Bbtechnol. Rag. 1994, IO, 207-213
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Intermolecular Electrostatic Interactions and Their Effect on Flux and Protein Deposition during Protein Filtration Sean P. Palecek and Andrew L. Zydney’ Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Although membrane filtration is used extensively to process protein solutions containing a variety of electrolytes, there is currently little fundamental understanding of the effect of the solution environment (and in particular, the solution pH) on the filtrate flux in these systems. We have obtained data for the flux and sieving coefficients during the batch (stirred cell) filtration of solutions of bovine serum albumin, immunoglobulins, hemoglobin, ribonuclease A, and lysozyme through 0.16-pm microfiltration membranes a t different pH values. The flux declined significantly for all five proteins due to the formation of a protein deposit on the upper surface of the membrane. The quasi-steady ultrafiltrate fluxes a t the individual protein isoelectric pH’s were essentially identical, despite the large differences in molecular weight and physicochemical characteristics of these proteins. The flux increased at pH’s away from the isoelectric point, with the data well-correlated with the protein surface charge density. These results were explained in terms of a simple physical model in which the protein deposit continues to grow, and thus the flux continues to decline, until the drag force on the proteins associated with the filtrate flow is no longer able to overcome the intermolecular repulsive interactions between the proteins in the bulk solution and those in the protein deposit on the surface of the membrane.
Introduction Many commercial membrane processes involve the filtration of protein solutionsin the presence of electrolytes, e.g., the concentration of whey proteins in the production of a variety of dairy products, the exchange of buffers in the downstream processing of proteins or enzymes, and the sterile filtration of therapeutic proteins. One of the critical factors determining the overall effectiveness of these membrane processes is the decline in flux (and protein transmission) that typically occurs during filtration, a phenomenon that is often referred to by the general term, membrane fouling. A number of previous studies have demonstrated that membrane fouling can be dramatically affected by the pH, salt concentration, and electrolyte composition of the protein solution. There has, however, been considerable discrepancy regarding the specific effects of electrolyte composition and concentration on the filtrate flux and protein transmission. For example, Fane et al. (1983a,b) showed that the filtrate flux during the filtration of bovine serum albumin (BSA) solutions through both nonpermeable and semipermeable ultrafiltration membranes was minimal at the protein isoelectric point (PI), i.e., under conditions where the proteins had no net charge. The flux also decreased with increasing ionic strength (I)for solutions above or below the protein isoelectric point (PI), with this behavior attributed to the effects of solution environment on the extent of protein adsorption within the membrane pores and/or deposition on the membrane surface. Bansal et al. (1991) also observed a distinct minimum in flux at the isoelectric point for the filtration of hemoglobin solutions through 0.2-pm microfiltration membranes, although this behavior was attributed to pore blockage effects coupled with conformational changes in ~~~
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the hemoglobin molecule at alkaline pH. In contrast to the above results, Heinemann et al. (1988) found that the flux during the filtration of whey proteins in a salt-free solution through 0.2-pm microfiltration membranes decreased monotonically with increasing pH from pH 3.5 to 8.5, even though the isoelectric point of the whey proteins was about pH -5.2. Protein transmission through these microfitration membranes was a complex function of time, but the transmission attained ita maximum value at the protein isoelectric point in essentially salt-free solutions, with the exact opposite behavior seen in 0.1 M NaC1. This behavior was attributed to the combined effects of (1) intermolecular electrostatic interactions between adjacent proteins within the deposit that was formed on the upper surface of the membrane, (2) electrostatic interactions between the charged proteins and the charged membrane, and (3) protein aggregation in the bulk solution due to a salting out phenomenon at high salt concentrations. Melling and Westmacott(1972) found that penicillinase transmission through a semipermeable microfiltration membrane was maximal at pH 6 (around the protein isoelectric point),with a sharp drop-off in transmission at higher pH. The transmission initially increased with increasing ionic strength, but then decreased at very high ionic strength. Bil’dyukevich et al. (1989) also found an initial increase in protein transmission at very low ionic strength for the filtration of a variety of proteins through several different types of membranes, with the transmission then decreasing at higher salt concentrations. The behavior at very high salt concentrations P1.0 M) was more complex; the transmission of hemoglobin, trypsin, and lysozyme decreased with increasing ionic strength, while the transmission of human and eggalbumin increased with increasing ionic strength. This behavior was attributed to a combination of electrostaticinteractions between the proteins and the membrane, protein conformational changes with changing pH and salt concentration, and
0 1994 American Chemical Society and American Instkute of Chemical Engineers
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protein aggregation effects, although no detailed analysis of these results was presented. Direct measurements of the amount of protein deposited during ultrafiltration showed that BSA deposition was a maximum at the p l and increased with increasing ionic strength at all pHs (Fane et al., 1983b). However,scanning electron micrographs obtained by Lee and Merson (1976) indicated that the deposition of whey proteins on a 0.4pm microfiltration membrane could be reduced upon the addition of either NaCl or CaClz to the whey solution. The reason for the discrepancy between these two studies is unclear. Iritani et al. (1991) evaluated the porosity and permeability of the protein deposit formed during dead-end filtration of BSA using a cake filtration model in which it was implicitly assumed that all of the BSA that was convected to the membranewas actually deposited within the growing protein cake on the upper surface of the membrane. The calculated porosity and permeability of the BSA deposit were minimal at the protein isoelectric point and decreasedwith increasingionic strength for pH’s both above and below the pl. Palecek et al. (1993)recently performed a detailed study on the effect of ionic environment on the properties of BSA deposits that had been formed on the surface of 0.16-pm microfiltration membranes. The permeability of the deposited BSA layers was minimal at the protein isoelectric point and decreased with increasing solution ionic strength at pH’s both above and below the pl. The permeability was also a function of ion valence, with this dependenceon ionic composition and concentration consistent with the effects of the electrolytes on the electrostatic repulsion between the charged BSA molecules within the protein deposit. Although these studies have provided some insights into the effects of solution environment on the flux decline during protein filtration, there is still no quantitative understanding of the underlying phenomena that determine the effects of the electrolyte composition (and in particular, the solution pH) on the filtration behavior of different proteins with different physicochemical characteristics. The objective of this study was to obtain quantitative data for the flux decline during filtration of several proteins with different molecular weights and isoelectric points over a range of solution pH values. These results were then used to obtain fundamental insights into the effects of solution environment,and the changes in the inter- and intramolecular electrostatic interactions between proteins that arise from alterations in solution pH and ionic strength, on the filtrate flux and the extent of protein fouling during membrane filtration.
Materials and Methods The different proteins examined in this study are listed in Table 1 along with some of their important physical characteristics. Powdered proteins were all obtained from Sigma Chemicals (St.Louis, MO): bovine serum albumin (Sigma catalog no. A7906), bovine immunoglobulin G (G5009), bovine hemoglobin (H2500), bovine pancreas ribonuclease A (R5503), and chicken egg white lysozyme (L6876). Protein solutions were prepared by dissolving preweighed quantities of the protein powders in a 0.15 M NaCl solution that had been prefiltered through a 0.2-pm pore size GA-8 membrane (Gelman Sciences Inc., Ann Arbor, MI) to remove particulates prior to use. The pH of the protein solution was then adjusted to the desired value by the dropwise addition of small amounts of 0.1 M NaOH or HCl as required. The pH was measured to within
0.1 unit using an Acumet 915 pH meter (Fisher Scientific, Pittsburgh, PA). Albumin concentrations were measured spectrophotometrically by the reaction of BSA with bromcresol green, with the absorbanceof the resulting complex measured at 628 nm using a Perkin-Elmer Lambda 4B UV/vis spectrophotometer (Perkin-Elmer Corp., Norwalk, CT). Hemoglobin concentrations were measured using the cyanomethemoglobin technique, which involved reacting the hemoglobin with Drabkin’s reagent and measuring the absorbanceat 540 nm. Lysozyme, immunoglobulin (IgG), and ribonuclease A (RNase A) concentrations were determined by reacting the proteins with copper to form a purple copper-protein complex, with the absorbance measured at 540 nm. In each case, the actual protein concentration was determined by comparing the solution absorbance with that of known protein standards. The majority of the filtration experiments employed asymmetric Omega poly(ether sulfone) microfiltration membraneswitha nominal pore diameter of 0.16 pm. These membranes were provided by the Filtron Technology Corporation (Northborough,MA) in sheet form and cut to 25 mm diameter disks (using a cutting tool fabricated in our lab) to minimize the membrane-to-membrane variability. A limited number of experiments were also performed with Omega 100 OOO (100K) and 30 OOO (30K) molecular weight cutoff poly(ether sulfone) ultrafiltration membranes (Filtron Technology Corporation), tracketched polycarbonate membranes that have very welldefined 0.1 pm diameter cylindrical pores (Poretics Corporation, Livermore, CA), and 0.2-pm asymmetric PTFE (poly(tetrafluoroethy1ene))microfiltration membranes (Microfiltration Systems, Dublin, CAI. Protein filtration experiments were performed in an Amicon stirred ultrafiltration cell (Model 8010, Amicon, Division of W.R. Grace & Co., Beverly, MA) connected to a 250-mL solution reservoir, which was air-pressurized using a Fisher heavy-duty single stage regulator. The pressure was measured to within f 2 kPa using an air pressure gauge (Fisher Scientific). The membrane was placed in the stirred cell and then flushed with 100 mL of distilled water to remove glycerin, which was used as a wetting agent. The permeability of the clean membrane was evaluated from data for the water flux, measured via timed collection, as a function of the applied pressure. The stirred cell was then carefully emptied, and the solution reservoir and stirred cell were refilled with a protein solution. The air pressure was set (typically at 69 kPa = 10 psig) and the stirring speed adjusted to 600 rpm using a calibrated Strobotac Type 1531-ABstrobe light (General Radio Co., Concord, MA). The protein filtration was then performed for 3 h at a constant pressure with the filtrate flow rate measured via timed collection. Filtrate samples were collected periodically for subsequentspectrophotometricdetermination of the protein concentration. All experiments were conducted at room temperature (22 f 3 O C ) . Additional details of the stirred cell apparatus and experimental procedures are provided by Palecek et al. (1993).
Results and Analysis The filtrate flux during the conatant-pressure (69 i 2 kPa) filtration of 5 g/L solutions of the different proteins in 0.15 M NaCl at pH 7.4 is shown in Figure 1. In each case,the initial flux with the protein solution was evaluated within the first 30 s of the protein filtration. This initial flux was only slightly less than the water flux evaluated for the clean membrane immediately prior to the protein
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Bioreahnd. Prog.., 1994, Vol. 10, No. 2
m Albumin Immunoglobulins
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Figure 1. Ultrafiitrate flux as a function of time during the fiitration of 6 g/L protein solutions at 69 kPa and pH 7.4.
Figure 2. Observed protein sieving coefficienta as a function of time during the filtration of 5 g/Lprotein solution at 69 kPa and pH 7.4.
fiitration experiment, with this small differenceprimarily due to the small flux decline that occurred during the time required for collection of the first filtrate sample. The small variation in the water flux for the different runs (ranging from about 1300 to 1900 pm/s) reflects the inherent variability between membranes, even for disks cut from a single flat sheet. A series of repeat experiments with BSA demonstrated that the flux after about 300 s was completelyunaffected by this variability in the initial permeability of the clean membrane. The flux declined quite rapidly during each of these protein filtrations, with the flux decreasingby an order of magnitude within the first several minutes of the experiment. In each case, the flux eventually approached a quasi-steadyvalue that was, under these conditions,about 2 orders of magnitude less than the initial flux. This quasisteady flux was highly reproducible; multiple repeat experiments with BSA gave quasi-steady fluxes varying from only 11.8 to 12.3 pm/s. This dramatic flux decline was due primarily to the formation of a protein deposit on the upper surface of the membrane, with scanning electron micrographs demonstrating that there were essentiallyno pores visible on the membrane surface after only a few minutes of BSA filtration under these conditions (Opong and Zydney, 1991). At long times, this protein deposit had a sieving coefficient of less than 1, leading to a significant osmotic pressure difference across the membrane, which also played a role in the flux decline (Palecek et al., 1993). This effect is discussed in more detail subsequently. The quasi-steady flux for lysozyme (33 pm/s) was more than a factor of 2 greater than that for BSA (12 pm/s) and more than a factor of 5 greater than that for IgG, hemoglobin, or ribonuclease A. These latter three proteins all had quasi-steady fluxes within about 20%,ranging from a low of 5.0 pm/s for the hemoglobin to a high of 6.0 pm/s for ribonuclease A. The similarity in the quasi-steady fluxes for hemoglobin,IgG, and RNase A appears to be due to the fact that these three proteins were relatively uncharged under these experimental conditions, with isoelectric points ranging from about 6.6 to 7.8 (the isoelectricpoint for IgG is just a rough average for the different IgG molecules present in the Sigma preparation). In sharp contrast, BSA has a net charge of -20.5 at this pH and ionic strength (Vilker et al., 1981), while lysozyme has a net charge of +7.9 under these conditions (Tanford and Wagner, 1954). The flux did not appear to be correlated in any way with protein size, with the fluxes
forribonucleaseA(MW = 13 700) andIgG (MW = 155 OOO) being within 10% throughout the entire course of the 3-h filtration. The observed protein sieving coefficient (So),which is also referred to as the protein transmission, was evaluated from the ratio of the protein concentration in the filtrate to that in the bulk solution in the stirred cell. The bulk protein concentration in the stirred cell increased with time over the course of the filtration due to the accumulation of protein within the stirred cell, arising from the partial retention of the proteins by the protein deposit that formed on the surface of these membranes. The bulk concentration could not be evaluated directly by sampling the stirred cell without disturbing the velocity profiles and/or applied pressure within the stirred cell; the bulk concentration was instead calculated from the data for the filtrate concentration by numerically integrating the differential mass balance for the stirred cell over the time of the filtration experiment. The lysozyme concentration remained essentiallyconstant throughout the 3-h filtration, reflectingthe absenceof any significantlysozymeretention under these conditions while the BSA and hemoglobin concentrationsincreased by nearly 60 % The overallmass balance closure, which was determined by comparison of the calculated values of the bulk protein concentration with those actually measured in a fluid sample taken directly from the stirred cell at the end of the experiment, was within about 5 5% for all of the filtration experiments reported in this article. The calculated values for the observed sievingcoefficient for the different proteins are shown as a function of time inFigure 2. The initial sieving coefficientsfor the different proteins were essentially equal to 1 due to the large pore size of these microfiltrationmembranes. However, protein deposition caused a significant reduction in the observed sieving coefficients (except for lysozyme), reflecting the retention of proteins in the stirred cell by the growing protein deposit on the upper surface of the membrane. The observed protein sieving coefficients at the end of the 3-h filtration ranged from a low of about 0.4 for hemoglobin to essentially1.0for lysozyme,with no obviousdependence on either the protein molecular weight or the protein charge. The sievingcharacteristicsof the albumin deposita formed on these microfiltration membranes have been studied in considerable detail by Mochizuki and Zydney (1993)using neutral polydispersedextrans to evaluate the sieving coefficients as a function of the solute molecular weight. The data indicated that the effective pore size
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Blotechnol. Prog.., 1994, Vol. 10, NO. 2
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Figure 3. Filtrate flux (top panel) and observed sieving coefficients (bottompanel) evaluated at the end of a 3-h fiitration performed at the isoelectric pH of the different proteins (filtrationsperformed with 5 g/L solutions at 69 Ea).
within the albumin deposit was a function of the applied pressure and solution environment, with the average pore diameter over a range of conditions being on the order of 100 A. An albumin deposit with this type of pore size would be expected to retain a significant amount of albumin in the bulk solution, consistent with the data seen in Figure 2. Experimental data for the quasi-steady flux (evaluated by averaging the last several data points obtained at the end of the 3-h filtration experiments) for the different proteins at their respective isoelectric points are shown in the top panel of Figure 3. The quasi-steady fluxes for BSA and lysozyme at their isoelectric points were much smaller than those obtained at pH 7.4, with these values now in very good agreement with the flux for the hemoglobin, IgG, and ribonuclease A from Figure 1. The small differences in flux seen in Figure 3 are due at least in part to the small differences between the solution pH in these experiments and the actual p1 of the particular proteins. There was no apparent dependence of the flux on protein molecular weight or on the specific chemical and/or physical characteristics of the proteins, with the fluxes at the isoelectric point all being within 15% of each other. In contrast, the observed sieving coefficients at the protein isoelectric points, again evaluated from the data obtained at the end of the 3-hfiltrations (bottom panel in Figure 3),varied significantlyfor the different proteins, ranging from a low of about 0.08 for BSA to a high of almost 0.8 for IgG. The sieving coefficients for BSA and
lysozymeat their isoelectric points were markedly smaller than those at pH 7.4, with the BSA sieving coefficient reduced from about 0.48 to 0.08, while the lysozymesieving coefficient decreased from essentially 1.0 to slightly less than 0.4. There was again no apparent dependence of the sieving coefficients at the protein p1 on the protein molecular weight or any other obviousphysical or chemical characteristic of these macromolecules. In order to examine further the dependence of the flux on the protein charge, a series of filtration experiments at 69 kPa was performed with 10 g/L BSA solutions in 0.15 M NaCl at pH’s from 3.7 to 7.45. The data are plotted in Figure 4 as the difference between the quasi-steady flux at any given pH and the quasi-steady flux at the BSA isoelectric pH (with Jpl = 5.8 pm/s) as a function of the square of the electronic charge ( q )on the BSA. The reason for this form of the plot will be discussed subsequently. The BSA charge was evaluated as a function of solution pH using the correlation presented by Vilker et al. (1981). The flux attained its minimum value at the isoelectric point of BSA, with the flux at pH 7.45 (J = 13.5 pmls) being more than a factor of 2 larger than the flux at pH 4.7 (5.8 pm/s). The quasi-steady flux increased linearly with q2 for t b set of experimental data, with a correlation coefficient of r2 = 0.99. Note that the quasi-steady flux at pH 3.7 was not shown in Figure 4, and it was not consistent with the above correlation (J = 8.7 pm/s at q = +31). This is probably due to the conformational changes in the albumin molecules that are known to occur at low pH (Loeb and Scheraga, 1956). In order to understand the origin of this linear relationship between the quasi-steady flux and the square of the protein charge, it is useful to consider the forces acting on a protein in the bulk solution as it approaches the protein deposit on the upper surface of the membrane, as shown schematically in Figure 5. The net motion of the protein will be determinedby the s u m of the hydrodynamic drag force associated with the fluid flow (F&& the electrostatic repulsion between the charged protein and the charged protein deposit (Fel&wt,&, and any other forces of interaction between the protein in solution and the protein deposit on the membrane, including van der Waals attraction, dipole-dipole interactions, hydration forces, etc. The s u m of these additional forces, denoted
Bbtechnol. Rw., 1994, Vol. I O , No. 2
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+ A
Hemoglobin Lysozyme RibonucleaseA
Figure 5. Schematic representation of the forces acting on a spherical protein in the bulk solution approaching the upper surface of a protein deposit on the membrane.
as Fp,will be a complex function of the intermolecular spacing, reflecting the different dependencies of the individual contributions to Fp on distance. Since the protein is undergoingno net acceleration,the s u m of these forces should be zero under all conditions. In order for the protein to ”stick” to the growing deposit, it must be convected into sufficiently close proximity that the attractive component of the van der Waals potential can overcome the repulsive forces associated with the electrostatic interactions and any other repulsive contributions to the overall interaction potential. The flux required to overcome these repulsive interactions, and thus the flux necessary for continued growth of the protein deposit, can be evaluated in terms of these forces by assuming that the hydrodynamicdrag force on the protein is given by Stokes’ law as
where p is the solvent viscosity and R is the effective hydrodynamic radius of the protein. Protein deposition will thus continue to occur as long as the flux is greater than that given by eq 1,with the quasi-steadyflux attained when the convective flow is too small to overcome the repulsive interactions (i.e., when the deposit cease8 to grow). The electrostatic repulsive force between two charged spheres of radius R (a rough approximation to the interaction between an approaching protein anda protein at the upper surfaceof the deposit)is given as (Israelachvili, 1985)
where AD is the Debye length, which is a function of the salt concentration in the solution (with AD = 7.8 A in 0.15 M NaCl), u is the surface charge density on the protein (a = q / A with A the protein surface area), e, is the permittivity of free space (e, = 8.854 X W2C2J-I m-9, Q is the dielectric constant of the solvent (e = 72 for water), and D is the distance between the spherical protein molecules. The nonelectrostatic contribution to the force between the protein and the deposit cannot be evaluated theoretically due to the unavailability of accurate expressions for the interaction potential between these complex macromolecules. However, application of eq 1 at the
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Surface Charge Density Squared, u2 (Cfh4 x IO4)
Figure 6. Ultrafiitrate flux as a function of the square of the surface charge densityfor the filtrationof 5 g/L protein solutions at 69 kPa over a range of pH values. protein isoelectric point (where Felectrostatic = 0)yields l 7
(3) This allows eq 1 to be solved for the flux at any given pH in terms of the flux at the protein isoelectric point: (4)
The BSA data presented in Figure 4 are in excellent agreementwith eq 4, with the distance between the surface of the approaching protein and the upper surface of the deposit (D)assumed to be a constant which reflects the distance of approach required for the protein to overcome the repulsive interactions and thus stick to the deposit. This critical distance can be evaluated from eq 4 using the data presented in Figure 4 as D = 31A, which is somewhat less than the size of an individual BSA molecule. Although this model is extremely simple, it suggests that the quasi-steadyflux for the different proteins should be effectively correlated simply in terms of the protein surface charge density, independent of the detailed physicochemical characteristics of the proteins. The charges on the proteins examined in this study were evaluated from HC1 titration data for hemoglobin (Beychok and Steinhardt, 1959), lysozyme (Tanford and Wagner, 1954),and ribonuclease A (Tanford and Hauenstein, 19561, assuming that chloride ion binding was independent of solution pH (Tanford, 1962). The results are shown in Figure 6, with the protein surface area evaluated from the ellipsoidal dimensions given in Table 1. No data are shown for IgG due to the unavailability of an accurate. HC1 titration curve. Two data points are shown for lysozyme at u2 = 0.035 C2 m-2 (corresponding to pH 7.4). The open symbol represents the flux obtained after a standard 3-h lysozyme filtration. Although the flux in this experiment had appeared to reach a quasisteady state after this 3-h filtration, a subsequent experiment performed over a 24-h period gave a much lower quasi-steady flux, which is shown in Figure 6. The origin of this very long transient for the lysozyme filtration is unclear. The quasi-steady flux data for the different proteins do appear to be very well-correlatedby the square of the surface charge density. This good correlation was seen for proteins that were either just positively or just
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Bbtechnol. Rog., 1994, Vol. 10, No. 2
Table 1. Protein Physical Characteristics [Data from Creighton (1984)l protein bovine serum albumin bovine immunoglobulin G bovine hemoglobin bovine pancreas ribonuclease A chicken egg white lysozyme
molecular weight 67 OOO 155 OOO 68 OOO 13 700 14 400
ellipsoidal diameters (A) 140 X 40 X 40 230 X 45 X 45 70 X 55 X 55 38 x 28 x 22 45 X 30 X 30
surface area (m2 x 10’6) 1.10 1.94 1.17 0.26 0.37
protein isoelectric pH 4.7 6.6 7.1 7.8 11.0
protein charge (at pH 7.4)o -20.5 -4.0 +1.6 +7.9
Protein charges at pH 7.4 are from references in the text.
negatively charged over the pH range studied in these experiments (e.g., lysozyme and BSA), as well as for proteins that varied from positive to negative charge as the pH increased (e.g., ribonuclease A, which went from +1.6 at pH 5 to -5.3 at pH 9). The data again display the linear relationship with u2 that was suggested by eq 4. In addition, the flux at zero charge (i.e., at the protein isoelectric point) is essentially identical for the different proteins, as was seen in Figure 3. This behavior will be discussed in more detail subsequently. This very simple physical model for the growth of the protein deposit also suggests that the quasi-steady flux during protein filtration shouldbe essentially independent of the membrane properties; the quasi-steady flux (i.e., the flux at which the deposit stops growing) is simply determined by the electrostatic interactions between the proteinsin the deposit and the proteins in the bulksolution. This behavior is seen experimentally in Figure 7, which shows the BSA flux through three different pore size poly(ether sulfone)membranes (bottom panel) and through three different polymeric microfiltration membranes (top panel). The initial flux through the track-etched polycarbonate membrane was well over a factor of 10less than that for the two asymmetric microfiltration membranes due to the large differences in membrane porosity and thickness for these membranes, but the quasi-steadyfluxes for these membranes were all very similar. The initial flux through the different poly(ether sulfone)membranes (bottom panel) varied by over an order of magnitude due to the very different pore sizes of these membranes, but the quasi-steady fluxes were all within about 20%, with the highest flux obtained with the partially permeable 100 OOO molecular weight cutoff membrane. The slightly higher flux seen for the data shown in the bottom panel of Figure 7 is most probably due to the slightly higher pH, and thus the slightly greater BSA charge, for this set of experiments.
Discussion The flux during protein filtration is determined by a large number of factors, including (1) the hydraulic resistance to flow provided by the protein deposit that accumulates during filtration, (2) the osmotic pressure of the concentrated protein solution that can build up at the membrane surface due to protein retention by the membrane, and (3) the extent of protein adsorption within the membrane pores. Each of these phenomena is in turn a function of the deviceoperatingconditions. However,both the bulk mass transfer (i.e., osmotic pressure or boundary layer effects) and protein adsorption occur fairly rapidly; typical time constants for the boundary layer growth in a stirred or cross-flow device are on the order of several seconds, and the kinetics of protein adsorption on these polymericmembranes are also generallyquite rapid, except under mass transfer limited conditions (Robertson and Zydney, 1990). Thus, the long-term flux decline seen in most protein filtration experiments (such as the stirred cell filtration experiments examined in this study), is
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determined primarily by the changes in the hydraulic resistance and protein retention provided by the growth of the protein deposit on the surface of the membrane. The data obtained in this study suggest that the quasisteady flux in these systems will ultimately be determined by the value of the flux at which the protein deposit ceases to grow. When the flux is greater than this critical value, additional protein will continue to add to the growing deposit, increasingthe overallhydraulic resistance to flow (and possibly reducing the effectivepressure driving force due to the increase in the osmotic pressure associatedwith any increase in protein retention), thereby decreasing the flux. Although the actual kinetics of protein deposition may be extremelycomplex (involvingelectrostaticinteractions, protein conformationalchanges,hydrophobicinteractions, hydrogen bonding, formation of intermolecular disulfide linkages, etc.), the results obtained in this study using BSA, hemoglobin, IgG, lysozyme, and RNase A indicate that considerable insights into this phenomenon can be obtained simply by examining the forces required for a protein in the bulk solutionto approachthe proteine within the deposit closely enough so that it is able to “stick” to the deposit. The flux thus continues to decline (and the
Bbtechnol. Rog., 1994, Vol. 10, No. 2
deposit continues to grow) until the hydrodynamic drag force on the bulk protein is insufficient to overcome the intermolecular repulsive interactions between the proteins in the bulk solution and those in the deposit. The quasisteady state flux is thus determined by the magnitude of the hydrodynamic drag force that just balances the repulsive interactions between the protein and the deposit. The minimum flux for each protein occurs when the proteins are uncharged, which is in agreement with a variety of previous experimental observations (Fane et al., 1983; B a n d et al., 1991), with this minimum in the flux reflecting the minimum in the intermolecularrepulsive interactions between proteins at the PI. The data presented in Figure 3 indicate that the flux at the protein p1 is largely unaffected by the detailed physical and chemical characteristics of the proteins (at least for the range of proteins examined in this study), suggesting that the nonelectrostatic interactions (e.g., the hydration forces) are also similar for the different proteins. The underlying basis for this result clearly requires further investigation. It is important to note that the sieving coefficients at the protein isoelectric point were quite different for the different protein filtration experiments, with no clear dependence on the protein molecular weight. This suggests that the structure or protein packing within the deposits is quite different for the different proteins, even though the quasi-steady flux (determined by the interactions between the bulk proteins and the deposit) is essentially identical for these different proteins at their PI. The flux at solution pH away from the protein isoelectric point is determinedprimarily by the protein surfacecharge density, with the flux increasing linearly with the square of the charge density (Figures4 and 6). This dependence of the flux on the charge density is in excellent agreement with the relatively simple physical model developed in this study in which the electrostatic repulsion between the proteins in the bulk solution and that in the deposit is evaluated using an expression for the intermolecular potential between two charged spheres. The increase in flux with increasing surface charge is thus a direct result of the increase in the hydrodynamic drag required to overcome the intermolecular repulsive potential between the proteins. Note that the actual thickness of the protein deposit may be a very complex function of solution pH due to the dependence of the deposit permeability on pH (Palecek et al., 19931, as well as the effect of solution pH on the protein osmotic pressure and bulk mass transfer coefficient. The relative contributions of each of these phenomena will be different under different experimental conditions, but the quasi-steady flux will still be determined by the flux at which the hydrodynamicdrag on the proteins is no longer sufficient to cause additional protein deposition. This simple physical model is also consistent with previous experimental observations that the flux increases monotonically with decreasingsolution ionic strength [e.g., Fane et al. (1983) and Palecek et al. (199311;this increase in the quasi-steady flux reflects the increase in the electrostatic repulsion between the proteins due to the reduction in shielding provided by the electrolytesin these low concentration salt solutions. The detailed dependence of the flux on the solution ionic strength is somewhat more complicated than that seen for the protein charge (Figures 4 and 6) due to the more complex dependence of the electrostatic repulsive interactions on the Debye length (as seen in eq 2).
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Acknowledgment The authors thank Filtron Corporation for its donation of the Omega poly(ether sulfone) membranes used in these experiments and Suzanne Wanalista and Jessica Yen for their assistance with some of the albumin experiments. This work was supported in part by Grant ROl-HL-3945502 from the National Institutes of Health.
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