Site-specific effects of compression on macromolecular diffusion in articular cartilage

Articular cartilage is the connective tissue that lines joints and provides a smooth surface for joint motion. Because cartilage is avascular, molecular transport occurs primarily via diffusion or convection, and cartilage matrix structure and composition may affect diffusive transport. Because of the inhomogeneous compressive properties of articular cartilage, we hypothesized that compression would decrease macromolecular diffusivity and increase diffusional anisotropy in a site-specific manner that depends on local tissue strain. We used two fluorescence photobleaching methods, scanning microphotolysis and fluorescence imaging of continuous point photobleaching, to measure diffusion coefficients and diffusional anisotropy of 70 kDa dextran in cartilage during compression, and measured local tissue strain using texture correlation. For every 10% increase in normal strain, the fractional change in diffusivity decreased by 0.16 in all zones, and diffusional anisotropy increased 1.1-fold in the surface zone and 1.04-fold in the middle zone, and did not change in the deep zone. These results indicate that inhomogeneity in matrix structure and composition may significantly affect local diffusive transport in cartilage, particularly in response to mechanical loading. Our findings suggest that high strains in the surface zone significantly decrease diffusivity and increase anisotropy, which may decrease transport between cartilage and synovial fluid during compression.     

Obstructed diffusion in phase-separated supported lipid bilayers: a combined atomic force microscopy and fluorescence recovery after photobleaching approach

Proteins and other macromolecules are believed to hinder molecular lateral diffusion in cellular membranes. We have constructed a well-characterized model system to better understand how obstacles in lipid bilayers obstruct diffusion. Fluorescence recovery after photobleaching was used to measure the lateral diffusion coefficient in single supported bilayers composed of mixtures of 1,2-dilauroylphosphotidylcholine (DLPC) and 1,2-distearoylphosphotidylcholine (DSPC). Because these lipids are immiscible and phase separate at room temperature, a novel quenching technique allowed us to construct fluid DLPC bilayers containing small disk-shaped gel-phase DSPC domains that acted as obstacles to lateral diffusion. Our experimental setup enabled us to analyze the same samples with atomic force microscopy and exactly characterize the size, shape, and number of gel-phase domains before measuring the obstacle-dependent diffusion coefficient. Lateral obstructed diffusion was found to be dependent on obstacle area fraction, size, and geometry. Analysis of our results using a free area diffusion model shows the possibility of unexpected long-range ordering of fluid-phase lipids around the gel-phase obstacles. This lipid ordering has implications for lipid-mediated protein interactions in cellular membranes.     

Lateral diffusion of proteins in the periplasm of Escherichia coli.

We have introduced biologically active, fluorescently labeled maltose-binding protein into the periplasmic space of Escherichia coli and measured its lateral diffusion coefficient by the fluorescence photobleaching recovery method. Diffusion of this protein in the periplasm was found to be surprisingly low (lateral diffusion coefficient, 0.9 X 10(-10) cm2 s-1), about 1,000-fold lower than would be expected for diffusion in aqueous medium and almost 100-fold lower than for an equivalent-size protein in the cytoplasm. Galactose-binding protein, myoglobin, and cytochrome c were also introduced into the periplasm and had diffusion coefficients identical to that determined for the maltose-binding protein. For all proteins nearly 100% recovery of fluorescence was obtained after photobleaching, indicating that the periplasm is a single contiguous compartment surrounding the cell. These data have considerable implications for periplasmic structure and for the role of periplasmic proteins in transport and chemotaxis.     

Lateral diffusion in inhomogeneous membranes. Model membranes containing cholesterol.

The problem of lateral diffusion in inhomogeneous membranes is illustrated by a theoretical calculation of the lateral diffusion of a fluorescent lipid probe in binary mixtures of phosphatidylcholine and cholesterol under conditions of temperature and composition such that this lipid mixture consists of alternating parallel domains of fluid and solid lipid, having separations that are small compared with the distance scale employed in photobleaching experiments. The theoretical calculations clearly illustrate how inhomogeneities in membrane composition affecting the lateral motion of membrane components on a small (10-100 nm) distance scale can give complex diffusive responses in experiments such as fluorescence photobleaching that employ comparatively macroscopic distances (10-100 micrometers) for the measurement of diffusive recovery. The theoretical calculations exhibit the unusual dependence of the apparent lateral diffusion coefficient of a fluorescent lipid probe on lipid composition in binary mixtures of cholesterol and phosphatidylcholines as reported by Rubenstein et al. (1979, Proc. Natl. Acad. Sci. U.S.A., 76:15-18).     

Extracellular space diffusion in central nervous system: anisotropic diffusion measured by elliptical surface photobleaching

Diffusion in the extracellular space (ECS) is crucial for normal central nervous system physiology. The determinants of ECS diffusion include viscous interactions with extracellular matrix/plasma membranes ("viscosity") and ECS geometry ("tortuosity"). To resolve viscosity versus tortuosity effects, we measured direction-dependent (anisotropic) diffusion in ECS in mouse spinal cord by photobleaching using an elliptical spot produced by a cylindrical lens in the excitation path. Anisotropic diffusion slowed fluorescence recovery when the long axis of the ellipse was parallel versus perpendicular to the direction of faster diffusion. A mathematical model was constructed to deduce diffusion coefficients (D(x), D(y)) from fluorescence recovery measured for parallel and perpendicular orientations of the long axis of the ellipse. Elliptical spot photobleaching was validated by photobleaching aqueous-phase fluorophores on a diffraction grating, where diffusion is one-dimensional. Measurement of the diffusion of 70 kDa FITC-dextran in spinal cord in living mice indicated that viscosity slows diffusion by approximately 1.8-fold compared with its diffusion in solution. ECS geometry hinders diffusion across (but not along) axonal fibers in spinal cord further by approximately fivefold. In cerebral cortex, however, approximately 50% of the hindrance to ECS diffusion comes from viscosity and approximately 50% from tortuosity. We suggest that the extracellular matrix might have evolved to facilitate rather than hinder diffusion even for large molecules.     

The vacuole system is a significant intracellular pathway for longitudinal solute transport in basidiomycete fungi

Mycelial fungi have a growth form which is unique among multicellular organisms. The data presented here suggest that they have developed a unique solution to internal solute translocation involving a complex, extended vacuole. In all filamentous fungi examined, this extended vacuole forms an interconnected network, dynamically linked by tubules, which has been hypothesized to act as an internal distribution system. We have tested this hypothesis directly by quantifying solute movement within the organelle by photobleaching a fluorescent vacuolar marker. Predictive simulation models were then used to determine the transport characteristics over extended length scales. This modeling showed that the vacuolar organelle forms a functionally important, bidirectional diffusive transport pathway over distances of millimeters to centimeters. Flux through the pathway is regulated by the dynamic tubular connections involving homotypic fusion and fission. There is also a strongly predicted interaction among vacuolar organization, predicted diffusion transport distances, and the architecture of the branching colony margin.     

Diffusion of green fluorescent protein in the aqueous-phase lumen of endoplasmic reticulum

The endoplasmic reticulum (ER) is the major compartment for the processing and quality control of newly synthesized proteins. Green fluorescent protein (GFP) was used as a noninvasive probe to determine the viscous properties of the aqueous lumen of the ER. GFP was targeted to the ER lumen of CHO cells by transient transfection with cDNA encoding GFP (S65T/F64L mutant) with a C-terminus KDEL retention sequence and upstream prolactin secretory sequence. Repeated laser illumination of a fixed 2-micrometers diameter spot resulted in complete bleaching of ER-associated GFP throughout the cell, indicating a continuous ER lumen. A residual amount (<1%) of GFP-KDEL was perinuclear and noncontiguous with the ER, presumably within a pre- or cis-Golgi compartment involved in KDEL-substrate retention. Quantitative spot photobleaching with a single brief bleach pulse indicated that GFP was fully mobile with a t1/2 for fluorescence recovery of 88 +/- 5 ms (SE; 60x lens) and 143 +/- 8 ms (40x). Fluorescence recovery was abolished by paraformaldehyde except for a small component of reversible photobleaching with t1/2 of 3 ms. For comparison, the t1/2 for photobleaching of GFP in cytoplasm was 14 +/- 2 ms (60x) and 24 +/- 1 ms (40x). Utilizing a mathematical model that accounted for ER reticular geometry, a GFP diffusion coefficient of 0.5-1 x 10(-7) cm2/s was computed, 9-18-fold less than that in water and 3-6-fold less than that in cytoplasm. By frequency-domain microfluorimetry, the GFP rotational correlation time was measured to be 39 +/- 8 ns, approximately 2-fold greater than that in water but comparable to that in the cytoplasm. Fluorescence recovery after photobleaching using a 40x lens was measured (at 23 degrees C unless otherwise indicated) for several potential effectors of ER structure and/or lumen environment: t1/2 values (in ms) were 143 +/- 8 (control), 100 +/- 13 (37 degrees C), 53 +/- 13 (brefeldin A), and 139 +/- 6 (dithiothreitol). These results indicate moderately slowed GFP diffusion in a continuous ER lumen.     

Anomalous diffusion in a gel-fluid lipid environment: a combined solid-state NMR and obstructed random-walk perspective

Lateral diffusion is an essential process for the functioning of biological membranes. Solid-state nuclear magnetic resonance (NMR) is, a priori, a well-suited technique to study lateral diffusion within a heterogeneous environment such as the cell membrane. Moreover, restriction of lateral motions by lateral heterogeneities can be used as a means to characterize their geometry. The goal of this work is to understand the advantages and limitations of solid-state NMR exchange experiments in the study of obstructed lateral diffusion in model membranes. For this purpose, simulations of lateral diffusion on a sphere with varying numbers and sizes of immobile obstacles and different percolation properties were performed. From the results of these simulations, two-dimensional 31P NMR exchange maps and time-dependent autocorrelation functions were calculated. The results indicate that the technique is highly sensitive to percolation properties, total obstacle area, and, within certain limits, obstacle size. A practical example is shown, namely the study of the well-characterized DMPC-DSPC binary mixture. The comparison of experimental and simulated results yielded obstacle sizes in the range of hundreds of nanometers, therefore bridging the gap between previously published NMR and fluorescence recovery after photobleaching results. The method could also be applied to the study of membrane protein lateral diffusion in model membranes.     

Continuous photobleaching in vesicles and living cells: a measure of diffusion and compartmentation

We present a comprehensive and analytical treatment of continuous photobleaching in a compartment, under single photon excitation. In the very short time regime (t<0.1 ms), the diffusion does not play any role. After a transition (or short time regime), one enters in the long time regime (t>0.1-5 s), for which the diffusion and the photobleaching balance each other. In this long time regime, the diffusion is either fast (i.e., the photobleaching probability of a molecule diffusing through the laser beam is low) so that the photobleaching rate is independent of the diffusion constant and dependent only of the laser power, or the diffusion is slow (i.e., the photobleaching probability is high) and the photobleaching rate is mainly dependent on the diffusion constant. We illustrate our theory by using giant unilamellar vesicles ranging from approximately 10 to 100 microm in diameter, loaded with molecules of various diffusion constants (from 20 to 300 microm2/s) and various photobleaching cross sections, illuminated under laser powers between 3 and 100 microW. We also demonstrated that information about compartmentation can be obtained by this method in living cells expressing enhanced green fluorescent proteins or that were loaded with small FITC-dextrans. Our quantitative approach shows that molecules freely diffusing in a cellular compartment do experience a continuous photobleaching. We provide a generic theoretical framework that should be taken into account when studying, under confocal microscopy, molecular interactions, permeability, etc.     

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.     

Effects of organelle shape on fluorescence recovery after photobleaching

The determination of diffusion coefficients from fluorescence recovery data is often complicated by geometric constraints imposed by the complex shapes of intracellular compartments. To address this issue, diffusion of proteins in the lumen of the endoplasmic reticulum (ER) is studied using cell biological and computational methods. Fluorescence recovery after photobleaching (FRAP) experiments are performed in tissue culture cells expressing GFP-KDEL, a soluble, fluorescent protein, in the ER lumen. The three-dimensional (3D) shape of the ER is determined by confocal microscopy and computationally reconstructed. Within these ER geometries diffusion of solutes is simulated using the method of particle strength exchange. The simulations are compared to experimental FRAP curves of GFP-KDEL in the same ER region. Comparisons of simulations in the 3D ER shapes to simulations in open 3D space show that the constraints imposed by the spatial confinement result in two- to fourfold underestimation of the molecular diffusion constant in the ER if the geometry is not taken into account. Using the same molecular diffusion constant in different simulations, the observed speed of fluorescence recovery varies by a factor of 2.5, depending on the particular ER geometry and the location of the bleached area. Organelle shape considerably influences diffusive transport and must be taken into account when relating experimental photobleaching data to molecular diffusion coefficients. This novel methodology combines experimental FRAP curves with high accuracy computer simulations of diffusion in the same ER geometry to determine the molecular diffusion constant of the solute in the particular ER lumen.     

Sources of anomalous diffusion on cell membranes: a Monte Carlo study

A stochastic random walk model of protein molecule diffusion on a cell membrane was used to investigate the fundamental causes of anomalous diffusion in two-dimensional biological media. Three different interactions were considered: collisions with fixed obstacles, picket fence posts, and capture by, or exclusion from, lipid rafts. If motion is impeded by randomly placed, fixed obstacles, we find that diffusion can be highly anomalous, in agreement with previous studies. In contrast, collision with picket fence posts has a negligible effect on the anomalous exponent at realistic picket fence parameters. The effects of lipid rafts are more complex. If proteins partition into lipid rafts there is a small to moderate effect on the anomalous exponent, whereas if proteins are excluded from rafts there is a large effect on the anomalous exponent. In combination, these mechanisms can explain the level of anomaly in experimentally observed membrane diffusion, suggesting that anomalous diffusion is caused by multiple mechanisms whose effects are approximately additive. Finally, we show that the long-range diffusion rate, D(macro), estimated from fluorescence recovery after photobleaching studies, can be much smaller than D(micro), the small-scale diffusion rate, and is highly sensitive to obstacle densities and other impeding structures.     

The Obstacle-Set Method for Representing Muscle Paths in Musculoskeletal Models

A computational method is introduced for modeling the paths of muscles in the human body. The method is based on the premise that the resultant muscle force acts along the locus of the transverse cross-sectional centroids of the muscle. The path of the muscle is calculated by idealizing its centroid path as a frictionless elastic band, which moves freely over neighboring anatomical constraints such as bones and other muscles. The anatomical constraints, referred to as obstacles, are represented in the model by regular-shaped, rigid bodies such as spheres and cylinders. The obstacles, together with the muscle path, define an obstacle set. It is proposed that the path of any muscle can be modeled using one or more of the following four obstacle sets: single sphere, single cylinder, double cylinder, and sphere-capped cylinder. Assuming that the locus of the muscle centroids is known for an arbitrary joint configuration, the obstacle-set method can be used to calculate the path of the muscle for all other joint configurations. The obstacle-set method accounts not only for the interaction between a muscle and a neighboring anatomical constraint, but also for the way in which this interaction changes with joint configuration. Consequently, it is the only feasible method for representing the paths of muscles which cross joints with multiple degrees of freedom such as the deltoid at the shoulder.     

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.     

Spatial Fourier analysis of video photobleaching measurements. Principles and optimization.

The major use of the fluorescence recovery after photobleaching (FRAP) technique is to measure the translational motion of the molecular components in various condensed media. In a conventional laser spot photobleaching experiment, a photomultiplier is used to measure the total brightness levels of the bleached region in the sample, so no spatial information can be directly obtained. In video-FRAP, a series of images after photobleaching is acquired, allowing the spatial character of the recovery to be determined; this permits direct detection of both anisotropic diffusion and flow. To utilize all of the available image data to determine the transport coefficients, a two-dimensional spatial Fourier transform analysis of the images after photobleaching was employed. The change in the transform between two time points reflects the action of diffusion during the interim. An important advantage of this method, which involves taking the ratio of image transforms at different time points, is that it does not require a specific initial condition to be created by laser photobleaching. The ability of the analysis to extract transport coefficients from computer-simulated diffusional recovery is assessed in the presence of increasing amounts of noise. Experimental data analysis from the diffusion of proteins in viscous solutions and from the diffusion of protein receptors on cell surfaces demonstrate the feasibility of the Fourier analysis to obtain transport coefficients from the video FRAP measurement.     

Analysis of lateral diffusion from a spherical cell surface to a tubular projection.

Cell surfaces are often heterogeneous with respect to the lateral distribution and mobility of membrane components. Because lateral mobility is related to membrane structure, measurement of a particular component's local diffusion coefficient within a distinct surface region provides useful information about the formation and maintenance of that region. Many structurally interesting cell surface features can be described as narrow tubular projections from the body of the cell. In a companion paper, we consider the thin "tethers" that can be mechanically drawn from the red blood cell membrane, and we measure the transport of fluorescent integral proteins from the surface of the cell body onto the tether. In this paper we present an analysis to describe the surface diffusion of membrane particles from a spherical shell onto a thin cylindrical process. Provision is made for different rates of diffusion within the two morphologically distinct regions. The relative role of each region in controlling the diffusive flux between regions is determined primarily by a single dimensionless parameter. This parameter incorporates the ratio of the two diffusion coefficients as well as the dimensions of each region. The analysis can be applied to a fluorescence photobleaching experiment in which the extended process is bleached. If the dimensions of the spherical cell body and the cylindrical extension are known, then the diffusion coefficients of both regions can be determined from the experimental fluorescence recovery curve.     

Diffusion of tricarboxylic acid cycle enzymes in the mitochondrial matrix in vivo. Evidence for restricted mobility of a multienzyme complex

It has been proposed that enzymes in many metabolic pathways, including the tricarboxylic acid cycle in the mitochondrial matrix, are physically associated to facilitate substrate channeling and overcome diffusive barriers. We have used fluorescence recovery after photobleaching to measure the diffusional mobilities of chimeras consisting of green fluorescent protein (GFP) fused to the C terminus of four tricarboxylic acid cycle enzymes: malate dehydrogenase, citrate synthase, isocitrate dehydrogenase, and succinyl-CoA synthetase. The GFP-enzyme chimeras were localized selectively in the mitochondrial matrix in transfected Chinese hamster ovary (CHO) and COS7 cells. Laser photobleaching using a 0.7-microm diameter spot demonstrated restricted diffusion of the GFP-enzyme chimeras. Interestingly, all four chimeras had similar diffusional characteristics, approximately 45% of each chimera was mobile and had a diffusion coefficient of 4 x 10(-8) cm(2)/s. In contrast, unconjugated GFP in the mitochondrial matrix (targeted using COX8 leader sequence) diffused freely (nearly 100% mobility) with a greater diffusion coefficient of 20 x 10(-8) cm(2)/s. The mobility of the GFP-enzyme chimeras was insensitive to substrate source, ATP depletion, or inhibition of the adenine nucleotide translocase. These results indicate similar mobility characteristics of unrelated tricarboxylic acid cycle enzymes having different sizes and physical properties, providing biophysical evidence for a diffusible multienzyme complex in the mitochondrial matrix.     

Multiscale Measurements Distinguish Cellular and Interstitial Hindrances to Diffusion In Vivo

Molecular cancer therapy relies on interstitial diffusion for drug distribution in solid tumors. A mechanistic understanding of how tumor components affect diffusion is necessary to advance cancer drug development. Yet, because of limitations in current techniques, it is unclear how individual tissue components hinder diffusion. We developed multiscale fluorescence recovery after photobleaching (MS-FRAP) to address this deficiency. Diffusion measurements facilitated by MS-FRAP distinguish the diffusive hindrance of the interstitial versus cellular constituents in living tissue. Using multiscale diffusion measurements in vivo, we resolved the contributions of these two major tissue components toward impeding diffusive transport in solid tumors and subcutaneous tissue in mice. We further used MS-FRAP in interstitial matrix-mimetic gels and in vivo to show the influence of physical interactions between collagen and hyaluronan on diffusive hindrance through the interstitium. Through these studies, we show that interstitial hyaluronan paradoxically improves diffusion and that reducing cellularity enhances diffusive macromolecular transport in solid tumors.