Faculty Bibliography

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

Diffusion of molecules in brain extracellular space is constrained by two macroscopic parameters, tortuosity factor lambda and volume fraction alpha. Recent studies in brain slices show that when osmolarity is reduced, lambda increases while alpha decreases. In contrast, with increased osmolarity, alpha increases, but lambda attains a plateau. Using homogenization theory and a variety of lattice models, we found that the plateau behavior of lambda can be explained if the shape of brain cells changes nonuniformly during the shrinking or swelling induced by osmotic challenge. The nonuniform cellular shrinkage creates residual extracellular space that temporarily traps diffusing molecules, thus impeding the macroscopic diffusion. The paper also discusses the definition of tortuosity and its independence of the measurement frame of reference

Spreading depression (SD) consists of a transient suppression of all neuronal activity that spreads slowly across regions of gray matter. The paper is divided into three parts. Martins-Ferreira describes 30 years of research on SD in the isolated retina. Much of this work has relied on the prominent intrinsic optical signals that accompany SD in the retina. By inducing SD to propagate in circles with a velocity of 3.7 mm min(-1), it is possible to investigate the finely balanced electrochemical equilibrium that maintains the traveling wave. SD is accompanied by a slow negative extracellular voltage and ion movements that are greatest in the inner plexiform layer of the retina. Nedergaard discusses the role of astrocytes in SD propagation. Astrocytes mediate slowly moving waves of intracellular Ca(2+) increase, for which gap junctions are essential. SD is accompanied by entry of Ca(2+) into cells and fails when gap junctions are blocked. SD, however, is blocked by glutamate receptor antagonists but glial Ca(2+) waves are not. Astrocytic Ca(2+) waves are probably involved in the initiation of SD but other factors, including K(+), glutamate and purinergic receptors, are necessary for sustained propagation. Nicholson describes studies on the different preparations that helped clarify the role of extracellular space in SD. It has long been known that extracellular K(+) reaches levels of 50 mM or more during SD. Studies with ion-selective microelectrodes showed that extracellular Na(+) and Cl(-) fall by as much as 100 mM during SD, and water leaves the extracellular space. Further work showed that extracellular Ca(2+) falls 10-fold during SD and significant changes in extracellular pH and ascorbate occur. These studies imply that large perturbations of the extracellular milieu occur during SD and are an essential part of the interlocking cascade of events that produce this still mysterious phenomenon

Ascorbate is an essential antioxidant in the CNS, localized predominantly in neuronal cytosol. Slices of mammalian brain rapidly lose ascorbate, however, when incubated in ascorbate-free media; brain slices also take up water and swell. Here we investigated water gain in coronal slices of rat forebrain incubated with and without ascorbate for 1-3 h at 34 degrees C. Slices progressively gained water in ascorbate-free media, with a significant 12% water increase after 3 h at 34 degrees C, compared with the water content of slices after a 1-h recovery period at 24 degrees C, immediately following slice preparation. Inclusion of 400 micro M ascorbate in the medium led to an increase in tissue ascorbate content and prevented water gain at 34 degrees C. By contrast, water gain was not inhibited by isoascorbate or thiourea, which are antioxidants that are not accumulated in brain cells. The oxidant H2O2 enhanced water gain, whereas a cocktail of NMDA and non-NMDA receptor blockers inhibited edema formation to the same extent as ascorbate. These data demonstrate that brain edema, linked to glutamate-receptor activation, can result from intracellular oxidative stress and that this can be prevented by ascorbate

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 molecules <500 Mr show that alpha approximately 0.2 and lambda approximately 1.6, although some brain regions are anisotropic. Molecules > or =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 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. 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

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