose and oxygen are delivered to the brain cells from the vascular system. It is also a medium for the transport of certain informational substances between the cells (called volume transmission), and for drug delivery. This work involves three-dimensional modeling of the extracellular space as void space in close-packed arrays of fluid membrane vesicles. These packings are generated by minimizing the configurational energy using a Monte Carlo procedure. Both regular and random packs of vesicles are considered. A random walk algorithm is then used to compute the geometric tortuosities, and the results are compared with published experimental data. For the random packings, it is found that although the absolute values for the tortuosities differ, the dependence of the tortuosity on pore volume fraction is very similar to that observed in experiment. The tortuosities we measure are larger than those computed in previous studies of packings of convex polytopes, and modeling improvements, which require higher resolution studies and an improved modeling of brain cell shapes and mechanical properties, could help resolve remaining discrepancies between model simulations and experiment. It is also shown that the specular reflection scheme is the appropriate technique for implementing zero-flux boundary conditions in random walk simulations commonly encountered in diffusion problems.     

Diffusion in the slice microenvironment and implications for physiological studies

The brain cell microenvironment includes the extracellular space surrounding the cell together with the cellular elements that define the space. The dense packing of cells in the mammalian nervous system ensures that the extracellular space is narrow but highly complex in geometry. Recent studies with ion-selective micropipettes have revealed that the cerebellar slice can support changes in [K+]o that resemble those seen in the intact preparation. In the slice, [K+]o responses of individual cells can even be resolved. Studies with iontophoretic techniques and quantitative analysis in the slice have shown that the extracellular space has diffusion properties, characterized by a volume fraction and a tortuosity, that are very similar to those seen in the intact animal. These data confirm that the microenvironment in the slice is comparable to that in the intact animal. The diffusion parameters can be used to make predictions about the time necessary for substances to diffuse into slices under various conditions. Such estimates, together with other studies, indicate that it is probably inadvisable to use slices with thicknesses in excess of 300--400 micrometers, and that the bathing conditions can be critical in maintaining slice viability.     

Poly[N-(2-hydroxypropyl)methacrylamide] polymers diffuse in brain extracellular space with same tortuosity as small molecules

Integrative optical imaging was used to show that long-chain synthetic poly[N-(2-hydroxypropyl)methacrylamide] (PHPMA) polymers in a range of molecular weights from 7.8 to 1057 kDa were able to diffuse through the extracellular space in rat neocortical slices. Tortuosity (square root of ratio of diffusion coefficient in aqueous medium to that in brain) measured with such polymers averaged 1.57, a value similar to that obtained previously with tetramethylammonium, a small cation. When PHPMA was conjugated with bovine serum albumin (BSA) to make a bulky polymer with molecular weight 176 kDa, the tortuosity rose to 2.27, a value similar to that obtained previously with BSA alone and with 70-kDa dextran. The method of image analysis was justified with diffusion models involving spherical and nonspherical initial distributions of the molecules.     

Astrocytes and extracellular matrix in extrasynaptic volume transmission

Volume transmission is a form of intercellular communication that does not require synapses; it is based on the diffusion of neuroactive substances across the brain extracellular space (ECS) and their binding to extrasynaptic high-affinity receptors on neurons or glia. Extracellular diffusion is restricted by the limited volume of the ECS, which is described by the ECS volume fraction α, and the presence of diffusion barriers, reflected by tortuosity λ, that are created, for example, by fine astrocytic processes or extracellular matrix (ECM) molecules. Organized astrocytic processes, ECM scaffolds or myelin sheets channel the extracellular diffusion so that it is facilitated in a certain direction, i.e. anisotropic. The diffusion properties of the ECS are profoundly influenced by various processes such as the swelling and morphological rebuilding of astrocytes during either transient or persisting physiological or pathological states, or the remodelling of the ECM in tumorous or epileptogenic tissue, during Alzheimer''s disease, after enzymatic treatment or in transgenic animals. The changing diffusion properties of the ECM influence neuron–glia interaction, learning abilities, the extent of neuronal damage and even cell migration. From a clinical point of view, diffusion parameter changes occurring during pathological states could be important for diagnosis, drug delivery and treatment.     

Maximum geometrical hindrance to diffusion in brain extracellular space surrounding uniformly spaced convex cells

Brain extracellular space (ECS) constitutes a porous medium in which diffusion is subject to hindrance, described by tortuosity, lambda = (D/D*)1/2, where D is the free diffusion coefficient and D* is the effective diffusion coefficient in brain. Experiments show that lambda is typically 1.6 in normal brain tissue although variations occur in specialized brain regions. In contrast, different theoretical models of cellular assemblies give ambiguous results: they either predict lambda-values similar to experimental data or indicate values of about 1.2. Here we constructed three different ECS geometries involving tens of thousands of cells and performed Monte Carlo simulation of 3-D diffusion. We conclude that the geometrical hindrance in the ECS surrounding uniformly spaced convex cells is independent of the cell shape and only depends on the volume fraction alpha (the ratio of the ECS volume to the whole tissue volume). This dependence can be described by the relation lambda = ((3-alpha)/2)1/2, indicating that the geometrical hindrance in such ECS cannot account for lambda > 1.225. Reasons for the discrepancy between the theoretical and experimental tortuosity values are discussed.     

New proline-rich proteins in isolated insect Z-discs.

1. Protoveratrine A increased the release of gamma-amino[3H]butyrate from small slices of rat cerebral cortex. This effect increased with increasing protoveratrine concentration, reaching a maximum at 100 microM. 2. Removal of Ca2+ from the superfusing medium did not change the increase in release due to 10 microM-protoveratrine; however, the Ca2+ antagonists, compound D-600, La3+, Mn2+, Mg2+ and also high Ca2+ concentration inhibited the effect of the alkaloid, as did procaine. 3. Protoveratrine A increased the uptake of 22Na+ into the slices with a similar dose-response curve to that found for gamma-aminobutyrate release. For the most part, the substances that inhibited protoveratrine-stimulated gamma-aminobutyrate release also inhibited 22Na+ uptake, although the correlation was not perfect. 4. Although extracellular Ca2+ is not required for protoveratrine-induced gamma-aminobutyrate release, an increase in Na+ influx that is susceptible to inhibition by some Ca2+ antagonists does appear to be associated with this phenomenon. However, the possibility remains that changes in the free intracellular Ca2+ concentration may be important for transmitter release induced by depolarizing veratrum alkaloids.     

Non-mitochondrial calcium ion regulation in rat ventricular myocytes

Ca2+ exchange has been measured in a suspension of rat ventricular myocytes treated with digitonin or saponin to render the sarcolemma permeable to small molecules and ions. Two fractions of exchange were identified, one that was attributed to the mitochondrial component of the cell and the other to a non-mitochondrial fraction. Mitochondrial Ca2+ uptake was blocked by sodium azide and depended on respiratory substrates whereas non-mitochondrial uptake occurred independently of these molecules but was dependent on ATP and creatine phosphate. Non-mitochondrial Ca2+ uptake could be induced at a Ca2+ concentration below 1 microM and the initial rate increased with concentration up to 100 microM. Uptake could be reversed by sulmazole (a caffeine-like substance) and this reversal in turn inhibited by ryanodine. These properties suggest that the major locus for non-mitochondrial Ca2+ exchange is at the sarcoplasmic reticulum. Ca2+ exchange could be modulated by a number of agents, including carnosine, but was unaffected by others, including Na+, inositol trisphosphate and cyclic AMP. A kinetic model of the data is presented, which incorporates similar data of Ca2+ uptake into the mitochondrial fraction. The rates of Ca2+ exchange measured in these experiments suggest that these two components of the cell can reduce the sarcoplasmic Ca2+ concentration rapidly enough to account for the observed transient nature of the isometric twitch. Furthermore, it is suggested that both non-mitochondrial and mitochondrial fractions of the cell could significantly contribute to tension relaxation in rat cardiac muscle.     

The existence of an optimal range of cytosolic free calcium for insulin-stimulated glucose transport in rat adipocytes

We have examined the effects of extracellular and intracellular Ca2+ concentrations upon basal and insulin-stimulated 2-deoxyglucose uptake in isolated rat adipocytes. In the absence of extracellular Ca2+, both basal and insulin-stimulated glucose uptake were significantly reduced. Insulin-stimulated glucose transport was optimal at 1 and 2 mM Ca2+. Further increases in extracellular Ca2+ concentration (3 mM) significantly diminished insulin-stimulated glucose uptake. When intracellular Ca2+ concentrations were augmented by ionomycin (1 microM), insulin-stimulated glucose uptake was significantly reduced at extracellular Ca2+ concentrations of 2 and 3 mM. The levels of intracellular free Ca2+ concentrations were then measured with Ca2+ indicator fura-2. The correlation between the levels of intracellular free Ca2+ and the magnitude of insulin-stimulated glucose uptake revealed that the optimal effect of insulin is observed at Ca2+ levels between 140 and 370 nM. At both extremes outside of this window, both low and high levels of intracellular Ca2+ result in diminished cellular responsiveness to insulin. These data suggest that intracellular calcium concentrations may exert a dual role in the regulation of cellular sensitivity to insulin. First, there must exist a minimal concentration of intracellular calcium to promote insulin action. Second, increased levels of intracellular calcium may provide a critical signal for diminution of insulin action.     

Quantitative dual-probe microdialysis: evaluation of [3H]mannitol diffusion in agar and rat striatum

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.     

Cell cavities increase tortuosity in brain extracellular space

Brain extracellular space (ECS) forms hindered pathways for molecular diffusion in chemical signaling and drug delivery. Hindrance is quantified by the tortuosity lambda; the tortuosity obtained from simulations using uniformly spaced convex cells is significantly lower than that measured experimentally. To attempt to account for the difference in results, this study employed a variety of ECS models based on an array of cubic cells containing open rectangular cavities that provided the ECS with dead-space microdomains. Monte Carlo simulations demonstrated that, in such ECS models, lambda can equal or exceed the typical experimental value of about 1.6. The simulations further revealed that lambda is relatively independent of cavity shape and the number of cavities per cell. It mainly depends on the total ECS volume fraction alpha, the cavity volume fraction alpha(c), and whether the cavity is located at the center of a cell face or formed at the junction of multiple cells. To describe the results from the different ECS models, an expression was obtained that related lambda to alpha, alpha(c), and an empirical exit factor beta that correlated with the ease with which a molecule could leave a cavity and its vicinity.     

The Impact of Alpha-Syntrophin Deletion on the Changes in Tissue Structure and Extracellular Diffusion Associated with Cell Swelling under Physiological and Pathological Conditions

Aquaporin-4 (AQP4) is the primary cellular water channel in the brain and is abundantly expressed by astrocytes along the blood-brain barrier and brain-cerebrospinal fluid interfaces. Water transport via AQP4 contributes to the activity-dependent volume changes of the extracellular space (ECS), which affect extracellular solute concentrations and neuronal excitability. AQP4 is anchored by α-syntrophin (α-syn), the deletion of which leads to reduced AQP4 levels in perivascular and subpial membranes. We used the real-time iontophoretic method and/or diffusion-weighted magnetic resonance imaging to clarify the impact of α-syn deletion on astrocyte morphology and changes in extracellular diffusion associated with cell swelling in vitro and in vivo. In mice lacking α-syn, we found higher resting values of the apparent diffusion coefficient of water (ADC_W) and the extracellular volume fraction (α). No significant differences in tortuosity (λ) or non-specific uptake (k′), were found between α-syn-negative (α-syn −/−) and α-syn-positive (α-syn +/+) mice. The deletion of α-syn resulted in a significantly smaller relative decrease in α observed during elevated K⁺ (10 mM) and severe hypotonic stress (−100 mOsmol/l), but not during mild hypotonic stress (−50 mOsmol/l). After the induction of terminal ischemia/anoxia, the final values of ADC_W as well as of the ECS volume fraction α indicate milder cell swelling in α-syn −/− in comparison with α-syn +/+ mice. Shortly after terminal ischemia/anoxia induction, the onset of a steep rise in the extracellular potassium concentration and an increase in λ was faster in α-syn −/− mice, but the final values did not differ between α-syn −/− and α-syn +/+ mice. This study reveals that water transport through AQP4 channels enhances and accelerates astrocyte swelling. The substantially altered ECS diffusion parameters will likely affect the movement of neuroactive substances and/or trophic factors, which in turn may modulate the extent of tissue damage and/or drug distribution.