Ind. Eng. Chem. Res. 2001, 40, 369-376
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Specific and Nonspecific Adsorption in Affinity Chromatography. Part I. Preliminary and Equilibrium Studies E. M. Martı´n del Valle and M. A. Gala´ n* Departamento de Ingenierı´a Quı´mica, Universidad de Salamanca, Plaza de los Caidos 1-5, 37008 Salamanca, Spain
The amount of enzyme adsorbed at equilibrium by hydrophobic and hydrophilic bonds or retained inside the adsorbent was studied for asparaginase on Sepharose 4B, Sepharose 4B activated with CNBr, activated Sepharose 4B with hexamethylenediamine as a spacer arm and activated Sepharose 4B with hexamethylenediamine and L-(+)-chlorosuccinamic acid as the spacer arm and ligand, respectively, in a batch reactor for the range of temperatures 298-302 K, the range of pH 7.5-8.6, and for different ionic strengths (0.0-1.5 M NaCl). Adsorption increased with pH and decreased with temperature. With respect to ionic strength, adsorption increased until an I value of 0.05 M NaCl. A change in the adsorption process was observed when the ionic strength was steadily decreased. The equilibrium data were correlated using a semiquantitative theory in which electrostatic and hydrophobic interactions between enzyme and ligand were considered. This correlation shows that hydrophobic effects increase with temperature, in very good agreement with the experimental data. Introduction Affinity chromatography is a very valuable technique for the separation of biological compounds. It is the only technique that enables purification of almost any biomolecule based on its biological function or individual chemical structure;1 however, its uses have been restricted to the laboratory scale. Affinity chromatography is a type of adsorption chromatography in which the molecule to be purified is specifically and reversibly adsorbed by a complementary binding substance (ligand) immobilized on an insoluble support (matrix). To scale-up this technique to the industrial scale, it is necessary to know the fundamental adsorption behavior and how it is affected by specific and nonspecific links2 and mass transfer effects. The main target of this paper is to understand some of these fundamentals of scaling-up in a safe and accurate way. Several attempts have been made to improve the selectivity of adsorbents. Thus, Rodes et al.3 studied the effect of immunoadsorbents on polyethyleneamine. Tennikov et al.4 observed the effect of the porosity of a polymeric matrix on the selectivity of separation. To study different kinds of bonds, Lakhiari et al.5 covered the surface of spheres of silica gel with dextrans of different molecular weights. They noticed that, when the temperature increased, nonspecific hydrophobic bonds increased, decreasing the selectivity of the separation. In view of the foregoing, the main objective of Part I of this work was to study the adsorption-desorption equilibrium of hydrophilic and hydrophobic bonds for asparaginase on nonactivated Sepharose 4B, Sepharose 4B activated with CNBr, Sepharose 4B activated with CNBr and with hexamethylenediamine as the spacer arm, and Sepharose 4B activated with CNBr with hexamethylenediamine and L-(+)-chlorosuccinamic acid as the spacer arm and ligand, respectively. * Author to whom correspondence should be addressed.
In the first three systems, asparaginase should be linked to nonspecific bonds, but in the fourth, asparaginase should be retained through specific and nonspecific linkages. All experiments were carried out in batch reactor for a temperatures range of 298-302 K at different pH values (7.5-8.6) and ionic strengths (0.0-1.5 M NaCl) because, in these ranges, asparaginase is stable.6 Materials Asparaginase (E.C. 3.5.1.1) and Sepharose 4B were purchased from Sigma Chemical Corporation. The other chemicals used, hexamethylenediamine, L-asparagine, D-asparagine, sodium chloride, cyanogen bromide, boric acid, and sodium tetraborate were obtained from E. Merck. All chemicals were of reagent grade. L-(+)-Chlorosuccinamic acid was obtained by a Walden conversion from D-asparagine, as described by Holmberg.7 The physical properties of this compound were determined by proton nuclear magnetic resonance spectroscopy (1H NMR) and by rotary power (+54), indicating a purity of 96%, with a synthesis yield of about 35%. Experimental Section Adsorbents. The method used for the activation and preparation of adsorbents was essentially that described by Cuatrecasas8 as follows: In a hood, a given volume (25-30 mL) of Sepharose 4B, washed with water, was mixed with an equal volume of distilled water. Then, 2.8 mmol of CNBr was added to the suspension, and the pH was raised immediately to 11 by addition of 8 M NaOH. This pH was maintained until the end of the reaction, which was completed in 12 min. The reaction was quenched by the addition of a large amount of ice, the preparation was filtered in a Bu¨chner funnel, and the solid was washed with a cold solution of 0.5 M NaHCO3. Spacer Arm Coupling. Hexamethylenediamine was used as a spacer arm, which was linked directly to Sepharose 4B activated with cyanogen bromide by the
10.1021/ie000401n CCC: $20.00 © 2001 American Chemical Society Published on Web 12/13/2000
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following method: To the washed, activated Sepharose 4B was added an equal volume of cold distilled water containing 2 mmol of hexamethylenediamine per milliliter of Sepharose, previously titrated to pH 10 with 6 N HCl. After being allowed to react for 16 h at 277 K, the gel was washed with a large volume of distilled water. Ligand Coupling. The ligand-coupling procedure was essentially that described by Kristiansen et al.9 A very large excess of hexamethylenediamine, 43 mmol, was melted in a thermostated batch reactor at 318 K. Then, 17 mmol of L-(+)-chlorosuccinamic acid was gently added. The mixture was left at 313 K for 80 h under magnetic stirring. Subsequently, 100 mL of distilled water was added to the oily product, and the resulting mixture was then concentrated in a rotary evaporator at the same temperature to a final volume of 15 mL. This operation was repeated three times to eliminate the excess of nonreacting hexamethylenediamine. Then, 40 mL of 0.5 M NaHCO3 solution was added, and the pH of the solution was adjusted to 8.5 with 50 mL of 2 N HCl solution. This block (spacer arm and ligand) was attached to activated Sepharose 4B. To do so, 50 mL of Sepharose 4B activated with CNBr was mixed with the amino solution. The suspension was gently shaken at room temperature for 2-3 h and then washed extensively with 200 mL of 0.1 M sodium borate (pH 8.0) and 0.1 M sodium acetate buffer, (pH 4.0) to desorb material not covalently bound. The amount of cyanogen bromide, hexamethylenediamine, and ligand coupled to Sepharose 4B was determined via a nitrogen balance, using the KJELDAHL method. According to this balance, the amount of CN+ linked to the Sepharose 4B was 30.5 µmol/g of resin. In the case of activated Sepharose 4B linked to hexamethylenediamine as the spacer arm, the amount of hexamethylenediamine was 12.7 µmol/g of resin. In the preparation of activated Sepharose 4B with hexamethylenediamine and L-(+)-chlorosuccinamic acid, the amount of ligand was 27.0 µmol/g of resin. Enzyme Assays. One unit of asparaginase will liberate 1.0 mmol of ammonia from L-asparagine per minute at pH 8.6 at 335 K. The enzymatic activity of asparaginase was measured using L-asparagine as the substrate, analyzing the ammonia produced by Nessler’s method.10 Preliminary Studies Before the adsorption-desorption equilibrium was studied, several runs were made to determine the best experimental conditions. The variables studied were the stability of the enzyme under different stirring conditions; the optimal stirring speed to avoid any possible mass transfer resistance; the mechanical strength of Sepharose 4B; and the effects of pH, temperature, etc. Asparaginase Stability at Different Stirring Speeds. In this work, we used a shaker rotator as stirring device because, in affinity chromatography shaker stirring or air bubbles with oxygen-free nitrogen are needed. Use of any other device for stirrer can damage the adsorbent structure, and also, denaturation of the enzyme can occur. The stirring speed used for these experiments is a very crucial factor for the stability of the enzyme because it can become denatured through modifications or destruction of its structure. To determine the effect
Figure 1. Activity of asparaginase vs time for different stirring speeds.
of stirring speed, 24 IU of asparaginase were added to 24 mL of 0.05 M borate buffer solution (pH 8.6) in a 250-mL jacketed thermostated reactor at 302 K. The system was stirred at three different speeds, namely, 160, 190, and 210 rpm, in an orbital shaker. After 5 min, the stirring was stopped, 1.5-mL samples were withdrawn from the reactor, and the asparaginase activity in solution was analyzed. The activity vs time data for the different speeds studied are plotted in Figure 1. From this figure, it can be observed that the activity of the enzyme at 160 and 190 rpm remains approximately constant over 70 min, a period longer than that necessary for adsorption equilibrium to be reached (35 min under those operating conditions). However, when the speed was 210 rpm, the enzyme activity decreased to 95% of its initial value after 1 h. From these experiments, it was concluded that, in the present, case the optimum speed was 190 rpm. At this speed, it was assumed that no external mass transfer resistance effect was occurring.11 Stirring Speed. Several experiments were performed to study the time required for adsorption equilibrium to be reached and to avoid external mass transfer resistance. To do so, experiments were carried out using an orbital shaker rotating at three different speeds: 130, 160, and 190 rpm. In a 250-mL jacketed reactor, 24 mL of 0.05 M borate buffer solution, at pH 8.6, was introduced, and then 0.5 g of Sepharose 4B activated with CNBr and hexamethylenediamine and L-(+)-chlorosuccinamic acid as the spacer arm and ligand, respectively, was carefully added. After stirring had been started, 28 IU of asparaginase was added to the mixture. Stirring was stopped every 5 min, and after the gel had settled, 1.5-mL samples were withdrawn and analyzed to determine the asparaginase activity. The data on the concentration of free asparaginase vs time, at different temperatures and stirring speeds, are shown in Figure 2a,b. From this figure, it can be observed that the time for equilibrium to be reached changes from 90 min at 130 rpm to 35 min at 190 rpm, probably because of external mass transfer resistance. No further increases in speed were possible because of enzyme deactivation. However, in all cases the final equilibrium value was the same at all three speeds studied for each of the temperatures tested.
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Figure 2. Concentration of asparaginase in solution vs time for different stirring speeds at 298 and 302 K.
Enzyme Stability over Time under the Operating Conditions Used. Enzyme stability was also studied for 5 h, more time than is necessary to complete all experiments, in temperature and pH ranges of 298302 K and 7.5-8.6, respectively, and at a stirring speed of 190 rpm. To investigate stability, the same procedure as previously described was followed. Figure 3a,b,c shows the percentage of enzyme activity vs time. From this figure it may seen that in the pH and temperature ranges studied, and for a period of 5 h, the enzyme did not change by more than 4%, within the standard error of the analytical method. It can thus be concluded that the enzyme activity remains constant for each of the experiments performed. Enzyme Stability with Different Ionic Strengths. Enzyme stability was also studied under different conditions of ionic strength, by changing the NaCl concentration at 190 rpm, pH 8.6, and 302 K. The 0.05 M borate buffer solution was taken as a reference for ionic strength, assuming a value equal to zero. The data are shown in Figure 4, where the percentage of enzyme activity is plotted vs time at different ionic strengths. These data show that, in an ionic strength range between 0 and 1.0 M NaCl, enzyme activity decreases by approximately 5% over the first 5 h, but for a 1.5 M concentration of NaCl, the activity decreases by approximately 8% over 5 h. This is not very important for the experiments carried out at this value (1.5 M NaCl), because the time required for equilibrium to be reached under those conditions was about 35 min
Figure 3. Activity of asparaginase vs time: (a) pH 7.5, (b) pH 8.0, (C) pH 8.6.
Figure 4. Activity of asparaginase vs time for pH 8.6, 302 K, and different values of ionic strength.
and the loss in activity over this time was about 0.5%; within the analytical error. Mechanical Strain of the Resin. Once enzyme stability at different stirring speeds had been studied,
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it was necessary to study the effect of stirring on the strain of Sepharose 4B spheres due to collisions among them or with the reactor wall. The experiments were carried out as before, working at 190 rpm, 302 K, and 0.05 M sodium borate buffer solution (pH 8.6) and with Sepharose 4B activated with CNBr with hexamethylenediamine and L-(+)-chlorosuccinamic acid as the spacer arm and ligand,respectively, for 9 h. Following this, the Sepharose 4B spheres were filtered and analyzed with an optical microscope, with the observation that the structure of the spheres had not been damaged. From the pictures obtained from the microscope, the size of the spheres was determined, the spheres proving to have a statistically mean diameter of 90 µm. Equilibrium Studies One of the main objectives of the present work was to study the adsorption-desorption equilibrium in order to understand and separate specific and nonspecific bonds in the equilibrium. It was assumed that specific bonds only arise when ligand is present; in the other cases, adsorption would be due to nonspecific hydrophobic bonds or would occur because the enzyme was retained inside the adsorbent. The equilibrium for each of the different adsorbents used was determined using a jacketed thermostated batch reactor with an orbital shaker rotating at 190 rpm at 298-302 K. A carefully measured amount of settled gel (1 mL) was mixed with 24 mL of sodium borate buffer solution (pH 7.5-8.6), and the mixture was brought to an appropriate ionic strength through the addition of NaCl. After stirring had been started, asparaginase (25 IU) was added to the mixture. After 40 min, stirring was stopped. When the gel had settled, 3-mL samples were withdrawn from the solution with a filtered pipet, and 1.5-mL aliquots were analyzed. After this, new buffer solutions of increasing ionic strength were added to the reactor; the resulting mixtures were allowed to stand for 40 min to reach the equilibrium again, after which the earlier described protocol was applied. From the known initial enzyme concentration, CE0, in this case, 1.6 × 10-6 mol/kg, and the measured concentration of enzyme in solution, CE, it was possible to evaluate the amount of enzyme bonded to the adsorbent, CEL via a mass balance. From these values, the adsorption-desorption equilibrium constant was obtained by assuming the following reaction:
E + L a EL
(1)
where the adsorption equilibrium constant is given by the expression
KA )
CEL CECL
(2)
with
CEL) CE0 - CE
(3)
CL ) CL0 - CEL
(4)
However, to compare the equilibrium constant at different ionic strengths, the effect of dilution must be
Table 1. Adsorption Equilibrium Constants for Asparaginase on Sepharose 4B Activated with Cyanogen Bromide-Hexamethylenediamine-L-(+)-Chlorosuccinamic Acid at pH 8.6 and with 0.05 M Sodium Borate Buffer
KA (kg/mol) KA modified (kg/mol)
I ) 0.0 M NaCl
I ) 0.5 M NaCl
I ) 1.5 M NaCl
90.1 85.5
61.4 60.2
14.1 13.2
Table 2. Percent of Asparaginase Retained in the Different Adsorbents Sepharose Sepharose T Sepharose Sepharose 4B-BrCN 4B-BrCN-HMDA pH (K) 4B 4B-BrCN -HMDA -L-(+)-cSA 298 7.5 300 302 298 8.0 300 302 298 8.6 300 302
17.0 16.2 11.2 18.2 17.9 12.6 18.8 17.6 12.7
19.4 17.5 10.9 19.5 19.6 14.3 19.9 17.5 17.4
19.8 18.6 14.7 19.9 19.8 14.4 26.0 22.1 17.3
42.7 35.9 30.7 48.9 42.4 40.7 74.1 64.3 63.2
a HMDA ) hexamethylenediamine. b CSA ) chlorosuccinamic acid.
taken into account. It was therefore necessary to correct the value of the equilibrium constant by a dilution factor. This correction was made by dividing each adsorption equilibrium constant by the dilution factor (21/24, 18/24, ... 3/24). To determine whether this was possible, several new experiments were performed to study the adsorption equilibrium at pH 8.6 and 298 K for Sepharose 4B activated with CNBr and with hexamethylenediamine and L-(+)-chlorosuccinamic acid as the spacer arm and ligand, respectively, at three different ionic strengths (0.0, 0.5, and 1.5 M NaCl) in three different and separate batch reactors following the same procedure described before and comparing the adsorption equilibrium constant with the values obtained following the elution procedure (Table 1). From these values, it was concluded that adsorption equilibrium constants values taking dilution into account should always be used. Table 2 shows, that under optimal operating conditions (pH 8.6, 298 K, and 0.05 M NaCl) almost 19% of the asparaginase was retained in Sepharose 4B; 20% in Sepharose 4B activated with CNBr; 26% when hexamethylenediamine was used as the spacer arm attached to Sepharose 4B activated with CNBr; and almost 75% when the adsorbent was activated Sepharose 4B with hexamethylendiamine and L-(+)-chlorosuccinamic acid as the spacer arm and ligand, respectivelyy. The enzyme retained when no ligand was present in the system was 1/ of the total enzyme for the system with ligand, and 3 it can probably be assumed that this enzyme is bonded to nonspecific links or is retained inside particles of Sepharose 4B. It can also be observed that, for Sepharose 4B activated with CNBr and with hexamethylenediamine and L-(+)-chlorosuccinamic acid as the spacer arm and ligand, respectively, a change of pH from 7.5 to 8.6 to the isoelectric point of the enzyme increased the amount of enzyme adsorbed from 40 to 70% because of electrostatic effects, as will be discussed later. To compare the adsorption equilibrium constant for each of the different adsorbents and because each of them had a different ligand concentration, CL, it was necessary to define a new constant called the distribu-
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Figure 5. Distribution coefficient vs ionic strength for asparaginase on different adsorbents, pH 8.6.
tion coefficient, KDIS
K AC L )
CEL ) KDIS CE
(5)
KDIS was plotted vs ionic strength for different pH values and at 298 K (Figure 5). Effect of pH. The experimental data (Table 2) show that, when pH was increased (7.5-8.6), the adsorption of asparaginase also increased under all of the operating conditions tested. For pH values lower than the isoelectric point (pH 8.6), the enzyme was positively charged. Therefore, because of the polar character of the solvent, the solvent-enzyme interaction was stronger, and hence, the enzyme remained in solution instead of being adsorbed. Adsorption reached a maximum value for I ) 0.05 M NaCl, regardless of the pH, for all of the systems studied. Additionally, the value of KDIS for all temperatures and pH values and under optimal conditions of ionic strength (0.05 M NaCl) was 0.2-0.4 for adsorbents without linked ligand, much lower than the KDIS value of 2.4 for activated Sepharose 4B with hexamethylenediamine as the spacer arm and L-(+)-chlorosuccinamic acid as the ligand. These values can be explained by assuming that, for the first three systems, the enzyme is adsorbed through nonspecific linkages, whereas the last system has
specific bonds, only L-(+)-chlorosuccinamic acid binds asparaginase, which is characteristic of this kind of separation process. Effect of Temperature. In addition, from the experimental data (Table 2), it can be concluded that adsorption decreases when temperature increases. Despite this finding, for all of the temperatures studied, the data show a maximum in KDIS for I ) 0.05 M NaCl for all of the adsorbents studied (Figure 5), as described above. Effect of Ionic Strength. For all of the systems studied, adsorption showed a maximum at 0.05 M NaCl, and hence, when I increased, desorption increased. A possible explanation for this is as follows: For given values of pH and temperature and an ionic strength of zero (0.0 M NaCl), an equilibrium exists between the enzyme in solution and in the adsorbent. When new ions (Na+ Cl-) are introduced into the system, the molecules of the solvent orient themselves toward these ions and the equilibrium is modified. When a very small number of ions is introduced into the system, molecules of solvent that are interacting with enzyme are reoriented toward the ions, and hence, the degree of solvation of the enzyme is reduced and adsorption increases. This effect can be observed at low ionic strength (0.05 M NaCl). When the number of ions increases, these ions interact not only with molecules of solvent but also with
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electrostatic sites in the matrix due to some ions in the matrix passing into the solution. More sites become available on the matrix. Also, the interaction of the ions with the enzyme (solvation effect) is lower and therefore it is easier for the enzyme to be adsorbed, and the adsorption equilibrium constant remains higher. Quantitative Analysis of Equilibrium Data. The models used to correlate the equilibrium data were those of Morrow et al.2 and Gonzalez Patino et al.,12 assuming that there is no internal mass transfer resistance in the adsorbent The model described by Morrow et al. is based on the Debye-Hu¨ckel theory of protein solubility
E + L / EL Figure 6. KA vs ionic strength for asparaginase on activated Sepharose 4B-hexamethylenediamine-L-(+)-chlorosuccinamic acid at pH 8.6 and 298 K.
enzyme, preventing adsorption and producing the desorption of enzyme linked to nonspecific sites. Moreover, for a very high concentration of ions, the ions also can compete with the enzyme for the active sites, producing new conditions for the equilibrium and decreasing the amount of enzyme adsorbed. Dilution Effect in the Adsoption Process. To study the possible change in the adsorption-desorption equilibrium of asparaginase on Sepharose 4B activated with CNBr and with hexamethylenediamine and L-(+)chlorosuccinamic acid when a dilution process occurs, the system was run until equilibrium had been reached in a jacketed thermostated reactor at 298 K, pH 8.6, and 1.5 M NaCl. The experiment was carried out with 1.5 M NaCl because the adsorption equilibrium constants for 0.0, 0.05, 0.1, 0.3, 0.5, 0.7, and 1.0 M NaCl were known from the experiments carried out before in the equilibrium studies. After the equilibrium was reached for 1.5 M NaCl, 3-mL samples were withdrawn to analyze the asparaginase activity. Then, 3 mL of sodium borate buffer solution was introduced into the reactor. This procedure was performed three times, corresponding to the three different NaCl concentrations of 1.31, 1.14, and 1.00 M. The data for a complete experiment are plotted in Figure 6. From this figure, a change in the adsorption constants can be observed. When the ionic strength was steadily decreased, the equilibrium constant values were different from those obtained when the ionic strength was increased. This effect can be explained because, for given values of pH and temperature and an ionic strength of zero (0.0 M NaCl), an equilibrium exists between the enzyme in solution and the adsorbed enzyme. When new ions (Na+ Cl-) are introduced into the system, the molecules of the solvent oriented toward these ions modify the equilibrium, as described above. When a very small number of ions is introduced into the system, the molecules of solvent interacting with the enzyme are reoriented toward the ions. Hence, the degree of solvation of the enzyme is lower, and adsorption increases. This effect can be observed at low ionic strength (0.05 M NaCl). When the concentration of ions becomes higher, greater than 0.05 M NaCl, ions interact with water and enzyme and compete with the enzyme for the specific and nonspecific sites on the matrix, and hence, adsorption becomes smaller. When the ionic strength of the solution decreases through dilution, there is a rearrangement in the
(1)
where L is a ligand on the surface gel, E is an enzyme molecule, and EL is an enzyme-ligand complex. The equilibrium dissociation constant KD(γ) is defined by
KD(γ) )
aEaL CECL γEγL ) aEL CEL γEL
(6)
where γ and C are the activity coefficient and the concentration, respectively, of each species. The concentration, C, can be measured, whereas the activity can not. Thus
KD KD(γ)
)
γEL γ Eγ L
(7)
and
KD log ) log γEL - log γE - log γL KD(γ)
(8)
KD is defined by
KD )
CECL CEL
(9)
Usually, solution activity coefficients are evaluated from the Debye-Hu¨ckel theory, where only electrostatic interactions are considered; however, interactions between the enzyme and the ligand are both electrostatic and hydrophobic, and Morrow et al.2 therefore extended the Debye-Hu¨ckel equation, taking both effects into account
log γi ) -
AZ2i xI I + aBxI
+ K0I
(10)
where A and B are functions of the dielectric constant, the temperature, and the ionic radius. K0 is an adjustable parameter that accounts for hydrophobic effects and can be positive, negative, or zero. If we make the assumptions that, in reaction 1, the charge on the enzyme-ligand complex is equal to the sum of the charges on the enzyme plus ligand, that is
ZEL ) ZE + ZL
(11)
and that the A and B terms are constant for all species, we can substitute eq 10 for the activity coefficients of
Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 375 Table 3. Values of A, B, and K0 Coefficients in Modified Debye-Hu 1 ckel Model pH 7.5 8.0 8.6
T (K)
2A (mol-1/2 L1/2)
aB (mol-1/2 L1/2)
K0 (L mol-1)
298 300 302 298 300 302 298 300 302
0.226 0.230 0.244 0.233 0.241 0.293 0.289 0.291 0.329
0.438 0.550 0.696 0.445 0.651 0.717 0.599 0.842 0.952
0.688 0.694 0.844 0.643 0.674 0.790 0.632 0.666 0.715
and hence, the adsorption decreases with increasing temperature, and the hydrophobic character of adsorption increases. This effect is in agreement with the findings of Lakhuri et al.5 In general, the hydrophobic character of adsorption is weaker in optimal adsorption conditions (pH 8.6, 298 K), a stronger hydrophobic character being seen when the adsorption conditions are less favorable (pH 7.5, 302 K). This is all probably due to electrostatic interactions, as described above. For a given pH value, the A and B values increase with temperature. This is because A and B are inversely proportional to the dielectric constant of the medium, which decreases when temperature increases. Conclusions
Figure 7. log[KD/KD(γ) I ) 0] vs ionic strength.
each species into eq 8 to obtain
log
KD KD(γ)
)
-2AZEZLxI I + aBxI
+ K0I
(12)
where
K0 ) KEL - KE - KL
(13)
The experimental data obtained for KD(γ) from CE, CL, and CEL at an ionic strength of I ) 0 gave approximately 1.12 × 10-2 mol/kg. The data are shown in Figure 7a,b,c, plotted as log KD/[KD(γ) I ) 0] vs ionic strength for all of the different conditions studied. These data were correlated by the described model, eq 12, through a regression analysis, and then the A, B, and K0 coefficients were obtained, (Table 3). Taking into account the A and B values (Table 3) and accordingly eq 12, it can be concluded that, for values of I lower than 0.8 M NaCl, the hydrophobic contribution is small, this effect increasing with I, especially for values higher than 0.8 M NaCl. In addition, the K0, parameter, which takes into account the hydrophobic effect, increases with temperature for a fixed pH value,
From the experiments reported here, it can be concluded that adsorption increases with pH and decreases when temperature rises, increasing the hydrophobic linkages. Adsorption increases with ionic strength up to an I value of 0.05 M NaCl, after which it decreases for all of the temperatures and pH studied. Under optimal operating conditions (298 K, pH 8.6, and 0.05 M NaCl) almost 75% of the enzyme in solution is adsorbed. Of this, about 2/3 of the enzyme is linked by specific hydrophobic bonds and the rest is linked by nonspecific sites or retained inside the adsorbent. In addition, when the ionic strength was steadily decreased, the equilibrium constant values were different from those obtained when the ionic strength was increased. This effect can be explained in terms of a possible change in the lattice of the matrix, namely, a rearrangement due to the adsorption-desorption of ionic species, in a manner similar to ion exchangers. The equilibrium data were correlated using a semiquantitative theory based on the Debye-Hu¨ckel theory for activity coefficients, in which electrostatic and hydrophobic interactions between the enzyme and ligand are considered. This correlation shows that the hydrophobic effects, K0, increase with temperature, in very good agreement with the experimental data. Acknowledgment This research was supported by funds from the Comision Interministerial de Ciencia y Tecnologı´a (CICYT). Ms. E. M. Martı´n del Valle gratefully acknowledges a fellowship from the same organization (CICYT). Notation A ) constant in the Debye-Hu¨ckel equation, L1/2 mol-1/2 a ) effective ion radius, cm aE, aL, aEL ) activities of enzyme, ligand, and enzyme-ligand complex, respectively, mol kg-1 of adsorbent
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B ) constant in the Debye-Hu¨ckel equation, L1/2 mol-1/2 cm-1/2 Ce ) enzyme concentration in the bulk solution, IU mL-1 CE, CL, CEL ) concentration of enzyme, ligand, and enzymeligand complex, respectively, mol kg-1 of adsorbent CE0, CL0 ) concentration of enzyme and ligand, respectively, at time t ) 0, mol kg-1 of adsorbent CTL ) concentration of total ligand attached to the particles, mol kg-1 of adsorbent I ) ionic strength, mol L-1 K0 ) hydrophobic constant, L mol-1 KA ) enzyme-ligand adsorption equilibrium constant, kg of adsorbent mol-1 KD ) enzyme-ligand dissociation equilibrium, mol kg-1 of adsorbent KD(γ) ) enzyme-ligand dissociation equilibrium constant as function of activities, mol kg-1 of adsorbent KDIS ) distribution coefficient, dimensionless KE,KL, KEL ) hydrophobic constants of enzyme, ligand, and enzyme-ligand complex, respectively, L mol-1 ZE, ZL, ZEL ) charges of enzyme, ligand and enzyme-ligand complex, respectively, dimensionless Greek Letters γE, γL, γEL ) activity coefficients of enzyme, ligand, and complex, respectively, dimensionless
Literature Cited (1) Lowe, C. R., Dean, P. D. G., Eds. Affinity Chromatography; Wiley-Interscience: London, 1974; p 12. (2) Morrow, D.; Carbonell, B.; McCoy, B. J. Electrostatic and hydrophobic effects in affinity chromatography. Biotechnol. Bioeng. 1975, 17, 895-914.
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Received for review April 11, 2000 Revised manuscript received July 31, 2000 Accepted September 20, 2000 IE000401N
