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Ind. Eng. Chem. Res. 2002, 41, 2296-2304
Effect of the Spacer Arm in Affinity Chromatography: Determination of Adsorption Characteristics and Flow Rate Effect 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 effect of the spacer arm in affinity chromatography based on the adsorption equilibrium of L-asparaginase on activated Sepharose 4B with aliphatic diamines (1,4-diaminobutane-1,8diaminooctane) as the spacer arms and L-(+)-chlorosuccinamic acid as the ligand was studied in a batch reactor and in a packed bed. The adsorption equilibrium constants were determined for all adsorbents. A maximum in the adsorption was observed when 1,6-diaminohexane was used as the spacer arm under optimum adsorption conditions (pH 8.6, 298 K, and 0.05 M NaCl) (Martı´n del Valle, E. M.; Gala´n, M. A. Ind. Eng. Chem. Res. 2001, 40 (1), 369-376). Partition coefficients were also obtained in the batch reactor. The values of these coefficients allowed us to quantify the amounts of specifically adsorbed, nonspecifically adsorbed, and occluded enzyme. A pulse-response chromatographic method and statistical moments were used to determine the adsorption equilibrium constants in the packed bed. The values of the adsorption equilibrium constants for different adsorbents were compared with those obtained previously in the batch reactor taking into account the mass-transfer resistance inside the particles of the adsorbent (partition coefficient). The difference in the values obtained was lower than 5-8%. In addition, the effect of the flow rate on adsorption was studied for different adsorbents with spacer arms of different lengths. When the flow rate was increased, the value of the adsorption equilibrium constant increased. This effect was observed when 1,8-diaminooctane was used as the spacer arm Introduction Over the past two decades, advances in biochemical and genetic engineering techniques have allowed for the development of a vast range of new biotechnology products and processes, as well as the replacement of many process involving conventional chemical techniques. Downstream processing of biomolecules obtained from fermentation broths is a fundamental step in biotechnology as it often represents the major manufacturing cost. The economic viability of such processes depends not only on the innovations achieved in production, but also on the innovations and optimization of such processes.2 Chromatography has been widely used as a highperformance purification step in biotechnology. Among the chromatographic techniques available, one of most important is affinity chromatography. This is because it is a powerful tool for the purification of biological macromolecules such as proteins, as well as a good example of a highly selective separation method.3 Many of the efforts carried out to scale-up a process are developed at the intermediate pilot-plant level using empirical or semiempirical methods.4 Several physical and mass-transfer processes, such as adsorption-desorption are very important in affinity chromatography because they involve complex mechanics. In addition, the role of the matrix in determining of the accessibility of the coupled ligand to the macromolecule is also a major factor. Nevertheless, despite the porosity of the adsorbent, if the ligand is coupled * To whom correspondence should be addressed.
directly to the matrix backbone, steric hindrance with the ligand interaction will occur. It is therefore clear that, for successful purification by affinity chromatography, the chemical groups critical in the interaction with the macromolecule must be sufficiently distant from the solid matrix support. This problem can be approached by placing the ligand at the end of a long chain or “arm”.3,5,6 No systematic studies have attempted to explain the effect that increasing the length of the spacer arm has on specific and nonspecific enzyme adsorption and on enzyme occluded inside the particles.3,6 As adsorbent particles are highly porous, the spacer arms and the ligand are immobilized inside them. The curtain effect produced by the spacer-arm concentration leads the enzyme concentration inside the particles to be different from the enzyme concentration in the bulk solution. Therefore, when the adsorption process is carried out in a batch reactor, the enzyme in solution inside the particle interacts with the ligands, with a reversible adsorption equilibrium between the adsorbed and nonadsorbed enzyme inside the particles being established. The adsorption constant of this equilibrium corresponds to the true adsorption constant of the adsorption process and can be determined using the equilibrium data and taking into account the partition coefficient.7 However, when a chromatographic process is carried out in a column, several steps are followed. First, the column is packed with the adsorbent, and an eluent is passed through it. The pores of the particles will therefore be filled with this eluent. Following this, the adsorption step, during which the enzyme with an eluent as carrier is passed through the column, is
10.1021/ie0106884 CCC: $22.00 © 2002 American Chemical Society Published on Web 04/09/2002
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2297
carried out. The eluent makes the enzyme enter the particle little by little and causes it to remain adsorbed. Therefore, because the amount of eluent is much greater than the amount of enzyme because the pores have been already filled with it (low enzyme concentration), equilibrium is reached in a short time. In this way, the nonadsorbed enzyme elutes with the carrier. Accordingly, when working in a column, the adsorption equilibrium constant will be the true constant of the process. The aim of the present work was to obtain a better knowledge of the effect of the length of the spacer arm in affinity chromatography. To this end, adsorption equilibria were studied for L-asparaginase on activated Sepharose 4B with spacer arms of different lengths (1,4diaminobutane-1,8-diaminooctane) and also for L-asparaginase on activated Sepharose 4B with spacer arms of different lengths and L-(+)-chlorosuccinamic acid as the ligand. The behavior of the system was studied in a batch reactor and in a packed bed. From the experiments carried out in the batch reactor the adsorption equilibrium constants; the partition coefficients; and the amounts of enzyme specifically bonded, nonspecifically bonded, and occluded inside the pores were determined for all of the systems studied. Experiments based on dynamic impulse-response methods were performed to study the system in a column. Thus, adsorption equilibrium constants were determined and compared with those obtained previously in the batch reactor. In-column experiments based on these methods have been used in affinity chromatography. Cantero et al.8 determined the physical properties and mass-transfer coefficients in a column packed with nonactivated Sepharose 6B-100 using pulses of blue dextran and L-asparaginase and moment theory. Other studies have also been carried out using impulse-response methods. For example, in 1996, Zuyi et al.9 determined the adsorption equilibrium constants of three amino acids on dextran-type ion-exchange columns using isocratic elution chromatography and the first absolute moment of the elution curves. Kempe et al.10 simulated a chromatographic process applied to protein separation. The program was based on a model including axial dispersion in the bulk solution, external and internal mass-transfer resistances, and a nonstationary nonlinear adsorption model. Frontal and pulse chromatography can be used for single and multicomponent systems. Materials L-Asparaginase (E.C. 3.5.1.1.) and Sepharose 4B were purchased from Sigma Chemical Corporation. The other chemicals used, 1,4-diaminobutane,1,5-diaminopentane, 1,6-diaminohexane, 1,7-diaminoheptane, 1,8-diaminooctane, L-asparagine, D-asparagine, sodium chloride, cyanogen bromide, boric acid and sodium tetraborate were obtained from Merck. All chemicals were of reagent grade. L-(+)-Chlorosuccinamic acid was obtained by a Walden conversion from D-asparagine, as described by Holmberg.11 The physical properties of this compound were determined by proton nuclear magnetic resonance (1H NMR) spectroscopy and by the rotary power (+54), indicating a purity of 96% and a synthesis yield of about 35%.
Figure 1. Spherical porous particle with liquid phases R and β inside and outside pores, respectively.
Experimental Section Adsorbents. Different adsorbents were prepared following the procedure described by Martı´n del Valle and Gala´n.1 Enzyme Assays. The enzymatic activity of L-asparaginase was measured using L-asparagine as substrate, analyzing the ammonia produced by Nessler’s method.12 Batch Reactor Studies One of the main objectives of the present work was to study the adsorption-desorption equilibrium for different systems comprising L-asparaginase on activated Sepharose 4B with spacer arms of different lengths (1,4-diaminobutane-1,8-diaminooctane) and Lasparaginase on activated Sepharose 4B with spacer arms of different lengths (1,4-diaminobutane-1,8-diaminooctane) and L-(+)-chlorosuccinamic acid as the ligand. Because the adsorbent particles are very porous (β ) 0.89), the enzyme retained in the particles is partially occluded inside rather than being adsorbed. In addition, the curtain effect produced by the spacer-arm concentration leads the enzyme concentration inside the particles to be different from the enzyme concentration in the bulk solution. Therefore, a reversible adsorption equilibrium is established between the enzyme adsorbed and not adsorbed inside the particles.7,13 To quantify this effect, the partition coefficients were determined, following the theory developed by Taylor and Swaisgood,14 for all adsorbents, both with ligand and without ligand, at pH 8.6, 298 K, and I ) 0.05 M NaCl; these are the optimum conditions for adsorption in this system.15 The partition coefficient is defined as the ratio between the concentration of enzyme inside the pores, phase R, and the concentration of enzyme in solution, phase β (Figure 1). Accordingly, a reversible adsorption equilibrium is established between the enzyme adsorbed and that not adsorbed in phase R. This can be described by
ER + L a ELR
(1)
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Table 1. Partition Coefficients and Adsorption Equilibrium Constants of L-Asparaginase on Activated Sepharose 4B with Spacer Arms of Different Lengths spacer arm
Kp
KD (mol/L)
K′A
1,4-diaminobutane 1,5-diaminopentane 1,6-diaminohexane 1,7-diaminoheptane 1,8-diaminoctane
0.21 0.27 0.30 0.28 0.22
2.97 × 10-3 2.00 × 10-3 1.97 × 10-3 2.25 × 10-3 2.34 × 10-3
336 498 507 445 426
Table 2. Partition Coefficients and Adsorption Equilibrium Constants of L-Asparaginase on Activated Sepharose 4B with Spacer Arms of Different Lengths and L-(+)-Chlorosuccinamic Acid as the Ligand spacer arm
Kp
KD (mol/L)
K′A
1,4-diaminobutane 1,5-diaminopentane 1,6-diaminohexane 1,7-diaminoheptane 1,8-diaminoctane
0.56 0.70 1.30 0.66 0.60
9.67 × 10-4 7.24 × 10-4 4.55 × 10-4 6.70 × 10-4 8.92 × 10-4
1034 1381 2196 1492 1120
The equilibrium dissociation constant K′D is defined as
K′D )
CRECL CREL
(2)
Taking into account that
CTL ) CL + CREL
(3)
CRTE
(4)
)
CREL
KP )
+
CRE
CRE CβE
CβE
- KP )
CTLKP K′D + KPCβE
Additionally, the partition coefficient allowed us to determine the concentration of enzyme occluded inside the pores, the amount specifically adsorbed, and the amount nonspecifically adsorbed. Accordingly, with the definition of the partition coefficient, it is possible to determine the concentration of enzyme in solution inside the pores
CRE ) KPCβE
(7)
and, taking into account that
(5)
by substituting into eq 2 and making some rearrangements, one obtains
CRTE
Figure 2. Percentage of enzyme specifically bonded to Sepharose 4B activated, with aliphatic diamines as the spacer arm and L-(+)chlorosuccinamic acid as the ligand. pH 8.6, 298 K, I ) 0.05 M NaCl.
(6)
where CRTE, CβE, and CTL are known because CβE is the concentration of enzyme in the bulk solution. The value of CRTE is the total concentration of enzyme in phase R, obtained by subtracting the concentration of enzyme in solution, CβE, from the total concentration of enzyme added to the reactor, CE0. CTL is the total amount of ligand attached to the particles (which is also on the surface, although this amount is assumed to be very small in comparison with the amount of ligand inside the pores). However, K′D and Kp are unknown. To determine these parameters, for each different adsorbent, several runs were carried out with different spacer arms and initial ligand concentrations on the adsorbents. From the experimental data thus obtained, the values of Kp and K′D were calculated (Tables 1 and 2). From these tables, it can be observed that the extension of the spacer arm affects the adsorption process. Thus, an adsorption maximum was observed when 1,6diaminohexane was used in the adsorbents with ligand as well as in the adsorbents without ligand. However, the adsorption equilibrium constant values decreased when the spacer arm had four or five methylene groups; adsorption was lower for these adsorbents.
CRTE ) CRE + CREL
(8)
CRTE ) CE0 - CβE
(9)
the concentration of enzyme adsorbed inside the pores, CREL, can be determined. Thus, for the adsorbents with ligand, this adsorbed enzyme will correspond to the enzyme specifically bonded. The rest of the enzyme will be in solution or nonspecifically bonded. Using the experimental data determined for the adsorbents without ligand and applying the previous reasoning, it is possible to quantify the percentage of enzyme adsorbed through nonspecific bonds and the percentage of occluded enzyme. The percentages of enzyme specifically bonded, nonspecifically bonded, and occluded were calculated for each of the adsorbents studied and are shown in Figures 2-4. These figures show that, for all of the adsorbents studied, of the total amount of enzyme inside the particles, some is specifically bonded, some is occluded, and a small percentage is nonspecifically bonded. However, when the length of the spacer arm was modified, these percentages changed. Figure 2 shows that specific adsorption reaches a maximum when 1,6-diaminohexane is used as the spacer arm. However, an increase or decrease in the length of the spacer arm leads to a decrease in the specific bonding. Figure 3, which represents the percentage of nonspecifically bonded enzyme, shows that such bonding is a minimum for the adsorbent with six methylene groups
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2299
amount of specifically bonded enzyme was higher, and the amounts of nonspecifically and occluded enzyme were lower. When the length of the spacer arm increases (1,7diaminoheptane and 1,8-diaminooctane), the aliphatic chain might fold up. The separation distance between the matrix and ligand would thus decrease. These two effects involve steric hindrance and, hence, a decrease in the amount of specifically bonded enzyme and an increase in the amounts of nonspecifically bonded and occluded enzyme. This was observed when 1,7-diaminoheptane and 1,8-diaminooctane were used. Column Studies Figure 3. Percentage of enzyme nonspecifically bonded to Sepharose 4B activated, with aliphatic diamines as the spacer arm and L-(+)-chlorosuccinamic acid as the ligand. pH 8.6, 298 K, I ) 0.05 M NaCl.
Figure 4. Percentage of enzyme occluded in Sepharose 4B activated, with aliphatic diamines as the spacer arm and L-(+)chlorosuccinamic acid as the ligand. pH 8.6, 298 K, I ) 0.05 M NaCl.
in the spacer arm. However, it increases when the spacer arm is shorter or longer than of 1,6-diaminohexane. Figure 4 shows that the highest percentage of occluded enzyme is obtained when the spacer arm has four and five methylene groups. Thus, the percentage decreases for 1,6-diaminohexane, and an increase in the length of the extension arm leads to an increase in the amount of occluded enzyme. To explain these experimental data, it must be considered that, to facilitate the access of the enzyme to the ligand and to avoid steric effects, the matrix and ligand must be sufficiently separated. If the spacer arm is too short, it can be ineffective because the ligand fails to bind the enzyme because of steric hindrance. Therefore, when the spacer arm has four and five methylene groups, it is ineffective. The amounts of enzyme nonspecifically bonded and occluded therefore increase. However, when 1,5-diaminopentane was used the amount of nonspecifically bonded enzyme was higher than when 1,4-diaminopentane was used, probably because the distance available to bond the enzyme was greater. When 1,6-diaminohexane was used, the separation distance between the matrix and ligand was sufficient to avoid steric hindrance. Thus, the accessibility of the enzyme to the ligand was greater. Therefore, the
Theory. The theoretical model used to describe the adsorption of enzyme from bulk solution onto the adsorbent takes into account (i) diffusion of the component from the bulk solution to the external surface of the adsorbent particle (external diffusion), (ii) diffusion through the porous network of the particle (internal diffusion), and (iii) the adsorption process itself. In addition, the following assumptions are used as the basis for construction of the model: (i) The fluid in the column is in isobaric and isothermal conditions. (ii) The particles are spherical, and mass transfer occurs only by diffusion through them. (iii) There is no concentration gradient in the radial direction in the bulk solution. (iv) The surface reaction between the adsorbate and an adsorption site is described by a reversible second-order reaction. (v) The enzyme concentration is low enough to describe the adsorption by a linear isotherm. Taking into account these assumptions, the Kubin15 theory was applied. In this theory, the moments of the chromatographic peak leaving the bed are related to the parameters describing the mass-transfer processes, namely, the axial dispersion coefficient, the external mass-transfer coefficient, intraparticle diffusivity, and the adsorption equilibrium constant. The result for the first absolute moment, which was developed elsewhere,15,16 is
µ1 ) (z/V)(1 + δ0) + (t0/2) + µd
(10)
where
δ0 )
[
][ ( ) ]
Fp (1 - R)β 1+ K R β A
(11)
The experimental chromatographic curves of the effluent from the bed can be used to determine the first absolute moment
∫0∞tCE(z,t) dt µ1 ) ∞ ∫0 CE(z,t) dt
(12)
It can be observed (eq 10) that the first absolute moment of the chromatographic curve is the sum of the moment of the compound injected, the first absolute moment in the dead volume, and the injection time
µ1 ) µ1bed + µd + µ1 )
t0 2
t0 z 1-R (β + FpKA) + µd + 1+ V R 2
[
]
(13) (14)
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Equation 14 can therefore be used to evaluate the adsorption equilibrium constants. Experiment. According to eq 14, to determine the adsorption equilibrium constants by the pulse-response method, it is first necessary to determine the first absolute moment of the dead volumes and the porosity of the bed. Column Studies with Adsorbents with Spacer ARMS of Different Lengths Determination of the First Absolute Moment of the Dead Volumes. To determine the first absolute moment of the dead volume, 1-mL pulses of blue dextran (0.15-0.20 wt %/vol), prepared just before use, were injected into an adjustable XK-16 Pharmacia borosilicate glass column of 16-mm inside diameter that was thermostated with a jacket made of acrylic plastic and kept at a constant temperature of 298 K. The column was packed with glass spheres with a diameter similar to the spheres of Sepharose 4B [(80-100) × 10-6 m]. It was assumed that this packing is inert and that KA ) 0. In addition, the high molecular weight of blue dextran (MW ) 2 × 106) prevents its penetration into pores, and hence, β ) 0. A UV-vis spectrophotometer was used to analyze the blue dextran according to the technique described in the work of Menta.17 In this work, turbulent flow was chosen because under these conditions, the external mass-transfer resistance is lower and the time required to carry out the experiments is also shorter. A 0.05 M boric/borate buffer solution, pH 8.6, was used as the carrier. The flow rate of this eluent carrier ranged from 1.1 × 10-2 to 3.0 × 10-2 m/min. Taking into account the above assumptions, eq 14 becomes
t0 Rz µ1 ) µd + + 2 V0
(15)
In this equation, µ1 was calculated experimentally from measurements of the response signals through expression 12. t0/2 is the duration of the injection. R is the porosity of the column and was determined previously to be 0.28, and z and V0 are the length of the bed (8 × 10-2 m) and the flow rate of the carrier, respectively. Therefore, it is possible to determine µd for each different flow rate. Plotting µd vs V0 and subjecting the experimental data to a linear regression afforded an expression that allowed us to determine µd for a flow rate in the range of (1.1-3.0) × 10-2 m/min.
µd ) -0.0734Q + 0.3657
(16)
Porosity of a Bed of Sepharose 4B. To determine the porosity of a bed of Sepharose 4B, the above column was packed with spheres of Sepharose 4B and glass spheres [(80-100) × 10-6 m inside diameter] as inert material. This packing was used because, when the column was packed with Sepharose 4B up to 8 cm, turbulent flow could not be obtained owing to the high ∆P. In the column, 1-mL pulses of blue dextran were injected and analyzed as described above. In this bed, the first absolute moment is given by
µ1 ) µinert + µd +
t0 zSepharoseRSepharose + 2 V0
(17)
where
µinert )
Rinertzinert V0
(18)
According to eq 17, a plot of µ1 - µinert - t0/2 - µd vs zSepharose/V0 (Figure 5) should be a straight line, the slope of which gives the porosity of a bed packed with Sepharose 4B. The porosity value found was 0.14. Determination of Adsorption Equilibrium Constants. The chromatographic curves of asparaginase on activated Sepharose 4B with aliphatic diamines of different lengths (1,4-diaminobutane-1,8-diaminooctane) were obtained. These curves were obtained by comparing the adsorption equilibrium constants determined chromatographically with the values measured in the experiments carried out in the batch reactor. The column was packed as described before with the respective adsorbent and with glass spheres as the inert material. Pulses of 1 mL of asparaginase (10 IU/mL) were injected into the column. The column was kept at 298 K and a 0.05 M boric borate buffer solution, pH 8.6, containing 0.05 M NaCl was used as the carrier. The flow was always turbulent. The first absolute moment is given by eq 14. In this bed, µ1 is the retention time of asparaginase on the adsorbent and on the inert material, where adsorption does not occur. Therefore, eq 14 becomes
µ1 ) µd +
[ (
)
t0 Radszads Rads 1+ (β + + µinert + 2 V0 1 - Rads
]
FpKA) (19) In eq 19, all parameters are known except KA. Plotting µ1 - µinert - t0/2 - µd vs zads/V0, straight lines are obtained (Figure 6) from whose slopes the value of the adsorption equilibrium constants were obtained. The values for the different adsorbents are shown in Table 3. In this table, good agreement is seen between the values of the adsorption equilibrium constants obtained in the column and the values obtained in the batch reactor taking into account the partition coefficients. When the chromatographic process is carried out in a column, the enzyme with an eluent, which is the carrier, are passed through the packed bed. Because the amount of eluent is much greater, as the pores are already filled with it (low enzyme concentration), equilibrium is quickly reached, and the nonadsorbed enzyme is eluted with the carrier. For this reason, when working in a column, the adsorption equilibrium constants are the true constants of the process. Therefore, the good agreement between the constant values confirms the notion that, when working in a batch reactor with porous particles, the enzyme inside the particles is partly retained instead of being adsorbed. Thus, an adsorption equilibrium is established inside the particles, and the adsorption equilibrium constant of this equilibrium is the true constant.
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2301 Table 3. Adsorption Equilibrium Constants of Asparaginase on Activated Sepharose 4B with Spacer Arms of Different Lengthsa
a
spacer arm
KA column (L/mol)
KA batch (L/mol)
1,4-diaminobutane 1,5-diaminopentane 1,6-diaminohexane 1,7-diaminoheptane 1,8-diaminooctane
375 414 468 431 419
335 498 507 445 433
pH 8.6, 298 K, and I ) 0.05 M NaCl.
Figure 5. First absolute moment of blue dextran in a column packed with glass spheres and Sepharose 4B.
Figure 7. First absolute moment of L-asparaginase on activated Sepharose 4B with 1,8-diaminooctane as the spacer arm. pH 8.6, 298 K, and I ) 0.05 M NaCl.
Figure 6. First absolute moment of L-asparaginase on activated Sepharose 4B with aliphatic diamines of different lengths as the spacer arm. pH 8.6, 298 K, and I ) 0.05 M NaCl.
Effect of Flow Rate on the Length of the Spacer Arm. Theoretically, the retention time of a compound
in a packed bed with an adsorbent will be zero for a high flow rate. However, in Figure 6, it can be observed that the plots are linear for the adsorbents with between four and seven methylene groups in the spacer arm, but nonlinear for the adsorbent with eight methylene groups in the spacer arm, at least within the range of flow rates studied. This effect was observed in several experiments. To explain this effect, it is necessary to take into account that the compounds used as the spacer arms are aliphatic diamines, whose structures are flexible. As described previously, when the length of the spacer arm increases, these molecules become curved because of their flexibility. If the spacer arms are folded, they can curl up into a ball or tangle, which hinders access of the enzyme to the interior of the pores. If the flow rate is increased in the system, an unfolding of the spacer arm could occur. This could therefore be more useful, and a change in the adsorption process could occur. To investigate this possibility, an experiment was carried out with higher flow rates using activated Sepharose 4B with 1,8-diaminooctane as the spacer arm and following the experimental procedure described above. The data obtained are plotted in Figure 7. The figure shows that, in this system, the adsorption process changes when the flow rate is increased. To account for this finding, it is also necessary to take into account what happens in this system, and hence, the mass-transfer resistance in the stagnant film was determined. Thickness of the Stagnant Film. According to stagnant film theory,18,19 the thickness of the film surrounding the beads is a function of the molecular diffusion coefficient and the external mass-transfer coefficient
δ)
DM kf
(20)
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Table 4. Thickness of Stagnant Film and External Mass-Transfer Coefficient of L-asparaginase on Activated Sepharose 4B with 1,8-Diaminooctane as the Spacer Arm V0 (m/s)
Rep
kf (m/s)
δ (µm)
2.16 × 10-4 2.60 × 10-4 3.10 × 10-4 4.00 × 10-4 4.50 × 10-4 6.06 × 10-4 8.30 × 10-4 1.03 × 10-4 1.36 × 10-4
0.14 0.17 0.20 0.26 0.29 0.42 0.53 0.66 0.87
1.40 × 10-6 1.54 × 10-6 1.67 × 10-6 1.89 × 10-6 2.00 × 10-6 2.38 × 10-6 2.67 × 10-6 2.97 × 10-6 3.40 × 10-6
2.38 2.17 2.00 1.77 1.67 1.40 1.25 1.12 0.98
(a) Molecular Diffusion Coefficient. According to the random-pore model,20 the molecular diffusion coefficient is given by
DE ) D M β 2
(21)
DE is known because it has already been determined for the same system by Martı´n del Valle and Gala´n.6 These authors found a value of DE ) 2.65 × 10-12 m/s2. Taking into account that β ) 0.89, one obtains
DM ) 3.34 × 10-12 m/s2 (b) External Mass-Transfer Coefficient. The masstransfer coefficient kf describes the external masstransfer resistance in the film surrounding the beads. This resistance can be estimated by numerous correlations, all of which give mass-transfer coefficients of the same order of magnitude. The correlation used here was that of Wakao,21 namely
Sh ) 2 + 1.45Rep1/2Sc1/3
Figure 8. Thickness of stagnant film vs Re for the system L-asparaginase on activated Sepharose 4B with 1,8-diaminooctane as the spacer arm and L-(+)-chlorosuccinamic acid as the ligand. pH 8.6, 298 K, and I ) 0.05 M NaCl.
(22)
response will be obtained at the outlet column because the enzyme remains specifically bonded to the adsorbent until the adsorbent becomes saturated. To obtain the breakthrough curves, the abovedescribed experimental procedure was followed. The same column as was used previously was packed with the inert material and the adsorbent: activated Sepharose 4B with aliphatic diamines as the spacer arm and L-(+)-chlorosuccinamic acid as the ligand. A solution of 0.05 M boric/borate buffer, pH 8.6, and 0.05 M NaCl was used as eluent. Measurement of the breakthrough curves was started by replacing the stream of buffer by the asparaginase solution. Fractions of this solution were collected at the column outlet and analyzed to determine enzyme activity. With the data thus obtained, the above theory was applied. The first absolute moment is given by
where
k fd p Sh ) DM
(23)
µ FDM
(24)
Sc )
From this correlation, kf was calculated for the different flow rates (Table 4). Using these data and the DM value determined above, the thickness of the stagnant film was calculated for each Reynolds number value. These data are plotted in Figure 8. This figure shows that, when the flow rate increases up to a Reynolds number of 0.3, the thickness of the stagnant film acquires an asymptotic shape up to a minimum that can be reached (1 µm). A favorable transport and an increase in the flow rate can generate an unfolding of the spacer arm inside the pores. Therefore, the spacer arm becomes more available for adsorption, which can therefore increase, as was observed experimentally. Column Studies with Adsorbents with Spacer ARMS of Different Lengths and with Ligand To obtain the adsorption equilibrium constant of asparaginase on the adsorbents with a spacer arm and ligand, it is necessary to determine the breakthrough curves. If pulses of asparaginase are injected into a column packed with the adsorbent and ligand, no
µ1 ) µd + µinert +
[ (
)
]
Radszads Rads 1+ (β + FpKA) V0 1 - Rads (25)
On plotting µ1 - µd - µinert vs z/V0 (Figure 9), straight lines were obtained from whose slopes the values of the adsorption equilibrium constants were obtained. The values for the different adsorbents are shown in Table 5. Table 5 shows that the adsorption equilibrium constants obtained from the experiments carried out in the column are similar to those obtained in the batch reactor, taking into account the partition coefficient values. This effect was also found for the adsorbents without ligand. From these results, it can be concluded that, when working in a batch reactor with highly porous particles, the true adsorption equilibrium is established inside the particle, as reported above. Effect of Flow Rate on the Length of the Spacer Arm. As described above, when working ina column, an increase in the flow rate can generate an unfolding of the spacer arm. Thus, steric hindrance will be lower, and adsorption can increase. To investigate this effect, two experiments using the adsorbents with seven and eight methylene groups in their spacer arms were carried out with a higher flow rate following the experimental procedure described above. The data obtained are plotted in Figure 10.
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2303
Figure 10. First absolute moment of L-asparaginase on two different adsorbents. pH 8.6, 298 K, and I ) 0.05 M NaCl.
Figure 9. First absolute moment of L-asparaginase on activated Sepharose 4B with aliphatic diamines of different lengths as the spacer arm and L-(+)-chlorosuccinamic acid as the ligand. pH 8.6, 298 K, and I ) 0.05 M NaCl. Table 5. Adsorption Equilibrium Constants of L-asparaginase on Activated Sepharose 4B with Spacer Arms of Different Lengths and L-(+)-Chlorosuccinamic Acid as the Liganda
a
spacer arm
KA column (L/mol)
KA batch (L/mol)
1,4-diaminobutane 1,5-diaminopentane 1,6-diaminohexane 1,7-diaminoheptane 1,8-diaminooctane
1136 1332 1822 1421 1139
1034 1381 1985 1492 1120
pH 8.6, 298 K, and I ) 0.05 M NaCl.
In this figure, it can be observed that, for the adsorbent with seven methylene groups, in the spacer arm the plots are linear for all flow rates studied. However, for the adsorbent with eight methylene groups, there are two different zones. When the flow rate was lower than 0.028 m/min, the retention time varied linearly with the flow rate. However, when the flow rate was higher than 0.028 m/min, the retention time still
varied linearly with the flow rate but with a different slope. Furthermore, it can be seen that the flow rate necessary to produce a change in the adsorption process with the adsorbent with ligand is higher than that necessary for the adsorbent without ligand. This is because of the electrostatic interactions in the adsorbent with ligand. From Figure 10, it can be inferred that, for the adsorbent with seven methylene groups in the spacer arm, an increase in the flow rate does not modify the adsorption process. However, an increase in the flow rate does modify the adsorption process when the spacer arm has eight methylene groups. To explain this effect, as described above, when the flow rate increases, the thickness of the stagnant film of the particles takes a minimum value, and transport is more favorable. In addition, when the flow rate is increased, the ball or tangle made by the spacer arm and ligand can unfold. Accordingly, steric hindrance is lower and the enzyme can approach the ligand, resulting in increased adsorption, as was observed experimentally. Conclusion From the experiments reported here, it can be concluded that, in affinity chromatography, the length of the spacer arm affects the adsorption process. Under optimum adsorption conditions (pH 8.6, 298 K, and 0.05 M NaCl), in both the adsorbents with ligand and in the adsorbents without ligand, maximum adsorption was observed when 1,6-diaminohexane was used as the spacer arm. However, an increase or decrease in the length of the spacer arm led to a decrease in the amount of specifically bonded enzyme and an increase in the amounts of nonspecifically bonded and occluded enzyme. The adsorption equilibrium constants determined from the experiments performed in the batch reactor, taking into account the partition coefficient, and those determined from the in-column experiments are similar. This confirms that, when working with a batch reactor, a true adsorption equilibrium is established inside the particle between the enzyme adsorbed and that in solution.
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In addition, it was found that, when the flow rate increased, a change occurred in the adsorption process; when the flow rate was increased, the value of the adsorption equilibrium constant was higher. This effect was observed when 1,8-diaminooctane was used as the spacer arm. Acknowledgment This research was supported with 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 CREL ) concentration of enzyme adsorbed inside pores, mol L-1 CRTE ) concentration of total enzyme inside pores, mol L-1 CE ) concentration of enzyme in the interparticle space, mol L-1 R CE ) concentration of enzyme in solution inside pores, mol L-1 CβE ) concentration of enzyme in the bulk solution, mol L-1 CE0 ) concentration of enzyme at time t ) 0, mol L-1 CL ) concentration of ligand, mol L-1 CTL ) concentration of total ligand attached to the particles, mol L-1 DE ) effective intraparticle diffusion coefficient, m2 s-1 DM ) molecular diffusion coefficient, m2 s-1 I ) ionic strength, mol L-1 K′A ) enzyme-ligand adsorption equilibrium constant, L mol-1 K′D ) enzyme-ligand dissociation equilibrium, mol L-1 kf ) external mass-transfer coefficient, m s-1 Kp ) partition coefficient Rep ) particle Reynolds number Sc ) Schmidt number Sh ) Sherwood number t ) time, min t0 ) duration of the injection, min V ) linear velocity of the eluent in the interparticle space, m min-1 V0 ) superficial velocity of the eluent in the bed, m min-1 z ) length coordinate of the bed of adsorbent measured from the inlet side, m. Greek Symbols R ) interparticle void fraction in the adsorbent bed β ) intraparticle void fraction (internal porosity) of adsorbent δ ) thickness of stagnant film, µm δ0 ) expression defined by eq 11 µd ) first absolute moment of dead volume, min µn ) nth absolute moment of the chromatographic curve, min µ′n ) nth central moment of the chromatographic curve, min F ) density, kg L-1 Fp ) apparent particle density, kg L-1
Literature Cited (1) Martı´n del Valle, E. M.; Gala´n, M. A. Specific and nonspecific adsorption in affinity chromatography. Part I. Preliminary and equilibrium studies. Ind. Eng. Chem. Res. 2001, 40 (1), 369376. (2) Wheelwright, S. M. Designing downstream processes for large-scale protein purification. Biotechnologia 1987, 5, 789. (3) Lowe, C. R., Dean, P. D. G., Eds. Affinity Chromatography; Wiley-Interscience: London, 1974. (4) Bautista, L. F.; Martı´nez, M.; Aracil, J. Adsorption equilibrium of R-amylase in aqueous solutions. J. AIChE 1999, 45, 4, 761-768. (5) Janson, J. C., Ryde´n, L., Eds. Protein Purification; VCH Publishers: New York, 1989; pp 289, 297, 306. (6) Hermanson, T. G., Mallia, A. K., Smith, P. K., Eds. Immobilized Affinity Ligand Techniques; Academic Press: New York, 1992; ppp 4, 137, 139. (7) Martı´n del Valle, E. M.; Gala´n, M. A. Specific and nonspecific adsorption in affinity chromatography. Part II. Kinetic and mass transfer studies. Ind. Eng. Chem. Res. 2001, 40 (1), 377383. (8) Cantero, D.; Gil de Rebolen˜o, R.; Gala´n, M. A. Mass transport coefficients in gel permeation by moment analysis. Anal. Quı´m. 1987, 83, 641-646. (9) Zuyi, T.; Changyin, Y.; Qing, H. Determination of adsorption equilibrium constant and HETP of amino acids on dextran-type ion exchangers columnssA study on isocratic elution chromatography and moment method. React. Funct. Polym. 1996, 28, 221226. (10) Kempe, H.; Axelsson, A.; Nilsson, B.; Zacchi, G. Simulation of chromatographic processes applied to separation of proteins. J. Chromatogr. 1999, 846, 1-12. (11) Holmberg, B. Stereochemische Studien. XIII. U ¨ ber β-Chlorsuccinamidsa¨uren. Chem. Ber. 1926, 59, 1569-1580. (12) Arranz, M. A.; Gala´n, M. A. Microencapsulacio´n de Enzimas, Sistema Urea-Ureasa. Ing. Quı´m. 1981, 11, 125-129. (13) Gonza´lez-Patino, F.; Catala´n, J.; Gala´n, M. A. Affinity chromatography: Effect of particle size on adsorption equilibrium and mass transfer kinetics. Chem. Eng. Sci. 1993, 48, 1567-1573. (14) Taylor, B. J.; Swaisgood, H. E. A unified partition coefficient theory for chromatography, immobilized enzyme kinetics, and affinity chromatography. Biotechnol. Bioeng. 1981, 23, 13491366. (15) Schneider, P.; Smith, J. M. Adsorption rate constants from chromatography. J. AIChE 1968, 14, 5, 762-771. (16) Ditkin, V. A.; Kuznestsov, P. I. Spravochnik po operacionnomu ischisleniju; Gostechizdat: Moscow, 1951. (17) Metha, R. V.; Merson, R. L.; McCoy, J. Moment analysis of experiments in gel permeation chromatography. J. AIChE 1973, 19, 5, 1068-1070. (18) Themelis, N. J., Ed. Transport and Chemical Rate Phenomena; Gordon and Breach Publishers: Langhorne, PA, 1995. (19) Deen, W. M., Ed. Analysis of Transport Phenomena; Oxford University Press: New York, 1998. (20) Smith, J. M., Ed. Chemical Engineering Kinetics, 3rd ed.; McGraw-Hill: New York, 1981. (21) Wakao, N.; Oshima, T.; Yagi, S. Mass transfer from packed beds of particles to a fluid. Chem. Eng. Jpn. 1958, 22, 780-785.
Received for review August 20, 2001 Revised manuscript received February 8, 2002 Accepted February 10, 2002 IE0106884
