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.     

Monte Carlo analysis of obstructed diffusion in three dimensions: application to molecular diffusion in organelles.

Molecular transport in the aqueous lumen of organelles involves diffusion in a confined compartment with complex geometry. Monte Carlo simulations of particle diffusion in three dimensions were carried out to evaluate the influence of organelle structure on diffusive transport and to relate experimental photobleaching data to intrinsic diffusion coefficients. Two organelle structures were modeled: a mitochondria-like long closed cylinder containing fixed luminal obstructions of variable number and size, and an endoplasmic reticulum-like network of interconnected cylinders of variable diameter and density. Trajectories were computed in each simulation for >10(5) particles, generally for >10(5) time steps. Computed time-dependent concentration profiles agreed quantitatively with analytical solutions of the diffusion equation for simple geometries. For mitochondria-like cylinders, significant slowing of diffusion required large or wide single obstacles, or multiple obstacles. In simulated spot photobleaching experiments, a approximately 25% decrease in apparent diffusive transport rate (defined by the time to 75% fluorescence recovery) was found for a single thin transverse obstacle occluding 93% of lumen area, a single 53%-occluding obstacle of width 16 lattice points (8% of cylinder length), 10 equally spaced 53% obstacles alternately occluding opposite halves of the cylinder lumen, or particle binding to walls (with mean residence time = 10 time steps). Recovery curve shape with obstacles showed long tails indicating anomalous diffusion. Simulations also demonstrated the utility of measurement of fluorescence depletion at a spot distant from the bleach zone. For a reticulum-like network, particle diffusive transport was mildly reduced from that in unobstructed three-dimensional space. In simulated photobleaching experiments, apparent diffusive transport was decreased by 39-60% in reticular structures in which 90-97% of space was occluded. These computations provide an approach to analyzing photobleaching data in terms of microscopic diffusive properties and support the paradigm that organellar barriers must be quite severe to seriously impede solute diffusion.     

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.     

Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion.

The green fluorescent protein (GFP) was used as a noninvasive probe to quantify the rheological properties of cell cytoplasm. GFP mutant S65T was purified from recombinant bacteria for solution studies, and expressed in CHO cell cytoplasm. GFP-S65T was brightly fluorescent in solution (lambda ex 492 nm, lambda em 509 nm) with a lifetime of 2.9 ns and a rotational correlation time (tc) of 20 ns. Recovery of GFP fluorescence after photobleaching was complete with a half-time (t1/2) in aqueous saline of 30 +/- 2 ms (5-micron diameter spot), giving a diffusion coefficient of 8.7 x 10(-7) cm2/s. The t1/2 was proportional to solution viscosity and was dependent on spot diameter. In contrast to fluorescein. GFP photobleaching efficiency was not affected by solution O2 content, triplet state quenchers, singlet oxygen scavengers, and general radical quenchers. In solutions of higher viscosity, an additional, rapid GFP recovery process was detected and ascribed to reversible photobleaching. The t1/2 for reversible photobleaching was 1.5-5.5 ms (relative viscosity 5-250), was independent of spot diameter, and was unaffected by O2 or quenchers. In cell cytoplasm, time-resolved microfluorimetry indicated a GFP lifetime of 2.6 ns and a tc of 36 +/- 3 ns, giving a relative viscosity (cytoplasm versus water) of 1.5. Photobleaching recovery of GFP in cytoplasm was 82 +/- 2% complete with a t1/2 of 83 +/- 6 ms, giving a relative viscosity of 3.2. GFP translational diffusion increased 4.7-fold as cells swelled from a relative volume of 0.5 to 2. Taken together with measurements of GFP translation and rotation in aqueous dextran solutions, the data in cytoplasm support the view that the primary barrier to GFP diffusion is collisional interactions between GFP and macromolecular solutes.     

Cytoplasmic viscosity near the cell plasma membrane: translational diffusion of a small fluorescent solute measured by total internal reflection-fluorescence photobleaching recovery.

Total internal reflection-fluorescence recovery after photobleaching (TIR-FRAP) was applied to measure solute translational diffusion in the aqueous phase of membrane-adjacent cytoplasm. TIR fluorescence excitation in aqueous solutions and fluorescently labeled cells was produced by laser illumination at a subcritical angle utilizing a quartz prism; microsecond-resolution FRAP was accomplished by acousto-optic modulators and electronic photomultiplier gating. A mathematical model was developed to determine solute diffusion coefficient from the time course of photobleaching recovery, bleach time, bleach intensity, and evanescent field penetration depth; the model included irreversible and reversible photobleaching processes, with triplet state diffusion. The validity and accuracy of TIR-FRAP measurements were first examined in aqueous fluorophore solutions. Diffusion coefficients for fluorescein isothiocyanate-dextrans (10-2000 kDa) determined by TIR-FRAP (recovery t1/2 0.5-2.2 ms) agreed with values measured by conventional spot photobleaching. Model predictions for the dependence of recovery curve shape on solution viscosity, bleach time, and bleach depth were validated experimentally using aqueous fluorescein solutions. To study solute diffusion in cytosol, MDCK epithelial cells were fluorescently labeled with the small solute 2',7'-bis-2-carboxyethyl-5-carboxyfluorescein-acetoxymethyl-ester (BCECF). A reversible photobleaching process (t1/2 approximately 0.5 ms) was identified that involved triplet-state relaxation and could be eliminated by triplet-state quenching with 100% oxygen. TIR-FRAP t1/2 values for irreversible BCECF bleaching, representing BCECF translational diffusion in the evanescent field, were in the range 2.2-4.8 ms (0.2-1 ms bleach times), yielding a BCECF diffusion coefficient 6-10-fold less than that in water. These results establish the theory and the first experimental application of TIR-FRAP to measure aqueous-phase solute diffusion, and indicate slowed translational diffusion of a small solute in membrane-adjacent cytosol.     

Lateral diffusion of rhodopsin in photoreceptor cells measured by fluorescence photobleaching and recovery.

Frog rod outer segments were labeled with the sulfhydryl-reactive label iodoacetamido tetramethylrhodamine. The bulk of the label reacted with the major disk membrane protein, rhodopsin. Fluorescence photobleaching and recovery (FPR) experiments on labeled rods showed that the labeled proteins diffused rapidly in the disk membranes. In these FPR experiments we observed both the recovery of fluorescence in the bleached spot and the loss of fluorescence from nearby, unbleached regions of the photoreceptor. These and previous experiments show that the redistribution of the fluorescent labeled proteins after bleaching was due to diffusion. The diffusion constant, D, was (3.0 +/- 10(-9) cm2 s-1 if estimated from the rate of recovery of fluorescence in the bleached spot, and (5.3 +/- 2.4) x 10(-9) cm2 s-1 if estimated from the rate of depletion of fluorescence from nearby regions. The temperature coefficient, Q10, for diffusion was 1.7 +/- 0.5 over the range 10 degrees--29 degrees C. These values obtained by FPR are in good agreement with those previously obtained by photobleaching rhodopsin in fresh, unlabeled rods. This agreement indicates that the labeling and bleaching procedures required by the FPR method did not significantly alter the diffusion rate of rhodopsin. Moreover, the magnitude of the diffusion constant for rhodopsin is that to be expected for an object of its diameter diffusing in a bilayer with the viscosity of the disk membrane. In contrast to the case of rhodopsin, FPR methods applied to other membrane proteins have yielded much smaller diffusion constants. The present results help indicate that these smaller diffusion constants are not artifacts of the method but may instead be due to interactions the diffusing proteins have with other components of the membrane in addition to the viscous drag imposed by the lipid bilayer.     

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.     

Simulations of (an)isotropic diffusion on curved biological surfaces

We present a computational particle method for the simulation of isotropic and anisotropic diffusion on curved biological surfaces that have been reconstructed from image data. The method is capable of handling surfaces of high curvature and complex shape, which are often encountered in biology. The method is validated on simple benchmark problems and is shown to be second-order accurate in space and time and of high parallel efficiency. It is applied to simulations of diffusion on the membrane of endoplasmic reticula (ER) in live cells. Diffusion simulations are conducted on geometries reconstructed from real ER samples and are compared to fluorescence recovery after photobleaching experiments in the same ER samples using the transmembrane protein tsO45-VSV-G, C-terminally tagged with green fluorescent protein. Such comparisons allow derivation of geometry-corrected molecular diffusion constants for membrane components from fluorescence recovery after photobleaching data. The results of the simulations indicate that the diffusion behavior of molecules in the ER membrane differs significantly from the volumetric diffusion of soluble molecules in the lumen of the same ER. The apparent speed of recovery differs by a factor of approximately 4, even when the molecular diffusion constants of the two molecules are identical. In addition, the specific shape of the membrane affects the recovery half-time, which is found to vary by a factor of approximately 2 in different ER samples.     

Analysis of rhodamine and fluorescein-labeled F-actin diffusion in vitro by fluorescence photobleaching recovery.

Properties of filamentous acetamidofluorescein-labeled actin and acetamidotetramethylrhodamine-labeled actin (AF and ATR-actin, respectively) were examined to resolve discrepancies in the reported translational diffusion coefficients of F-actin measured in vitro by FPR and other techniques. Using falling-ball viscometry and two independent versions of fluorescence photobleaching recovery (FPR), the present data indicate that several factors are responsible for these discrepancies. Gel filtration chromatography profoundly affects the viscosity of actin solutions and filament diffusion coefficients. ATR-actin and, to a lesser degree, AF-actin show a reduction in viscosity in proportion to the fraction labeled, presumably due to filament shortening. Actin filaments containing AF-actin or ATR-actin are susceptible to photoinduced damage, including a covalent cross-linking of actin protomers within filaments and an apparent cleavage of filaments detected by a decrease of the measured viscosity and an increase in the measured filament diffusion coefficients. Quantum yields of the two photoinduced effects are quite different. Multiple cross-links are produced relative to each photobleaching event, whereas less than 1% filament cleavage occurs. Substantial differences in the filament diffusion coefficients measured by FPR are also the result of differences in illumination geometry and sampling time. However, under controlled conditions, FPR can be used as a quantitative tool for measuring the hydrodynamic properties of actin filaments. Incremented filament shortening caused by photoinduced cleavage or incremental addition of filament capping proteins produces a continuous and approximately linear increase of filament diffusion coefficients, indicating that filaments are not associated in solution. Our results indicate that actin filaments exhibit low mobilities and it is inferred that actin filaments formed in vitro by column-purified actin, under standard conditions, are much longer than has conventionally been presumed.     

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.     

Random-walk model of diffusion in three dimensions in brain extracellular space: comparison with microfiberoptic photobleaching measurements

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises ∼20% of brain parenchymal volume and contains cell-cell gaps ∼50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (α), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (D_o/D). Experimental D_o/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D_o/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling after water intoxication. D_o/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D_o/D using realistic α, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D_o/D for different solute sizes. Also, the modeling showed unanticipated effects on D_o/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.     

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.     

Fast diffusion along defects and corrugations in phospholipid P beta, liquid crystals.

The diffusion of a fluorescent lipid analogue in liquid crystals of the anisotropic P beta, phase of dimyristoylphosphatidylcholine (DMPC) had been found to be highly variable, suggesting structural defect pathways. Fluorescence photobleaching recovery (FPR) experiments imply two effective diffusion pathways with coefficients differing by at least 100. This is consistent with fast diffusion along submicroscopic bands of disordered material ("defects") in the bilayer corrugations characteristic of this phase. Due to strains during transformation from the L alpha phase, the axis of the corrugations is ordinarily disrupted by mosaic patches rotationally disoriented within the mean plane of the molecular bilayers, although larger oriented domains are sometimes adventitiously aligned into microscopically visible striped textures. The corrugations are also systematically aligned along positive disclinations pairs or "oily streaks." Thus, fast diffusion occurs parallel to the disclination lines and along the textured stripes. FPR results yield an upper limit on the effective diffusion in the ordered material of D less than or equal to 2 X 10(-16) cm2/s at 22 degrees C, D less than or equal to 3 X 10(-17) cm2/s at 13 degrees C. In contrast the diffusion coefficient along defect pathways where disordered ribbons are aligned is D approximately 4 X 10(-11) cm2/s at 16 degrees C.     

Inhomogeneous translational diffusion of monoclonal antibodies on phospholipid Langmuir-Blodgett films.

The translational mobility of fluorescent-labeled monoclonal antibodies specifically bound to supported phospholipid bilayers containing hapten-conjugated phospholipids has been measured as a function of the surface concentration of bound antibodies using fluorescence recovery after photobleaching. Fluorescence recovery curves are fit well by a model that assumes the presence of two populations of antibodies with different lateral diffusion coefficients. The larger diffusion coefficient equals 3.5 x 10(-9) cm2/s, the smaller diffusion coefficient ranges from 1.5 x 10(-9) cm2/s to 2.5 x 10(-10) cm2/s, and the fractional fluorescence recovery associated with the smaller coefficient increases from approximately 0 to approximately 0.7 with increasing concentration of bound antibody. These results suggest that complexes of haptenated phospholipids and antibodies in phospholipid Langmuir-Blodgett films form clusters or domains in a concentration-dependent fashion.     

Analysis of fluorophore diffusion by continuous distributions of diffusion coefficients: application to photobleaching measurements of multicomponent and anomalous diffusion.

Fluorescence recovery after photobleaching (FRAP) is widely used to measure fluorophore diffusion in artificial solutions and cellular compartments. Two new strategies to analyze FRAP data were investigated theoretically and applied to complex systems with anomalous diffusion or multiple diffusing species: 1) continuous distributions of diffusion coefficients, alpha(D), and 2) time-dependent diffusion coefficients, D(t). A regression procedure utilizing the maximum entropy method was developed to resolve alpha(D) from fluorescence recovery curves, F(t). The recovery of multi-component alpha(D) from simulated F(t) with random noise was demonstrated and limitations of the method were defined. Single narrow Gaussian alpha(D) were recovered for FRAP measurements of thin films of fluorescein and size-fractionated FITC-dextrans and Ficolls, and multi-component alpha(D) were recovered for defined fluorophore mixtures. Single Gaussian alpha(D) were also recovered for solute diffusion in viscous media containing high dextran concentrations. To identify anomalous diffusion from FRAP data, a theory was developed to compute F(t) and alpha(D) for anomalous diffusion models defined by arbitrary nonlinear mean-squared displacement <x2> versus time relations. Several characteristic alpha(D) profiles for anomalous diffusion were found, including broad alpha(D) for subdiffusion, and alpha(D) with negative amplitudes for superdiffusion. A method to deduce apparent D(t) from F(t) was also developed and shown to provide useful complementary information to alpha(D). alpha(D) and D(t) were determined from photobleaching measurements of systems with apparent anomalous subdiffusion (nonuniform solution layer) and superdiffusion (moving fluid layer). The results establish a practical strategy to characterize complex diffusive phenomena from photobleaching recovery measurements.     

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.     

FRAP analysis of membrane-associated proteins: lateral diffusion and membrane-cytoplasmic exchange

Obtaining quantitative kinetic parameters from fluorescence recovery after photobleaching (FRAP) experiments generally requires a theoretical analysis of protein mobility and appropriate solutions for FRAP recovery derived for a given geometry. Here we provide a treatment of FRAP recovery for a molecule undergoing a combined process of reversible membrane association and lateral diffusion on the plasma membrane for two commonly used bleach geometries: stripes, and boxes. Such analysis is complicated by the fact that diffusion of a molecule during photobleaching can lead to broadening of the bleach area, resulting in significant deviations of the actual bleach shape from the desired bleach geometry, which creates difficulty in accurately measuring kinetic parameters. Here we overcome the problem of deviations between actual and idealized bleach geometries by parameterizing, more accurately, the initial postbleach state. This allows for reconstruction of an accurate and analytically tractable approximation of the actual fluorescence distribution. Through simulated FRAP experiments, we demonstrate that this method can be used to accurately measure a broad range of combinations of diffusion constants and exchange rates. Use of this method to analyze the plextrin homology domain of PLC-δ1 in Caenorhabditis elegans results in quantitative agreement with prior analysis of this domain in other cells using other methods. Because of the flexibility, relative ease of implementation, and its use of standard, easily obtainable bleach geometries, this method should be broadly applicable to investigation of protein dynamics at the plasma membrane.     

Physical and chemical modifications of collagen gels: impact on diffusion

The extracellular matrix (ECM) represents a major barrier for delivery of therapeutic drugs, and the transport is determined by the ECM composition, structure, and distribution. Because of the high interstitial fluid pressure in tumors, diffusion becomes the main transport mechanism through ECM. The purpose of this work was to study the impact of the structure of the collagen network on diffusion, by studying to what extent the orientation and chemical modification of the collagen network influenced diffusion. Collagen gels with a concentration of 0.2-2.0% that is comparable with the amount of collagen in the tumor ECM were used as a model system for ECM. Collagen gels were aligned in a low-strength magnetic field and geometrical confinement, and chemically modified by adding decorin or hyaluronan. Diffusion of dextran 2-MDa molecules in the collagen gels was measured using fluorescence recovery after photobleaching. Alignment of the collagen fibers in our gels was found to have no impact on the diffusion coefficient. Adding decorin reduced the diameter of the collagen fibers, but no effect on diffusion was observed. Hyaluronan also reduced the fiber diameter, and high concentration of hyaluronan (2.5 mg/ml) increased the diffusion coefficient. The results indicate that the structure of the collagen network is not a major factor in determining the diffusion through the ECM. Rather, increasing the concentration of collagen was found to reduce the diffusion coefficient. Concentration of the collagen network is more important than the structure in determining the diffusion coefficient.     

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.     

Separation of translational and rotational contributions in solution studies using fluorescence photobleaching recovery

Although fluorescence photobleaching recovery (FPR) experiments are usually interpreted in terms of the translational motions of a fluorescently labeled species, rotational motions can also modulate recovery through the cosine-squared laws for dipolar absorption and emission processes. In a complex interacting system, translational and rotational contributions may both be simultaneously present. We show how these contributions can be separated in solution studies using an FPR setup in which (a) the linear polarization of the low-intensity observation beam and the high-intensity photobleaching pulse can be varied independently, and (b) all emitted fluorescent photons are counted equally. The fluorescence recovery signal obtained with the observation beam polarized at the magic angle, 54.7 degrees, from the bleach polarization direction is independent of label orientation, whereas the anisotropy function formed from a combination of parallel and perpendicular polarizations isolates the orientational recovery. The anisotropy function is identical to that in fluorescence correlation spectroscopy and, for rigid-body rotational diffusion, can be expressed as a sum of five exponential terms.