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Protein Transport in Constrained Anionic Hydrogels: Diffusion and Boundary-Layer Mass Transfer Rebecca K. Lewus and Giorgio Carta* Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22903-2442
The partitioning and transport of proteins in anionic, polyacrylamide-based gels were characterized by a direct visualization method using cytochrome c as the probe molecule. Homogeneous gels stabilized against mechanical and osmotic forces were made by synthesizing them inside fused-silica capillaries with a square cross section. Mixtures of 2-acrylamido-2-methylpropane sulfonic acid and acrylamide as the starting co-monomers and N,N′-methylene bisacrylamide as a cross-linker were used in preparing these gels. After polymerization and equilibration of the samples in a buffer, the diffusional transport of cytochrome c was studied via the microscopic determination of the evolution of concentration profiles in the gel upon exposure to a protein solution. Calibrated digitized profiles were used to determine the protein diffusivity in the gel and the effects of boundary-layer mass-transfer resistance on transient adsorption and desorption. The effects of protein and salt concentrations in solution and the effects of the gel composition were determined. The ranges of experimental conditions covered gels with cross-link densities between 2.5 and 10%, total polymer concentrations between 0.05 and 0.42 g/cm3, and charge densities between 97 and 970 µequiv/cm3. In each case, the concentration profiles observed had a diffuse character and evolved in time in a manner consistent with Fick’s law. However, the experimental diffusivity values varied with protein concentration in the gel and were strongly influenced by the composition of the gel and by the salt concentration in solution. Introduction Polymeric hydrogels have many current and potential applications in biotechnology as a result of their biocompatibility and ability to selectively allow molecules to enter and diffuse on the basis of size. Whereas neutral hydrogels serve as size-exclusion media, incorporation of a fixed charge, bound to the polymer backbone, introduces the ability to concentrate oppositely charged molecules, including macromolecules such as proteins. These solutes can then be released, for example, by changing the ionic strength or the solution pH, by introducing competitive displacers, or, in some cases, by changing temperature or applying electric fields.1 Potential applications of charged hydrogels include their use as systems for the delivery of therapeutic agents to tissues and cells,2,3 as components in transdermal delivery of drugs by electroporation and iontophoresis methods,4,5 as elements in diagnostic application instruments,6 and as physical models for in vitro studies of partitioning and transport in tissues.7 Finally, charged hydrogels have important applications in separations based on chromatography and membrane methods. In general, free-standing charged hydrogels undergo large volume changes in response to solution composition changes. This is a desirable property in certain applications including osmotic devices1 and drug delivery systems controlled by the gel swelling rate,8 as well as in the use of gels as “gel extraction solvents”.9 Applications to adsorptive and membrane separations are, however, often hampered by this characteristic. Moreover, homogeneous ionic hydrogels that are sufficiently “soft” to enable macromolecule diffusion are * Author to whom correspondence should be addressed. Phone: (804) 924-6281. Fax: (804) 982-2658. E-mail: gc@ virginia.edu.
subject to mechanical compression when used in chromatography columns or as membranes. Recently, however, ionic hydrogels that are stabilized against mechanical and osmotic forces by being incorporated into rigid porous structures have been developed. For example, composite particles made by incorporating homogeneous, charged polyacrylamide-based gels within the pores of rigid silica or ceramic particles have been described by Girot and Boschetti10 and have become commercially available with the trade name HyperD as protein chromatography media.11,12 In these materials, the rigid backbone of the supporting matrix provides structural integrity, while the gel provides a high adsorptive capacity that allows for efficient chromatographic operations at high flow rates of the mobile phase.13-15 Membranes obtained by synthesizing ionic hydrogels within the pores of rigid filter media have also been developed. Such composite membranes have been shown to retain the hydraulic permeability of equivalent free-standing gels while being largely unaffected by changes in ionic strength.16 Transport rates are, of course, critical in the aforementioned applications, especially for macromolecules. However, whereas diffusional transport of macromolecules in neutral gels is generally well understood both experimentally and theoretically,17-20 the literature on diffusion of charged macromolecules in oppositely charged ion-exchange gels is scant. In the case of neutral gels, the partition coefficient is typically less than one, and diffusional transport rates are always lower than in free solution as a result of steric and hydrodynamic hindrances. On the other hand, oppositely charged macromolecules can be very favorably partitioned into ionic hydrogels as a result of electrostatic interactions.21 Thus, although the mobility or diffusion coefficient of these molecules is low compared to that in free solution,
10.1021/ie0006054 CCC: $20.00 © 2001 American Chemical Society Published on Web 02/16/2001
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high transport rates can, in principle, be obtained. This effect is well-known for small ions in ion-exchange resins,22 but it can also be significant for macromolecules in low-density hydrogels. For example, a number of previous studies of protein adsorption in the gelcomposite HyperD media have shown that mass transfer is very rapid and, in some cases, it is faster than could be predicted for ordinary diffusion in the bulk liquid phase.15 This behavior has been described in a semiempirical way using a Fickian diffusion model where the driving force is expressed in terms of the adsorbed protein concentration, implying that the protein molecules retain diffusional mobility within the charged gel. From a macroscopic viewpoint, this modeling approach has been found to be consistent with the experimental behavior, thereby allowing for a prediction of performance under ample ranges of conditions and in both batch and packed column systems.14,15,23 In previous work, we developed a technique for a direct microscopic visualization of protein diffusion in charged polyacrylamide-based gels synthesized within fused-silica capillaries, which can provide greater insight into the nature of protein transport in these gels.24 For ease of microscopic observation, we use capillaries with a square cross section that eliminates optical artifacts. Optically transparent anionic gels can be synthesized in situ, and colored or fluorescent proteins can be used as probes. The evolution of concentration profiles obtained by exposing the end of the capillary-gel composite to a dilute protein solution can thus be followed by direct observation with a microscope. For these conditions, transport can be observed in an essentially semi-infinite, “flat plate” geometry, which simplifies the mathematical analysis of the experimental profiles. For the case of cytochrome c diffusing in an anionic polyacrylamide gel, we observed diffuse concentration profiles consistent with Fick’s law. More complicated profiles were seen under desorption conditions when a protein-loaded gel was exposed to a salt solution, suggesting that complex interactions between counter-diffusing ions take place in these ion exchangers. Analysis of the evolution of concentration profiles can obviously provide a direct measurement of diffusivities and is a powerful means of testing hypothesized transport theories. Thus, the objective of this paper is threefold. The first objective is to determine the effects of boundary-layer mass transfer at the gel-fluid interface. Because transport in the gel can be rapid, the fluidphase resistance can become significant at low protein concentrations. Hence, its effect needs to be determined. The second objective is to determine the reversibility of the mass-transfer process under protein binding conditions. In particular, we are interested in exploring what happens when the protein concentration is reduced to zero in the bulk fluid following an initial loading of the gel from a more concentrated protein solution. Finally, the third objective is to determine the protein diffusivity in the gel as a function of polymer concentration, polymer charge density, and salt concentration in solution. For each of these variables, concentration profiles were obtained under transient adsorption or desorption conditions using cytochrome c as the probe. The experimental profiles were analyzed in terms of a model that incorporates the fluid-phase resistance and an empirically determined concentration-dependent diffusivity in the gel.
Table 1. Composition of Standard Gel Used in This Work polymer concentration cross-link density charge density φ
0.21 5% 970 0.15
g/cm3 g/g µequiv/cm3 v/v
Experimental Section Materials. The materials used in the preparation of gels were 2-acrylamido-2-methylpropane sulfonic acid (AMPS, 98% purity), N,N′-methylene bisacrylamide (MBA, 98% purity), ammonium persulfate (AP), N,N,N,Ntetraethylenediamine (TEMED), and acrylamide. These materials were obtained from Lancaster Synthesis Inc. (Windham, NH) and Sigma Chemical Co. (St. Louis, MO). Bind-silane (γ-methacryloxypropyltrimethoxysilane) was obtained from Pharmacia (Piscataway, NJ). Cytochrome c from bovine heart (Mr ) 13 300, pI ) 10.6) was obtained from Sigma Chemical Co. Other chemicals were obtained from Sigma Chemical Co. or Fisher Scientific (Pittsburgh, PA). Fused-silica, polyimidecoated capillary tubing with a square cross section was obtained from Polymicro Technologies, Inc. (Phoenix, AZ). This tubing has a nearly perfect square cross section with internal and external widths of 100 and 300 µm, respectively. The tubing was cut into approximately 1-cm sections, and the polymer coating was burned off from the top 0.5-0.6 cm. The sections were then treated with bind-silane as described by Lewus and Carta24 to provide a way of anchoring the polyacrylamide gel by covalent attachment to the capillary. Preparation of Gels. The procedure used to prepare the capillary-constrained gels used in this work is described in detail by Lewus and Carta24 and is similar to the methods described by Girot and Boschetti10 for the preparation of gel-composite particles. Thus, only the main steps are described here. A monomer mixture is first prepared in filtered, degassed water by dissolving the AMPS monomer and the MBA cross-linker in the desired proportion. After the solution is titrated to pH 7 with NaOH, the volume is adjusted to the desired value with additional water. The AP initiator and the TEMED promoter are then added and stirred into the solution. The reaction mixture is then quickly loaded into the capillary sections and allowed to polymerize at room temperature. Upon completion of the polymerization (∼1 h), the capillaries are placed into a large volume of 10 mM Na2HPO4 buffer at pH 6.5 for at least 24 h. The composition and basic properties of a “standard” gel used in this work are summarized in Table 1. Gels with different polymer concentrations were obtained by varying the total concentration of the monomer solution while maintaining the same ratio of AMPS and MBA. Conversely, gels with the same polymer concentration and cross-linking ratio but with different charge densities were obtained by substituting acrylamide for the AMPS monomer in the initial mixture. Microscopic observation of the capillaries after equilibration in the buffer revealed that minimal volume change occurred, as the gel was covalently bound to the ligands at the inner surface of the capillary. The charge density, based on the gel volume, can thus be estimated from the composition of the polymerization mixture. The polymer volume fraction φ ) mpvp/(mpvp + mwvw) was estimated from the initial monomer composition using a value of vp ) 0.7 cm3/g for the polymer density, as suggested by Kapur et al.25 The degree of incorporation of the monomers in the gels prepared in this work was estimated by filling
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Figure 1. Schematic of cells used for diffusion studies.
several test tubes with 5 cm3 of a monomer mixture with the composition in Table 1 and allowing the polymerization to proceed. After 1 h, the gel was removed from each test tube, cut into small pieces 1-2 mm in size, and placed into a 200 cm3 volume of buffer solution for 48 h to remove any potentially unreacted monomer. The gel particles were recovered by filtration through filter paper; rinsed with distilled, deionized water; and then dried in an oven at 120 °C for 48 h. The weight of dried polymer was determined and compared with the initial weight of monomer loaded into each test tube. The results gave a 98 ( 0.5% recovery of the initial monomer weight, which is within the monomer purity stated by the supplier. This determination confirms that essentially all of the monomer is incorporated in the gel. Similar results have been obtained by Gelfi and Righetti,26 who, using a different method, determined that acrylamide-bisacrylamide gels with a 5% cross-link density are fully polymerized within 30 min at room temperature. Measurement of Concentration Profiles. A schematic of the diffusion cell used in this work is shown in Figure 1. The cell was realized by sandwiching a 1/8in.-thick Teflon slab between two microscope slides as described in detail by Lewus and Carta.24 One end of a capillary tube section prepared as described above was sealed by gluing it to the tip of a syringe needle with a cyanoacrylate adhesive. The needle was then inserted into the cell. The protein solution was allowed to flow in to and out of the cell through stainless steel tubes (1/32-in. o.d., 1/64-in. i.d.) and recirculated with a peristaltic pump (Cole-Parmer Instrument Co., Chicago, IL) at a flow rate of 0.5 cm3/min. Two flow configurations were used, as shown in Figure 1. In the parallel-flow configuration, the solution flow is perpendicular to the capillary. In this case, the velocity past the tip of the capillary has the same magnitude as the mean velocity in the flow channel, or about 0.033 cm/s (120 cm/h) for our experimental conditions. This velocity is comparable to values typically used in packed columns for preparative protein chromatography. In the impinging-flow
configuration, the inlet tube is positioned at a distance of approximately 3 mm from the tip of the capillary. Thus, in this case, the approach velocity is similar to the mean velocity in the feed tubing, or about 7.8 cm/s (28 000 cm/h) for our experimental conditions. The vastly different velocities obtained in the two configurations should result in highly different boundary-layer mass-transfer-resistance effects. The evolution of concentration profiles in the gel was followed by direct observation with a microscope, as described by Lewus and Carta.24 Cytochrome c is intensely colored (reddish-brown) and is favorably partitioned in these gels at low ionic strength.27 Thus, diffusional transport in the gel can be characterized by direct visual observation. Gray-scale values of the digitized images were obtained using the public domain NIH Image program (developed at the U.S. National Institutes of Health and available on the Internet at http://rsb.info.nih.gov/nih-image/) and were converted to protein concentrations in the gel using a calibration curve obtained by determining the gray scale for identical capillaries filled with cytochrome c solutions of different concentrations.24 The equilibrium binding capacity of the gels for cytochrome c was also determined. To obtain these data, capillary tubes prepared as discussed above were suspended in cytochrome c solutions of known concentrations. After 72 h, the capillaries were placed into the flow cell, and images were recorded. The gray-scale level of the saturated gel was then used to determine the equilibrium binding capacity. At low protein concentrations, however, external mass transfer under stagnant conditions was so slow that equilibrium was not established even after 72 h. Thus, at protein concentrations of 0.1 and 0.25 mg/cm3, the capacity was determined by allowing the tubes to come to equilibrium under flow conditions in the diffusion cell. The equilibrium binding capacity was also determined through a direct measurement by equilibrating several capillary tubes in a 1 mg/ cm3 cytochrome c solution and then eluting the protein by immersing the tubes in a known volume of a 500 mM buffered NaCl solution. For these conditions, the protein was completely desorbed. Hence, the amount of protein initially bound could be calculated from a material balance based on the analytical determination of the concentration of the desorbed protein in the salt buffer. The latter was done by measuring the absorbance at 405 nm with a spectrophotometer (Beckman, model DU50). All experiments were conducted at room temperature, 23 ( 2 °C, in a 10 mM Na2HPO4 buffer at pH 6.5. Results Protein Adsorption Equilibrium. The protein binding isotherm for the standard gel having the composition given in Table 1 is shown in Figure 2. The maximum capacity is in excess of 400 mg/cm3, which is in agreement with the value of 410 ( 80 mg/cm3 obtained independently by measuring the amount of protein desorbed, as discussed in the Experimental Section. This value is consistent with the high protein binding capacity values observed for commercial HyperD particles27 and is a result of the high charge density of the gel and the apparent accessibility of the charged groups. Assuming a value of 0.7 cm3/g for the specific volume of the protein,28 the measured protein binding capacity corresponds to a volume fraction of protein in the gel of 0.29 ( 0.06, indicating that protein
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Figure 2. Equilibrium isotherm for cytochrome c adsorption in standard gel.
intensity between the solution and gel phases. Some imperfections clearly exist near the cut end of the capillary, and the gel is seen to protrude slightly beyond the boundaries of the fused-silica tube. However, because the times of the observations were quite long and the depth of penetration of cytochrome c was substantial, these imperfections at the boundary should be of limited significance in the interpretation of the results. Concentration gradients in the direction transverse to the capillary also appear to be absent. From gray-scale analysis of the digitized images, variations in this direction were very small (
