Heparan Sulfate Mediates bFGF Transport through Basement Membrane by Diffusion with Rapid Reversible Binding*

Basic fibroblast growth factor (bFGF) is a pluripotent cytokine with a wide range of target cells. Heparan sulfate binds bFGF, and this interaction has been demonstrated to protect bFGF against physical denaturation and protease degradation. The high concentrations of heparan sulfate in basement membranes have implicated these matrices as storage sites for bFGF in vivo . However, the mechanisms by which basement membranes modulate bFGF storage and release is unknown. To gain insight into these mechanisms, we have developed experimental and mathematical models of extracellular growth factor transport through basement membrane. Intact Descemet’s membranes isolated from bovine corneas were mounted within customized diffusion cells and growth factor transport was measured under a variety of conditions that decoupled the diffusion process from the heparan sulfate binding phenom-enon. Transport experiments were conducted with bFGF and interleukin 1 b . In addition, bFGF-heparan sulfate binding was disrupted in diffusion studies with high ionic strength buffer and buffers containing protamine sulfate. Transport of bFGF was enhanced dramatically when heparan sulfate binding was inhibited. This process was modeled as a problem of diffusion with fast reversible binding. Experimental parameters were incorporated into a mathematical model and independent simulations were run that showed that the experimental data were accurately predicted by the mathematical model. Thus, this study indicated that basement membranes function as dynamic regulators of growth factor transport, allowing for rapid response to changing en-vironmental conditions. The fundamental principles controlling bFGF transport through basement membrane

Basic fibroblast growth factor (bFGF) is a pluripotent cytokine with a wide range of target cells. Heparan sulfate binds bFGF, and this interaction has been demonstrated to protect bFGF against physical denaturation and protease degradation. The high concentrations of heparan sulfate in basement membranes have implicated these matrices as storage sites for bFGF in vivo. However, the mechanisms by which basement membranes modulate bFGF storage and release is unknown. To gain insight into these mechanisms, we have developed experimental and mathematical models of extracellular growth factor transport through basement membrane. Intact Descemet's membranes isolated from bovine corneas were mounted within customized diffusion cells and growth factor transport was measured under a variety of conditions that decoupled the diffusion process from the heparan sulfate binding phenomenon. Transport experiments were conducted with bFGF and interleukin 1␤. In addition, bFGF-heparan sulfate binding was disrupted in diffusion studies with high ionic strength buffer and buffers containing protamine sulfate. Transport of bFGF was enhanced dramatically when heparan sulfate binding was inhibited. This process was modeled as a problem of diffusion with fast reversible binding. Experimental parameters were incorporated into a mathematical model and independent simulations were run that showed that the experimental data were accurately predicted by the mathematical model. Thus, this study indicated that basement membranes function as dynamic regulators of growth factor transport, allowing for rapid response to changing environmental conditions. The fundamental principles controlling bFGF transport through basement membrane that have been identified here might have applications in understanding how growth factor distribution is regulated throughout an organism during development and in the adult state.
Basic fibroblast growth factor (bFGF) 1 is a pluripotent growth factor that affects a wide range of cell types of meso-dermal, endodermal, and ectodermal origin. It has been implicated in processes ranging from wound healing to tumor growth (1,2). Like the other members of the FGF family, bFGF binds heparin and heparan sulfate (HS). The association of bFGF with heparin/HS is characterized by a dissociation constant in the nanomolar range. This interaction stabilizes the growth factor and protects it from proteolytic degradation (3). In vivo, HS is found linked to a protein core as a heparan sulfate proteoglycan. Basic FGF has been localized to HS sites in a specific extracellular matrix (ECM), the basement membrane, and it is a potent mitogen for the endothelial cells that border basement membranes (4,5). However, under normal physiological conditions these cell layers remain relatively quiescent. This observation, in conjunction with other in vivo and in vitro evidence, suggests that basement membrane HS plays a critical role in modulating the activity of bFGF by providing a natural reservoir for bFGF (6 -10). However, it is unclear how the basement membrane HS functions as a reservoir and regulates the transport of bFGF through ECM.
Several mechanisms have been proposed for the ECM-bFGF reservoir. Release of bFGF could be triggered by degradation of HS or the membrane by glycosaminoglycan degrading enzymes or protease activity. Alternatively, the growth factor could take advantage of nonspecific interactions with the HS chains and experience a form of one-dimensional diffusion along the HS chains allowing for accelerated movement through the matrix. This type of process might require that the HS concentrations reach a level where a continuous HS pathway through the matrix is available. Another possibility is that the rapid kinetics of bFGF association and dissociation from HS could provide a dynamic reservoir of bFGF that could release or incorporate bFGF in response to changes in the local bFGF or HS concentrations. Our previous studies on the kinetics of bFGF⅐HS binding suggest that the average lifetime of an bFGF⅐HS complex is approximately 1 min (11). Thus, the rapid binding could facilitate a dynamic storage and release system for bFGF that would not absolutely require matrix degradation to trigger release.
Researchers using in vitro systems have studied the properties of bFGF movement through artificial extracellular matrices and negatively charged hydrogels. Dabin and Courtois (12) conducted diffusion experiments with radiolabeled bFGF through Matrigel TM , an extract of Engelbreth Holm Swarm tumor matrix that is rich in HS. In their studies, either increasing the concentration of bFGF or adding soluble heparin along with bFGF, increased the amount of bFGF that crossed a layer of matrigel. Likewise, Flaumenhaft et al. (13) showed that positively charged proteins such as cytochrome c and bFGF demonstrated reduced diffusion through negatively charged agarose gels, and that both heparin and protamine sulfate can increase the radius of diffusion of bFGF and cytochrome c. They reported similar phenomena for diffusion within fibrin gels and * This work was supported by National Institutes of Health Grants HL46902 and EY11004, a Whitaker Foundation Biomedical Engineering Research grant, and Departmental grants from the Massachusetts Lions Research Fund and Research to Prevent Blindness, Inc. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
While these critical studies identified heparan sulfate as an important factor that can control the movement of bFGF through matrices, they did not provide information about the mechanism of this matrix transport. In addition, no data currently exist on the movement of bFGF through actual basement membrane samples. More controlled experimental systems need to be developed using actual basement membrane samples to obtain mechanistic information, and to determine how changes in the nature of bFGF, or its concentration, would affect transport in basement membranes. Furthermore, critical elements in the process can be identified by building mathematical models that incorporate the potentially important interactions between the matrix and its soluble components, thus enabling a comparison of the model's predictions to empirical studies. In this way, a systematic framework for understanding the interplay of key matrix/growth factor parameters can be developed.
In the present study we analyzed the transport of bFGF across Descemet's membrane (DM), the basement membrane of the corneal endothelium, using a model that considers the diffusion of bFGF through the interstices of the membrane coupled with fast, reversible association of bFGF to resident HS chains. Descemet's membrane is situated in the anterior region of the cornea between the corneal stroma and the endothelium. Its molecular structure is dominated by a dense meshwork of collagen VIII (15)(16)(17). The presence of the other major basement membrane components, collagen IV, laminin, entactin, fibronectin, and perlecan heparan sulfate proteoglycan has also been demonstrated (18,19). The ultrastructure of the DM has been determined by electron microscopy to be based on a lamellar hexagonal lattice of 80 nm nodes connected by rods approximately 120 nm long and 25 nm in diameter (16). Bovine DM can be as much as 100-m thick making it possible to physically isolate it for diffusion studies. Furthermore, the DM was the first basement membrane identified as a potential in vivo bFGF reservoir (4).
Basic FGF diffusion through the DM was measured with a diffusion chamber apparatus under different conditions that decoupled the diffusion process from the binding phenomenon. The diffusivity data was incorporated into a diffusion/binding model along with independent measurements of the bFGF-HS interaction. This model was used to simulate experimental results and suggests that the essential elements of the basement membrane bFGF reservoir are governed by diffusion and binding of bFGF.
Membrane Dissection and Storage-Whole bovine eyes were obtained from Pel-Freeze (Rodgers, AK) and shipped overnight on ice after harvest. The cornea was removed by cutting along its periphery with curved scissors, and placed endothelium face up on a spherical surface. The endothelium was removed by repeated wiping with a tissue followed with PBS rinses. A curved Teflon spatula was used to score the surface of the DM into quarters, and the DM was wetted with PBS. The exposed edge of the DM was gradually teased away from the stroma using the wedge-shaped edge of the Teflon spatula. Upon removal, the DM was placed in a vial with storage buffer (PBS, 0.1% sodium azide, 1 g/ml pepstatin, 0.5 g/ml leupeptin, and 1 mM N-ethylmaleimide). Membrane sections were stored in the refrigerator for as long as 2 months with no noticeable change in transport properties, but they were generally used within 3 weeks of dissection. In control studies, the permeability of freshly isolated membranes was analyzed over 4 days using a mixture of fluorescent dextrans and no time-dependent changes were noted. Furthermore, the permeability of bFGF was measured under identical experimental conditions in membranes stored for 5, 14, 27, and 36 days. In these studies FGF permeability varied by Յ13% from experiment to experiment with neither an increasing nor decreasing trend with time of membrane storage. The variability in bFGF permeability between experiments was generally less than or equal to that observed with multiple membranes in a single experiment.
Histology-Dissected membranes were fixed in formaldehyde, embedded in paraffin, and stained for basement membrane with the periodic acid shiff reagent (22). Visual inspection of membrane preparations revealed no evidence of residual corneal stroma or endothelium (data not shown).
bFGF Purification on Heparin-Sepharose-Immediately prior to each diffusion experiment, 125 I-bFGF samples were purified on heparin columns to separate non-heparin binding bFGF and dissociated free 125 I from native 125 I-bFGF. Heparin-Sepharose CL-6B was dissolved in deionized water to form a 1:2 gel to water slurry. A 100-l column was poured using U. S. Biochemical Corp. compact reaction columns and 1 liter of PBS was run over the column overnight. Leaching rates of heparin from the column after this wash were shown to be negligible. The column was equilibrated with approximately 30 ml of chilled PBS, 1 mg/ml BSA (PBS-BSA) buffer. All buffers that contacted bFGF were prepared with PBS with 1 mg/ml BSA as a carrier protein to reduce surface adsorption losses of bFGF. A 100-l aliquot of 125 I-bFGF (1-3 g/ml) diluted with 200 l of PBS-BSA was applied to the column. The column with bFGF was maintained in suspension on ice for a 10-min incubation period to allow bFGF to bind the heparin. 30 ml of chilled 0.5 M NaCl PBS were passed over the column to remove free label and unbound bFGF. After draining the column to its bed surface, 300 l of 3.0 M NaCl in 1 mg/ml PBS was added to the gel, and incubated on ice for another 10 min. The column was centrifuged (10,000 ϫ g for 30 s) into a 2-ml centrifuged tube to remove the eluant. In experiments conducted in 3.0 M NaCl buffer, the centrifugation step was omitted, and bFGF was eluted with 4 ϫ 200-l volumes of 3.0 M NaCl. The final concentration of 125 I-bFGF was determined by trichloroacetic acid precipitation. The radioactivity in the heparin-Sepharose purified material was greater than 99.0% precipitable by trichloroacetic acid.
Purification of Non-heparin Binding bFGF and IL-1␤-Size exclusion gel filtration chromatography was used to separate free 125 I-label from 125 I-IL-1␤ and inactive 125 I-bFGF. In these cases, a PD-10 column containing Sephadex G-25 gel filtration media was used to remove the free label. The column was equilibrated and the separation was conducted in PBS-BSA buffer. The radioactive peak that eluted in the void volume was collected as the radioactive protein. Greater than 98.5% of the radioactivity in the void volume was trichloroacetic acid precipitable. Additional gel filtration chromatographic analysis of the non-binding bFGF showed no evidence of oligomerization as compared with native bFGF. Thus, the inactive bFGF fraction appears to be similar in size yet without the heparin-binding affinity of native bFGF.
Diffusion Experiments- Fig. 1 is a schematic of the diffusion cell apparatus with membrane slide mounts. The chamber apparatus was secured with a metal clamp attached to a Lucite base. The glass diffu-bFGF Transport through Basement Membrane sion cells and mounts were coated to reduce protein adsorption through the covalent attachment of short carbohydrate chains to their glass surfaces (23). The chambers and membrane mounts were soaked in 6 N HCl overnight and washed exhaustively with deionized water to remove impurities. The coating solution was prepared with 25 ml of 3-glycidoxypropyltrimethoxysilane, 225 ml of deionized water, and 62.5 l of 1 M HCl to adjust the solution pH to 3.5. The chambers and slides were coated for 6 h at 90°C, including a 1-h warm-up period to prevent the glass chambers from fracturing. Following the coating the chambers were rinsed thoroughly with deionized water and placed in a dry box for storage. Control experiments using model compounds (urea and sucrose), with known aqueous diffusion coefficients, and a synthetic hydrophilic membrane (Durapore 0.65 m) were conducted to ensure that the membrane slide mounts did not introduce significant boundary layer effects near the surface of the membranes.
Membranes were placed between the two slide mounts, bolted in place, and the slides were positioned between the two diffusion cells. A bead of vacuum grease (Dow Corning Silicone vacuum grease) was applied around the face of each of the diffusion cells to maintain a water-tight seal. The clamp was tightened only until resistance was felt so as not to puncture the membranes. 3 ml of 0.22-m filtered PBS-BSA was added to each chamber and the apparatus was placed on a stir plate at 4°C. A coated Teflon microstir bar was added to each cell. These stir bars were surface modified by Corning Inc. with a polyethylene oxidelike, non-ionic, hydrophilic coating to limit protein adsorption to the Teflon (Corning, Inc., Corning, NY). The stirring rate was adjusted to 500 rpm. The assembled chambers were allowed to equilibrate for 15-20 h prior to initiating diffusion experiments.
The buffer in the sink chamber was removed and replaced with fresh buffer immediately prior to the start of the experiment. The contents of the source chamber was replaced with a phosphate buffer (10 mM NaPO 4 pH 7.4) lacking salt in experiments with native bFGF, since the 125 I-bFGF sample provided enough salt to bring the final concentration in the source chamber to 150 mM. Standard PBS-BSA was used in the source chamber in studies with non-heparin binding bFGF or IL-1␤. Experiments were initiated by introducing purified radiolabeled protein to the source chamber. Over the course of the experiment, 200-l samples were removed from the sink chamber at each time point. This volume was replaced with fresh PBS-BSA. The source chamber was also sampled at various time points during the course of the experiment. All samples were subjected to trichloroacetic acid precipitation to quantify 125 I-protein.
Trichloroacetic Acid Precipitation-Trichloroacetic acid precipitation was used to distinguish free radiolabel from radiolabeled protein. For a 200-l sample to be precipitated, the following volumes were added: 1) 1.25 ml of PBS or saline; 2) 100 l of 10 mg/ml BSA; and 3) 200 l of 10 mM KI. The samples were precipitated with 250 l of 100% trichloroacetic acid, vortexed vigorously, and placed on ice for 10 min. The samples were centrifuged for 10 min at 1,800 ϫ g and the supernatant was removed. The pellets were washed with 500 l of 14% trichloroacetic acid, and centrifuged again. Radioactivity in the pellet, supernatant, and wash solutions was measured in a ␥-counter (Packard Auto-␥ 5650).
Measuring Membrane Thickness-The thickness of the membrane is a critical parameter in the diffusion process. The thickness of each membrane was measured after each diffusion experiment by taking advantage of its natural tendency to curl over on itself. The membrane was viewed in cross-section and photomicrographs were made at ϫ 200 using a Nikon Diaphott microscope (Nikon). Membrane thicknesses were measured with a calibrated micrometer photographed at the same magnification. Based on 26 individual diffusion experiments with Descemet's membrane, the average membrane thickness was 40 m with a standard deviation of 8 m. The total thickness variation across a given membrane averaged 14 m. The data from each diffusion study was normalized to the thickness of the particular membrane used. While experiments conducted in 3.0 M NaCl buffer were also normalized to the thickness of the particular membrane used in those experiments, theoretical considerations suggest that membranes might be altered physically by the high ionic strength. Thus to evaluate whether the high salt conditions were altering membrane thickness, individual membranes were fixed in place in a continuous flow viewing chamber constructed of two glass slides and a neoprene gasket. Membranes within chambers containing 150 mM NaCl PBS were positioned on a microscope and photographed for baseline thickness measurements and then the buffer was exchanged to 3.0 M NaCl phosphate buffer through 20-gauge needle input and export ports within the chamber. Ionic strength was monitored in the outflow with an on-line conductivity meter and flow was stopped when the buffer was fully exchanged. Membrane thickness measurements were taken at the exact same positions along the fixed membrane over a 24-h period. An ϳ10% reduction in membrane thickness was noted after membrane equilibration into 3.0 M NaCl phosphate buffer.
Western Blotting and Autoradiography of Sink Cell bFGF-At the end (24 h) of diffusion experiments using high bFGF concentrations (1 M) samples were removed from the sink chambers and subjected to SDS-polyacrylamide gel electrophoresis (15% running gel) under reducing conditions (24). Control lanes were included containing PBS-BSA buffer alone. Proteins were electrotransferred to Immobilon P membranes and bFGF was detected with an anti-bFGF antibody (25). The membranes were blocked overnight in 10% milk in PBS with 0.1% Tween 20, probed for 1 h at 37°C with mAb anti-bFGF type II at 1:1000 dilution, and incubated with horseradish peroxidase-linked anti-mouse IgG (from sheep) at 1:1000 dilution. The bands were visualized with Renaissance Western blot chemiluminescent reagent (NEN Life Science Products Inc.) on X-Omat AR scientific imaging film (Kodak, Rochester, NY). After the chemiluminescent reagent had been exhausted, a fresh piece of film was placed over the blot and allowed to expose for 2 months at Ϫ70°C to detect radioactive samples. Sink chamber bFGF was also determined to retain its heparin binding activity as determined by heparin-Sepharose chromatography.
Measuring Partition Coefficients-Descemet's membranes were dissected as described above and diced until the larger pieces were approximately 1 mm 2 . U. S. Biochemical Corp. microcolumns were incubated in PBS-BSA and then weighed dry. Membranes (0.052-0.065 g) were added to each column and allowed to incubate in PBS-BSA while being constantly inverted at 4°C for 12 h. The wet mass of the membranes was determined by centrifuging the columns for 30 s at 50 ϫ g to remove excess solution and subsequently by measuring the total mass. Five hundred microliters of PBS-BSA containing non-heparin binding 125 I-FIG. 1. Diffusion chamber apparatus. The diffusion chamber apparatus consisted of a portion of Descemet's membrane secured with a pair of glass slide mounts. The slide mounts were placed between the two diffusion chambers. Both chambers were mixed with 3 ϫ 10-mm stir bars. Samples ports provided access to each chamber.
bFGF Transport through Basement Membrane bFGF or 125 I-IL-1␤ were added to the membranes in the columns and incubated at 4°C with constant rotation for 5 h. The centrifugation step was repeated. The membrane containing columns and their incubation solutions were weighed and the radioactivity was measured with a ␥-counter. The volume of incubation solution was determined by mass difference. PBS-BSA was applied through the membrane containing columns at 4°C at a flow rate of 1 ml/min and 2-ml fractions were collected. Radioactivity in these fractions was measured in a ␥-counter. The partition coefficient was determined from the known membrane volume (V mem ), the total amount of elutable radioactivity from the membranes (␥ mem ), the volume of incubation solution (V bulk ), and the total cpm of the incubation solution (␥ bulk ).
The partition coefficient for bFGF in the DM was 1.48 Ϯ 0.03 and for IL-1␤ was 1.49 Ϯ 0.05. The reported errors represent half the total range for duplicate determinations.
Diffusion/Binding Analysis-The goal of this study was to determine if the complex process of bFGF transport through basement membrane could be described with a simple diffusion/binding model. Thus, bFGF would diffuse through the matrix of the basement membrane and experience rapid, reversible association with the resident HS chains. Diffusion with reaction can be represented by the following equation, Here, b is the molar concentration of free bFGF in the membrane. The concentration of bFGF⅐HS complex is represented by c. As this is a one-dimensional equation for diffusion, t is time, and is the distance through the matrix. D eff is the effective diffusivity of bFGF in the ECM. The diffusivity of bFGF through the tight meshwork of ECM is expected to be much lower than the free aqueous diffusivity of bFGF. K is a partition coefficient that relates the concentration of unbound bFGF in the matrix to its bulk concentration. This value will be influenced by the nature of bFGF's interaction with the membrane and the proportion of the total aqueous volume of the matrix that is available to bFGF. In this formulation of the problem, the partition coefficient does not encompass the equilibrium binding interaction of bFGF with HS. The association of bFGF with HS sites in the membrane was modeled as a reversible association with a single class of binding sites with no cooperativity.
where k on and k off are the on-and off-rate constants for the interaction of bFGF with HS and h is the concentration of uncomplexed HS sites in the membrane. The concentrations of complex and free HS sites are also subject to the following constraint, where h tot is the total number of HS sites. Values for both the concentration of complexes (c) and the total concentration of HS sites (h tot ) reflect the presence of multiple bFGF binding sites per HS molecule. If the binding events take place on a much shorter time scale than diffusion, then the free bFGF and HS will be at local equilibrium with bound bFGF⅐HS complexes at each point in the membrane. This condition is satisfied when the Damkholer numbers for binding and release are much greater than 1.
Under these circumstances, the equilibrium dissociation constant (K d ) is sufficient to describe the reaction, At steady-state both time derivatives approach 0 in Equation 2, and the flux through the membrane becomes a constant.
Here, l is the membrane thickness. In our diffusion experiments, where radiolabeled proteins moved from a source chamber of high concentration to a sink chamber of much lower concentration, ⌬C was effectively the source concentration. Membrane thicknesses and the partition coefficient were measured directly. With these values, D eff was determined experimentally from the slope of a plot of flux versus time. The assumptions outlined above are true even in the presence of a reversible binding event in the membrane. Once the binding and release have reached a steady state throughout the membrane, the flux through the membrane becomes independent of the binding interaction. Thus, the relevant parameters are the effective diffusivity, the partition coefficient, the equilibrium binding constant, and the concentration of binding sites.
Numerical Solution to Diffusion Reaction Problem-Equations 2-4 were solved with a semi-implicit finite difference method (26) using the following boundary and initial conditions, Where A is the area available to diffusion, b°is the initial concentration of bFGF in the source chamber, V is the sink chamber volume, and the other variables are as described above.
The FORTRAN code was run on a Hewlett-Packard workstation. Case studies were conducted to check the validity of the model. The model successfully reproduced the analytical solutions to the simple diffusion problem and to the specialized case of diffusion with fast reversible binding to unsaturable binding sites.

RESULTS
Heparin Binding Slows bFGF Transport-The ability of bFGF to bind HS is likely to have a significant impact on its transport through an HS-rich matrix (12,13). To gain insight into the role of bFGF heparin binding in controlling transport, we conducted transport studies with the non-heparin binding (inactive) bFGF fraction that was isolated from the flowthrough during heparin-Sepharose affinity chromatography. This subfraction of 125 I-bFGF likely represented protein that had lost its ability to bind heparin as a result of the labeling process or from the freeze/thaw involved in storage. Thus inactive 125 I-bFGF represented a chemical analog of bFGF that was the same size and charge yet was structurally altered such that it did not bind heparin/HS. The transport characteristics of active (heparin binding) 125 I-bFGF and inactive 125 I-bFGF across Descemet's membrane were evaluated (Fig. 2). Over the time course of these studies native bFGF that retained its capacity to bind heparin was unable to cross the membrane with appreciable flux. The flux of the non-heparin binding form of bFGF, normalized for membrane thickness and bFGF source concentration, was approximately 20-fold greater than the normalized flux of native bFGF. The non-binding bFGF had reached steady state flux by 10 min, however, the native bFGF had still not reached steady state even after 24 h (1440 min). The diffusion of bFGF that bound heparin was dramatically reduced (Ͼ125-fold) compared with the non-binding bFGF. Using a steady state analysis (see Equation 8) an effective diffusivity of 7.0 ϫ 10 Ϫ9 cm 2 /s was calculated for the non-binding bFGF (Table I). Effective diffusion coefficients could not be determined for the native bFGF since steady state flux was not reached over the time course analyzed.
In the diffusion experiments, bFGF was detected in the sink chamber by measuring the trichloroacetic acid precipitable radioactivity. Detailed analysis of the sink contents were performed after some experiments to ensure that the radioactive protein accurately reflected the presence of intact bFGF. West-bFGF Transport through Basement Membrane ern blot analysis using anti-bFGF antibodies identified a protein band at 18 kDa, identical to that of the native bFGF starting material. Furthermore, autoradiographic analysis revealed that the band was the only protein containing 125 I-bFGF (Fig. 3). Thus, trichloroacetic acid precipitable radioactivity in the sink chamber accurately reflected the presence of 125 I-bFGF.
To confirm that HS was involved in modulating bFGF movement through DM, membranes were predigested with heparinase I (10 units/ml, 20 h, 37°C). Heparinase I was used since this enzyme targets the highly sulfated (heparin-like) sequences within heparan sulfate that have been implicated in bFGF binding (27). Diffusion studies with these membranes and 125 I-bFGF resulted in a 30% increase in bFGF normalized flux (data not shown). Although transport limitations, enzyme stability issues, and product inhibition prevented the enzyme treatment from digesting a significant percentage of DM HS, this study indicated that the HS retards native bFGF transport. Thus, the specificity of the enzyme treatment confirmed that HS is an important modulator of bFGF transport, however, additional methods were needed to completely remove the HS binding component from the transport process in order to obtain accurate values for the effective diffusivity parameter.
Decoupling Diffusion from Binding-Several complementary approaches were employed to obtain a reliable value for the effective diffusivity (D eff ) and to test our assumptions about the nature of bFGF interaction within and movement through the DM.
The diffusion of bFGF was compared with that of IL-1␤. IL-1␤ is a cytokine of 17 kDa, with a pI of 7.0. Although it contains little overall sequence homology with bFGF, the tertiary structure of IL-1␤ is very similar to bFGF, making bFGF and IL-1␤ structural homologs (28). Structures from both solution NMR and x-ray crystallography show that the two molecules have very similar molecular volumes (29, 30) with bFGF having a diameter of approximately 29 Å and IL-1␤ having a diameter of 32 Å. Hence, we assumed that the two proteins have similar aqueous diffusivities. Consequently, IL-1␤ was used as a bFGF "analog" that cannot bind heparin. Indeed, IL-1␤ demonstrated very similar transport properties to the non-heparin binding bFGF (Figs. 2 and 4). Based on this data and the partition coefficients for IL-1␤, an effective diffusivity for IL-1␤ of 6.6 ϫ 10 Ϫ9 cm 2 /s was obtained.
If the association of native bFGF with heparan sulfate is disrupted, the binding term is eliminated from the diffusion equation, and the flux of native bFGF should be comparable to fluxes measured for non-binding bFGF and IL-1␤. High ionic strength disrupts general electrostatic interactions in the membrane, and since ionic interactions are required for bFGF-HS binding, high salt concentrations will prevent bFGF binding to HS (31,32). The diffusion of bFGF and IL-1␤ through Descemet's membrane was conducted in 3.0 M NaCl PBS-BSA (Fig. 4). As expected, in a high salt environment, the flux of bFGF through the membrane was dramatically increased as compared with native bFGF in a physiological ionic strength buffer, by preventing bFGF from associating with the HS in the DM. The normalized flux of bFGF and IL-1␤ in 3.0 M NaCl were almost identical. However, the normalized fluxes for both proteins in a 3.0 M NaCl/PBS-BSA buffer were approximately 60% of the normalized flux of IL-1␤ in physiological saline buffer. In an independent experiment, the DM was seen FIG. 2. DM diffusion of heparin-binding and non-heparin binding bFGF. The time course for diffusion of native bFGF (E) and non-heparin binding bFGF (q) across two separate pieces of the same DM is presented. Initial bFGF source concentrations were set at 0.5 nM. Multiple samples were taken and subjected to trichloroacetic acid precipitation and each fraction (pellet, wash, supernatant) was counted and corrected for experimentally determined crossover and the averaged 125 I-bFGF concentrations in the source and sink chambers were calculated for each time point. At the end of the experiment, the membranes were removed and their thickness measured. Data presented represent the average sink concentration normalized to the membrane thickness and source chamber concentration (c sink ⅐l mem /c source ) in one representative experiment. Multiple (3-6) counts of source or sink chamber contents at given time points produced errors that were smaller than the data points presented. The averaged effective diffusivity for non-heparin binding bFGF was calculated to be 7.0 ϫ 10 Ϫ9 cm 2 /s. It was not possible to determine an effective diffusivity from the native bFGF transport data since steady state flux was not reached over this time course.  125 I-bFGF in the sink chamber was identified by Western blot and autoradiography. Sink chamber samples were taken after a 24-h transport study with an initial 125 I-bFGF source concentration of 1 M. Samples were subjected to reducing SDS-polyacrylamide gel electrophoresis (15% running gel) and transferred to Immobilon P membranes. Blots were hybridized with a monoclonal antibody to bFGF and a single band with a relative molecular mass of 18 kDa was revealed by chemiluminescence (lane 1). The chemiluminescence was exhausted by 2-day incubation at room temperature and autoradiography was conducted to identify radioactive protein (lane 2). Subsequent sectioning of the Western blot filter itself, followed by determining the radioactivity in a ␥-counter, showed that all of the radioactivity on the filter was associated with the 18-kDa bFGF. Similar results were observed in one additional experiment.

TABLE I Effective diffusion coefficients calculated from diffusion experiments
bFGF Transport through Basement Membrane to reduce in thickness approximately 10% in 3.0 M NaCl. The change in thickness probably translated into a reduced effective pore size (16) and resulted in reduced fluxes. The possibility that the high salt extracted the HS chains from the matrix during the experiment was also explored. Isolated Descemet's membranes were extracted overnight at 4°C in 3.0 M NaCl and the supernatant was collected after centrifugation. This supernatant was dialyzed against water with 3,000 MWCO tubing, lyophilized, and analyzed for heparan sulfate by using selective lyase treatment and the dimethylmethylene blue dye binding assay (33). No HS was present in the extract supernatant. Based on the limits of detection of the heparan sulfate assay and the total amount of HS present within the DM we calculate that Յ0.01% of DM HS was extracted by 3.0 M NaCl.
Protamine sulfate binds heparan sulfate, thereby preventing the association of bFGF with the HS chains (34). Consequently, protamine sulfate was used to more specifically decouple bFGF binding from diffusion without altering the bulk properties of the membrane. Membranes were preincubated with protamine sulfate (10 mg/ml) for 48 h at 4°C to ensure that all the HS sites in the membrane were occupied, and the diffusion studies were subsequently conducted in this concentration of protamine sulfate. With an average molecular mass of approximately 6 kDa, the protamine sulfate concentration was 1.7 mM, over 1 million times the source concentration of bFGF. The presence of protamine sulfate resulted in a dramatic increase in bFGF flux (Fig. 5) as compared with the flux of bFGF in PBS-BSA. The normalized flux of bFGF with protamine sulfate was within 10% of the normalized flux of IL-1␤. The effective diffusivity of bFGF determined from this data was 5.8 ϫ 10 Ϫ9 cm 2 /s. The similar results for bFGF with protamine sulfate and IL-1␤ diffusion were as expected. Both proteins have similar molecular dimensions, and in the protamine sulfate environment bFGF flux was not influenced by the HS in the DM.
Taken together the above data strongly implicates the HS-bFGF interaction as the primary determinant of flux through the membrane. Theoretically, if experiments with the low concentrations of bFGF used in Fig. 1 (0.5 nM) could be carried over very long time periods (days to weeks), bFGF would be expected to eventually saturate HS sites in the membrane and then the bFGF flux would be equal to the flux measured when the HS-bFGF interaction was blocked. However, control experiments revealed that denaturation of bFGF within the mixed diffusion chamber apparatus becomes significant between 24 and 48 h, making such experiments unfeasible. The approach to steady state can be greatly accelerated using higher concentrations of bFGF. Thus, transport was evaluated using a 2000fold higher concentration of bFGF (1 M based on enzymelinked immunosorbent assay) (Fig. 6). After a lag period of 11 h during which the HS sites were occupied, the normalized flux rose to approximately 80% of that derived from previous experiments with bFGF and protamine sulfate (Fig. 5).
Numerical Model of bFGF Transport-In order to determine if the experimental results could be explained by the diffusion/ binding model, key parameter values were measured experimentally and incorporated into a numerical solution of the diffusion/binding equations (Equations 2-4). The diffusion/ binding mathematical model requires information about the kinetics of the bFGF-HS interaction and the concentration of HS-binding sites. Thus, HS was extracted from the DM by ␤-elimination using alkaline borohydride treatment, and the HS was subsequently purified by ion exchange chromatography and chondroitinase ABC and keratinase III/endo-␤-galactosidase treatment. The number averaged molecular mass of the purified DM HS was determined to be 42 kDa. Based on the M r and the calculated purification yield, the concentration of HS in DM was determined to be 13 M (relative error estimates based on initial extraction yields indicate a possible range of 6.5-26 M). bFGF binding to purified DM HS was conducted using a rapid gel filtration method to separate and quantitate the relative amount of bFGF bound to DM HS. Using this method the K d of the interaction of bFGF with DM HS was determined to be 23.6 Ϯ 2.2 nM with a stoichiometry of 4 mol of bFGF bound per mole of HS chains. 2 The binding kinetics are fast, but minimum values were assigned to the k on and k off of 4.2 ϫ 10 5 /M Ϫ1 s Ϫ1 and 1 ϫ 10 Ϫ2 /s, respectively. The Damkholer numbers calculated from these kinetics and the measured effective diffusivities show that binding is, indeed, much faster FIG. 4. bFGF and IL-1␤ DM diffusion. Representative data for bFGF (E) and IL-1␤ (q) diffusion through DM in 3.0 M NaCl/PBS-BSA buffer and for IL-1␤ in PBS-BSA at physiological ionic strength (ϫ) are presented (initial concentrations, 0.5 nM). Averaged effective diffusivities for bFGF (3.8 ϫ 10 Ϫ9 cm 2 /s) and IL-1␤ (3.7 ϫ 10 Ϫ9 cm 2 /s) in 3.0 M NaCl and IL-1␤ (6.6 ϫ 10 Ϫ9 cm 2 /s) at physiological ionic strength were calculated from multiple experiments. Fluxes in all experiments were much higher than for heparin binding bFGF in PBS-BSA (Fig. 1). The sink chamber concentration was determined as described in the legend to Fig. 1 and under "Experimental Procedures," and has been normalized to the individual membrane thicknesses and source chamber concentrations (c sink ⅐lmem/c source ).
FIG. 5. bFGF DM diffusion with protamine sulfate. A representative set of data is presented for the diffusion of bFGF (0.5 nM source concentration) through DM in the presence of 10 mg/ml protamine sulfate (q) in PBS-BSA buffer. An averaged effective diffusivity (D eff 5.8 ϫ 10 Ϫ9 cm 2 /s) was calculated from multiple experiments. The sink chamber concentration was determined as described in the legend to Fig. 1 and under "Experimental Procedures," and has been normalized to the individual membrane thickness and source chamber concentrations (c sink ⅐l mem /c source ).
bFGF Transport through Basement Membrane than diffusion (Da off Ϸ 30; Da on Ϸ 1 ϫ 10 4 ). Consequently, a local equilibrium will always exist between soluble and bound bFGF at any position within the membrane. These parameters were entered into the mathematical diffusion/binding model and simulated experiments were conducted. The parameter values, obtained from independent experiments, that were included in the mathematical model are summarized in Table II. Fig. 7 shows the results of simulated bFGF (1 M, as in Fig.  6) diffusion experiments through Descemet's membrane using the parameter values described above. These simulations were conducted at a range of DM HS (6.5-26 M) concentrations that included the measured value and those at the extremes of the estimated error. For the concentration of HS that we measured in the DM (13 M), the model predicted a lag time of ϳ11 h, followed by a constant steady state flux that was within 10% of the experimental flux. Over the range of HS concentrations analyzed, the steady state flux varied only slightly while the predicted lag time ranged from 6.5 h at 6.5 M, to 23 h at 26 M HS. Thus within the estimated errors of the various model parameters, the simulations predicted transport data that were remarkably similar to the experimental values (Figs. 6 and 7). These results suggest that the transport of bFGF across a complex tissue can be represented with a comparatively simple diffusion/binding model. DISCUSSION The generation of growth factor, hormone, and morphogen gradients as a means to regulate cell function and differentiated state has become increasing appreciated as an important regulatory mechanism throughout biology (35)(36)(37)(38)(39)(40)(41). However, there remains little understanding of how such gradients are formed or stabilized over short distances within developing and adult organisms. A general hypothesis has been presented that the extracellular matrix might participate in generating morphogen gradients (36,38,42,43). In particular, the direct binding of growth factors, such as members of the FGF and transforming growth factor ␤ families, with extracellular matrix components has been suggested to be a critical element in cell and tissue regulation (43). In the present study we have addressed the role of the extracellular matrix as a regulator of growth factor transport at a fundamental level. By focusing on a model system of bFGF transport through an acellular extra-cellular matrix, Descemet's membrane, we have identified diffusion with rapid reversible binding to resident heparan sulfate as the critical elements that control bFGF movement. Furthermore, we have established and tested mathematical models of bFGF movement that can be applied to more general circumstances that are not amenable to controlled experimentation.
Although the transport of bFGF through the extracellular matrix is a complex process, we applied a simple model of solute diffusion with reversible binding to resident matrix sites to this process. We conducted experiments using the DM as a model to allow quantitative measurements of the effective diffusivity of bFGF under various conditions in which binding of bFGF to HS chains in the matrix was either blocked or saturated (Figs. 2 and 4 -6). Similar effective diffusivities were measured in all cases (Table I). The results from these studies, as well as direct determination of membrane HS concentration, bFGF binding kinetics, and partition coefficients were incorporated into a numerical solution of the diffusion/binding equation set (Equations 2-4). Simulated diffusion experiments were conducted to determine if these processes alone could accurately explain our data. The experimental results were represented very well by the diffusion/binding model (Figs. 6 and 7). Thus, our results suggest that reversible binding of bFGF to resident heparan sulfate can provide a mechanism for slow release, relative to the non-binding case, of active bFGF in vivo   7. Simulation of bFGF transport through DM. Simulation of bFGF (1 M source concentration) transport through DM by numerically solving the diffusion/binding problem with independent experimentally determined parameters (Table II)  bFGF Transport through Basement Membrane that does not require enzymatic degradation of the ECM or its components. However, in our studies where bFGF binding was prevented, we observed an enormous acceleration of bFGF transport. Hence, our data predicts that acute degradation of matrix resident heparan sulfate would dramatically enhance bFGF release rates. We saw no experimental evidence to support models where the ability of bFGF to bind HS can accelerate bFGF movement through the matrix. A mechanism for accelerated bFGF movement by HS might require greater concentrations of HS than we observed in the DM or simply might not exist in the extracellular matrix.
Other studies on bFGF transport through extracellular matrix have previously identified the interaction with heparin as critical to this process. In a study by Dabin and Courtois (12), transport of bFGF across a reconstituted basement membrane gel, Matrigel TM , could be enhanced by increasing the bFGF concentration or by adding soluble heparin. These investigators concluded that binding to resident heparan sulfate sites functioned to slow bFGF movement and that saturating these sites with bFGF or blocking the heparin-binding site on bFGF with heparin could decrease bFGF-gel interactions. While the present study is consistent with their hypothesis, the nature of the experimental system used by Dabin and Courtois and the fact that several key parameters (i.e. membrane thickness, HS concentration) were not determined, prevent quantitative analysis and direct comparison to the present study. Furthermore, work by Flaumenhaft et al. (13) also concluded that binding of bFGF to resident charged sites within an insoluble matrix would limit bFGF's diffusion radius. In this study, bFGF diffusion in agarose or fibrin gels was enhanced in the presence of soluble protamine, heparin, or suramin, suggesting that these agents were disrupting ionic interactions of bFGF with sites in the gels. Together these studies suggested a diffusion with binding model for bFGF movement through gels. In the present study we have extended these observations by treating this process quantitatively in order to develop a generalized mechanistic model of this transport process.
The experimental approach we employed using isolated pieces of DM should be generally applicable to studying the diffusion of other proteins or drugs through the basement membrane. Since this is the first report of an experimental system that allows quantitative measurements of solute transport through intact, nonextracted or homogenized, basement membrane tissue specimens, the literature contains no previous direct measurements of diffusivities in Descemet's membrane for comparison. The flux of inulin (5,200 g/mol) through corneal stroma with and without Descemet's membrane was measured (44), and a permeability for the DM of 1.7 ϫ 10 Ϫ6 cm/s for 70-m thick membranes was reported. If we use our measured partition coefficient of 1.5, this permeability corresponds to a D eff of 8 ϫ 10 Ϫ9 cm 2 /s for inulin in DM. Given the smaller size of the inulin molecule, this value is in good agreement with the diffusivities measured here for bFGF and IL-1␤. Thus, data generated with our experimental system is likely to be a good indicator of basement membrane transport properties within the context of an intact tissue.
Diffusivities for a globular protein of bFGF's dimensions in free aqueous solution (D o ) would be expected to be approximately 1.5 ϫ 10 Ϫ6 cm 2 /s using the Stokes-Einstein equation based on a bFGF radius of 14.5 Å. Hence the ratio D eff /D o is 0.004. This analysis indicates that the structure of the DM presents a very significant transport barrier to small proteins even in the absence of binding. It is likely that the combination of the viscous drag and tortuosity provided by the tight meshwork of protein and hydrated polysaccharide within the membrane results in significantly retarded protein diffusion (45).
The diffusivities reported here (Table I) were all based on the steady state method. However, a lag time method can also be used to determine effective diffusivities under conditions where binding does not occur. The lag time (t lag ) is defined as the x-intercept of the line describing steady state flux in a plot of total solute in the sink chamber as a function of time (D eff ϭ l 2 /6 t lag ). However, this approach relies heavily on gaining accurate data points at the early times, where error is maximal, and is much more sensitive to varying membrane thickness than the steady state approach. For these reasons the steady state method produced more accurate values of D eff and was the method of analysis we used. Nevertheless, effective diffusivities determined using the lag time method were calculated (2 ϫ 10 Ϫ9 to 9 ϫ 10 Ϫ9 cm 2 /s) and found to be in good agreement with the values obtained from the steady state approach.
When heparan sulfate binding was allowed with high concentrations of bFGF, lag times of 10 and 14 h were observed experimentally which compared very well with a model lag time of 11.5 h (Figs. 6 and 7). The largest sources of error in the parameter values for the simulations were in the concentration of HS sites. The effect of this error was most pronounced on the lag time. Simulated lag times ranged from 6 to 22 h when maximum and minimum values for the HS concentration were used. However, across the entire error range of HS concentrations, the steady state flux was within 10% of the experimentally measured flux. These results indicate that the diffusion/ binding model accounts very accurately for the movement of bFGF through the DM, and suggest that this model can be a useful tool for exploring the role of ECMs in controlling the bioavailability of bFGF in various tissue environments once the necessary parameters (Table II) are known.
The diffusion/binding model can provide insights into the role of basement membranes in regulating bFGF activity in vivo. Most basement membranes are much thinner than Descemet's membrane and are typically 50 -100 nm thick. On this length scale, diffusion and binding events will occur on similar time scales. Consequently, a 100-nm thick basement membrane would be expected to behave very differently than a 50-m thick Descemet's membrane with regard to its ability to act as a bFGF reservoir. In order to determine the implications of our diffusion/binding model for bFGF storage and release from thin basement membranes, several simulations were conducted employing the model parameters determined for Descemet's membrane. However, in this case, a 100-nm thick FIG. 8. Simulated bFGF loss from 100-nm thick basement membrane. The diffusion/binding model was used to simulate the loss of bFGF from a saturated membrane 100 nm thick exposed to infinite sinks on both faces (thick line). The fractional saturation of the HS sites along the membrane's center line is plotted as a function of time.
membrane was initially saturated with bFGF. In the simulation, this membrane is exposed to infinite sinks on both faces, and the loss of bFGF from the membrane was tracked over time (Fig. 8). The concentration of bFGF along the centerline of the membrane is plotted as a function of time. After 10 min virtually all the bFGF has been lost from the membrane.
The simulation of bFGF through thin membranes (Fig. 8) was an extreme example. In an organism, the basement membrane is likely bound on one surface by a tightly connected cell layer, and on the other face by tissue. The cell and tissue layers are likely to contain heparan sulfate as well. Consequently, bFGF loss from a basement membrane will be, to some extent, determined by the local environment of the membrane. One conclusion that can be drawn from the simulation is that basement membranes provide dynamic reservoirs for bFGF. While in the basement membrane, the bFGF is protected from protease activity and generally stabilized by its interaction with heparan sulfate (46 -48). However, changes in the environment of the basement membrane, such as physical damage, could result in rapid release of bFGF. Indeed, we and others have identified a number of physiologically relevant situations where bFGF binding and release from extracellular matrix is a critical component to cell and tissue response to injury (49,50). These include: the regulation of vascular smooth muscle cell proliferation (33,51,52), control of elastogenesis in pulmonary fibroblasts (25), and corneal wound healing (53).
The complex process of bFGF transport through the DM extracellular matrix can be represented with a simple model encompassing bFGF diffusion with reversible binding to the HS chains of the DM. Extracellular matrices are critical components in all multicellular organisms. They play important roles in development, in normal tissue function, and in disease states. Understanding the roles of ECMs in controlling extracellular signaling is an essential step toward understanding aspects of development, tissue repair, and tumor pathogenesis. This study has demonstrated that a comparatively simple mathematical model that describes the basic physics and chemistry of bFGF diffusion coupled with association to HS chains can capture the essentials of the complex process of bFGF transport across actual basement membrane.