Purification of a Large Protein Using Ion-Exchange Membranes

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Ind. Eng. Chem. Res. 2002, 41, 1597-1602

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Purification of a Large Protein Using Ion-Exchange Membranes Heewon Yang,† Clarivel Viera,† Joachim Fischer,† and Mark R. Etzel*,†,‡ Department of Chemical Engineering, 1415 Engineering Drive, and Department of Food Science, 1605 Linden Drive, University of Wisconsin, Madison, Wisconsin 53706

Anion-exchange membranes were evaluated for the capture of a small protein (R-lactalbumin, 3.5-nm diameter) and a large protein (thyroglobulin, 20-nm diameter). The static binding capacity equaled the dynamic binding capacity and increased with increasing protein size. This result was in agreement with calculations based on monolayer coverage on the membrane surface and an absence of mass-transfer limitations. In contrast, for anion-exchange beads, the static capacity was the same for both proteins, and the dynamic capacity decreased strikingly with increasing protein size. These observations were attributed to very slow intrapore diffusion for large proteins in the beads, resulting in surface binding only. This work has important applications in the selection of chromatography media for the purification of viruses and plasmid DNA. Specifically, membranes with a high capacity for large biomolecules (20-300 nm) and a low capacity for small host-cell proteins and endotoxin contaminants are preferable to beads for the purification of such biomolecules. Introduction Chromatography is widely used for the separation, isolation, purification, and analytical characterization of biomolecules. Traditionally, chromatography uses columns packed with beads, where throughput is typically limited by either slow intrapore diffusion for large beads or slow flow rates and high pressure drops for small beads. Membrane chromatography is a relatively new purification technology designed to bypass the fundamental limitations of columns packed with beads.1-10 In membrane chromatography, the packing consists of microporous membranes wherein the internal pores contain adsorptive moieties that bind the target protein. Because the membranes are thin, pressure drop is not a limitation. Furthermore, convection through the fine micrometer-sized pores of the membrane reduces or eliminates mass-transfer limitations, increasing the dynamic binding capacity and throughput. We hypothesized that the convective flow pattern characteristic of chromatographic membranes would be particularly advantageous in the isolation and purification of large biological macromolecules such as viruses, plasmid DNA, and very large proteins. Viruses and plasmid DNA are macromolecules or supramolecular assemblies with megaDalton molecular weights and hydrodynamic diameters of 20-300 nm. These large biomolecules are of increasing importance in the manufacture of biopharmaceuticals. In an effort toward defining the importance of size in adsorptive chromatography using beads or membranes, we measured the static and dynamic binding capacities of each medium for two model proteins: R-lactalbumin (ALA, 0.0144 MDa, 3.5-nm diameter) and thyroglobulin (THY, 0.66 MDa, 20-nm diameter).11,12 Using our results, we demonstrate the particular advantages of * Corresponding author. E-mail: [email protected]. Telephone: (608) 263-2083. Fax: (608) 262-6872. † Department of Chemical Engineering. ‡ Department of Food Science.

membranes for the adsorptive separation of large biomolecules. Materials and Methods Anion-exchange beads (Q Sepharose Fast Flow, Amersham Pharmacia Biotech, Piscataway, NJ), 90 µm in diameter, with an exclusion limit of 4 MDa and containing immobilized quaternary amino moieties on a 6% cross-linked agarose matrix, were used in batch incubation experiments. Flat-sheet affinity membranes (Immobilon AV, Millipore, Bedford, MA) made of poly(vinylidene difluoride) activated with an acylimidazole leaving group were used to make anion-exchange membranes.13 The membrane surface was modified during manufacture to contain a hydrophilic coating that reduces nonspecific adsorption. Membranes were 140 µm thick and had an average pore size of 0.65 µm, an internal surface area of 155 cm2 per cm2 of frontal area, and a void fraction of 0.7. The two proteins, THY (porcine, T1126) and ALA (bovine, L6010), as well as ethanolamine and 2-aminoethyltrimethylammonium chloride (AETMA) were purchased from Sigma (St. Louis, MO). The ALA was partially depleted in calcium (0.1 mol of Ca/mol of ALA). Dimethyl sulfoxide (DMSO) was purchased from Fluka (Buchs, Switzerland), and bicinchoninic acid (BCA) assay reagent was purchased from Pierce (Rockford, IL). Salts were ACS analytical grade. Buffers were vacuum filtered through 0.2-µm filters (Super-200, Gelman Science, Ann Arbor, MI). Flow experiments used vacuumdegassed buffers. Protein solutions were prepared shortly (∼1 h) before each experiment and filtered using 0.22µm syringe filters (Millex-GV, Millipore). For batch incubation experiments using the anionexchange beads, each protein was dissolved in 0.05 M tris(hydroxymethyl)aminomethane (Tris), pH 8.3, containing 0.05% sodium azide. Initial protein concentrations were determined from the absorbance at 280 nm and the extinction coefficients of THY and ALA at 280 nm [10.0 and 20.1 au dL/(g cm),14 respectively] and were 19 mg/mL for both proteins. Anion-exchange beads were

10.1021/ie010585l CCC: $22.00 © 2002 American Chemical Society Published on Web 02/26/2002

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first equilibrated in buffer, and then, entrained water was removed by suction. Wet beads (1 g) and protein solution (10 mL) were incubated with agitation for 8 days. Duplicate samples were taken at different time intervals. Final protein concentrations were used to calculate the equilibrium capacity by mass balance. Anion-exchange membranes (Q membranes) were prepared by gentle, agitated incubation for 3 days at 22 °C of the activated membranes suspended in a solution containing 3% (w/v) AETMA dissolved in a solvent mixture of 95% (v/v) DMSO and 5% (v/v) water. Following immobilization, the membranes were rinsed with water several times and incubated in 7-10% (v/v) ethanolamine in 0.1 M sodium carbonate, pH 9.5-9.8, for 1 h to cap unreacted activation sites. Finally, membranes were washed several times in sequence using water and 2 M NaCl solution. Capped membranes (CAP membranes) were prepared to examine nonspecific protein adsorption by reacting fresh membranes with ethanolamine only. For batch incubation experiments, fresh membranes were cut into 1-cm2 squares prior to the immobilization protocol. After immobilization, each membrane square was incubated separately for 2 h in 2 mL of protein in 20 mM sodium phosphate buffer, pH 7.5 (PB). Incubations were conducted in quadruplicate. The initial protein concentration was 0.55 mg/mL for ALA and 0.56 mg/mL for THY, and the calculated final concentrations were 0.53 and 0.50 mg/mL, respectively. Each membrane square was rinsed several times with PB and then incubated for 30 min in 0.5 mL of BCA reagent. Each supernatant (200 µL) was pipetted into a microwell plate, and the amount of protein bound was determined from the absorbance at 570 nm. Breakthrough curves (BTCs) were measured to determine the dynamic capacities of the membranes. Fresh membranes were cut into 25-mm-diameter disks prior to use in the immobilization protocol. After immobilization, the membranes were stacked in a membrane holder (11100, Amicon, Beverly, MA) in the order bottom part of the holder, screen, 2 CAP membranes, 7 Q membranes, 2 CAP membranes, O-ring, and top part of the holder. The total membrane volume was 0.76 mL. The loading and washing buffer was 0.05 M Tris, pH 8.3. The elution buffer consisted of 2 M NaCl in the loading buffer. The flow rate was measured gravitmetrically and set to 1 mL/min. Feed solutions consisted of the desired protein dissolved in loading buffer. Protein concentrations were determined from the absorbance at 280 nm. Prior to BTC experiments, the membranes were equilibrated with the loading buffer. Experiments were conducted in duplicate. For experiments involving the membranes and THY only, a cleaning step was used to remove residual bound THY from the membrane that was not desorbed by the elution buffer. The membranes were incubated for 2 h with a solution of 0.5 mg/mL porcine pepsin (P7012, Sigma) in 50 mM sodium citrate, pH 2, in a beaker. The membranes were then rinsed four times using elution buffer to destroy pepsin activity and desorb any residual bound protein. This procedure was found to be unnecessary for ALA, where the elution buffer desorbed all of the bound protein. Less than 100% elution of THY and ALA was not observed for the beads. Dynamic capacity was measured using two slightly different procedures. Procedure I followed the protocol of Amersham Pharmacia Biotech15 wherein protein

solution (1 mg/mL) was loaded into the membranes until the effluent absorbance rose to 50% of the feed solution absorbance. The membranes were then washed with loading buffer until the effluent absorbance approached baseline. The elution peak solution was collected until the absorbance returned to the baseline. This procedure was chosen to allow for comparison of the dynamic capacities of the membranes with values reported in the literature using beads. Procedure II was similar to procedure I except that the feed solution concentration was 0.05 mg/mL and loading was stopped when the effluent absorbance rose to 95% of the feed solution absorbance. This procedure was chosen to record the shape of the entire BTC, including the approach to saturation, which would have been missed by stopping loading at 10% of the feed solution absorbance as is the common practice in industry. All of the figures containing BTCs, washing curves, and elution curves were from single uninterrupted experiments conducted using procedure II. The system dispersion curve (SDC) was measured to characterize the extent of mixing in the flow system and the system dead volume. A nonbinding protein was used as the tracer, namely, 0.05 mg/mL ALA in elution buffer. Results Effect of Protein Size on the Static and Dynamic Capacities of Anion-Exchange Beads. In batch incubation experiments, THY bound very slowly to the anion-exchange beads compared to ALA, but the observed static (equilibrium) capacities were similar for the two proteins (Figure 1). For example, the time required to reach 80% of the static capacity was about 60 h for THY and less than 1 h for ALA, but the static capacities were 115 mg/mL for THY and 108 mg/mL for ALA. The rate of THY adsorption onto the anion-exchange beads was modeled by assuming that the beads were spheres 45 µm in radius (R). The continuity equation was

( )

∂cs Ds ∂ 2 ∂cs r ) 2 ∂t ∂r r ∂r

(1)

and the initial and boundary conditions were

cs ) 0 at R g r g 0, t ) 0

(2)

c ) c0 at t ) 0

(3)

∂cs ) 0 at r ) 0, t > 0 ∂r

(4)

cs )

c*cl at r ) R, t > 0 Kd + c*

(5)

In eq 5, the Langmuir isotherm, c* is the fictitious concentration of THY in the liquid phase in equilibrium with cs. After eqs 1-5 were solved, the amount of protein bound to the beads was calculated from

mbound(t) ) Vl[c(t) - c(t)0)]

(6)

Initially, boundary-layer mass transfer was included in the model. However, in fitting the model to the data, the boundary-layer mass-transfer coefficient was found

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Figure 1. Kinetics of adsorption of THY and ALA onto anionexchange beads determined by batch incubation in 0.05 M Tris, pH 8.3. Table 1. Protein Binding Capacities for Anion-Exchange Beads dynamic capacitya (mg/mL of gel) THY ALA

3 110

Figure 2. Static and dynamic binding capacities of THY and ALA to Q membranes. Values are mean ( standard error. To facilitate comparison, the dynamic and static binding capacity determinations used the same buffer system (0.05 M Tris, pH 8.3). Table 2. Dynamic Binding Capacities for Anion-Exchange Membranesa

static capacity (mg/mL of gel)

procedure I

115 108

a Eluted capacity of procedure I, from Amersham Pharmacia Biotech.15

THY ALA a

to be an insensitive parameter. The rate of mass transfer was controlled by diffusion inside the bead for THY. Therefore, c* was set equal to the bulk THY concentration, which decreased over time as the THY in solution bound to the beads. Fitted parameter values were Ds ) 1.0 ( 0.2 × 10-11 cm2/s, cl ) 119 ( 4 mg/mL, and Kd ) -0.2 ( 0.4 mg/mL (mean value ( standard error). The model was insensitive to the value of Kd. The dynamic capacity of the beads for THY was 3 mg/ mL or 2.6% of the static capacity, whereas, for ALA, the dynamic capacity was 110 mg/mL or 100% of the static capacity (Table 1). The dynamic capacity of the beads for THY corresponded to a batch incubation time of about 0.23 h (Figure 1), which was about the contact time of the feed solution with the column of beads during the determination of the dynamic binding capacity. Therefore, the small dynamic capacity of the beads for THY was consistent with the batch incubation results and with the small fitted diffusion coefficient of THY in the beads. Effect of Protein Size on the Static and Dynamic Capacities of Anion-Exchange Membranes. The static capacity of the Q membranes was measured by batch incubation (Figure 2). The static capacity of the Q membranes was 10 ( 2 mg/mL for THY and 3.0 ( 0.8 mg/mL for ALA. Neither protein bound to the CAP membrane (static capacities of -0.02 ( 0.01 mg/mL for ALA and 0.04 ( 0.04 mg/mL for THY). The dynamic capacity of the Q membranes for each protein was not statistically significantly different from the corresponding static capacity (Figure 2). Specifically, the dynamic capacities were 160-200% greater for THY than for ALA (Table 2). The choice of definition of the point of breakthrough (c/c0 ) 0.5 for procedure I; c/c0 ) 0.95 for procedure II) did not strongly affect the observed dynamic capacity. Neither BTC was symmetric (Figure 3). Instead, the BTCs were bipartite, first rising sharply toward a c/c0 value of 0.6-0.8 and then rising slowly toward, but

procedure II

bound (mg/mL)

eluted (mg/mL)

bound (mg/mL)

eluted (mg/mL)

11 ( 0.9 4.30 ( 0.03

7.7 ( 0.1 4.23 ( 0.03

10 ( 0.7 3.3 ( 0.5

7.6 ( 0.1 3.3 ( 0.3

Values are mean ( standard error for duplicate experiments.

Figure 3. System dispersion curve (SDC) and breakthrough curves for loading THY or ALA in 0.05 M Tris, pH 8.3, onto the Q membranes using procedure II. For the SDC, the solid line is experimental data, and the dotted line is the prediction from the model.

never reaching, c/c0 ) 1.0. Even after a loading of 500 membrane volumes () τ) of feed solution, THY rose to c/c0 ) 0.924 and ALA rose to c/c0 ) 0.986. Breakthrough (c/c0 ) 0.1) occurred sooner for ALA (τ ) 93.6) than for THY (τ ) 232), indicating the greater dynamic binding capacity of the Q membranes for the larger protein. For the BTC to rise to c/c0 ) 0.5 required about 10% more time: τ ) 103 for ALA and τ ) 257 for THY. However, rising to 90% of equilibrium (c/c0 ) 0.9) required the loading of 150% more feed solution past the point of breakthrough for THY and 65% more for ALA. Thus, equilibrium was approached more slowly for THY than for ALA. Initially, a small amount of early breakthrough was observed in each BTC (Figure 3). For example, the BTC for THY rose to about c/c0 ) 0.047, and that for ALA to about c/c0 ) 0.014, before the major point of breakthrough. This behavior was attributed to trace protein

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Figure 4. Washing curves for rinsing THY or ALA from the Q membranes using 0.05 M Tris, pH 8.3. Membranes were first loaded with THY or ALA using procedure II.

contaminants in THY and ALA, which were used as received from Sigma. According to the manufacturer, minor bands were detected by gel electrophoresis in the THY and ALA preparations. Any trace proteins that did not bind to the anion-exchange membrane at pH 8.3 would produce the observed small amount of early breakthrough. The SDC was not bipartite and rose quickly to c/c0 ) 1.0 (Figure 3). Breakthrough for the SDC occurred at τ ) 7.1, more than 1 order of magnitude faster than breakthrough for ALA and THY. A simplified but sufficiently accurate method for describing the SDC is the serial combination of the model of the membrane with those for a continuously stirred tank reactor and an ideal plug-flow reactor (PFR).2,8 The first temporal moment16 method was used to calculate the system volume of 3.5 mL (τsys ) 6.6) and the PFR volume of 2.2 mL (τPFR ) 4.2). Judging from a comparison of the SDC with the BTCs, the effect of flow nonidealities on the shape of the BTCs was negligible. The bipartite shape of the BTCs for ALA and THY was not caused by flow nonidealities. In the washing curves (Figure 4), the protein concentration decreased rapidly after the mean residence time was reached (τsys). Washing was more rapid for THY than for ALA, e.g., the washing curve fell to c/c0 ) 0.1 at τ ) 19 for THY and τ ) 78 for ALA. More protein was washed off the membrane for ALA than for THY. Recovery of bound protein in the elution peak (eluted after washing) was determined by mass balance to be 97% for ALA and 77% for THY (Table 2). Because the elution buffer did not remove a small amount of the THY bound to the membrane, the remainder was removed using a pepsin cleaning solution as mentioned above. This probably explains the 23% of THY not accounted for in the mass balance. Perhaps once THY bound to the surface of the membrane by an ionexchange mechanism, the close proximity of the THY molecules to the surface might have facilitated secondary binding that was not sensitive to elution using salt. In contrast to the BTCs, the shape of the elution curves was not a function of the particular protein (Figure 5). Although the elution curves had different areas because of the different binding capacities, the retention times and shapes were similar for ALA and THY: a symmetric main peak that emerges at τ ≈ 6.2, which is about the mean residence time of the flow system (τsys ) 6.6); peaks at about τ ≈ 8; and is followed by a tailing portion.

Figure 5. Elution curves for desorption of bound THY or ALA from the Q membranes using 0.05 M Tris, 2 M NaCl, pH 8.3. Membranes were first loaded with THY or ALA using procedure II and then rinsed using 0.05 M Tris, pH 8.3.

Discussion Although originally developed for protein separations, chromatographic membranes might have a special niche in the purification of large biopharmaceutical products such as viral vaccines, plasmid DNA vaccines, and viral vectors for gene therapy. Additionally, the isolation of protein therapeutics from fermentation or cell culture broth or from transgenic animal milk requires the highly efficient clearance of viruses and DNA. The hydrodynamic diameters of viruses and DNA range from 20 to 250 nm;17-19 thus, these large biomolecules are too large to diffuse easily into traditional chromatographic beads. Indeed, confocal laser microscopy images have been used to show clearly that plasmid DNA (6.3 kbp, 880-nm superhelix axis length, 11-nm diameter)19 binds to the surface only of agarose anion-exchange beads.20 Similarly, Yamamoto and Miyagawa21 found that hepatitis B virus surface antigen (∼20-nm diameter) adsorbed to the surface only of sulfate cellulose beads. In a related study, it was observed that the volumetric static capacity (mg/mL) of chromatographic beads for adsorption of plasmid DNA (4.8 kbp) decreased with increasing bead size, although the surface capacity (mg/m2) stayed constant.22 Taken together, these reports clearly demonstrate the difficulties in achieving high adsorptive capacity on beads for large biomolecules. The primary objective of this work was to compare the relative capacities of beads and membranes as adsorptive chromatographic media for the isolation and purification of large biomolecules. We chose ALA (3.5nm diameter) as a model small protein and THY (20nm diameter) as a model large biomolecule. The static capacity of Q beads was essentially identical for THY and ALA. However, when used in a column under flow, the dynamic capacity of the Q beads for THY dropped substantially to only ∼3% of the static capacity. In contrast, the dynamic capacity of the Q beads for ALA was essentially the same as the static capacity. Masstransfer limitations are the likely cause of the reduced dynamic capacity for THY adsorption onto Q beads. In particular, the diffusion of THY within the porous beads is very restricted. Using the diffusion coefficient of THY in free solution (2.4-2.6 × 10-7 cm2/s),12 the calculated time for 80% uptake in the Q beads () 0.11R2/D)24 is about 9 s, which is about 0.004% of the observed time (Figure 1). Two possible explanations for such restricted diffusion in the Q beads are (1) hindered transport and

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(2) simultaneous adsorption and diffusion of THY in the liquid-filled pores of the Q beads. The exclusion limit of the Q beads for globular proteins is 4 MDa, whereas the molecular weight of THY is 0.66 MDa, which is large enough to cause hindered diffusion such that the intrapore diffusion coefficient is 2.5% of the diffusion coefficient in free solution.23 The second explanation for the small fitted value of the diffusion coefficient is that adsorption of THY during diffusion lowers the apparent rate of transport. A shock front forms inside the bead wherein the supply of THY to the front is governed by the rate of THY diffusion through the pores aka the “shrinking core” model.24 Not until the front moves forward to the center of the bead can THY saturate the entire bead. Further reduction in the effective diffusion coefficient would result from blockage of the pores by adsorbed THY, as well as the pore tortuosity factor, which lowers the effective diffusion coefficient by about 70% compared to the free solution value.24 These results graphically illustrate the difficulties inherent in using standard chromatographic porous beads for the purification of large biomolecules. Ideally, chromatographic media for viruses and plasmid DNA would have a high capacity for large biomolecules and a low capacity for small host-cell proteins and endotoxins. Chromatographic beads exhibit just the opposite behavior. It should be pointed out that THY (20 nm) is on the low end of the size range of interest for virus and plasmid DNA purification (20-300 nm); hindered intrabead diffusion leading to low dynamic capacities would only be worse for larger biomolecules. In contrast to the Q beads, the static capacity of the Q membranes was about 225% greater for THY than for ALA (Figure 2). This result can be understood by comparing the experimental observations with calculations of monolayer coverages of protein on the membrane surface. It was assumed that a monolayer consists of a face-centered-cubic array on the surface, wherein each protein occupies an area of 2x3Rp2, where Rp is the geometric radius of the protein. For a spherical protein molecule of density 1 g/mL, Rp ) (3Mw/4πNA)1/3, where Mw is the protein molecular weight and NA is Avogadro’s constant. Each protein has a mass of mp ) Mw/NA. The calculated monolayer coverage is 2.2 mg/ m2 for ALA (0.0144 MDa) and 7.7 mg/m2 for THY (0.66 MDa). The internal surface area of the membranes is 1.1 m2/mL. Therefore, the calculated static capacity is 8.5 mg/mL for THY and 2.4 mg/mL for ALA, in remarkable agreement with the experimental observations. Note that the theoretical static capacity (in mg/mL) increases according to (Mw)1/3. In essence, larger proteins form thicker layers on the membrane, resulting in greater static capacities. In further contrast to the Q beads, the dynamic capacities of the Q membranes for THY and ALA were the same as the static capacities for these proteins, and again the dynamic capacity was greater for the larger protein. This result further confirms the absence of mass-transfer resistances in membranes. The elimination of diffusional limitations in the microporous membrane format, coupled with the increase in monolayer thickness as the protein size grows, means that membranes become more attractive chromatographic media compared to beads as the protein size increases. With the Q membranes, the BTCs were asymmetric and bipartite, initially rising sharply but then rising

more slowly in asymptotic approach to equilibrium (Figure 3). Neither BTC reached complete equilibrium even after 500 membrane volumes of feed solution had been loaded. Equilibrium was approached more slowly for THY than for ALA. In contrast, the shape of the elution curve and the retention time were not functions of the particular protein (Figure 5). The areas under the elution curves were different for ALA and THY because the binding capacities were different. The following hypothesis is proposed to explain these observations. The elution curves were independent of the protein size because protein binding was quickly and completely disrupted in the elution buffer and mass transfer was not rate-limiting; mixing in the flow system was the primary cause of broadening of the elution curve. For adsorption, on the other hand, because of surface crowding effects, the protein adsorption rate slowed as the membranes approached monolayer coverage. This effect caused the change in the shape of the BTC from initially sharp, when adsorption was fast and surface crowding was not a factor, to a slowly inclining shape as the adsorption rate slowed and monolayer coverage was approached. Surface crowding effects increase with increasing protein size because of the increase in footprint and the increase in the number of binding sites covered per protein.25 The shape of the washing curves (Figure 4) is determined by the removal of unbound protein from the void volume, plus the dissociation of any weakly bound protein. In contrast to the elution buffer, the washing buffer does not disrupt the binding of the protein. Therefore, weakly bound protein will dissociate from the membrane surface during washing, but not during elution. If only unbound protein were removed from the Q membranes, then the washing curves would have dropped to the baseline at about the mean residence time of the flow system (τsys ) 6.6). Instead, it took about 3 times longer than this for THY and 12 times longer for ALA to wash to c/c0 ) 0.1. Thus, for both THY and ALA, some dissociation of weakly bound protein probably occurred during washing, but dissociation was less for THY than for ALA. Stronger binding to the membrane of THY compared to ALA would cause shorter tails for THY than for ALA during washing, as was observed in the experiments. Conclusions Promising applications for membrane chromatography exist in the manufacture of biopharmaceuticals. For example, because large biomolecules bind to the surface only of traditional chromatography beads, the dynamic capacity is much lower than it is for small biomolecules, which are able to access the full volume of the beads. This phenomenon causes two problems. First, the dynamic binding capacity is much greater (∼30-100 times) for small impurities, host-cell protein and endotoxin, than for the large target, virus or plasmid DNA. Second, the volume of resin required to manufacture a given mass of therapeutic material increases by orders of magnitude. This has not been a problem for viral vaccines for which the worldwide demand is on the order of 5 g/year (e.g., hepatitis A vaccine),17 but it will become an exacting challenge for new biopharmaceutical products such as viral vectors and plasmid DNA for gene therapy applications where dosages are 6000 times greater, yet the tolerable mass of host-cell protein and endotoxin per dose is the same.26-30

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In contrast, as demonstrated in this work, chromatographic membranes have a high capacity for large biomolecules and a low capacity for small biomolecules. Furthermore, the relative advantage of membranes over beads increases markedly as the size of the biomolecule increases. For example, assuming a surface capacity of 33 mg/m2 for plasmid DNA adsorption onto Q beads, the static capacity of Q membranes would be ∼36 mg/ mL, 10-50 times greater than the reported static capacity of Q beads.22 Thus, adsorptive separations of large biomolecules, which are highly inefficient using traditional chromatographic beads, might become quite efficient if membranes were used instead. On the basis of these results, then, chromatographic membranes might fill an increasingly important niche in the isolation and purification of new biotechnology products that consist of large biomolecules such as viruses and DNA. Acknowledgment Funding for this work was provided by the National Science Foundation (BES-9631962) and the College of Agricultural and Life Sciences. Symbols c ) solute concentration in the liquid phase, mg/mL c* ) solute concentration in the liquid phase in equilibrium with cs, mg/mL cl ) membrane capacity based on the solid volume, mg/ mL cs ) solute concentration in the solid phase based on the solid volume, mg/mL c0 ) feed solute concentration, mg/mL D ) diffusion coefficient of the solute in free solution, cm2/s Ds ) diffusion coefficient of the solute inside beads, cm2/s ka ) association rate constant, mL/(mg s) kd ) dissociation rate constant, s-1 Kd ) desorption equilibrium constant, M () kd/ka) L ) length of membrane, cm mbound ) amount of protein bound to the membrane, mg r ) spatial coordinate, cm R ) radius of a bead, cm t ) time, s v ) interstitial liquid velocity, cm/s Vl ) liquid-phase volume, mL  ) membrane void fraction τ ) dimensionless time () vt/L)

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Received for review July 9, 2001 Revised manuscript received January 8, 2002 Accepted January 22, 2002 IE010585L