Ind. Eng. Chem. Res. 1995,34, 2805-2810
2805
Effect of Modulator Sorption on Gradient Shape in Ion-Exchange Chromatography Ajoy V e l a p a a n * Department of Bioresource Engineering, Oregon State University, Corvallis, Oregon 97331 -3906
Michael R Ladisch Laboratory of Renewable Resources Engineering, Department of Agricultural Engineering, Purdue University, 1295 Potter Center, West Lafayette, Indiana 47907-1295
Mobile phase additives, or modulators, are used in gradient elution chromatography to facilitate separation and reduce separation time. The modulators are usually assumed to be linearly adsorbed or unadsorbed. Here, the consequences of nonlinear modulator adsorption are examined for ion-exchange gradient elution through a series of simulations. Even when the buffer salt is identical to the modulator salt, gradient deformation is observed; the extent of deformation increases as the volume of the feed is increased. When the modulator salt is different from the buffer salt, unusual effects are observed, and the chromatograms are quite different from those predicted by classical gradient elution theory. In particular, local increases in the buffer concentration are found between feed bands, and serve to improve the separation. These effects become more pronounced as the feed volume increases, and could therefore prove valuable in preparative applications.
Introduction Chromatography is a sensitive and versatile separation technique that is widely used in biotechnological downstream processing. One of the most common modes of preparative chromatography is gradient elution, in which the mobile phase composition entering the column changes with time. The mobile phase additive whose concentration varies at the column inlet is here called the mobile phase modulator, because it modulates the retention of the feed components,thereby reducing the overall time required for the chromatographic separation. The modulator in ion-exchange chromatography is typically a salt and, in classical theoretical treatments of gradient elution, is assumed t o be itself either unretained or linearly retained (Jandera and Churacek, 1985; Snyder and Stadalius, 1986; Yamamoto et al., 1988). This paper examines the consequences, through a series of simulations, of accounting for the nonlinear adsorption of the salt itself to the sorbent in preparative separations. The motivation for this study came from a previous examination of nonlinear modulator adsorption in reversed-phase chromatography (Velayudhan and Ladisch, 1991, 1992). Concave-down isotherms for the modulator were found to cause gradients (that were linear a t the column inlet) to deform as they moved down the column. In extreme cases, a modulator shock layer-a narrow region of column across which the modulator concentration changed sharply-was formed. Simulations of separations under conditions where modulator shock layers were formed showed that feed peaks found in the vicinity of the shock were deformed and in particular could become concentrated (Velayudhan and Ladisch, 1991). Experiments were then carried out for amino acid separations on a methacrylate-based sorbent with acetonitrile as the modulator, and were found to agree with the theory (Velayudhan et al., 1995). This agreement led to the question of
* To whom correspondence
should be addressed.
0888-588519512634-2805$09.00/0
whether gradient deformation could also be significant in ion-exchange chromatography. Ion-exchange chromatography is characterized by electroneutrality, the requirement that the sorbent be saturated with counterions at all times. Consequently, the chromatographic column must be saturated with a buffer salt even before the introduction of feed components. The first set of simulations below considers the case where the modulator salt is identical t o the buffer salt. Even in this case, considerable deformation of the gradient is found, particularly at high feed loadings. The second and third sets of simulations consider the case where the modulator salt is different from the buffer salt. The interference between the buffer and the modulator causes gradient deformation of a different type from the kind described above for the first simulation set. It is found that the interplay of buffer, modulator and feed components can improve separation quality. Finally, this novel version of gradient elution is compared to other modes of preparative chromatography.
Multicomponent Isotherm Formalism The isotherm equations are developed below under the assumption that the modulator is different from the buffer; the case where the modulator and buffer are identical is easily seen t o be a special case. The formalism is that of simple mass action; electroneutrality requires that any adsorbable component bind to the sorbent by displacing a stoichiometricallyequivalent number of molecules of another component that is already bound. For simplicity we consider a monovalent buffer salt W (for “weak” salt) and a monovalent modulator salt S. ’Ityo macromolecular feed components A and B are considered, with characteristic charges of a and b, respectively. The characteristic charge is that fraction of the macromolecule’s surface charges that interacts with the sorbent when the macromolecule has aligned itself into its binding configuration, i.e., one in which the free energy of the sorbate-sorbent system is minimized. 0 1995 American Chemical Society
2806 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995
The binding of A can then be represented as
+
A + aW-A aW (1) where overbars represent stationary phase concentrations. The mass-action formalism gives
where CA and qA* represent the equilibrium mobile and stationary phase concentrations of A, respectively; cw and qw* are the analogous equilibrium concentrations for W. Equations 1and 2 represent an extremely simple view of competitive ion-exchange as the stoichiometric exchange of counterions. Donnan effects are not directly accounted for; neither are nonideal effects such as activity coefficients treated explicitly. However, there is some implicit allowance for such factors since the isotherm parameters, such as KAand a,are determined from experimental data. The binding of B is analogous:
B + bW
B + bW
Table 1. Isotherm Parameters Used for the Adsorbable Components in All the Simulationsa characteristic charge
footprint
adsorb ate
f
equilibrium constant K
a-chymotrypsinogen cytochrome c lysozyme
4.8 6.0 5.3
11.3 9.93 7.41
9.22 x 10-3 1.06 x 1.84 x lo-’
a The parameters for the proteins are from Gadam et al. (19931, where the weak salt or buffer is sodium (phosphate). A = 567 mM.
Table 2. Parameters Used in the Simulations Shown in Figures 1-3 column length L column inner diameter d, interstitial porosity €b particle porosity cp flow rate F lumped mass transfer coefficient for all components
50 cm 0.78 cm 0.4 0.6 1 mumin 25 min-l
the ith component, is of the form
(3) (4)
Similarly, the binding of S is given by
S+W-S+W
(5)
The binding of all these adsorbable components is coupled through the electroneutrality condition:
(7) afAqA* + bfBqB* + qS* + qW* = A This expression introduces footprint factors f A and f B for the macromolecular adsorbates to reflect the fact that the area a bound molecule “occupies”(in the sense of preventing another macromolecule from binding in this area) is generally larger than is fully accounted for by its characteristic charge. In other words, if we consider the sorbent to consist of a uniform distribution of fixed charges, the binding of a single molecule to the sorbent will, in general, result in a number of fixed charges that, while not directly interacting with the adsorbed macromolecule, are nevertheless shielded by its physical presence from interacting with any other large molecule. This steric “shielding effect” is encapsulated in the footprint. These “shielded”fured charges can, and do, bind small adsorbates like S and W t o ensure electroneutrality, and such shielded bound small molecules must be accounted for in the mass balances (eq 8 below). This model of macromolecular binding onto ionexchange sorbents was quantsed by Velayudhan (1990), and it has since been systematically developed (Brooks and Cramer, 1992; Gadam et al., 1993) to protein separations by displacement chromatography, after determining from experiment the isotherm parameters for various proteins. The simulations presented here will use isotherm parameters determined by Cramer and co-workers (Gadam et al., 19931, as shown in Table 1, and apply them to gradient elution. Numerical Method The method of characteristics is used here with a lumped version of the governing equation, which, for
(10) The equilibrium concentration of the ith component, qi*, is represented in its general form in eq 10. For these simulations, the mass-action isotherm introduced in the previous section will be used. The lumped mass-transfer coefficient, K M T , ~ ,can be used in linear chromatography to represent the combined contributions of axial dispersion, film mass transfer, pore diffusion, and finite sorption kinetics (Ruthven, 1984). The same relationship is used here even in the presence of nonlinear equilibria. The details of calculating the appropriate K M T , ~for a given system are given by Velayudhan et al. (Velayudhan and Ladisch, 1992; Velayudhan et al., 1995). In the present context, where only the representative features of preparative gradient , i not reruns are examined, exact values of k ~ ~are quired. Estimates of the right order of magnitude are sufficient. The conditions used in all the simulations are given in Table 2.
Simulations The isotherm data for all the simulations used here are taken from Gadam et al. (1993), who determined equilibria for proteins on ion-exchange sorbents in the presence of a salt. The data used here are for a-chymotrypsinogen (Chy), cytochrome c (Cyt), and lysozyme (Lys) on a strong (sulfopropyl) cation exchanger at pH 6.0 with sodium phosphate buffer. Gadam et al. (1993) represent the shielding effect of large adsorbates in a slightly different form from that of eq 7, but the two versions can easily be shown to be identical, with their steric factor ua being related to our footprint factor f A by ua = a ( f A - 1) (11) The isotherm parameters for these proteins are listed in Table 1. Simulation Set I. Here the modulator is identical to the buffer. The column is preequilibrated with 75 mM buffer. The feed, consisting of Chy and Cyt at 1
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2807
a
1.0
250 225 200 2 175 g 150 5 125 2 100 8 75 50
;
0.8
ti e
0.6
Y
c;
0.4
e
2
h
- salt
E
E
b
chymo cyto
4
0.2 0.0
I
----
258 20
40 60 Time (minutes)
80
0 2
1.o 0.8
$ +.E
0.6
150 5 125 100 u
E:
8E; 8
0.4
o.2 0.0
20
40
60
80
Time (minutes)
Time (minutes)
Figure 1. Gradient elution runs of a-chymotrypsinogen (chymo) and cytochrome c (cyto), each at a feed concentration of 1 mM. Buffer identical to modulator; initial concentration of buffer (75 mM) also found in feed; modulator gradient (linear from 75 to 250 mM a t 3 mM/min) started immediately after end of feed introduction. Column parameters are given in Table 2, isotherm parameters in Table 1. Scaled feed volume y (ratio of feed volume to column void volume) is (a)0.22, (b) 0.33, and (c) 0.44, respectively.
mM each, is then introduced, also in 75 mM buffer. Subsequent to feed introduction, the buffer (modulator) gradient begins; a linear gradient of slope 3 mM/min is used, from 75 to 250 mM. Figure 1 shows the simulations for increasing feed volume, represented by the volumetric loading fraction y :
(12) where Vinj and tinj are the volume and time of the feed injection pulse (the flow rate is assumed constant throughout), and VO and to are respectively the void volume of the column and the time of emergence of an unretained solute. At y = 0.22 (Figure la), two interesting features are immediately evident. The gradient suffers deformation in the vicinity of the feed components, and a zone of enriched buffer is found ahead of the feed. The latter effect derives from the displacement of adsorbed buffer molecules upon feed introduction. These displaced buffer molecules cannot bind again, since the column
has already been saturated with buffer, and must move down the column at the mobile phase velocity, giving rise to the enriched zone. In practice, many feed mixtures contain impurities that are unretained or weakly retained. The enrichment zone ensures that these impurities are well separated from the desired products. At y = 0.33 (Figure lb), an additional effect can be seen. The feed volume is so large that a small fraction of Chy (the less retained protein) escapes into the enriched zone. Thus, if Chy were the desired product, further increase in feed volume would in practice lead to some loss of productivity into the enriched zone, where the impurities (if any) would be found. However, if Cyt were the desired product, the separation quality is still excellent, and further increase in feed volume is conceivable. Figure ICshows the chromatogram corresponding to y = 0.44,which represents a significant volumetric loading. The loss of Chy into the enriched zone is increased, but the separation quality (as assessed by the degree of mixing between the feed bands) remains high. Simulation Set 11. Now the modulator is different from the buffer. A hypothetical monovalent modulator ("strong" salt) that is more retentive than the buffer ("weak" salt) is considered, with KS= 2. As before, the column is preequilibrated with 75 mM buffer, and the feed (again, 1mM of both Chy and Cyt) is dissolved in 75 mM buffer. The linear gradient, which begins immediately after feed introduction, consists of the strong salt going from 0 to 250 mM a t 3 mM/min. This gradient is accompanied by a constant 75 mM concentration of buffer. Figure 2a shows the simulation for y = 0.22. As in the previous set of simulations, feed introduction causes displacement of previously bound buffer counterions, which then migrate down the column at the mobile phase velocity to form a zone of enrichment. The rest of the chromatogram, however, is very different from the previous set. The most important change is that competition between the buffer and the modulator now allows for gradient deformation that is independent of interactions with the feed components. This allows for self-sharpening deformation of a kind discussed previously for reversed-phase chromatography (Velayudhan and Ladisch, 1992;Velayudhan et al., 1995). In Figure 2a, the gradient of the modulator is indeed deformed, but also does not cross the Chy peak. This is reminiscent of displacement, and is in fact caused by the modulator being more retentive than Chy under these conditions. The interference of the buffer separately with each of the three more retained components is also significant, each such interference resulting in a local increase in buffer level. In particular, the interaction between the buffer and Cyt generates a local excess of buffer just ahead of the Cyt band. This excess helps to decrease the retention of the Chy found in this region. In other words, the separation factor between Cyt and Chy is increased locally, just ahead of the Cyt band, thereby improving the separation. This effect could be extremely useful in preparative applications. At y = 0.33 (Figure 2b), the feed volume is again large enough, as in simulation set I, for a small portion of the Chy band to be pushed ahead during the process of feed introduction into the enrichment zone. The separation remains good.
2808 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995
a-
1.0
I
I.
J
2005j
I:
tla::;
- strongsalt
1
a
1.0 I
'
'
'
'
I
'
'
I
h
175 150 125 100
0.8 E
0 'i:
E
0.6
Y
@ 8
3
-
.{
- - - chymo . - - -weaksalt
p:
- strongsalt
1
0.4 50 3 9 25
'
0.2
d 0.0
b
1.0
5
0.8
20
40 60 Time (minutes)
80
h
cyto . - - -weaksalt
fd
02/, 0.0
1.0
j
,/
'
,
40 60 Time (minutes)
20
I
il', j
'
'
' 'I
_
,
80
strong salt
5 E
- - weaksalt strong salt
0.6
Y
0.4
8
50
3
9
0.2
d
0 2
0.0
Time (minutes)
c
I
200
1.0
h
--
- 1 2 5 m2 - 100
2
:75
8
25'
d 0.0
0 2
40 60 80 Time (minutes) Figure 2. Gradient elution runs of a-chymotrypsinogen and cytochrome c, with modulator different from buffer (Ks= 2). Buffer (''weak salt) at 75 mM throughout; modulator ("strong" salt) gradient (linear from 0 to 250 mM at 3 mhllmin) starts immediately after end of feed introduction. All other parameters as in Figure 1.Ratio of feed volume to column volume is (a) 0.22, (b) 0.33, and ( c ) 0.44. 20
At y = 0.44 (Figure 2c), Cyt is concentrated to the extent that its maximum exceeds the feed value of 1 mM. The feed bands remain well separated, and the migration of Chy into the enrichment zone increases. This set of simulations depicts the possibilities inherent in using two salts in preparative ion-exchange separations. The buffer ("weak" salt) interacts with the feed components and the modulator in such a way as t o generate local excesses of buffer in between feed components, thereby improving the separation. Simulation Set 111. This set uses a hypothetical monovalent modulator with Ks = 3. All other conditions are as in set 11. The fundamental difference between these two sets of runs is that here the modulator is strong enough to "displace" both Cyt and Chy, under the conditions used. Thus, Figure 3 shows that the modulator does not cross any feed band. Since the modulator is more retentive relative to Figure 2, the extent of gradient deformation is correspondingly greater. As in set 11, local excesses of the buffer are generated in between feed bands, and this again results in the feed components being well separated. The triangular shape of the feed components is even more pronounced here
175;
0.8
chymo
cyto - - weaksalt - strongsalt
ti
3
150
$
0.6
0.4
75
0.2
50 25
-43
0
3
r:
3
3
125 100
Y
8E 8
2
d 0.0
2 g
strong salt
40 60 80 Time (minutes) Figure 3. Gradient elution runs of a-chymotrypsinogen and cytochrome c, with modulator different from buffer (Ks= 3). All other parameters as in Figure 2. Ratio of feed volume to column volume is (a) 0.22, (b) 0.33, and (c) 0.44. 20
than in set 11. At no point does the local concentration of either feed component exceed its feed value of 1mM, as occurred in set 11,but in other respects the features of set I11 are comparable to those of set 11. In practice, if operating conditions can be found such that a modulator will displace either one or both components of a binary feed mixture, it is not clear which approach is to be preferred. These simulations indicate that comparable results might be obtained, and detailed comparisons must be made on a case-by-case basis.
Discussion In classical gradient elution chromatography, when the modulator is assumed to move with the mobile phase velocity, the effect of the modulator on the retention of the feed components can be regarded as thermodynamic, in the sense that the modulator is not treated as a component whose concentration can change as a result of column dynamics. Allowing the modulator to be linearly retained ascribes to it a limited dynamic character: it is held up by the column, but in a fashion that does not allow gradient deformation. Once the modulator is allowed to adsorb according to its nonlinear
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2809 isotherm, it becomes a full-fledged dynamic component. This was done previously for reversed-phase chromatography (Velayudhan and Ladisch, 1992; Velayudhan et al., 1995). The present paper treats dynamic modulators in ion-exchange chromatography. The ion-exchange isotherm used here couples all adsorbing components through the electroneutrality condition, eq 7. It therefore captures not only the influence of the modulator on itself and on the feed components, but allows the feed components to affect the behavior of the modulator. This is what gives rise to local increases in the buffer concentration in simulation sets I1 and I11 above, which in turn increases the local separation factor and facilitates separation. The isotherm incorporated footprint factors so as to be applicable to macromolecular adsorption. It is obviously directly applicable t o the adsorption of small molecules as well, with all f s set to 1. Thus the unusual results we have seen above do not derive from shielding, but directly from the interference effect of the feed components on the buffer and modulator. The gain in separation quality as a result of nonlinear interactions between the buffer, modulator, and feed components is an instance of exploiting nonlinearity in preparative adsorption and chromatography. The most fundamental example is the “displacement effect” in binary nonlinear isocratic elution, where the more retained component competes so effectively with the less retained component that the former pushes the latter ahead of it, thus decreasing mixing between the feed bands (Newberger et al., 1987; Golshan-Shirazi and Guiochon, 1989a,b). A more involved example, which bears some resemblance to the present approach, is spacer displacement chromatography, in which a series of components with different retentions (“spacers”)are introduced into the feed, in the hope that they will intercalate between the feed components, allowing for complete recovery of the feed (Tiselius and Hagdahl, 1950; Peterson, 1978; Peterson and Torres, 1983). Of course, this approach only works if the spacers themselves can subsequently be easily separated from the feed components. In the approach discussed here, a single component-the buffer salt-takes the place of the various spacers, and helps to minimize mixing between the feed components.
Conclusions In summary, the use of two judiciously chosen salts in gradient elution using ion-exchange chromatography may prove to be valuable in preparative separations. The next step would be a series of experiments t o test whether the gains seen in the simulations are realized in practice, and to identify when such separations are t o be preferentially used. If such improvements are found experimentally, the issue of optimizing the retention properties and gradient shapes of the buffer and modulator will become important. Acknowledgment This work was supported by NASA through the NSCORT program under grant NAGW-2329. We thank Joseph Weil and Subir Basak for helpful comments on the manuscript. Nomenclature a = characteristic charge on macromolecule A b = characteristic charge on macromolecule B
c = mobile phase concentration, mM F = volumetric flow rate, mumin KA = equilibrium constant for A against W KB = equilibrium constant for B against W KS = equilibrium constant for S against W f A = footprint of macromolecule A f~= footprint of macromolecule B kMT = lumped rate coefticient q = stationary phase concentration, mM q* = equilibrium stationary phase concentration, mM S = “strong”modulator salt t = time, s ti,, = duration of feed pulse, s to = residence time for an unretained unexcluded trace
component, s = chromatographic velocity, m/s VO= column void volume, m3 Vinj = volume of feed pulse, m3 W = “weak”buffer salt Uchrom
Greek Characters = interstitial porosity cp = intraparticulate porosity Eb
4 = volumetric column phase ratio y = fractional feed volume (=VinjNo) A = sorbent saturation concentration, mM “A = shielding factor for macromolecule A as used by Gadam et al. (1993) Subscript
i = ith component
Literature Cited Brooks, C. A,; Cramer, S. M. Steric Mass-Action Ion Exchange: Displacement Profiles and Induced Salt Gradients. AIChE J. 1992,38,1969. Gadam, S. D.; Jayaraman, G.; Cramer, S. M. Characterization of non-linear adsorption properties of dextran-based polyelectrolyte displacers in ion-exchange systems. J. Chromatogr. 1993, 630,37. Golshan-Shirazi, S.;Guiochon, G. Analytical Solution for the Ideal Model of Chromatography in the Case of a Pulse of a Binary Mixture with Competitive Langmuir Isotherms. J. Phys. Chem. 1989a,93,4143. Golshan-Shirazi, S.;Guiochon, G. Analytical Solution of the Ideal Model of Elution Chromatography in the Case of a Binary Mixture with Competitive Langmuir Isotherms 11. Solution Using the h-transform. J. Chromatogr. 1989b,484,125. Jandera, P.; Churacek, J. Gradient Elution in Column Liquid Chromatography. Theory and Practice; Elsevier: Amsterdam, 1985. Newburger, J.; Liebes, L.; Colin, H.; Guiochon, G. Investigation of the Influence of Particle Size on the Productivity of Preparative HPLC Columns. Sep. Sci. Technol. 1983,22,1933. Peterson, E. A. Ion-Exchange Displacement Chromatography of Serum Proteins, Using Carboxymethyldextrans as Displacers. Anal. Biochem. 1978,90,767. Peterson E. A.; Torres, A. R. Ion-Exchange Displacement Chromatography of Proteins, Using Narrow-Range Carboxymethyldextrans and a New Index ofAffinity. Anal. Bwchem. 1983,130, 271. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. Snyder, L. R.; Stadalius, M. A. In High-Performance Liquid Chromatography, Advances and Perspectives; HorvBth, Cs., Ed.; Academic: New York, 1986; Vol. 1. Tiselius, A.; Hagdahl, L. A Note on “Carrier Displacement” Chromatography. Acta Chem. Scand. 1950,4,394. Velayudhan, A. Studies in Nonlinear Chromatography. Ph.D. Dissertation, Yale University, New Haven, 1990.
2810 Ind. Eng. Chem. Res., Vol. 34, No. 8,1995 Velayudhan, A.; Ladisch, M. R. Role of the Modulator in Gradient Elution Chromatography. Anal Chem. 1991,63,2028. Velayudhan, A.;Ladisch, M. R. Effect of Modulator Sorption in Gradient Elution Chromatography: Gradient Deformation. Chem. Eng. Sci. 1992,47,233. Velayudhan, A,; Hendrickson, R. L.; Ladisch, M. R. Simultaneous Concentration and Purification Through Gradient Deformation in Gradient Elution Chromatography. AIChE J . 1995,41,1184. Yamamoto, S.;Nakamishi, K.; Matsumo, R. Zon-Exchange Chromatography of Proteins; Dekker: New York, 1988.
Received for review November 15,1994 Revised manuscript received March 30, 1995 Accepted April 20, 1995@ I39406759
Abstract published in Advance ACS Abstracts, July 1, 1995. @
