Foundations of Biochemical Engineering - American Chemical Society


Foundations of Biochemical Engineering - American Chemical Societypubs.acs.org/doi/pdf/10.1021/bk-1983-0207.ch017Similar...

1 downloads 90 Views 948KB Size

17 Immobilized Cells Catalyst Preparation and Reaction Performance J. KLEIN and K.-D. VORLOP

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

Technical University of Braunschweig, Institute of Chemical Technology, Federal Republic of Germany Immobilized cells have proven to be effective cata­ lysts i n the enzymatic conversion of organic com­ pounds. Such catalysts are typically prepared by entrapment of cells i n polymeric carriers, and the methods of ionotropic gelation and polycondensation of epoxids w i l l be described. Depending on enzymatic activity and particle size the transformation may proceed i n the reaction or diffusion controlled re­ gime. Quantitative estimation of the effectiveness factor-Thiele modulus relation w i l l be presented for different reaction types. This includes the experi­ mental determination of the catalytically active c e l l concentration and the effective d i f f u s i v i t y i n the porous polymeric carrier. Transport limitation can also be a controlling factor i n the experimental determination of the operational s t a b i l i t y of such biocatalysts.

A large number of products i n the pharmaceutical and food industry i s obtained from fermentation processes. Examples are amino acids, stereoregular organic acids, antibiotics, ethanol, etc. In a classical fermentation process the product formation is s t r i c t l y coupled to c e l l growth resulting i n a possibly unfav­ orable byproduction of biomass. Furthermore these processes are typically performed as batch operations. As has been shown already on an industrial scale, fermenta­ tion can be substituted by heterogeneous catalysts with resting microbial cells immobilized i n polymeric carriers. Repeated use of the once formed biomass, continuous process operation, and elim­ ination of costly separation steps of product solution from bio­ mass are obvious advantages of this new technology. Some p r i n c i ­ pal aspects of a) immobilization methodology, b) catalyst effect­ iveness, and c) operational s t a b i l i t y shall be outlined i n this contribution. 0097-6156/83/0207Ό377$06.00/0 © 1983 American Chemical Society

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

378

ENGINEERING

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

Polymer Entrapment V a r i o u s methods h a v e b e e n p r o p o s e d f o r w h o l e c e l l i m m o b i l i z a ­ t i o n i n c l u d i n g a d s o r p t i o n and c o v a l e n t a t t a c h m e n t t o a p r e f o r m e d c a r r i e r , c r o s s l i n k i n g , f l o c c u l a t i o n , m i c r o e n c a p s u l a t i o n , and e n ­ t r a p m e n t . P h y s i c a l e n t r a p m e n t i n a p o r o u s m a t r i x i s by f a r t h e most f l e x i b l e and most commonly u s e d t e c h n i q u e . Considering the f a c t t h a t t h e p o l y m e r n e t w o r k has t o be f o r m e d i n t h e p r e s e n c e o f t h e f i n a l l y entrapped b i o l o g i c a l m a t e r i a l , the performance c r i t e r i a of c h e m i c a l and p h y s i c a l n a t u r e a r e as f o l l o w s : (1) The n e t w o r k f o r m a t i o n has t o p r o c e e d u n d e r m i l d c o n d i ­ t i o n s (pH and t e m p e r a t u r e ) i n an aqueous e n v i r o n m e n t ; (2) t h e n e t w o r k has t o be c h e m i c a l l y s t a b l e u n d e r v a r i o u s r e ­ a c t i o n c o n d i t i o n s (pH, b u f f e r s o l u t i o n , i o n i c and n o n i o n i c s u b ­ strates, etc.); (3) t h e s i z e and t h e p o r o s i t y o f t h e p o l y m e r i c c a r r i e r ( p r e f ­ e r a b l y as b e a d s ) has t o be c o n t r o l l e d ; (4) t h e p o s s i b i l i t y f o r a l a r g e v a r i a t i o n o f b i o m a s s c o n t e n t i n t h e c a t a l y s t s h o u l d be g i v e n ; (5) t h e c a t a l y s t b e a d s s h o u l d be m e c h a n i c a l l y s t a b l e t o be used i n v a r i o u s r e a c t o r c o n f i g u r a t i o n s (packed bed, f l u i d i z e d bed, s t i r r e d tank). A p p r o p r i a t e p o l y m e r i c c a r r i e r s c a n be o b t a i n e d f r o m p o l y m e r i c , o l i g o m e r i c , and monomeric p r e c u r s o r s . Due t o unwanted c h e m i c a l i n ­ t e r a c t i o n of such chemicals w i t h the c e l l m a t e r i a l l a r g e r s i z e of t h e s e p r e c u r s o r s i s f a v o r a b l e . The i o n o t r o p i c g e l a t i o n , s t a r t i n g f r o m p o l y e l e c t r o l y t e s and t h e p o l y c o n d e n s a t i o n , s t a r t i n g f r o m o l i ­ g o m e r i c epoxy r e s i n s , a r e t y p i c a l p r o b l e m s o l u t i o n s . I o n o t r o p i c G e l a t i o n of P o l y e l e c t r o l y t e s T h i s method o f n e t w o r k f o r m a t i o n i s d e f i n e d as a c r o s s l i n k i n g r e a c t i o n of p o l y e l e c t r o l y t e s w i t h lower molecular weight m u l t i v a ­ lent counterions. C o n s i d e r i n g t h e p o l y m e r i c component, a n i o n i c ( e . g . , a l g i n a t e , CMC (I) o r c a t i o n i c ( c h i t o s a n (2)) substances can be u s e d . T h i s v a r i e t y o f p o l y m e r s and t h e a p p r o p r i a t e c o u n t e r i o n s a r e s u m m a r i z e d i n F i g u r e 1. The c h o i c e o f t h e p o l y m e r i s d e t e r ­ m i n e d by t h e pH r e g i o n o f t h e r e s p e c t i v e b i o c a t a l y t i c r e a c t i o n , s i n c e a l l i o n o t r o p i c g e l s a r e r e v e r s i b l e s t r u c t u r e s w h i c h c a n be r e d i s s o l v e d by i n c r e a s e ( a l g i n a t e ) o r d e c r e a s e ( c h i t o s a n ) o f pH b e ­ yond c e r t a i n l i m i t s . A second important c r i t e r i o n i s the i o n i c c o m p o s i t i o n o f t h e r e a c t i o n medium and t h e p o s s i b i l i t y o f i n s o l u b l e byproduct o r complex f o r m a t i o n w i t h the network forming i o n s . I n a t y p i c a l a l g i n a t e entrapment process the c e l l s are sus­ pended i n a 3% s o d i u m a l g i n a t e s o l u t i o n and t h i s v i s c o u s s u s p e n ­ s i o n i s p r e c i p i t a t e d d r o p w i s e i n a 1% C a C l 2 s o l u t i o n . A f t e r 30 m i n u t e s s t a b l e C a - a l g i n a t e g e l s a r e f o r m e d where t h e c e l l s a r e i m ­ m o b i l i z e d i n a macroporous s t r u c t u r e . F o l l o w i n g to t h i s p r e c i p i ­ t a t i o n p r o c e s s a p a r t i a l d r y i n g s t e p c a n be a p p l i e d w h i c h r e s u l t s i n a homogeneous s h r i n k i n g o f t h e p a r t i c l e s , t h u s i n c r e a s i n g c o n -

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

KLEIN

A N D VORLOP

Immobilized

POLYELECTROLYTES

Cells

379

as Catalysts

MULTIVALENT COUNTERIONS

POLYANIONS ALGINATE '""cOO^

Χ

CARBOXYMETHYLCELLULOSE

φ

CARBOXY-GUARGUM

Ca . Fe . Zn 2 +

Al \ 3

2 +

Fe

2 +

...

3 +

COPOLY-STYRENEMALEIC ACID POLYCATIONS CHITOSAN

Fe(CN)

6

4

\

Fe(C^

3

"

POLY-PHOSPHATE /

^ΝΗ3

Φ

Χ

θ

POLY-ALDEHYDO-CARBONIC ACID P0LY-1-HYDR0XY-1SULF0NATE-PR0PEN-2 ALGINATE

Figure 1. Summary of polymer-counterion systems to be used in ionotropic gelation for whole cell entrapment. Reprinted, with permission, from Ref. 13. Copy­ right 1982, Plenum Publishing Corp.

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

380

ENGINEERING

s i d e r a b l y t h e m e c h a n i c a l s t a b i l i t y as w e l l a s t h e p a c k i n g d e n s i t y of the entrapped c e l l s i t s e l f . A l l these f a c t o r s are very advanta­ geous f o r t h e b i o c a t a l y t i c a p p l i c a t i o n . The f l e x i b i l i t y o f t h e a l g i n a t e - m e t h o d c a n be d e m o n s t r a t e d a c c o r d i n g t o t h e f o l l o w i n g p a r ­ a m e t e r b o u n d a r y v a l u e s : p o l y m e r c o n c e n t r a t i o n f r o m 0.5 t o 8%, CaC^ c o n c e n t r a t i o n f r o m 0.05 t o 2%, c e l l c o n c e n t r a t i o n (on wet w e i g h t b a s i s ) f r o m 0.1 t o 100%, b e a d d i a m e t e r s f r o m 0.1 t o 5 mm, and p r e p a r a t i o n t e m p e r a t u r e s f r o m 0 t o 80° C. Cells of different s t r u c t u r e ; e.g., a e r o b i c (1) o r a n a e r o b i c m i c r o b e s ( 3 ) , p l a n t c e l l s ( 4 ) , mammalian c e l l s ( 5 ) , c a n be e n t r a p p e d and t h u s s t a b i l i z e d without c o n s i d e r a b l e t o x i c i t y problems. A p r o b l e m o f p r a c t i c a l i m p o r t a n c e i s t h e s c a l e up o f t h e i m ­ m o b i l i z a t i o n p r o c e s s f r o m amounts o f s e v e r a l grams t o s e v e r a l hundred l i t e r s . W h i l e s m a l l amounts c a n e a s i l y be p r e p a r e d u s i n g one c a p i l l a r y o r i f i c e , a b u n d l e o f s u c h c a p i l l a r y i n a s i e v e p l a t e t y p e c o n s t r u c t i o n w i l l g i v e l a r g e r amounts o f i d e n t i c a l p a r t i c l e s , i f the c a p i l l a r y c h a r a c t e r i s t i c s a r e not changed. These d e v i c e s a r e shown i n F i g u r e 2. Polycondensation

o f Epoxy

Resins

I n t h i s c a s e c o v a l e n t n e t w o r k s o f h i g h m e c h a n i c a l and c h e m i ­ c a l s t a b i l i t y a r e o b t a i n e d as a r e s u l t o f c r o s s l i n k i n g r e a c t i o n of e p o x i d e s w i t h m u l t i f u n c t i o n a l a m i n e s ( 6 ) . The m a i n p r o b l e m s o f t h i s t e c h n i q u e a r e t h e t o x i c i t y o f t h e amino-component and t h e u s u a l l y l o w p o r o s i t y o f t h e p o l y m e r i c n e t w o r k . The t o x i c i t y , mea­ s u r e d by t h e v i a b i l i t y o f i m m o b i l i z e d y e a s t c e l l s , c o u l d be m i n i ­ m i z e d a) by p r o p e r s e l e c t i o n o f e p o x y and amino components and b) by i n t r o d u c t i o n o f a p r e g e l l i n g t i m e i n t h e o r d e r o f 15 m i n u t e s b e f o r e m i x i n g t h e c e l l s w i t h t h e c o n d e n s a t i n g o l i g o m e r s ( 7 ) . The p o r o s i t y o f t h e m a t r i x i s i n t r o d u c e d by t h e i m m o b i l i z e d c e l l s i t ­ s e l f and by an i n t e r m e d i a t e p r e p a r a t i o n o f an i n t e r p e n e t r a t i n g n e t w o r k w i t h an i o n o t r o p i c g e l . The i o n o t r o p i c g e l a t i o n i s a l s o u s e d t o c o n t r o l t h e p a r t i c l e s h a p e and s i z e . A c o m p l e t e scheme o f s u c h a n i m m o b i l i z a t i o n p r o c e s s i s shown i n F i g u r e 3. A g a i n q u i t e h i g h c o n c e n t r a t i o n s (up t o 70% on wet w e i g h t b a s i s ) o f c e l l s c a n be f i n a l l y i n c o r p o r a t e d i n s u c h a p o l y m e r i c s t r u c t u r e . The v i a b i l i t y o f t h e y e a s t c e l l s , and t h u s t h e r e d u c e d t o x i c ­ i t y o f t h e e n t r a p m e n t m e t h o d , c a n be d e m o n s t r a t e d by c e l l g r o w t h i n the m a t r i x , which gives r i s e to a corresponding a c t i v i t y i n ­ crease f o r ethanol p r o d u c t i o n from glucose ( 7 ) . This behavior i s shown i n F i g u r e 4. The f a c t o r o f a c t i v i t y i n c r e a s e compared t o t h e i n i t i a l v a l u e i n c r e a s e s w i t h d e c r e a s i n g i n i t i a l l o a d i n g ; however, i t i s o b v i o u s t h a t an u p p e r l i m i t o f a c t i v i t y w i l l f i n a l l y be reached. The r e a s o n f o r t h i s phenomenon, as w e l l as f o r t h e a c ­ t i v i t y d e c r e a s e w i t h i n c r e a s i n g i n c u b a t i o n t i m e , w i l l become obvious from the d i s c u s s i o n s o f the f o l l o w i n g chapter.

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

KLEIN

Immobilized

A N D VORLOP

Cells as Catalysts

381

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

PRESSURE

Figure 2.

Scheme for catalyst bead formation by ionotropic gelation, including scale-up device.

10g tpoxy resin • 33g curing agent (30%-soUn H^O) * 7 ml H 0



2

±

precondensotion (15m. n.)

mixing periodical injection

6g bake i*s yeast • 2ml • 20g β % alginate- sol.

, Qoooonnnnnooo drying (24h)

0

crosslink!ng (20min)

ο.ο

9r^-> ol

2wt%CaCl2-solution

EP0XY-BEADS alginate-dissolution (40min) in 0.1« phosphate-buffer (pH> 6.0)

Figure 3. Process scheme for preparation of biocatalysts by cell entrapment in epoxy beads. Reprinted, with permission, from Ref. 14. Copyright 1982, Science and Technology Letters.

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

382

BIOCHEMICAL

ENGINEERING

Figure 4. Dependence of biocatalytic activities for the batch fermentation of ethanol from glucose with immobilized yeast cells as a function of incubation time (time for cellgrowth in the carrier) for various initial cell loadings in epoxy carriers.

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

17.

KLEIN A N D VORLOP

Immobilized

Cells

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

Effectiveness o f Immobilized C e l l

as Catalysts

383

Catalysts

I t i s a w e l l known f a c t i n h e t e r o g e n e o u s c a t a l y s i s , t h a t t h e c a t a l y t i c a c t i v i t y i s generally not d i r e c t l y proportional to the c o n c e n t r a t i o n o f a c t i v e s i t e s b u t depends a l s o o n h y d r o d y n a m i c c o n d i t i o n s i n t h e s u r r o u n d i n g o f t h e p a r t i c l e s , on p a r t i c l e s i z e and m a t r i x p o r o s i t y . I t i s furthermore w e l l understood, that v a r i o u s t r a n s p o r t phenomena h a v e t o be t a k e n i n t o a c c o u n t , m a i n l y d i f f u s i o n a l transport processes which n e c e s s a r i l y a r e preceding to the r e a c t i o n step i t s e l f . A d i m e n s i o n l e s s number, u s u a l l y c a l l e d T h i e l e - m o d u l u s , c a n be used t o q u a n t i t a t i v e l y account f o r t r a n s p o r t - r e a c t i o n c o u p l i n g phenomena. A s s u m i n g t h e v a l i d i t y o f M i c h a e l i s - M e n t e n r a t e e q u a ­ t i o n - which i s j u s t i f i e d f o r simple enzymatic r e a c t i o n s i n whole c e l l s t o o - t h e f o l l o w i n g e x p r e s s i o n f o r t h e T h i e l e modulus has been d e r i v e d ( 8 ) : 1/2

f

where R i s t h e p a r t i c l e r a d i u s , v t h e r a t e o f r e a c t i o n , the M i c h a e l i s c o n s t a n t , S t h e s u b s t r a t e c o n c e n t r a t i o n and D the e f ­ f e c t i v e s u b s t r a t e d i f f u s i v i t y i n the porous c a t a l y s t p a r t i c l e . On t h e o t h e r hand t h e e f f e c t i v e n e s s f a c t o r η i s d e f i n e d a s t h e r a t i o o f t h e e f f e c t i v e r e a c t i o n r a t e ν t o t h e maximum r e a c t i o n rate ν w h i c h w o u l d be o b s e r v e d w i t h o u t t r a n s p o r t l i m i t a t i o n max e

n = ~ -

(2)

max F o r i m m o b i l i z e d c e l l c a t a l y s t s t h e r e a r e two p o s s i b i l i t i e s t o ob­ t a i n t h i s f a c t o r . F i r s t l y , t h e p a r t i c l e s o f l a r g e r r a d i u s can be g r i n d e d down t o s u c h a s m a l l s i z e t h a t p o r e d i f f u s i o n becomes neg­ ligible. I n t h i s case = v ^ + . Due t o t h e s i z e and t h e s i m p l e entrapment o f t h e c a t a l y t i c s p e c i e s l o s s from t h e m a t r i x may b e c o n s i d e r a b l e . Therefore, secondly, the free c e l l a c t i v i t y can be used i n t h e denominator, i f t h e e x a c t c o n c e n t r a t i o n o f c a t a l y t i c a l l y a c t i v e immobilized c e l l s ( X ) known. Since e

Q

i

s

a c t

v.-I.ilfi

(3)

i s t h e s p e c i f i c r e a c t i o n r a t e o f t h e f r e e l y suspended c e l l s , t h e equation ν = ν ' X = v* (4) max act 1

h o l d s , w h i c h f u r t h e r m o r e d e f i n e s v i n E q n . ( 1 ) . B a s e d o n numer­ i c a l calculations t y p i c a l functions

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

384

BIOCHEMICAL ENGINEERING

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

η - f (Φ)

(5)

h a v e b e e n d e v e l o p e d , w h i c h i n t e r r e l a t e t h e two d i m e n s i o n l e s s p a r ­ ameters and w h i c h c a n be checked e x p e r i m e n t a l l y . To e v a l u a t e t h e a p p l i c a b i l i t y o f E q n . ( 5 ) , t h e p a r a m e t e r s i n Eqns. (1-4) have t o be determined i n d e p e n d e n t l y . T h i s has been done f o r t h e c l e a v a g e r e a c t i o n o f P e n i c i l l i n G t o 6APA w i t h immo­ b i l i z e d E. Qoli c e l l s i m m o b i l i z e d i n e p o x i d e b e a d s ( 9 ) . The r a d i u s R: The r a d i u s o f p a r t i c l e s o b t a i n e d f r o m i o n o t r o p i c g e l a t i o n i s u s u a l l y c o n t r o l l e d w i t h i n v e r y narrow l i m i t s and t h e s i z e c a n e a s i l y b e d e t e r m i n e d by m i c r o s c o p i c m e a s u r e m e n t s . Reaction K i n e t i c s ; The r e a c t i o n r a t e s h a v e b e e n m e a s u r e d a t pH = 7.8 a n d Τ = 37o C, u s i n g a 5% P e n G s u b s t r a t e c o n c e n t r a t i o n . T i t r a t i o n w i t h 0.1 m o l a r NaOH h a s b e e n u s e d t o d e t e r m i n e t h e amount o f p r o d u c t f o r m a t i o n . The K^j v a l u e s o f f r e e a n d i m m o b i l i z e d c e l l s h a v e b e e n o b t a i n e d f r o m t h e L i n e w e a v e r - B u r k p l o t s a s shown f o r some e x a m p l e s i n F i g u r e 5. F o l l o w i n g t o i r r e v e r s i b l e d e a c t i v a t i o n o f enzymes d u r i n g t h e p r o c e s s o f i m m o b i l i z a t i o n , t h e i n e q u a l i t y X £ < ^ m m o b i l . °lds. f o l l o w i n g approach has been developed f o r the determination o f X : i n a c e r t a i n experiment, i n a f i r s t ap­ proximation X - Ximm.; i . e . , 100% o f a l l i m m o b i l i z e d c e l l s a r e assumed t o b e a c t i v e . I n t h i s case, η 0.23 h a s b e e n d e t e r m i n e d . act ^mm. » become l a r g e r , due t o t h e d e c r e a s e o f t h e a C

n

a c t

a c t

β

I

f

x

<

η

d e n o m i n a t o r i n E q n . ( 2 ) . I n t h e same way a s e r i e s o f Φ-values c a n be c a l c u l a t e d f r o m E q n . ( 1 ) o n t h e b a s i s o f d i f f e r e n t v ' - v a l u e s . The c o r r e s p o n d i n g s e t s o f v a l u e s f o r d i f f e r e n t a s s u m p t i o n s o f X are l i s t e d i n Table I : a c t

Table I .

:

C a l c u l a t e d η- a n d Φ- v a l u e s b a s e d on d i f f e r e n t assumptions o f r e ­ s i d u a l c e l l a c t i v i t y a f t e r immo­ bilization.

X

act^ imm.

%

η cale.

10 20 30 40 50 60 70 80 90 100 The t r u e v a l u e o f X

a c t

2.36 1.18 0.79 0.59 0.47 0.39 0.34 0.30 0.26 0.24

Φ cale. 0.59 1.34 1.44 1.63 2.11 2.32 2.50 2.68 2.84 3.00

has t o s a t i s f y Eqn. ( 5 ) , w h i c h has been

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

KLEIN

AND VORLOP

Immobilized

Cells as Catalysts

385

Figure 5. Determination of the Michaelis constant, K , for 6 ΑΡΑ formation from penicillin G with immobilized E . coli cells. Conditions: pH 7.81, 37°C, 5% penicillin G solution, epoxy carrier. v

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

386

BIOCHEMICAL

ENGINEERING

g e n e r a l l y c a l c u l a t e d ( 8 ) . P l o t t i n g a l l data from Table I together w i t h t h e f u n c t i o n Eqn. ( 5 ) i n F i g u r e 6 g i v e s a p o i n t o f i n t e r s e c ­ t i o n , w h i c h d e t e r m i n e s t h e t r u e p a i r o f η/Φ-values and t h u s X « C o m p a r i s o n o f s e v e r a l i m m o b i l i z e d c e l l p r e p a r a t i o n s gave p r a c t i c ­ a l l y i d e n t i c a l r e s u l t s , showing that a value X = 0*43X i s a t y p i c a l one f o r t h i s e p o x i d e - i m m o b i l i z a t i o n p r o c e d u r e . E f f e c t i v e Pore D i f f u s i v i t y : The e f f e c t i v e p o r e d i f f u s i v i t y o f p e n i c i l l i n G has been determined e x p e r i m e n t a l l y i n a b a t c h ex­ p e r i m e n t ( 1 0 ) . M i x i n g a c e r t a i n number o f c a t a l y s t b e a d s h a v i n g a homogeneous s u b s t r a t e c o n c e n t r a t i o n S ( g / 1 ) , w i t h a c e r t a i n v o l u m e o f f r e s h , n o n - c o n d u c t i n g w a t e r , t h e d i f f u s i o n p r o c e s s c a n be f o l ­ l o w e d by t h e c o n d u c t i v i t y a n d t h e c o n c e n t r a t i o n i n c r e a s e i n t h e supernatent l i q u i d . I f S i s the s u b s t r a t e c o n c e n t r a t i o n i n the p a r t i c l e a t t + «> a n d S t h e c o n c e n t r a t i o n a t t i m e t , R t h e p a r t i ­ c l e r a d i u s (cm) a n d D t h e e f f e c t i v e d i f f u s i v i t y ( c m / s e c ) t h e d i f f u s i o n c o e f f i c i e n t c a n be o b t a i n e d f r o m t h e s l o p e p l o t t i n g I n ( S - S ) / ( S - S ) v s . t , f o l l o w i n g t o Eqn. ( 6 ) : a c t

a c t

i m m #

a

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

e

2

e

e

a

e

(6)

Such a p l o t i s shown i n F i g u r e 7. Comparison o f Theory and E x p e r i m e n t : I f t h e s i m p l e model o f t r a n s p o r t l i m i t a t i o n due t o p o r e d i f f u s i o n h o l d s , a l l e x p e r i m e n t ­ a l l y d e t e r m i n e d p a i r s o f η and Φ s h o u l d f a l l o n t h e n o n - d o t t e d η = ί(Φ) - f u n c t i o n shown i n F i g u r e 6. U s i n g t h e i n d e p e n d e n t l y d e t e r m i n e d parameters as d e s c r i b e d b e f o r e such v a l u e s have been d e t e r m i n e d f o r a number o f c a t a l y s t p r e p a r a t i o n s u s e d i n t h e p e n ­ i c i l l i n G c l e a v a g e r e a c t i o n . The e x c e l l e n t agreement b e t w e e n c a l ­ c u l a t i o n o f Eqn. (5) a n d e x p e r i m e n t a l d e t e r m i n a t i o n c a n b e s e e n f r o m F i g u r e 8. I n t h i s s e r i e s o f e x p e r i m e n t s two d i f f e r e n t s t r a i n s o f E. ooli c e l l s h a v e b e e n u s e d , t h e one o f them h a v i n g been o b t a i n e d by g e n e t i c e n g i n e e r i n g l e a d i n g t o a t e n f o l d a c t i v i t y i n c r e a s e compared t o t h e c o n v e n t i o n a l s t r a i n ATCC 11 105 (1)· C a t a l y s t O p t i m i z a t i o n : I n a n o t h e r r e a c t i o n example t h e a p ­ p l i c a t i o n o f the Thiele-modulus concept f o r the o p t i m i z a t i o n o f c a t a l y s t c o m p o s i t i o n c o u l d be demonstrated. Here t h e o x i d a t i o n o f g l u c o s e t o g l u c o n i c a c i d , c a t a l y z e d by A c e t o b a c t e r s i m p l e x c e l l s has been s t u d i e d , where oxygen i s t h e r a t e l i m i t i n g s u b s t r a t e . I n t h i s case a C a - a l g i n a t e m a t r i x has been used f o r c e l l immobil­ ization. U s i n g s i m p l i f i e d e q u a t i o n s f o r t h e c a l c u l a t i o n o f D and furthermore assuming X = Xi ( 1 2 ) , t h e r e l a t i o n between r e l a ­ t i v e a c t i v i t y (η i n %) a n d p a r t i c l e d i a m e t e r c o u l d be c a l c u l a t e d for different c e l l concentrations. As c a n be shown i n F i g u r e 9, a good agreement w i t h e x p e r i m e n t a l d a t a i s o b t a i n e d . The a b s o l u t e a c t i v i t y f o r g l u c o n i c a c i d p r o d u c t i o n i s o b ­ t a i n e d i f the s p e c i f i c a c t i v i t y o f the d i f f e r e n t preparations i s m u l t i p l i e d w i t h t h e c e l l c o n c e n t r a t i o n . The n o n - d o t t e d c u r v e i n F i g u r e 10 i s t h e r e s u l t o f t h i s c a l c u l a t i o n , w h i c h g i v e s a good e

a c t

m

m

#

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Downloaded by CORNELL UNIV on October 5, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch017

KLEIN

Figure 6.

AND

Immobilized

VORLOP

Cells as Catalysts

387

Determination of catalytically active cell concentration, X , basis of the effectiveness factor/Τhiele modulus relation. act

on the

Ο Γ



Î

ln[(S -

S ) / (S e

a

-

Se)]

-2 -

-4 h

i

t

100

i

i

200

i

l

»

1

300

400 t