Modeling of Precipitation Phenomena in Protein ... - ACS Publications

9

Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 11, 2014 | http://pubs.acs.org Publication Date: July 11, 1986 | doi: 10.1021/bk-1986-0314.ch009

Modeling of Precipitation Phenomena in Protein Recovery C. E. Glatz and R. R. Fisher Department of Chemical Engineering, Iowa State University, Ames, IA 50011

A review of efforts to experimentally characterize and model the phenomena important in protein precipitation shows that, despite successes, continued work is necessary to produce accurate mechanistic descriptions of this method of protein recovery. The formation and growth of the primary particle in acid precipitation has been described in terms of the protein supersaturation. Aggregate growth by collision results in a size-dependent rate expression. Aggregate breakage, by shear or collision, remains to be adequately described in light of recent work. Population balances serve to model the combined phenomena. Recent work identifies mixing during precipitant addition as a determinant of aggregate physical properties; such effects are described with a floc-strength model. R e a p i n g t h e b e n e f i t s o f t h e new b i o l o g y a n d e v e n t h e c o n t i n u e d development o f t r a d i t i o n a l biotechnology poses problems i n s e v e r a l areas. Two o f t h e s e , s y n t h e s i s o f t h e d e s i r e d p r o d u c t a n d i t s e n d u s e , h a v e b e e n a n d w i l l c o n t i n u e t o b e t h e f o c u s o f much r e s e a r c h . R e l a t i v e l y n e g l e c t e d has been the r e c o v e r y and p u r i f i c a t i o n o f these b i o l o g i c a l p r o d u c t s , the i n t e r m e d i a t e s t e p s t h a t c o n s t i t u t e the a r e a o f "downstream p r o c e s s i n g . " I t i s t h i s l a s t area that i s proving t o r e q u i r e the g r e a t e s t e f f o r t i n p r a c t i c e and t h a t h a s the p o o r e s t base o f f u n d a m e n t a l e n g i n e e r i n g u n d e r s t a n d i n g on w h i c h t o draw. The t o p i c o f t h i s p a p e r i s t h e m o d e l i n g o f e v e n t s o c c u r r i n g i n the r e c o v e r y o f p r o t e i n s and i nthe c o n d i t i o n i n g o f the product streams f o r f u r t h e r p u r i f i c a t i o n u s i n g p r e c i p i t a t i o n . The t y p i c a l g o a l o f downstream p r o c e s s i n g i s the r e c o v e r y o f a d e s i r e d p r o d u c t from a very d i l u t e stream w h i l e m i n i m i z i n g the l o s s o f the m a t e r i a l i n what i s u s u a l l y a m u l t i - s t e p s e p a r a t i o n p r o c e s s . Precipitation enables an e a r l y c o n c e n t r a t i o n o f the p r o d u c t and c a n s i m u l t a n e o u s l y s e r v e t o remove c o n t a m i n a n t s t h a t would i n t e r f e r e w i t h s u b s e q u e n t purification steps. F u r t h e r , the wide v a r i e t y o f p o t e n t i a l

0097-6156/86/0314-0109$06.00/0 © 1986 American Chemical Society

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

110

SEPARATION, RECOVERY, A N D PURIFICATION IN BIOTECHNOLOGY

p r e c i p i t a t i n g a g e n t s t h a t e x i s t s p e r m i t s s e l e c t i o n o f the p a r t i c u l a r agent c a p a b l e o f r e c o v e r i n g the t a r g e t s p e c i e s under c o n d i t i o n s where a c t i v i t y i s retained. The t a r g e t s p e c i e s c o n s i d e r e d here a r e p r o t e i n s , and the p r i n c i p l e s d e v e l o p e d may be a p p l i e d t o any p r o t e i n - c o n t a i n i n g aqueous stream, i n c l u d i n g f e r m e n t a t i o n b r o t h s , p l a n t e x t r a c t s , and waste streams, whether the m a t e r i a l i s d e s t i n e d f o r f o o d , p h a r m a c e u t i c a l , or c h e m i c a l a p p l i c a t i o n .


Protein

Precipitation

The s t a b i l i t y o f p r o t e i n s i n s o l u t i o n i s d e t e r m i n e d by a number o f f a c t o r s t h a t govern p r o t e i n - p r o t e i n , p r o t e i n - s o l v e n t , and solvent-solvent interactions. S u f f i c i e n t a l t e r a t i o n o f any o f t h e s e i n t e r a c t i o n s can r e s u l t i n d r a m a t i c r e d u c t i o n s i n s o l u b i l i t y . Hence, p r o t e i n s can be p r e c i p i t a t e d by a v a r i e t y o f agents i n c l u d i n g o r g a n i c s o l v e n t s , d i v a l e n t c a t i o n s , h e a t , a c i d s / b a s e s (pH a d j u s t m e n t ) , s a l t s , n o n i o n i c polymers ( e g . p o l y e t h y l e n e g l y c o l ) , and p o l y e l e c t r o l y t e s . These means o f a l t e r i n g s o l u b i l i t y have been known and used f o r some time. What had been l a c k i n g was a d e s c r i p t i o n o f the mechanism o f f o r m a t i o n o f the p a r t i c u l a t e phase, the e n v i r o n m e n t a l d e t e r m i n a n t s o f the c h a r a c t e r i s t i c s o f t h i s phase, and the c o n n e c t i o n between t h e s e c h a r a c t e r i s t i c s , p a r t i c u l a t e b e h a v i o r i n the subsequent p u r i f i c a t i o n s t e p s , and r e t e n t i o n o f f u n c t i o n a l a c t i v i t y . There was, t h e r e f o r e , l i t t l e knowledge on which t o base d e s i g n o f the p r e c i p i t a t i o n s t a g e so t h a t the p r e c i p i t a t e would be e a s i l y r e c o v e r e d , the maximum amount of p r o t e i n would be i n i t s n a t i v e or a c t i v e s t a t e , and as many c o n t a m i n a n t s as p o s s i b l e would be removed. Recent r e s e a r c h , the b u l k o f which has been g a t h e r e d from s t u d y o f the i s o e l e c t r i c p r e c i p i t a t i o n o f soy p r o t e i n , has p r o v i d e d a good deal of t h i s missing i n f o r m a t i o n . Grabenbauer and G l a t z (l_) and V i r k a r e t a l . (2) have shown t h a t p r e c i p i t a t i o n p r o c e e d s by an i n i t i a l r a p i d f o r m a t i o n o f submicron p r i m a r y p a r t i c l e s f o l l o w e d by c o l l i s i o n - c o n t r o l l e d a g g r e g a t i o n of these p r i m a r y p a r t i c l e s . The l a t t e r growth phase i s c o m p l i c a t e d by the s i m u l t a n e o u s s h e a r - c o n t r o l l e d breakup o f the a g g r e g a t e s . We w i l l examine each s t e p i n t u r n , i n c l u d i n g m o d e l i n g approaches f o r each. Primary P a r t i c l e Formation. The i n i t i a l s t a g e o f p r i m a r y p a r t i c l e f o r m a t i o n had been o b s e r v e d by P a r k e r and D a l g l e i s h (3) f o r enzymatically destabilized casein. They used l i g h t s c a t t e r i n g and t u r b i d i t y measurements to f o l l o w the weight-average m o l e c u l a r weight (M ) o f the a s s o c i a t i n g c a s e i n p a r t i c l e s . A f t e r an i n i t i a l p e r i o d o f a c c e l e r a t i n g r a t e , the k i n e t i c b e h a v i o r c o u l d be d e s c r i b e d by von Smoluchowski s t h e o r y o f p e r i k i n e t i c c o a g u l a t i o n . The r e s u l t i n terms o f was w

1

1^ = M

0

+ 2 wkt

(1)

where M i s the m o l e c u l e weight o f the i n d i v i d u a l p r o t e i n s , k i s the c o a g u l a t i o n r a t e c o n s t a n t , w i s the c o n c e n t r a t i o n (weight b a s i s ) o f p r o t e i n , and t i s t i m e . N e l s o n and G l a t z (4) examined the r o l e o f e n v i r o n m e n t a l c o n d i t i o n s i n d e t e r m i n i n g the s i z e and number o f these p r i m a r y particles. They found s i z e t o depend on the p r e c i p i t a t i n g agent Q


9.

111

Modeling of Precipitation Phenomena

GLATZ A N D FISHER

(HCl, H 2 S O 4 , or C a ) and t o t a l protein concentration, but not on mixing conditions. Their conclusion was that primary p a r t i c l e growth i s governed by supersaturation-controlled nucleation/growth phenomena· This mechanism f o r the formation of primary p a r t i c l e s can be described using Nielsen's (5) expressions f o r homogeneous nucleation with d i f f u s i o n - c o n t r o l l e d growth i n p r e c i p i t a t i o n . In h i s discussion, the nucleation rate, J ( c ) , i s expressed as a power-law function of supersaturation, c, Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 11, 2014 | http://pubs.acs.org Publication Date: July 11, 1986 | doi: 10.1021/bk-1986-0314.ch009

2+

J(c) = ν

Μ

(2)

where 1^ i s the nucleation rate constant and m i s the nucleation power constant. The number of primary p a r t i c l e s per unit volume, N>|, formed i n a batch p r e c i p i t a t i o n can be calculated as CO

CO

N-, = '/ J(c) dt = k 0

n

/c

m

dt

(3)

0

Supersaturation, c, may be expressed as a function of i n i t i a l supersaturation, c , Q

c = (1 - a ) c

(4)

0

where a i s the f r a c t i o n of supersaturated protein that has been precipitated. Combining a d i f f u s i o n - c o n t r o l l e d growth-rate expression with the assumption of spherical primary p a r t i c l e s gives the volumetric growth rate of formed p a r t i c l e s as f i r s t order i n supersaturation -3—

dt

= 4πϋ rev m

, \ (5) c

where V i s the p a r t i c l e volume, D i s the protein d i f f u s i v i t y , ν i s the protein molecular volume, and r i s the molecular radius. Solving Equations 3-5 together with an overall mass balance, Nielsen obtained the approximate r e s u l t m

where C ρ i s a weak function of m, approximately equal to one. Hence thé stronger the dependence of nucleation on supersaturation, the greater w i l l be the increase i n number of primary p a r t i c l e s as i n i t i a l supersaturation increases. For (3m-l)/5 > 1 ( i . e . m > 2), the size of those p a r t i c l e s w i l l decrease with i n i t i a l supersaturation. No dependence on mixing conditions appears; the concentration dependence f o r soy protein p r e c i p i t a t e s (via hydrochloric acid addition) was found (4) to be m

= 2.67 x 1 0

1 1

0

8

c - 4 o

(7)

requiring m = 1.7. Over the range of concentrations studied (0.15 -


112



30 kg/m3) the size of primary p a r t i c l e s increased from 0.16 to 0.27 Um.

Aggregate growth and breakup. The primary p a r t i c l e s (produced as described above) form the starting material f o r the aggregation stage. This stage p a r a l l e l s what occurs i n other aggregation/coagulation/flocculation systems. I t d i f f e r s from many of these however, i n that the aggregates are p a r t i c u l a r l y prone to breakup and their size i s smaller than the Kolmogorov microscale of turbulence, subjecting them to d i f f e r e n t c o n t r o l l i n g f l u i d forces during growth and breakup (6^). Since p a r t i c l e size i s one of the determinants of the e f f i c i e n c y of s o l i d - l i q u i d separations ( f i l t r a t i o n rate and s e t t l i n g v e l o c i t y are both proportional to the square of p a r t i c l e diameter (7)), the modeling and characterization of the p a r t i c l e size d i s t r i b u t i o n s i s important. Population balances were combined with the proposed mechanisms to model the size d i s t r i b u t i o n s from continuous s t i r r e d p r e c i p i t a t o r s . The postulated f a i l u r e of c o l l i s i o n s between larger aggregates to form lasting agglomerates reduces the growth process to one where only primary p a r t i c l e s and small aggregates can serve as growth units, though larger sizes may serve as c o l l e c t o r s . Modelled in t h i s way, growth becomes a continuous process. P a r t i c l e size d i s t r i b u t i o n s have been successfully modelled over a wide range of conditions f o r continuous stirred-tank precipitators ( 1_, 6^ 8). Models of the p a r t i c l e size d i s t r i b u t i o n Asssumptions. The mathematical models based on the population balance incorporate the following physical features and simplifying assumptions : 1.

Protein comes out of solution very quickly and therefore an accounting i s needed only f o r the s o l i d material. This i s supported by tubular reactor studies (2, 9) where p r e c i p i t a t i o n , in terms of removal of soluble protein, i s completed within 1 s for the protein concentrations above 2 kg/m^.

2.

Growth of an aggregate occurs by c o l l i s i o n with primary p a r t i c l e s and smaller aggregates. However, c o l l i s i o n s between larger aggregates are i n e f f e c t i v e i n forming lasting aggregates. Gregory (10) has shown that c o l l i s i o n e f f i c i e n c y decreases considerably with increasing size of equal-sized c o l l i d i n g species. In addition, aggregate-aggregate attachments would be r e l a t i v e l y weak as the result of the lower bond densities at these points compared to bond densities within aggregates. A r a t i o of 10 to 1 has been reported as t y p i c a l (11) f o r the r a t i o of contacts within an established aggregate to contacts between two such aggregates. Growth i s therefore viewed as the incremental addition of small units to the growing aggregates.

3.

The effectiveness of these c o l l i s i o n s of small p a r t i c l e s with growing aggregates i s independent of the size of the growing species.


113


9. G L A T Z A N D FISHER


Population Balances. Three d i f f e r e n t models based on two a p p r o x i m a t i o n s r e g a r d i n g t h e mode o f b r e a k a g e a n d t w o a p p r o x i m a t i o n s r e g a r d i n g t h e s i z e d e p e n d e n c e o f g r o w t h r a t e h a v e b e e n e x a m i n e d . The d i f f e r e n t i a l e q u a t i o n s f o r m o d e l i n g the s i z e d i s t r i b u t i o n are based on a p o p u l a t i o n b a l a n c e o n a g g r e g a t e s o f s i z e L w h i c h , f o r a CSTR a t s t e a d y s t a t e , mean r e s i d e n c e t i m e τ , a n d w i t h n o p a r t i c l e s i n t h e feed, reduces t o

^ i

= 0

+ ^ + D - B τ

at

(8)

w h e r e η i s t h e n u m b e r d e n s i t y o f p a r t i c l e s , τ i s t h e r e a c t o r mean r e s i d e n c e t i m e , a n d w h e r e G, D, a n d Β a r e t h e r a t e s f o r d i f f e r e n t i a l growth, v o l u m e t r i c death by breakup, andv o l u m e t r i c b i r t h by breakage o f l a r g e r p a r t i c l e s , r e s p e c t i v e l y ; n , G, D, a n d Β may b e f u n c t i o n s o f L. The f i r s t m o d e l i n c o r p o r a t e s e x p r e s s i o n s f o r e a c h o f t h e s e t e r m s (6), i n which growth i s approximated as l i n e a r w i t h aggregate s i z e ; G = A,,v L = K L g

(9)

0

where A i s a c o n s t a n t i n c o r p o r a t i n g c o l l i s i o n e f f e c t i v e n e s s , Φ^ i s the volume f r a c t i o n o f p r i m a r y p a r t i c l e s , V g i s t h e r o o t - m e a n - s q u a r e v e l o c i t y g r a d i e n t , andK i s the product o f these t h r e e , c a l l e d the growth rate c o n s t a n t . Breakage i s d e s c r i b e d b y Q

D = k'V ( ^ g ) n= k L n (10) tfya where k a n d k a r e d e a t h - r a t e c o n s t a n t s , y i s the s o l u t i o n v i s c o s i t y , o i s the a g g r e g a t e y i e l d s t r e s s , a n d 6 a n d β a r e b r e a k a g e power constants. Breakup r e q u i r e s terras a c c o u n t i n g f o r the sudden d i s a p p e a r a n c e (death) o f parent aggregates and c o r r e s p o n d i n g appearance ( b i r t h ) o f daughter fragments. The f i r s t a n d s e c o n d m o d e l s assume t h a t a g g r e g a t e s b r e a k up t o f o r m a s m a l l n u m b e r o f d a u g h t e r f r a g m e n t s o f s i g n i f i c a n t mass. The number o f d a u g h t e r f r a g m e n t s w o u l d t e n d t o be greater f o r l a r g e r parent aggregates; t h i s i s approximated as an a v e r a g e f r a g m e n t n u m b e r , f , d e p e n d e n t o n t h e mean s i z e o f t h e distribution. Daughter f r a g m e n t s from a g i v e n p a r e n t a r e assumed t o be o f e q u a l v o l u m e . This gives Ô

3

g

1

v a

1

Β = fD(f /3L) The

resulting

dn

(11)

e q u a t i o n r e l a t i n g number d e n s i t y

=

k

L

B - l

(

f

« / 3 > + l

n

(

f

l / 3

L

)

_

n

)

_

η

to size i s

1

}

S u m m a r i z i n g , t h e m o d e l p a r a m e t e r s a r e K , k, 3, a n d f . T h e d e a t h and b i r t h e x p r e s s i o n s assume b r e a k a g e i n t o e q u a l - s i z e d Q


(

1 2

)

114


fragments such t h a t t o t a l p a r t i c l e volume i s c o n s e r v e d and t h a t a power law d e s c r i b e s the i n c r e a s e d s u s c e p t i b i l i t y o f a g g r e g a t e s t o breakup as s i z e i n c r e a s e s . The growth term assumes t h a t c o l l i s i o n due t o the s p a t i a l v a r i a t i o n o f t u r b u l e n c e i s the predominant f a c t o r , as has been demonstated ( e . g . ( 1 2 ) ) . The second model c o n s i d e r e d here (1_) r e s u l t s from assuming t h a t the growth r a t e , G , i s independent o f s i z e , g i v i n g


m

dn

.K_ P L

( f

(e/3)+l

n

(

f

l / 3

L

πι

)

_

n

)

m

The boundary c o n d i t i o n used f o r E q u a t i o n s 12 and 13 i s t h a t t h e c a l c u l a t e d t o t a l volume o f a g g r e g a t e s e q u a l s the measured aggregate volume. Parameters. P a s t work has s u g g e s t e d t h a t f o r a g i v e n p r o t e i n c o n c e n t r a t i o n , 3 and f c o u l d be f i x e d a t r e a s o n a b l e v a l u e s , l e a v i n g o n l y two f u l l y v a r i a b l e p a r a m e t e r s . The method o f s o l u t i o n i s d i s c u s s e d elsewhere (θ). F i g u r e 1, from d a t a o f Brown and G l a t z (13), shows t h a t breakup o f l a r g e a g g r e g a t e s r e s u l t s i n two o r more main fragments and a number o f s m a l l fragments c o m p r i s i n g r e l a t i v e l y l i t t l e mass. The l a t t e r can be n e g l e c t e d i n the b a l a n c e , a l t h o u g h t h e y w i l l s e r v e t o i n c r e a s e φ-j as t h e y a r e c o n s i d e r e d c a p a b l e o f b e i n g growth u n i t s . The l a r g e r a g g r e g a t e s a r e e x p e c t e d t o form the g r e a t e r number o f daughter f r a g m e n t s . However, Pandya and S p i e l m a n (13) f o u n d t h a t a l l o w i n g f o r t h i s w i t h i n a g i v e n d i s t r i b u t i o n o f kaolin-Fe(OH)-* f l o e s was no b e t t e r than u s i n g a c o n s t a n t f = 2.5. The model based on a growth r a t e i n d e p e n d e n t o f a g g r e g a t e s i z e , E q u a t i o n 13, gave r e a s o n a b l e f i t s by r e s i d u a l sum o f s q u a r e s c r i t e r i a except a t high p r o t e i n c o n c e n t r a t i o n s . However, a t a l l p r o t e i n c o n c e n t r a t i o n s s t u d i e d , the p r e d i c t e d c u r v e s were b i a s e d i n t h e manner i n which t h e y d e v i a t e d from e x p e r i m e n t a l o b s e r v a t i o n . This was p a r t i c u l a r l y e v i d e n t a t s m a l l s i z e s where the l o c a l minimum/maximum t r a i t s were l a r g e l y l o s t . The f i r s t model, based on a growth r a t e l i n e a r i n a g g r e g a t e s i z e , E q u a t i o n 12, gave s a t i s f a c t o r y f i t s o f the p a r t i c l e s i z e d a t a ( i n f a c t , f o r most runs the model f i t the e x p e r i m e n t a l p o i n t s more c l o s e l y t h a n d i d the s i x - p a r a m e t e r Chebyshev p o l y n o m i a l on which the model f i t t i n g was a c t u a l l y based) as w e l l as s u c c e s s f u l l y d e s c r i b i n g the l o c a l minimum/maximum t r a i t s . The c u r v e s p r e s e n t e d i n F i g u r e 2 a r e based on t h i s model, u s i n g the d a t a o f G l a t z e t . a l . (0) who d i s c u s s the b e h a v i o r o f model parameters k and K a t d i f f e r e n t r e a c t o r conditions. The t h i r d and f i n a l p a r t i c l e s i z e d i s t r i b u t i o n model assumes t h a t growth i s l i n e a r as i n the f i r s t b u t t h a t breakup r e s u l t s i n p r e d o m i n a n t l y s m a l l p a r t i c l e s ( t h o r o u g h breakage) which a r e t o o s m a l l to measure by the e l e c t r o n i c p a r t i c l e c o u n t e r s used t o c h a r a c t e r i z e the s u s p e n s i o n . P e t e n a t e and G l a t z (6) have p r o v i d e d a n a l y t i c a l s o l u t i o n s f o r t h i s model. The f o c u s o f the above m o d e l i n g has been on c o n t i n u o u s stirred-tank reactors. The g e n e r a l p r i n c i p l e s have been extended t o i n t e r p r e t r e s u l t s from b a t c h and t u b u l a r r e a c t o r s , as w e l l , though d e t a i l e d m o d e l i n g has n o t y e t been attempted (8). Q



9.

115


G L A T Z A N D FISHER

AGGREGATE SIZE, ym

F i g u r e 1. P l o t o f c h a n g e i n a g g r e g a t e v o l u m e v s . a g g r e g a t e s i z e f o r given time i n t e r v a l during breakup o f i s o e l e c t r i c a l l y p r e c i p i t a t e d soy p r o t e i n . P a r t i c l e volume f r a c t i o n , 0.00531. Shear r a t e , 1010 s " . 1

71 0

I

I

I

I

5

10

15

20

I 25

SIZE, μ

F i g u r e 2. P a r t i c l e ( n u m b e r ) s i z e d i s t r i b u t i o n s f o r i s o e l e c t r i c a l l y p r e c i p i t a t e d soy p r o t e i n showing t h e e f f e c t s o f shear r a t e and p r o t e i n c o n c e n t r a t i o n . Points are experimental data; curves a r e t h e m o d e l f i t u s i n g E q u a t i o n 12. S h e a r r a t e s : Δ , 417 - l ; V , 108 s " ; ο , 8 5 s " . s

1

1


116



P r e v i o u s a t t e m p t s h a v e b e e n made t o m o d e l s i z e d i s t r i b u t i o n s a l l o w i n g f o r growth by c o l l i s i o n s o fa l l aggregate-aggregate combinations. S u c h m o d e l s (2, 14) p r e d i c t e d much h i g h e r g r o w t h r a t e s t h a n were o b s e r v e d , o f f e r i n g f u r t h e r e v i d e n c e f o r t h e i n e f f e c t i v e n e s s of a g g r e g a t e - a g g r e g a t e c o l l i s i o n s . The m o d e l i n g e q u a t i o n s , when a l l p a r t i c l e - p a r t i c l e c o l l i s i o n s are assumed e f f e c t i v e , a r e r e p r e s e n t e d ( i n a b a t c h r e a c t o r ) b y

(14)

w h e r e N, t h e n u m b e r c o n c e n t r a t i o n o f p a r t i c l e s , a n d r , t h e p a r t i c l e r a d i i , a r e s p e c i f i e d f o r p a r t i c l e s i z e s i , j , and k such t h a t r ^= k

r

i

3

+

r

3

j T h i s e q u a t i o n r e p l a c e s E q u a t i o n 8, b u t d o e s n o t e x p l i c i t l y account f o r aggregate breakage. V i r k a r (2) i n t r o d u c e d b r e a k a g e t o t h i s balance b y n o t a l l o w i n g c o l l i s i o n s t h a t would r e s u l t i n a p a r t i c l e l a r g e r t h a n a f i x e d maximum s i z e . Breakage Models. We a r e c o n t i n u i n g o u r s t u d y o f s t i r r e d t a n k behavior o f i s o e l e c t r i c p r e c i p i t a t e s by examining the breakup p h e n o m e n a a n d t h e m o d e l i n g e q u a t i o n f o r b r e a k u p i n more d e t a i l . Data are i n t e r p r e t e d i n t h e l i g h t o f t h r e e p r o p o s e d t r e a t m e n t s o f b r e a k u p (15)· Two a r e b a s e d o n b r e a k u p u n d e r f l u i d s h e a r , u s i n g t h e c o n c e p t s o f a maximum s t a b l e s i z e ( 1 6 - 1 8 ) a n d s i m i l a r i t y (19-20). The t h i r d i s based on c o l l i s i o n a l breakage which has been d i s c u s s e d b u t n o t o b s e r v e d b y Glasgow and Luecke (21), and t h o u g h t t o o c c u r w i t h p r o t e i n a g g r e g a t e s i n l a m i n a r s h e a r (22). O t h e r Précipitants. E x t e n s i o n a n d m o d i f i c a t i o n o f t h e s e m o d e l i n g e f f o r t s w i l l be r e q u i r e d f o r t h e i r a p p l i c a t i o n t o p r e c i p i t a t i o n s other than i s o e l e c t r i c . O t h e r l o w m o l e c u l a r w e i g h t précipitants h a v e b e e n s h o w n t o r e s u l t i n t h e same s o r t o f a g g r e g a t e m o r p h o l o g y (Ca ; (4)) a n d g r o w t h k i n e t i c s ( e t h a n o l , C a , ( N H ^ ^ S O ^ ; 0 9 ) ) . F o r t h e s e précipitants n o m o d i f i c a t i o n s h o u l d b e n e c e s s a r y , a l t h o u g h t h e dependence o f aggregate s t r e n g t h on t h e p h y s i c o c h e m i c a l c o n d i t i o n s w i l l change and w i t h i t t h e s t r e n g t h - d e p e n d e n t model p a r a m e t e r s . B a s e d o n v e r y p r e l i m i n a r y r e s u l t s (23) t h e b e h a v i o r o f p o l y e t h y l e n e g l y c o l i s a l s o e x p e c t e d t o be q u a n t i t a t i v e l y s i m i l a r . 2 +

2 +

Precipitate

Behavior

Beyond d e s c r i b i n g what i s o c c u r r i n g i n t h e p r e c i p i t a t i o n s t e p i t s e l f , work h a s b e e n done i n r e l a t i n g t h e c h a r a c t e r i s t i c s o f t h e m a t e r i a l l e a v i n g the p r e c i p i t a t o r t o i t s b e h a v i o r i n subsequent o p e r a t i o n s . The i m p o r t a n c e o f a g g r e g a t e " a g i n g " t o c o n d i t i o n t h e a g g r e g a t e s t o r e s i s t b r e a k u p d u r i n g s h e a r e n c o u n t e r e d i n pumps a n d c e n t r i f u g e s i s d o c u m e n t e d (24-25)· The i n f l u e n c e o f p r e p a r a t i o n c o n d i t i o n s o n



9.



117

c e n t r i f u g e c a p a c i t y a n d s l u d g e r h e o l o g y h a s b e e n o b s e r v e d (26), a n e x p l a n a t i o n f o r a g g r e g a t e s t r e n g t h and r h e o l o g i c a l p r o p e r t i e s p r o p o s e d (4) i n t e r m s o f a n e l a s t i c f l o e m o d e l ( 1 1 ) , a n d t h e p r e p a r a t i o n - ( 2 7 ) a n d a g i n g - (14) d e p e n d e n t s e t t l i n g b e h a v i o r reported. The w o r k o f F i s h e r e t a l . ( 2 7 ) i l l u s t r a t e s some d e s i g n c o n s i d e r a t i o n s beyond t h a t o f the p a r t i c l e s i z e a t the p r e c i p i t a t i o n outlet. These w o r k e r s were c o n c e r n e d w i t h the m i x i n g c o n d i t i o n s d u r i n g the a d d i t i o n o f a c i d t o the p r o t e i n s o l u t i o n . L o c a l extremes i n pH a r e known t o c a u s e i r r e v e r s i b l e d e n a t u r a t i o n o f p r o t e i n s (28) which w i l l a l t e r t h e i r p r e c i p i t a t i o n behavior. F u r t h e r , H o a r e (297 has r e p o r t e d t h a t the p r e c i p i t a t e p r o p e r t i e s d i f f e r w i t h e x t r e m e s i n operating conditions. One e x t r e m e e x p l o i t e d i n i n o r g a n i c p r e c i p i t a t i o n s i s h o m o g e n e o u s p r e c i p i t a t i o n (30), w h i c h i n v o l v e s t h e homogeneous p r o d u c t i o n o f t h e p r e c i p i t a n t , u s u a l l y b y a c o n t r o l l e d c h e m i c a l r e a c t i o n , w i t h i n the s o l u t i o n . Advantages o f t h i s i n c l u d e the p r o d u c t i o n o f denser p r e c i p i t a t e and reduced c o p r e c i p i t a t i o n . F i s h e r e t a l . (27) a p p r o x i m a t e d homogeneous i s o e l e c t r i c p r e c i p i t a t i o n by the a d d i t i o n o f a c i d from a d i a l y s i s b a g suspended i n the p r o t e i n s o l u t i o n on a r o t a t i n g s h a f t . The d e g r e e o f f r a c t i o n a t i o n o f t w o p r o t e i n s ( g l y c i n i n , p i = 6.0, a n d 3 - c o n g l y c i n i n , p i = 4·$) from a t o t a l soy e x t r a c t and the p h y s i c a l c h a r a c t e r i s t i c s o f the p r e c i p i t a t e s w e r e c o n t r a s t e d w i t h t h e same p r o p e r t i e s o f p r e c i p a t e s f o r m e d d u r i n g r a p i d a c i d a d d i t i o n . P r e c i p i t a t e f r a c t i o n s were t a k e n a t p H 6.0 a n d 4.8. The c o m p o s i t i o n s o f t h e f r a c t i o n s , T a b l e I , i n d i c a t e t h a t s e p a r a t i o n o f the g l y c i n i n and 3 - c o n g l y c i n i n d i d occur, with s u b s t a n t i a l e n r i c h m e n t o f t h e g l y c i n i n p h a s e i n t h e p H 6.0 f r a c t i o n . T a b l e I a l s o shows t h a t no d i f f e r e n c e s i n the f r a c t i o n a t i o n o f g l y c i n i n o r 3 - c o n g l y c i n i n can be a t t r i b u t e d t o t h e m i x i n g d u r i n g a c i d addition. I n h i n d e r e d s e t t l i n g t e s t s o n t h e pH 4 · 8 p r o d u c t t h e a g g r e g a t e prepared by slow a c i d a d d i t i o n c l e a r l y s e t t l e d f a s t e r than that prepared by rapid a c i d a d d i t i o n . Since aggregate s i z e and d e n s i t y , as measured p r i o r t o s e t t l i n g , c o u l d n o t a c c o u n t f o r the d i f f e r e n t s e t t l i n g r a t e s , a n o t h e r e x p l a n a t i o n was s o u g h t . I t was c o n c l u d e d t h a t the c o n t r o l l i n g c h a r a c t e r i s t i c o f the hindered s e t t l i n g i s the a g g r e g a t e ' s a b i l i t y t o a g g r e g a t e f u r t h e r a n d become l a r g e e n o u g h t o settle. The c h a r a c t e r i s t i c s o f t h e i s o e l e c t r i c a l l y p r e c i p i t a t e d a g g r e g a t e s were i n t e r p r e t e d i n l i g h t o f a model o f f l o e s t e n g t h a s d e v e l o p e d b y F i r t h a n d H u n t e r (11) a n d a p p l i e d b y N e l s o n a n d G l a t z (4)· T h i s model h o l d s t h a t the s t r e n g t h , a , o f an a g g r e g a t e o f p r i m a r y p a r t i c l e s i s a p r o d u c t o f the number o f b o n d s p e r a r e a a n d the a t t r a c t i v e f o r c e per bond. They f u r t h e r showed t h a t y a

σ

ya

Q dT

(15)

w h e r e Q i s a n i n t e r a c t i o n p o t e n t i a l f u n c t i o n — t h e sum o f c h a r g e - c h a r g e r e p u l s i v e a n d van der Waals a t t r a c t i v e c o n t r i b u t i o n s — a n d w h e r e d>j i s t h e d i a m e t e r o f t h e p r i m a r y p a r t i c l e . The a p p l i c a t i o n o f t h i s m o d e l h e l p e d t o i d e n t i f y o r i e n t a t i o n o f t h e p r o t e i n d u r i n g i t s i n c o r p o r a t i o n i n t o the p r i m a r y p a r t i c l e a s a d e t e r m i n i n g s t e p i n the subsequent s t r e n g t h o f the a g g r e g a t e .


118


T a b l e I . P h y s i c a l and C o m p o s i t i o n a l P r o p e r t i e s o f t h e P r o t e i n E x t r a c t and t h e R a p i d and Slow P r o t e i n P r e c i p i t a t e s


Fraction

Property

protein a extract

pH

Total

% glycinin in fraction

27.6

%3-conglycinin in fraction^

16.7

Slow

8.1

4.0

4.1

27.4

21.8

0.13

0.19

hindered s e t t l i n g time (min)f

Determined

by b i u r e t

Slow

10.0

(ym)

5 Q

4.8

Rapid

52.-6

49.3

(ym) d

Rapid

pH

6.0

colorimetric

0.51

0.36

11.31

7.88

17

7

assay.

^Immunologically a c t i v e p r o t e i n expressed as percent of t o t a l p r o t e i n , determined by r o c k e t - g e l immunoelectrophoresis. P r i m a r y p a r t i c l e d i a m e t e r , measured from micrographs of the aggregate.

scanning

electron

^Mean a g g r e g a t e d i a m e t e r ( o n a v o l u m e b a s i s ) , d e t e r m i n e d particle size distribution.

from

e

T h e pH 6.0 a g g r e g a t e s size distribution.

from

f

Time f o r i n t e r f a c e t o drop

g

T h e pH 6.0 a g g r e g a t e s tling test.

w e r e t o o weak t o b e c h a r a c t e r i z e d

t o 30% of i n i t i a l

slurry height.

d i dnot s e t t l e i n the hindered


set-

9.



119


Conclusion Models f o r continuous, s t i r r e d p r e c i p i t a t i o n behavior are a t a r e a s o n a b l y s u c c e s s f u l s t a g e , t h o u g h t h e e x p r e s s i o n f o r b r e a k u p c a n be improved i n t h e l i g h t o f r e c e n t s t u d i e s . Batch and t u b u l a r r e a c t o r models must a d d i t i o n a l l y i n c l u d e an e x p l i c i t a c c o u n t i n g f o r p r i m a r y p a r t i c l e formation and behavior o f small p a r t i c l e s . Some o f t h e d a t a n e c e s s a r y t o do s o h a v e b e e n c o l l e c t e d , b u t n u m b e r d e n s i t y d a t a a t the s m a l l s i z e s i s s t i l l l a c k i n g . F i n a l l y i t r e m a i n s t o b e s e e n how s u c c e s s f u l t h e m o d e l s d e v e l o p e d f o r i s o e l e c t r i c p r e c i p i t a t i o n w i l l be i n d e s c r i b i n g p r e c i p i t a t i o n w i t h o t h e r c l a s s e s o f précipitants. Acknowledgments T h i s work was s u p p o r t e d b y t h e E n g i n e e r i n g R e s e a r c h I n s t i t u t e o f Iowa S t a t e U n i v e r s i t y t h r o u g h N a t i o n a l S c i e n c e F o u n d a t i o n G r a n t No. CPE-8120568.

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Grabenbauer, G. C.; Glatz, C. E. Chem. Eng. Comm. 1981, 12, 203219. Virkar, P. D.; Chan, M. Y. Y.; Hoare, M.; Dunnill, P. Biotechnol. Bioeng. 1982, 24, 871-887. Parker, T. G.; Dalgleish, D. G. Biopolymers 1977, 16, 2533-2547. Nelson, C. D.; Glatz, C. E. Biotechnol. Bioeng. 1985, 27, 14341444. Nielson, A. E. "Kinetics of Precipitation"; Macmillan Co.: New York, 1964, Chap. 7. Petenate, A. M.; Glatz, C. E. Biotechnol. Bioeng. 1983, 25, 3059-3078. McCabe, W. L.; Smith, J. C. "Unit Operations of Chemical Engineering, 3rd Edition"; McGraw-Hill, Inc.:New York, 1976; p. 938971. Glatz, C. E.; Hoare, M.; Landa-Vertiz, J. AIChE J. 1986, in press. Chan, M. Y. Y.; Hoare, M.; Dunnill, P. Biotechnol. Bioeng., 1985, accepted for publication. Gregory, J. Chem. Eng. Sci. 1981, 36, 1789-1794. Firth, Β. Α.; Hunter, R. J. J. Colloid Interface Sci., 1976, 57, 266-275. Yuu, S. AIChE J. 1984, 30, 802-807. Pandya, J. D.; Spielman, L. A. J. Colloid Interface Sci. 1982, 90, 517-532. Hoare, M. Trans. Inst. Chem. Eng. 1982, 60, 157-163. Brown, D. L.; Glatz, C. E. Paper presented at the AIChE Annual Meeting 1985, Chicago. Tomi, D. T.; Bagster, D. F. Trans. Inst. Chem. Eng. 1978, 56, 1-8. Parker, D. S.; Kaufman, W. J.; Jenkins, D. J. J. Sanit Eng. Div. ASCE 1982, 98, 79-99. Tambo, N.; Hozumi, H. Water Res. 1979, 13, 421-427. Ramkrishna, D. Chem. Eng. Sci. 1974, 29, 987-992.


120

20. 21. 22.


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SEPARATION, RECOVERY, AND PURIFICATION IN BIOTECHNOLOGY

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Received March 26, 1986


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