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Polymer Fractionation in Aqueous Two-Phase Polymer Systems H. Hartounian and S. I. Sandler' Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 We consider the effects of the addition of poly(ethy1ene glycol) (PEG) of different molecular weights to aqueous two-phase systems of PEG 8000 and dextran 500. The first purpose of this study was to determine the molecular weight partitioning of the polymers themselves so that, for example, aqueous two-phase separations using affinity ligands can be improved. The second purpose was to examine whether this molecular weight partitioning could be predicted by using solution thermodynamic models so that it would be possible to optimize affinity partitioning without extensive laboratory work. Experimentally, we find that, by increasing the PEG concentration of any molecular weight in the feed, the high molecular weight PEG concentration in the dextran-rich phase is reduced. This observation can be used to reduce the loss of expensive ligated PEG used in affinity partitioning. Further, there is generally good agreement between our experimental data and the predictions of a solution thermodynamic model.
Introduction Aqueous two-phase systems are formed by the addition of two water-soluble but incompatible polymers to water. Each phase contains mainly water and is richer in one of the phase-forming polymers. One class of aqueous twophase systems frequently used in the partitioning of biological molecules is dextran and poly(ethy1ene glycol) (PEG); this is the system of interest to us here. Each of these polymers is polydisperse; that is, they contain molecules of a range of molecular weights. Koningsveld (1) has shown that polymer dispersivity can have an important effect on the liquid-liquid binodal curve of aqueous polymer solutions, and Lau et al. (2) have experimentally found that the phase-forming polymers themselvesfractionate. Kang and Sandler (3)have shown that the phenomenon of polymer fractionation is predicted from solution thermodynamic models. Our research here is directed toward determining whether we can make use of polymer fractionation to improve the efficiency of the partitioning of biomolecules in aqueous two-phase systems and especially in the recovery of affinity ligand and affinity ligand-biomolecule complexes attached to one of the phase-forming polymers. Consequently, we report here the results of our experimental study on the effect of changing the feed compositionof PEG of different molecular weights on the liquid-liquid equilibrium of the PEG 8000/dextran 500/ water system. We also compare the measured effects with predictions of a solution thermodynamic model for this system.
Materials and Methods PEG 8000 (lot 18F-00331,PEG 1000 (lot 86F-04481,and dextran 500 (lot 58F-0628) were purchased from Sigma Chemical Co. Stock solutions of PEG 8000, PEG 1000, and dextran 500 were made by dissolving weighed amounts of the dry polymers in water and confirmed by using refractive index and polarimetry measurements, respectively. Two-phasesystems were prepared gravimetrically in microcentrifuge tubes from PEG 8000 and dextran 500 stock solutions and deionized water. In order to determine the effect of the addition of PEG 1000 on the equilibrium
* Author to whom correspondence should be addressed. 875&7938/9 1/3007-0279$02.50/0
compositionsof dextran 500 and PEG 8000 in the aqueous two-phasesystems, five groups of two-phase systems were prepared. Each group consisted of four different but related feed compositions. Letting X,Y,and Z denote the feed compositions in weight percent of dextran 500, PEG 8000, and PEG 1000, respectively, each group consisted of the following feeds: (1)X,Y,Z = 0;(2) X, Y,2 = 1.5; (3) X,Y- 1.5,Z = 1.5; and (4) X,Y+ 1.5,Z = 0. It should be noted that the feeds of systems 1 and 3 have the same total PEG concentration (Y + 2) but a different average molecular weight. The same relationship exists between feeds 2 and 4. In addition two other aqueous two-phase systems with higher PEG 1000 feed concentration (3 wt 76) were also studied; these are (5) X,Y,Z = 3.0. In each case the samples were allowed to equilibrate and were centrifuged for at least 10 min, and when complete phase separation was achieved, a sample of the upper phase was withdrawn by using a pipette and a sample lower phase was obtained by inserting a syringe through the bottom of the plastic tube. Samples were then volumetrically diluted and analyzed at room temperature (25 "C)by using a high-performance liquid chromatography system with a multisolvent delivery system (Waters Model 600) with four Waters gel-permeation columns in series (two Ultrahydrogel linear, one Ultrahydrogel 250, and one Ultrahydrogel 120) and a differential refractometer (Waters, Model 410) detector. Data were collected by using a chromatography data station (Waters Maxima 820 on an IBM-AT personal computer). In all cases the mobile phase was 0.1 N sodium nitrate solution at a flow rate of 1 mL/min.
Experimental Results The results of the experiments are presented in Tables I-V, together with partition coefficients for PEG 8000, dextran 500, and PEG 1000. The direct effect of merely adding the low molecular weight sacrificial polymer on the bottom-phase concentration of the PEG 8000 can be determined by comparing the partition coefficients of PEG 8000 in sets 1 and 2 of each group. The addition of the PEG 1000 to a two-phase system at fixed PEG 8000 and dextran 500 concentrations results in a reduction of the concentration of the high molecular weight PEG in the bottom phase, as expected. In contrast, the replacement
0 1991 American Chemical Society and American Instltute of Chemlcal Engineers
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Table I. Exmrimental Results for System A dextran 500 PEG8000 PEG 100 % % % volume system (w/w) K (w/w) K (w/w) K ratio A1 feed 7.0 0.00 5.0 22.6 0.0 0.00 1.37 0.38 0.0 bottom 16.3 0.0 8.6 0.0 top
Table IV. Experimental Results for System D dextran 500 system D1
(w/w) K feed 5.0 0.0 bottom 14.9 0.00 top
feed bottom bP
7.0 17.8 0.0
0.00
5.0 0.38 8.6
31.7
1.5 1.17 1.97
1.68
1.58
D2
feed 5.0 bottom 16.2 top 0.0
A3
feed bottom top
7.0 14.3 0.05
0.00
5.0 0.38 8.6
13.6
1.5 1.14 1.8
1.58
1.04
D3
feed bottom top
A4
feed bottom top
7.0 20.17 0.0
0.00
5.0 0.38 8.6
95.5
0.0 0.0 0.0
0.00
1.94
D4
feed 5.0 0.0 bottom 18.33 top 0.0
B1
feed bottom top
8.4 18.7 0.1
0.00
B
feed bottom top
8.4 20.77 0.04
0.00
5.8 0.07 9.87
B3
feed bottom top
8.4 0.00 17.99 0.0
B4
feed bottom top
8.4 22.6 0.0
0.00
5.8 22.6 0.137 10.5
volume ratio 1.29
31.7
1.5 0.82 0.70
2.06
1.55
4.3 0.15 8.07
13.6
1.5 0.98 1.76
1.80
1.19
E3
7.3 0.05 11.75
95.5
0.0 0.0 0.0
0.00
1.79
E4
E5
system
Cl C2
C3
C4
CS
feed 6.2 bottom 14.01 0.1 top
(w/w) K 0.008 4.4 14.1 0.49 7.04
feed 6.2 bottom 16.48 top 0.04
0.002
feed 6.2 bottom 10.44 0.0 top
0.0
feed 6.2 bottom 18.12 top 0.0
0.0
feed 6.2 0.0 bottom 16.5 top 0.0001
4.4 0.28 6.96 2.9 0.7 5.2
24.4
7.43
5.9 0.14 8.8
62.8
4.4 0.23 6.5
28.3
PEG1000 % (w/w) K 0.0 0.0 0.0
0.00
1.5 0.82 1.67
2.04
5.0 0.0126 11.88 0.15
3.5 0.76 5.6 6.5 0.19 8.69
(w/w) K 0.0 0.00 0.0 0.0
22.6
7.37
47.9
PEG8000
volume ratio
14
1.63
12
1.78
6:
10
‘
a
d 0
0.0 0.0 0.0
0.00
3.0 2.18 3.5
1.6
1.65
1.5 1.00 1.59
1.59
2.38
1.5 1.14 1.74
1.53
1.40
0.0 0.0 0.0
0.00
3.06
PEG1000
feed 4.0 0.0073 bottom 13.66 0.1 top feed 4.0 0.0036 bottom 19.35 0.07 top
4.5 0.67 6.27 7.5 0.18 9.7
feed 4.0 bottom 18.3 top 0.0
6.0 0.15 7.82
0.0
9.36
1.5 0.96 1.48
1.54
2.38
53.9
0.0 0.0 0.0
0.00
3.86
52.1
3.0 1.87 3.86
2.06
3.57
0
1.5 1.482 1.23 1.83
volume ratio
% % volume % (w/w) K (w/w) K ratio system (w/w) K El feed 4.0 0.0004 6.0 19.75 0.0 0.00 3.18 0.4 0.0 bottom 16.0 7.04 0.0 0.1 top 6.0 22.28 1.5 1.85 3.30 E2 feed 4.0 0.0 0.35 0.83 bottom 16.3 7.8 1.54 0.0 top
0.00
%
5.0 0.31 7.0
0.0
dextran 500
0.0 0.0 0.0
PEG8000
%
(w/w) K 5.0 13.7 0.57 7.81
Table V. Exwrimental Results for System E
Table 111. Exuerimental Results for System C dextran500 % (w/w) K
PEG 1000
%
%
A2
Table 11. Experimental Results for System B dextran 500 PEG 8000 PEG 1000 % % % system (w/w) K (w/w) K (w/w) K
PEG8000
~
0.97
8
L
ISsPEGlWo
Expcnmcnl
-Model-1 5% PEGlOOO +T)c.L~~c.I
-
5s peoim
8 -TIc-LIM.No
PEGIWo
6 4
2.11 a.
,
25
1.79
of some of the PEG 8000 by PEG 1000 (feeds 1 and 3) decreases the partition coefficient of the PEG 8000. The largest improvement in the partition coefficient of PEG 8000 results from adding additional PEG 8000 rather than PEG 1000 to the feed (compare experimental results for feeds 1 and 4). We also see that the partitioning of the dextran is almost complete in all cases and was very little affected by the molecular weight of the PEG. However, as the volumes of the two phases change with PEG molecular weight changes, the concentration of the dextran in the bottom phase does change. The experimental binodal data both with and without PEG 1000 addition for the PEG 8000/dextran 500/water system are shown in Figure 1. It can be seen that the addition of the PEG 1000 to the feed results in a shift of
DextranSOO, w/w%
+
Figure 1. Binodal curves of the P E G 8000 dextran 500 aqueous two-phase system with various amounts of added P E G 1O00. T h e points are the experimental data and the lines are predicted from the thermodynamic model described in the text.
the location of the binodal curve. This shift is larger a t low polymer concentrations and smaller at high concentrations. The shift in the tie lines is somewhat greater, and this is illustrated by the one tie line also shown in Figure 1. We see that the length, and to a smaller extent the slope, of the tie lines on a PEG 1000 free basis are changed by addition of the PEG 1000 to the feed. The results of our experiments for the higher PEG 1000 feed concentrations for systems C and E are given in Tables I11 and V. It can be seen from these tables and Figure 2 that increasing the concentration of PEG 1000 in the feed results in a reduction in the concentration of PEG 8000 in the bottom phase and an increase of the tie-line length,
28 1
Botechnol. Prog.., 1991, Vol. 7, No. 3
lo
1
500 A
i?
0
400
I
500
0 OD
k k
a,
.-2
300
8
200
E L
PEClOOO 1.5% PEGlOOO 3%
i
a
Concentrating Coefficient Partition Coefficient
1
/
4
25
30
200
1
PEGlOOoO% IO
15
20
e
3
Dextran,w/w%
0 10
Figure 2. Effect of the higher PEG loo0 concentration on the equilibrium composition of PEG 8000 and dextran 500.
15
20 Tie Line Length
Figure3. Concentratin and partition coefficients of PEG 8OOO aa a function of the t i e k e length.
so that there is a higher recovery of the PEG 8000. Also, increasing the PEG 8000 feed concentration at fixed dextran and PEG 1000 feed compositionsresults in a decrease in the concentration of the PEG 8000 in the bottom phase. In contrast, in all our experimenta, the partition coefficient of the PEG loo0 was essentially independent of the concentration of other polymers. To illustrate the effect of increasing the PEG 8000 concentration on the percent recovery of the PEG 8000 in the top phase we define the concentrating coefficient C for polymer i, Ci,as total amount of i in top phase ci = total amount of i in lower phase concn i in top phase X volume of top phase - concn of i inof bottom phase X volume of bottom phase In order to calculate the concentrating coefficient, the volume ratio of the two-phase system has to be determined. The overall and polymer mass balance equations are
the interfacial tension and viscosity of the phases increase. Ryden and Albertsson (4)point out that at higher polymer feed compositions (and thus higher interfacial tensions) the tendency for particles to adsorb on the interface is increased. This nonspecific interfacial adsorption results in a decrease in the efficiency of the partitioning process (5). Also, while higher polymer feed compositions increase the tie-line length and thus the driving force for the separation, the resulting increase in viscosity (especially in the bottom, dextran-rich phase) may increase the time necessary for the phase separation. Thus, one has two alternatives to achieve a higher recovery of polymers: add additional PEG lo00 or add PEG 8000. Per unit weight of PEG added, the second alternative produces the greatest recovery of PEG 8OOO but at the expense of greater viscosity and interfacial tension, which may or may not be acceptable.
MF = MB + MT
Phase Equilibrium Calculations
(1)
where MF,MT,and MBare the total masses of the feed, top, and bottom phases, respectively, and WF,WTand WPg are the weight percents of polymer in the feed, top, and bottom phases, respectively. By using eq 1and the relations MT = VT PT and MB = VB p ~ where , VT and VB are the total volumes of the top and bottom phases, eq 2 can be written
(3) Here PT and PB are the densities of the top and bottom phases, which we obtained using a pycnometer. The results of the calculations for this volume ratio are also given in Tables I-V. It can be seen that in each data set the volume ratio increases with increasing total PEG concentration in the feed, and for fixed total PEG concentration, the volume ratio decreases as PEG 8000 is replaced by PEG 1000. The results for the concentrating coefficient calculated from our data are plotted in Figure 3 together with the partition coefficients. Clearly, the longer the tie-line length, the larger the concentrating coefficient becomes, which establishes that increasing the concentration of the PEG 8000 in the feed result an increase in the PEG 8OOO recovery. Although increasing the PEG 8000 concentration in the feed will increase the partition and concentrating coefficients of the PEG 8000 in the two-phase systems, it may lead to difficulties in biomolecules partitioning, since both
It is of interest to see if the experimental results reported here can be understood, and even predicted, by a model since calculations are more easily done than experiments. In such calculations the polymer polydispersity is an important factor in their phase behavior, and the difference in phase behavior predictions between considering aqueous two-phase systems to be monodisperse and polydisperse can be considerable. There have been many attempts to describe the polymolecularity of the polymers and its effect on the phase diagrams of aqueous two-phase polymer systems. Some investigators, such as Scott and Magat (6),have extended the Flory-Huggins model to study the effect of the polydispersity of the polymers in a mixture of the solvents, while others have characterized polydisperse polymers by choosing a number of pseudocomponents, sometimes in a rather arbitrary manner (7). The major problem with this last approach is that it requires a trial-and-error calculation in order to obtain the optimal number and type of pseudocomponents. Continuous distribution of molecular weight or some other property to represent polydisperse polymers has also been used for characterizing the intensive properties of polydisperse mixtures (8). Using a molecular weight distribution function, Cotterman et al. (9) and independently Shibata et al. (10) proposed methods based on Gaussian quadrature procedures to choose pseudocomponents to represent a continuous distribution in a mathematically correct and optimal way. With such a characterization approach, Kang and Sandler (11) used the UNIQUAC (12)solution model to accurately describe the phase behavior of a PEG/dextran/water two-phase sys-
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282
Table VI. Pseudocomponents Obtained from the Gauss Quadrature Method for Polydisperse Dextran 500 MW, pseudo componenta 1 2 3
dextran 500 2.06 x 107 8.40 x 107 2.08 X 108
system as we found by direct measurement. We also see in Figure 1that the model predicts only a modest effect of increasing the PEG 1000 concentration to 3%.
PEG 8OOO
PEG lo00
8920
1100
tem. One of the interesting findings of their calculations was that the phase-forming polymers also fractionate. In particular, the smaller the molecular weight of a polymer, the closer its partition coefficient is to unity; consequently, high molecular weight polymers partition very unevenly, and the average molecular weight of each polymer is different in each phase. In this work, phase equilibrium calculatons were performed with the thermodynamic model proposed by Kang and Sandler (3). The complete description of the model is given elsewhere ( 3 , l l ) . In brief, the model uses the UNIQUAC equation with preset parameters to represent solution nonidealities, and each component may be considered to be polydisperse. To incorporate the effect of the polydispersity of the phase-forming polymers, a molecular weight distribution function for each polymer is chosen; the distribution we use here is the LansigKramer (L-K) function: (4)
where b and MOare adjustable parameters. Knowing the values of the polydispersity parameter b, defined as
and one of the number or weight average molecular weights of the polymer, one can calculate the values of b and Mo. After choosing the molecular weight distribution function, the optimal pseudocomponents to represent the continuous distribution are chosen on the basis of the Gauss quadrature method. Thus each polydisperse polymer is considered to be a multicomponent mixture with each component described by a discrete molecular weight and concentration. The equilibrium compositions of each species are obtained by equating the chemical potentials of the component in both phases by using the UNIQUAC model. In our calculations, PEG 8000 ( b = 1.05)and PEG 1000 ( b = 1.1)were considered to be monodisperse due to their narrow molecular distributions. A L-K distribution function for polydisperse dextran 500 ( b = 2.75) was used, and three pseudocomponents were chosen for dextran on the basis of the quadrature method. These pseudocomponents are reported in Table VI. Also, in the calculation of the activity coefficients by using UNIQUAC,the interaction parameters between the species and physical properties of the components were obtained from the work by Kang and Sandler (3). As shown in Figure 1(and also in other cases we have not plotted), the model predictions are in excellent qualitative agreement and in reasonably good quantitative agreement with the experimental observations. It can be seen that by introducing the PEG 1000 to the two-phase system, the calculated partition coefficient of the PEG 8000 is increased, as is observed experimentally, and that the calculations predict that PEG 8000 concentration in the feed will result in an increase in the total recovery of the PEG 8000 in the two-phase
Conclusions We have shown here that the addition of PEG of any composition to a two-phase system would decrease the amount of high molecular weight PEG in the bottom, dextran-rich phase as a result of the polymer fractionation phenomenon. This could have application in affinity partitioning for the purification of the biological molecules. For example, by attaching a specific affinity ligand to the high molecular weight PEG and introducing a sacrificial PEG of the same or lower molecular weight to the aqueous two-phase system, our results indicate that the loss of the expensive ligand-biomolecule complex to the bottom, dextran-rich phase could be minimized and the recovery of the biomolecule improved. On an equal weight basis the larger polymer is more efficient but with the result of greater viscosity and interfacial tension. Thus it is debatable whether the use of low molecular weight sacrificial polymers is useful. A solution thermodynamic model that had previously been developed for predicting the phase behavior of aqueous two-phase systems was found to be in reasonably good agreement with our experimental measurements, even for such subtle effects as the fractionation of the phase-forming polymers. This suggests that the polymer fractionation phenomenon is predictable to good accuracy, so that process optimization, without a great deal of experimental measurements, may be possible in the future.
Acknowledgment This work was supported, in part, by Grant CBT 8812343 from the U.S. National Science Foundation to the University of Delaware.
Literature Cited (1) Koningsveld, R.; Staverman, A. J. J. Polym. Sci., Polym. Phvs. Ed. 1968,6, 367. (2)Liu, W.W.Y.; Burn, C. M.; Huang, R. Y. M. J.Appl. Polym. Sci. 1986,30, 1187. (3) Kang, C. H.;Sandler, S. I. Macromolecules 1988,21,3088. (4) Ryden, J.; Albertsson, P. A. J. Colloid Interface Sci. 1971, 37,219. (5) Walter, H.,Brooke, D. E., Fisher, D., Eds. Partitioning in Aqueous Two-Phase Systems; Academic Press: New York, 1986. (6) Scott, R.L.; Magat, M. J. Chem. Phys. 1945,13, 178. (7) Shiskov, A. K.;Krivobokov, V. V.; Chubarova, Ye. V.; Frenkel, S. Ya. Polymer Sci. USSR (Engl. Transl.) 1981,23,1330. (8) Ratzsch, M. T.; Kehlen, H. Fluid Phase Equilib. 1983,14, 225. (9) Cotterman, R.L.;Chou, C. F.; Prausnitz, J. M. Znd. Eng. Chem. Process Des. Dev. 1985,25,840. (10) Shibata, S.K.; Sandler, S. I.; Behrens, R. A. Chem. Eng. Sci. 1987,42, 1977. (11) Kang, C. H.;Sandler, S.I. Fluid Phase Equilib. 1987,38, 245. (12) Abrams, D.S.;Prausnitz, J. M. AZChE J. 1975,21,116. Accepted March 25, 1991.
Registry No. PEG, 25322-68-3;dextran, 9004-54-0.
