Radial-Flow Affinity Chromatography for Trypsin Purification

Chapter 8

Radial-Flow Affinity Chromatography for Trypsin Purification 1

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Wen-Chien Lee , Gow-Jen Tsai, and George T. Tsao School of Chemical Engineering and Laboratory of Renewable Resources Engineering, Purdue University, West Lafayette, IN 47907

The dynamic performance of a radial-flow affinity chromatographic system for trypsin purification has been studied experimentally and theoretically. A mathematical model, which considers both axial dispersion in the mobile phase and pore diffusion inside the fiber, has been developed for simulation and parameter estimation. Based on this model, a design equation has been derived for scale-up of column operation. The design equation employs the concept of volume equivalent of a theoretical stage (VETS) instead of height equivalent of a theoretical plate (HETP) commonly used in the axial-flow chromatography. Experiments from the frontal elution approach were designed and tested for verification of this design equation. A methodology of estimating system parameters from breakthrough experiments was also proposed and applied to the model system.

For the purification of biomolecules such as proteins, liquid chromatography ( L Q , in its various forms, is by far the most efficient method. It was reported (1) that bioseparation has been the largest segment of the LC market and that a user-wish list of the chromatographic equipment for bioseparation includes high productivity, rigidity, rapid scale-up, high performance without high pressure, reproducibility, biocompatibility and low non-specific adsorption. To meet some of the demands radial flow chromatography has been considered as an alternative because of its new geometry. Two companies, CUNO (2 ,3A) and Sepragen (5,6,7), have marketed their equipment for radial flow chromatography, which is commonly mentioned as one of the most interesting innovations of the last several years although its advantages have not been fully evaluated. The radial flow column consists of three main parts, i.e., outer channel, column packing, and inner channel (Figure 1). On operation, the sample is distributed into the outer channel and flows radially inward through the column packing. Then, the elution fluid flows down 1

Current address: Department of Chemical Engineering, Chung Yuan Christian University, Chung Li, Taiwan 32023, Republic of China 0097-6156/90/0427-0104$06.00A) © 1990 American Chemical Society

In Protein Purification; Ladisch, Michael R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

Radial-Flow Affinity Chromatography

105


8. LEE ET AL.

Figure 1. (a)Experimental set-up of radial flow chromatographic system for trypsin purification. (b)Dimensions of the radial flow cartridge.


PROTEIN PURIFICATION


106

the inner channel and through a collector to the column outlet. The column packing is where the biospecific adsorption occurs. In the CUNO product, the column packing is a cartridge in which the matrix is fabricated into thin paper sheets and then spirally wound around a center plastic core. Warren (8) mentioned that CUNO's radial-flow cartridge is a typical product of the marriage of chromatography and membrane techniques. Radial flow chromatography is ideal for fast-flow rate systems because of the low pressure drop across the chromatographic packing. The advantages in fast-flow rate and low pressure are especially important in the treatment of large volumes of dilute products from some bioprocesses. Radial flow chromatography becomes more powerful for fast purification when it is combined with the principle of affinity chromatography. The successful scaling-up of affinity chromatography will realize the commercial applications of various proteins and enzymes, which are now too expensive to use in large quantities. Radial-flow affinity chromatography may be one of the best choices for down-stream purification in production scale. In this work, the dynamic performance of radial-flow chromatography was studied by per forming thefrontalelution experiments on a trypsin purifying cartridge. Theoretical study of the radial-flow affinity system led to design equations for scaling-up. The results from exper iments on cartridge were used to compare those from theoretical predictions. A methodology for parameter estimation was also presented. Theory The process by which soluble protein molecules are transported by fluid flow through the void space of porous matrix media and adsorbed on the surfaces of the matrix in radial-flow affinity chromatography can be highly complex. When the method of local volume averag ing (9) is applied to the column cartridge (Figure lb), the governing equation of protein (tryp sin) concentration in the mobile phase can be simplified as

The process is considered to be isothermal and a constant volumetrical flow rate Q is imposed in inward direction. The r" denotes the net mass transfer rate from the bulk fluid to the adsorbed phase and can be expended as follows. ,,_ 4(1-ε) 2

^ , dC

1 de .

k (C-c| f

3c.

M l p / 2

(2)

dc

dq

) =D -|-| ^ i

I

Λ

p / 2

/ Ο Λ

(4)

£ u - 0

(5)

!j=Mq*-q)

(6)

In this model, a uniform diameter of dp is assumed for the cylindrical,fibrousmatrix with monodisperse pores, an external film separating the bulk fluid and solid phase is present, and an effective diffusion coefficient based on the entire fiber volume is used to describe the diffusion of solute into the pores. The parameter k accounts for the adsorption rate, while the mass transfer rate through the film is accounted for by k . The equilibrium isotherm describes a

f


8. LEE ET A L

107


the relationship between concentrations c and q. To account for the possibility that all sites can be filled with the adsorbed molecules, many researcher considered the equilibrium relation to be of the Langmuir type, Qs K

q* = 4

C

L

(7)

l+K c


L

Equations 1 to 7 are solved numerically by spatially discretizing Equations 1 and 3 into a set of ordinary differential equation (ODE) using finite difference and orthogonal collocation methods, respectively. The ODEs are then solved by the well known Gear's backward difference method (10). In order to scale-up the radial-flow system, the concept of plate theory from the axial-flow system has been extended (77). The definition of HETP, i.e., H = L/N, is still needed but with small modification. Instead of using the plate height H and column length L, we define a Volume Equivalent Theoretical Stage (VETS) V in the following equation to replace the plate height H and use the bed volume V to replace the column length L. s

B

V

= i

V

(8)

* = -S- Î B

Ν μϊ By following the generalized methodology developed in the previous work (77), the design equation for this particular radial-flow affinity chromatographic system can be obtained as V

=

'

4

+

B

+

C

( 9 )

f

where 2

2

A =4 ,D jt h (RÎ+R§) y

(10)

m

8

RÏ-Ro C =- 4 f?

(12)

with f^l+i-^Hep +

ft.q.KL)

and ZPdQsKL

l-ε

f 2

=

(

i _ i

)

[

^ J ,

+

(

d

_ Z

d

o r

+

o

_L

r ) (

e

2

p

+

P p q s

ο

K ) ] L

In the first step of scaling-up, fixed Ν means that the chromatographic efficiency is preserved. The volume of a theoretical stage V can be evaluated by the design equations once the parameters in these equations are estimated experimentally. Finally, the packed bed volume for a given operating flow rate is obtained by a product of Ν and V . The value of Ν can be estimated experimentally by injecting a standard sample into the chromatography system. s

s

When the isotherm nonlinearity is considered, the equations derived above are not proper but still useful. Equations 9 to 12 provide the first approximation of the true values of V . In order to calculate μι and ^ in Equation 8, the following two definitions are needed in fron tal elution. s


108


c

ο

o

oo

μ ' = /(1-7?-)12 fragments of horse immunoglobulins (16) and monoclonal antibody IgG (17). Table III summarizes the results from breakthrough experiments with Type II trypsin as sample. The chromatographic behaviors in these cases are very similar to that in which pure trypsin is applied. From this, one may conclude that the interference of non-specific com ponents on the bio-specific adsorption is insignificant. Figures 6 and 7 report the break through behaviors with Q = 40 and 67 ml/min, respectively. In these twofigures,circles are data points, while solid lines represent the predicted values resulting from model simulation with the parameters estimated from the system using Type I trypsin. It is obvious that the model prediction agrees fairly well with the experimental data. Parameter Estimation. In this work, a methodology of estimating parameters from break through experiments has been developed. (1) .

Binding constant K and maximum binding capacity ( l - e ) p q were deter mined from a reciprocal plot of retention volume vs. sample concentration. In this step Equation 16 has been used.

(2) .

Dispersion coefficient was estimated from the change of retention volume vs. flow rate. The faster the flow rate, the more significant the dispersion. It is proved that retention volume ((5μ0 strongly depends on dispersivity, but is nearly independent offinitemass transfer rate. Figure 8 shows the dependency of retention volume on dimensionless reciprocal dispersivity at two different sample concentrations.

L

p

(3) .

s

Pore diffusivity Dj and film mass transfer coefficient k were determined by fitting breakthrough curves with model, i.e. Equations 1 to 7. In this work, only the results from experiments using Type I trypsin, are used for curve fitting. The adsorption rate constant k should be also estimated from this curve fitting. In this affinity system, k is very large compared to the mass transfer rate constant due to higher specific interaction. Here we also assume that kf is not dependent on flow rate. Notice that some of the system parameters could be estimated from independent experi ments other than the breakthrough experiment, depending on which is more convenient. As we have evaluated all parameters, either from literature or from the estimation method men tioned above, we can (1) predict breakthrough behavior and (2) predict VETS. Solid lines in Figures 6 and 7 come from this prediction. Good agreement between predictions and experi ments can be observed from these two figures. Figure 9 shows the experimental and predicted VETS in the system when Type II trypsin is applied. Although they show general agreement, a deviation is observed in the range of small flow rate. The reason probably is model limitation. The model might not exactly simulate the true behaviors in the cartridge, because the made-up packing in the CUNO car tridge is not homogeneous for its special fabrication which makes the flow distribution diversified. It was observed that the occasional blockades contribute imperfection of the flow pattern. Figure 10 shows the comparison of experimentally obtained VETS with the design equa tion given by Equation 9. In those experiments, Type I trypsin was used. A close agreement exists because the parameters used in Equation 9 are estimated from the same experiments. f

a

a



(f/l)

2.8

2.83

2.75

4.67

(g/1)

10

10

10

10

4.1

2

Activity

3.8

2

Sample Concentration

3.9

2

95.7

187

18.1

2054

18.2 40

1.39

1.41 67 80

1.37

2.32

1109

1926

2003

(=μ, Q, ml)

(ml/min)

trypsin

based on Type I

Retention Volume

m

74

444

31.7

125

75.6

65.6 13.9

84

47.2

232 28.7

98

42.1

105

31.2 2376 631

(%)

(ml)

2

(min )

Activity Recovery

50.1

112.9

μι. (min)

VETS

97

94

93

(%)

Activity Recovery

Second Central Moment

II trypsin

First Moment

Results of breakthrough experiments with Type

1085

1183

33

VETS

938

2

69

2

(ml)

μ,, (min)

First Moment

Flow Rate

0

c

Table III.

60

37.3

1339

(= μι Q, ml)

(ml/min)

φ ο

19.4

Retention Volume

Flow Rate

Activity

(g/D

Second Central moment μ' (min )

Results of breakthrough experiments with Type I trypsin

Sample Concentration

Table II.



114


THROUGHPUT, mL.

Figure 6. Comparison of experimentally obtained breakthrough curves (circles) with the model prediction (solid line). Flow rate Q = 40 ml/min; sample: Type II trypsin.

THROUGHPUT, mL.

Figure 7. Comparison of experimentally obtained breakthrough curves (circles) with the model prediction (solid line). Flow rate Q = 67 ml/min; sample: Type II trypsin.


8. LEE ET A L

115


2,500

•J 2,000

1,500


g

K000

500

0

10

20

30

40

50

DIMENSIONLESS RECIPROCAL DISPERSIVITY

Figure 8. Effect of dimensionless dispersivity on the retention volume. 100 • 80

EXPT. DATA MODEL PREDICTION

60

40

20

0 I 0

1 1 1 1 1 1 0.2 0.4 0.6 0.8 1 1.2 VOLUMETRIC FLOW RATE (Q), mL/sec.

1—ι 1.4

Figure 9. Comparison of experimentally obtained VETS with the model prediction using Equations 1 to 7.

I 0

ι 0.2

ι ι ι ι 1 0.4 0.6 0.8 1 1.2 VOLUMETRIC FLOW RATE (Q), mL/sec.

1 1.4

Figure 10. Comparison of experimentally obtained VETS with the design equations given by Equation 9.


116



Conclusion Radial-flow affinity Chromatography has been found to be successful for fast purification of trypsin. In frontal elution, as expected, therate-determiningsteps of adsorption and elution are the mass transfer in the pores of the fibrous matrix and through the external film. There fore, the volumetricflowrateQ is the most important factor for production in large scale. The design equations using Q as the design variable have been verified experimentally to be use ful and recommended for scaling-up of theradial-flowaffinity system. The use of the CUNO cartridge as an example ofradial-flowchromatography has exposed a problem of imperfect flow distribution. But this problem becomes minor if we operate the system simply in the adsorption/desorption mode. Despite the flow distribution problem, the experiments on the radial-flow purification system result in useful data. The parameters characterizing the perfor mance of the purification system were evaluated from breakthrough datafittingthe proposed model. Once the system parameters are estimated, we can predict breakthrough behavior for any sample concentration and operating condition and predict the values of VETS. Acknowledgments This work was supported by the National Science Foundation Grant (EET-8613167A2). We also thank Professor Michael R. Ladisch, Department of Agricultural Engineering, Purdue University, for his helpful comments during preparation of this manuscript, and Dr. Kenneth C. Hou of CUNO, Inc. (Meriden, Connecticut) for the gift of the radial flow cartridge. Legend of Symbols c Co c D

protein concentration in bulk fluid phase inlet concentration of protein in frontal elution protein concentration in pores dispersion coefficient (column dispersivity),

Di D dp h K

effective pore diffusivity of protein in pores molecular diffusivity of protein diameter of cylindrical packing fiber height of the radial flow chromatography Langmuir or association (binding) constant adsorption rate constant fluid film mass transfer coefficient of soluble protein volumetricflowrate sorbate concentration, kg/(kg particle) maximum concentration of sorbate, kg/(kg particle) radial coordinate of chromatography radius of the inner channel radius of the outer channel radial distance in fiber time unretard void volume volume of packed bed volume of a theoretical stage retention (elution) volume

D = YiL\i+Y2dpV

m

L

k

a

k

f

Q> q q R Ro Ri r t Vo v V v s

B s

t

V

= linear velocity, ν = —-~-— 2 7chRe J


8. LEE ET A L


117

ε void fraction of the packed bed ερ porosity of particle p fiber density μι first moment \ii second central moment ν dimensionless reciprocal dispersivity, defined as ν = ——— 4πηεϋ Yi constant Y2 constant Downloaded by UNIV OF CALIFORNIA SAN DIEGO on February 29, 2016 | http://pubs.acs.org Publication Date: June 12, 1990 | doi: 10.1021/bk-1990-0427.ch008

p

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. p 13. 14. 15. 16.

McCormick, D. Bio/Technol. 1988, 6, 158. Hou, K. C.; Mandara, R. M. Bio Techniques. 1986, 4, 358. Mandara, R. M.; Roy, S.; Hou, K. C. Bio/Technol. 1987, 5, 928. McGregor, W. C.; Szesko, D. P.; Mandara, R. M.; Rai, V. R. Bio/Technol. 1985, 4, 526. Saxena, V. U. S. Patent, 4 676 898, 1987. Saxena, V.; Weil, A. E. BioChromatogr. 1987, 2, 90. Saxena, V.; Subramanian, K.; Saxena, S.; Dunn, M. BioPharm 1989, March, 46. Warren, D. C. In Chemical Separation, Vol. II Application; King; Navratil, Eds., Litarvan Literature; Denver, CO, 1986. Slattery, J. C. Momentum, Energy and Mass Transfer; McGraw Hill, New York, NY, 1981. Gear, C. W. Numerical Initial-Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1972. Lee, W.-C. Ph.D. Thesis, Purdue University, West Lafayette, 1989. Geiger, R.; Fritz, H. In Method in Enzymatic Analysis; Bergmeyer, Ed., 1984; Vol. V, 119. Kasai, K.-I.; Oda, Y. J. Chromatogr. 1986, 376, 33. Adamski-Medda, D.; Nguyen, Q. T.; Dellacherie, E. J. Membrane Sci. 1981, 9, 337. Benanchi, P. L.; Gazzei, G.; Giannozzi, A. J. Chromatogr. 1988, 450, 133. Jungbauer, Α.; Unterluggauer, F.; Unl, K.; Buchacher, Α.; Steindl, F.; Pettauer, D.; Wenisch, E. Biotechnol. Bioeng. 1988, 32, 326.

RECEIVED December 28,1989


Radial-Flow Affinity Chromatography for Trypsin Purification

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