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Influence of surface structure on the ion exchange of proteins—The effect of protein charge on uptake of acid proteases
Reactive Polymers, 6 (1987) 21-31
21
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
INFLUENCE OF SURFACE S T R U C T U R E O N THE I O N EXCHANGE OF P R O T E I N S - - T H E EFFECT OF P R O T E I N CHARGE O N UPTAKE OF ACID P R O T E A S E S * ALFRED CARLSON
Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802 (U.S.A.) (Received May 29, 1986; accepted in revised form December 15, 1986)
This paper describes the results of a brief but systematic experimental investigation and mathematical analysis of the ion exchange of proteins. A preliminary model of protein ion exchange, which explains some of our own experimentally observed behavior, is developed The model emphasizes the influence of protein charge and solution ionic strength on the nature of the protein sorption isotherm. The experimental results and their comparison to model predictions have lead us to a new point of view on the mechanism of protein ion exchange and suggest that protein sorption, even to so called "coated" resins, is not a surface phenomenon but rather a bulk sorption process.
INTRODUCTION
Since the development of suitable resins in the early 1950s, ion-exchange chromatography has become the leading method for both laboratory and industrial-scale protein purifications. However, most studies of the process have been directed at the application of the method to a particular protein purification problem rather than at the fundamental aspects of the process itself. In fact, there is very little by way of a general understanding of ion exchange of proteins--the quantitative behavior of protein ion exchange remains obscure. Two protein sorption models have been * Paper presented at the Annual AIChE Conference, Chicago, IL, November 12-13, 1985.
proposed and used to fit limited experimental data. The first model [1] is based on the assumption that proteins sorb according to a Langmuir isotherm. The resin is assumed to have a certain affinity for the proteins, as measured by a binding constant, and a certain maximum capacity, as measured by the maximum uptake of the protein into the resin. A two-parameter model of this kind can be effective in describing protein isotherms well enough to aid in (for example) column breakthrough predictions, but does not use or describe any fundamental relationship between the resin and protein. Another model, which incorporates some fundamental relationships in the system, has recently been proposed [2]. The model is based on the assumption that sorption takes place at an internal surface of the resin. It specifi-
22
cally relates the salt concentration to the binding behavior in chromatographic retention systems. It also takes into account (indirectly) the charge on the protein. The model contains two adjustable parameters, one which describes the strength of the protein-resin interaction and another which correlates to the protein charge. The deficiencies inherent in the models mentioned above are significant. In the first model, each protein isotherm must be measured to obtain the Langmuir constants. There is no way to use the model to predict how changes in the resin, protein, or salt concentration will influence separation. Multiprotein sorption behavior is also not addressed by the model. In the second model, there is no real accounting for maximum uptake and the parameter describing the protein charge in the model does not correlate well with other charge predictors. Finally, the assumption that sorption is to a surface is hard to reconcile with the fact that gel resins have no interior surfaces and the polymer matrix is more closely represented as a homogeneous polymer phase. Definitive experimentation is needed to elucidate the mechanism of ion exchange before a better model can be developed. "Definitive" experiments of protein ion exchange are hard to design, however, since sorption behavior depends on molecular-level forces and interactions which are complex and difficult to predict. Most researchers agree that protein ion exchange should be influenced by the structure of the proteins. Simple reasoning tells one that protein structure will have a major impact on separation properties, since each molecule presents certain amino acids at its surface and these can interact with the separation media giving separation properties. Hydrophobic, hydrogen-bonding, and ionic groups all appear at the surface of proteins and can potentially participate in interactions with a resin.
The main effect of protein structure in ion-exchange systems seems to be the net charge of the protein. Proteins are polyionic and can carry large net positive or net negative charge. This amplifies the electrostatic interactions of the proteins with a resin relative to other binding mechanisms. One evidence for the importance of protein ionic groups on separation behavior is that changing the pH of the separation solution has a dramatic effect on the chromatographic retention time of the protein. The net charge on the protein is positive at low pH where only basic groups tend to be ionized, and negative at high pH where only acidic groups are ionized. One pH (the isoelectric pH or pI) exists where a given molecule has no net charge. Studies have shown that (in general) proteins are retained on cation exchange resins at pH values below their pI and on anion exchange resins at pH values above their pI. They tend to remain substantially unretained under all other conditions, presumably reflecting the effect of charge on the molecule and general rejection from a resin containing fixed charges of the same sign as the net charge on the molecule * If ionic effects are important, salts should also have a major influence on the retention of proteins in ion-exchange resins. In gradient elution systems, increases in the concentration of salt in the mobile phase cause "re* Some proteins also seem to be slightly retained at or even below (or above) their pI on anion (or cation) exchange resins, respectively. This has lead to another proposal that the particular distribution of ionic groups around the surface of the molecule may also influence retention. However, while certainly a factor in protein ion-exchange behavior, the magnitude of this effect has not been determined, nor has such behavior been correlated in any way to the structure of any particular molecule. Such a view does not take into account other (and in the author's view) more likely explanations for anomalous separation behavior. The idea that charge distribution influences separation behavior appears to be based on the unlikely assumption that ionic surfaces on a resin are responsible for protein binding [2].
23 lease" of protein from the resin and elution from the column [3]. In isocratic systems the salt concentration has" a major effect on the value of the retention factor for a given protein [2]. For example, it has been shown that there is a linear relationship between the logarithm of the retention factor and the logarithm of the salt concentration for several proteins on particular resins [2,4]. This sharp functional relationship between these parameters illustrates the magnitude of the salt effect. In addition, other experiments make it clear that the particular salt may also play a role in protein retention [5]. Our approach to developing an experimental study system is to use two homologous proteins as molecular probes for ion-exchange studies. The main difference between the two proteins is that they have different surface structures, particularly with respect to charged groups. The size, shape, and hydrophobicity/ hydrophilicity ratio of the molecules are similar, assuring that surface charge will dictate differences in separation behavior. Preliminary experiments (see text) showed that it is unlikely that the area available for surface sorption limits the uptake of these molecules in either gel-like or macroporous resins. This fact has led us to propose a homogeneous resin model of protein ion exchange, which takes into account the potential differences between the resin phase and external phase and the attractive effect of this difference for protein uptake into the resin. The model is based on Donnan equilibrium between the resin and external phase and includes a term for exclusion effects resulting from protein accumulation in the resin. The model both addresses the nature of the protein-resin interaction in a mechanistic manner, and predicts how salts and protein charge will influence binding behavior. It is particularly useful for predicting and understanding protein isotherms, but also can predict chromatography behavior in pulse-injection systems. We believe that this model con-
tains all the exchange and starting point of protein ion
main features of protein ion therefore can be considered a for more detailed descriptions exchange.
MATERIAL AND M E T H O D S The enzymes used in this study were purchased from Sigma Chemical Co. The chymosin was a purified preparation from calf stomach with a specific activity of 60 units/mg. The preparation was determined to be around 90% pure enzyme by A280 absorbance analysis in ion-exchange separation. The pepsin was a purified preparation of 3300 u n i t s / m g from hog stomach, also around 90% pure by UV analysis. The resins were commercial materials, DEAE-Sepharose ® from Pharmacia Inc. purchased from Sigma, and Accell ® QMA resin from Waters Inc. Non-fat dry milk used in the analysis was obtained from Beatrice Foods. All other chemicals were reagent grade or better from Sigma. In a typical experiment, a known amount of resin (usually 10 m g / m l ) was preequilibrated with 0.01 M imidazole buffer or buffer and salt solutions (pH 6.0) by repeated slurrying, settling and decanting of buffer. Enzymes were dissolved in the buffer or salt solution to the concentration of interest, generally 1.0 m g / m l , and then appropriate amounts of the protein were pipetted into 1.5 ml test tubes and mixed with buffer for a total volume of 950 ~1. An amount of 50/~1 of equilibrated resin slurry was added to the tubes with an automatic pipettor (with a cut tip to allow resin to enter). The tubes were sealed and rotated with a tumbling motion overnight ( - 14 h) to establish equilibrium. The supernatant from each tube was analyzed for enzymatic activity by injecting 2-5 /~1 into 1.0 ml of 2% reconstituted milk containing 0.01 M CaCI 2 at 3 0 ° C [6]. The
24 TABLE 1 Ionic charges on pepsin a n d chymosin Enzyme
Basic residues a
Pepsin Chymosin
Acidic residues b
Isoelectric
Net
R
K
H
D
E
point
charge ¢
2 4
1 9
1 6
30 19
13 10
< 1.0 4.6
- 39.5 - 13
a R = arginine, K = lysine, H = histidine. b D = aspartic acid, E = glutamic acid. ¢ N e t charge is c o m p u t e d at p H 6.0 assuming that R = + 1, K = + 1, H = + 1 / 2 , D = - 1 , a n d E = - 1 .
milk-containing tubes were rotated and clotting times were observed. The amount of active enzyme remaining in solution was then calculated by standard methods [7].
Protein description Chymosin and pepsin were chosen as the proteins for this study because they are closely related in structure and composition. Both molecules are from the acid protease family. Comparison of the primary structures to Xrays of other acid proteases indicates that both have similar tertiary structures. About 40% of the amino acids are different between the two molecules and most of the substitu-
Amino a c i d d i s t r i b u t i o n
tions ( - 80%) are on the molecules' surface. The main difference between the structure of chymosin and pepsin is in the number of acidic and basic residues. Pepsin has only 4 basic residues (2 arginine, 1 histidine, and 1 lysine) but 43 acid groups around its surface (see Fig. 1 and Table 1). Chymosin has 19 basic residues and 29 acidic residues on its surface. Because of these amino acid distributions, pepsin has a large net negative charge ( - 39.5) and low isoelectric point ( - 1.0) while chymosin has a charge of around - 13 (at pH 6.0) and an isoelectric point of 4.6. Other surface features of the two molecules are similar.
Amino a c i d d i s t r i b u t i o n
Peps in 128
Chymosin
hydrophoblc
i3t
hydrophobic ocldtc
340cldlc |9
basic
Oesic
i52
hydrophlllc
t39 nydrophtllc
Fig. 1. C o m p a r i s o n of the a m i n o acid make-up of porcine pepsin a n d bovine chymosin. Phe, Tyr, Trp, Val, Leu, Ile, Met, a n d Ala are considered hydrophobic. Ser, Thr, Gln, Asn, Cys, a n d Gly are considered hydrophilic. Asp a n d G l u are acidic. Lys, Arg, a n d His are basic.
25 2.00
RESULTS
c
Uptake Figures 2 and 3 show the results when chymosin and pepsin are sorbed at pH 6.0 to DEAE-Sepharose ® and Accell ® resins, respectively. The value of the intercept of a straight line with slope 1.0 extrapolated back to the x-axis represents the maximum amount of protein which can be sorbed to the amount of resin which had been added to the solution. The significant finding in this experiment is that the maximum amount of chymosin uptake is almost three times the amount of pepsin uptake on both resins. Accell sorbed about 0.3 mg of pepsin and 0.83 mg of chymosin per milligram of dry resin. Under the same conditions DEAE-Sepharose sorbed around 2.0 and 7.0 mg protein/mg of dry resin for each of the proteins, respectively. (The capacity difference is explained by the significantly different structures of the two resins--the volumetric capacities are similar because Sepharose is a much less dense resin.) Similar capacity measurements were made on Accell resin in systems containing different NaC1 concentrations. The experimental results are shown in Figs. 4 and 5. Whereas at 25 --
o
1.20
/
o,;; 080 k--
5m c 0~
o/° /
& 0.0
n
e/i 0.40 Protein
0.80
origlnally i n
t.20 1.60 solution-(mg/mg-resin)
Fig. 3. Sorption of pepsin and chymosin onto Accell ~.
0 M NaC1, maximum chymosin sorption was about three times that of pepsin (see above), as the salt concentration was increased to 0.1 M and 0.2 M, chymosin uptake dropped without much change in pepsin uptake. At 0.2 M NaC1 the uptake of chymosin was smaller than the uptake of pepsin. Further increases in the salt concentration to 0.5 and 1.0 M NaC1 (data not shown) caused the maximum uptake to drop to zero for both proteins.
Affinity When the data are replotted in normal isotherm form (as shown in Figs. 6 and 7), it .00
= 20 - -
2.00
0. BO
*O.OM °O.~M *0.2M ~0.5M
×
NaCI NaCl NaCI NaCI
/
/
0.50
/X
x/
c ~ m
0.40
~0--
/ c oJ
5
0
/ /
/
0.20
--
D/
&
D
%-/ 5~ ,-
* //
x
/
I
I
10 15 20 Protein originally in solution-(mg/mg-resin)
i 25
Fig. 2. Sorption of pepsin and chymosin onto DEAESepharose ®.
o.oo, 0.00
0.20
-/~
I
I
0.40
0.50
i 0 .BO
1.00
Protein originally in solution-(mg/mg-resin)
Fig. 4. Influence of salt concentration on the sorption of pepsin to Accell ® resin.
26
~..00 - -
+O.OM NaC] [ aO.IM NaCI I *0.2M NaCI|
0.60
~' o.6o
*
--
~o.~-N~e~'l
~- 0 . 8 0
x
D ~ .
L 0.40
-
.g 0.20
-/
D
#
/
o
• 0.00
0.20 0.40 0.60 0.80 Protein originally in solution-(mg/mg-resin)
i.O0
Fig. 5. Influence of salt concentration on the sorption of chymosin to Accell ® resin.
is clear that although the maximum uptake is greater for chymosin than pepsin at low salt, the affinity of chymosin for the resin is smaller than the affinity of pepsin. At all salt concentrations where sorption was observed, the pepsin isotherm is very steep, and the concentration in the resin is at a maximum even at low solution concentrations. In contrast, the chymosin isotherm is relatively shallow, and significant protein remains unbound at relatively high solution concentrations. This binding behavior for the two proteins leads to
a_ 0 . 0 0 f 0.00
.I J *I J t 0.20 0.40 0.60 0.80 :t.O0 P r o t e i n in s o q u t l o n - ( m g / m g - P e s i n )
Fig. 7. Isotherm plot of chymosin sorption to Accell ®.
a cross-over effect at low salt concentration, less chymosin than pepsin binding at low solution concentration but more chymosin than pepsin binding at high solution concentration. Finally, when the salt concentration is increased to 0.2 M, both the uptake and affinity of chymosin for the resin drop so that the chymosin isotherm is completely below the pepsin isotherm at all concentrations.
DISCUSSION
Experimental "~ 1 . 0 0
-
~0.80 E
i 0.60
-
c
L
0.40
~0.20
4-~
-
~-
o.
.
0-
o. oo 0.00
J,
.I
~1
.I
J,
0.20 0.40 0.60 0.80 P r o t e i n in s o l u t i o n - ( m g / m g - r e s i n )
1.00
Fig. 6. Isotherm plot of pepsin sorption to Accell ®.
The experimental results described above demonstrate two important features of protein isotherm behavior. The first feature is that the maximum sorption of proteins on ion exchange resins at low ionic strength is dictated by the protein charge and not its size. Other things being equal, as they are in the case of chymosin and pepsin, a greater amount of a protein with a lesser charge will sorb to a resin than will a protein with a greater charge. The sorption seems to be roughly inversely proportional to the net protein charge as determined by the amino acid composition. This is evidenced by the fact that both resins sorb three times as much chymosin, which has a
27 charge of - 1 3 , as pepsin, which has a charge of - 39. (While one may argue that this should be obvious, since the protein must titrate the resin charge, it has not been reported to our knowledge, and is contradictory to other models which are based on surface coverage assumptions.) The second feature of isotherm behavior illustrated by these experiments is that the maximum sorption and affinity for the resin are both influenced by the salt concentration and that the nature of the influence depends on the protein involved. For chymosin the isotherm maximum and the apparent affinity both drop gradually as the salt concentration increases. For pepsin, the binding remains high at 0.2 M NaC1 and there is a sudden decrease in binding capacity at 0.5 M salt. This data seems to illustrate that proteins with larger charges resist elution by salts more than lesser-charged molecules. M o d e l description
Data such as described above signify the complex behavior that is to be expected in protein sorption systems, and rule out the simple behavior of other proposed models. We also think that the data indicate that a new model of protein sorption is warranted, and suggest the following as an alternative to previous models. In this analysis, we consider the resin and included solvent as a separate and homogeneous phase containing evenly distributed fixed charges. All other ions in the system are mobile and can freely distribute between the resin and the external phases. For simplicity, the system can be assumed to consist of only three types of mobile ion: (1) a cation (c) of charge zc; (2) an anion (a) of charge Za; and (3) a protein of net charge zp. Thermodynamic arguments dictate that the mobile ions will distribute between the resin and external phases in such a way as to make the electrochemical potentials (~te) constant
everywhere in the system. Between the two phases,
(1)
t
~a =/La t
(2)
!
(3)
where we use the (') to indicate the resin phase; absence of a superscript refers to the external phase. The electrochemical potential for each species can be formally represented as the sum of a purely "chemical" potential and an electrostatic term which accounts for the ionic charge on the species: ~i = l~io + R T
In a i + ZiCp
(4)
Here a, is the activity of species i, /~0 is the standard-state chemical potential of the species, and qo is the local electrical potential to which the species is exposed. The local electrical potential is generally a function of position within the system. This function can be determined by properly solving Poisson's equation for the two phases with appropriate boundary conditions. (See Ref. [8] for example.) But under normal conditions there is a practical discontinuity in the potential at the phase boundary, and the electrical potential is approximately constant within each phase. In such a case, a singlephase potential can be used to represent the electrochemical potential of a species in a given phase. Making an additional assumption that the system behaves "ideally" allows one to replace the activity with the concentration of the species to give, ~#a = tZ~O + R T
In CJa + Za(~ j
(5)
In C¢J + z~cpj
(6)
and J + RT I~cJ-- I~co
for the anion and cation species within the j t h phase respectively. From eqns. (1) and (2)
28
one can obtain, R T In C ~ / C , = G ( ep - ep' )
of the polymer, (7)
G = Go + RT[In
+ (1-
and R T In C ~ / C c = zc(eg - ep')
G = Go + Rr[ln v/, + (1 -
+ zp J (9)
where here we have added the electrostatic term to the standard Flory expression for chemical potential. The term Vp is the volume fraction of the solvent, and 0 is the ratio of the molecular volumes of the protein and solvent * (10)
O = Vv/Vo
The equation can be further simplified by assuming that the volume fraction of the resin material within the resin phase is small so that, t
v~- 1-Vp
+ZpCp;
(8)
These equations relate the concentrations of the anion and cation in each of the phases to the difference in the electrostatic potential and the charge on the species, and are the "Donnan" equations for these two ionic species. The third mobile species (the protein) is a macromolecule and it is much larger than the solvent (water) species. Because of this difference in molecular size, free-volume theories will predict that entropy of mixing effects will not be the same as they would be when small molecules are mixed. In such a case, the electrochemical potential of the protein must include terms for the volume fraction of the protein and for the relative difference in size of the protein and solvent. Accordingly, as in Flory-Huggins theory [9], for the protein,
(11)
which gives for the electrochemical potential * The molar volume of the polymer has been taken to be infinity on the grounds that the resin can be considered a single large molecule. This has the peculiar effect that the resin does not enter into this equation.
p)(1- v~)] (12)
Equation (12) is the protein equilibrium analogue of eqns. (5) and (6). Practically speaking, it is safe to assume that the volume fraction of protein in the external phase is very small in almost all systems and can therefore be neglected in the external-phase electrochemical potential equation. With this assumption, equating the electrochemical potentials in the two phases gives, RT[lnvp/Vp+(p-1)Vp]=Zp(Cp-cp')
(13)
This is the analogue of eqns. (7) and (8). The relationship between the concentration of protein outside the resin and inside the resin can be solved in terms of the composition of the salts in the external phase if certain additional assumptions are made. The main assumption is that the resin phase is electrically neutral. To a very close approximation, the local charge density within the resin will be zero everywhere except in a thin region very near the resin-external phase interface. In this case, if the fixed charges on the resin are cationic, C o + zpCp + ZaC; + zcC~' = 0
(14)
C', C', and Cp refer to the concentration of anion, cation and protein in the resin and Co refers to the concentration of fixed charges within the resin phase. The molar concentration of the protein can be related to the volume fraction of the protein through the molar volume of the molecule, (Vp), C;-
t
op/Vp
(15)
with this substitution and rearrangement, eqn. (14) can be written as, Z t t ! 1 ~'- p U p / C o Yp q- z a C a / C 0 -J¢-Z c C c / C 0
0
(16)
29 Equations (7), (8), and (13) can be used together to relate the ratios of the anion and cation concentrations to the volume fraction of the protein in the two phases, t
t
!
In C ' / C a = z , / Z p In % / % + ( P - 1 ) % Z J Z p
(17) and !
t
In C ' / C ~ = Zp/Zc In Up~Up + (p -- l)VpZc/Z p
(18) These can be rearranged to give, C; = C a ( v ; / V p ) zjzp e x p [ ( p
-
l)V;Za/Zp]
(19) and
The parameter a is the ratio of the charge concentration for anions in the external phase to the fixed-charge concentration in the resin. The parameter 7 is the charge concentration ratio (note sign) of the cation in the external phase to the resin charge concentration, and fi is a parameter which reflects the relative size of the protein molecule to the fixed-charge density within the resin. The variable ~ ' has the physical significance that it is the fractional protein uptake required to neutralize the resin. In most actual systems the concentration of salts in the external phase is the same as the concentration of salts initially dissolved in the buffer and, ZaCa = - zcC c
C" = Cc(%/C,p) zJ% e x p [ ( p - l)%zc/Zp]
If the salt used is an equivalent salt,
(20) Equations (19) and (20) can be used to eliminate Ca and Cc in eqn. (16) to give, t
×exp[(p
-
1)V;Za/Zp]
--Z c
t
× e x p [ ( p - 1)VpZJZp] = 0
(21)
By defining the following dimensionless parameters and variables: OL= - z a C a / C 0
(22)
~, = - z ~ C J C o
(23)
fl = (P - 1) CoVp
(24)
and t
(25)
• " = -Zp%/CoV p
(26)
= -ZpUp/CoV p
the equation can be written
fi*tZa/Z 2 )
-y((I)'/(I)) zjzp exp(-fl(I) t z c / Z p2 ) = O
(29)
and a simplified form of eqn. (27) is,
+ a ( * ' / < b ) --'"/-'" e x p ( f l * ' Z a / Z 2 ) = O
+ ( Z c C J C o ) ( Up/Up '" ]
1 - qS'- a ( * ' / * ) z,/z, e x p ( -
Za =
1 - * ' - a(qS'/qS) z,,/~ e x p ( - f l * ' Z a / Z 2)
¢
1 + zp%/CoVp +
(28)
(27)
(30)
This equation describes an isotherm for protein sorption which takes into account the effect of protein size, charge, and external phase salt concentration. We use this below to investigate the shape of protein isotherms under various conditions. Model results
The model described above qualitatively predicts the behavior observed experimentally with chymosin and pepsin sorption on Accell resin. At low salt concentration, a maximum sorption, dictated by the net protein charge and concentration of fixed charges within the resin, is predicted by the model ( q S ' ~ 1.0). The protein charge affects the shape of the isotherm, primarily by changing the affinity for the resin (Fig. 8), but also dictates the
30
alpha - 0.I0;
1.00
Oeta = I00
z p / z a - 30
alpha
1.00
--
= 0.1;
zp/za
=
iO
r"
beta
=
lO
beta
-
lO0
beta
~
iO00
.5 0.80 -
.5 0.8o zp/za
10
=
f
k
L
S o. 8o
.5 0.60 ~ /
5
.5 03 g 0.40 k
03
"~ 0.40
O_ 03 03 >
-~ 0.20 ,-.-i
g: o ~
__
7p/z- ~ 4J
-
f
O. 20 f
I
I
I
L
I
o.oo
Fig. 8. Effect of protein charge on the uptake of protein into an ion exchange resin (z a is assumed to be 1.0).
I
I
I
l
I
0.00 0.10 0.20 0.30 0.40 0.50 R e l a t i v e p r o t e i n in s o l u t i o n (x 1000)
' 0~. O0 O. I0 0.20 0.30 0.40 0.50 R e l a t i v e p r o t e i n in s o l u t i o n (x 1000)
Fig. 10. Effect of protein size (fl) on the uptake of protein into an ion exchange resin (z a is assumed to be
1.o). maximum uptake by competition with the salt. The isotherms are dramatically influenced by the salt concentration. For proteins with small charges, the model predicts a significant drop in both the affinity and capacity of the resin as salt is added (Fig. 9). The reduction in the maximum binding is larger for lessercharged molecules than it is for higher-charged molecules. (Calculations not shown.)
1,00 -
b e t a = t00;
z p / z e = t0
Finally, the molecular size of the protein has an effect on binding behavior (Fig. 10). For a given resin, the larger the molecules, the fewer that bind. Beta values for protein systems are typically between 100 and 1000. Although we have not explored all the combinations of these effects in this brief report, it is clear that the main parameters of influencing the isotherm behavior are the ratio of the protein and displacing (salt) ion charge, the dimensionless salt concentration, a, and the exclusion parameter, ft.
alpha = 0.01
CONCLUSIONS
O. 80 alpha -
0.I0
c_
.5 o.6o - I -
S 03
go.4o CCI e3 >
%
alpha
= 0.50
0.20 --
Y: o.oo / "
I
I
I
I
1
0.00 O. 10 0.20 0.30 0.40 0.50 R e l a t i v e p r o t e i n in s o l u t i o n (x 1000)
Fig. 9. Effect of external phase salt concentration on uptake of protein into an ion exchange resin (z~ is assumed to be 1.0).
We have made no attempt to fit the experimental data to the model predictions, yet it is clear that the model has characteristics seen in the experimental data which go beyond fortuitous behavior. For instance, no other model can predict accurately that similar molecules with different charges will be influenced by the salt concentration in the way pepsin and chymosin are, nor do other models predict the stoichiometric sorption observed for the molecules. More than others, this model is based on
31
reasonable physical assumptions. For example, the assumption that the resin is a homogeneous phase is justifiable for most soft gel resins, since there is no internal "pore structure" for these gels and since the spacing of the ionic groups inside the resin is relatively small compared with the size of the molecules. In addition, even in so-called "coated" resins, where the resin particle does have an internal pore structure, it is reasonable to assume that there is a surface layer of resin polymer which is thick enough to be considered a separate phase. In such a case there would be a potential difference between the polymer phase (coating) inside the pore and the free pore space. All other assumptions of the model would hold and the same result would be obtained. Probably the most severe assumptions of the model are those surrounding the relationship between the activity of the species of interest and the concentration. Any specific interactions between the resin ions and the protein or salt ions could change the actual binding behavior as compared with model predictions since the predicted behavior is based on the assumption that interactions are purely electrostatic. Further work will be required to determine the magnitude of these effects and to elucidate how important interactions other than pure electrostatic ones are
on the sorption behavior of various molecules. REFERENCES 1 Hai-Shung Tsou, Adsorption kinetics of proteins on sephadex ion exchanger, M.Sc. Thesis, Chemical Engineering, The Pennsylvania State University, 1983. 2 W. Kopaciewicz, M.A. Rounds, J. Fausnaugh and F.E. Regnier, Retention model for high-performance ion-exchange chromatography, J. Chromatogr., 266 (1983) 3-21. 3 K.M. Gooding and M.N. Schmuck, Ion selectivity in the high-performance cation-exchange chromatography of proteins, J. Chromatogr., 296 (1984) 321-328. 4 M.A. Rounds and F.E. Regnier, Evaluation of a retention model for high-performance ion-exchange chromatography using two different displacing salts, J. Chromatogr., 283 (1984) 37-45. 5 L.R. Snyder and J.J. Kirkland, Introduction to Modern Liquid Chromatography, Wiley, New York, NY, 1979, p. 422. 6 A. Carlson, The enzymatic coagulation of milk, Ph.D. Thesis, Chemical Engineering, University of Wisconsin-Madison, 1982. 7 A. Carlson, C.G. Hill Jr. and N.F. Olson, Improved assay procedure for determination of milk clotting enzymes, J. Dairy Sci., 68 (1985) 290-299. 8 S. Ohki and H. Ohshima, Donnan potential and surface potential of a charged membrane and the effect of ion binding on the potential profile, in: M. Blank (Ed.), Electrical Double Layers in Biology, Plenum Press, New York, NY, 1986. 9 P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca and London, 1971, p. 512.
21
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
INFLUENCE OF SURFACE S T R U C T U R E O N THE I O N EXCHANGE OF P R O T E I N S - - T H E EFFECT OF P R O T E I N CHARGE O N UPTAKE OF ACID P R O T E A S E S * ALFRED CARLSON
Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802 (U.S.A.) (Received May 29, 1986; accepted in revised form December 15, 1986)
This paper describes the results of a brief but systematic experimental investigation and mathematical analysis of the ion exchange of proteins. A preliminary model of protein ion exchange, which explains some of our own experimentally observed behavior, is developed The model emphasizes the influence of protein charge and solution ionic strength on the nature of the protein sorption isotherm. The experimental results and their comparison to model predictions have lead us to a new point of view on the mechanism of protein ion exchange and suggest that protein sorption, even to so called "coated" resins, is not a surface phenomenon but rather a bulk sorption process.
INTRODUCTION
Since the development of suitable resins in the early 1950s, ion-exchange chromatography has become the leading method for both laboratory and industrial-scale protein purifications. However, most studies of the process have been directed at the application of the method to a particular protein purification problem rather than at the fundamental aspects of the process itself. In fact, there is very little by way of a general understanding of ion exchange of proteins--the quantitative behavior of protein ion exchange remains obscure. Two protein sorption models have been * Paper presented at the Annual AIChE Conference, Chicago, IL, November 12-13, 1985.
proposed and used to fit limited experimental data. The first model [1] is based on the assumption that proteins sorb according to a Langmuir isotherm. The resin is assumed to have a certain affinity for the proteins, as measured by a binding constant, and a certain maximum capacity, as measured by the maximum uptake of the protein into the resin. A two-parameter model of this kind can be effective in describing protein isotherms well enough to aid in (for example) column breakthrough predictions, but does not use or describe any fundamental relationship between the resin and protein. Another model, which incorporates some fundamental relationships in the system, has recently been proposed [2]. The model is based on the assumption that sorption takes place at an internal surface of the resin. It specifi-
22
cally relates the salt concentration to the binding behavior in chromatographic retention systems. It also takes into account (indirectly) the charge on the protein. The model contains two adjustable parameters, one which describes the strength of the protein-resin interaction and another which correlates to the protein charge. The deficiencies inherent in the models mentioned above are significant. In the first model, each protein isotherm must be measured to obtain the Langmuir constants. There is no way to use the model to predict how changes in the resin, protein, or salt concentration will influence separation. Multiprotein sorption behavior is also not addressed by the model. In the second model, there is no real accounting for maximum uptake and the parameter describing the protein charge in the model does not correlate well with other charge predictors. Finally, the assumption that sorption is to a surface is hard to reconcile with the fact that gel resins have no interior surfaces and the polymer matrix is more closely represented as a homogeneous polymer phase. Definitive experimentation is needed to elucidate the mechanism of ion exchange before a better model can be developed. "Definitive" experiments of protein ion exchange are hard to design, however, since sorption behavior depends on molecular-level forces and interactions which are complex and difficult to predict. Most researchers agree that protein ion exchange should be influenced by the structure of the proteins. Simple reasoning tells one that protein structure will have a major impact on separation properties, since each molecule presents certain amino acids at its surface and these can interact with the separation media giving separation properties. Hydrophobic, hydrogen-bonding, and ionic groups all appear at the surface of proteins and can potentially participate in interactions with a resin.
The main effect of protein structure in ion-exchange systems seems to be the net charge of the protein. Proteins are polyionic and can carry large net positive or net negative charge. This amplifies the electrostatic interactions of the proteins with a resin relative to other binding mechanisms. One evidence for the importance of protein ionic groups on separation behavior is that changing the pH of the separation solution has a dramatic effect on the chromatographic retention time of the protein. The net charge on the protein is positive at low pH where only basic groups tend to be ionized, and negative at high pH where only acidic groups are ionized. One pH (the isoelectric pH or pI) exists where a given molecule has no net charge. Studies have shown that (in general) proteins are retained on cation exchange resins at pH values below their pI and on anion exchange resins at pH values above their pI. They tend to remain substantially unretained under all other conditions, presumably reflecting the effect of charge on the molecule and general rejection from a resin containing fixed charges of the same sign as the net charge on the molecule * If ionic effects are important, salts should also have a major influence on the retention of proteins in ion-exchange resins. In gradient elution systems, increases in the concentration of salt in the mobile phase cause "re* Some proteins also seem to be slightly retained at or even below (or above) their pI on anion (or cation) exchange resins, respectively. This has lead to another proposal that the particular distribution of ionic groups around the surface of the molecule may also influence retention. However, while certainly a factor in protein ion-exchange behavior, the magnitude of this effect has not been determined, nor has such behavior been correlated in any way to the structure of any particular molecule. Such a view does not take into account other (and in the author's view) more likely explanations for anomalous separation behavior. The idea that charge distribution influences separation behavior appears to be based on the unlikely assumption that ionic surfaces on a resin are responsible for protein binding [2].
23 lease" of protein from the resin and elution from the column [3]. In isocratic systems the salt concentration has" a major effect on the value of the retention factor for a given protein [2]. For example, it has been shown that there is a linear relationship between the logarithm of the retention factor and the logarithm of the salt concentration for several proteins on particular resins [2,4]. This sharp functional relationship between these parameters illustrates the magnitude of the salt effect. In addition, other experiments make it clear that the particular salt may also play a role in protein retention [5]. Our approach to developing an experimental study system is to use two homologous proteins as molecular probes for ion-exchange studies. The main difference between the two proteins is that they have different surface structures, particularly with respect to charged groups. The size, shape, and hydrophobicity/ hydrophilicity ratio of the molecules are similar, assuring that surface charge will dictate differences in separation behavior. Preliminary experiments (see text) showed that it is unlikely that the area available for surface sorption limits the uptake of these molecules in either gel-like or macroporous resins. This fact has led us to propose a homogeneous resin model of protein ion exchange, which takes into account the potential differences between the resin phase and external phase and the attractive effect of this difference for protein uptake into the resin. The model is based on Donnan equilibrium between the resin and external phase and includes a term for exclusion effects resulting from protein accumulation in the resin. The model both addresses the nature of the protein-resin interaction in a mechanistic manner, and predicts how salts and protein charge will influence binding behavior. It is particularly useful for predicting and understanding protein isotherms, but also can predict chromatography behavior in pulse-injection systems. We believe that this model con-
tains all the exchange and starting point of protein ion
main features of protein ion therefore can be considered a for more detailed descriptions exchange.
MATERIAL AND M E T H O D S The enzymes used in this study were purchased from Sigma Chemical Co. The chymosin was a purified preparation from calf stomach with a specific activity of 60 units/mg. The preparation was determined to be around 90% pure enzyme by A280 absorbance analysis in ion-exchange separation. The pepsin was a purified preparation of 3300 u n i t s / m g from hog stomach, also around 90% pure by UV analysis. The resins were commercial materials, DEAE-Sepharose ® from Pharmacia Inc. purchased from Sigma, and Accell ® QMA resin from Waters Inc. Non-fat dry milk used in the analysis was obtained from Beatrice Foods. All other chemicals were reagent grade or better from Sigma. In a typical experiment, a known amount of resin (usually 10 m g / m l ) was preequilibrated with 0.01 M imidazole buffer or buffer and salt solutions (pH 6.0) by repeated slurrying, settling and decanting of buffer. Enzymes were dissolved in the buffer or salt solution to the concentration of interest, generally 1.0 m g / m l , and then appropriate amounts of the protein were pipetted into 1.5 ml test tubes and mixed with buffer for a total volume of 950 ~1. An amount of 50/~1 of equilibrated resin slurry was added to the tubes with an automatic pipettor (with a cut tip to allow resin to enter). The tubes were sealed and rotated with a tumbling motion overnight ( - 14 h) to establish equilibrium. The supernatant from each tube was analyzed for enzymatic activity by injecting 2-5 /~1 into 1.0 ml of 2% reconstituted milk containing 0.01 M CaCI 2 at 3 0 ° C [6]. The
24 TABLE 1 Ionic charges on pepsin a n d chymosin Enzyme
Basic residues a
Pepsin Chymosin
Acidic residues b
Isoelectric
Net
R
K
H
D
E
point
charge ¢
2 4
1 9
1 6
30 19
13 10
< 1.0 4.6
- 39.5 - 13
a R = arginine, K = lysine, H = histidine. b D = aspartic acid, E = glutamic acid. ¢ N e t charge is c o m p u t e d at p H 6.0 assuming that R = + 1, K = + 1, H = + 1 / 2 , D = - 1 , a n d E = - 1 .
milk-containing tubes were rotated and clotting times were observed. The amount of active enzyme remaining in solution was then calculated by standard methods [7].
Protein description Chymosin and pepsin were chosen as the proteins for this study because they are closely related in structure and composition. Both molecules are from the acid protease family. Comparison of the primary structures to Xrays of other acid proteases indicates that both have similar tertiary structures. About 40% of the amino acids are different between the two molecules and most of the substitu-
Amino a c i d d i s t r i b u t i o n
tions ( - 80%) are on the molecules' surface. The main difference between the structure of chymosin and pepsin is in the number of acidic and basic residues. Pepsin has only 4 basic residues (2 arginine, 1 histidine, and 1 lysine) but 43 acid groups around its surface (see Fig. 1 and Table 1). Chymosin has 19 basic residues and 29 acidic residues on its surface. Because of these amino acid distributions, pepsin has a large net negative charge ( - 39.5) and low isoelectric point ( - 1.0) while chymosin has a charge of around - 13 (at pH 6.0) and an isoelectric point of 4.6. Other surface features of the two molecules are similar.
Amino a c i d d i s t r i b u t i o n
Peps in 128
Chymosin
hydrophoblc
i3t
hydrophobic ocldtc
340cldlc |9
basic
Oesic
i52
hydrophlllc
t39 nydrophtllc
Fig. 1. C o m p a r i s o n of the a m i n o acid make-up of porcine pepsin a n d bovine chymosin. Phe, Tyr, Trp, Val, Leu, Ile, Met, a n d Ala are considered hydrophobic. Ser, Thr, Gln, Asn, Cys, a n d Gly are considered hydrophilic. Asp a n d G l u are acidic. Lys, Arg, a n d His are basic.
25 2.00
RESULTS
c
Uptake Figures 2 and 3 show the results when chymosin and pepsin are sorbed at pH 6.0 to DEAE-Sepharose ® and Accell ® resins, respectively. The value of the intercept of a straight line with slope 1.0 extrapolated back to the x-axis represents the maximum amount of protein which can be sorbed to the amount of resin which had been added to the solution. The significant finding in this experiment is that the maximum amount of chymosin uptake is almost three times the amount of pepsin uptake on both resins. Accell sorbed about 0.3 mg of pepsin and 0.83 mg of chymosin per milligram of dry resin. Under the same conditions DEAE-Sepharose sorbed around 2.0 and 7.0 mg protein/mg of dry resin for each of the proteins, respectively. (The capacity difference is explained by the significantly different structures of the two resins--the volumetric capacities are similar because Sepharose is a much less dense resin.) Similar capacity measurements were made on Accell resin in systems containing different NaC1 concentrations. The experimental results are shown in Figs. 4 and 5. Whereas at 25 --
o
1.20
/
o,;; 080 k--
5m c 0~
o/° /
& 0.0
n
e/i 0.40 Protein
0.80
origlnally i n
t.20 1.60 solution-(mg/mg-resin)
Fig. 3. Sorption of pepsin and chymosin onto Accell ~.
0 M NaC1, maximum chymosin sorption was about three times that of pepsin (see above), as the salt concentration was increased to 0.1 M and 0.2 M, chymosin uptake dropped without much change in pepsin uptake. At 0.2 M NaC1 the uptake of chymosin was smaller than the uptake of pepsin. Further increases in the salt concentration to 0.5 and 1.0 M NaC1 (data not shown) caused the maximum uptake to drop to zero for both proteins.
Affinity When the data are replotted in normal isotherm form (as shown in Figs. 6 and 7), it .00
= 20 - -
2.00
0. BO
*O.OM °O.~M *0.2M ~0.5M
×
NaCI NaCl NaCI NaCI
/
/
0.50
/X
x/
c ~ m
0.40
~0--
/ c oJ
5
0
/ /
/
0.20
--
D/
&
D
%-/ 5~ ,-
* //
x
/
I
I
10 15 20 Protein originally in solution-(mg/mg-resin)
i 25
Fig. 2. Sorption of pepsin and chymosin onto DEAESepharose ®.
o.oo, 0.00
0.20
-/~
I
I
0.40
0.50
i 0 .BO
1.00
Protein originally in solution-(mg/mg-resin)
Fig. 4. Influence of salt concentration on the sorption of pepsin to Accell ® resin.
26
~..00 - -
+O.OM NaC] [ aO.IM NaCI I *0.2M NaCI|
0.60
~' o.6o
*
--
~o.~-N~e~'l
~- 0 . 8 0
x
D ~ .
L 0.40
-
.g 0.20
-/
D
#
/
o
• 0.00
0.20 0.40 0.60 0.80 Protein originally in solution-(mg/mg-resin)
i.O0
Fig. 5. Influence of salt concentration on the sorption of chymosin to Accell ® resin.
is clear that although the maximum uptake is greater for chymosin than pepsin at low salt, the affinity of chymosin for the resin is smaller than the affinity of pepsin. At all salt concentrations where sorption was observed, the pepsin isotherm is very steep, and the concentration in the resin is at a maximum even at low solution concentrations. In contrast, the chymosin isotherm is relatively shallow, and significant protein remains unbound at relatively high solution concentrations. This binding behavior for the two proteins leads to
a_ 0 . 0 0 f 0.00
.I J *I J t 0.20 0.40 0.60 0.80 :t.O0 P r o t e i n in s o q u t l o n - ( m g / m g - P e s i n )
Fig. 7. Isotherm plot of chymosin sorption to Accell ®.
a cross-over effect at low salt concentration, less chymosin than pepsin binding at low solution concentration but more chymosin than pepsin binding at high solution concentration. Finally, when the salt concentration is increased to 0.2 M, both the uptake and affinity of chymosin for the resin drop so that the chymosin isotherm is completely below the pepsin isotherm at all concentrations.
DISCUSSION
Experimental "~ 1 . 0 0
-
~0.80 E
i 0.60
-
c
L
0.40
~0.20
4-~
-
~-
o.
.
0-
o. oo 0.00
J,
.I
~1
.I
J,
0.20 0.40 0.60 0.80 P r o t e i n in s o l u t i o n - ( m g / m g - r e s i n )
1.00
Fig. 6. Isotherm plot of pepsin sorption to Accell ®.
The experimental results described above demonstrate two important features of protein isotherm behavior. The first feature is that the maximum sorption of proteins on ion exchange resins at low ionic strength is dictated by the protein charge and not its size. Other things being equal, as they are in the case of chymosin and pepsin, a greater amount of a protein with a lesser charge will sorb to a resin than will a protein with a greater charge. The sorption seems to be roughly inversely proportional to the net protein charge as determined by the amino acid composition. This is evidenced by the fact that both resins sorb three times as much chymosin, which has a
27 charge of - 1 3 , as pepsin, which has a charge of - 39. (While one may argue that this should be obvious, since the protein must titrate the resin charge, it has not been reported to our knowledge, and is contradictory to other models which are based on surface coverage assumptions.) The second feature of isotherm behavior illustrated by these experiments is that the maximum sorption and affinity for the resin are both influenced by the salt concentration and that the nature of the influence depends on the protein involved. For chymosin the isotherm maximum and the apparent affinity both drop gradually as the salt concentration increases. For pepsin, the binding remains high at 0.2 M NaC1 and there is a sudden decrease in binding capacity at 0.5 M salt. This data seems to illustrate that proteins with larger charges resist elution by salts more than lesser-charged molecules. M o d e l description
Data such as described above signify the complex behavior that is to be expected in protein sorption systems, and rule out the simple behavior of other proposed models. We also think that the data indicate that a new model of protein sorption is warranted, and suggest the following as an alternative to previous models. In this analysis, we consider the resin and included solvent as a separate and homogeneous phase containing evenly distributed fixed charges. All other ions in the system are mobile and can freely distribute between the resin and the external phases. For simplicity, the system can be assumed to consist of only three types of mobile ion: (1) a cation (c) of charge zc; (2) an anion (a) of charge Za; and (3) a protein of net charge zp. Thermodynamic arguments dictate that the mobile ions will distribute between the resin and external phases in such a way as to make the electrochemical potentials (~te) constant
everywhere in the system. Between the two phases,
(1)
t
~a =/La t
(2)
!
(3)
where we use the (') to indicate the resin phase; absence of a superscript refers to the external phase. The electrochemical potential for each species can be formally represented as the sum of a purely "chemical" potential and an electrostatic term which accounts for the ionic charge on the species: ~i = l~io + R T
In a i + ZiCp
(4)
Here a, is the activity of species i, /~0 is the standard-state chemical potential of the species, and qo is the local electrical potential to which the species is exposed. The local electrical potential is generally a function of position within the system. This function can be determined by properly solving Poisson's equation for the two phases with appropriate boundary conditions. (See Ref. [8] for example.) But under normal conditions there is a practical discontinuity in the potential at the phase boundary, and the electrical potential is approximately constant within each phase. In such a case, a singlephase potential can be used to represent the electrochemical potential of a species in a given phase. Making an additional assumption that the system behaves "ideally" allows one to replace the activity with the concentration of the species to give, ~#a = tZ~O + R T
In CJa + Za(~ j
(5)
In C¢J + z~cpj
(6)
and J + RT I~cJ-- I~co
for the anion and cation species within the j t h phase respectively. From eqns. (1) and (2)
28
one can obtain, R T In C ~ / C , = G ( ep - ep' )
of the polymer, (7)
G = Go + RT[In
+ (1-
and R T In C ~ / C c = zc(eg - ep')
G = Go + Rr[ln v/, + (1 -
+ zp J (9)
where here we have added the electrostatic term to the standard Flory expression for chemical potential. The term Vp is the volume fraction of the solvent, and 0 is the ratio of the molecular volumes of the protein and solvent * (10)
O = Vv/Vo
The equation can be further simplified by assuming that the volume fraction of the resin material within the resin phase is small so that, t
v~- 1-Vp
+ZpCp;
(8)
These equations relate the concentrations of the anion and cation in each of the phases to the difference in the electrostatic potential and the charge on the species, and are the "Donnan" equations for these two ionic species. The third mobile species (the protein) is a macromolecule and it is much larger than the solvent (water) species. Because of this difference in molecular size, free-volume theories will predict that entropy of mixing effects will not be the same as they would be when small molecules are mixed. In such a case, the electrochemical potential of the protein must include terms for the volume fraction of the protein and for the relative difference in size of the protein and solvent. Accordingly, as in Flory-Huggins theory [9], for the protein,
(11)
which gives for the electrochemical potential * The molar volume of the polymer has been taken to be infinity on the grounds that the resin can be considered a single large molecule. This has the peculiar effect that the resin does not enter into this equation.
p)(1- v~)] (12)
Equation (12) is the protein equilibrium analogue of eqns. (5) and (6). Practically speaking, it is safe to assume that the volume fraction of protein in the external phase is very small in almost all systems and can therefore be neglected in the external-phase electrochemical potential equation. With this assumption, equating the electrochemical potentials in the two phases gives, RT[lnvp/Vp+(p-1)Vp]=Zp(Cp-cp')
(13)
This is the analogue of eqns. (7) and (8). The relationship between the concentration of protein outside the resin and inside the resin can be solved in terms of the composition of the salts in the external phase if certain additional assumptions are made. The main assumption is that the resin phase is electrically neutral. To a very close approximation, the local charge density within the resin will be zero everywhere except in a thin region very near the resin-external phase interface. In this case, if the fixed charges on the resin are cationic, C o + zpCp + ZaC; + zcC~' = 0
(14)
C', C', and Cp refer to the concentration of anion, cation and protein in the resin and Co refers to the concentration of fixed charges within the resin phase. The molar concentration of the protein can be related to the volume fraction of the protein through the molar volume of the molecule, (Vp), C;-
t
op/Vp
(15)
with this substitution and rearrangement, eqn. (14) can be written as, Z t t ! 1 ~'- p U p / C o Yp q- z a C a / C 0 -J¢-Z c C c / C 0
0
(16)
29 Equations (7), (8), and (13) can be used together to relate the ratios of the anion and cation concentrations to the volume fraction of the protein in the two phases, t
t
!
In C ' / C a = z , / Z p In % / % + ( P - 1 ) % Z J Z p
(17) and !
t
In C ' / C ~ = Zp/Zc In Up~Up + (p -- l)VpZc/Z p
(18) These can be rearranged to give, C; = C a ( v ; / V p ) zjzp e x p [ ( p
-
l)V;Za/Zp]
(19) and
The parameter a is the ratio of the charge concentration for anions in the external phase to the fixed-charge concentration in the resin. The parameter 7 is the charge concentration ratio (note sign) of the cation in the external phase to the resin charge concentration, and fi is a parameter which reflects the relative size of the protein molecule to the fixed-charge density within the resin. The variable ~ ' has the physical significance that it is the fractional protein uptake required to neutralize the resin. In most actual systems the concentration of salts in the external phase is the same as the concentration of salts initially dissolved in the buffer and, ZaCa = - zcC c
C" = Cc(%/C,p) zJ% e x p [ ( p - l)%zc/Zp]
If the salt used is an equivalent salt,
(20) Equations (19) and (20) can be used to eliminate Ca and Cc in eqn. (16) to give, t
×exp[(p
-
1)V;Za/Zp]
--Z c
t
× e x p [ ( p - 1)VpZJZp] = 0
(21)
By defining the following dimensionless parameters and variables: OL= - z a C a / C 0
(22)
~, = - z ~ C J C o
(23)
fl = (P - 1) CoVp
(24)
and t
(25)
• " = -Zp%/CoV p
(26)
= -ZpUp/CoV p
the equation can be written
fi*tZa/Z 2 )
-y((I)'/(I)) zjzp exp(-fl(I) t z c / Z p2 ) = O
(29)
and a simplified form of eqn. (27) is,
+ a ( * ' / < b ) --'"/-'" e x p ( f l * ' Z a / Z 2 ) = O
+ ( Z c C J C o ) ( Up/Up '" ]
1 - qS'- a ( * ' / * ) z,/z, e x p ( -
Za =
1 - * ' - a(qS'/qS) z,,/~ e x p ( - f l * ' Z a / Z 2)
¢
1 + zp%/CoVp +
(28)
(27)
(30)
This equation describes an isotherm for protein sorption which takes into account the effect of protein size, charge, and external phase salt concentration. We use this below to investigate the shape of protein isotherms under various conditions. Model results
The model described above qualitatively predicts the behavior observed experimentally with chymosin and pepsin sorption on Accell resin. At low salt concentration, a maximum sorption, dictated by the net protein charge and concentration of fixed charges within the resin, is predicted by the model ( q S ' ~ 1.0). The protein charge affects the shape of the isotherm, primarily by changing the affinity for the resin (Fig. 8), but also dictates the
30
alpha - 0.I0;
1.00
Oeta = I00
z p / z a - 30
alpha
1.00
--
= 0.1;
zp/za
=
iO
r"
beta
=
lO
beta
-
lO0
beta
~
iO00
.5 0.80 -
.5 0.8o zp/za
10
=
f
k
L
S o. 8o
.5 0.60 ~ /
5
.5 03 g 0.40 k
03
"~ 0.40
O_ 03 03 >
-~ 0.20 ,-.-i
g: o ~
__
7p/z- ~ 4J
-
f
O. 20 f
I
I
I
L
I
o.oo
Fig. 8. Effect of protein charge on the uptake of protein into an ion exchange resin (z a is assumed to be 1.0).
I
I
I
l
I
0.00 0.10 0.20 0.30 0.40 0.50 R e l a t i v e p r o t e i n in s o l u t i o n (x 1000)
' 0~. O0 O. I0 0.20 0.30 0.40 0.50 R e l a t i v e p r o t e i n in s o l u t i o n (x 1000)
Fig. 10. Effect of protein size (fl) on the uptake of protein into an ion exchange resin (z a is assumed to be
1.o). maximum uptake by competition with the salt. The isotherms are dramatically influenced by the salt concentration. For proteins with small charges, the model predicts a significant drop in both the affinity and capacity of the resin as salt is added (Fig. 9). The reduction in the maximum binding is larger for lessercharged molecules than it is for higher-charged molecules. (Calculations not shown.)
1,00 -
b e t a = t00;
z p / z e = t0
Finally, the molecular size of the protein has an effect on binding behavior (Fig. 10). For a given resin, the larger the molecules, the fewer that bind. Beta values for protein systems are typically between 100 and 1000. Although we have not explored all the combinations of these effects in this brief report, it is clear that the main parameters of influencing the isotherm behavior are the ratio of the protein and displacing (salt) ion charge, the dimensionless salt concentration, a, and the exclusion parameter, ft.
alpha = 0.01
CONCLUSIONS
O. 80 alpha -
0.I0
c_
.5 o.6o - I -
S 03
go.4o CCI e3 >
%
alpha
= 0.50
0.20 --
Y: o.oo / "
I
I
I
I
1
0.00 O. 10 0.20 0.30 0.40 0.50 R e l a t i v e p r o t e i n in s o l u t i o n (x 1000)
Fig. 9. Effect of external phase salt concentration on uptake of protein into an ion exchange resin (z~ is assumed to be 1.0).
We have made no attempt to fit the experimental data to the model predictions, yet it is clear that the model has characteristics seen in the experimental data which go beyond fortuitous behavior. For instance, no other model can predict accurately that similar molecules with different charges will be influenced by the salt concentration in the way pepsin and chymosin are, nor do other models predict the stoichiometric sorption observed for the molecules. More than others, this model is based on
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reasonable physical assumptions. For example, the assumption that the resin is a homogeneous phase is justifiable for most soft gel resins, since there is no internal "pore structure" for these gels and since the spacing of the ionic groups inside the resin is relatively small compared with the size of the molecules. In addition, even in so-called "coated" resins, where the resin particle does have an internal pore structure, it is reasonable to assume that there is a surface layer of resin polymer which is thick enough to be considered a separate phase. In such a case there would be a potential difference between the polymer phase (coating) inside the pore and the free pore space. All other assumptions of the model would hold and the same result would be obtained. Probably the most severe assumptions of the model are those surrounding the relationship between the activity of the species of interest and the concentration. Any specific interactions between the resin ions and the protein or salt ions could change the actual binding behavior as compared with model predictions since the predicted behavior is based on the assumption that interactions are purely electrostatic. Further work will be required to determine the magnitude of these effects and to elucidate how important interactions other than pure electrostatic ones are
on the sorption behavior of various molecules. REFERENCES 1 Hai-Shung Tsou, Adsorption kinetics of proteins on sephadex ion exchanger, M.Sc. Thesis, Chemical Engineering, The Pennsylvania State University, 1983. 2 W. Kopaciewicz, M.A. Rounds, J. Fausnaugh and F.E. Regnier, Retention model for high-performance ion-exchange chromatography, J. Chromatogr., 266 (1983) 3-21. 3 K.M. Gooding and M.N. Schmuck, Ion selectivity in the high-performance cation-exchange chromatography of proteins, J. Chromatogr., 296 (1984) 321-328. 4 M.A. Rounds and F.E. Regnier, Evaluation of a retention model for high-performance ion-exchange chromatography using two different displacing salts, J. Chromatogr., 283 (1984) 37-45. 5 L.R. Snyder and J.J. Kirkland, Introduction to Modern Liquid Chromatography, Wiley, New York, NY, 1979, p. 422. 6 A. Carlson, The enzymatic coagulation of milk, Ph.D. Thesis, Chemical Engineering, University of Wisconsin-Madison, 1982. 7 A. Carlson, C.G. Hill Jr. and N.F. Olson, Improved assay procedure for determination of milk clotting enzymes, J. Dairy Sci., 68 (1985) 290-299. 8 S. Ohki and H. Ohshima, Donnan potential and surface potential of a charged membrane and the effect of ion binding on the potential profile, in: M. Blank (Ed.), Electrical Double Layers in Biology, Plenum Press, New York, NY, 1986. 9 P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca and London, 1971, p. 512.