2104
I n d . Eng. Chem. Res. 1996,34, 2104-2109
The Concentration Polarization Effect of a Macroligand on Affinity Ultrafiltration Cheng-Kang Lee Department of Chemical Engineering, National Taiwan Institute of Technology, Taipei 10672, Taiwan
The concentration polarization effect of a macroligand on the affinity ultrafiltration of an important glycopeptide antibiotic, vancomycin, was studied. The affinity ultrafiltration was carried out in a stirred cell, and the system was operated in a circulating and once-through mode. The macroligand was prepared by coupling the ligand D-alanyl-D-alanine to a water soluble polymer, dextran. The concentration polarization of dextran itself did not show any effect on vancomycin retention in the ultrafiltration cell. On the other hand, the retention of vancomycin was enhanced in the presence of concentration polarization of the macroligand on the membrane surface. The enhancement was due to the affinity binding of vancomycin to the macroligand in the concentratioo polarization layer. The observed affinity binding behaviors of vancomycin in the affinity ultrafiltration systems were in good agreement with that predicted by the thin film model coupled with the Langmuir isotherm and fast binding kinetics. 1. Introduction
Affinity membrane filtration was first introduced by Adamski-Medda and co-workers (Adamski-Meddaet al., 1981) for the purification of biological products. Since then, many investigators (Mattiasson et al., 1984,1986; Luong et al., 1988; Ling et al., 1989; Herak et al., 1989; Male et al., 1990a,b; Powers et al., 1990; Weiner et al., 1994) have demonstrated that affinity cross-flow membrane filtration bears a great potential for application in large scale and continuous protein purifications. This process combines the high selectivity of affinity chromatography with the high-volume processing capacity of membrane filtration. The main feature of affinity membrane filtration is that it employs a macroligand to specifically adsorb the desired biological product so that it can be retained by the ultrafiltration or microfiltration membrane. After all contaminations present in solution are removed during a washing step, conditions such as pH or ionic strength are changed to release the desired product from the macroligand. The so-called macroligand consists of ligands covalently attached to a water soluble high molecular weight polymer or t o a small size particle. Unlike the solid macroligand particle, the water soluble macroligand has the general advantage that homogeneous binding can be achieved, steric hindrance and mass transfer resistance can be reduced, and attrition or degradation of the carrier during the harsh cross-flow conditions can be prevented. Several water soluble polymers (Adamski-Meddaet al., 1981; Choe et al., 1986; Luong et al., 1988; Male et al., 1990a) have been used as a ligand carrier to purify various proteins in affinity ultrafiltration. However, the inevitable problems of concentration polarization of the macroligand on the separation performance have never been mentioned. Concentration polarization not only decreases the filtration flux but also changes the selectivity of the membrane. In other words, the concentration polarization layer of macroligand on the membrane surface may retard the transport of the desired product through the membrane. Besides, the depletion of the macroligand in the bulk solution and the localization of a high concentration of macroligand in the polarization layer may affect the binding capacity of the affinity ultrafiltration system. In the present work, the effect of the concentration polarization of a water soluble macroligand on the 0888-5885/95/2634-2104$09.00/0
binding of a biomolecule in an affinity ultrafiltration system was studied. A small size biomolecule, vancomycin (mol wt ca 1500) and its macroligand D-alanylD-alanine-dextran (mol wt ca 500 000) were used as our model system. A stirred cell attached to an ultrafiltration membrane of 20000 MWCO (molecular weight cutoff)was employed to carry out the affinity ultrafiltration. The affinity ultrafiltration was operated in a circulating and once-through mode. On the basis of the thin film model for macroligand concentration polarization and the Langmuir isotherm for vancomycin affinity binding, a theoretical analysis of the affinity binding in the stirred UF cell was carried out. 2. Experimental Section
Materials. The biomolecule vancomycin (Sigma Chem. Co.) is an important glycopeptide antibiotic which binds very tightly to peptides that contain D-alanyl-D-alanine a t the free carboxyl end (Perkins, 1969). Dextran with a molecular weight ( M W ) of 500 000 Da (Fluka Chem. Co., Switzerland) was used as the soluble carrier for the ligand D-alanyl-D-alanine. The macroligand was prepared by coupling D-alanyl-D-alanine t o the l-1’-carbonyldiimidazoleactivated dextran (Lee et al., 1994). A centrifugal ultrafiltration device, Centricon 30, with a membrane of MWCO 30 000 (Amicon Corp, MA) was used to study the affinity binding isothem of the macroligand. A homemade stirred cell (inside volume 15 mL) attached to a 25 mm cellulose membrane of MWCO 20 000 (Spectrum, CA) was used to carry out the affinity ultrafiltration. The solution inside the cell was stirred by a magnetic bar which was located about 3 mm above the membrane surface. In order to keep a constant permeate flux, a HPLC pump (Gilson, France) was employed to pump the solutions into the stirred UF cell. Experimental Procedure. For the determination of the affinity binding isotherm, a macroligand solution of 0.1 mL and 1.9 mL phosphate buffer (0.05 M, pH 7.0) containing various amounts of vancomycin were added into the centrifugal ultrafiltration device, Centricon 30. The Centricon was then incubated in the rotor for 1h and centrifuged at 4000 rpm for 15 min at a constant temperature using a Beckman centrifuge R2-21. The vancomycin concentration in the permeate was consid-
0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 6 , 1995 2105
r
! & I
c2
I
1
L+
(a) Circulating mode
cp
:&,
I .
I 1
I
..' (b) Once-through mode
Figure 1. Schematic diagrams of stirred cell affinity ultrafiltration systems. (1)vancomycin, (21, macroligand, (3) ultrafiltration membrane, (4) vancomycin solution, (5) HPLC pump, and ( 6 ) magnetic stirrer.
ered as the equilibrium concentration. The difference between the initial and equilibrium concentrations of vancomycin was used t o calculate the amount of vancomycin bound to the macroligand. The stirred cell ultrafiltration system, operated in a circulating and once-through mode as shown in Figure l a and b, was used to study the concentration polarization effect of the macroligand on the affinity binding of vancomycin. The affinity binding was carried out in 0.05 M, pH 7.0 phosphate buffer. The stirred cell was first filled with a macroligand solution prepared in phosphate buffer with a concentration of 4.5 mg/mL. The cell was immersed in a 25 "C water bath and stirred at 300 rpm. In order to have the concentration polarization of the macroligand reach steady state, phosphate buffer was pumped into the stirred cell a t flow rate of 0.25 mL/ min for 4 h. Two modes of affinity binding operations were employed respectively after the macroligand concentration polarization had been established. For the circulating mode of operation, 10 mL of vancomycin solution with various starting concentrations was circulated between the UF cell and the stirred circulation cell. The vancomycin concentration in the circulation cell was determined with respect to time. The oncethrough operation was carried out by pumping a vancomycin solution of various starting concentrations into the stirred UF cell. The vancomycin concentration in the permeate was measured with respect t o time. The vancomycin concentration was determined by U V adsorbance at 280 nm using a Shimadzu spectrophotometer (model W-16OA). 3. Theoretical Analysis
When the macroligand (MW ca 500 000) solution flows through the ultrafiltration membrane (MWCO 20 000), macroligands are totally rejected by the membrane. The rejected macroligands will accumulate in a film region immediately next to the membrane. This is the cause
(2EO)
Figure 2. Schematic diagram of the concentration distribution of the macroligand and vancomycin in the stirred UF cell. C1, Cz, and c, are vancomycin concentrations. Cmband ,c , are macroligand concentrations.
of the concentration polarization. In the stirred UF cell, the macroligands are distributed in the well-mixed bulk phase and the concentration polarization layer as shown in Figure 2. Hong et al. (1981) have calculated the concentration distribution of enzyme in an ultrafiltration enzymatic membrane reactor by applying the thin film theory above the membrane and solving the steadystate mass balance equation of the enzyme. On the basis of the same derivation, the distribution of macroligand concentration in the polarization layer can be obtained as
C,
= C,
exp(J,(G - z)/D)
where C, and c m b are the macroligand concentrations in the polarization layer and the bulk solution, respectively, J, is the filtration flux, 6 is the thickness of the polarization layer, z is the distance from the membrane surface, and D is the diffusivity of the macroligand. The ratio of the macroligand concentration in the bulk solution to that initially loaded is
CmdCm0= 1 4 0 - a) + (a/p)(exp(p) - 1))
(2)
where a=GU
p = J,SID C,O is the initially loaded macroligand concentration in the cell with no concentration polarization formation, and V is the volume of the bulk solution. After the steady-state macroligand concentration polarization is established, the vancomycin solution is then fed into the stirred UF cell. Since the size of vancomycin is much smaller than the membrane pore size, vancomycin is assumed to flow through the membrane without any hindrance. For the circulating mode of operation, the material balance of vancomycin in the well-mixed bulk phase, polarization layer, and stirred circulation cell of the ultrafiltration system are a. well-mixed bulk phase F C 2 - F C l = V -dC, +VC dt
'
'
dq, mb
dt
(3)
b. polarization layer (4)
2106 Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995
c. stirred circulation cell 4 *c
where the initial and boundary conditions are
C,(O) = 0; C,(O) = c,; Cp(0q)= 0; Cp(t,6)= c,
10% 20% 30%
bo \
30% ,Dextran
The affinity binding between the macroligand and vancomycin is assumed to follow the Langmuir isotherm
where the maximum binding capacity of the macroligand, qm,and the dissociation constant, Kd, between the macroligand and vancomycin can be obtained from equilibrium binding experiments. Since the macroligand is water soluble, the binding of vancomycin to the macroligand is assumed to be very fast and have no mass transfer limitation. Equation 6, therefore, is directly substituted into eqs 3 and 4. In these material balance equations, the macroligand concentration in the polarization layer, Cmp, is only a function of distance. The vancomycin concentration in the polarization layer, C,, is a function of time and distance. By using the finite difference method, eq 4 can be transformed into ordinary differential equations (ODES) with respect to time. The polarization layer thickness, 6, is divided into 10 segments, and 10 ODES can be obtained from eq 4. The 12 simultaneous ODES for the material balance of vancomycin in combination with the macroligand material balance equations (eqs 1and 2) can be solved using the DIVPAG subroutine in the IMSL software package. By deleting the material balance equation of vancomycin in the stirred circulation cell, assuming the vancomycin concentration in the feed stream, CZ,is a constant, and using the same solving technique, the vancomycin concentration in the permeate during the once-through mode of operation can be determined. For the system without a macroligand or an ideal system which has uniformly distributed macroligand in the stirred UF cell, the vancomycin concentration in the circulation cell and the permeate during the affinity ultrafiltration operations can be determined in a straightforward manner by solving the simple material balance equations of vancomycin.
Figure 3. Equilibrium binding isotherms of vancomycin to the macroligand and dextran. Macroligand (10 mg) was used in a 2 mL centrifugal UF device for determination of isotherms.
Figure 4. Scatchard plot of the equilibrium binding isotherms of vancomycin to the macroligand. Table 1. Affinity Binding Prouerties of the Macroligand
4. Results and Discussion
Equilibrium Isotherm of Vancomycin. The equilibrium binding of vancomycin to the macroligand was studied in a centrifugal UF device. Figure 3 shows the equilibrium binding isotherms of vancomycin to the macroligand and dextran. The vancomycin does not bind with dextran. The amount of vancomycin bound to the macroligand increases with the free vancomycin concentration and temperature. The binding isotherms of Figure 3 were analyzed according t o the Scatchard equation (Scatchard, 1949)
As shown in Figure 4, a straight line was obtained by ploting q versus qIC. The straight line indicates that the affinity binding behavior between vancomycin and the macroligand can be described by the Langmuir
4 10 20
30
5.42 3.39 1.11 0.41
182 180 183 187
isotherm (eq 6). The maximum binding capacity qmand equilibrium binding constant Kd were obtained from the intercept and slope of such a plot, respectively. The affinity binding properties of the macroligand are listed in Table 1. The maximum binding capacity is nearly a constant with respect t o temperature. On the other hand, the temperature has a strong effect on the vancomycin binding to the macroligand. The dissociation binding constant decreases with temperature. Thus, the vancomycin binding t o the macroligand is an endothermic process. However, the affinity binding study between vancomycin and a short chain ligand, diacetyl- L-lysine-D-alanyl-D-alanine in free solution (Nieto and Perkins, 1971) shows that the binding is an
n
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Observed
n
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o macroligand Calculated without macroligand ---_--absence of macroligand polarization presence of macroligand polarization
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- Calculated ---- without macroligand
---__-absence of macroligand polarization
E
presence of macroligand polarization
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*3 0.00~""""""""""""""""'~ 100 200
300
Time (min) Figure 6. Vancomycin concentration in the stirred circulation cell during the affinity ultrafiltration operated under a circulating mode. Three experimental runs with a macroligand concentration of 4.5 mg/mL and starting vancomycin concentrations of 0.032, 0.07, and 0.124 mg/mL, respectively, were carried out. The dotted and solid lines are calculated results; the closed and open circles represent the observed experimental results from the dextran and macroligand systems, respectively.
exothermic process. A possible explanation for the endothermic binding behavior of vancomycin t o the macroligand is the reduction of steric hindrance as the temperature is raised. Since the coiled macroligand molecule becomes more flexible and has a relatively open structure as temperature increases, vancomycin has easier of access to the ligand D-alanyl-D-alanine. Concentration Polarization Effect of the Macroligand. Dextran, the ligand carrier, has been employed in the centrifugal UF device to explore the nonspecific binding with vancomycin. The same vancomycin concentration in the retentate and permeate was observed (data not shown). This indicates that the dextran itself does not bind with vancomycin. Neither does the concentration polarization of dextran ( M W 500 000) retard the transport of vancomycin ( M w 1500) through the membrane. Figure 5 shows the concentration polarization effect of the macroligand on the retention of vancomycin in a stirred UF cell operated under the circulating mode. Three experimental runs were carried out with different starting vancomycin concentrations in the stirred circulation cell. The vancomycin concentration in the circulation cell decreases with time and levels off to a steady-state value, because vancomycin is not only diluted by the permeate from UF cell but also retained by the macroligand in the UF cell. As shown in Figure 5 , the observed vancomycin concentration in the macroligand system is much lower than the calculated vancomycin concentration in the system with no macroligand in the UF cell. The steady-state concentration difference between these two systems represents the amount of vancomycin retained in the UF cell by the macroligand. The larger the difference, the more vancomycin molecules are retained. The observed vanco,mycin concentrations in the dextran system with a starting concentration of 0.124 mg/mL are same as the calculated vancomycin concentration in the system with no macroligand. This again shows that the concentration polarization of dextran (the carrier of the macro-
0.00
Time (min) Figure 6. Vancomycin breakthrough curves of the affinity ultrafiltration operated under a once-through mode. The experimental conditions and symbols are the same as in Figure 5.
ligand) will not retain vancomycin in the cell. The retention of vancomycin in the UF cell is completely due to affinity binding to the macroligand. Figure 5 also shows a slight concentration difference between the system without macroligand and the ideal system in which the macroligand is uniformly distributed and the polarization of the macroligand does not exist. The slight concentration difference indicates that only a small amount of vancomycin is retained in the ideal system by affinity binding t o the macroligand. The low retention of vancomycin is expected, since part of the vancomycin molecules that are fed at the inlet will directly leave the UF cell in the ideal system. On the other hand, in the presence of concentration polarization, the vancomycin that leaves the well-mixed bulk phase will be caught by the macroligand in the polarization layer. The concentration polarization layer of macroligand in the UF cell is exactly the same as a fixed bed. As we know, for an adsorption process governed by the Langmuir isotherm, the efficient use of adsorbents is achieved by a fured bed operation instead of well-stirred batch operation. This is why affinity binding of vancomycin to the macroligand is enhanced significantly in the presence of concentration polarization of the macroligand. As also shown in Figure 5, the affinity binding enhancement by the concentration polarization of the macroligand increases with the starting vancomycin concentration. This can be expected, since the affinity binding between the macroligand and vancomycin follows the Langmuir isotherm which shows that the amount of adsorbate adsorbed by the adsorbent increases with free absorbate concentration. Figure 6 shows the affinity binding of vancomycin in the stirred UF cell operated in the once-through mode. The plot of the vancomycin concentration in the permeate versus time can be considered as a breakthrough curve. The area between the blank and affinity binding breakthrough curves represents the amount of vancomycin bound to the macroligand. The blank breakthrough curve is obtained in the system without any macroligand. As can be seen in Figure 6, only a very small amount of the vancomycin is retained if the macroligand is uniformly distributed in the UF cell with
2108 Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995
no polarization formation. A much higher amount of vancomycin, however, is retained in the UF cell with macroligand polarization on the membrane surface. This shows that the presence of concentration polarization of macroligand significantly enhances the affinity binding capacity of the UF system. In other words, efficient use of the macroligand binding capacity can be achieved by inducing concentration polarization in a well-stirred membrane cell. The affinity retention behaviors of vancomycin in the UF cell were calculated by solving the governing material balance equations. The affinity binding constants a t 25 "C were obtained by interpolating the constants listed in Table 1. The diffusivity of the protein myosin (MW 524 800) 1.1x cm2/s (Lehninger, 1975) was employed as the diffusivity of the macroligand, because the macroligand has about the same molecular weight as this protein. However, the diffusivity is a function of the size and shape of the molecule. The adopted macroligand diffusivity should be quite different from its intrinsic value, since the shapes of these two molecules are very different. Fortunately, there are no significant variations in the calculated results when the employed diffusivities are of the same order of magnitude. The observed affinity retention of vancomycin in the run with a starting concentration of 0.07 mg/mL was first curve-fitted by adjusting the polarization layer thickness to 2 x cm. As shown in Figure 5, the data are well fitted by the calculated curve. Using the same diffusivity and polarization thickness, the observed affinity retention data in the experimental runs with starting concentrations of 0.124 and 0.032 mg/mL are also well fitted by the calculated curves. Furthermore, as shown in Figure 6 the observed breakthrough curves in the once-through mode of operation can also be predicted with good accuracy by solving the governing equations using the same diffusivity and polarization thickness parameters.
Nomenclature A = effective area of membrane C = vancomycin concentration CO= initial vancomyin concentration C1 = concentration of vancomycin in the well-mixed bulk solution Cz = concentration of vancomycin in the stirred circulation cell C, = concentration of vancomycin in the polarization layer C m b = concentration of macroligand in the bulk solution Cm0= initially loaded macroligand concentration C, = concentration of macroligand in the polarization layer D = diffusivity of macroligand F = filtration flow rate or pumping flow rate J, = filtration flux & = dissociation constant between vancomycin and macroligand V1,Vz = volume of UF cell and circulation cell, respectively q = amount of vancomycin adsorbed per unit mass of macroligand q1 = amount of vancomycin adsorbed per unit mass of macroligand in the bulk solution q p = amount of vancomycin adsorbed per unit mass of macroligand in the polarization layer qm = maximum amount of vancomycin adsorbed per unit mass of macroligand z = distance above membrane surface Greek Symbols a = dimensionless film thickness (6A/V1)
p = dimensionless convection velocity (Jv/(D/6) 6 = concentration polarization thickness
Literature Cited 5. Conclusion The affinity binding between the macroligand D-alanyl-D-alanine-dextran and vancomycin follows a Langmuir type isotherm. The affinity binding increases with temperature. The endothermic binding process is probably due t o the fact that the structure of the coiled macroligand molecule becomes relatively open as temperature increases such that it allows more vancomycin to be bound with the ligand. In comparison with the ideal system in which the macroligands is uniformly distributed, the inevitable problem of macroligand concentration polarization enhances the retention of vancomycin in the affinity ultrafiltration operation. The concentration polarization of dextran (the carrier of the macroligand), on the other hand, does not increase the retention of vancomycin in the UF cell. The vancomycin retention enhancement is due t o the affinity binding to the macroligand in the polarization layer. The enhancement increases with the starting vancomycin concentration. The thin film model coupled with the Langmuir binding isotherm and fast binding kinetics can well describe the observed affinity binding behaviors of vancomycin in a stirred UF cell filled with D-alanyl-Dalanine-dextran. It can be concluded that the existence of concentration polarization of the macroligand can make the macroligand more efficiently for use in binding adsorbates in the affinity UF system.
Adamski-Medda, D.; Nyugen, Q . T.; Dellacherie, E. Biospecific Ultrafiltration: a Promise Purification Technique for Proteins. J . Membr. Sci. 1981, 9, 337. Choe, T. B.; Masse, P.; Verdier, A. Separation of Trypsin from Trypsin a-chymotrypsin Mixture by Affinity Ultrafiltration. Biotechnol. Lett. 1986, 8, 163. Heark, D. C.; Merill, E. W. Minity Cross-Flow Filtration: Experiments and Modeling Work Using the System of HSA and Cibacron Blue-Agrose. Biotechnol. Prog. 1989,5, 9. Hong, J.; Tsao, G . T.; Wankat, P. C. Membrane Reactor for Enzymatic Hydrolysis of Cellobiose. Biotechnol. Bioeng. 1981, 23, 1501. Lee, C. K.; Pan, L. C.; Ju, Y. H. Macroligand D-Alanyl-D-alaninedextran for Vancomycin Purification. Appl. Biochem. Biotechnol. 1994, 44, 21. Lehninger, A. L. Biochemistry, 2nd ed.; Worth: New York, 1975; p 178. Ling, T. G. I.; Mattiasson, B. Membrane Filtration Affinity Purification of Dehydrogenase Using Cibacron Blue. Biotechnol. Bioeng. 1989, 34, 1321. Luong, J. H. T.; Male, K. B.; Nguyen, A. L. A Continuous Affinity Ultrafiltration Process for Trypsin Purification. Biotechnol. Bioeng. 1988,31, 516. Male, K. B.; Luong, J. H. T.; Nguyen, A. L. Studies on the Application of a Newly Synthesized Polymer for Trypsin Purification. Enzyme Microb. Technol. 199Oa, 9 , 374. Male, K. B.; Nguyen, A. L.; Luong, J. H. T. Isolation of Urokinase by AMinity Ultrafiltration. Biotechnol. Bioeng. 1990b, 35, 87. Mattiasson, B.; Ramstorp, M. Ultrafiltration of Affinity Purification: Isolation of Concanavalin A from Seeds of Canavalia ensiformis. J . Chromatogr. 1984,283, 323.
Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 2109 Mattiasson, B.; Ling, T. G. I. Ultrafiltration Affhity Purification. In Membrane Separations in Biotechnology; McGregor, W. C., Ed.; Marcel Dekker: New York, 1986; pp 99-114. Nieto, M.; Perkins, H. R. Physicochemical Properties of Vancomycin and Iodovancomycin and their Complexes with DiacetylL-lysyl-D-alanyl-D-alanine. Biochem. J . 1971,123,773. Perkins, H. R. Specificity of Combination between Mucopeptide Precursors and Vancomycin or Ristocetin. Biochem. J . 1969, 111, 195. Powers, J. D.; Kilpatrick, P. K.; Carbonell, R. G. Trypsin Purification by Affinity Binding to Small Unilamellar Liposomes. Biotechnol. Bioeng. 1990,36,506. Scatchard, G.The Attractions of Proteins from Small Molecules and Ions. Ann. N.Y. Acad. Sei. 1949,51,600.
Weiner, C.; Sara, M.; Dasgupta, G.; Sleytr, U. B. Affinity Crossflow Filtration: Purification of IgG with a Novel Protein A Affinity Matrix Prepared from Two-Dimensional Protein Crystals. Bzotechnol. Bioeng. 1994,44, 55.
Received for review October 12, 1994 Revised manuscript received February 21, 1995 Accepted March 13, 1995@ IE9405908 t 3 Abstract published in Advance ACS Abstracts, April 15, 1995.
