J Neurophysiol 92: 3471-3481, 2004.
First published July 21, 2004; doi:10.1152/jn.00352.2004
0022-3077/04 $5.00
Diffusion of Epidermal Growth Factor in Rat Brain Extracellular Space Measured by Integrative Optical Imaging
Robert G. Thorne,
Sabina Hrab
tová and
Charles Nicholson
Department of Physiology and Neuroscience, New York University School of Medicine, New York, New York 10016
Submitted 6 April 2004;
accepted in final form 19 July 2004
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ABSTRACT
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Epidermal growth factor (EGF) stimulates proliferation, process outgrowth, and survival in the CNS. Understanding the actions of EGF necessitates characterizing its distribution in brain tissue following drug delivery or release from cellular sources. We used the integrative optical imaging (IOI) method to measure diffusion of fluorescently labeled EGF (6,600 Mr; 4 µg/ml) in the presence of excess unlabeled EGF (90 µg/ml) to compete off specific receptor binding and reveal the "true" EGF diffusion coefficient following injection in rat brain slices (400 µm). The effective diffusion coefficient was 5.18 ± 0.16 x 10–7 (SE) cm2/s (n = 22) in rat somatosensory cortex and the free diffusion coefficient, determined in dilute agarose gel, was 16.6 ± 0.12 x 10–7 cm2/s (n = 27). Tortuosity (
), a parameter representing the hindrance imposed on EGF by the convoluted brain extracellular space (ECS), was 1.8, the lowest yet measured by IOI for a protein in brain. Control experiments with fluorescent dextran of similar molecular weight and tetramethylammonium confirmed EGF did not affect local ECS structure. We conclude that transport of smaller growth factors such as EGF through brain ECS is less hindered than that of larger proteins (>10,000 Mr, e.g., nerve growth factor) where typically > 2.1. Modeling was used to predict that low will allow EGF sources in the brain to be further from target cells and still elicit a biological response. High values for larger growth factors imply more constrained local biological effects than with smaller proteins such as EGF.
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INTRODUCTION
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Neurotrophic factors such as epidermal growth factor (EGF) and nerve growth factor (NGF) are diffusible signals capable of regulating the development, growth, and survival of neurons (Loughlin and Fallon 1993
). The spatial and temporal aspects of neurotrophic factor concentration gradients are thought to regulate many processes (e.g., axon guidance and dendritic branching) in both the developing and mature nervous system (Cao and Shoichet 2001; Goodhill 1998; Horch and Katz 2002). During development, limited amounts of specific neurotrophic factors are secreted by target cells, supporting the survival of neurons close enough to receive a sufficient supply (Levi-Montalcini 1987). Similarly, therapeutic delivery of exogenous growth factors to the CNS is constrained by limitations on protein spread, so that target sites of action must be close to sites of release (Thorne and Frey 2001). Diffusion governs the movement of molecules through brain extracellular space (ECS) and determines, along with clearance (enzymatic breakdown or efflux across the blood-brain barrier) and cellular uptake, the distribution of molecules after their release into the ECS (Nicholson 2001; Nicholson and Syková 1998). Although the diffusion coefficients of small ions (Cserr et al. 1991; Kume-Kick et al. 2002; Lehmenkühler et al. 1993; Nicholson and Phillips 1981; Pérez-Pinzón et al. 1995) and macromolecules such as dextrans (Nicholson and Tao 1993) and albumins (Tao and Nicholson 1996) have been determined in brain tissue, there is no information about the diffusion characteristics of neurotrophic factors other than NGF (Stroh et al. 2003).
Two independent factors govern the diffusion of molecules through biological tissues (Nicholson 2001; Nicholson and Syková 1998), the volume fraction of the ECS (
), and tortuosity (). Studies using electron microscopy, radiotracers, or iontophoresis of small ions all indicate a value for in normal brain of about 0.2 (i.e., ECS accounts for 20% of the total tissue volume). The hindrance experienced by molecules as they travel through the porous brain ECS and encounter obstructions is described by , a dimensionless parameter formally defined as = (D/D*)1/2 where D is the diffusion coefficient of the molecule in a free medium (water or dilute agarose) and D* is the effective diffusion coefficient of the same molecule in brain (Nicholson 2001). Whereas is a property of the tissue, is sensitive to tissue properties such as geometry (Chen and Nicholson 2000; Hrabtová et al. 2003; Kume-Kick et al. 2002; Tao 1999) and extracellular matrix composition (Rusakov and Kullmann 1998; Vargová et al. 2003; Vo
í
ek et al. 2002), as well as to binding (Berk et al. 1997) and the physicochemical properties (size, shape, and charge) of the diffusing molecule (Nicholson and Tao 1993; Prokopová-Kubinová et al. 2001; Tao and Nicholson 1996). In theory, diffusion analysis using appropriate small markers can isolate the effects of tissue properties on , because the influences of binding and the physicochemical properties of the diffusing molecule are negligible. Accordingly, measurements with small ions such as tetramethylammonium have yielded 
1.6 in most brain regions, both in vivo (Cserr et al. 1991; Lehmenkühler et al. 1993; Mazel et al. 1998; Nicholson and Phillips 1981; Roitbak and Syková 1999) and in the rat brain slice preparation (Cragg et al. 2001; Hrabtová and Nicholson 2000; Hrabtová et al. 2002; Kume-Kick et al. 2002; Pérez-Pinzón et al. 1995; Rice and Nicholson 1991). Studies with dextran macromolecules have shown increases from about 1.8 for 3,000 and 10,000 Mr dextrans to about 2.2 for 40,000 and 70,000 Mr dextrans (Nicholson and Tao 1993), suggesting globular molecules experience an increase in hindrance abovea critical size. To date, measurements with protein macromolecules have shown to be in the range of 2.1–2.5 (Stroh et al. 2003; Tao and Nicholson 1996), although these studies have been limited to three albumin species (14,500–66,000 Mr) and NGF (26,500 Mr). The question of whether a smaller protein might diffuse through brain ECS with less hindrance, approaching the low observed with smaller (
10,000 Mr) dextrans, is as yet unresolved.
EGF is a small (53 amino acids; 6,100 Mr), negatively charged [isoelectric point (pI) 4.6] neurotrophic factor (Taylor et al. 1972) that is capable of stimulating proliferation, chemotaxis, process outgrowth, and survival in the CNS (Yamada et al. 1997). Expression of EGF and its receptor in the CNS are regionally and developmentally dependent (Gómez-Pinilla et al. 1988; Yamada et al. 1997). In adult rat telencephalon, EGF levels are low, while EGF receptor immunoreactivity is prominent in cortical neurons of layers IV and V (Gómez-Pinilla et al. 1988). Much is known about the signal transduction mechanisms following EGF binding to its receptor (Sako et al. 2000; Schlessinger 2002), but EGF diffusion has not been explicitly studied.
We hypothesized that EGF would diffuse through brain ECS with lower than larger proteins and that this enhanced transport could be physiologically important. Here, we have measured the diffusion of EGF in the rat neocortical slice preparation using integrative optical imaging (IOI) and show the possible significance of the results through appropriate modeling.
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METHODS
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Neocortical slice preparation
All experiments were carried out at NYU School of Medicine in accordance with National Institutes of Health guidelines and local Institutional Animal Care and Use Committee regulations. Neocortical slices were prepared from 145- to 180-g female Sprague-Dawley rats (postnatal day 40–50; Taconic) as described previously (Nicholson and Tao 1993; Rice and Nicholson 1991). Animals were anesthetized with sodium pentobarbital (60 mg/kg ip) and decapitated by guillotine. The brain was rapidly removed, mounted onto a specimen plate using cyanoacrylate, and immersed in chilled artificial cerebrospinal fluid (ACSF). The composition of ACSF was as follows (in mM): 124 NaCl, 5 KCl, 26 NaHCO3, 1.25 NaH2PO4, 1.3 MgCl2, 1.5 CaCl2, and 10 D-glucose equilibrated with 95% O2/5% CO2. The osmolality of ACSF, determined with a freezing point osmometer (Osmette A, model 5002, Precision Systems), was 300 ± 5 mOsm/kg. Coronal slices (400 µm) were prepared using a vibrating blade microtome (VT-1000 S, Leica Microsystems AG) and incubated in ACSF at room temperature for 
1 h. Slices were taken from the interaural 5- to 6-mm planes for EGF experiments and the interaural 5- to 6.7-mm planes for dextran experiments.
For diffusion measurements, individual slices were transferred to a submersion chamber (model RC-27L, Warner Instruments) in the center of a fixed platform (Gibraltar, Burleigh Instruments) under an upright microscope (BX61WI, Olympus Optical). A peristaltic pump (Minipuls 3, Gilson) provided continuous perfusion (2.0 ml/min) of the chamber with ACSF, maintained at 34 ± 1°C using a solution in-line heater (model SH-27A, Warner Instruments) and heated chamber platform (PH-6D, Warner Instruments) under the control of a dual-channel automatic heater controller (TC-344B, Warner Instruments). All measurements were made at a depth of 200 µm in the barrel field and trunk region of the primary somatosensory cortex, layers III–VI (Swanson 1998).
Fluorescent conjugates
Initial diffusion measurements were conducted in agarose with fluorescein, tetramethylrhodamine, and Oregon Green 514 (OG514) conjugates of mouse submaxillary gland EGF (catalog E-3478, E-3481, and E-7498, respectively, Molecular Probes). Since OG514-EGF showed better photostability than fluorescein-EGF, and tetramethylrhodamine-EGF tended to aggregate in solution, we used OG514-EGF (Fig. 1) in all experiments reported here. The OG514 dye, a fluorinated analog of fluorescein, contributes two negative charges because its phenol (pKa 4.7) and carboxylic acid (pKa < 5) functional groups are almost completely ionized at physiological pH. The overall net charge of the OG514-EGF conjugate is therefore approximately –5, from the dianion OG514 (fluorophore to protein molar ratio = 1.0 by HPLC; Molecular Probes; personal communication) and the net –3 charge of unconjugated murine EGF, taking into account the loss of one positive charge from the N-terminal conjugation of OG514. The position of EGF's N-terminal amine is located away from residues important for receptor binding (Fig. 1). As a consequence, N-terminal EGF-fluorophore conjugates retain EGF receptor binding capacity (Sako et al. 2000; Molecular Probes) and are nearly equivalent to unconjugated EGF in terms of their activity (Whitson et al. 2004). The OG514-EGF (6,600 Mr) was reconstituted to a final concentration of 4 µg/ml (610 nM) with 90 µg/ml unlabeled EGF (catalog E1257, Sigma) in phosphate buffered saline containing 0.1% BSA. Texas Red–labeled 3,000 Mr dextran (TR-dex3; catalog D-3329, Molecular Probes) was used at a concentration of 1 mM in 154 mM NaCl, as described previously (Nicholson and Tao 1993). An additional 1 mM TR-dex3 solution containing 100 µg/ml unlabeled EGF (catalog E1257, Sigma) was prepared to assess the influence of EGF on ECS structure. All solutions were vortexed for 1–2 min, centrifuged at 12,000 x g for 5 min, and loaded into micropipettes, pulled from thin-wall borosilicate capillary glass (catalog 6170, A-M Systems), with tip diameters of 3–6 µm.
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FIG. 1. Structure of murine epidermal growth factor (EGF) with covalently attached Oregon green 514 (OG514) fluorophore. Charges associated with the fluorophore and specific amino acids of EGF at physiological pH are shown. Amino acid residues important for binding to the EGF receptor (Ogiso et al. 2002) are also indicated (*).
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IOI
The IOI method uses epifluorescence microscopy and quantitative image analysis to measure the diffusion of molecules over time after a brief pressure ejection, approximating a point source (Nicholson and Tao 1993). A small volume U of fluorescently labeled macromolecules at concentration Cp was ejected into a slice from a micropipette by a 50- to 200-ms nitrogen pulse delivered from a pressure ejection system (Picospritzer II, General Valve). When the pulse is very brief compared with the times (t) of subsequent diffusion measurements, the concentration C can be described by (Nicholson 2001)
 | (1) |
where r is the distance from the injection site, D is the free diffusion coefficient (cm2/s), and ke (s–1) is a linear elimination constant. A virtual point source-time origin, t0 (s), arises in practice due to experimental deviation from a true point source at t = 0, but it can be shown that this approximation makes little difference to the analysis under typical experimental conditions (Prokopová-Kubinová et al. 2001). Fluorescently labeled molecules such as EGF may reversibly bind to receptors as they diffuse through brain tissue so they stop moving but remain visible. The effect of a fast, reversible linear binding process would be to retard the rate of diffusion, with the resulting D* (D* = D/2) reduced in proportion to the magnitude of the equilibrium binding constant (Saltzman 2001). To minimize the effects reversible binding in the brain slice might have on measured values of D*, fluorescently labeled EGF was injected with excess unlabeled EGF to compete off specific binding. The >20-fold molar excess of unlabeled EGF (15 µM compared with 600 nM OG514-EGF) was expected to saturate local receptor binding sites, because its concentration was well above reported values for the EGF receptor affinity constant (KD = 0.67 nM) (Waters et al. 1990).
The basic experimental setup for IOI has been thoroughly described (Nicholson and Tao 1993). The system used for this study (shown schematically in Fig. 2 A) consisted of an Olympus BX61WI microscope with a water-immersion objective (UM PlanFl 10x, NA 0.3; Olympus), 75-W xenon epi-illuminator, and dichroic mirror system and filters appropriate to the fluorophore under study. Successive images of the diffusing cloud of molecules were collected at intervals of 1.5–10 s by a cooled charge-coupled device (CCD) camera (CoolSnap HQ Monochrome, Photometrics) at constant gain and acquired by computer using image processing software (V++ version 4.0, Digital Optics) running under a custom program (written by C. Nicholson) in MATLAB (The MathWorks). Measurements were made over rectangular images in the (x, y) plane at a depth z = 200 µm (i.e., the center of the slice). We used concentrations of fluorescently labeled EGF that were significantly lower than that for other macromolecules in previous IOI studies. Consequently, 4 x 4 binning of image pixels was employed to enhance the signal-to-noise ratio and improve curve fitting for diffusion analysis.
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FIG. 2. The integrative optical imaging (IOI) method. A: schematic diagram of the experimental setup. B: typical 2D (top) and 3D (bottom) representations of fluorescence intensity obtained shortly after pressure injection of fluorescently labeled macromolecules at the center of the image. Fluorescence intensity is extracted along 1 of 4 lines (a horizontal line labeled row in the figure, a vertical line labeled column, and 2 diagonal lines). C: fluorescence intensity data along a horizontal (row) line through images captured just after pressure ejection of fluorescently labeled 3,000 Mr dextran into a brain slice and 80 s later. Theoretical curves showing the best fit of Eq. 2 to the upper 75% of the data are superimposed. Fitting of the data resulted in D* (row, 33.4°C) = 6.60 x 10–7 cm2/s. The average D* obtained from fitting along all 4 lines was 5.96 x 10–7 cm2/s (33.4°C) or 6.05 x 10–7 cm2/s after correction to 34°C using the Einstein relationship (see APPENDIX). D: application of the IOI method allows calculation of the tortuosity, = (D/D*)1/2, a parameter reflecting the ratio of the effective path length in the brain to the path length in a free medium. Molecules migrate through the extracellular space (ECS) along a tortuous path that is governed by their size. Smaller molecules (small circles) are less restricted and can travel shorter paths (shown) as well as longer paths (not shown), whereas larger molecules (large circles) are limited to longer paths. The actual calculation of tortuosity involves a weighted average over all paths so that smaller molecules experience less tortuosity than larger molecules.
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Diffusion analysis was performed with an image analysis program (written by C. Nicholson) running under MATLAB. The theory of how the image of the diffusing cloud of molecules maps onto the camera sensor is complex (Nicholson and Tao 1993; Tao and Nicholson 1995) but it can be derived from Eq. 1 and described by
 | (2) |
and
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where Ii is the fluorescence intensity of the image at radial distance r, and Ei embodies the de-focused point spread function of the objective (Tao and Nicholson 1995). Here, we have set ke = 0 in Eq. 1, a simplification justified by the use of a slice preparation (the absence of blood flow eliminates most clearance mechanisms normally present in vivo), the short period over which measurements were taken (<2 min; minimizing enzymatic breakdown), and the presence of excess unlabeled EGF (competing off specific EGF receptor-mediated binding and uptake). Equation 2 was fit to the fluorescence intensity along one of four lines through each image (Fig. 2, B and C) at a succession of ti, yielding a sequence of estimates for 
i (Nicholson and Tao 1993; Prokopová-Kubinová et al. 2001). Constant illumination was maintained throughout the image acquisition process, and images were only used for analysis when the full range of fluorescence intensity contained in the image was within the linear range of the camera. Note that since does not appear in the final expression for Ii, it is not determined. In practice, fitting excluded the lower 25% of the fluorescence intensity curve for each image (Fig. 2 C, solid horizontal line) to reduce the consequences of light scattering in the tissue (Prokopová-Kubinová et al. 2001). Linear regression of (i)2 on ti allowed D* or D to be obtained from Eq. 3. Because the fluorescence intensity profile for each sequence of images was determined along each of the four lines, four replicate estimates of D* or D were obtained for each measurement. Values reported for n therefore each typically contain four separate estimates of D or D* for a total of 4 x n estimates. Determination of D was made in 0.3% Isogel agarose (Cambrex Bioscience Rockland) made up in 154 mM NaCl. This agarose is uncharged (i.e., there is no measureable electroendosmosis) due to minimization of normally present fixed anions (pyruvate and sulfate). Determination of both D and D* by IOI enabled calculation of , a parameter reflecting the ratio of the increased path length traveled in an obstructive medium (i.e., brain) to the path length traveled in a free medium for the average diffusing molecule (Fig. 2D).
Real-time iontophoretic method
The real-time iontophoretic (RTI) method employs iontophoresis of small ions, most commonly tetramethylammonium (TMA+; 74 Mr), from a source microelectrode and the measurement of the resultant local concentration over time about 100 µm away from the release site by an ion-selective microelectrode (ISM) to obtain diffusion parameters (Nicholson 1993; Nicholson and Phillips 1981). In addition to yielding both D and D* for the diffusing ion, diffusion analysis with the RTI method also yields , the volume fraction of the ECS. We used the RTI method with TMA+, as described previously (Hrabtová et al. 2003; Nicholson 1993; Nicholson and Phillips 1981), to determine whether is altered by pressure injection of a 1 mM TR-dex3 solution containing 100 µg/ml unlabeled EGF. Briefly, both source microelectrodes and ISMs were constructed from double-barreled theta glass (catalog TG200-4, Warner Instruments). Both barrels of the iontophoretic source microelectrodes were filled with 150 mM TMA+ chloride. For TMA+-ISMs, the ion-detecting barrel was filled with 150 mM TMA+ chloride above a charged liquid membrane ion exchanger (Corning 477317; currently available as IE 190 from World Precision Instruments) in the tip and the reference barrel, for detection of the local DC potential, was filled with 150 mM NaCl. Each TMA+-ISM was calibrated in a set of standard solutions (0.5, 1, 2, 4, and 8 mM TMA+ in 150 mM NaCl), and the resulting voltages were used to obtain the slope and interference of the ISM by fitting the data to the Nicolsky equation (Nicholson 1993).
The iontophoretic source microelectrode and TMA+-ISM were held in separate robotic micromanipulators (MP 285; Sutter Instrument) at an angle of 30° from the horizontal plane and positioned in dilute agarose or a brain slice so that their tips were 100 µm apart. For iontophoresis, a small positive bias current of 20 nA was continuously applied using a constant-current, high-impedance source (Axoprobe-A1 Amplifier, Axon Instruments) and stepped up to 100 nA for 50 s to obtain diffusion measurements. The TMA+ signal was extracted by continuously subtracting the potential of the reference barrel from the potential of the ion-detecting barrel using a dual-channel microelectrode preamplifier (IX2-700, Dagan). Recorded TMA+ signals and DC potentials were amplified and low-pass filtered (6 Hz) using a CyberAmp 320 (Axon Instruments) and monitored continuously on a chart recorder and intermittently on a computer following A/D conversion. The resulting data were fitted to an appropriate solution to the diffusion equation (Nicholson 1993) using a custom program in MATLAB. The transport number of the TMA+-ISM and D were obtained by performing diffusion measurements in 0.3% agarose (NuSieve GTG, FMC BioProducts) dissolved in 150 mM NaCl solution containing 0.5 mM TMA+ chloride. For measurements in brain, slices were prepared as described above except that ACSF also contained 0.5 mM TMA+ chloride to provide a stable reference baseline for the concentration measurements. A third micromanipulator was used to position the tip of an injecting micropipette (loaded with the TR-dex3 + EGF solution) between the tips of the iontophoretic source microelectrode and the TMA+-ISM (at a distance of 50 µm from each). TMA+ measurements in brain were performed both before and immediately after pressure injection of TR-dex3 + EGF (using a 100- to 200-ms nitrogen pulse). Inclusion of TR-dex3 in the injecting solution allowed us to use the fluorescent image to ensure that the TR-dex3 + EGF solution was applied between the iontophoretic source microelectrode and the TMA+-ISM. The data were fitted to extract D* for TMA+, which, together with the transport number of the ISM, allowed to be calculated.
Modeling
Models were generated and plotted in MATLAB using Eq. 1 for instantaneous release from a point source (t0 = 0) or an equation describing the concentration profile at steady state with continuous release from an interface held at constant concentration, Cv (Nicholson 2001)
 | (4) |
where x is the distance from the interface, and other variables are as described above.
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RESULTS
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EGF diffusion is hindered in somatosensory cortex
Diffusion coefficients were determined for a fluorescent analog of EGF, OG514-EGF (4 µg/ml), in the presence of excess (90 µg/ml) unlabeled EGF to compete off specific receptor binding and uptake. Measurements of D for OG514-EGF were first made following brief pressure injections in a dilute (0.3%) gel of uncharged agarose. Dilute agarose is an essentially "free" medium that eliminates thermal convection currents. All measurements of D* for OG514-EGF in primary somatosensory cortex were made in the center of a 400-µm slice in layers III–VI. After acquisition of a background image, OG514-EGF was pressure injected into either dilute agarose or cortex, and 10 subsequent images were taken at regular intervals (average interval in agarose, 2 s; average interval in brain, 8 s). Typical sequences of images taken after OG514-EGF injection into agarose or cortex are shown in Fig. 3 A. The concentration of OG514-EGF is proportional to the amplitude of fluorescence intensity, represented in pseudocolor (red highest, blue lowest). It is apparent that both sets of images are spherically symmetric about the injection point. Spherical diffusion of EGF away from the site of injection in somatosensory cortex confirmed earlier results that this area is isotropic (Mazel et al. 1998; Nicholson and Tao 1993; Tao and Nicholson 1996). We needed longer pressure pulses in cortex (200 ms) than in agarose (100 ms) to achieve sufficient fluorescence intensity, likely a consequence of greater light scattering in tissue. Figure 3B shows the Gaussian-shaped fluorescence intensity distributions, measured along an axis through the center of each image, along with the superimposed curve fits. The curves showing diffusion in agarose flatten and broaden characteristically over this short time period, a phenomenon predicted for point source diffusion and also clearly seen in cortex when curves for longer times are examined (data not shown). It is evident that the diffusion of EGF is hindered in cortex relative to agarose, a finding reflected in the diffusion coefficients obtained in each medium (Table 1). This hindrance was characterized by = 1.79 ± 0.03, similar to values reported previously for 3,000 and 10,000 Mr dextrans (Nicholson and Tao 1993; Tao and Nicholson 1996).
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FIG. 3. A: representative images taken after injection of OG514-EGF in 0.3% agarose or somatosensory cortex. B: fluorescence intensity data extracted from images in A and fitted with the diffusion equation. Fitting of data yielded D (34°C) = 16.4 x 10–7 cm2/s (agarose) and D* (34°C) = 5.64 x 10–7 cm2/s (somatosensory cortex). Pressure pulses (pressure/duration) used for injection were 20 psi/100 ms and 25 psi/200 ms in agarose and somatosensory cortex, respectively.
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EGF does not alter neocortical ECS structure over the short time span of IOI measurements
Following each injection of OG514-EGF and subsequent image acquisition, the micropipette was withdrawn from the slice and moved to a new location, greater than 600 µm from the previous injection. In this manner, repeat injections of OG514-EGF were never performed in the same parenchymal location to eliminate the possibility that EGF might affect the local environment and influence OG514-EGF diffusion after later injections. However, it was still possible that the first injection might immediately trigger a tissue response that could affect the ECS and influence the diffusion of OG514-EGF. To rule out this possibility, control experiments assessed whether simultaneous injections of 100 µg/ml EGF [approximately the same concentration as the total EGF (94 µg/ml) in the micropipette for OG514-EGF diffusion measurements] and TR-dex3 (1 mM) influenced the diffusion of TR-dex3 in somatosensory cortex. TR-dex3 was chosen because its diffusion in somatosensory cortex has been studied extensively with IOI (Nicholson and Tao 1993; Tao 1999; Tao and Nicholson 1996), and its size and D* are similar to that of EGF. Figure 4 shows a sequence of images taken over 90 s following injection of TR-dex3, alone or with EGF. No differences were observed in the dispersion of TR-dex3 with time in the absence or presence of EGF. Similarly, values obtained with either solution of TR-dex3 were indistinguishable from one another (Table 1) or from those reported in previous studies for fluorescent dex3 analogs (Nicholson and Tao 1993; Tao and Nicholson 1996).
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FIG. 4. Representative images taken after injection of Texas Red labeled 3,000 Mr dextran (TR-dex3) in the absence or presence of 100 µg/ml EGF. Fitting of the fluorescence intensity data resulted in D* (34°C) values of 6.14 x 10–7 and 6.05 x 10–7 cm2/s for TR-dex3 and TR-dex3 + EGF, respectively.
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Because the IOI method presently does not allow us to determine , we used a different technique, the RTI method, to evaluate whether may have been altered by the pressure injection of EGF. The RTI method involves iontophoretic release of the small ion TMA+ from a point source and its measurement over time at a known distance with an ion-selective microelectrode (Nicholson and Phillips 1981). The RTI method was employed before and immediately after pressure injection of a solution containing 100 µg/ml EGF and 1 mM TR-dex3, as above, and was evaluated in the area around the pressure injection over a duration of about 200 s. Diffusion analysis showed that was unaffected by pressure injection of EGF: before injection = 0.26 ± 0.01 (n = 6) and after injection = 0.25 ± 0.01 (n = 6). Taken together, these results suggest exposure to 100 µg/ml EGF did not affect the ECS in the vicinity of the injection site over the short period (<2 min) required for a single sequence of IOI measurements in brain.
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DISCUSSION
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D is appropriate for monomeric EGF
One of the first considerations for studies that measure protein diffusion coefficients experimentally is to determine what the value of D might mean for the oligomeric state of the protein. The pertinent question for EGF is whether D is consistent with a monomer or dimer in solution. Most of the available evidence suggests that EGF exists in solution primarily in monomeric form. Interest in this topic stems from questions regarding how EGF interacts with its functional receptor. The four distinct EGF receptor (EGFR) tyrosine kinases form homo- or hetero-dimers following ligand activation, ultimately leading to stimulation of multiple intracellular signaling cascades (Yarden 2001). The mechanism of EGF-induced receptor dimerization is thought to involve 1:1 binding of monomeric EGF to EGF receptors, resulting in stable 1:1 EGF:EGFR intermediates that go on to form 2:2 EGF:EGFR complexes (Lemmon et al. 1997; Schlessinger 2002). The formation of these complexes is consistent with ligand-induced conformational change in the EGFR and subsequent EGFR:EGFR dimerization mediated entirely by interactions between the receptors, not the ligands (Ogiso et al. 2002). Accordingly, small angle X-ray scattering has shown that human EGF at concentrations 8.7 mg/ml remains monomeric (Lemmon et al. 1997). Although one report has suggested that human EGF may form dimers in solution (Lu et al. 2001), it was based on the crystal structure of EGF prepared from a much higher concentration (50 mg/ml) than that used in our study (94 µg/ml) or in others (10 mg/ml) that have shown monomeric EGF in solution (Lemmon et al. 1997; Ogiso et al. 2002).
To our knowledge, D for EGF has not been reported in the literature. Prediction of D for proteins greater than about 1,000 Mr using various correlations typically results in errors of 10–20% compared with reliable experimental data (He and Niemeyer 2003; Tyn and Gusek 1990). Nevertheless, correlations can provide useful information for interpreting new experimental data. We determined D (20°C) = 11.7 ± 0.18 x 10–7 cm2/s (n = 8) for OG514-EGF. Using several different methods for estimating D for monomeric EGF (with molecular weights of 6,200–6,600 depending on the correlation method), Dpredicted (20°C) ranged from 12.1 to 15.3 x 10–7 cm2/s (see APPENDIX). The simplest correlations, based on a power law relationship of the form Dpredicted = constant/(Mr)1/3 (Polson 1950; Saltzman et al. 1994), yield Dpredicted (20°C) ranging from 12.1 to 14.6 x 10–7 cm2/s for a 6,600 Mr protein such as OG514-EGF. The lowest estimate (12.1 x 10–7 cm2/s), unlike the others, is based exclusively on data for fluorescently labeled proteins (Saltzman et al. 1994) and therefore may be more applicable to our result. Covalently attached fluorophores might be expected to reduce the observed diffusion coefficient of a protein, particularly for smaller proteins where the dye makes a greater relative contribution to the protein's mass and surface area. Additionally, use of a power law relationship will overestimate D for proteins that adopt ellipsoidal shapes instead of spheres because the long axis of the protein is not properly accounted for (He and Niemeyer 2003). Given that the shape of murine EGF is roughly that of a prolate ellipsoid (Montelione et al. 1987; Whitson et al. 2004), our result appears reasonable. Figure 5 plots experimental values of D for various fluorescently labeled proteins including OG514-EGF (1,200 Mr 150,000). Nonlinear regression returned a power law relationship of D = 2.28 x 10–5/(Mr)1/3 that fit the data quite well (r2 = 0.866).
Comparison with experimentally derived D for proteins of similar size to EGF could be helpful, but available data are limited. Bovine pancreatic trypsin inhibitor (6,500 Mr) has been reported to exhibit D (20°C) ranging from 12.9 to 14.4 x 10–7 cm2/s (Gallagher and Woodward 1989; Squire and Himmel 1979). Ultracentrifugation of adrenocorticotropic hormone (4,700 Mr) has yielded a D (20°C) of 13.2 x 10–7 cm2/s (Squire and Himmel 1979). A previous IOI study (Tao and Nicholson 1996) yielded a D (20°C) of 8.3 x 10–7 cm2/s for lactalbumin (14,500 Mr), after correcting for temperature with the Einstein relationship (see APPENDIX). Taken together, our experimental value seems reasonable compared with these previous experimental data.
EGF diffusion in brain is characterized by low
Table 2 summarizes diffusion-related parameters for all proteins and dextrans that have been studied to date in brain tissue. With the exception of the recent application of two photon microscopy to measure D* for NGF in the striatum (Stroh et al. 2003), all other data have been obtained using IOI in the neocortical slice preparation, as in this study. Two distinct groups of are evident from the data in Table 2 (indicated by the dashed line), a low group ( 1.8), comprising EGF and the two lower molecular weight (3,000 and 10,000 Mr) dextrans, and a high group ( 2.3), comprising all proteins and dextrans >10,000 Mr. Our result shows for the first time that a globular protein can diffuse in brain with low . Previously, it had been suggested that the dimensions of the ECS might further hinder transport of macromolecules above a critical size (Nicholson and Tao 1993), based on work with dextrans where the transition from low to high occurred between 10,000 and 40,000 Mr dextrans, with corresponding hydrodynamic diameters of 45 and 146 Å, respectively. This study allows for a much better estimate of this critical region. Considering the size of EGF, lactalbumin, and NGF in Table 2, the low and high groups suggest macromolecules experience significantly greater hindrance in brain ECS once their hydrodynamic diameters reach a critical region somewhere between 40 and 50 Å.
It is reasonable to expect that a protein's net charge might also affect its migration through the ECS because brain extracellular matrix contains high amounts of polyanionic glycosaminoglycans (Novak and Kaye 2000). The diffusion of charged globular proteins in a charged environment is known to be influenced by electrostatic interactions (Busch et al. 2000), and there is evidence that fixed negative charges in skin and muscle interstitia exclude negatively charged proteins due to electrostatic repulsion (Gyenge et al. 2003). Conversely, growth factors containing surface regions rich in positive charge may bind to components of the extracellular matrix (Taipale and Keski-Oja 1997), retarding their diffusion in the ECS unless the binding can be attenuated. This may explain the increased diffusion of basic fibroblast growth factor [18,000 Mr, pI 10 (Thorne and Frey 2001)] that has been observed in negatively charged agarose, fibrin gels, or cellular monolayers on addition of a polyanionic molecule such as heparin (Flaumenhaft et al. 1990). Co-infusion of heparin with certain growth factors in vivo also increases their volume of distribution in rat CNS (Hamilton et al. 2001). All the molecules in Table 2 are either neutral (dextrans) or negatively charged (EGF and the albumins) at physiological pH, with the exception of NGF, a positively charged protein with a pI 10 (Thorne and Frey 2001). However, the value of for NGF, determined in neostriatum, was very similar to that observed in neocortex for the negatively charged albumins (Tao and Nicholson 1996; Stroh et al. 2003). This would seem to suggest that net charge is not a significant factor affecting migration through the ECS in normoxic tissue, at least for this limited group of proteins. It may be of interest to explore this issue further with positively charged, low molecular weight proteins (e.g., insulin-like growth factor-I or transforming growth factor-).
Low will allow EGF to elicit effects further from sources in some cases
What might be the significance of low for a neurotrophic factor such as EGF? Figure 6 shows two hypothetical cases (assuming = 0.20), the first of which depicts EGF and NGF concentration profiles following their release from a point source (Eq. 1), such as after quantal release from a cell or a brief local injection (Fig. 6A). Two curves are shown for EGF, one in which it migrates through tissue with the experimentally determined low (1.79) and the other in which its diffusion is more hindered, with a typical of the proteins and dextrans >10,000 Mr in Table 2 (average = 2.26). Only EGF exhibiting a low reaches a level substantially above the receptor affinity constant (KD = 0.67 nM; Waters et al. 1990) at this distance from the release site (r = 600 µm). EGF exhibiting high manages only a slightly higher peak concentration than NGF. The curves are illustrative of a trend, with the specific distance and concentrations chosen arbitrarily. While the difference in may not seem too dramatic for the two cases, it is important to recognize that the high situation represents nearly a 40% reduction in the value of D*. Similarly, continuous release of EGF or NGF from an interface (Eq. 4; e.g., the ventricular wall during intracerebroventricular infusion) shows the increased penetration distance of low EGF compared with high EGF or NGF (Fig. 6B). Particularly with lower rates of elimination, EGF can reach a given concentration hundreds of microns further into the tissue when diffusing with low as opposed to high .
It is obvious that the magnitude of the elimination rate constant significantly affects the concentration profile (Fig. 6B). For our experiments, elimination was assumed to be negligible for three reasons: 1) the use of a slice preparation eliminated normal clearance processes that depend on circulation of blood and cerebrospinal fluid in the living animal, 2) D* was determined by IOI over a time span on the order of 100 s or less, so significant enzymatic processing of OG514-EGF could likely be neglected, and 3) specific EGF receptor-mediated binding and uptake was obviated by the presence of excess unlabeled EGF in the injected solution. Of course, in vivo concentration distributions are more complex because elimination and diffusion are occurring simultaneously, and neither can be neglected. For a protein such as NGF, it has been argued that elimination plays a greater role than diffusion in effectively limiting the protein's distribution to a few millimeters in vivo (Stroh et al. 2003). However, even with high rates of elimination, the magnitude of D* can still affect concentration profiles in a meaningful fashion (Fig. 6). Thus in the face of competing elimination mechanisms, the relative magnitude of should influence biological responses.
Diffusion parameters obtained in brain and spinal cord are known to change with pathology and aging (Syková 2004). For example, the RTI method has been used in vivo to show that increases significantly for the small TMA+ ion (74 Mr) during progressive ischemia (Syková et al. 1994), terminal anoxia (Syková et al. 1994; Voíek and Syková 1997), and astrogliosis (Roitbak and Syková 1999; Voíek et al. 2002). Increases in have also been described for 3,000 Mr dextran in a thick slice model of ischemia (Hrabtová et al. 2003) and in slices exposed to osmotic stress by hypotonic media (Tao 1999). Therefore for EGF and other biologically important macromolecules will likely increase in injured tissue (i.e., D* will be reduced), so that their effects will be constrained. It is also likely that some types of pathology will further enhance the differences in observed between high and low groups of macromolecules under normal conditions. For instance, the relative increase in for TMA+ is significantly less than that observed for 3,000 Mr dextran during both ischemia (20 and 64% increase, respectively; Hrabtová et al. 2000, 2003) and osmotic stress resulting from slice incubation in 150 mOsm/kg ACSF (10 and 34% increase, respectively; Kume-Kick et al. 2002; Tao 1999). Therefore, the diffusion of EGF may be significantly modified during injury or disease of the CNS, with consequences for both its normal action and its effects relative to that of larger growth factors such as NGF.
In summary, we have determined the free diffusion coefficient (D) and the effective diffusion coefficient (D*) in rat primary somatosensory cortex for fluorescently labeled EGF, a biologically relevant protein. Correction of the experimental values to 37°C using the Einstein relationship results in D = 17.8 x 10–7 and D* = 5.55 x 10–7 cm2/s. Although significant receptor binding would be expected to further hinder EGF spread at concentrations near or below the receptor affinity constant, the value of D* measured in this study is important in that it sets an upper limit for physiological diffusion of EGF in brain ECS. EGF exhibits much lower in adult neocortical tissue than larger proteins, an observation that may yet prove to be general for other biologically important proteins of similar size. Transport of low molecular weight neurotrophic factors (<10,000 Mr; e.g., EGF, transforming growth factor-, and insulin-like growth factor-I and -II) through brain might therefore be less constrained than that of larger proteins such as the neurotrophins (e.g., NGF and brain-derived neurotrophic factor) or fibroblast growth factors. It is also possible that high proteins such as NGF may be excluded from some ECS microdomains that a low protein like EGF may enjoy ready access to. Size selectivity of microdomains could allow cells another means of discriminating between different extracellular signals beyond expression and abundance of receptor proteins at the cell surface. Diffusional limitations placed on protein signals may have dramatic biological consequences. For example, it has been reported that EGF immobilized on an artificial matrix (nondiffusible) stimulates the differentiation of PC12 cells while soluble (diffusible) EGF stimulates their proliferation (Ito et al. 2001). Our characterization of the diffusion behavior of EGF should facilitate study of the EGF receptor system, one of the most highly studied and modeled receptor systems in biology (Lauffenburger and Linderman 1993). Furthermore, it will aid in the optimization of strategies for delivering EGF and other neurotrophic proteins to target sites within the CNS for the treatment of disease.
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APPENDIX
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Most relationships that predict D for proteins use the Stokes-Einstein equation (Einstein 1906)
 | (5) |
where k is Boltzmann's constant, T is the absolute temperature (K), 
is the viscosity of water (Pa · s), and RH is the hydrodynamic radius of the protein (Å), whose shape is assumed to be rigid and spherical.
Correlations for prediction of D based on molecular weight (Mr)
Molecular radius is proportional to Mr1/3 for a solid spherical protein {i.e., RM = [(3Mr
)/(4
NA)]1/3 where RM is the radius determined from the molar volume, NA is the Avogadro constant, and is the partial specific volume, typically 0.65–0.79 cm3/g for globular proteins (Smith 1968); note that RM and RH have different physical meanings}, allowing Eq. 5 to be rewritten as a power law. Polson (1950) was the first to develop this relationship for the estimation of D or Mr, based on limited experimental data
 | (6) |
where A = 2.74 x 10–5 cm2s–1g1/3mol–1/3 (20°C). For OG514-EGF (6,600 Mr), the Polson correlation predicts D (20°C) = 14.6 x 10–7 cm2/s. Saltzman et al. (1994) later determined the best fit of Eq. 6 to both a large compendium of experimental values from the literature or their own data for fluorescein and 11 fluorescently labeled proteins (1,200–970,000 Mr) and obtained A = 3.00 and 2.60 x 10–5 cm2s–1g1/3mol–1/3 (25°C), respectively. Using these values for A and correcting for temperature using the Einstein relationship [DA = DB(TA/TB)(B/A), where = 1.0019 x 10–3 and 8.902 x 10–3 Pa · s at 20 and 25°C, respectively], Eq. 6 predicts D (20°C) = 14.0 x 10–7 or 12.1 x 10–7 cm2/s.
Correlations for prediction of D based on radius of gyration
Correlations using the radius of gyration have been developed to more accurately predict D for proteins whose shape deviates from spherical. Tyn and Gusek (1990) have suggested a correlation based on experimental data for 86 proteins (12,640–50,000,000 Mr), using an adaptation of the Stokes-Einstein equation
 | (7) |
where B = 1.69 x 10–5 cm2s–1Å–1 (20°C) and RG is the radius of gyration (Å). Although RG for OG514-EGF is not available, small angle X-ray scattering has been used to determine RG = 11.5 ± 0.44 Å for recombinant human EGF (6,200 Mr) (Lemmon et al. 1997), yielding D (20°C) = 14.7 x 10–7 cm2/s when used with Eq. 7. He and Niemeyer (2003) recently proposed a new correlation using both the molecular weight and radius of gyration as parameters, based on the same experimental data set used by Tyn and Gusek (1990)
 | (8) |
where is the viscosity of water (Pa · s) and T is the absolute temperature (K). Using RG stated above for recombinant human EGF (6,200 Mr), Eq. 8 predicts D (20°C) = 13.8 x 10–7 cm2/s.
Prediction of D based on ultracentrifugation data
The classical Svedberg equation, used to determine protein sedimentation coefficients in ultracentrifugation studies (Laue and Stafford 1999), may be rearranged in the form
 | (9) |
where s is the sedimentation coefficient (s), R is the gas constant, T is the absolute temperature (K), is the partial specific volume (cm3/g), and 
is the density of water (20 = 0.99823 g/cm3). During the initial characterization of mouse submaxillary gland EGF, Cohen and colleagues determined (0.69 cm3/g) and s20 (1.25 x 10–13 s) for EGF (6,400 Mr) by sedimentation equilibrium ultracentrifugation (Cohen 1962; Taylor et al. 1972). Substitution of these values into Eq. 9 yields D (20°C) = 15.3 x 10–7 cm2/s.
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GRANTS
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This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-28642.
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ACKNOWLEDGMENTS
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We thank Drs. Aparna Lakkaraju and Lian Tao for critical comments on this manuscript.
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FOOTNOTES
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Address for reprint requests and other correspondence: R. G. Thorne, Dept. of Physiology and Neuroscience, New York Univ. School of Medicine, 550 First Ave., New York, NY 10016 (E-mail: robert.thorne{at}med.nyu.edu).
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