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Chemical Engineer& Science, Vol. 40, No. 8, pp. 1321-1354. 1985. ooo9-2x9/85 53.00+0.00Printed in Great Britain. Pergamon Press Ltd.

REVIEW ARTICLE NUMBER 17THE IMMOBILIZATION OF WHOLE CELLS: ENGINEERINGPRINCIPLES

STEVEN F. KAREL, SHARI B. LIBICKI and CHANNING R. ROBERTSONDep ar t m en t o f Ch em i ca l En g i n eer i n g , S t an fo rd Un i v er s i t y , CA 9 4 30 5 , U .S .A .(Received 18 June 1984)

Abstrac t -The i mm o b i l iza t i o n o f wh o l e ce l ls i n v o l v es t h e r e t e n t i o n o f ca t a l y t i ca l ly ac t i v e ce l l s w i t h i n ar e s t r i c t e d r e g i o n o f a b i or e a c t o r . T e c h n i q u e s w h i c h h a v e b e e n u s e d t o i m m o b i li z e w h o l e c e l ls in c l u d ea d s o r p t i o n , a g g r e g a t i o n , c o n f in e m e n t a n d e n t r a p m e n t . T h e s e t e c h n i q u e s ca n b e a p p l ie d t o e s s e n t i a l ly a l l o ft h e v i ab l e o r n o n -v iab l e wh o l e ce ll sy s t em s o f p o t en t i a l i n t e r es t : mi c r o o rg an i sms , an i ma l an d p l an t ce l l s. Th ef a c t t h a t i m m o b i li z e d c e l ls m a y b e l i v in g le a d s t o u n i q u e e f fe c t s i n t h i s f or m o fh e t e r o g e n e o u s c a t a l y s is . Th e s ei n c l u d e t h e i mp a c t o f i mm o b i l i za t i o n o n ce ll p h y s i o lo g y an d ce ll mo b i l i t y , p h y s i ca l in t e r a c t i o n s o fi m m o b i l iz e d c e l ls w i t h t h e su p p o r t , a n d t h e cr e a t i o n o f a m i c r o e n v i r o n m e n t . T h e t h e o r y o f m a s s -t r a n s fe r a n dr e a c t i o n i n t h e s e t y p e s o f s y s t e m s i s w e l l u n d e r s t o o d , b u t s c h e m e s ca p a b l e o f p r e d i c t i n g s u b s t r a t e a n d p r o d u c td i ff u s iv i t ie s a n d t h e i n t r i n s i c k in e t i c s in t h e a g g r e g a t e m u s t s t i ll b e d e v e lo p e d . N e w e x p e r i m e n t a l a p p r o a c h e sa r e b e i n g u s e d t o e lu c i d a t e t h e b a s i c m e c h a n i s m s t h a t d e t e r m i n e t h e s e p h y s i c a l a n d m e t a b o l ic p r o p e r t i e s o fi m m o b i l iz e d c e l ls . S e v e r a l r e a c t o r c o n f ig u r a t i o n s h a v e b e e n s u c c e s s fu l l y u s e d w i t h i m m o b i li z e d c e l ls , a n dm a n y m o r e h a v e b e e n p r o p o s e d . T h e c h o i c e o f a p a r t i c u l a r d e s i g n f or a g iv e n p r o c e s s d e p e n d s o n t h er e q u i r e m e n t s f o r m a s s - t r a n s f e r , t h e gr o w t h b e h a v i ou r o f t h e c e l ls , a n d t h e st r u c t u r a l p r o p e r t i e s o f t h ea g g r e g a t e .

1. INTRODUCTION1.1 . Scope of th e re v iew1 .1 .1 . P rev i o u s r e v i ewsCONTENTS

132213221 .2 . Object ives o f wh ole-cel l imm obi l izat ion 13221 .3 . Def in i t ion of wh ole-cel l imm obi l izat ion 1323

2 . CLASSIFICATION OF IMMOBILIZED CELL SYSTEMS2 .1 . Ce l l s a t t ach ed t o a su r f ace2 .2 . C e l l s e n t r a p p e d i n a p o r o u s m a t r i x2 .2 .1 . P re fo rm ed p o ro u s ma t r i ces2 .2 .2 . P o r o u s m at r i ces fo rmed i n s i r t l2 .3 . C e l l s c o n t a i n e d b e h i n d a b a r r i e r2 .4 . Sel f -aggregat ing cel l s2 .5 . E t h a n o l p r o d u c t i o n u s i n g i mm o b i l i zed ce l l s: an ex am p l e

3 . PH YSICAL AND CHEMICAL P ROP ERT IES OF IMMOBILIZED CELLAGGREGATES

132413241326

132713271327

3 .1 . E ffect ive d i f fusiv i ty in cel l aggr ega tes3 .1 .1 . E f fe c t i ve d i f fu s i v it y m e a s u r e m e n t s w h e r e t h e t r a c e r i s n o t c o n s u m e d3 .1 .2 . E f fec t i v e d i ffu s i v i t y measu rem en t s w h er e t h e t r a ce r i s co n su med3 .1 .3 . E f fec t i v e d i ffu s i v i t y mea su r em en t s i n an i ma l t i s su e3 .1 .4 . S o u r ces o f d i fF u s i v e r es i s t a n ce i n ce ll ag g reg a t es3 .2 . I n t e r a c t i on s a m o n g c o m p o n e n t s i n t h e a g g r e g a t e3 .2 .1 . Ce l l mo b i l i t y wi t h i n t h e ag g r eg a t e3 .2 .2 . C h e m i c a l i n t e r a c t i o n s b e t w e e n t h e s u p p o r t a n d t h e so lu t i o n3 .2 .3 . D i r e c t i n t e r a c t i o n s b e t w e e n t h e ce l ls a n d t h e s u p p o r t3 .3 . P h y s i c a l i n t e r a c t i o n s o f t h e a g g r e g a t e w i t h t h e e n v i r o n m e n t

13281328

1330

13324 . BIOLOGICAL P R OP E RTIES OF IM M OBILIZED CELLS4.1 . Cel l mor ph ology4 .2 . Ce l l ph ysio logy

1333133313334 .2 .1 . E f fec t o f su r f ace s o n t h e g ro wt h o f ce l l s4 .2 .2 . I n f l u en ce o f i mm o b i l i za t i o n met h o d o n ce ll v i ab i l i t y4 .2 .3 . P er me ab i l izat ion of cel l s4 .2 .4 . Ca ta ly t ic s tab i l i ty o f imm obi l ized cel l s4 .2 .5 . Imm obi l ized re s t in g cel l s4 .2 .6 . Tech n i q u es fo r ch a ra c t e r i z i n g t h e met ab o l i c an d p h y s i ca l s t a t e o f i mm o b i l i zedcel l s5 . INTt iRACTIONS BETWEEN REACTION AND DIFF USION INIMMOBILIZED CELL SYSTEMS5 .1 . I n t r i n s i c k i n e t i c s o f imm o b i l i zed ce l l s5 .2 . M a s s t r a n s f e r a n d t h e ob s e r v e d r e a c t i o n r a t e : e x a m p l e s

1338133913391321ES 40:x-*


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1322 STEVEN F . KAREL e t a l .5 .3 . M a s s t r a n s fe r a n d t h e o b s e r v e d r e a c t i o n r a t e : t h e o r y5 .3 .1 . P ro b l em fo rm u l a t i o n an d s i mp l i f i ca t i o n5 3 .2 . Asymp t o t i c so l u t i o n s an d g en er a l i zed mo d u l i5 .4 . Ex p er i men t a l d e t ec t i o n o f ma ss -t r an s f e r l i mi t a t i o n s

1340

13466 . REACTOR CONFIG URATIONS FOR IMMOBILIZED CELLS 13466 .1 . S t a t i o n a r y p a r t i c l e or s u r f a c e r e a c t o r s6 .2 . M o v i n g su r f ace r ea c t o r s6 .3 . M i xed p a r t i c l e r ea c t o r s7. SUMMARY

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NOTATION 1348R E F E R E N C E S 1349

1. INTRODUCTIONAlth o u g h th e in t en t io n a l u se o f immo b i l i zed ce l l s b yma n i s a r ecen t d ev e lo p men t , t h e se lf -immo b i l i za t io no f c e l ls i s a w i d e s p r e a d p r o c e s s i n n a t u r e . T h e a t t a c h -m e n t o f m i c r o o r g a n i s m s t o s u r f a c e s p l a y s a n i m p o r t -an t r o l e in mic r o b ia l eco lo g y an d p a th o g en ic i ty [ 1 43 .B io fi lms r e su l t in g f r o m th e g r o wth o f ce l ls o n su r f acesa r e o ft e n p r e s e n t i n co n v e n t i o n a l i n d u s t r i a l p r o c e s s e su s in g mic r o o r g an i sm s [ 5] . I n t e r e s t i n en zy me im-m o b i li za t i o n d u r i n g t h e l a s t t w o d e c a d e s m o t i va t e d t h ed e v e lo p m e n t o f n e w i m m o b i li za t i o n t e c h n i q u e s , m a n yo f wh ich a r e ap p l i cab le to ce l l s , an d p r o v id ed a n ewp e r s p e c t i v e fo r e x a m i n i n g t h e c on v e n t i o n a l p r o c e s s e swh ich in v o lv e su r f ace -a t t ach ed ce l l s . New tech n iq u est o g e n e t i c a l l y m a n i p u l a t e i n d u s t r i a l l y i m p o r t a n tm i c r o o r g a n i s m s h a v e p r o v i d e d a d d i t i o n a l i n c e n t i v efo r t h e d e v e lo p m e n t o f n o v e l t e c h n i q u e s f o r t h emic r o b ia l p r o d u c t io n o f b io ch emica l s , an d immo b i -l i zed ce l l s ma y p lay a s ig n i f ican t r o l e in th i s r eg a r d .

1.1.1. Previous rev iews. T h e r e v i ew b y Bi r n b a u m eta l . [ 7] i s an ex ce l len t o v e r a l l i n t r o d u c t io n to t h e fi e ld o fimmo b i l i zed ce l ls . Th e co l lec t io n o f r ev iews ed i t ed b yC h i b a t a a n d Wi n g a r d [S ] of fe r s a t h o r o u g h t r e a t m e n to f m e t h o d s a n d a p p l i c a t i on s . T h e t w o v o lu m e s e d i t e db y Mat t i a sso n [ 9] co n s id e r a n u mb er o f su b - to p ic sasso c ia t ed wi th immo b i l i zed ce l l s i n co n s id e r a b led ep t h . Over v iews o f imm o b i l ized ce l l t ech n o log y , i t sh i s t o r y a n d i t s fu t u r e d i r e c t i on s fr o m s e v e r a l d i ff er e n tp e r s p e c t i v e s h a v e b e e n g i v e n i n s e v e r a l r e v i e w s[l&21].

1.1. Scope of the rev iewAl t h o u g h a w i d e v a r i e t y o f n a t u r a l a s w e l l a s

a r t i f ic i a l s y s t e m s a r e c h a r a c t e r i z ed b y t h e r e t e n t i o n o fce l l s a t a su r f ace o r w i th in a p a r t i c l e , we wi l l f o cu s o u ra t t e n t i o n o n s y s t e m s w h i c h m a y b e o f t e c h n o l o g i c a li n t e r e s t , a n d e x c lu d e f r o m c o n s id e r a t i o n t h e e c ol og ic a lan d p a th o g en ic r o le s o f mic r o b ia l a t t a ch m en t [ Z, 6 3.

Th e e n g in ee r in g a sp e c t s o f immo b i l i zed ce l l s h a v en o t b e e n r e v ie w e d i n a s m u c h d e t a i l . A n u m b e r o fr e c e n t p u b l i c a t i on s h a v e a d d r e s s e d s p e c if ic e n g i n e e r i n gp r o b l e m s a s s oc i a t e d w i t h im m o b i l iz e d e n z y m e s y s t e m s[ 22 -2 41 , an d Vie th an d Ven k a ta su b r am an ian g iv e af r amew o r k f or d i scu ss io n o f so me o f th e r ea c to ren g in ee r in g co n ce r n s wh ich ap p ly to immo b i l ized ce l l s[ 25 ]. O th e r r ev iews a r e co n ce r n ed m o r e sp ec i fi ca l lyw i t h t h e i n t e r a c t i o n b e t w e e n k i n e t i c s a n d m a s s t r a n s f e rin b io logical sy stem s [26-281. This su bject wi l l bed i scu ssed in mo r e d e ta i l i n Sec t io n 5 .3 .

A n u m b e r o f t o p i cs t h a t m i gh t b e c o n s id e r e d w i t h i nth e r ea lm o f immo b i l i zed ce l l t ech n o lo gy h a v e a l sob e e n t h e s u b j e c t o f r e c e n t r e v i e w s :

Th e s t a t e -o f-th e -a r t i n imm o b i li zed ce l l t ech n o log yh a s d e v el op e d t o t h e p o i n t t h a t m e t h o d s f or i m -mo b i l i zin g an y giv en ce l l t y p e a r e co n s id e r ed r o u t in e .Micr o b ia l p r o cesses in wh ich imm o b i li zed ce l ls h a v et h e p o t e n t i a l t o b e a p p l i e d f a r o u t n u m b e r t h o s e w h e r e .t h e y a r e n o t a p p l ic a b l e . M e t h o d s a n d a p p l i ca t i o n sh a v e a l r ea d y b een r ev iewed in so me d e ta i l (see b e lo w).O n t h e o t h e r h a n d , t w o i m p o r t a n t i s s u e s w h i c h h a v en o t b e e n a d e q u a t e l y r e v i e w e d a r e :

-u s e o f s u r f a c e -a t t a c h e d f il m s i n w a s t e w a t e r t r e a t -ment [S, 29-321;-f or m a t io n o f p e l l e t s o r f lo es in su sp en s io n cu l tu r e

c33, 341;-us e of imm obi l ized cells in b iosensor s [35 , 361;-imm obi l iza t ion of p la n t ce l ls in cu l t ur e [37-391;-g r o wth o f su r f ace -a t t ach ed an ima l ce l l s i n cu l tu r e

[4042 ]_

( 1) to ev a lu a te wh e th e r imm o b i l ized ce l l sy s t em s canb e s u c c e s s fu l l y a d a p t e d t o a n i n d u s t r i a l s c a l e a n d( 2) to e lu c id a te th e p h y s ica l an d b io ch em ica l p r in -

c ip le s u n d e r ly in g wh o le - ce l l immo b i l i za t io n .

1.2. Objec t ives o f wh ole-ce l l im m obil iza t ionI n mo s t t ech n o lo g ica l ap p l i ca t io n s o f immo b i l i zed

ce l ls , t h e o b jec t iv e i s t o in c r ea se th e ex ten t o f r ea c t io n .Sp ec i f i ca l ly , o n e mig h t d es i r e to :

T h e fo r m e r t o p i c a d d r e s s e s t h e q u e s t i o n o f p r o c e ssd e s i g n a n d w i l l n o t b e c o n s i d e r e d h e r e . As fo r t h e l a t t e r ,we wi l l g iv e an o v e r v iew o f p r ev io u s f u n d a men ta ls tu d ie s on t h o se a sp e c t s o f wh o le -ce l l imm o b i l iza t io nw h i c h a r e i m p or t a n t i n u n d e r s t a n d i n g t h e b e h a v io u r o fimmo b i l i zed ce l l ca t a ly s t s , an d p a r t i cu la r ly o n s tu d ie sf o cu s in g o n ev en t s o ccu r r in g o n a mic r o sco p ic sca le ,th a t i s , a t t h e l ev e l o f a ce l l ag g r eg a te .

-in c r ea se th e v o lu m et r i c p r o d u c t iv i ty ;-i n c r e a s e t h e p r o d u c t c o n c e n t r a t i o n i n t h e o u t l e t

s t r e a m ;-d e c r e a s e 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 i n t h e o u t l e ts t r e a m .

I mm o b i l iz in g ce l l s ma y s imp l i fy p r o cess d es ig n intwo w ay s . C o n f in emen t o f th e ce ll s t o l a r g e p a r t i c l e s o rto su r f aces fac i l it a t e s th e sep a r a t io n o f ce l ls fr o mp r o d u c t s i n so lu t i o n , a n d m a y p e r m i t t h e u s e o f


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Immobilization of whole cells I323continuous reactors while avoiding washout. It m a yalso allow reactors to contain more cells and thereforepresumably to have higher volumetric reaction rates.

In certain immobilized cell applications, however,the extent of reaction is not of primary interest indesign. For example, immobilized cells have beenconsidered for use as a hybrid artificial pancreas[4346]. Here, the objective is to mimic the dynamicsof insulin secretion by the pancreatic islet cells in ahealthy individual. In another application, immobi-lized cells have been coupled to analytical devices foruse as biosensors [35,36]. In this instance a linear andrapid response of the output signal to changes in theconcentration of the detected species is generally thedesign objective.

Immobilized cell systems may be viewed as analternative either to the use of immobilized enzymes orto free cells. Two primary considerations in the choiceof a biological catalyst are the difficulty of producingthe catalyst, and the ability to maintain the desiredactivity and specificity of the catalyst under reactionconditions. In the former case, the more difficult it is toproduce the catalyst, the longer is the lifetime requiredfor a feasible process. In general, immobilized cellsmust have a considerably longer working lifetime thanfree cells in order to be a reasonable alternative. In thelatter case, immobilized enzymes may have betterspecificity and higher activity than immobilized cells orfree cells. Reduction of the observed reaction rate d u eto mass transport limitations in substrate supply andproduct removal must be considered in all of thesecases. In considering the use of immobilized cells, wewill therefore be concerned with activity, specificity,and longevity.1.3. De $ n i t i o n o f wh o le -c e l l imm o b i li za t i o n

Whole-cell immobilization may be defined as thephysical confinement or localization of intact cells to acertain defined region of space with the preservation ofsome desired catalytic activity. This definition issimilar to those given in other reviews [47,48], which inturn are extensions of a widely accepted definitionapplied to immobilized enzymes [49]. Three issues areimplicit in this definition: the extent of the region ofconfinement, the catalytic activity and the longevity ofthe catalyst.

The first issue concerns the size of the region of spacein which the cells or enzymes are immobilized. Forexample, certain reviewers have considered cells sus-pended in bulk fluid in a cell recycle reactor to beimmobilized [l 1, 501. On the other hand, there is thequestion of how large a cell aggregate must be for thecells contained in it to be considered immobilized. Forthe purposes of this paper, this question is resolved byconsidering only those systems where cells are local-i zed wi th in a r eg io n o f sp a ce wi th in wh ich d i f fu s io n i st h e d o m i n a n t m a s s t r a n s fe r m e c h a n i s m , t h a t is , w h e r en o ap p r ec iab le con v ec t iv e mix in g t a k es p lace .

I n t h e r e m a i n d e r o f t h i s p a p e r w e w i ll r e fe r t o t h er e g i on i n w h i c h t h e c e ll s a r e l o ca l i ze d a s t h e i m -mo b i l i zed ce i l ag g r eg a t e, r eg a r d le ss o f th e me t h o d b y

which the cells are immobilized. Within the aggregatethree components can be distinguished, as shown inFig. 1. These are the cells; the support, which may be as o li d o r a g e l; a n d t h e s o l u t i on t h a t f il ls t h e r e m a i n d e rof the space i n t h e a g g r e g a t e . Th e c h e m i c a l p r o p e r t i e so f t h e s o lu t i o n i n t h e a g g r e g a t e m a y b e q u i t e d i ffe r e n tfr o m t h o s e i n t h e b u l k s ol u t i o n . Th i s p h e n o m e n o n h a sb e e n r e fe r r e d t o i n t h e l it e r a t u r e a s t h e e s t a b l is h m e n t o fa mic r o en v i r o n m en t . I n sp i t e o f th i s co mp lex s t r u c -t u r e , fo r e n g i n e e r i n g p u r p o s e s t h e a g g r e g a t e i s u s u a l lyt h o u g h t o f a s a h o m o g e n e o u s p h a s e in a s i m p l eg eo met r y ( e .g . a sp h e r e o r a th in fi lm).

T h e s e c o n d issue pertains to t h e extent of theretention of catalytic activity. A wid e v a r i e ty o fca ta ly t i c ac t iv i t i e s a r e a sso c ia t ed wi th a l i vin g ce l l . I flo ss o f v i ab i li t y acco mp a n ies immo b i l i za t io n , t h e ce l l so u g h t a t l e a s t t o r e t a i n t h e e n z ym a t i c a c t i vi t y a s -s o ci a t e d w i t h t h e d e s ir e d a p p l i c a t io n . T h e d e g r e e o fr e t e n t i o n o f e a c h p a r t i c u la r a c t iv it y n o r m a l ly p r e s e n tin f r ee ce l l s wi l l d ep e n d o n t h e immo b i l iza t io n t ech -n i q u e a n d o n t h e r e a c t i o n c on d i t i o n s . I f t h e d e s i r e dac t iv i ty consists only of a single enzymatic step, theelimination of competing activities may be advan-tageous. On the other hand, if the continued growth ofcells is desired, the bulk of the enzymatic complementshould be retained. In Table 1 a number of processes towhich immobilized cells have been applied are ar-ranged by the complexity of the reaction pathwayinvolved. The use of immobilized cells as ligands inafinity chromatography [Sl] i s a sp ec ia l ca se in w h ichn o r e t en t io n o f en zy ma t i c ac t iv i ty in th e ce l l s i sr e q u i r e d .T h e t h i r d issue implicit i n t h e d e f i n i t io n i s t h a t o fca ta ly s t s t ab i l i t y . To be u se f u l , an imm o b i l ized ce l lp r e p a r a t i o n s h o u l d h a v e a n o p e r a t i n g l i fe t i m e r a n g in g

(b )

Fig. 1. (a) The three phases that comprise many immobi-lized cell systems: cells, cell support, interstitial fluid. (b) Anengineering representation of an immobilized cell system.


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I324 STEVEN F. KAREL~~~~.Tab l e 1 . Typical biochemical p r o c e s s e s p e r f o r m e d b y i m m o b i li z e d c e l ls ( a r r a n g e d i n o r d e r o fi n c r e a s i n g e n z y m a t i c c o m p l e x it y )I so mer i za t i o n o f g l u co se t o fru c t o se [55 ]P r o d u c t i o n o f a s p a r t i c a c i d fr o m f u m a r i c a c i d [ 56 ]Tra n s fo rm at i o n o f s t e r o i d s [57 ]Ox i d a t i o n o f g l u co se t o g lu co n i c ac i d [S S]Reg en era t i o n o f ATP [59 ]F e r m e n t a t i o n o f g l u c o se t o e t h a n o l [ 5 2]

S i n g l e - s t ep ca t a l y s i s

IM u l t i p l e - s t ep ca t a l y s i sOx i d a t i o n o f ca f f e i n e [6 0]S y n t h es i s o f g l u t ami c ac i d [6 1 ]S y n t h es i s o f p r o i n su l i n [62 ]G r o w t h o n d i lu t e or g a n i c s ( w a s t e w a t e r t r e a t m e n t )C631 IGro wt h o f ce l t s

from weeks to months. Prospects for long operatinglifetimes are extremely good because viable cells willreplicate under conditions permitting growth, so thatthe catalysts can be regenerated. This regenerationby growth may be continuous [52] or periodic [53]. Itis therefore important in considering literature reportsof catalytic lifetime to consider whether ce l l g r o wthcould have been taking place during the experiment. Acomparison of catalytic lifetime between viable andnon-viable immobilized cells is valuable only in thesense of a practical assessment of processes, as theunderlying causes of deactivation in the two cases aredistinct. With immobilized non-viable cells, the factorsaffecting catalytic lifetime will be similar to those thatapply to immobilized enzymes, and which have beenexamined in some depth [54]. With viable cells, thepresence of environmental constraints that may limitthe ability of the cells to continue to grow willdetermine the useful lifetime of the system.

In Section 2 of this review, the diverse forms of cellimmobilization are classified and discussed with exam-ples. Sections 3 and 4 treat the physical and bio-chemical properties of immobilized cell preparations.The application of the mathematical theory of reactionand diffusion in permeable media as this applies to

immobilized cell systems is presented in Section 5. Thereview concludes in Section 6 with a brief overview ofimmobilized cell reactor design.2 . CLASSIFICATION OF IMMOBLLlZED CELL SYSTEMS

A multitude of whole cell immobilization methodsexist. These can be divided into four major categoriesbased on the physical mechanism causing im-mobilization:(1) attachment to a surface;(2) entrapment within a porous matrix;(3) containment behind a barrier and(4) self aggregation.

A schematic showing the different methods ofimmobilization, and their interrelationship is shown inFig. 2. Examples of the various types of immobiliz-ation are sketched in Fig. 3.2.1. C el l s a t tac he d to a su r fac e

Any immobilization method in which cells arebound to a surface, regardless of the type of binding,can be classified as a surface-attached process. Thethickness of the cell layer may range from less than amonolayer of cells to a film one millimeter or more in

F i g . 2 . I m m o b i l i za t i c n m e t h o d s a n d t h e i r c l a s s if ic a t i o n i n t e r m s o f t h e p h y s i c a l m e c h a n i s m o f lo c a l iz a t i o n .


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Imm o b i l i za t i o n o f wh o l e ce l l s I325(a) ce l ls at tached to a sur face

biof i lm suppor t

semi-permeablemembrane

(b) cell s entrap ped I,, a porous n,atr,x

F i g . 3. Th e fo u r c l as ses o f imm o b i l iza t i o n o f wh o l e ce l ls .

d e p t h . Ad s o r b e d c e ll s a r e u b i q u i t o u s i n n a t u r e (e .g .d en ta l p l aq u e ) a s we l l a s in b io tech n o lo g ica l p r o cesses .T h e a d s o r p t i o n o f m i c r o o r g a n i s m s i s a m a j o r fa c t o r i nt h e fo u l in g o f h e a t t r a n s f e r e q u i p m e n t a n d o t h e rsu r f aces [6 4] . On e o f th e ea r l i e s t immo b i l i zed ce l lp r o c e s s e s u s e d ce l ls a d s o r b e d t o w o o d c h i p s i n a p a c k e db ed r ea c to r to p r o d u ce ace t i c ac id ( v in eg a r ) [6 5] .S c h e m a t i c s o f s o m e s u r f a c e -a t t a c h e d s y s t e m s a r esh o w n in F ig . 3 (a ) .

S y s t e m s i n w h i c h c e ll s a r e i m m o b i l iz e d b y a d s o r p -t i o n a r e p o p u l a r d u e t o t h e e a s e o f t h i s t y p e o fi m m o b i li za t i o n . T h e s t r e n g t h w i t h w h i c h t h e c e ll s a r eb o n d e d t o t h e su p p o r t v a r i e s w i t h c e ll t y p e a n d s u p p o r tty p e [ 66 ,6 7] , t h u s th e sy s t em i s mo r e u se f u l f or so mec e ll s t r a i n s t h a n f or o t h e r s . As t h e r e is n o b a r r i e rb e t w e e n t h e c e ll s a n d t h e s o lu t i o n i n t h i s s y s t e m , t h i sm e t h o d c a n n o t b e u s e d w h e r e a ce l l-fr e e e fR u e n ti s d es i r ed . Th e d ep t h o f th e b io fi lm o ft en v a r i e s ,e sp ec ia l ly wi th feed f lo w r a t e an d i s n o t r ea d i lyd e te r min ed . Th u s , i t i s o f t en d i ff icu l t t o accu r a te lyco n t r o l b io f ilm p r o cesses , su ch a s th o se u sed in sewag et r e a t m e n t [S ]. E v e n w i t h t h e s e d r a w b a c k s t h i s t y p e o fi m m o b i li za t i o n h a s b e en w i d e l y e m p l o y e d i n i n d u s t r y .

T h e i n d u s t r i a l u s e o f s u r f a c e -a t t a c h e d c e ll sy s t e m s( b iof ilms) h a s b een ex ten s iv e ly ex amin ed in th e f i e ld o fwas t ewa t e r t r ea tmen t [ 32 ]. Th ese b io f ilms a r e o ft enc o m p r i s e d o f a n u n c h a r a c t e r i z e d m i x e d c u l t u r e of c el lsg r o w i n g i n a fi lm o n s a n d o r r o c k s . T h e r e i s a w e a l t h o fe n g i n e e r i n g d a t a a n d m o d e l s f o r t h e s e k i n d o f i m -

mo b i l i zed sy s t ems . Mu ch o f th i s d a t a can b e g en e r -a l i ze d a n d a p p l i e d t o m a n y o f t h e ot h e r i m m o b i li ze dc e ll s ys t e m s c u r r e n t l y u n d e r i n v e s t ig a t i on , a l t h o u g ht h e y b y n o m e a n s s o l v e o r a d d r e s s a l l t h e r e l e v a n te n g i n e e r i n g q u e s t i o n s i n t h i s f ie ld .An o t h e r t y p e of a d s o r b e d c e ll s y s t e m i s m a m m a l i a nce l l cu l tu r e . As a g en e r a l r u l e , t h e o n ly m am ma l ian ce l l st h a t d o n o t r e q u i r e a s o li d s u p p o r t fo r g r o w t h a r e s o -c a l le d t r a n s f o r m e d c e l ls w h i c h a r e of t e n t u m o r i ge n i c[ 68 ]. I n ad d i t io n , mamm al ian ce l l s co n su m e o x y g en .a n d p r o d u c e c a r b o n d i ox i d e a n d t h e c o n c e n t r a t i o n s o ft h e s e t w o g a s e s m u s t b e co n t r o l le d o v er a n a r r o w r a n g e[ 42 ]. Th e r eq u i r emen t s fo r th e th e accu r a te co n t r o l o fo x yg e n a n d c a r b o n d i ox id e c on c e n t r a t i o n s a n d t h en e e d fo r s u r fa c e a t t a c h m e n t m a k e l a r g e s c a le p r o -d u c t i o n w i t h m a m m a l i a n c e ll s d i ffi c u lt u s i n g s t a n d a r ds u b m e r g e d c u l t u r e t e c h n o l o gi e s .

T h e m a j o r i t y o f in d u s t r i a l m a m m a l i a n c e ll c u l t u r et ak es p lace in r o l le r b o t t l e s [ 68 ]. Th ese a r e semi -b a tchc u l t u r e s i n w h i c h c e l ls a d h e r e t o t h e i n s i d e o f b o t t l e sr o t a t i n g a r o u n d t h e i r a x e s o f sy m m e t r y . T h e b o t t l e sa r e ap p r o x ima t e ly o n e -th i r d f u l l o f med iu m. Th i sa l lo w s t h e c e ll s a c c e s s t o b o t h l iq u i d n u t r i e n t s a n do x yg e n fr o m t h e a ir . B e c a u s e t h e m e d i u m m u s t b ec h a n g e d p e r i o d i ca l ly t o i n t r o d u c e f r e s h n u t r i e n t s a n dd i s ca r d w a s t e p r o d u c t s , t h i s is a v e r y l a b o u r i n t e n s i v ea p p r o a c h t o l a r g e s ca l e c e ll c u l t u r e . Te c h n i q u e s w h i c ho ffe r b o t h s u r f a c e a t t a c h m e n t a n d h i g h g a s c o n t a c t i n gr a t e s h a v e b e e n r e v ie w e d [ 69 ]. O n e s u c h m e t h o d i s t h e


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i 326 STEVEN F. KAREL et al.use of microcarriers as a support for the adsorptionof cells. These are small porous beads (lOC-200 p indiameter) to which the cells adhere [70, 711. Afterinitial seeding, the cell laden microcarriers are placed ina packed bed reactor or continuous stirred tankreactor (CSTR).

Cells can be chemically bound to a surface by avariety of methods which include crosslinking byglutaraldehyde, silanization to a silica support andchelation to metal oxides [72,73). From an engineer-ing viewpoint, covalently bonded cells are similar tocells that are immobilized by adsorption. Because ofthe relative size of the cell (major axis ca. 1 p) to thecovalent bonds, the strength of the covalent bond tothe surface is similar to the strength of the hydrogenbonds or electrostatic attractions characteristic ofsimple adsorption. They will be considered as onecategory for the purposes of this review.2.2. Cells e n t r a p p ed i n a p or o u s m a t r i x

The second major category of cell immobiij~tion isentrapment within a porous matrix. Two methods ofentrapment are possible. In the first, cells are allowedto diffuse into a preformed porous matrix. After thecells begin to grow, their mobility is hindered by thepresence of other cells and the matrix and they are thuseffectively entrapped. In the second method, theporous matrix is synthesized i n s i tu around the cells tobe immobilized. Both these types of methods are fertileground for research and will be discussed in moredetail below. A schematic of this type of immobiliz-ation is shown as Fig. 3(b).

2.2.1. Pre fo rmed p o ro u s ma t r i ces . Whole cell en-trapment within a porous matrix is rapidly coming intowidespread use as an immobilization method [7]. Thecells are entrapped in a matrix which protects themfrom the shear field outside the particles. The distri-bution of microorganisms is easily measured byexamining particles removed from the reactor. As withthe adsorption method, cells are not completely sep-arated from the efAuent in these systems. A high degreeof cell viability is retained in most entrapmentmethods. These systems are therefore useful for avariety of growth-related processes.

Many types of porous matrices have been used toentrap cells. These include cordierite, bricks, kieseiguhr,volcanic rock and various types of ceramics [74-761.Messing [63] used controlled pore glass to immobilizecells for the production of methane from wasteproducts. The preformed supports have two mainadvantages over the in situ formation of matricesaround cells. First, the preformed support particles aremore resistant to the compression and disintegrationthat can occur in packed beds and stirred vessels.Second, adsorption of cells to the preformed supportscan take place under conditions which are not harmfulto the cells. A disadvantage of entrapment withinpreformed porous matrices is that the high cell volu-metric Racking densities associated with other im-mobilization methods are difficult to achieve.

The use of porous matrices with very large pores(100 p and greater) represents a form of immobiliz-ation which lies between self-flocculation and entrap-ment. These supports encourage the growth andaggregation of cells in the quiescent zones formed bythe large pores. Surface-attached cells play a minor rolein this system as a result of the small surface area forattachment. Cell growth is controlled by the continu-ous flow of fluid past the particles, since cells beyondthe boundary defined by the flow field around theparticle are swept into the eflluent [77,78].

2.2.2. Po rou s m a t r i ces fo rmed in situ. Most of thecurrent research in the general area of immobilizedcells involves porous supports that are formed aroundceeils. A variety of compounds can be gelled intohydrophilic porous matrices under conditions mildenough to allow cell entrapment with a minimal loss ofviability [79]. The polymer-cell mixture is either gelledimmediately into the final desired shape and size, orgelled in sheets and then cut into particles of the correctdimensions. The most common forms are small beads,about l-5 mm in diameter, although gels have beencast into membrane form. The gel beads can be used ascatalyst particles in a packed bed or fluidized bedreactor. Methods for gel entrapment have beenthoroughly discussed elsewhere [7,48,80].

The first demonstration of whole cell immobiliz-ation in porous gels was the use of polyacrylamide gelto immobilize the lichen Un b i l i ca r ia p u s tu ia ta [S l ] .Since then, a variety of polymer matrices have beenused to immobilize whole cells, including K-carrageenan, agar and alginate gels [7]. There aremany examples of the use of gel entrapment in theliterature, including industrial processes for the pro-duction of amino acids [ 133. Some of the immobilizingmatrices are highly hydrated, allowing almost un-hindered diffusion for low molecular weight ( < 10,000Daltons) products and substrates [SZ]. The retentionof cellular viability permits the catalyst to be used formulti-step reactions and reactions which require cofac-tors and allows growth in the gel after immobilization.It has been proposed that inoculation of gels with asmall number of cells and subsequent growth improvesthe quality of the catalyst [52]. Gel entrapment is arelatively straightforward immobilization techniqueand can be used with a variety of systems.Catalytic ultrafiltration membranes consisting of gelentrapped microorganisms have also been investigated[83---851. Membranes of different polymeric com-positions were used to entrap the thermophilic micro-organism C a ld a r ie i k z a c id o p h i ln . The use of this heatresistant culture was necessitated by the high tempera-tures encountered in the membrane casting procedure.Reactant was ultrafiltered through the 50 p thickmembranes and high activities were reported in allcases. A rapid decay in activity was noted for cellsimmobilized in a polysulfone membrane formed by aphase inversion process. The same cells demonstratedlong-range stability (> 140 h) when immobilized in aglutaraldehyde cross-linked albumin membrane.


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Immobilization of whole cells 13272.3. Cells contained behind a barrier

The third major category of cell immobilization iscontainment behind a barrier. Again, this barrier canbe preformed, or formed around the cells to beimmobilized. Schematics of this type of immobiliz-ation are shown in Fig. 3(c).This kind of cell immobilization is ideal for severalspecialized systems. When cell separation from theef8uent is required, or when some high molecularweight product needs to be separated from the effluent,these systems are highly useful [86]. These advantagesare countered by the fact that it is often difficult tosample cells immobilized behind a barrier and theuniform supply of sparingly soluble nutrients to thecell mass is often problematic [87].

The barrier which immobilizes cells can be as simpleas the liquid/liquid phase interface between twoimmiscible fluids. Mohan and Li [SS] immobilized thedenitrifying bacteria, Micrococcus denitrificans, byemulsifying the cell suspension with a surfactant intoan hydrocarbon solvent. The surfactant-enclosedaqueous droplets were then resuspended in theaqueous phase containing the substrate. The authorsreport that cells did not leak from the aqueous phasethrough the organic phase to the cell-free aqueousphase surrounding the droplets. The liquid boundarycould also be in the geometry of a planar liquidmembrane [89].

Microencapsulation has been recently applied as amethod for whole cell immobilization. This techniquewas first used in biotechnology for the immobilizationof enzymes [90]. Recently, mammalian cells have beensuccessfully grown in polylysine enclosed dropletssuspended in culture broth [86]. The semipermeablemembrane allows nutrients to diffuse to the cells, butretains the cells and some of the higher molecularweight products produced by the cells. It has beenreported that bacterial cells have been similarly im-mobilized [91]_

The growth of cells behind a preformed semi-permeable membrane is the third major area within theclassification of whole cell immobilization behind abarrier. This technique was also pioneered with theimmobilization of enzymes [92,93]. Since the cells areretained behind a semi-permeable wall or membrane,this type of system is very similar to microencapsu-lation in an engineering sense. Nutrients are suppliedto, and products are removed from, the cell mass bydiffusion. In addition, the geometry used in thesereactors could conceivably be manipulated to allownutrient supply by convection across the semi-permeable membrane. Immobilized cell systems havebeen demonstrated using microbes in both the non-growing [94] and the growing state [95-973 for avariety of microbial species and membrane types. Plantcells [98] and mammalian cells [99] have been grownin this configuration. This type of system has also beendemonstrated successfully for the large scale growth ofmammalian cells [100] and for use as an artificialpancreas [4345]. Both ultrafiltration and microfil-tration membranes have been used for this purpose.

2.4. Self-aggregating cellsCells that naturally aggregate or flocculate can also

be considered immobilized within the scope of thedefinition of immobilization presented earlier. Thelarge size of the aggregates makes their use possible inreactors designed for immobilized cells, such as packedbed reactors, fluidized beds and CSTRs. Cell typesthat belong in this category include molds whichnaturally form pellets and plant cells in culture.Artificial flocculating agents or cross-linkers may beadded to enhance the process of aggregation for cellsthat do not naturally flocculate. It has been shown thatsimilar mechanisms govern both artificially and nat-urally induced flocculation [lOI]_ Aspects of microbialflocculation have been reviewed elsewhere [33]. Thisapproach to cell immobilization is shown sche-matically in Fig. 3(d).2.5. Ethanol production using immobilized cells:an example

As a possible application of immobilized cells weconsider the production of ethanol from simple sugars.This process, carried out by yeast or certain bacteria,has been extensively studied from a technologicalpoint of view. Novel continuous processes proposedfor this fermentation include tower fermentors, ex-tractive or vacuum fermentation and cell recyclereactors [102, 1031. More recently effort has focusedon the development of continuous processes usingimmobilized living cells. This particular application is agood example of the interchangeability of immo-bilization techniques, since, as detailed in Table 2,essentially all of the techniques mentioned inSections 2.1-2.4 have been used with some success.This table lists a number of particular examples of theuse of immobilized cells for ethanol production, anexhaustive compilation of which can be found in otherreviews [104, 1051.

Future efforts need to be focused on the develop-ments of principles to guide the selection of animmobilization technique for a given application andits particular requirements. Goals in the design of acommercial ethanol fermentation often include a longoperating lifetime for the reactor, a high ethanolconcentration in the outlet stream and a high volu-metric productivity. The ability to use inexpensive bu till-defined substrates (e.g. whey) is also important. Incertain ethanol processes, subjective criteria such as thetaste of the final product are important.

The prediction of the rate of ethanol production byimmobilized cells is a difficult problem. Under the lowgrowth conditions prevalent in immobilized cell pro-cesses, the regulation of glycolysis with respect to theproduction and destruction of biomass is not wellunderstood. In addition, substrate inhibition andespecially product inhibition may have a significanteffect on both the rates of growth and ethanolproduction. Mass transfer within the reactor andwithin the immobilized cell aggregate is also likely toplay an important role in all of the proposed processes.

We therefore suggest that a fundamental description


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I 3 2 8 S TEVEN F . KAREL et al.Tab l e 2 . Immo b i l i zed ce l l s f o r e t h an o l p ro d u c t i o n

I m m o b i l i z a t i o n m e t h o d M ed i u m O r e a n i s m R e f .a d s o r p t i o n t o w o o d c h i p sa d s o r p t i o n t o i o n e x c h a n g e r e s i n sad so r p t i o n t o g las s fi b e r fi l t e r sa d s o r p t i o n t o g e la t i n -c o a t e d s u p -p o r te n t r a p m e n t i n p o ly u r e t h a n e f oa mo r i n s t a i n l e s s s t e e l m e s he n t r a p m e n t i n r c -c a r r a g e e n a nc o e n t r a p m e n t i n C a a l g in a t e w i t hm a g n e t i t ec o e n t r a p m e n t i n C a a l gi n a t e w i t hf i -D-g lucosidasee n t r a p m e n t i n p o l ya c r y l a m i d ee n t r a p m e n t i n N a a l g i n a t ee n t r a p m e n t n p ol ya c r y l a m i d e r inK - c a r r a g e e n a ne n t r a p m e n t i n p e c t inc o n t a i n m e n t b y h o l lo w f ib e r m e m -b r a n e sco n t a i n m en t o f ce l l s w i t h ce ll u l asea n d c e l l o b ia s e b y m e a n s o f a

l iq u i d -l iq u i d p h a s e b o u n d a r yf lo ccu l a t i o n o f y eas tf lo ccu l a t i o n o f y eas t w i t h a l b u -m i n /p h o s p h a t i d y l c h o l in e co m -p l ex

g l u c o s e + n u t r i e n t sg lucose + bufferg l u c o s e + n u t r i e n t sg l u c o s e + n u t r i e n t sg l u c os e + n u t r i e n t sg l u c o s e + n u t r i e n t sg l u c os e + n u t r i e n t sglucose b u f f e r +p e r i o d i c n u t r i e n t

S U P P l Yce l l o b i ose + n u t r i en t sg l u co se + sa l t sg l u c os e + n u t r i e n t si n u l i n s u g a r s+ n u t r i e n t sw h e yg l u c o se + n u t r i e n t sg l u co se + sa l t sg i u c o s e + n u t r i e n t scel lu lose

g l u c o s e + n u t r i e n t sg l u c o s e + n u t r i e n t s

S a c c h o r o m y c e sc e r e u i s i a e

S . c e r e v i s i a eZ y m o m o n a s

m o b i l i sS . c e r e u i s i n eS . c e r e v i s i a eS . u v a r u mS . c e r e v i s i a eS . c e r e u i s i a e

Z. mobi l i sS . f o r m o s e n s i sK l u v e r o m y c e s

m a r x i a n u sKI . f rag iS . c e r e v i s i a eS . ce r ev i s i aeS. c e r e v i s i a e

S c h i z o s a c c h a r o m y c e sp o m b e

S . c e r e v i s i a e

CJWCl071Cl@31CJW

C78f[::]

C l J OlC l J l lIJ 121CJ 131

CJJSICJJ61CJJ71

o f an imm o b i l ized l ivin g ce ll sy s t em i s n o t p o ss ib le wi tht h e i n fo r m a t i o n a v a i la b l e a t t h e p r e s e n t t i m e . M a n y o ft h e p h y s ic a l a n d b i o c h e m i c a l p a r a m e t e r s t h a t a r er e q u i r e d t o d e s c r i b e t h e s y st e m a r e , a t b e s t , o n ly k n o w nto wi th in an o r d e r o f mag n i tu d e . A d esc r ip t io n o f, an dm e a n s f o r e s t im a t i n g , t h e s e p a r a m e t e r s i s p r e s e n t e d i nSec t io n s 3 an d 4 .

3 . P H YS ICAL AND CHE M ICAL P R OP E RTIES OFIMMOBILIZED CELL AGGREGATES

To u n d er s t an d th e e f fec t s o f immo b i l i za t io n o n ce l ls ,o n e m u s t f ir s t u n d e r s t a n d t h e p h y s ic a l a n d c h e m i c a lp r o p e r t i e s of th e ag g r eg a te co mp o sed o f th e ce l ls an dt h e s u p p o r t . T h e d i ffu s i v e t r a n s p o r t a n d d i s t r i b u t i o no f su b s t r a t e s a n d p r o d u c t s a r e of t h e u t m o s t i m p o r t -a n c e . I n a d d i t io n , o n e r e q u i r e s a n u n d e r s t a n d i n g o f t h em e c h a n i s m b y w h i c h t h e c e ll s a r e r e t a i n e d w i t h i n t h eag g r eg a te . Th e d u r a b i l it y o f th e ag g r eg a t e w i l l d ep e n do n i t s h y d r o d y n a m i c i n t e r a c t i o n s w i t h t h e e n -v i r o n m e n t .3.1. Ef l ec t i ve d l j i i s i v i t y i n ce l l aggrega t es

T h e p h y s ic a l p r o p e r t y m o s t r e l e v a n t t o t h e s t u d y o fimm obi l ized ce l ls i s th e ef fec t ive d i f fusiv i ty of so lu tes inth e ag g r eg a te . Kn o wled g e o f th e d i f fu s iv i ty o f b o ths u b s t r a t e s a n d p r o d u c t s o f c e ll u l a r r e a c t i o n s i s r e -q u i r e d fo r t h e a c cu r a t e p r e d i c t i on o f o ve r a l l r e a c t i onr a te s . C e l l s co mp r i se so m e o f t h e d i ff u s iv e r e s i s t an ce ina lmo s t a l l immo b i l i zed ce l l sy s t em s . F ig u r e 3 sh o w s th e

co n f ig u r a t io n o f th r e e ty p es of sy s t ems d i scu ssede a r l i e r . S u b s t r a t e s m u s t d i f fu s e t h r o u g h t h e d e n s e c e l lm a s s a n d o ft e n t h r o u g h a ca t a l y s t s u p p o r t t o r e a c hin d iv id u a l ce l ls . I n f o r ma t io n co n ce r n in g th e e ff ect iv ed i f fu s iv i ty of so me ch em ica l sp ec ie s in v a r io u s su p -por ts i s ava i lab le [82 , 118, 1191. In gen er a l , th e ac-q u i s i t io n o f t h i s t y p e o f d a t a i s s t r a i g h t f or w a r d .

O n t h e o t h e r h a n d , li t t l e i s k n o w n a b o u t t h ed i f fu s iv i ty o f so lu t e s , sp ec i fi ca l ly n u t r i en t s an d f e r men -ta t io n p r o d u c t s , i n d en se ce ll ma sses . Th e v o lu mef r ac t io n o f ce l l s i n th e ag g r eg a te ( ce ll p ack in g ) ma yaf fec t t h e d i ff u s iv ity o f so lu te s in th e ce l l ma ss . Ver yl it t l e w o r k h a s b e e n d o n e t o c or r e l a t e t h e d i ffu s i v ep r o p e r t i e s o f a mic r o b ia l m ass wi th ce l l p ack in g o ro th e r ce l l p r o p e r t i e s . Measu r emen t s o f d i ff u s iv it i e s o fv a r i o u s s u b s t a n c e s i n d i f fe r e n t t y p e s o f c e l l m a s s e s a r es u m m a r i z e d i n Ta b l e 3 a n d t h e i r s i gn i fi c a n c e i s d i s -cu ssed b e lo w.I n g en e r a l , e f fec t iv e d i f fu s iv i ty measu r em en t s a r em a d e b y i m p o s i n g a k n o w n c o n c e n t r a t i o n o f a t r a c e ro n o n e b o u n d a r y o f a c e ll a g g r e g a t e , a n d m e a s u r i n ge i t h e r t h e s t e a d y -s t a t e f lu x t h r o u g h t h e a g g r e g a t e o rt h e t r a n s i e n t r a t e o f e ff u s io n i n t o o r o u t o f t h ea g g r e g a t e . I n e i t h e r c a s e a m o d e l t h a t i n c o r p o r a t e sc e r t a i n a s s u m p t i o n s a b o u t t h e d if fu s i o n p r o c e s s i sr e q u i r e d . T h e d i ff u s io n p r o c e s s i s g e n e r a l l y a s s u m e d t ob e F i ck i a n i n n a t u r e , a n d d e p e n d e n t o n l y on t h eco n cen t r a t io n g r ad ien t an d e f fec t iv e d i f fu s iv i ty o f th es u b s t r a t e i n t h e a g g r e g a t e . Co n v e c t iv e t r a n s p o r t w i t h i n


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Imm o b i l i za t i o n o f wh o l e ce l l sTab l e 3 . Va l u es of d i f fu s i v i t i e s o f - su b s t an ces i n ce l l ma sses

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the a g g r e g a t e i s a s s u m e d t o b e n e g l ig i b le . T w o e x p e r -i m e n t a l a p p r o a c h e s a r e g e n e r a l l y u s e d . I n o n e , c a r e i st a k e n t o e n s u r e t h a t c o n s u m p t i o n o f t h e t r a c e r d o e sn o t a f fe c t t h e r e s u l t s . I n th e o th e r , b o th d i ff u s iv et r a n s p o r t a n d c o n su m p t i o n o f t h e su b s t a n c e a r ec o n s id e r e d . S o m e a s s u m p t i o n s m u s t b e m a d e a b ou tt h e f or m o f t h e k i n e t i c e x p r e s s i on g o ve r n i n g t h e t r a c e rc o n s u m p t i o n . T h e s e a r e i n c o r p o r a t e d i n t o a m o d e lth a t ca l cu la t e s th e e f fec t iv e d i ff u s iv ity f r o m th e ex p e r -i m e n t a l d a t a . T h e m e t h o d t h a t c o n s i d e r s o n l y d i ff u s io ni s m o r e d e s i r a b l e , a s f e w e r a s s u m p t i o n s a r e r e q u i r e d t oc a l c u la t e t h e t r a n s p o r t p r o p e r t i e s .

3.1.1. Efec t ive d@utsiv i t y m easurem ents wh ere thetracer is no t c onsum e d . The ef fec t ive d i f fusiv i t ies of av a r i e ty of su b s ta n ces in mic r o b ia l b io fi lms i so la t edfr o m w a s t e t r e a t m e n t fa c i li t ie s h a v e b e e n s t u d i e d b ysev e r a l g r o u p s . Wi l li amso n an d McC ar ty [ 12 0]mea su r ed t h e d i f fu s iv i ty o f o x y g en a n d o f v a r io u s io n st h r o u g h a l a y e r o f N irrosom onas cells a n d d e b r i s f il t e r e do n t o a m e m b r a n e . To i n s u r e t h a t n o co n s u m p t i on o fs u b s t r a t e s oc cu r r e d d u r i n g t h e m e a s u r e m e n t s , t h ed i ffu s i v it y o f e a c h s u b s t r a t e w a s d e t e r m i n e d i n t h ea b s e n c e o f ot h e r s u b s t r a t e s n e e d e d b y t h e m i cr o b e s fo rr ea c t io n . Th e v a lu es o f th e d i f fu s iv i t e s f o r each o f th es u b s t a n c e s m e a s u r e d h a d a l a r g e s t a n d a r d d e v i a t i o n ,p r o b a b l y d u e i n p a r t t o t h e u n e v e n n e s s o f t h e b a ct e r i a lfi lm a n d t h e v a r y i n g c e l l d e n s i t i e s u s e d i n t h ee x p e r i m e n t s .

Matson and Characklis [121] measured the diffus-i v ity o f g lu co se an d o x y g en t h r o u g h a l ay e r o f was tet r e a t m e n t b i o fi lm w h i c h w a s s cr a p e d o n t o a s u p p o r t e dfi lt e r m e s h . T h e m i c r o b e s w e r e d e a c t iv a t e d b y m e r c u r i cc h l or i d e a n d u l t r a v i o le t l i gh t t o p r e v e n t c o n s u m p t i o no f t h e t r a c e r s i n t h e s ys t e m . T r a n s i e n t c o n c e n t r a t i o nm e a s u r e m e n t s w e r e m a d e t o d e t e r m i n e t h e d iff u s iv it yt h r o u g h t h e ce l l m a s s . A s im i l a r m e t h o d w a s u s e d t omea su r e th e e f fec t iv e d i ff u s iv ity o f g lu co se , o x y gen an di o n s t h r o u g h a l a y e r o f c e ll s b y O n u m a a n d O m u r a[122].

Den ta l p l aq u e , a n a tu r a l ly o ccu r r in g b io f i lm , i s am i x t u r e o f o r a l m i c r o b es a n d e x t r a c e l lu l a r p r o d u c t s .Ta tev o ss i an [ 12 3] mea su r ed th e d i f fu s iv i t i e s o f su g a r sin th i s ty p e o f mic r o b ia l ma ss u s in g a p l aq u e - fi l ledt u b e , on e e n d o f w h i c h w a s p l a c e d i n a r a d i ol a b e le dso lu t io n f or a sp ec i f ied p e r io d . Th e tu b e was sec t io n edan d each p iece was a ssay ed f o r r ad io ac t iv i ty . Th ed i ffu s i v it y t h r o u g h t h e p l a q u e w a s c a lc u l a t e d u s i n g ao n e - d imen s io n a l in f in i t e s l ab d i f fu s io n m o d e l . No n -r e a c t i v it y a p p e a r s t o h a v e b ee n a s s u m e d . T h e l a r g es t a n d a r d d e v i a t i o n i n t h e m e a s u r e m e n t s i s p r o b a b l yd u e t o t h e u n c h a r a c t e r i z e d n a t u r e o f d e n t a l p la q u e .An o t h e r m e a s u r e o f d i ffu s i v it y t h r o u g h d e n t a l p l a q u e sy ie ld ed v a lu es in th e sam e r an g e 1 12 41 . Th e p laq u e w ash ea t -k i l l ed b e f o r e b e in g p laced in a two - ce l l d i ff u s io na p p a r a t u s . R a d i ol a b e le d t r a c e r s w e r e u s e d t o m e a s u r et h e d i ffu s i v it y t h r o u g h t h e p l a q u e s . T h e r e w a s n om e a s u r e o f c e ll d e n s i t y r e p o r t e d i n t h i s s t u d y a n d n oa t t e m p t w a s m a d e t o c h a r a c t e r i ze t h e p l a q u e s .


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1330 STEVEN F . KAREL~~ al.3.1.2. Efec t ive d @iusiv i ty m easurem ents wh ere th e

t rac e r i s c onsum e d . A n u m b e r o f s t u d i e s h a v e b e e np e r f or m ed to e s t ima te t h e e f fec t iv e d i f fu s iv i ty u n d e rc o n d i t io n s w h e r e r e a c t i o n s a n d d i f fu s i o n o c cu r s i m u l -t a n e o u s l y . T h e a s s u m p t i o n s m a d e a b o u t t h e k i n e t i ce x p r e s s i on d e s c r i b in g t h e r e a c t i o n r a t e i n e a c h c a s e a r ed i s c u s s e d a lo n g w i t h t h e e x p e r i m e n t a l r e s u l t s i n t h i ssec t io n . Th e ap p l i ca t io n o f th eo r y to co mb in edr ea c t io n -d i f fu s io n wi l l b c d i scu ssed in Sec t io n 5 .

O x yg e n t r a n s f e r i s a n im p o r t a n t p r o b l e m i n t h eg r o wth o f mo ld in th e fo r m o f p e l l e t s . I n an ea r ly s tu d y ,c o n s u m p t i o n a n d d i ffu s i o n p a r a m e t e r s w e r e e s t i m a t e db y a s s u m i n g z e r o -o r d e r o x yg e n u p t a k e a n d h o m o -g en eo u s ce l l d i s t r ib u t io n in a sp h e r i ca l mo ld p e l l e t[ 12 5] . Th e ze r o -o r d e r u p tak e a ssu mp t io n w as l a t e rq u e s t i o n e d a n d t h e d a t a r e i n t e r p r e t e d a c c o r d i n g t oMo n o d -ty p e k in e t i c s [ 12 6] . I n an ex ten s io n to th i sm o d e l , t h e a g e a n d , t h e r e fo r e , r e a c t i o n r a t e o f t h e m o l dmy ce l i a was p e r mi t t ed to v a r y wi th lo ca t io n . Th ee x p e r i m e n t a l d a t a s h o w e d g o o d a g r e e m e n t w i t h t h et h r e e p a r a m e t e r r e p r e s e n t a t i o n t h a t w a s u s e d [ 1 27 1.Muel ler et al. [ 1 28 1 emp lo yed an an o x ic cen t r e mo d e lto d esc r ib e d i f fu s io n in a Zoogloea ram igera f loe . A twop a r a m e t e r m o d e l w a s u s e d w i t h t h e d a t a t o ca l c u la t eth e v a lu e s o f e ff ect iv e d i f fu s iv i ty an d th e k in e t i cc o n s t a n t . A s i m i la r p r o c e d u r e h a s b e e n u s e d t o e s -t ima t e th e e ff ect iv e d i f iu s iv i ty th r o u g h a b ac te r i a l fi lmmod eled as an inf in i t e s lab [129, 1303.

3.1.3. Ejk c t i v e d l@us iv i t y m e asure m e n t s in an im a lt issue . Measu r emen t s o f d i f fu s iv i ty of g ases in ma m-m a l i a n m u s c le h a v e a l s o b e e n m a d e . As i d e f r o m t h elack o f ce l l wa l l, ma mm al ian t i s su e i s s t r u c tu r a l lys i m i l a r t o a d e n s e b a c t e r i a l m a s s . I n a s t u d y t od e te r min e th e e f fec t iv e d i ff u s iv ity o f sev e r a l g ases in r a tmu sc le i t was d e te r min e d th a t t h e e f fec t iv e d i ff u s iv ity i ss imi l a r t o t h a t i n d en se b ac te r i a l ce l ls [ 1 31 1. Oth e ri n v e s t ig a t i o n s h a v e b e e n p e r f or m e d t o m e a s u r e t h er a t e o f d ex t r a n , flu o r esce in , o x y gen an d g lu co se d i ff u -s io n in n o r ma l an d tu m o r t i s su e [1 31 --1 33 1, an d th er a t e o f o x yg en d i f fu s io n in sa l am an d er mu sc le [ 13 4] .

3.1.4. Sou rces o f d@iisive resistan ce in ce l l ag-gregates. Al t h o u g h m a n y s t u d i e s h a v e b e e n c on d u c t e dt o d e t e r m i n e t h e d i ff u s iv i t y o f v a r i o u s s u b s t a n c e st h r o u g h c e ll m a s s e s , v e r y li t t l e i s u n d e r s t o o d a b o u t t h eso u r ce o f th e d i f fu s iv e r e s i s t an ces . I t h as b een ac -k n o wled g ed [ 12 1] th a t t h e ty p e of ce ll an d th es t r u c t u r e o f t h e c c l1 m a s s m i g h t h a v e a n i m p a c t o n t h ed i ffu s i v it y , b u t a fu n d a m e n t a l u n d e r s t a n d i n g o f t h i sp r o b l e m h a s n o t ye t b e e n a c h i e ve d . An o t h e r p a r a m e t e ra f fec t in g th e d i ff u s iv e r e s i s t an ce in a ce l l ma ss i s t h ep r o d u c t i o n a n d e x c r e t io n o f e x t r a c e l lu l a r . s u b s t a n c e s .Man y ce l ls p r o d u ce ex t r a ce l lu l a r p o ly sacch a r id es ,s o m e o f w h i c h ca n a c t t o p r o m o t e t h e co h e s i on o f ab i o fi h n . Th e s e s u b s t a n c e s m i g h t b e i m p o r t a n t d e -t e r m i n a n t s o f t h e d i ff u s iv e r e s i st a n c e i n t h e s e fi lm s .T h e d e n s i t y of t h e c e ll m a s s w a s m e a s u r e d i n s om e o fth e s tu d ies me nt ioned above [120 , 121 , 1291, bu t th e

o n ly co r r e l a t io n o f d en s i ty wi th d i f fu s iv e r e s i s t an ce in ac e ll m a s s i s p r e s e n t e d b y Y a n o e t a l . [125] . This sh owsa w e a k i n c r e a s e of d i ffu s i v e r e s i s t a n c e w i t h i n c r e a s i n gce l l d en s i ty . Th e d a ta o f Wi l li amso n an d McC ar ty[ 12 0] r ev ea led n o cor r e l a t io n b e tw een d r y ce l l we ig h tan d d i f fu s iv i ty . Al th o u g h Matso n an d C h ar ack l i s[ 12 1] mea su r ed th e d r y we ig h t o f th e ce l l s i n eache x p e r i m e n t , n o c o r r e l a t io n b e t w e e n t h i s a n d d i ffu s i v it yw a s r e p o r t e d . I n o n e o f t h e d e n t a l p l a q u e s t u d i e s ,p l aq u es o f v a r y in g ce l l d en s i t i e s wer e u sed . Hig h e rd i ffu s i v e r e s i s t a n c e s w e r e m e a s u r e d i n t h e d e n s e rp l a q u e s . U n f or t u n a t e l y , t h e d e n s i t y d a t a w e r e p r e -s e n t e d i n t e r m s o f c e n t r i f u g a t io n s p e e d u s e d t o s e p -a r a t e t h e p la q u e f r o m t h e p l a q u e f lu i d ( t h e p a c k i n gd e n s i t y o f t h e c e ll s in t h e s a m p l e i n c r e a s e s w i t hi n c r e a s i n g c c n t r i fu g a t i o n s p e e d ) a n d n o t d e n s i t y o r d r ycel l weight [123] .U s in g a d i ff er e n t a p p r o a c h , M a t s u n a g a e t a l . [135]m e a s u r e d t h e d i ffu s i v e r e s i st a n c e i n a m e m b r a n eco n s i s t in g o f g e l - en t r ap p ed C los t r id ium bu ty r i c um a tv a r io u s mic r o b ia l v o lu met r i c p ack in g d en s i t i e s . Th eyfo u n d t h a t t h e d i ff u s iv i t y o f gl u c o se t h r o u g h t h ec o m p o s it e m e m b r a n e d e c r e a s e d w i t h i n c r e a s i n g c e llp ack in g . Th e d i f fu s iv i ty o f h y d r o g en th r o u g h a d en se lyp ack e d ce ll /g e l memb r a n e w as ab o u t two - th i r d s o f i t sv a l u e t h r o u g h t h e em p t y g e l.

K le i n a n d S c h a r a [ 13 6] h a v e m e a s u r e d t h e d if fu s -iv ity o f p h en o l in p o ly ac r y lamid e d i sc s co n ta in in ge n t r a p p e d c e ll s o v er a r a n g e o f p o l ym e r v o lu m ef r ac t io n s an d ce l l l o ad in g s . Th ey su g g es ted a n em-p i r i ca l co r r e l a t io n o f th e fo r m :

~ = (1 -vv,)Zexp (-qv ,)a *wh er e 2 i s t h e e f fec t iv e d i ff u s iv ity o f th e t r a ce r , B *i s th e d i ff u s iv ity o f th e t r a ce r in f r ee solu t io n , v X i s th ev o lu me f r ac t io n o f ce l l s , v p i s t h e v o lu me f r ac t io n o f th ep o l y m e r a n d q i s a p a r a m e t e r c h a r a c t e r i zi n gth e mo lecu la r s i ze o f th e t r ace r . Fo r sma l l mo lecu le s ,t h e p a r a m e t e r q was a ssu m ed to b e eq u a l to 4. Kle ina n d M a n e c k e [ 11 8] l a t e r p r o p o s e d a n a l t e r n a t e e x-p r ess io n o f th e f or m :

- = exp ( - q(v, + up)).9*A th eo r e t i ca l mo d e l d esc r ib in g o x y g en t r an sp o r t i nt i s s u e s a s t r a n s p o r t t h o u g h a h e t e r o g e n e o u s m a t e r i a lh a s b een p r o p o sed b y Ta i an d C h a n g [ 13 7] .

I n f o r ma t io n to co r r e l a t e d i f fu s iv e r e s i s t a n ces wi thc e ll p a c k i n g a n d m i c r o o r g a n i s m t y p e i s n e c e s s a r y t oa l lo w p r ed ic t io n o f th e d i f fu s iv i ty o f su b s tan ces(s p e c if ic a l ly p r o & c t s a n d s u b s t r a t e s ) t h r o u g h t h ed en se ce l l ma sses fo u n d in immo b i l ized wh o le -ce l lr ea c to r s . Th e e f fec t of ex t r a ce l lu l a r p r o d u c t s o n t h ee f fec t iv e d i ff u s iv ity in a ce l l ma ss a l so n eed s t o b ein v es t ig a ted .3.2. In t e rac t ions am ong c om pone n t s in the aggre ga teAm o n g t h e ot h e r p h y s i c a l o r c h e m i c a l i n fl u -en ces ac t in g o n immo b i l i zed ce l l s, we a r e e sp ec ia l lyi n t e r e s t e d i n t h o s e r e s p o n s i b l e f or t h e i m m o b i li za t i o n .


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Imm o b i l iza t i o n o f wh o l e cel ls 1331I n t h e c a s e of e n t r a p p e d o r c on t a i n e d c e ll s , t h e i m p e t u sf or imm o b i li za t io n i s a r e s t r i c t io n o f th e mo b i l i ty o ft h e ce l ls w it h i n t h e p o r o u s m a t r i x o r a c r o s s t h ec o n fi n i n g b a r r i e r . I n c a s e s w h e r e c e ll s a r e a t t a c h e d t o asu r f ace o r to each o th e r , t h e immo b i l i z in g f or ce i s ap h y s ica l o r ch em ica l in t e r a c t io n amo n g ce l ls o r b e -t w e e n t h e ce l ls a n d t h e s u p p o r t .

3.2.1. Cell mobility within the aggregate. T h e d e g r e eto wh ich th e r e s t r i c t io n o f ce l l mo b i l i ty in th e ag g r eg a t ei s d e s i r a b l e d e p e n d s o n t h e p a r t i c u l a r p r o c e s s . Wi t hn o n -v iab le ce l l s , t h e ma jo r p r o b lem ma y b e th e l eak ag eo f d es i r ed en zy m es fr o m th e immo b i l i z in g ma te r i a l ; i ti s t h e r e f o r e u s e fu l t o m a k e t h e c on f in e m e n t b a r r i e ri m p e r m e a b l e t o h i g h m o l e cu l a r w e i g h t sp e c i e s. O n t h eo th e r h a n d , if l i vin g imm o b i l ized ce l l s a r e u sed , ag r ea t e r d eg r ee o f mo b i l i ty m ay b e d es i r ed to a l lo ww a s t e p r o d u c t s a n d d e a d c e l l s t o b e r e m o v e d fr o m t h eag g r eg a t e a s th e ce l ls g r o w. A s t ead y -s t a t e ma y th u s b ea c h i e v e d i n w h i c h t h e r a t e of s y n t h e s i s o f n e w c e l l u la rma te r i a l i s b a lan ced b y th e r a t e o f lo ss o f ce l l ma te r i a li n t h e e ff lu e n t o f a co n t i n u o u s r e a c t o r . I n t h i s s e n s e , t h er o le o f immo b i l i za t io n i s t o in c r ease th e ce ll h o ld -u p ina co n t i n u o u s r e a c t o r a s c o m p a r e d t o a c a s e w h e r e fr e ecel ls are used [25] .A n u m b e r , o f d i ffe r e n t m e c h a n i s m s m e d i a t e c e l lt r a n s p o r t w i t h i n t h e a g g r e g a t e . C e ll s m a y d i f fu s ep ass iv e ly a s a r e su l t o f B r o wn ian mo t io n . I n ad d i t io n ,ce r t a in st r a in s ex h ib i t mo t i l i t y an d ch emo ta x i s [ 13 9] .T h e v o lu m e e x p a n s i on c a u s e d b y t h e s yn t h e s i s o f n e wce l l ma te r i a l i s i t se l f a f or m o f t r an sp o r t . Th e l a r g e s i zean d co n seq u en t lo w d i ff u s io n co e f fi c i en t o f th e ce l l sm a k e t h e p r e s e n c e of e v e n a s m a l l d e g r e e o f c o n v ec t i onwi th in th e ag g r eg a te a s ig n i fi can t f ac to r in f ac i li t a t in gt h e t r a n s p o r t o f c e l l s .Ve r y l it t l e h a s b e e n d o n e t o d i r e c t l y m e a s u r e t h emo b i l i ty o f ce l l s u n d e r an y o f th e co n d i t io n s ty p ica l o fimm obi l ized ce l ls . In t he case of b iofi lms, i t i s o f tena s s u m e d t h a t a s t e a d y -s t a t e i s a c h i e v e d w i t h a s p a t i a l lyun iform pop ula t ion of ce l ls [14O, 1411. In th is s tea dy-s t a t e , t h e g r o w t h r a t e o f t h e c e ll s i s m a t c h e d b y t h ec o m b i n e d r a t e s o f c e ll d e a t h a n d t h e p h y s i c a l r e m o v a lo f ce l l s. Th e r e l a t iv e imp o r tan ce o f th ese two r a t e s ma yv ar y fr o m sy s tem to sy s t em [ 14 2, 1 43 1. Th e t r a n sp o r to f ce l ls a l so o ccu r s a s a r e su l t o f s lo u g h in g , th eo ccas io n a l d e ta ch m en t o f la r g e sec t io n s o f th e b io fi lm .S lo u g h i n g i s t h o u g h t i n s o m e i n s t a n c e s t o b e a r e s u l t o ft h e fo r m a t i o n o f a n a n a e r o b i c o r o t h e r w i s e n u t r i e n t -l im i t e d z o n e w i t h i n t h e f il m ow i n g t o m a s s t r a n s f e rl imi t a t io n s . Th e fo r m a t io n o f b u b b les d u e to an ae r o b icme t ab o l i sm ma y a l so lead to s lo u g h in g [ S]. Th e f ac tt h a t t h e r e is l it t l e r e s is t a n c e t o e xp a n s i on a n d c o n t r a c -t io n o f th e fi lm a l so h e lp s to p r o v id e an ev en d i s t r i -b u t io n o f ce ll s wi th in th e f ilm .O n e i n d i r e c t m e t h o d o f a s s e s s i n g t h e d e g r e e o fimmo b i l i ty o f imm o b i l ized ce l l s i s t o ex amin e th ep a t t e r n o f g r o w t h u n d e r d i ffu s i o n a l l im i t a t i o n s . I f t h ec e ll s a p p e a r t o f or m a u n i f or m l a y e r , t h e n t h e r a t e a tw h i c h c e l ls m o v e a b o u t w i t h i n t h e a gg r e g a t e i s r e l a -t iv e ly r a p id ; o n t h e o th e r h a n d , i f t h e ce l l s a r e l e ssmobi le , a d e n s e l a y e r of c e l ls m a y f o r m n e a r t h e

n u t r i en t so u r ce . On e ex amp le o f th i s e f fec t o b se r v ed int h e a b s e n c e o f a n y p h y s i ca l s u p p o r t i s t h e fo r m a t i o n o fm y c e li a l p e l le t s w it h h o l l ow c o r e s s u r r o u n d e d b y ad en se lay e r o f gr o win g ce l l s u n d e r co n d i t io n s o fd if fusion- l imi t ed grow th [34 , 1441. The grow th of ce l lsi n la r g e n u m b e r s i n a t h i n l a y e r n e a r t h e s u r fa c e o f t h eg e l wh i l e th e in t e r io r co n ta in s v e r y few ce l ls a l so a t t e s t sto th e r e l a t iv e immo b i l i ty o f ce l ls i n g e l p a r t i c le s [ 1 45 ].

I n g e ls co n ta in in g l ivin g mic r o b es , t h e mo s t imp o r t -an t a sp ec t o f m o b i li ty i s t h e r a t e o f ce l l e f fu s io n f r o mt h e ge l . A n u m b e r o f i n v e s t ig a t o r s h a v e r e p o r t e d t h er a t e o f a p p e a r a n c e o f ce l ls i n t h e m e d i u m i n e xp e r -ime nt s using gel-en tr ap ped cel ls [52 , 113, 1461. Ther a t e o f l e a k a g e g e n e r a l ly is a s s o c ia t e d w i t h t h e g r o w t ho f th e o r g an i sms . I t can b e r ed u ced s ig n i fi can t ly e i th e rb y s lo win g th e g r o wth r a t e o f th e or g an i sm [ 10 8, 1 47 1o r b y a l t e r in g t h e ge l a t i on p r o c e d u r e t o e n g e n d e r at ig h te r ma t r ix [ 1 46 , 1 48 1. Th e a p p ea r a n ce o f mic r o -in te r s t i ce s o n t h e su r f ace o f a ge l p a r t i c l e ma y in d ica t eth a t ce ll d iv i s io n ex p an d s an d f r ac tu r e s th e g e l [ 14 9] .Ex p an s io n o f th e ce l l-co n ta in in g p o ck e t s in th e g e l s h a salso b een obser ved [ 150, 1513. Since ce l l leaka ge isa s s o ci a t e d w i t h g r o w t h , i t p r o b a b ly i s n o t a m a j o rcau se o f d eac t iv a t io n o f th e ca ta ly st . Th e g r o wth o fce l ls ex te r io r t o g e l s ma y , h o wev er , l ead to o b s t r u c t io nof flow wit h in th e rea ctor [96 , 108, 1523.

I n p r e fo r m e d p o r o u s m a t r i c es , m o b i li t y i s i m p o r t a n ti n a l lo w i n g t h e s u p p o r t t o b e i n o c u la t e d a s w e ll a sp r e v e n t i n g l e a k a g e a ft e r i n o c u l a t i on . M e s si n g a n d c o -wo r k e r s [ 15 3, 1 54 1 h a v e ex amin ed th e e ff ec t o f p o r es i ze o n ce l l immo b i l i za t io n u s in g co n t r o l led p o r e g la ss .T h e o p t i m a l p o r e s i z e i s d e t e r m i n e d b y a b a la n c eb e t w e e n t w o e f fe c t s : t h e p o r e s m u s t b e l a r g e e n o u g h t oa l lo w p e n e t r a t i o n a n d g r o w t h o f c e l ls w it h i n t h em a t r i x, ye t t h e y m u s t b e s m a l l e n o u g h t o h i n d e rl eak ag e o f th e g r o win g ce l ls . Th e o p t ima l p o r e s i ze f orb a c t e r i a or y e a s t w a s d e t e r m i n e d t o b e b e t w e e n o n e t of ou r t imes th e ma jo r d imen s io n o f th e ce l l s. Wh enm y c e li a l o r g a n i s m s w e r e g r o w n a ft e r e n t r a p m e n t o fs p o r e s , t h e o p t im a l s i ze r a n g e w a s s o m e w h a t l a r g e r .T h i s d o e s n o t p r e c lu d e t h e u s e o f p o r o u s m a t e r i a l s w i t ha l a r g e r p o r e s i z e , w h i c h h a s b e e n s h o w n t o b e u s e fu l i ncer t a in s i tua t ion s [78 , 1551 .S y s t e m s u s i n g p r e f o r m e d m e m b r a n e s fo r c e ll e n -t r a p m en t o f fe r t h e p o ss ib i l it y o f ob ta in in g a s t e r i l ep r o d u c t s t r e a m f r o m a n i m m o b i li ze d c e ll r e a c t o r b ye n s u r i n g t h a t a b s o lu t e l y n o c e ll s c r o s s t h e co n f in i n gm e m b r a n e . G r o w i n g c e ll s h a v e , h o w e v e r , s h o w n a na m a z in g a b i li t y t o p e n e t r a t e m e m b r a n e s w i t h p o r es i ze s s m a l le r t h a n t h e c e ll s . T h e u l t r a t h i n r e t e n t i v e w a l lc h a r a c t e r i s t ic o f c e r t a i n a s y m m e t r i c h o l lo w fi b e r u lt r a -fi lt r a t i o n m e m b r a n e s a p p a r e n t l y d o e s n o t h a v e t h em e c h a n i c a l s t a b i l it y t o r e s i st t h e p r e s s u r e o f g r o w i n gce l ls [ 96 ]. Th e s t r e ss cau sed b y ce ll g r o wth ma y in d u cef is su r es in th e memb r an e , a l lo win g ce l l s t o p r o l if e r a t et h r o u g h o u t t h e r e a c t o r . O t h e r i n v e s t ig a t o r s h a v e a ls on o t i c ed t h a t g r o w i n g c e l l s c a n p e n e t r a t e a n d e v e n t u a l lyp a s s t h r o u g h m e m b r a n e s w i t h p or e s t r u c t u r e s s i gn i fi -can t ly sma l le r t h a n th e ce il s t h emse lv es [ 1 X%1 58 ]. Th em e c h a n i s m f or t h i s p a s s a g e i s u n c l e a r . I n o u r o w nex p er i en ce , so me ty p es o f h o l lo w mic r o p o r o u s i so -


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1332 STEVEN F. KAREL~I al.tropic fibers can prevent cell breakthrough, althoughthe membrane may collapse under the concertedpressure of cell growth around the fiber.

3.2.2. Chemical interactions between the support anathe solution. The chemical properties of the phase inwhich the cells are immobilized may exert a directeffect on the reactivity by changing the solubilities ofsubstrates and products in the local environment.Indirect effects arise from changes in the enzymaticproperties of the cell as a result of the changedenvironment. It has been argued that the high polymerconcentrations found in gels can alter the activities ofmetabolic pathways by depressing the water activity[163]. In this regard one may note that biofilms canhave high concentrations of extracellular polymers,especially under conditions of carbon excess [29].

The effects of gel composition have been quantifiedin terms of a partition coefficient relating the concen-trations in the aggregate and in the bulk of a givenchemical species. Many substrates are relatively in-soluble in water, so that organic solvents have beenused to increase the substrate concentration in im-mobilized cell processes [159,160]. The work of Fukuiand his associates [160, 1611 on the bioconversion ofsteroids by cells immobilized in hydrophobic gelsdemonstrates the importance of understanding par-titioning effects. Polymer mixtures were used to formgels having a range of chemical properties. The analysisof such systems is complicated by the possible toxicityof the organic solvents, and by the fact that the cellsthemselves may affect the partitioning behaviour oforganic substrates [162].

3.2.3. Direct interactions between the cells and thesupport. An examination of the wide variety of sur-faces onto which cells adhere suggests that no singlemechanism can be responsible for all the effectsreported. Attachment is observed on surfaces havinghigh surface free energies such as glasses or clays aswell as on low energy surfaces such as polyethylene orwood. The accumulation of cells at liquid-liquid or atgas-liquid interfaces has been exploited as the basis forseparation processes [164-l 663.

The colonization of surfaces by cells may be as-sociated with an ecological advantage Cl673 due toadsorption of nutrients or to the microbial degra-dation of the support to provide nutrients for growth[168-1701. Even artificial supports such as PVC maybe degraded [171].Either hydrophobic or ionic interactions can causecell adsorption. Attempts have been made to build atheoretical framework in both cases. Hydrophobicinteractions have been quantified by measurements ofcontact angle [172] and of the liquid-liquid partition-ing properties of the cells [173]. Theories have beenproposed to treat cells as macroscopic ions to explainbinding of cells to charged surfaces [67, 174, 1751. Theadsorption of proteins and other organic material onsurfaces prior to cell attachment and the possibilitythat cells produce extracellular or membrane polymers

which enhance adhension cast doubt on the universalapplicability of these theoretical approaches. Manyexperiments suggest that cell adhesion is a two-stepprocess consisting of a reversible weak binding fol-lowed by a time-dependent irreversible attachmentwhich may be due to the synthesis of extracellularpolymers [29, 1761.

The growth of animal cells in culture represents anextreme case of the sensitivity of cells to the chemicalnature of the support. Levine and co-workers Cl773found that both adhesion and growth of animal cellson DEAE-dextran microcarriers were strongly de-pendent on the surface charge of the support. Theability to alter the strength of adhesion by manipulat-ing the calcium concentration in the medium has beenused to facilitate bead-to-bead transfer of cells [178]. Anumber of investigators are continuing to examine theeffects of different surface chemistries on the growth ofanimal cells, including collagen [ 1791, glass [ 1801 andderivatized polyacrylamides [ 181, 1821. The role ofspecific cell surface glycoproteins such as fibronectinsin the adhesion of animal cells has been considered insome depth [183].3.3. Physical interactions of the aggregate with theenvironment

In reactors using immobilized cells, a certainamount of fluid motion is required to enhance massand heat transfer within the reactor. Hydrodynamicinteractions between the particles and the environmentfall into three categories: (1) structural changes in theaggregate caused by hydrodynamic shear stresses andby inter-particle collisions; (2) changes in the flowpattern and mixing of fluid and particles within areactor and (3) enhancement of mass transfer ofsolutes and/or cells to and from the aggregate byincreasing the relative fluid velocity at the surface. Thestructural effects include abrasion and compression ofsupport particles, which may have detrimental effectson the stability of the reactor. Detachment ofadsorbedcells by shear stress or by interparticle collisions maybe detrimental or advantageous, depending on theparticular process.The shape and size of immobilized cell particles orfilms is of central importance in modeling hydro-dynamic interactions. Nevertheless, even these simpleparameters are not always easily characterized. Bothcell growth and physical interactions can change thesize of the particles. Many gels and ion-exchange resinsswell or shrink with varying solute concentrations.Physical processes leading to the breakdown of theimmobilized cell aggregate have been examined pri-marily in particulate systems and then mostly with gelparticles. Specifically, attention has been focused onthe compression of particles in packed columns, andon the abrasion of particles in agitated systems [22,23,1841. It has been observed that the mechanical prop-erties of the aggregate deteriorate at very high ag-gregate cell concentrations [22, 1481. In a number ofcases the treatment of gel particles with cross-linkingagents such as dialdehydes or diamines results in an


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Imm obi l iza t ion of wh ole ce l ls I333a g g r e g a t e w i t h i m p r o v e d m e c h a n i c a l p r o p e r t i e s E S ,185, 1863.

I n c e r t a i n c a s e s t h e c o n fi n e m e n t o f ce l ls t o l a r g ep a r t i c le s m a y e n h a n c e t h e ov e r a l l r a t e o f m a s s t r a n s f e r .T h e f o r m a t i o n o f m y ce l ia l p e l le t s r a t h e r t h a n t h e m o r eo p e n h y p h a l s t r u c t u r e u s u a l ly a s s o ci a t e d w i t h m y c e li a lg r o w t h d r a m a t i c a l ly r e d u c e s t h e s o lu t i o n v is c os i t y,t h u s fa c i li t a t i n g a g it a t i o n a n d g a s -l iq u i d m a s s t r a n s fe r1 18 71 . Fo r m y ce li a imm o b i li zed wi th in p o r o u s b ea d s ,Gb ewo n y o an d Wan g [ 18 8] f o u n d th a t t h e l imi t a t io nt o oxygen t r a n s fe r im p o s e d b y i n t e r n a l m a s s t r a n s fe rr e s i s t a n c e w it h i n t h e b e a d s w a s l e s s s e v e r e t h a n t h el im i t a t i o n t o o x yg e n t r a n s fe r c r e a t e d b y t h e i n c r e a s e dv i scos i ty o f t h e f r ee ce l ls i n so lu t io n .

H y d r o d y n a m i c e ffe c t s on t h e c e ll s a t t h e s u r f a c ed ep e n d o n th e v e loc i ty f ie ld ex te r io r t o th e ag g r eg a te .F o r s u s p e n d e d p a r t i c le s , t h e r e l a t iv e v e lo c it y d e p e n d sc r i t i ca l ly o n th e d en s i ty d i ff e r en ce b e tw een th e ag -g r e g a t e a n d t h e s u s p e n d i n g s o lu t i o n . T h u s , t h e p r e d i c -t io n o f ex te r n a l ma ss t r a n s f e r co e ff ic i en t s f o r im-mob i l ized ce i l pa r t ic les i s d i f f icu l t [ 1891 . Oth er pr op-e r t i e s d e p e n d i n g o n b u o y a n c y s u c h a s fl u i d iz a t i onc r i t e r i a a r e a l so a f fec ted [ 19 0] .

Th e v e loc i ty f ie ld n ea r a su r f ace is a l so th o u g h t toh a v e a n e ffe c t o n t h e t r a n s p o r t o f c e ll s t o a n d fr o m t h es u r f a c e . A n u m b e r o f e xp e r i m e n t a l s t u d i e s h a v e b e e np e r f or m ed to in v es t ig a te th e e f fec t s of su r f ace sh ea rs t r e s s o n t h e o v er a l l r a t e o f a d s o r p t i o n a n d d e s o r p t i o nw i t h c l e a n s u r f a c e s , b u t n o c l e a r t r e n d h a s e m e r g e d[143, 191-1933.

A c o m p l e t e k n o w l e d g e o f t h e p h y s i ca l a n d c h e m i c a lp r o p e r t i e s o f immo b i l ized ce l l ag g r eg a t e s , ev en if i twer e av a i l ab le , wo u ld s t i l l b e in su f fi c i en t fo r anu n d e r s t an d in g o f th e i r b eh av io u r , s in ce ce l l p h y s io lo g ym u s t c e r t a i n l y b e c o n s id e r e d . T h e b i o c h e m i ca l p r o p -e r t i e s o f t h e c e ll s a r e d e t e r m i n e d n o t o n l y b y t h ein t r in s i c a t t r ib u te s o f th e ce l l s t h emse lv es , b u t a l so b yt h e e n v ir o n m e n t i n t h e a g g r e ga t e , w h i c h i n t u r nd e p e n d s o n p h y s i ca l p r o c e s s e s in t h e a g gr e g a t e . I n t h ef ol lo win g sec t io n , we wi l l co n s id e r th e cu r r en t s t a t e ofr e sea r ch co n ce r n in g th e b io lo g ica l p r o p e r t i e s o fce l l s i nt h e i m m o b i h z e d s t a t e .

4. BIOLOGICAL PROPERTIES OF IMMOBILIZEDCELLS

T h e r e a r e m a n y e x a m p l e s i n t h e li t e r a t u r e s h o w i n gt h a t c e ll u l a r p h y s i o lo g y a n d m o r p h o l o gy s o m e t i m e sc h a n g e u p o n i m m o b i li za t i o n . T h e r e a r e a n u m b e r o fp o ss ib le r easo n s f or th i s . Th e imm o b i li za t io n p r o -ced u r e can a l t e r t h e me ta b o l ic ac t iv i ty or v i ab i li t y o ft h e c e l ls . As m e n t i o n e d e a r l i e r , t h e m i c r o e n v ir o n m e n ti s o ft e n d i ffe r e n t t h a n t h a t o f c e l ls i n a s u s p e n s i o nc u l t u r e . I n a d d i t i on , t h e p h y s ic a l s t r e s s e s t h a t c l o se l yp a c k e d g r o w i n g c e l ls e x e r t o n o n e a n o t h e r a n d o n t h es u p p o r t a r e n o t p r e s e n t i n t r a d i t io n a l f e r m e n t a t i o n s .Th ese p r o p e r t i e s o f immo b i l i za t io n o ft en a f f ec t t h ece l l s i n a va r i e ty o f way s wh ich wi l l b e d i scu ssed b e lo w.4.1. Cell morphology

T h e m o s t o b v io u s d i ff er e n c e b e t w e e n a n i m m o b i l -i ze d c e ll c u lt u r e a n d a s u s p e n s i o n c u l t u r e i s t h e f r a c t i on

o f to t a l v olu me o ccu p ied b y ce i l s . Th e v o lu met r i cf r ac t io n o f ce l ls i n co n v en t io n a l su sp en s io n cu l tu r e sv a r i e s b e twee n 1 an d 3 0 % [1 94 ]. Me th o d s to in c r easec e ll d e n s i t y i n s u s p e n s i o n c u l t u r e s s u c h a s va c u u mf er m e n t a t i o n t o s e le c t i ve l y r e m o v e g r o w t h i n h i b i t or sa n d c e ll r e cy c le s y s t e m s h a v e b e e n s u c c e s s fu l l y u s e d t oin c r ea se th i s f r ac t io n t o a s mu ch a s 60 7;. Th e ce l lp ack in g d en s i ty in so me imm o b i li zed ce l l r ea c to r s ,h o wev er , ap p r o ach es 1 00 /, o f th e av a i l ab le v o lu m eC961.T h e r e a r e s e v e r a l e x a m p l e s i n t h e l it e r a t u r e w h e r ee l e ct r o n m i c r o s c op y h a s b e e n u s e d t o e x a m i n e t h ee f fec t s o f th e c lose ce l l p ack in g ch a r ac te r i s t i c o f so mei m m o b i li za t i o n p r o c e d u r e s . Sc a n n i n g e l e ct r o n m i c r o -g r a p h s o f c e l ls i s ol a t e d f r o m r a w s e w a g e a d s o r b e d t oa l u m i n a a n d c o r d i er i t e s h o w n i n F i g. 4 i l lu s t r a t e t h eh i g h c e ll p a c k in g t h a t c a n b e a c h i e v e d w i t h t h i s t yp e o fimmo b i l i za t io n [ 63 ]. Th e h ig h v o lu m et r i c fr a c t io n ofP s e t u f o m u n a sce l ls immo b i l i zed o n a Mi ll ip o r e f il t e r a sw e l l a s s o m e o f t h e r e t a i n e d e x t r a c e ll u l a r p r o d u c t ssu r r o u n d in g th e ce l ls [2 9] i s sh o w n in F ig . 5 . Scan n in ge l e ct r o n m i c r o s c op y h a s b e e n u s e d t o d i s t i n g u i s h t h ed i f fe r en t b io fi lm mo r p h o lo g ie s cau sed b y d i st in c to r g an i sms in mix ed cu l tu r e s [ 1 95 , 1 9 61 .T r a n s m i s s io n e l ec t r o n m i cr o g r a p h s o f E. coli a n dS. ce r ev i s i ae g r o wn a r o u n d a sy mm et r i c h o l lo w f ib e rmem b r a n es a r e sh o w n in F ig s 6 an d 7 18 7, 96 1. F i s s io nan d b u d d in g , each in d ica t iv e o f ce llu l a r v i ab i li t y , canb e s e e n i n b ot h m i c r o g r a p h s . T h e m i c r o b e s a r e d i s -t o r t e d b y t h e p r e s s u r e o f t h e s u r r o u n d i n g o r g a n i s m s ,e sp ec ia l ly in th e case o f th e in d iv id u a l y eas t ce l ls .S imi la r d e f or m a t io n o f ce l l s wa s a l so r ep o r t ed [ 19 7]fo r g r o w i n g y e a s t c e ll s e n t r a p p e d i n a p o l yc r y la m i d eg e l . La r e t t a - Gar d e [ 19 8] r ep o r t ed th a t g r o win gRhodopse udom onas c apsu la ta ce l l s ex e r t ed su f f ic i en tp r e s s u r e t o i n d u c e d e fo r m a t i on o f t h e su r r o u n d i n gca lc iu m a lg in a te g e l .4.2. Cell physiology

T h e f u n d a m e n t a l a s s u m p t i o n u s u a l ly m a d e i n m o d -e l in g th e b eh a v io u r o f imm o b i l ized ce l l s i s t h a t t h ec e ll u l a r m e t a b o li s m d e p e n d s o n l y o n t h e m i c r o en -v i r o n m e n t . T h i s a s s u m p t i o n c a n n o t b e c o r r e c t fo r t h ecase o f ma mm al ian ce l ls , ma n y o f wh ich ab so lu te lyr e q u i r e s u r f a c e a t t a c h m e n t fo r g r o w t h ; t h e r e fo r e ,p h y s i c a l i n t e r a c t i o n s a t t h e ce l l s u r f a c e in som e w a yr eg u la t e th e me ta b o l i sm o f th e ce l ls . A n u

cell immobil

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