Bbtechnol. Rag. 1992, 8, 553-561
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Effect of Protein Adsorption on the Transport Characteristics of Asymmetric Ultrafiltration Membranes Seiichi Mochizuki and Andrew L. Zydney' Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
The effects of bovine serum albumin adsorption on the transport characteristics of asymmetric poly(ether sulfone) ultrafiltration membranes were determined using polydisperse dextrans with gel permeation chromatograhy. Actual dextran sieving coefficients were evaluated from observed sieving data for both the clean and preadsorbed membranes using a stagnant film model. The flux dependence of the actual dextran sieving coefficients was used to evaluate the intrinsic membrane hindrance factors for convective (i.e., sieving) and diffusive transport for the different molecular weight dextrans using classical membrane transport theory. Protein adsorption caused a reduction in both dextran sieving and diffusion, with the magnitude of the reduction a function of the dextran molecular weight and pore size. The effects of adsorption on the specific pore area and the membrane porosity were then determined using a recent model for solute transport through asymmetric ultrafiltration membranes. The data indicate that protein adsorption occurs preferentially in the larger membrane pores, causing a greater reduction in solute sieving compared to the membrane hydraulic permeability and porosity than would be predicted on the basis of either a simple pore blockage or pore constriction model.
Introduction Selectively permeable ultrafiltration membranes are currently used in a variety of bioreactor applications in which they provide both a support for the biocatalyst (e.g., immobilized cells or enzymes) and a barrier that can provide at least partial separation of the products, waste metabolites, and nutrients. Such devices are also used as hybrid bioartificial organs with the selectively permeable membrane immuno-isolating the transplanted cells while permitting relatively unhindered transport of the smaller nutrients and therapeutic agents (e.g., insulin in the bioartificial pancreas). These membranes have also been examined for use in fractionation of complex protein mixtures both in plasma fractionation and in the downstream processing of fermentation effluents, although previous studies of this type of selective protein filtration have been largely unsuccessful due to the relatively poor selectivity obtained in these devices (e.g., Ingham et al., 1980). One of the critical factors governing, and often limiting, the overall effectiveness of these devices is the effect of protein adsorption on the transport characteristics of the membranes. A number of investigators have demonstrated that the extent of protein adsorption is a function of the physicochemical properties of both the protein and membrane, including the membrane pore size. Much of the previous work on protein adsorption to polymeric membranes has been reviewed by Robertson and Zydney (1990a,b)and Nilsson (1990);thus, the following discussion will focus on those studies most pertinent to the current investigation. Matthiasson (1983) obtained data for bovine serum albumin (BSA, MW = 69 000) adsorption on small-pore (molecular weight cutoffs less than 20 000) asymmetric polymeric membranes. Significant protein adsorption
* Address correspondence to this author; phone, (302) 831-2399. 8756-7938/92/300&0553$03.00/0
occurred on the upper surface of the membranes and in the porous support structure, with BSA adsorption in the support attributed to the presence of a small number of large pores in the membrane skin. Robertson and Zydney (1990b) obtained data for BSA adsorption on partially permeable asymmetric poly(ether sulfone) membranes, with adsorption in the membrane skin layer evaluated by subtracting off the contributions of the large support structure. Data indicated that BSA surface coverage in the skin was minimal for the 50 OOO molecular weight cutoff (50K) membrane, but attained essentially monolayer values for membranes with pores that were only slightly larger than the size of a BSA molecule. Sheldon et al. (1991) examined the actual location of BSA adsorbed on polysulfone and regenerated cellulose membranes using thin-section transmission electron microscopy with immunochemical staining. Although the membranes had a 10 OOO molecular weight cutoff, significant quantities of BSA were observed throughoutthe porous structure, which was attributed to the broad pore size distribution in these membranes. There have also been a number of studies of the effects of protein adsorption on the membrane hydraulic permeability or membrane resistance (the inverse of the permeability). Dejmek and Nilsson (1989) found a significant increase in membrane resistance upon adsorption of whey proteins, @-lactoglobulin,or a-lactalbumin to 20K polysulfone membranes. Data for the relative increase in resistance suggested that the adsorbed protein altered the membrane pore structure instead of just forming a layer on the upper surface of the membrane. Similar results were obtained by Nilsson and Hallstrom (1992),with their data suggesting that the increase in resistance was due to the combined effects of pore blockage and pore constriction. Sheldon et al. (1991) have attributed the observed differences in the specific resistance of adsorbed BSA on cellulosic and polysulfone membranes to the differences in the location and structure of the adsorbed protein in
0 1992 American Chemical Society and American Instkute of Chemical Engineers
554
these membranes, although no detailed discussion of these effects was provided. Experimental studies of the effects of protein adsorption on solute transport are more limited. Wong and Quinn (1976) obtained data for BSA diffusion through relatively large pore track-etched mica membranes, with the data indicating that the effective membrane pore size was reduced by a monolayer of adsorbed BSA. Zeman (1983) obtained data for the convective transport (or sieving) of relatively small linear poly(ethy1ene oxide)s through 10K membranes. The dependence on polymer molecular weight was much steeper than predicted by available hydrodynamic models, which Zeman attributed to the reduction in the effective pore size associated with monolayer adsorption of the different polymers within the membrane pores. Robertson and Zydney (1990a) obtained data for hindered diffusion of BSA through asymmetric poly(ether sulfone)membranes with molecular weight cutoffs ranging from 50K to 1M. Comparison of the data with available hydrodynamic models suggested that BSA adsorption in the large-pore membranes constricted the membrane pores by the size of a BSA monolayer, while BSA adsorption in the smaller molecular weight cutoff membranes was better described using a pore-blockage model in which BSA completely blocks some of the pores to subsequent protein transport. Meireles et al. (1991) studied the effects of protein fouling on dextran sieving by IRIS polysulfone membranes. BSA fouling had no effect on dextran sieving for a 10K membrane, but significantly increased dextran retention for a 40K membrane. Data were analyzed using available hydrodynamic models, with the membrane pore size distribution described using a log-normal distribution function. BSA adsorption caused a significant reduction in the maximum pore size as well as an apparent increase in the breadth of the distribution (ascharacterized by the increase in the geometric standard deviation of the lognormal distribution). These effects were even more pronounced for adsorption of the smaller proteins ovalbumin and a-lactalbumin. Some care must be taken in drawing any quantitative conclusions from these results since Meireles et al. (1991) evaluated the actual membrane retention Coefficients by extrapolating data for the observed retention to zero pressure, which ignores the potentially important effect of dextran diffusion on the overall rate of dextran transport at low pressure as discussed by Mochizuki and Zydney (1992). Although these studies clearly demonstrate that protein adsorption can significantly alter the membrane pore size characteristics of partially permeable ultrafiltration membranes, there is no data on the magnitude of this effect on all of the different transport properties (hydraulic permeability, the hindered diffusivity, and sieving coefficient) for a given membrane. In addition, there is still considerable uncertainty regarding the detailed mechanism by which the adsorbed protein alters the membrane (e.g., pore blockage versus pore constriction) or how these effects are actually related to the size of the proteins and pores. There is also no detailed understanding of the possible role of the broad pore size distribution in commercial asymmetric ultrafitration membranes on either the extent of protein adsorption or its effect on the overall transport characteristics of these membranes. The objective of this study was to obtain quantitative data for the effect of bovine serum albumin adsorption on the membrane hydraulic permeability, the membrane sieving coefficient, and the hindered diffusion coefficient for asymmetric poly(ether sulfone) ultrafiltration membranes with different pore sizes. Transport data were obtained using polydisperse dextrans, with the dextran
Bbtechnol. hog... 1992, Vol. 8, No. 6
molecular weight distribution evaluated using gel permeation chromatography, thus allowingmeasurements of the membrane transport coefficients over a broad range of solute molecular weights in a single experimental run. Experimental data for the flux dependence of the observed sieving coefficient were then used to evaluate both the asymptoticmembrane sievingcoefficientand the hindered diffusion coefficient using the procedure described by Mochizuki and Zydney (1992). The different effects of protein adsorption on each of the membrane transport properties (hydraulic permeability, asymptotic sieving coefficient, and hindered diffusion coefficient) were then used to obtain insights into the underlying effects of protein adsorption on both the pore size and the transport characteristics of these ultrafiltration membranes.
Materials and Methods All filtration experiments were performed using OMEGA poly(ether sulfone) ultrafiltration membranes, provided by Filtron Technology Corporation (Northborough, MA), with molecular weight cutoffs ranging from 30 OOO (30K) to 300 000 (300K). These membranes are anisotropic, consisting of (1)an ultrathin functional poly(ether sulfone) skin which determines the sieving characteristics of the membrane, (2) a porous poly(ether sulfone) substructure, and (3)aporous support matrix. Allmembranes were flushed with filtered deionized distilled water prior to use to remove the glycerin, which is used as a wetting agent. Experiments were performed using dextrans with weight-averaged molecular weights of 38 900 (38.9K), 67.9K, or 539K (Sigma Chemical Company, St. Louis, MO). These different polydisperse dextrans allowed data to be obtained over a molecular weight range from 9OOO to slightly more than 1OOO OOO. Dextran solutions were prepared by dissolving the powdered dextrans in 0.15 M phosphate buffer solution (PBS), which had been prefiltered through a 0.2-pm membrane prior to use. Solution pH was adjusted to 7.4 by the addition of NaOH as required. All dextran filtration experiments were conducted with a 25 mm diameter Amicon stirred ultrafiltration cell (Model 8010, Amicon, Division of W. R. Grace & Co., Beverly, MA) connected to a 2-L solution reservoir. The transmembrane pressure drop was set by adjusting the height of the solution reservoir (for pressures up to 6.9 kPa = 1psi) or by air pressurization. The filtrate flux was measured by timed collection. Filtrate samples were collected for subsequent chromatographic analysis after the system attained stable operation. Data were obtained over a wide range of pressure, corresponding to a broad range of filtrate flux, to evalute both the convective and diffusive contributions to dextran transport. All experiments were conducted at room temperature (22 f 3 OC) and at a stirring speed of loo0 rpm. The dextran sieving experiments were first performed using the clean poly(ether sulfone) membranes. These membranes were then carefully removed from the stirred cell and soaked in a 5 g/L solution of bovine serum albumin (Sigma) in 0.15 M PBS for about 2 days to ensure equilibrium adsorption (Robertson and Zydney, 1990b). These preadsorbed membranes were gently rinsed with 0.15 M PBS to remove any labile protein and returned to the stirred cell. The dextran sieving experiments were then repeated using the same procedure as that used for the clean membrane. The flux of 0.15 M PBS was measured before and after each dextran sieving experiment to determine whether there were any changes in the membrane hydraulic permeability associated with dextran
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adsorption and/or deposition during the dextran filtration experiments. Chromatographic Analysis. Dextran samples were analyzed by gel permeation chromatography (GPC) using a TSK G3000SW column (Toyo Soda Manufacturing Co., Ltd., Tokyo, Japan) for the 38.9K and 67.9K dextran solutions and a TSK G4000SW column for the 539K dextran solutions. The eluent was 0.15 M PBS at a flow rate of 1.00 f 0.01 mL/min. Dextran concentrations were determined using a refractive index detector (LC-30 RI detector, Perkin-Elmer Corporation, Norwalk, CT) with an accuracy of fO.O1 g/L. The retention time was related to the dextran molecular weight using calibration curves constructed from dextran standards (American Polymer Standards Corporation, Mentor, OH). All calculations and data analyses were performed on a Model 2100 PC integrator (Revision 5.1, PE Nelson, Cupertino, CA) using a Gateway 2000 personal computer. Data Analysis. The concentration data for the bulk and filtrate solutions were sliced into segments covering small molecular weight ranges (typically about 1 % of the dextran molecular weight). The observed sieving coefficients (So) were evaluated for each segment from the ratio of the filtrate (Cf) to bulk (Cb)concentrations. The actual membrane sieving coefficients (Sa),defined as the ratio of the filtrate concentration to the solute concentration at the membrane surface (Cd, were then evaluated as a function of dextran molecular weight from the So values using a stagnant film model (Blatt et al., 1970; Mochizuki and Zydney, 1992) to account for the bulk mass transfer effects:
where k is the average mass transfer coefficient in the device and Jvis the filtrate flux. The average mass transfer coefficient (k)was calculated from the experimental correlation developed by Smith et al. (1968):
kb = * ( ~ e ) " . 5 6 7 ( ~ C ) 0 . 3 3
D,
(2)
where Re = wb2/v is the Reynolds number, Sc = u/D, is the Schmidt number, b is the cell radius, w is the stirring speed, and v is the kinematic viscosity. The coefficient a function of device geometry and possibly membrane porosity, was evaluated by Opong and Zydney (1991) for the Model 8010 stirred cell as \k = 0.23 from experimental data for the BSA filtrate flux as a function of the transmembrane pressure drop. The free solution dextran diffusion coefficients (D,) were evaluated as a function of the dextran molecular weight (MW) using the correlation developed by Granath (1958):
*,
log D, = -4.1154 - 0.47752 log (MW)
(3)
The calculated values of the actual sieving coefficients (Sd for each dextran molecular weight were then plotted as a function of filtrate flux as described by Mochizuki and Zydney (1992). The flux dependence of the actual sievingcoefficient,which arises from the combined effects of dextran convection and diffusion, was described using membrane transport theory (Anderson and Quinn, 1974) as
sa=
S,
S , exp(Pem> + exp(Pe,) - 1
(4)
vp
t
\
\\
\\
0 103
lo4
lo5
Dextran Molecular Weight
Figure1. Observedsievingcoefficientafor filtrationof the 38.9K weight-averaged molecular weight dextran through an OMEGA 30K membrane before and after BSA adsorption. Experimental conditions: c b = 5 g/L; w = lo00 rpm; and J, = 4.8 X lp m/s for the clean membrane and 4.9 X lo* m/s for the preadeorbed membrane.
where the membrane Peclet number (Pe,) is given as
with e the membrane porosity and 6, the membrane thickness. The coefficients K , and Kd, the hindrance factors for convective and diffusive transport, are both functions of the geometry and size of the solutes and pores as well as the magnitude of any long-range interactions. The asymptotic sieving coefficient (S,),the value of Sa attained at infinite Peclet numbers, is equal to the product of the hindrance factor for convection (K,)and the solute equilibrium partition coefficient (4) between the membrane and bulk solution (Deen, 1987):
s, = 4Kc
(6)
The membrane transport parameters, S , and 8d€4&, were evaluated in this study by minimizing the sum of the squared residuals between the calculated (eqs 1-5) and experimental values of the observed sieving coefficients using the method of steepest descent. Additional details on the experimental procedures and data analysis are provided by Mochizuki and Zydney (1992).
Results Experimental data for the observed sieving coefficienta (So)as a function of dextran molecular weight are shown in Figure 1 for filtration of a 5 g/L 38.9K weight-averaged molecular weight dextran solution through a 30K membrane and in Figure 2 for filtration of a 5 g/L 67.9K weightaveraged molecular weight dextran solution through a lOOK membrane. In each case, the data for the clean membrane and for the membrane after BSA adsorption were obtained at essentially the same flux to minimize the differences in concentration polarization. The data were thus obtained at slightly different pressures since BSA adsorption caused a 26 5% reduction in permeability (L,) for the 30K membrane and a 36 % reduction in L, for the lOOK membrane. There was no evidence of any dextran adsorption or deposition during the dextran sieving experiments, with the PBS flux before and after the dextran filtration differing by less than 10% in all cases. The observed sieving coefficients decrease with increasing dextran molecular weight as expected, with the values for
Biotechnol. hog., 1992, Vol. 8, No. 6
556
lo4 lo5 Dextran Molecular Welght
lo6
Figure 2. Observedsievingcoefficientsfor filtrationof the 67.913 weight-averaged molecular weight dextran through an OMEGA l00K membrane before and after BSA adsorption. Experimental conditions: Cb = 5 g/L; w = 1OOO rpm; and J, = 8.1 X 10" m/s for the clean membrane and 8.7 X 1O-B m/s for the preadsorbed membrane.
0' 0
1.o
0.5 FIUX, J,
(X
1.5
I 2.0
WS)
Figure 3. Observed sieving coefficients for filtration of the dextran with 15 OOO molecular weight through a 30K membrane before and after BSA adsorption aa a function of filtrate flux. Solid curves represent the values of Socalculated from eqs 1-5 using the best fit values of S, = 0.094 i 0.003 and e4Kd/hm= (3.5 & 0.2) X 109m-l for the clean membrane and S, = 0.053 i 0.003 and e4Kd/6, = (1.3 i0.3)X 109m-l for the preadsorbed membrane.
the lOOK membrane being larger than those for the 30K membrane. The observed sieving coefficients after BSA adsorption were significantly smaller than those for the clean membrane, with this effect being greater for the l00K membrane. The magnitude of the decrease in the observed sieving coefficient was a function of the dextran molecular weight,with the reduction being greatest at some intermediate molecular weight. The experimental data for the observed sieving coefficients for both the clean and preadsorbed 30K membranes shown in Figure 1 for the dextran with a molecular weight of 15 000 have been replotted as a function of the filtrate flux in Figure 3 along with data a t several fluxes which were not shown in Figure 1 for clarity. The observed sieving coefficient for the clean membrane decreases with increasing flux a t low J,, but then passes through a minimum before rising a t high flux. The minimum in the observed sieving coefficient reflects the combined effects of the large increase in concentration polarization a t high flux and the reduction in the actual sieving coefficient a t low flux, with this latter effect reflecting the decreased contribution of dextran diffusion relative to convection as
the flux increases (Mochizuki and Zydney, 1992). The solid curves represent the values of Socalculated from eqs 1-5 using the best fit values of the hydrodynamic coefficients, S, and e+Kd/bm, which were determined by minimizing the s u m of the squared residuals between the calculated and experimental values of Sousing the method of steepest descent. The fitted curves for So are in very good agreement with the experimental data, indicating that eq 1 accurately describes the bulk mass transfer phenomenon in the stirred cell, with the mass transfer coefficient given by eqs 2 and 3,and that eq 4 accurately describes the flux dependence of the actual sieving coefficient. The ratio of the calculated values for So for the clean membrane to those for the preadsorbed membrane, both determined using the best fit values of S, and e4Kd/bm, attains its maximum value of approximately 2.2 a t Jv = 1.2 X lo4 mls and then decreases as one moves to either higher or lower flux. At very low flux, dextran transport is governed primarily by diffusion; thus, the dextran concentrations on the two sides of the membrane become nearly equal and So and Sa approach unity for both the clean and preadsorbed membranes. Soalso approaches a value of 1 at very high flux due to the high degree of concentration polarization. The differencein the observed sieving coefficients for the clean and preadsorbed membranes is thus minimal in the limits of both very low and very high fluxes. This flux dependence for the observed sieving coefficients can easily result in the misinterpretation of experimental data for Soif these effects are not properly taken into account. The best fit values of So and €4Kd/Smfor filtration of dextrans with molecular weights of 9K,10K,15K,20K, 30K,and 40K through the clean and preadsorbed 30K membranes were determined as described above, with the results plotted in Figure 4 as a function of the dextran molecular weight. All of these data were obtained using the 38.9K weight-averaged molecular weight dextran solution that was examined in Figure 1. The solid and dashed curves are model fits which are discussed subsequently. Both S, and E4Kdbm decrease with increasing dextran molecular weight due to the increased hindrance to transport for the larger solutes. BSA adsorption caused a reduction in both S, and €4Kd/bm,with the reduction in the hindrance factor for diffusion being somewhat greater than that for the sieving coefficient. In addition, the percent reduction in both transport parameters is greater for the larger molecular weight dextrans: S, for the 10K dextran decreased from 0.16 to 0.11,while that for the 30K dextran decreased from 0.021to 0.001. The corresponding reductions in €$Kd/bmwere from 5100 to 4200 m-l for the 10K dextran and from 380 to 35 m-l for the 30K dextran. The experimental data for the observed sieving coefficients for the 50K,100K,and 300K poly(ether sulfone) membranes were all analyzed as described above, with the best fit values for S, and c$Kd/bm determined by minimizing the s u m of the squared residuals between the data and model calculations for each of a large number of different molecular weight dextrans. The results are plotted in Figures 5-7,with the solid and dashed curves representing model fits which are described in the next section. The values for S, and €4Kdbmfor the preadsorbed membranes were uniformly smaller than those for the clean membranes, with the decrease in t4Kd/bmbeing somewhat greater than that for S, for all three membranes, analogous to the behavior seen in Figure 4 for the 30K membrane. These effects are discussed in more detail subsequently. Comparison with Hydrodynamic Theories. The molecular weight dependence of S , and E$Kd/bm for the
557
Biotechnol. Rog., 1992, Vol. 8, No. 6 i._ nac
. . . .....,
.
. ......,
.
. .....-
a
m
10''
10"
10''
10'~
Dextran Molecular Weight
Dextran Molecular Weight
Figure 4. Best fit values for the asymptotic sieving coefficient
(top panel) and the hindered diffusion factor (bottom panel) as a function of the dextran molecular weight for the clean and preadsorbed 30K membrane. Data were obtained with the 38.9K weight-averaged molecular weight dextran. Solid and dashed curves represent the calculated values of S, and e#Kdldm determined using the best fit values of s and c/6, as given in Table I. Solid curves for e#Kd/d, were determined using Bungay and Brenner's analysis (eq lo), and the dashed curve was determined using Davidson and Deen's analysis (eq 13).
different membranes can be examined in more detail by comparison of these results with available hydrodynamic models. Opong and Zydney (1991) and Mochizuki and Zydney (1992) have shown that the effective solute to pore size ratio (A) for the asymmetric polytether sulfone) membranes employed in this study, which have a relatively broad pore size distribution, can be evaluated as Xe1-G
(7)
The solute equilibrium partition coefficient (4) was evaluated using the theoretical expression developed by Giddings et al. (1968) for partitioning of rigid solutes in an isotropic porous network formed by a random arrangement of parallel planes:
cb = exp(-Rsds) (8) where s is the ratio of the pore volume (V,)to the pore surface area (S,) and RSEis the Stokes-Einstein radius of the macromolecule
General expressions for S , = r#JK, and e4Kd/hm for complex solutes like the branched dextrans used in this study are unavailable. However, Bungay and Brenner (1973) have developed expressionsfor the hindrance factors
Figure 5. Best fit values for the asymptotic sieving coefficient (top panel) and the hindered diffusion factor (bottom panel) as
a function of the dextran molecular weight for the clean and preadsorbed 50K membrane. Data were obtained with the 38.9K weight-averaged molecular weight dextran. Solid and dashed curves represent the calculated values of S, and e4Kd6, as described in the text.
K, and& for hard-sphere solutes in cylindrical pores using matched asymptotic expansions for both small and closefitting spheres, yielding where the equilibrium partition
coefficient (4) for a spherical solute in a cylindrical pore is simply (from eq 7) r#J = (1 - XI2 (12) The hydrodynamicfunctions K, and Kt are both expressed as expansions in X [parameter values given in Bungay and Brenner (1973) and Mochizuki and Zydney (1992)l. In contrast, Davidson and Deen (1988) have developed an expression for Kd for linear random-coilingmacromolecules in cylindrical pores:
+
+
Kd 1- 2.848X 3.269X2 1.361X3 (13) which predicts a somewhat smaller dependence on solute size than that given by eq 10. The solid and dashed curves shown in Figures 4-7 represent the calculated values of S , and ecbKdIiimdetermined using these hydrodynamic models. The S , (=cbK,) values were determined with 4 evaluated from eq 8 and K, evaluated from eq 11. The effective solute to pore size
Biotechnol. Prog., 1992, Vol. 8, No. 0
558
-a z Q) 5
-
\\
0 c c
0 e
sa E
a E
2
P
\\ 1
4:
E
-i
lo5
Q E t('P
d
lo4
e
0
U
0
io3
I
8
g
lo2
f E
IO'
I loor lo3
. .
' * . ' . . I
io4
'
. ..""' 105
*\,\,Ll IOS
Dextran Molecular Welght
Figure 6. Best fit values for the asymptotic sieving coefficient (top panel) and the hindered diffusion factor (bottom panel) as a function of the dextran molecular weight for the clean and preadsorbed 100Kmembrane. Data were obtained with the 67.9K weight-averaged molecular weight dextran. Solid and dashed curves represent the calculated values of S., and e4KJbm as described in the text. ratio (A) was evaluated using the best fit value of s for each membrane, which was determined by minimizing the s u m of the squared residuals between the experimental and calculated values of S, for all of the different molecular weight dextrans. The model calculations for S, are in excellent agreement with the experimental data for both the clean and preadsorbed membranes over the entire range of dextran molecular weights. This good agreement between model and data, using only a single value of s for each of the clean and preadsorbed membranes, indicates that eqs 7 and 8 provide a reasonable description of the effective solute to pore size ratio for these asymmetric poly(ether sulfone) membranes. The best fit values for s for the different membranes are summarized in Table I, with the error bars representing the standard deviations in the fitted values as determined from the minimization of the s u m of the squared residuals. The standard deviations in s were all quite small (less than 7% of the best fit value) due to the high degree of sensitivity of the model predictions to the actual value of s. The s values increase significantly with increasing membrane molecular weight cutoff, ranging from s = 9.9 A for the clean 30K membrane to s = 65.4 A for the clean 300K membrane, with these results being in good agreement with those reported previously by Mochizuki and Zydney (1992) for these OMEGA membranes. The best fit values for s for the preadsorbed membranes are all statistically less than those for the .clean membranes, reflecting the reduction in the asymptotic sieving coef-
loo
io4
10'
lo6
IO'
Dextran Molecular Weight
Figure 7. Best fit values for the asymptotic sieving coefficient (top panel) and the hindered diffusion factor (bottom panel) as a function of the dextran molecular weight for the clean and preadsorbed300Kmembrane. Data were obtainedwiththe 53913 weight-averaged molecular weight dextran. Solid and dashed curves represent the calculated values of S., and cc#X,j/bm as described in the text. ficient associated with BSA adsorption; this effect is discussed in more detail subsequently. The calculated values of t4KdBmwere determined using both Bungay and Brenner's model for hard-sphere solutes (eq 10; solid curves) and Davidson and Deen's model for linear flexible macromolecules (eq 13;dashed curves).The calculations were performed using the best fit values for s determined from the sieving data with the best fit values of €16, determined by comparison of the model calculations and data for t4Kd8m using the method of steepest descent. The results for the different molecular weight cutoff membranes are summarized in Table I. The standard deviations in c/6, were larger than those for s (on the order of 50% of the best fit value), which reflects the somewhat larger deviation between the calculated and experimental values of t/6, seen in Figures 4-7. The calculated values of t6Kdbmusing Bungay and Brenner's analysis were in good agreement with the experimental data for the 30K and 50K membranes, but they show a much greater dependence on the dextran molecular weight than was observed experimentally for either the l00K or 300K membranes. In contrast, the calculated values of c4Kd/6m determined using Davidson and Deen's model were in relatively good agreement with the data for the l00K and 300K membranes, but tended to underestimate the with dextran molecular weight for variation of c@d/6, both the 30K and 50K membranes. This very different behavior for the small (30K,50K)and large (loOK, 300K) molecular weight cutoff membranes is probably associated with the different molecular weight dextrans used to
sse
Biotechnol. Prog., 1992, Vol. 8, No. 6
Table I. Experimental Results for the Hydraulic Permeability, Ratio of Pore Volume to Pore Surface Area, and Ratio of Skin Porosity to Skin Thickness for Clean and Preadsorbed Membranes Dreadsorbed
clean membrane
L,, A
30K
0.011
8,
A
9.9 f 0.4
50K
0.016
14.2 f 1.0
100K
0.028
23.3 f 1.1
300K
0.046
65.4 f 2.8
clb,, m-14 (2.2 h 0.5) X 108 (2.1 f 0.9) x 105 (2.9 h 0.4) X 108 (3.9 f 1.9) x 106 (7.4 f 1.2) x 106 (3.9 f 0.1) x 106 (4.6 f 1.1)X 108 (1.8 f 0.3) X 108
0.008
8.5 & 0.3
0.012
12.2 & 0.6
0.018
17.1 & 0.2
0.032
56.8 h 2.3
(2.1 h 0.1) x (2.0 f 1.4) X (2.4 f 0.6) X (2.9 f 0.8) X (3.3 h 0.8) X (3.3 h 0.1) x (5.8 h 1.5) X (1.7 h 0.4) X
10s 105
106 105 108 105
108 108
a Numbers in the first row in d6, for each membrane were determined using eq 10, while those in the second row were determined using eq 13.
Table 11. Effect of Protein Adsorption on the Hydraulic Permeability. Ratio of Pore Volume to Pore Surface Area, and Skin Porosity 30K 50K 100K 300K
0.74 0.74 0.64 0.69
0.86 f 0.04 0.86 f 0.07 0.74 f 0.03 0.87 f 0.06
0.95 f 0.22 0.83 f 0.23 0.84 h 0.03 0.94 f 0.26
Results for the 30K and 50K membranes were evaluated using eq 10. Results for the lOOK and 300K membranes were evaluated using eq 13.
evaluate the transport characteristics of these membranes (9-40K for the 30K membrane; 10-BOK for the 50K membrane; 15-200K for the lOOK membrane; and BOK1Mfor the 300K membrane). The larger molecular weight dextrans used in the experiments with the larger molecular weight cutoff membranes appear to be better modeled as flexible linear molecules (i.e., using the model developed by Davidson and Deen), with the smaller molecular weight dextrans better described as “rigid” spheres using the model developed by Bungay and Brenner. Protein Adsorption Effects. The effects of protein adsorption on the membrane hydraulic permeability, the membrane porosity, and the specific area of the skin layer (the ratio of the pore volume to the pore surface area) are summarized in Table 11. In each case, the data are shown as the ratio of the parameter value after adsorption to that obtained prior to BSA adsorption. The ratios of the membrane porosity before and after adsorption were determined directly from the best fit values of t/Sm for the clean and preadsorbed membranes, assuming that the membrane thickness (6,) was unaffected by BSA adsorption. The e/6, values for the 30K and 50K membranes were determined using Bungay and Brenner’s analysis, while those for the lOOK and 300K membranes were determined using Davidson and Deen’s analysis as discussed in the previous section. The error bars for s&/ Sclem and tadsltclean were determined by propagation of error analysis using the standard deviations in the fitted parameters. The errors in Eads/Eclean were d l quite large due to the large standard deviations in t/6m as seen in Table I. The standard errors for Lp (as determined from the standard deviation in the slope of the saline flux versus applied pressure data) were all negligibly small; the corresponding errors in Lp,ads/Lp,&an were less than 2 % and are not shown for clarity. The results in Table I1 clearly indicate that the membrane permeability,porosity, and specificsurface area all decrease after BSA adsorption. The percent reduction in the membrane permeability was larger than that for either the porosity or the specific surface area for all four membranes, while the percent reduction in the porosity tended to be the smallest (the reduction in t was actually somewhat larger than that for s for the 50K membrane, although this effect was not statistically significant due to
the very large standard deviations in the best fit values for t/6m). There was no obvious trend in any of the parameters with increasing membrane molecular weight cutoff, despite the much greater pore size of the larger molecular weight cutoff membranes. In order to obtain greater insight into the effects of BSA adsorption on the pore structure of these asymmetric membranes, it is instructive to examine the possible effects of protein adsorption on the membrane permeability, porosity, and specific area for a membrane composed of uniform cylindrical pores of radius R. In this case, the membrane properties are given simply as
L, = NrR4 86,
=N ~ R ~
(15)
where N is the pore number density (pores per m2 of membrane). According to eqs 14-16, pore blockage (i.e., a reduction of h9 would cause an identical percentage decrease in both the permeability and porosity, but would have no effect at all on the specific area (SI. This indicates that pore blockage would have no effect on the membrane sieving coefficients (S4.This somewhat unusual result arises from the identical reduction in both solute and solvent transport through the membrane arising from blockage of some fraction of the pores. The experimentaldata in Table I1 are clearly inconsistent with this type of pore-blockage model; all of the membranes displayed a significant reduction in s due to BSA adsorption, while the reduction in the permeability was consistently larger than that for the porosity. In contrast to pore blockage, pore constriction would reduce the effectivepore radius, leading to a corresponding reduction in the permeability,porosity, and specificsurface area. However, the extent of reduction in these three parameters would be very different, with the ratio of the specific surface area after adsorption to that before adsorption simply equal to Rads/Rclean while the porosity and permeability ratios would vary as (Rad$Rc1m)2 and (Rad$Rc1ead4, respectively. Although our experimental data indicate that L,, e, and s all decrease after BSA adsorption, the percentage reduction ins is proportionally greater than that predicted by this type of pore-constriction model: the values of Sads/Sclean are all smaller than the corresponding values of both (Lp,ads/Lp,clem)’l4 and ( € a d€clean)1’2.
This greater effect of protein adsorption on the specific pore area (as determined from the experimental data for
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the asymptotic sieving coefficients) compared to that on the membrane permeability or porosity is most probably a reflection of the effects of the membrane pore size distribution on the transport characteristics of these asymmetric poly(ether sulfone) membranes. The asymptotic sieving coefficient varies very strongly with the membrane pore size, particularly for solutes that are comparable in size to the membrane pores (like the dextrans employed in this study). Thus the asymptotic sieving coefficient in a membrane with a broad pore size distribution will be heavily weighted by the largest pores since they allow the most unhindered transport of these large solutes. If protein adsorption occurs preferentially in these largest pores, the percent reduction in s will tend to be greater than that determined using data for either the permeability (which varies as R4) or the porosity (which varies as R2). This is in fact exactly what is observed in our experiments, with the ratio of Sad$Sclean being smaller than either (tads/€clem)1/2 or (Lp,&/Lp,clem)l/* for d l four molecular weight cutoff membranes. This preferential adsorption in the largest pores would also tend to cause agreater reduction in the permeability than in the porosity, a prediction which is also consistent with our experimental results [the value of (Lp,ad~/Lp,clem)~/~ for the 50K membrane is actually slightly larger than the corresponding value of (€&/€&an)’/*, although the magnitude of the difference was not statistically significant due to the large standard errors in the porosities].
Discussion The experimental data obtained in this study clearly indicate that BSA adsorption significantly alters the transport characteristics of the OMEGA poly(ether sulfone) membranes, with the observed and actual sieving coefficients after BSA adsorption being significantly smaller than those obtained with the clean membranes. This was true even for the 30K membrane which is essentially impermeable to the large BSA molecules (MW = 69 000) examined in this study (independent measurements indicate that BSA retention by the 30K membranes was greater than 99.9 % 1. Note that similar effects have been reported previously by Sheldon et al. (1991) with thin-section transmission electron microscopy used to demonstrate that BSA adsorption occurs throughout the porous structure of “fully retentive” 10K polysulfone and regenerated cellulose membranes. The magnitude of the reduction in the observed sievingcoefficientwas dependent not only on the membrane pore size but also on the dextran molecular weight and the filtrate flux due to the combined effects of dextran diffusion, dextran sieving, and concentration polarization on the observed sieving. Although the detailed transport characteristics of these poly(ether sulfone) membranes are quite complex due to the size distribution and irregular shape of the pores in the skin of these asymmetric membranes, our analysis indicates that the overall transport properties of these membranes can be relatively well described using available hydrodynamic models, with the effective solute to pore size ratio evaluated using a partitioning model which explicitly accounts for the presence of a random pore size distribution (Opong and Zydney, 1991; Mochizuki and Zydney, 1992). Our experimental data for the asymptotic sieving coefficients(S,) were in good agreement with model calculations for both the clean and preadsorbed membranes over a wide range of different molecular weight dextrans using only a single value for the specific membrane area (s) for each membrane. This good agreement with the model indicates that the transport characteristics of different molecular weight dextrans can be effectively
a, NO.
6
predicted from experimental data obtained with only a limited number of dextrans. The membrane transport model examined in this study can also be used, at least in principle, to predict the transport characteristics of other macrosolutes through these asymmetric membranes using information only on the solute size and geometry. In particular, the best fit values for s obtained in this study for the preadsorbed membranes can be used to calculate the hindrance factors for BSA transport through these poly(ether sulfone) membranes. For the ellipsoidal BSA molecules, the effective solute size in eq 8 should be evaluated as the mean projected solute radius (R*) on the basis of the analysis of solute partitioning developed by Giddings et al. (1968). This gives R* = 40.3 A for BSA (Opong and Zydney, 1991),which is only slightlylarger than the StokesEinstein radius of 36 A. The predicted values for the asymptotic sieving coefficientsfor the 50K, 100K,and 300K membranes are thus 0.045, 0.13 and 0.70. These values are slightly larger than the experimental values of the BSA sieving coefficients (Robertson and Zydney, 1988; Opong and Zydney, 1991): S , = 0.001-0.01 for the 50Kmembrane, S , = 0.021-0.12 for the lOOK membrane, and S , = 0.48 for the 300K membrane. This discrepancy is probably due to the differences in geometry and flexibility between the dextrans and BSA, with the calculated value of s determined from the dextran sievingdata underestimating the steric hindrance to BSA transport. A similar reduction in BSA transport could also arise from electrostatic repulsion between the BSA in solution and the adsorbed BSA in the pores. The transport model can also be used to predict the hindrance factors for BSA diffusion using the best fit values of 46, in combination with the best fit values for s. In this case, the model gives C4KdBm = (1.01.2) X lo3 m-l for the 50K membrane (where the range reflects the cia, values determined using Bungay and Brenner’s and Davidson and Deen’s analyses) compared to about 0.1 X lo3m-l as determined experimentally, c$Kd ,6 = (0.4-1.4) X lo4 m-l compared to (0.8-1.4) X lo4 m-l for the lOOK membrane, and €r#JKd/6, = (0.3-1.2) X lo6 m-l compared to 0.1 X lo6 m-l for the 300K membrane (experimental values from Opong and Zydney, 1991).The model provides a reasonable estimate for cr#J&i6m for BSA in the larger pore membranes, but significantly overestimates €&d/bm for the 50K similar to the results seen with S,. The application of this transport model to the analysis of the dextran sieving data allowed us to quantify the alteration in the membrane transport characteristics associated with BSA adsorption in terms of the changes in two key membrane properties: the ratio of the membrane pore volume to pore surface area (s) and the ratio of the membrane porosity to membrane thickness (€/a,). These results, in combination with the experimental data for the membrane hydraulic permeability, indicate that BSA adsorption occurs throughout the porous structure of these asymmetric membranes, with preferential adsorption of BSA in the largest pores in the pore size distribution. Although there is no independent data specificallyshowing the preferential adsorption of BSA in such large pores, Robertson and Zydney (1990b) showed that the uptake of radiolabeled BSA by these asymmetric poly(ether sulfone) membranes increased monotonically with an increase in the membrane molecular weight cutoff, with values of 0.11, 0.12, 0.21, and 0.31 wg for the 30K, 50K, 100K, and 300K membranes, respectively (these uptake data were all obtained using a total BSA concentration of 5 g/L with 100pg of labeled BSA/liter of solution). The small BSA uptake in the smaller molecular weight cutoff membranes was attributed to steric interactions in
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Prog., 1992, Vol. 8, No. 6
these small membrane pores, with the increase in uptake with increasing membrane pore size due to the greater accessibility of the pore surface (at least on average) in the larger molecular weight cutoff membranes. These data are completely consistentwith the preferential adsorption of BSA in the larger membrane pores, which was implied by t h e dextran transport d a t a obtained in this study. This type of preferential adsorption can lead t o very different effects of protein adsorption on the membrane hydraulic permeability, the membrane sieving coefficients, and the hindered (or effective) solute diffusion coefficients, as was seen in this study for dextran transport through t h e poly(ether sulfone) membranes. This phenomenon has not been appreciated in most previous studies of protein adsorption on asymmetric ultrafiltration membranes, althoughit can be a critical factorin determining the overall performance and effectiveness of many membrane devices employing partially permeable membranes.
Notation stirred cell radius, m bulk dextran concentration, g/L filtrate dextran concentration, g/L dextran concentration at membrane surface, g/L free solution diffusion coefficient, m2/s volumetric filtrate flux, m/s bulk mass transfer coefficient, m/s Boltzmann constant, J/K hindrance factor for convection hindrance factor for diffusion hydrodynamic functions in Bungay and Brenner’s analysis membrane hydraulic permeability, 8, pore number density, pores per cm2 of membrane membrane Peclet number pore radius, A Reynolds number (obVv) Stokes radius, A ratio of pore volume to surface area (Vp/Sp),A actual sieving coefficient (Cf/C,) Schmidt number (v/D,) observed sieving coefficient (Cf/Cb) pore surface area, A2 asymptotic sieving coefficient solution temperature, K pore volume, A3 Greek Letters thickness of membrane skin, m am c membrane porosity 4 partition coefficient h ratio of solute radius to pore radius (R$Rp) P solvent viscosity, g/m/s Y kinematic viscosity, m2/s 9 coefficient in mass transfer correlation 0 stirring speed, rpm
Acknowledgment T h e authors thank the Filtron Technology Corporation for their generous donation of t h e OMEGA membranes used in this study. This work was supported in part by
Grant CTS-8812943 from the National ScienceFoundation and by Grant R01 HL 39455-02 from the National Institutes of Health.
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