2294
I n d . Eng. C h e m . Res. 1994,33, 2294-2300
Aqueous Two-Phase Systems. 2. Protein Partitioning H a r t o u n Hartounian,? Eric
W.Kaler, and S t a n l e y I. Sandler'
Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
The role of polymer concentration, ionic strength, and salt type on the partitioning of proteins in aqueous two-phase systems is studied both experimentally and theoretically. Polymer-induced protein-protein interactions are also considered in terms of a perturbation theory, and are shown to not significantly affect the protein partition coefficient a t moderate concentrations. A thermodynamic model combining the UNIQUAC and extended Debye-Huckel equations accounts for changes in salt type and salt concentration on protein partitioning with good accuracy, and calculated protein partition coefficients are in good agreement with experimental observations. Based on this detailed thermodynamic analysis, a simple model for the protein partition coefficient is developed and is shown to be useful for correlating measurements. Introduction Aqueous two-phase systems offer a method for separation of biologically active materials. One of the interesting features of these systems is that partitioning of the biomolecules in the solution can be altered by changing the solution pH, ionic strength, or the type of the electrolyte. In particular, salts partition unequally between the two aqueous polymer phases. The difference in salt concentration establishes a Donnan-type electrochemical potential difference between the phases that greatly affects the partitioning of charged biomolecules. In addition, since the surface charge of a protein depends on pH, a change in the pH of the solution can result in a significant change in the partitioning behavior of the protein. The partitioning behavior of biomolecules also depends on the physical and chemical nature of the phaseforming polymers. Extensive experimental investigations of the partitioning of biomolecules in aqueous two-phase systems (Walter et al., 1991; Huddleston et al., 1991) have shown that the factors determining the partitioning behavior of biomolecules are the size and conformation of the partitioned particle, the ionic composition and salt type of the solution, the number of hydrophobic and hydrophilic groups on the surface of the biomolecule, and the concentrations and structures of the phase-forming polymers (Albertsson, 1986). Several theoretical descriptions of the partitioning of biomolecules in aqueous two-phase systems have been offered. Albertsson (1986) andBrooks (Walter et al., 1985) treated the protein as a polymer and used Flory-Huggins theory (Flory, 1942)to describe the phase equilibria. King et al. (1988),Forciniti and Hall (1990),Haynes et al. (19891, and Cabezas et al. (1990)used the osmotic virial expansion of McMillan-Mayer theory (McMillan and Mayer, 1945) truncated at the second osmotic virial coefficient to calculate protein partitioning. Most recently, Haynes et al. (1993)have used a very detailed, but complicated model which coupled several elements from statistical mechanics to describe aqueous two-phase partitioning. Kang and Sandler (1988) used the UNIQUAC (Abrams and Prausnitz, 1975) solution model to describe polymer solution nonidealities and a molecular weight distribution function for each polymer to incorporate the effect of
* Author to whom correspondence should be addressed. E-mail:
[email protected]. + Depo Tech Corporation, 11025 N. Torrey Pines Rd., Suite 100,La Jolla, CA 92037. OSSS-5885/94/2633-2294$04.50/0
polydispersity. Here we develop a relatively simple molecular model for biomaterial partitioning between two aqueous phases that includes the effects of pH, ionic strength, and salt type. These effects are due to electrostatic interactions, the hydrophobic effect, and polymerinduced protein-protein interactions which we describe in the context of colloid science, since large biological molecules can be considered to behave as colloidal particles. This model builds upon the description of polymer/ polymer/salt/water behavior given in the previous paper (Hartounian et al., 1994). However, since our main interest is in two-phase, two-polymer (dextran and polyethylene glycol) systems, and not salt-polymer-water two-phase systems, the model we develop is applicable only to low salt concentrations. Experimental Methods PEG 8000 (Lot No. 18F-00331, dextran 500 (Lot No. 58F-0628), bovine serum albumin (BSA) (Lot No. 23C5679), and lysozyme (Lot No. 23d-4567) were purchased from Sigma Chemical Company. Sodium chloride, and the monobasic sodium salt of phosphate were purchased from Fisher Scientific Company. Solutions were prepared and concentrations of all species except the proteins were determined as described in the previous paper. The concentrations of the protein in both phases were determined by measuring the absorbance at 280 nm using a spectrophotometer. Thermodynamic Formulation Our goal is to develop a general thermodynamic model describing the equilibrium compositions of proteins in aqueous two-phase systems with changing pH, ionic strength, salt type, and polymer composition. To construct such a model, we combine various contributions to the excess Gibbs free energy of the solution in which each phase is a mixture of protein, solvent, electrolyte, and polymer molecules. We consider a protein to be a macroion with the structure of a rigid sphere and a net surface charge that changes with solution pH. As a further simplification, we assume that the addition of a small concentration of the protein (0.1% w/w) to the system does not alter the equilibrium compositionsof the polymers and ions in solution. This assumption enables us to decouple the protein partitioning calculation from the phase equilibrium computation for the aqueous mixture of polymers and salt. Our experiment supports this 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 2295 approximation for the protein concentrations considered here, though Haynes et al. (1993) show that this may not be accurate at higher protein concentrations. Thus, at low protein concentrations, the distributions of the polymers and ions are first obtained from the direct equilibrium calculation for the aqueous two-phase system described in the previous paper. Then, using the fixed concentrations for water, polymer, and salt obtained from the previous step, the equilibrium distribution of the protein is obtained by equating the chemical potentials of the protein in the top and bottom phases.
Electrostatic and Short-Range Interactions of the Proteins Electrostatic effects are due to the presence of salts and of ionizable groups on the surface of the protein. At low ionic strength, electrostatic interactions are important since there is not significant ion screening and the electrical double layer is diffuse. To account for the long-range interactions between charged proteins and the short-range interactions between proteins with each other and with polymers and ions, we use the Guggenheim extension of the Debye-Hackel expression (Newman, 1973).
2
- a d 1 7 ( ~ a d ~C )z : n j 3
J
+ Z C p i j n i m j (1) Z#OJ#O
where n,and pwo are the number of moles and standard state chemical potential of water, Xje is the standard state activity of the ion, B is the Debye-Hiickel parameter, a is the average value of the sum of the radii of pairs of hydrated ions, z is the protein charge, pij is the shortrange interaction coefficient, and 7 ( x = BadZ), where I is the ionic strength, is defined by the following relation:
The first two terms in eq 1account for the "ideal" Gibbs free energy of the solvent and ions in solution. The third term is due to long-range electrostatic interactions, and the last term is the contribution from the short range protein-protein, protein-ion, and protein-polymer interactions (Newman, 1973). Differentiating the above relation with respect to the number of moles of proteins gives the following expression for the chemical potential of the protein in solution
where q j is the electrostatic potential of phase i and F is the Faraday's constant. The last term in eq 3 accounts for the electrochemical potential of each phase. This equation is applicable only a t low ionic strength. At higher ionic strength the average distance between macromolecules is decreased and ions bind to the protein surface. This binding causes the protein to behave like a neutral dipole (Melander and Horvath, 1977). Thus, at high salt concentrations, one possible correction to the Debye-Huckel electrostatic expression is to add the Kirkwood dipole expression, which assumes the electrostatic free energy to be proportional to the dipole moment and ionic strength. Another
improvement would be to replace the extended DebyeHiickel term with one based on the generalized mean spherical approximation. In our experiments the ionic concentrations were low, so no such corrections were added.
Polymer-Induced Protein-Protein Interactions The polymer-induced protein-protein interaction has not previously been studied in the modeling of protein partitioning in aqueous two-phase systems. This interaction, also known as depletion flocculation or depletion phase separation (Asakura and Oosawa, 1958; Napper, 1983), has, however, been extensively studied within the framework of the stabilization of colloidal particles by polymers. Qualitatively, this phenomenon arises because, in the close approach of particles in solution, the domain between them becomes so small as to exclude polymer molecules. Consequently, the region between colloidal particles contains only solvent molecules. The unbalanced inward osmotic pressure which arises from the difference in the concentrations of the polymer in the bulk and between particles forces the colloids to flocculate. Evidence for polymer-induced protein-protein interactions comes from experimental studies of protein flocculation or precipitation in aqueous solution induced by the addition of water-soluble polymers such as PEG and dextran. The solubility of proteins in the presence of PEG has been studied extensively (Chun et al., 1967; Arakawa and Timasheff, 1985a,b;Atha and Ingham, 1981;Ingham, 1978;Knoll and Hermans, 1983;Lee and Lee, 1987). The main conclusion from these measurements is that the primary mechanism for protein precipitation is the socalled excluded volume effect. For example,Arakawa and Timasheff (1985a,b)studied the mechanism of interaction between PEG and different proteins. They found that the addition of polymer results in a preferential hydration of protein molecules in solution, and suggested that the increased hydration was due to steric exclusion of the polymer from the surface of the protein. We have used the perturbation theory method originally proposed by Gast et al. (1983) and extended to proteins by Mahadevan and Hall (1990) to calculate the depletion forces in each phase (Hartounian, 1993). Despite their importance at higher polymer concentrations, they are found to be negligible in the cases of interest here, as shown below.
Results and Discussion The results for the measured partition coefficient for BSA and lysozyme in systems containing 50 mM feed compositions of, separately, NaCl and NaHzPO4 are presented in Figures 1and 2. In these figures, the partition coefficients of the proteins, which are defined as the ratio of the molality of the protein in the top phase to the molality of the protein in the bottom phase, are plotted for various tie-line lengths. The negatively-charged BSA in a neutral pH solution is partitioned preferentially into the bottom phase in both salt systems, and its partition coefficientis higher in NaH2P04than in NaC1. In contrast, lysozyme, which is a positively charged protein at neutral pH, preferentially partitions into the top phase in the NaC1-containing system and into the bottom phase in the NaH2P04 system. Experimental measurements of the partitioning of the salts NaC1, NaHS04, and NaH2PO4 in aqueous two-phase polymer systems are given in the previous paper (Hartounian et d. 1994). The partition coefficients of these salts decrease from unity with increasing the tie-linelength.
2296 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 2.5
O h
-Model
-1.5 X0 e
-
-2
Nai$FQ4
. Haynes et al.. 1989
t
1
1
1
c
0.5
1
-
1
e
L
-2.5
I
VaCl . Haynes et a l . 1989
rn
r
-1
1
l
I /
I
NaCl
0
5
10
15
Tie-Line Length.
25
20
L t
ia
t
NaYPO4
F
A
1 6
-Model
10
'5
20
25
30
Tie-Line Length, w/w%
w/w%
Figure 1. Effects of salt and polymer compositionon the partitioning of BSA. 2
5
3
30
NaCl
Figure 3. Calculated electrochemical potential difference (mV) between the two aqueousphases for NaH2P04 and NaCl as a function of tie-line length. Table 1. Physicochemical Properties of the Polymers and Proteins 2,net charge species diameter (cm) MW pH = 7 pH = 5.5 PEG 8000 2.97 X lO-' 8 920" 167 W dextran 500 1.16 X 10-8 65 OOO -13 -10 BSA 7.22 X 10-' 14 100 +8.5 +10 lysozyme 4.12 X 10-' ~~
'
I
PEG protein 8000 BSA 910 lysozymeb 111.3 lysozymeC 100.4
Interaction Parameters (a&;) dextran 500 NaCl NaH2P04 BSA lysozyme 2590 5340 1.26 -3.17 1532.2 -58 262.6 -222.23 1084.8 -4.77
a Number-average molecular weight. * 50 mM NaH2P04. 50 mM NaC1.
76 1
04 10
15
20
25
30
Tie-Line Length, w/w%
Figure 2. Effecta of salt and polymer compositionon the partitioning of lysozyme.
The partitioning to the bottom phase of monobasic sodium phosphate is stronger than that of sodium chloride, so that the electrostatic potential difference generated between the two phases by the uneven partitioning of NaH,PO4 is higher than that of NaCl (Figure 3). To calculate protein partitioning, we assumed that the small concentration of protein in solution does not significantly affect the concentrations of the polymers and water in both phases, and we made use of the fact that the concentrations of the ions on a molar basis are much higher than the protein concentration. Therefore, the term for protein concentration in the electroneutrality relation for each phase was neglected. In this framework there is no effect of protein concentration on the equilibrium distributions of ions and polymers in the biphasic system, and the equilibrium distributions of the polymers, ions, and water were obtained from phase equilibrium calculations of the aqueous mixture of polymers and salt described in the previous paper (Hartounian et al., 1994). Then,
using these concentrations and the values of the measured protein-ion and protein-polymer osmotic second virial coefficients reported by Haynes et al. (1989) and King et al. (1988) (Table l),the equilibrium concentration of the protein in each phase was obtained by equating the chemical potentials of the protein in the top and bottom phases (Figure 3). The results of our calculations for partitioning of BSA and lysozyme are shown in Figures 4 and 5. The calculated partition coefficients for these proteins are in good agreement with the experimental observations. In the presence of excess salt, the following relation for the partition coefficient of the protein holds:
+
p i ~ T o ~RT
In yTopmTop + ~ Z ~ \ k T o=p pi0Bot + R T in y p m p + FziSBot(4)
where pio is the standard state chemical potential of the protein, \k is the electrical potential of the phase, F is the Faraday constant, 2; is the protein charge, and y i and mi are the activity coefficient and the molality of the protein, respectively. Rearranging eq 4 yields
Ind. Eng. Chem. Res., Vol. 33, No. 10,1994 2297 0.5 In
K"
O
d
-0.5 7 -1
1 I
0.35
0.3 Is KTM"
0.25
: 0.2
.& =
-
-1.5
/
Io
:
IC
/
/ /
c
0.15
-2
/
:
/
Io,"K
/
0.1
I
/
I I I
-2.5 7 0.05
5
10
20
15
25
30
n
10
15
20
Figure 4. Measured partition coefficient (pointa) of BSA in an aqueous two-phase polymer system made with 50 mM NaC1. The lines show the calculated KT* and ita contributions KO and Kd.
' i
Figure 6. Measured partition coefficient (points) of lysozyme in an aqueous two-phase polymer system made with 50 mM NaCl. The lines are the calculated K T o M and ita contributions KO and Kd.
A* =
(-)
y_BOtypp
Y-TopY+Bot
1 0
a t
5
j
I
I
I
(
I
j
I
1
20 Tie-Line Length, w/w% 10
15
20
contributions dominate the partitioning behavior of a protein in aqueous two-phase systems. The electrochemical (Kel)contribution to the partition coefficient of the protein depends on the electrostatic potential difference between the two phases for different salts, which, in turn, is calculated from our thermodynamic model for the aqueous mixture of polymers and salt. The electrochemical potential difference between the two phases for 1:l electrolyte is
-0.5
-3
25
Tie-Line Length, w / w %
Tie-Line Length, w i w %
18,1'i
25
30
Figure 6. Measured partition coefficient (points) of BSA in an aqueous two-phase polymer system made with 50 mM NaHzPO,. The lines are the calculated KT* and ita contributions KO and Kel.
or
In this equation, K = miTOpJm,Ws the partition coefficient of the protein in the presence of the electrolyte and KO = 7Pt/yiToP is the partition coefficient when A* = 0. The value of KO depends on the relative solvation of the protein in the twophases, andKel = exp[(FzJRT)A\kl depends on the net charge of the protein and the electrochemical potential difference between the coexisting phases. Specifically, Kel reflects electrostatic effects, and KO depends upon the solubility, hydrophobic and hydrophilic character, size, and conformation of the protein in polymer solution (Johansson, 1974). Our objective was to separate the effects of the eleutrostatic potential difference and the protein surface charge from the other contributions that can then be lumped into a single parameter KO. The relative values of Kel and KO will show which of the
(7)
The calculated electrostatic potential difference between coexisting phases containing separately 50 mM NaCl and NaHzP04 increases with tie-line length (Figure 3). The values of KO and Kelfor BSA in aqueous two-phase systems containing 50 mM NaCl and 50mM NaH2P04 obtained from our model are shown in Figures 4 and 5. Comparing the values for KO and Kel for various tie-line lengths showsthatKO is the dominant factor in determining the partition coefficient of BSA in a biphasic system containing 50 mM NaC1. In the case of NaH2P04 (Figure 5 ) , both KO and Kel are important in determining the partitioning of BSA. Increasing the tie-line length decreases the values of KO and Kel for both cases. The decrease in Kelfor the negatively charged BSA reflects the increase in the electrostatic potential difference caused by increasing the tie-line length in both salt systems. Also, the effect of increasing polymer composition on KO is greater than its effect on Kelfor systems containing NaC1. The values of KO andKel are shown for positively-charged lysozyme in Figures 6 and 7. In NaC1, lysozyme partitions preferentially into the top phase and both KO and Kel are important in determining the partitioning behavior of the protein, although KO dominates slightly for NaCl (Figure 6) and more strongly for NaHzPO4 (Figure 7). With NaCl both KO and Kel for lysozyme change in the same direction as the polymer composition increases. However, an opposite trend is observed when NaH2P04 is used. In the latter case lysozyme preferentially partitions into the bottom phase, and Kel increases and KO decreases as a function of the tie-line length.
2298 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994
.1
o
r
"
Ft
i
A Simplified Model
5 5
example, for a hydrophilic protein like lysozyme in the case of NaC1, one would expect that increasing the tie-line length will result in increasing the hydrophilicity of the bottom phase, thus making it a better solvent for the protein. However, the opposite trend is observed: lysozyme preferentially partitions into the top phase. This might be due to a change in the protein conformation when NaCl is added; i.e., hydrophobic residues from the interior of the protein could be exposed at the protein surface and thereby make it more hydrophobic. We conclude that the electrochemical potential difference between two phases does not alone drive protein partitioning, but that other factors such as hydrogen and hydrophobic bonding and protein self-association are also important.
10
15
20
25
30
Tie-Line Length, w / w %
Figure 7. Measured partition coefficient (points) of lysozyme in an aqueous two-phase polymer system made with 50 mM NaHzP04. The lines are the calculated Pod and its contributions KO and K*l.
Why do proteins such as lysozyme and BSA show different partitioning behavior when different salts are used? In the absence of salt, lysozyme preferentially partitions into the bottom phase. PEG is more hydrophobic than dextran, and consequently the dextran-rich phase is a better solvent for lysozyme than the PEG-rich phase. Also, the addition of a salt reduces the solubility of lysozyme in aqueous solution at pH = 4.5, and the solubility of lysozyme depends on the type of salt in the following order (Reis-Kautt and Ducruix, 1991): SCN- > NO; > C1- > citrate2- > CH,COO-
i=
H2PO; > SO4'-
Thus, C1- precipitates lysozyme more effectively than does HzPOd-. Preferential partitioning of NaH2P04 into the bottom phase decreases the partition coefficient of the lysozyme since the bottom phase, with its higher concentration of NaHzP04, is a better solvent for the protein. Therefore the negative slope of KO (KO < 1)in Figure 7 can be understood in terms of the higher affinity of lysozyme for the bottom phase due to (1)the increase in the relative difference in the hydrophobicity of the phases when the concentration of polymers increases and ( 2 ) the preferential partitioning of the added salt into the bottom phase. The electrochemical contribution tends to offset the effect of decreasing KO on the total K, and the result is a net increase in the total partition coefficient of the protein. It is interesting to note (Figure 6) that with NaCl both Kel and KO change with approximately the same slope as the tie-line length increases. Since the effect of the electrochemical potential difference between the two phases is small, the tendency for lysozyme to partition into the PEG-rich phase is probably due to a change in the surface hydrophobic-hydrophilic balance of the protein. Such a change is consistent with the known variation of lysozyme structure at neutral pH as a function of salt concentration (Walter et al., 1985). The partitioning behavior of proteins is affected by the electrochemical potential difference between the two phases, but also depends on the solvation properties of the phases, i.e., the change in the hydrophobic and hydrophilic character of the protein in the solution. For
A quantitative engineering model for protein partitioning would be useful for scale-up and design, as well as for the selection of materials to be used in aqueous two-phase extraction processes. The thermodynamic framework proposed here takes into account all the interactions among the components in aqueous biphasic systems and describes protein partitioning behavior. However, this model, which is composed of highly nonlinear equations and needs extensive experimental data to obtain the model parameters, is not easy to use for engineering design. This is also true of the model of Haynes et al. (1993) which uses, among others, information from low angle light scattering, dilatometry (for partical molar volumes at infinite dilution), and membrane osmometry. In general, one cannot expect all such data to be available. To simplify the model developed in this work, we first determine which contributions are dominant in the partitioning of a protein, and then reduce the model to a simple correlation for the partitioning of proteins as a function of these contributions. In the model here, the chemical potential was calculated by considering three interactions: the electrostatic interactions of the proteins, short-range interactions of the proteins with the phase-forming polymers and salt, and polymer-induced protein-protein interactions. In the first attempt to simplify our model, the chemical potential was calculated by only considering electrostatic and shortrange interactions. The protein partition coefficient was then calculated using eq 3, and the results of this calculation are compared with the model predictions including all contributions to the chemical potential (Figure 8). As mentioned above, the contribution of depletion flocculation to the chemical potential of the protein is not significant compared to the combination of the electrostatic and short-range interactions and need not be considered further. The partition coefficient of a protein, obtained by equating the chemical potentials of the protein in the top and bottom phases, is
zi2adPP lnK=-
+
1 BudPP
+
z;adIBot
+
1 BUdIBOt
+
Since the difference between the ionic strength of the top and bottom phases is very small (PI = 0.0005), eq 8 can be further simplified by neglecting the difference between the first two terms so,
Ind. Eng. Chem. Res., Vol. 33, No. 10,1994 2299
I
1-
Exp.- 50mM NaCl
1.6
Model
0
0.8
2
Model-No Depletion Form
16
1
m
NqPO,-50mM
0
NaCl-50mM
-Model- 50 mM Ionic Smngrh - _ . Model- 70 m M Ionic Strength
I: v
..
b
0
0
L
0.4 10
15
20
25
30
Tie-Line Length, w/w%
The first term in eq 9 takes into the account the shortrange interactions of the proteins with the phase-forming polymers and salts, and the second term describes the effect of the electrostatic potential difference as a result of the uneven partitioning of the ions between the two phases on the protein partition coefficient. Analysis of our model calculations shows that the partition coefficient of the protein is a linear function of tie-line length (Figures 4 and 8). Consequently, eq 9 can be further simplified by specifyingthe partition coefficient as a function of tie-line length (TLL) rather than the compositions of each phase. The advantage of this simplification is that the number of parameters is reduced and the partition coefficient of the protein is expressed in terms of a single parameter representative of the total polymer composition in the aqueous two-phase system. Thus
+2
f i i j ( m y- mj'op) + CAP ions
(10)
where A is a constant. This equation can be used to calculate the partition coefficientof a protein in an aqueous two-phase system in the presence of any electrolyte. Using the electroneutrality equation for each phase, eq 10 can be further simplified to In K = A[TLLl
+ &Am+) + CAP
(11)
mz
where Am+ = - m?, A and B are the constants representing the interactions of the protein with the phaseforming polymers and salt, and C = ziFIRT. Comparing eq 11 with eq 6 shows In and
= A[TLL]
+ B(Am+)
I
10
15
,
,
,
,
,
20
,
,
.
I
,
,
25
30
Tie-Line Length, w/w%
Figure 8. Measured partition coefficient (points) of lysozyme in aqueous two-phase polymer systems made with either 50 mM NaCl or Na&PO4, and the calculated G o * with and without accounting for depletion forces.
In K = A[TLL]
04
(12)
Figure9. Calculatedeffectof ionicstrengthonlysozymepartitioning for two different salts compared with the measured partitioning for 50 mM salta. Table 2. Parameters A, B, and C of Different Salts BSA NaCl Nd'f2PO4 A -0.238 -0.175 B 541.01 193.78 C -0.634 -0.533
Eq 11 for Proteins in
lysozyme NaCl NaHzP04 -0.027 -0.062 175.64 21.9 0.331 0.389
The parameters A, B , and C are obtained by fitting experimental data. The parameters for BSA and lysozyme are presented in Table 2. Parameter A is a function of the compositionof the phase-forming polymers, and B depends on the types of the salt and protein. Parameter C, given previously, is a function of the solution pH and the protein used. If zi is known, eq 11 is a two-parameter (A and B ) correlation; otherwise all three parameters are used in the correlation. This correlation requires a minimum amount of experimental information to obtain the model parameters, and it is easy to use in engineering scale-up. That is its virtue. Its limitation is that it is probably restricted to dilute salt and protein concentrations. To demonstrate the use of eq 11,the effect of increasing the ionic strength from 0.05 to 0.07 M on protein partitioning was examined. For given polymer feed compositions, increasing the ionic strength led to a slight increase in tie-line length, increases in the differences between the top and bottom phase cation concentrations, Am+= mBot + - m y , and a slight increase in the electrostatic potential difference for both NaCl and NaHzP04. These effects can be seen in the partition coefficient values of lysozyme in Figure 9. The lysozymepartition coefficient in NaCl increases as the total ionic strength of the solution is increased. Since the change in the electrostatic potential difference between the two phases due to the increase in the ionic strength of NaCl is small, the increase in the lysozyme partition coefficient is due to other effects. This is in agreement with the experimental results obtained by Albertsson (1986),who observed that increasing the ionic strength of NaCl resulted in the partitioning of lysozyme into the top phase. Increasing the ionic strength of NaH2PO4also results in an increase in the partition coefficient of the lysozyme (Figure 9). Comparing the values of the different contributions in eq 11, the increase in the
2300 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994
concentration of HP04- in the bottom phase may be the key factor in increasing the lysozyme partition coefficient. Equation 11shows that the dominant factors governing protein partitioning coefficients can be decoupled. This decoupling simplifies the thermodynamic description of protein partitioning and reduces the amount of experimental work necessary to obtain a complete set of model parameters. Measurements are only necessary to determine the contributions of the factors accounted for in eq 11. Other effects have only a minor impact upon protein partitioning.
Summary
The partitioning of BSA and lysozyme in aqueous twophase systems of polymers and salt (NaC1 and NaH2P04) has been studied. For both salts, BSA partitions preferentially into the bottom phase. However, different partitioning behavior for lysozyme is observed when different salts are used. In the case of NaC1, lysozyme partitions into the top phase, and the partition coefficient increases with increasing polymer concentrations. On the other hand, NaH2P04 causes lysozyme to partition preferentially into the bottom phase. The different partitioning behavior of the two proteins in the presence of the two electrolytes is attributed to the electrochemical potential difference between the phases, changes in the solvation properties of each phase due to the addition of the salt, and changes in the polymer compositions. We have developed a thermodynamic model to describe the role of polymer concentration, salt type, and pH on the protein partitioning in aqueous two-phase polymer solutions. The model accounts for interactions between the protein and the different components of the solution, and incorporates the effects of polymer-induced protein interactions, protein size, and the net surface charge of the protein. A simple three-parameter correlation for protein partitioning is obtained, and provides a means of correlating the partitioning of proteins in different aqueous two-phase mixtures of polymers and salt. Nomenclature a = average value of the s u m of the radii of pairs of hydrated ions B = Debye-Huckel parameter F = Faraday constant I = ionic strength K = protein partition coefficient Kel = electrostatic contribution to the partition coefficient KO = partition coefficient when A 9 = 0 mi = molality n, = number of moles of water R = gas constant zi = charge of ion i pij = short-range interaction coefficient yi = activity coefficient Aje = standard state activity of ion i pio = standard state chemical potential of component i \ki = electrostatic potential in phase i
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Received for review September 23, 1993 Revised manuscript received June 14, 1994 Accepted June 28, 1994' Abstract published in Advance ACS Abstracts, September 1, 1994.
