Separation, Recovery, and Purification in Biotechnology - American

11

Downloaded by KTH ROYAL INST OF TECHNOLOGY on August 26, 2015 | http://pubs.acs.org Publication Date: July 11, 1986 | doi: 10.1021/bk-1986-0314.ch011

Mathematical Modeling of Bioproduct Adsorption Using Immobilized Affinity Adsorbents Somesh C. Nigam and Henry Y. Wang Department of Chemical Engineering, The University of Michigan, Ann Arbor, MI 48109-2136

The use of small affinity adsorbent particles immobilized in hydrogel beads has been investigated for whole broth processing (1). The adsorbent particles can contain biospecific ligands covalently attached to a porous solid support. A mathematical model was developed to study bioproduct adsorption using immobilized affinity adsorbent beads in batch operation. The performance of immobilized and freely suspended affinity adsorbents was compared by calculating adsorption rates and selectivities for four different bead geometries. Simulation results indicate that the performance of finely ground adsorbent particles immobilized in hydrogel beads is superior compared to freely suspended adsorbents. The mathematical model was further used for simulation studies to investigate the effect of bead design parameters on product adsorption. A f f i n i t y a d s o r p t i o n , due t o i t s h i g h degree o f s e l e c t i v i t y , o f f e r s a viable alternative to conventional crude bio-product separation schemes. However, t h e r e a r e s e v e r a l problems a s s o c i a t e d w i t h u s i n g f r e e l y suspended a f f i n i t y adsorbent p a r t i c l e s i n t h e whole b r o t h . L a r g e adsorbent p a r t i c l e s i z e i s r e q u i r e d t o ensure easy h a n d l i n g i n the b r o t h . But t h i s l e a d s t o h i g h i n t e r n a l mass t r a n s f e r r e s i s t a n c e w h i c h s i g n i f i c a n t l y r e d u c e s the a d s o r p t i o n r a t e . The p r e s e n c e o f v a r i o u s o r g a n i c macromolecules i n t h e b r o t h c a n l e a d t o r a p i d f o u l i n g of t h e adsorbent p a r t i c l e s . A l s o , t h e b r o t h may c o n t a i n b y - p r o d u c t s i n s u b s t a n t i a l c o n c e n t r a t i o n which may compete w i t h the d e s i r e d product f o r the l i g a n d . The use o f s m a l l a f f i n i t y adsorbent p a r t i c l e s immobilized i n h y d r o g e l beads has been p r o p o s e d t o circumvent some o f these problems (1). The h y d r o g e l matrix c a n be p r o v i d e d by Ca-Alginate, K-Carrageenan o r any o t h e r r e v e r s i b l e g e l . P r e v i o u s r e s e a r c h i n our l a b o r a t o r y has i n d i c a t e d t h a t s i g n i f i c a n t l y h i g h e r a d s o r p t i o n r a t e s and overall adsorption capacities c a n be achieved by using i m m o b i l i z e d a f f i n i t y adsorbent beads i n t h e whole b r o t h . These beads p r o v i d e low o v e r a l l i n t e r n a l mass t r a n s f e r r e s i s t a n c e due t o the

0097-6156/ 86/ 0314-0153506.00/ 0 © 1986 American Chemical Society

In Separation, Recovery, and Purification in Biotechnology; Asenjo, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986.


154

SEPARATION, RECOVERY, A N D PURIFICATION IN BIOTECHNOLOGY

small adsorbent p a r t i c l e s i z e . A r e l a t i v e l y l a r g e bead s i z e (1-3 mm) ensures easy r e c o v e r y from the whole b r o t h at the end o f a d s o r p t i o n process. Polymerization of these hydrogels can be reversed by manipulating the c o n c e n t r a t i o n o f exogenous c a t i o n s and inducing temperature s h i f t s . Adsorbent p a r t i c l e s w i t h bound p r o d u c t can be e a s i l y recovered by d i s s o l v i n g away the hydrogel matrix. Large macromolecules p r e s e n t i n the whole b r o t h are e x c l u d e d from the h y d r o g e l because of pore s i z e r e s t r i c t i o n . U n d e s i r e d macromolecules t h a t do p e n e t r a t e f o u l the o u t e r h y d r o g e l l a y e r f i r s t . T h i s saves most of the ligand distributed i n s i d e the bead. Many of the available biospecific ligands used for bioseparation are more e x p e n s i v e compared t o the p r o d u c t i t s e l f . R e t r i e v i n g and r e u s i n g the l i g a n d s a f t e r b i o s e p a r a t i o n i s c r u c i a l t o the economic s u c c e s s o f an a f f i n i t y bioseparation process. C o v a l e n t attachment of the l i g a n d t o an i n s o l u b l e support was used t o m i n i m i z e l e a k a g e . Therefore, the l i g a n d can be r e - u s e d f o r subsequent b i o s e p a r a t i o n s . The purpose o f t h i s a r t i c l e i s to formulate a model w h i c h considers s i m u l t a n e o u s d i f f u s i o n and b i n d i n g r e a c t i o n w i t h i n the i m m o b i l i z e d adsorbent p a r t i c l e s . The model has been d e v e l o p e d f o r batch adsorption processes. I t can however be e a s i l y m o d i f i e d t o p r e d i c t product a d s o r p t i o n i n other r e a c t o r c o n f i g u r a t i o n s . Theory A f f i n i t y a d s o r p t i o n i s a s e p a r a t i o n t e c h n i q u e based on s p e c i f i c and r e v e r s i b l e b i n d i n g o f two b i o l o g i c a l l y a c t i v e compounds. Numerous b i o l o g i c a l compounds r e c o g n i z e and b i n d t o s p e c i f i c compounds. For example enzymes form complexes w i t h s u b s t r a t e s i n the course of t h e i r normal c a t a l y t i c mechanisms. S i m i l a r l y , a n t i b o d i e s form v e r y s t r o n g complexes w i t h their respective antigens. Various proteins also i n t e r a c t s e l e c t i v e l y with other macromolecules. Graves and Wu have d e v e l o p e d a simple e q u i l i b r i u m model f o r describing a f f i n i t y binding reactions (2). The binding reaction between a p r o d u c t and an a f f i n i t y l i g a n d c o v a l e n t l y a t t a c h e d t o a s o l i d support can be r e p r e s e n t e d as:

Ρ

+ L

P.L

(1)

-1 In the s i m p l e s t w r i t t e n as:

K

r

ads =

r

des = *-iIP.L*l

1

[

P

]

case

[

L

*

the

rates

of

adsorption

and

desorption

]

can

be

( 2 )

(3)

where [P] i s the p r o d u c t c o n c e n t r a t i o n , [L*] i s the c o n c e n t r a t i o n o f the bound ligand and [P.L ] is the concentration of the p r o d u c t - l i g a n d complex. T h i s y i e l d s an e q u i l i b r i u m

constant:


11.

NIG A M AND WANG

F K

q

155

s (4)

K

e

= ΓΡΙ Π *-3 i = — - i [P.L ]


Mathematical Modeling of Bioproduct Adsorption

fA

*Ί

In t h i s approach i t i s assumed t h a t t h e p r o d u c t m o l e c u l e b i n d s t o a s i n g l e b i n d i n g s i t e on t h e l i g a n d t h r o u g h monovalent i n t e r a c t i o n . F o r t h i s mechanism, t h e r a t e o f a d s o r p t i o n c a n be e x p r e s s e d by a r e l a t i o n which is first order w i t h respect t o both, product and l i g a n d concentration ( E q u a t i o n 2 ) . However, t h e r e may be c i r c u m s t a n c e s where t h e p r o d u c t m o l e c u l e c o n t a i n s more than one b i n d i n g s i t e t h a t i s r e c o g n i z e d by t h e l i g a n d . Such a m u l t i v a l e n t i n t e r a c t i o n r e q u i r e s a more complex a n a l y s i s (3.). Most o f t h e a f f i n i t y b i n d i n g r e a c t i o n s are c h a r a c t e r i z e d by v e r y s n a i l e q u i l i b r i u m b i n d i n g c o n s t a n t s . We w i l l assume t h e r a t e o f a d s o r p t i o n ( r ^ ) t o be much h i g h e r compared to the r a t e o f d e s o r p t i o n ( ) so t n a t the a f f i n i t y b i n d i n g c a n be c o n s i d e r e d as e s s e n t i a l l y i r r e v e r s i b l e . F i g u r e 1 shows a schematic diagram o f an i m m o b i l i z e d affinity adsorbent bead. H y d r o g e l , by v i r t u e o f i t s e x t r e m e l y h i g h water content 0 9 0 % ) , o f f e r s l i m i t e d d i f f u s i o n a l r e s i s t a n c e t o the d e s i r e d product. I t i s t h e r e f o r e used as an i n e r t matrix t o support relatively small adsorbent particles which otherwise cannot be r e a d i l y r e c o v e r e d from a h i g h l y heterogenous whole b r o t h . The reduced adsorbent p a r t i c l e s i z e leads t o s i g n i f i c a n t d e c l i n e i n internal diffusional resistance which offsets any m a r g i n a l increase i n r e s i s t a n c e due t o t h e h y d r o g e l m a t r i x i t s e l f . Several assumptions a r e made to mathematically model the immobilized adsorbent. The s m a l l a d s o r b e n t p a r t i c l e s a r e assumed t o be d i s t r i b u t e d u n i f o r m l y i n s i d e t h e h y d r o g e l bead. The e x t e r n a l mass t r a n s f e r r e s i s t a n c e due t o t h e boundary l a y e r i s assumed t o be n e g l i g i b l e i f the bulk s o l u t i o n i s w e l l s t i r r e d . T h i s assumption i s s u p p o r t e d by t h e e x p e r i m e n t a l o b s e r v a t i o n s o f Tanaka e t a l . who studied d i f f u s i o n of several s u b s t r a t e s from w e l l stirred batch s o l u t i o n s i n t o C a - a l g i n a t e g e l beads ( 4 ) . However, t h e boundary c o n d i t i o n s c a n be e a s i l y m o d i f i e d t o i n c o r p o r a t e e x t e r n a l d i f f u s i o n effects i f needed. Furthermore product diffusion i n both the h y d r o g e l and t h e porous adsorbent i s c o n s i d e r e d t o f o l l o w F i c k i a n laws and i t s d i f f u s i v i t y i n each r e g i o n i s assumed t o be c o n s t a n t . r

d e s

The unsteady s t a t e p r o d u c t and l i g a n d m a t e r i a l b a l a n c e s i n the d i f f e r e n t r e g i o n s c a n be e x p r e s s e d as f o l l o w s . The p r o d u c t mass b a l a n c e i n t h e h y d r o g e l c a n be r e p r e s e n t e d a s :

2.L. 2 3R

3R

( 3 Ν Ρ

"

Α1 Ο> 3 γ

R

ε ac. i ~ at

9 C

Ai 3r

(5)

r=r ο The p r o d u c t mass b a l a n c e i n t h e a d s o r b e n t p a r t i c l e s u s i n g a f i r s t o r d e r b i n d i n g r e a c t i o n w i t h r e s p e c t t o b o t h p r o d u c t and l i g a n d i s g i v e n by:

4

1

2

I 3r

Γ * OT

4

" " *.C C- ι Ai 1

A|

3t

r



156

SEPARATION, RECOVERY, AND PURIFICATION IN BIOTECHNOLOGY

Adsorbent matrix

Figure 1. bead.

Schematic diagram o f an i m m o b i l i z e d a f f i n i t y

adsorbent


11.


N I G A M A N D WANG

Product by:

d e p l e t i o n i n the b u l k s o l u t i o n o f the b a t c h a d s o r b e r

2

9C . bi 3t V

-47tnR D. ο ι V

_

dC. ι dR

157

i s given

(7) R=R ο

The

l i g a n d b a l a n c e w i t h i n the a d s o r b e n t


aC

particle i s :

-K.C..CJ i L l a

1

1 . ot

(8)

In the case o f n e g l i g i b l e e x t e r n a l d i f f u s i o n r e s i s t a n c e , the and boundary c o n d i t i o n s f o r e q u a t i o n s 5-8 can be w r i t t e n as: Initial C

£

t=0):

C o n d i t i o n s (at = C

= 0;

A i

(zero i n i t i a l

= ^lo*

=

initial

product

l o a d i n g on the bead)

(uniform l i g a n d c o n c e n t r a t i o n )

S)i'

(uniform bulk concentration)

Boundary C o n d i t i o n s 3C. R = 0:

R

=

- j g = 0;

RQ:

=

9 C

r = 0:

r

—

=

r 0

Ai =

(radial

symmetry o f h y d r o g e l bead)

C^;

(concentration continuity solution interface)

0;

(radial

:

=

at

hydrogel-bulk

symmetry o f a d s o r b e n t

particle)

C^; (concentration continuity hydrogel-adsorbent i n t e r f a c e )

at

The mass b a l a n c e e q u a t i o n s g i v e n above can be r e p r e s e n t e d i n non-dimensional form by employing the following dimensionless v a r i a b l e s and p a r a m e t e r s : τ = r /

C

^1 "

l

/

V

C

ΐ

o

lo:

2 ψ

5 = R/R ;

%i

t =

D

K

r

C

i o lo

t/R^

= %i' C

2 =

r e f

= c X - ;

A

2 / D

Aiï

H

=

E

r

D

a o ref

f

Ï

2 / R

ref

=

A 1

C

2 D

Ai

;

*i

"

A i

/C^ 2

«A fCbi e

i ;

ο ref»s

/ D


158


2

γ. = 4nnR D.R /VD ι ο ι ref ref r

2

2

,/R J), A. = 3ND .r /D.R ; Β. = ε R D ι g o ref ref ι Αι ο ι ο ι A

r=l

B.3C. ι ι 3F

(9)


(10)

an

(11) R=l

(12) i=l In the p a s t , s i m i l a r b i d i s p e r s e d systems have been i n v e s t i g a t e d and modeled i n the c a t a l y s t d e a c t i v a t i o n area (5-7). However, modeling of immobilized a f f i n i t y adsorbent beads i s more complex due to the non-linearity introduced by the rapid ligand b i n d i n g r e a c t i o n w h i c h i s dependent on the p r o d u c t c o n c e n t r a t i o n . The mathematical model described above involves non-linear, coupled, p a r t i a l d i f f e r e n t i a l equations. The e q u a t i o n s were s o l v e d using a F i n i t e - D i f f e r e n c e method. D e t a i l s of t h i s mathematical technique have been d e s c r i b e d elsewhere i n the l i t e r a t u r e (8,9). F i g u r e 2 shows a f l o w s h e e t f o r the n u m e r i c a l s o l u t i o n o f these model equations. Simulation

Studies

S e v e r a l s i m u l a t i o n r u n s were c a r r i e d out t o g a i n i n s i g h t i n t o the e f f e c t o f bead d e s i g n parameters on the a d s o r p t i o n c h a r a c t e r i s t i c s o f i m m o b i l i z e d a d s o r b e n t beads. The p h y s i c a l parameters ( r a t e c o n s t a n t , d i f f u s i v i t y e t c . ) f o r the s i m u l a t i o n s t u d i e s were determined from e x p e r i m e n t a l data on the a d s o r p t i o n o f c y c l o h e x i m i d e , a low m o l e c u l a r weight antibiotic, onto XAD-4 n o n - i o n i c polymeric resin (10,11) (Table I). The f i t between the model and the experimentally determined a d s o r p t i o n c u r v e s i s q u i t e good ( F i g u r e 3 ) . S i n g l e component d i f f u s i o n and b i n d i n g . F i g u r e 4 shows f o u r c a s e s w h i c h were s i m u l a t e d t o observe the e f f e c t s o f i m m o b i l i z a t i o n i n hydrogel and reduction of adsorbent particle size. Case (a) r e p r e s e n t s a f r e e l y suspended a d s o r b e n t p a r t i c l e of r a d i u s 1.1 mm. Case (b) r e p r e s e n t s the same s i z e p a r t i c l e i m m o b i l i z e d i n a h y d r o g e l bead o f 2.8 mm. In case ( c ) , the same a d s o r b e n t p a r t i c l e as i n cases (a) and (b) was assumed t o be c r u s h e d t o 80 s m a l l e r p a r t i c l e s which were i m m o b i l i z e d w i t h i n a h y d r o g e l bead o f r a d i u s 2.8 mm. Case (d) r e p r e s e n t s the extreme s i t u a t i o n i n which the a d s o r b e n t p a r t i c l e was c r u s h e d t o f i n e powder such t h a t the t o t a l number of p a r t i c l e s w i t h i n the i m m o b i l i z e d bead may be r e g a r d e d as i n f i n i t e . This i s also


11.



159


Initial Conditions

t +At I Use eqn.(9) to calculate Cj from R = 0 to 1

Use eqn.(10) to calculate C j A

from R = 0 to 1

=0

r

Compute

to 1

dC j A

r = 1 from R = 0 to 1

Use eqn.(l 1) to calculate

Use eqn.(12) to calculate fromR= 0 to 1 r = 0 to 1

No

F i g u r e 2 . Flowsheet model e q u a t i o n s .

of basic

s t e p s i n the n u m e r i c a l s o l u t i o n o f


160



' J

θ.

β.2

θ.4

θ.6

β.8

1

TIME dimensionless F i g u r e 3. Concentration p r o f i l e of cycloheximide in a a d s o r b e r employing i m m o b i l i z e d adsorbent beads (see T a b l e experimental c o n d i t i o n s ) .

(a) Free adsorbent

(b) Immobilized adsorbent N=1

batch I for

(c) Immobilized adsorbent N=80

(d) Immobilized adsorbent Ν = oo

F i g u r e 4. Diagrammatic r e p r e s e n t a t i o n o f f o u r c a s e s the s i m u l a t i o n s t u d i e s .

employed i n


11.


Table

I.


P h y s i c a l Parameters used f o r S i m u l a t i o n

161

Studies

Adsorber parameters: V = 50 ml

η = 107

Ν = 81 R


ε

ο a

= R

r = 2.8 mm

ο

= 0.25 mm 1.0 g m / l i t e r

bi

ref = 0.513

D i f f u s i o n and R e a c t i o n

0.95 8

g

=

parameters: 3

K. = 7.05x10*" s e c "

1

6

2

D. = D = 5.8xl0" cm /sec ι ref —6 2 D.. = 1.1x10 cm / s e c Ai α = 0.13 gm cycloheximide/gm

adsorbent

equivalent t o d i s p e r s i n g the l i g a n d i n the hydrogel without another immobilization matrix. F i g u r e 5 shows n u m e r i c a l l y g e n e r a t e d p l o t s o f a d s o r p t i o n r a t e as a f u n c t i o n o f time f o r t h e above mentioned c a s e s . The a d s o r p t i o n r a t e was d e f i n e d as t h e amount o f l i g a n d consumed p e r u n i t time u s i n g d i m e n s i o n l e s s u n i t s . As e x p e c t e d , a d d i t i o n o f the h y d r o g e l l a y e r on the f r e e l y suspended a d s o r b e n t p a r t i c l e i n case (b) causes t h e mass t r a n s f e r r e s i s t a n c e t o go up which r e d u c e s t h e a d s o r p t i o n rate compared t o case ( a ) . As shown i n F i g u r e 4, t h e i n t e r n a l mass t r a n s f e r r e s i s t a n c e i n ( c ) i s reduced because t h e a d s o r b e n t p a r t i c l e s are s m a l l e r . T h i s d e c r e a s e i n mass t r a n s f e r r e s i s t a n c e more t h a n overcomes the e f f e c t of a d d i t i o n a l hydrogel resistance. The a d s o r p t i o n r a t e f o r ( c ) t h e r e f o r e shows a sharp i n c r e a s e over t h a t f o r f r e e l y suspended a d s o r b e n t p a r t i c l e s . T h i s i l l u s t r a t e s one o f the advantages o f u s i n g immobilized a d s o r b e n t beads over t h a t o f f r e e l y suspended adsorbent p a r t i c l e s . A f t e r c r u s h i n g the adsorbent i n t o an i n f i n i t e number o f p a r t i c l e s and d i s p e r s i n g i t w i t h i n t h e h y d r o g e l bead (case d ) , o n l y a m a r g i n a l i n c r e a s e i n the a d s o r p t i o n r a t e over case ( c ) i s o b s e r v e d . T h i s happens because below a c e r t a i n s i z e the i n t e r n a l mass t r a n s f e r r e s i s t a n c e w i t h i n t h e a d s o r b e n t p a r t i c l e becomes low enough t h a t i t does n o t c o n t r o l t h e o v e r a l l a d s o r p t i o n r a t e . Based on these r e s u l t s i t can be c o n c l u d e d t h a t the a d s o r p t i o n r a t e increases m o n o t o n i c a l l y with r e d u c t i o n i n adsorbent p a r t i c l e s i z e w i t h i n t h e h y d r o g e l bead. However, below a c e r t a i n s i z e the a d s o r p t i o n r a t e does not i n c r e a s e a p p r e c i a b l y . As d i s c u s s e d e a r l i e r , t h e r e may be added d i f f i c u l t i e s i n recovering very fine a d s o r b e n t p a r t i c l e s from t h e bead a f t e r d i s s o l v i n g the hydrogel. Thus, o p t i m i z a t i o n o f t h e adsorbent p a r t i c l e s i z e s h o u l d take i n t o account the a d d i t i o n a l c o s t a s s o c i a t e d w i t h t h e l o s s o f a d s o r b e n t during recovery compared t o the advantages o f i n c r e a s i n g the adsorption rates.



162


0.8

0.

0.2

0.4

0.6

0.8

1

TIME cHm«nsionless

Figure 5. Adsorption simulated cases.

rate

as

a

function

of

time

for


four


11.

NIGAM AND WANG

163


The diffusivity of the d e s i r e d product i n the hydrogel will depend on t h e g e l m a t e r i a l , t h e g e l c o n c e n t r a t i o n and t h e d e g r e e o f c r o s s - l i n k i n g by m u l t i v a l e n t c a t i o n s . The d i f f u s i v i t y o f t h e p r o d u c t i n t h e a d s o r b e n t p a r t i c l e s c a n a l s o v a r y d e p e n d i n g on t h e c h o i c e o f t h e a d s o r b e n t m a t r i x u s e d f o r l i g a n d i m m o b i l i z a t i o n . The c h o i c e o f t h e h y d r o g e l and t h e a d s o r b e n t m a t r i x w i l l u s u a l l y depend on s e v e r a l f a c t o r s such as the s t a b i l i t y o f the b e a d a g a i n s t s h e a r f o r c e s , the s u s c e p t i b i l i t y t o f o u l i n g by v a r i o u s a g e n t s , and the presence of competing by-products. F o r e f f i c i e n t b e a d d e s i g n one w i l l t h e r e f o r e need t o know t h e effect of diffusivity on product adsorption. F i g u r e s 6a a n d 6b show t h e e f f e c t o f v a r y i n g t h e p r o d u c t d i f f u s i v i t y i n t h e h y d r o g e l and i n t h e a d s o r b e n t m a t r i x r e s p e c t i v e l y . I t was found that i n both cases, l i g a n d s are consumed faster as d i f f u s i v i t i e s are increased. However, s i m i l a r t o e a r l i e r runs the ligand consumption p r o f i l e approaches a l i m i t as t h e r e s p e c t i v e d i f f u s i o n a l r e s i s t a n c e s become s m a l l e r . Two component diffusion and binding. There is a frequent possibility of having one or more oompounds present in the f e r m e n t a t i o n b r o t h w h i c h may c o m p e t e f o r t h e a v a i l a b l e l i g a n d s i n t h e adsorbent particles. The o b j e c t i v e here i s t o o p t i m i z e the bead d e s i g n so as t o m a x i m i z e t h e p u r i t y o f t h e d e s i r e d p r o d u c t adsorbed onto the adsorbent p a r t i c l e s . I n order t o n u m e r i c a l l y s i m u l a t e such a s i t u a t i o n i t was a s s u m e d t h a t two c o m p o u n d s a r e b e i n g a d s o r b e d onto t h e i m m o b i l i z e d a d s o r b e n t s : a d e s i r e d p r o d u c t '1' a n d a n u n d e s i r e d by-product '2'. The adsorption rate constant f o r the desired product, i s a s s u m e d t o be 10 t i m e s t h a t o f t h e u n d e s i r e d p r o d u c t , The d i f f u s i v i t i e s f o r b o t h o f t h e s e p r o d u c t s a r e a s s u m e d t o be similar. Two a d d i t i o n a l p a r a m e t e r s a r e d e f i n e d t o s t u d y t h e d y n a m i c b e h a v i o r of such systems.

, ^. . ^ Selectivity 0

Adsorption rate of d e s i r e d product ( S ) = 73 ~ —r— — r Adsorption rate of undesired product

/ Λ Χ

C

A1 1

C

A V

S A2 1

A V

( C

Product

purity

C

1 3 )

(Pu)

Amount o f p r o d u c t

Amount o f p r o d u c t ' 1' a d s o r b e d Ί ' a d s o r b e d + A m o u n t o f p r o d u c t '2'

(\A) adsorbed

F i g u r e 7 shows t h e v a r i a t i o n o f s e l e c t i v i t y w i t h r e s p e c t t o t i m e f o r t h r e e t y p e s o f a f f i n i t y b e a d s ( C a s e s ( a ) , (b) and ( c ) ) . I n a l l t h r e e c a s e s , s e l e c t i v i t y d e c r e a s e s f r o m t h e i n i t i a l maximum v a l u e a s time p r o g r e s s e s . Due t o i d e n t i c a l d i f f u s i v i t i e s , t h e two products have v e r y similar concentration profiles within the immobilized adsorbent bead at i n i t i a l time. Thus the i n i t i a l s e l e c t i v i t y i s j u s t the r a t i o of t h e i r a d s o r p t i o n r a t e c o n s t a n t s . However, s i n c e p r o d u c t



164

S E P A R A T I O N , R E C O V E R Y , A N D P U R I F I C A T I O N IN B I O T E C H N O L O G Y

β.

0.2

0.4

8.6

0.8

1

TIME dimensionless

0.5—J 0.

ι

ι

1 1 1 1 1—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—"—Γ 0.2

0.4

0.6

0.8

TIME dimensionless F i g u r e s 6 a , b . E f f e c t o f b i o p r o d u c t d i f f u s i v i t y i n h y d r o g e l (D) and i n adsorbent matrix (D^) o n l i g a n d consumption using immobilized adsorbent beads.



11.



165

'1' i s adsorbed at a higher rate, (Figure 7, right), the c o n c e n t r a t i o n o f p r o d u c t Ί ' w i t h i n t h e bead g r a d u a l l y becomes lower than t h a t o f p r o d u c t '2' due t o s i g n i f i c a n t d i f f u s i o n a l r e s i s t a n c e . The b u l k c o n c e n t r a t i o n o f d e s i r e d p r o d u c t Ί ' a l s o d e c l i n e s f a s t e r than t h a t o f the u n d e s i r e d p r o d u c t . The combined e f f e c t o f these two mechanisms l e a d s t o the i n i t i a l d e c r e a s e o f the s e l e c t i v i t y i n a l l t h r e e c a s e s . D i f f u s i o n a l r e s i s t a n c e e f f e c t s d i m i n i s h as the l i g a n d g e t s consumed and the c o n c e n t r a t i o n w i t h i n t h e bead becomes c l o s e r t o the b u l k c o n c e n t r a t i o n . I n some c a s e s , t h i s l e a d s t o an i n c r e a s e i n the s e l e c t i v i t y near the end o f the a d s o r p t i o n p r o c e s s . I t was found t h a t the d e c l i n e i n s e l e c t i v i t y was l e a s t i n case (c) because o f a s m a l l e r o v e r a l l d i f f u s i o n a l r e s i s t a n c e o f t h e bead. F i g u r e 8 shows the v a r i a t i o n o f p r o d u c t p u r i t y (Pu) as a f u n c t i o n o f time f o r these t h r e e c a s e s . The p r o d u c t p u r i t y c u r v e s show t h e same g e n e r a l t r e n d as the s e l e c t i v i t y c u r v e s . F i n a l p r o d u c t p u r i t y was a l s o found t o be h i g h e s t f o r case ( c ) . By v i r t u e o f t h e i r lower o v e r a l l mass t r a n s f e r r e s i s t a n c e case ( c ) i m m o b i l i z e d adsorbent beads not o n l y d i s p l a y a h i g h e r a d s o r p t i o n r a t e but a l s o o f f e r a h i g h e r s e l e c t i v i t y f o r the d e s i r e d product. Conclusions The use o f s m a l l adsorbent p a r t i c l e s i m m o b i l i z e d i n h y d r o g e l beads f o r whole b r o t h p r o c e s s i n g r e p r e s e n t s a n o v e l approach t o i n c r e a s e the o v e r a l l e x t r a c t i o n y i e l d o f b i o s y n t h e t i c a l l y d e r i v e d p r o d u c t s . Immobilized adsorbent beads d i s p l a y major advantages over freely suspended adsorbents both i n terms of adsorption r a t e and selectivity. Other practical advantages o f these immobilized adsorbent beads are easy handling and reduced fouling characteristics. A mathematical model was d e v e l o p e d and used t o investigate simultaneous mass transfer and b i n d i n g w i t h i n the immobilized adsorbent beads. Numerical simulation of a batch a d s o r p t i o n p r o c e s s employing these i m m o b i l i z e d beads was found t o be a u s e f u l way t o study t h e i r dynamic b e h a v i o r and o p t i m a l d e s i g n . Acknowledgments We would l i k e t o acknowledge t h e f i n a n c i a l support S c i e n c e F o u n d a t i o n which made t h i s work p o s s i b l e .

from

National

Legend o f Symbols

"Ai

lo

product

c o n c e n t r a t i o n i n adsorbent

product

c o n c e n t r a t i o n i n h y d r o g e l , gm/ml

ligand concentration ( f r a c t i o n of s i t e s remaining) i n i t i a l l i g a n d c o n c e n t r a t i o n (1.0) bulk c o n c e n t r a t i o n o f the product,

bi

particle,

initial

gm/ml

original

binding

gm/ml

bulk c o n c e n t r a t i o n o f the product,

gm/ml

Legend o f Symbols c o n t i n u e d on p, 167



166

SEPARATION, RECOVERY, AND PURIFICATION IN BIOTECHNOLOGY

β.

θ.2

8.4

β.6

8.8

1

TIME dinrwnslonlMS

Figure 7. (left) Selectivity as a function o f time f o r c o m p e t i t i v e a d s o r p t i o n o f two compounds, ( r i g h t ) Concentration p r o f i l e s w i t h i n the immobilized adsorbent bead and t h e b u l k solution.

PROOUCTPURfTY-

PRODUCT Ί'ADSORBED — PRODUCT Τ ADSORBED • PRODUCT 7 ADSORBED

«·« I 8.

1 8.5

1

1.5

2

HMEdta»ntlonlMS

F i g u r e 8. adsorption

Product p u r i t y as a f u n c t i o n o f two compounds.

o f time

f o r competitive


11.



c o n c e n t r a t i o n o f d e s i r e d p r o d u c t i n adsorbent p a r t i c l e , gm/ml concentration of undesired product i n adsorbent p a r t i c l e , gm/ml r a d i a l d i s t a n c e w i t h i n adsorbent p a r t i c l e , cm

r

r a d i u s o f adsorbent


R

radial

R

Q

R

r e

r e

p a r t i c l e s , cm

d i s t a n c e i n h y d r o g e l bead, cm

r a d i u s o f h y d r o g e l bead, cm £

a r b i t r a r y r e f e r e n c e d i s t a n c e f o r making d i m e n s i o n l e s s , cm time, sec

t

D

167

£

product

diffusivity

i n adsorbent

product

diffusivity

2 i n h y d r o g e l , cm / s e c

matrix,

arbitrary reference d i f f u s i v i t y s c a l e d i m e n s i o n l e s s , cm / s e c a d s o r p t i o n r a t e c o n s t a n t , 1/sec

Ν

the time

scale

2 cm / s e c

f o r making

η

number o f adsorbent particles h y d r o g e l bead number o f beads i n a b a t c h

immobilized

NC

number o f a d s o r b i n g components i n t h e b r o t h

ε

&

p o r o s i t y o f adsorbent

8

g

p o r o s i t y of hydrogel

t h e time

within

a

matrix

AV

volume element i n s i d e adsorbent

particle

α

u l t i m a t e l o a d i n g c a p a c i t y , gm/unit

ligand

Subscripts : i

r e p r e s e n t s i ' t h a d s o r b i n g component

i n the b r o t h

Superscripts : represents variable

i n dimensionless

form.

Literature Cited 1. 2. 3. 4. 5.

Wang, Η. Y. Annals of the New York Academy of Sciences, Biochemical Engineering III, 1984, 413, 313. Graves, D. J.; Wu, Y. T. Methods Enzymol. 1974, 34, 140. Chase, H. A. Chem. Eng. Sci., 1984, 39, 1099. Tanaka, H.; Matsumura, M.; Veliky, I. A. Biotech. Bioeng., 1984, 26, 053. Ors, Ν.; Dogu, R. AIChE J., 1979, 25, 723.


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S E P A R A T I O N , R E C O V E R Y , A N D P U R I F I C A T I O N IN B I O T E C H N O L O G Y


6.

Kulkarni, B.D.; Jayaraman, V. K.; Doraiswamy, L. K. Chem. Eng. Sci., 1981, 36, 943. 7. Maheshwari, J.; Nigam, S. C.; Kunzru, D. AlChE J., 1985, 31, 1393. 8. Carnahan, B.; Luther, Η. Α.; Wilkes, J. O. 'Applied Numerical Methods'; John Wiley Sons; New York, NY, 1969. 9. von Rosenberg, D. U. 'Methods for the Numerical Solution of Partial Differential Equations'; American Elsevier Publishing Co., Inc.; New York, 1969. 10. Wang, Η. Y.; Sobnosky, Κ., unpublished data, 1984. 11. Payne, G. F., Ph.D. Thesis, The University of Michigan, Michigan, 1984. Received April 1, 1986


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