Diffusion in the extracellular space

The rate of diffusion of molecules through intact tissues in an animal is difficult to measure, so the amount of information currently available is limited. Diffusion coefficients for size-fractionated dextrans, albumin, and antibodies have been measured in granulation tissue and tumor tissue [20, 21] similar measurements have been made in slices of brain tissue [87]. In both cases, the diffusion coefficient was estimated by fitting solutions to the diffusion equation, similar to Equation 3-36, to data obtained by direct visualization of fluorescent tracers in the interstitial space. These measurements, as well as others made by a variety of techniques, are compiled in 

Compounds with different lipid solubility have different fates in tissue. This is most clearly demonstrated in the brain using ventriculocisternal perfusion [88]. In these experiments, solutes delivered into the cerebrospinal fluid permeate through the ependyma into the extracellular space of the brain. Three classes of compounds, with different patterns of local distribution, have been identified (a) water-soluble compounds that remain in the extracellular space of the brain, occupying a volume fraction of 15-20% (e.g., sucrose and EDTA), (b) large, lipid-soluble compounds that have slow capillary transport, but quickly enter the cells of the brain, occupying a volume fraction of 50-200% (e.g., mannitol, creatinine, cytosine arabinoside), and (c) small, lipid-soluble compounds that are rapidly removed from the brain by capillary transport (e.g., H2O, ethanol, l,3-bis(2-chloroethyl)-l-nitrosourea (BCNU). Similar behavior probably occurs in extracranial tissues as well. 

Diffusion coefficients in tissue can change with disease and injury these changes often correlate with changes in tissue structure. Again, this effect has been observed in the brain. The normal volume fraction of the brain extracellular space is 0.18 [89, 90], but it decreases after ischemic injury to the brain (to 0.07), probably due to osmotic swelling of brain cells upon injury. 

This change is accompanied by a corresponding decrease in the diffusion coefficient for ions. Similarly, the apparent diffusion coefficient for water in normal rat cortex and caudate putamen is 6 x 10 and 5 x 10 cm /s, respectively [91]. The diffusion coefficient increases in rats with experimental brain tumors (8 X 10 cm /s) and experimental edema (9 x 10 cm /s), consistent with the increase in extracellular volume that occurs during these states [91], 

The effective diffusion coefficient for solute diffusion in a complex microstructure is related to the diffusion coefficient in an unbounded fluid  

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Excitatory amino acid transporters (EAATs) are the primary regulators of extracellular glutamate concentrations in the CNS. Glutamate clearance (and consequently glutamate concentration and diffusion in the extracellular space) is associated with the degree of astrocytic coverage of its neurons (Oliet et al. 

While neurotransmitters diffuse in the extracellular space, they are subject to clearance processes that either transport them back to nerve terminals or metabolize them to inactive products in the extracellular space. For example, the membranes of many nerve terminals are equipped with transporters, which are transmembrane proteins that transport neurotransmitter from the extracellular space into the cytoplasm of the terminal. On the hand, as in the case of acetylcholine, the extracellular space may contain enzymes that rapidly metaboKze the neurotransmitter. The impact of these clearance processes on the concentration of the diffusing substance can be considered with an equation of the following type ... 

FI G U RE 10.2 Schematic representation of alveolar cells and possible mechanism of transport of molecules from the alveolar space into the circulation. Particles will release molecules of interest (gray circles) into the mucus in which the particle is embedded. The molecule can either be lost in the mucus, taken up by alveolar macrophages by phagocytosis or diffusion, taken up by alveolar epithelial cells by passive or active transport, or bypass the alveolar cells via paracellular transport depending upon the properties of the drug. Once a molecule has reached the extracellular space, the same mechanisms are possible for transport from the extracellular space into the blood. Molecules in the extracellular space may also reach to circulation via the lymph. 

The conservation of mass equations listed in the final row of Table 3.2 are frequently used to describe the movement of solutes through tissues and cells. These equations were developed by assuming that the tissue is homogeneous throughout the region of interest. Diffusing solute molecules must have equal access to every possible position within the volume of interest and Da must be constant with respect to both space and time. This assumption is not valid for the diffusion of certain molecules in tissues for example, consider a molecule that diffuses through the extracellular space of the tissue and does not readily enter cells. The limitations of this assumption are discussed in Chapter 4. 

Consider a solute that diffuses within the extracellular space of the tissue, but also interacts with the tissue by reversibly binding to some fixed component of the tissue. For example, the diffusing solute might bind to a protein on the cell surface or to a protein in the extracellular matrix. When bound the solute may... 

The extracellular space of tissues is an aqueous gel of proteins and polysaccharides. This gel potentially provides an additional resistance to the diffusion of molecules in the extracellular space due to volume exclusion and hydrodynamic interactions. Reconstituted gels of extracellular matrix components (e.g., collagen) are often used to evaluate the magnitude of this resistanee. In general, the diffusion coefficient for a protein depends on the properties of the gel and the size of the protein (Figure 4.10). 

Consider the different tissue structures shown schematically in Figure 4.15. For molecules that diffuse through the extracellular space, the rate of movement through each of these tissues could be substantially different. In addition, a molecule that can dissolve in the extracellular fluid and also permeate cell membranes will encounter less geometrical complexity in its diffusional path, but it will diffuse through mieroscopic regions that differ substantially in composition. Prediction of effective diffusion coefficients in either situation is difficult. 

Figure 4.22 Tortuosity for size-fractionated dextrans and three albumins in the brain. Dashed line indicates the reduced diffusion coefficient for a small ion (TMA), and is probably a reasonable estimate for the intrinsic tortuosity of the diffusional path in the extracellular space.

Furthermore, changes in the extracellular space may contribute to decreased diffusion associated with... 

In aqueous solutions, at a physiological pH, HA is represented by negatively charged hyaluronate macromolecules (pK = 3.21) [15] with extended conformations. In a polyanionic form, hyaluronan functional groups make the biopolymer so hydrophilic that it binds 1000 times more water than is predicted from its molar mass. The heterogeneity and hydrophilicity of HA facilitate its interaction with a variety of tissue constituents inside and outside the cells. In the extracellular space, HA controls the retention of water, ionic and molecular diffusion and provides a 3D-structural meshwork [16]. 

Prokopova-Kubinova S, Vargova L, Tao L, Subr V, Sykova E, Nicholson C. Poly[N-(2-hydroxypropyl)methacrylamide] polymers diffuse in brain extracellular space with the same totruosity as small molecules. Biophys J 2001 80 542-548. 

The minimal amount of brain injury that microelectrodes cause renders them uniquely well suited to monitoring ongoing neurochemical events in the brain. Carbon fiber electrodes can be implanted to within a few micrometers of viable nerve terminals, which comprise the loci of the neurochemical events we desire to monitor. The intimate proximity of the electrodes to nerve terminals is of critical importance to the quality of the neurochemical information that is obtained. Most neurotransmitters are rapidly cleared from the extracellular space by either transporter mechanisms or metabolic processes [28]. These clearance events limit the lifetime of neurotransmitters in the extracellular space to the millisecond regime, which provides the neurotransmitter molecules with very limited opportunity to diffuse the necessary distance to reach an implanted sensor. Hence, if the sensor is not extremely close to functional nerve terminals, the sensor may not be capable of providing accurate neurochemical information about events that occur in the immediate vicinity of neuronal terminals. The full significance of this critical point has only recently begun to be fully appreciated. 

Many of the applications of in vivo voltammetry have focused on monitoring the release of dopamine, and other neurotransmitters, as evoked by the electrical stimulation of axons. The use of electrical stimulation is convenient because it evokes dopamine release at a specific and known time. Moreover, the combination of voltammetry and electrical stimulation has revealed a large amount of useful information about the regulation of dopamine release, the kinetics of dopamine uptake, and the diffusion of dopamine in the extracellular space [67]. Nevertheless, the study of evoked dopamine release does not provide information about spontaneous dopamine release, that is, dopamine release triggered by the endogenous neuronal activity of the brain. Such information is also of great interest. 

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