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A Rational Approach to the Scale-up of Affinity Chromatography F. H. ARNOLD, J. J. CHALMERS, M. S. SAUNDERS, M. S. CROUGHAN, H. W. BLANCH, and C. R. WILKE Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720 Affinity chromatography has great potential for the separation of high-value products from dilute fermentation broths; one of the drawbacks is the lack of i n formation that can be applied to scale-up. Most a f f i nity chromatography is i n fact a rather special case of a fixed-bed adsorption process: the equilibrium is highly favorable, and the breakthrough curve is likely to be constant pattern. These characteristics greatly simplify the modeling. When presented in the proper nondimensional form, the experimental breakthrough curves from small, lab-scale columns can be used to predict the performance of large affinity columns. This paper discusses the breakthrough models applicable to affinity chromatography i n terms of the rate-limiting mass transfer mechanisms. We have compared the breakthrough data from a model monoclonal antibody-antigen affinity column to the predictions of two of these models. A rational approach to the scale-up of affinity chromatograph is presented. The remarkable selectivities shown by numerous biological molecules have been used to great advantage i n recovery and purification by affinity chromatography. Monoclonal antibodies can be produced against a wide variety of substances, making affinity chromatography applicable to the purification of practically any macromolecule from complex mixtures. This technique is quickly becoming feasible for industrial separations. Janson and Hedman (1) recently published an excellent review of large-scale chromatography. Many of the broad process design and operation considerations are the same for affinity chromatography as they are for ion exchange or gel f i l t r a t i o n . Most chromatography models, however, are based on the assumption of small feed pulses with linear equilibria (such as the widely-used plate theories (2)) and are not directly useful for affinity separations. In this paper we discuss and compare experimental results with two fixed-bed adsorption models that can be used to predict the performance of a f f i nity columns. These two models differ only i n the form of the rate0097-6156/85/0271-0113506.00/0 © 1985 American Chemical Society In Purification of Fermentation Products; LeRoith, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
PURIFICATION O F FERMENTATION PRODUCTS
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l i m i t i n g mass t r a n s f e r s t e p — o n e case b e i n g d i f f u s i o n i n t h e pore l i q u i d and t h e o t h e r a d i f f u s i o n s t e p i n t h e p a r t i c l e phase. These mod e l s can be used t o o p t i m i z e a s e p a r a t i o n o r t o p r e d i c t t h e p e r f o r mance o f a l a r g e - s c a l e column, based on d a t a from l a b o r a t o r y - s c a l e experiments. For systems w i t h t h e f a v o r a b l e e q u i l i b r i a t y p i c a l o f a f f i n i t y chromatography, t h e b r e a k t h r o u g h curve f o r an i d e a l o p e r a t i o n i s a s t e p f u n c t i o n . The s o l u t e i n t h e f e e d i s taken up c o m p l e t e l y , up u n t i l t h e time a t which t h e bed i s s a t u r a t e d . A t t h i s i n s t a n t t h e e f f l u e n t s o l u t e c o n c e n t r a t i o n becomes e q u a l t o t h e f e e d c o n c e n t r a t i o n . The o p e r a t i o n i s then s w i t c h e d t o wash and e l u t i o n . T h i s ads o r p t i o n s t e p i s c o n s i d e r e d i d e a l because 100% o f t h e bed c a p a c i t y has been used, and no f e e d has been w a s t e d . The t o t a l uptake i s simply the e q u i l i b r i u m c a p a c i t y of the a f f i n i t y packing. J u s t as i n o t h e r types o f chromatography, mass t r a n s f e r , a x i a l d i s p e r s i o n , and d e v i a t i o n s from p e r f e c t p l u g f l o w a l l a c t t o spread out t h e b r e a k t h r o u g h c u r v e . I f t h e column i s s w i t c h e d t o wash a t a p a r t i c u l a r e f f l u e n t c o n c e n t r a t i o n , c , than a p o r t i o n o f t h e bed c a p a c i t y has n o t been used ( F i g u r e 1 ) . I f , on t h e o t h e r hand, t h e a d s o r p t i o n s t e p i s c o n t i n u e d u n t i l t h e e n t i r e bed i s s a t u r a t e d , an amount o f s o l u t e e q u a l t o t h e a r e a under t h e curved p o r t i o n o f t h e b r e a k t h r o u g h h i s t o r y i s w a s t e d . A l o n g e r a d s o r p t i o n c y c l e time i s needed t o r e a c h t h e f u l l bed c a p a c i t y . An o u t l i n e f o r d e v e l o p i n g a q u a l i t a t i v e s c a l e - u p s t r a t e g y has been p r e s e n t e d by E v e l e i g h ( 3 ) . A q u a n t i t a t i v e study o f p r o c e s s o p t i m i z a t i o n and t h e e f f i c i e n t use of r e s o u r c e s r e q u i r e s an unders t a n d i n g o f t h e b e h a v i o r o f t h e l a r g e - s c a l e column. I f t h e immobil i z e d l i g a n d ( a n t i b o d y ) i s s c a r c e , o p e r a t i o n may be o p t i m i z e d by u s i n g t h e f u l l bed c a p a c i t y each c y c l e , g o i n g t o h i g h e r b r e a k t h r o u g h c o n c e n t r a t i o n s . On t h e o t h e r hand, i f t h e f e e d r e c o v e r y i s t h e most i m p o r t a n t f a c t o r , t h e a d s o r p t i o n s t e p may be t e r m i n a t e d a t s m a l l b r e a k t h r o u g h c o n c e n t r a t i o n s , w i t h l e s s than f u l l use o f t h e column c a p a c i t y . I n o r d e r t o p r e d i c t t h e e f f e c t s o f changes i n o p e r a t i n g c o n d i t i o n s , one must know how each i n f l u e n c e s the shape o f t h e breakthrough curve. B T
Breakthrough
models
An a n a l y t i c a l e x p r e s s i o n f o r t h e b r e a k t h r o u g h curve can be o b t a i n e d by s o l v i n g the e q u a t i o n s d e s c r i b i n g c o n t i n u i t y o f a s o r b a t e s p e c i e s i n a f i x e d b e d , t h e e q u i l i b r i u m r e l a t i o n between t h e s o l u t e and t h e s o r b a t e , and t h e r a t e o f a d s o r p t i o n and mass t r a n s f e r , w i t h t h e app r o p r i a t e i n i t i a l and boundary c o n d i t i o n s . The e x a c t s o l u t i o n o f the complete s e t o f e q u a t i o n s i s o f t e n i m p o s s i b l e , b u t a f f i n i t y chromatography l e n d s i t s e l f t o s e v e r a l c o n v e n i e n t s i m p l i f i c a t i o n s , w i t h t h e r e s u l t t h a t a n a l y t i c a l s o l u t i o n s a r e a v a i l a b l e . The not a t i o n used h e r e i s t h a t o f Vermeulen (4) . D u r i n g t h e a d s o r p t i o n s t e p , t h e b i n d i n g o f s o l u t e by t h e a f f i n i t y l i g a n d i s o f t e n v e r y t i g h t , e s s e n t i a l l y i r r e v e r s i b l e . F o r Langmuir, o r constant s e p a r a t i o n f a c t o r a d s o r p t i o n , the e q u i l i b r i u m r e lation i s
* q Q
K m
L
c
1 + K
L
c
In Purification of Fermentation Products; LeRoith, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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7.
ARNOLD ET AL.
Scale-up of Affinity
Chromatography
115
unused column capacity
feed "wasted
processing time Time — •
F i g u r e 1.
Breakthrough curve f o r a f f i n i t y a d s o r p t i o n . I f feed i s stopped a t e f f l u e n t c o n c e n t r a t i o n CBT» a p o r t i o n o f t h e column c a p a c i t y has n o t been used. A s m a l l amount o f s o l u t e i s l o s t i n the e f f l u e n t .
In Purification of Fermentation Products; LeRoith, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
PURIFICATION OF FERMENTATION PRODUCTS
116 The
separation
f a c t o r R, d e f i n e d by
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R
=
1/(1
+
K
l
c
f
e
e
d
i s analogous t o t h e r e l a t i v e v o l a t i l i t y i n v a p o r - l i q u i d e q u i l i b r i a . For f a v o r a b l e e q u i l i b r i a (R
