Diffusion limitation — friend or foe?

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Nocardiae (Goodfellow, M. and Brownell, G.H., eds), pp. 337-367, Academic Press Goodfellow, M. (1971)J. Gen. Microbiol. 69, 33-80 Stanier, R. Y., Palleroni, N.J. and Doudoroff, M. (1966) ]. Gen. Microbiol. 43,159-271 Barkesdale, L. and Kim, K. S. (1977) Bacterio]. Rev. 41,217-232 Minnikin, D. E., Minnikin, S.M., Goodfellow, M. and Stanford, J.L. (1982) J. Gen. Microbiol. 128, 817-822 Minnikin, D. E. and Goodfellow, M. (1976) in The Biology of the Nocardiae (Goodfellow, M. and Brownell, G.H., eds), pp. 160-219, Academic Press []

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13 Watkinson, R. J. (1980) in Hydrocarbons in Biotechnology (Harrison, D. E. F., Higgin, I. J. and Watkinson, R., eds), pp. 11-24, Institute of Petroleum 14 Tipper, D. J. and Wright, A. (1979) in The Bacteria, Vol. VII: Mechanisms of Adaptation (Gunsalus, I. C., Sokatch, J.R. and Ornston, L.N., eds), pp. 291-426, Academic Press 15 Beaman, B. L. (1976) in The Biology of the Nocardiae (Goodfellow, M. and Brownell, G.H., eds), pp. 386-417, Academic Press 16 Rat]edge, C. (1980) in Hydrocarbons in Biotechnology (Harrison, D. E. F., Higgins, I. J. and Watkinson, R., eds), pp. 133-154, Institute of Petroleum 17 Markovetz, A. J. (1972) Crit. Rev. []

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Diffusion limitation - friend or foe? W h e n constructing a process based u p o n the use of an i m m o b i l i z e d biocatalyst, a n u m b e r of factors must be taken into account. F r o m the chemical engineering point of view, one of the more i m p o r t a n t of these is the substrate/product diffusion limitation to w h i c h the catalyst is subject, s o m e t h i n g w h i c h conventional w i s d o m dictates s h o u l d be avoided at all costs 1-3. (The term 'diffusion limitation' is used here s y n o n y m o u s l y w i t h mass transfer limitation: see Fig. 1.) In practice, the c o m b i n a t i o n of reaction and diffusion in an imm o b i l i z e d biocatalyst particle leads to the creation of non-linear substrate c o n c e n t r a t i o n gradients w i t h i n the particle 4. A steady state is e v e n t u a l l y r e a c h e d where, for any v o l u m e e l e m e n t in the i m m o b i l i z e d e n z y m e particle, the rate of net influx of substrate equals its rate of removal by the enzyme. The rates of e n z y m e catalysed reactions are d e p e n d e n t in part on the substrate concentration. Thus as one goes further into an i m m o b i l i z e d e n z y m e particle, the substrate c o n c e n t r a t i o n is r e d u c e d , causing lower reaction rates w h i c h in t u r n dictate lower rates of flux of substrate. It is entirely possible that the substrate concentration towards the centre of an

i m m o b i l i z e d e n z y m e particle m a y be zero. For the e n z y m e to be used with 100% efficiency, all of it must be fully saturated w i t h substrate. Where diffusion limitation is present this is clearly not the case and thus the effectiveness of the e n z y m e is reduced. The effectiveness factor (see Glossary) of an i m m o b i l i z e d e n z y m e reactor is therefore one m e a s u r e m e n t that the chemical engineer can use in the calculation of reactor perform a n c e 5. T h e lower the effectiveness factor the more (expensive) e n z y m e must be added, possibly in a bigger reactor, in order to obtain a given rate of p r o d u c t output. Thus, in chemical engineering terms, diffusion limitation is an u n w a n t e d and costly effect requiring the use of more e n z y m e than necessary. Diffusion limitation m a y be overcome in two ways: either by reducing the quantity of e n z y m e activity i n c o r p o r a t e d into the immobilized e n z y m e particle, and/or b y increasing the surface area to v o l u m e ratio of the particle. Both a p p r o a c h e s lessen the substrate c o n c e n t r a t i o n gradient w i t h i n the i m m o b i l i z e d e n z y m e particle, thus allowing all of the e n z y m e to come into contact with a m a x i m a l c o n c e n t r a t i o n of substrate. In theory, diffusion limita-

Microbiol. 1,225-237 18 Britton, L. N. and Markovetz, A. J. (1977) J. Biol. Chem. 252, 8561-8566 19 Taylor, D. G., Trudgill, P. W., Cripps, R. E. and Harris, P. R. (1980) J. Gen. Microbio]. 118, 159-170 20 Hartmans, S. and de Bont, J: A. M. (1986) FEMS Lett. 36, 155-158 21 Dalton, H. and Stirling, D. I. (1982) Philos. Trans. R. Soc. London Set. B 297, 481-496 G I L L I A N M. STEPHENS A N D HOWARD DALTON

D e p a r t m e n t o f Biological Sciences, U n i v e r s i t y o f Warwick, C o v e n t r y CV4 7AL, UK.

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tion can be o v e r c o m e by raising the substrate concentration, but in practice the operating conditions of an -- Fig.

1

Immobilized enzyme membrane

Substrate concentration gradients in an immobilized enzyme membrane. Under diffusion ~limitation, the transfer of substrate into the catalyst particle is limited not by the physical velocity of individual molecular motion, but by the reduction in substrate concentration brought about by the reaction within the particle lowering the net rate of flux of substrate through the particle. (1)-(4) indicate either increasing enzyme Ioadings for a given membrane porosity, or decreasing porosity for a given enzyme loading. Thus high enzyme Ioadings and low porosities give the steepest (4) concentration gradients. Increasing the width of the membrane will also increase the substrate concentration gradient.

(~) 1987, Elsevier Science Publishers B.V., Amsterdam 0166- 9430/87/$02.00

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TIBTECH - JANUARY 1987 [Vol. 5]

--Fig. 3 --Substate

diffusion velocity

./

Intrinsic enzyme activity immobilized enzyme reactor offset this: stirred tank reactors operate at substrate concentrations of less than 10% of the input substrate concentration; in packed bed reactors, the input end of the reactor may have substrate concentrations of the same order as the input substrate concentration, but at the outflow end the substrate concentration may be nearly two orders of magnitude less. The intrinsic Km of the enzyme also has a bearing on the magnitude of the effect of diffusion limitation: the lower the Km value, the less likely is diffusion limitation, because for a given input substrate concentration an enzyme with a low Km value is more likely to be fully saturated throughout both the immobilized enzyme particle and the reactor.

~1.0

J

/ .J"

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--3

Substrate concentration in bulk phase

Fig. 2. 1.0,

2

The interaction of substrate diffusion limitation and chemical inhibition for an immobilized enzyme. Solid lines represent intrinsic enzyme activity of immobilized enzyme: uninhibited (1), subjected to competitive inhibition (2), and subjected to non-competitive inhibition (3). Clearly, competitive inhibition may not be apparent if substrate diffusion limitation is severe. The effective rate of reaction is the lower of the diffusion velocity or the intrinsic enzyme activity. Reproduced with permission from Ref. 7.

(a) free

particle with a m i n i m u m of enzyme with a low Km value.

(b) immobilized

'Designer' diffusion limitation

4

pH

6

pH Profiles of free (a) and immobilized (b) glucose oxidase at 1.0 M (I) and O.1 M (2) glucose concen-

trations. Reproduced with per-

mission from Ref. 6. The moral of this is that to enhance the effectiveness of an immobilized enzyme the chemical engineer will strive to: (1) raise the input substrate concentration to the highest practicable level, (2) decrease the immobilized enzyme particle size, and (3) load the immobilized enzyme

However, in the field of immobilized enzymes (as opposed to purely chemical catalysts), the chemical engineer's traditional view of diffusion limitation as the enemy within may be misguided. In practice, some degree of diffusion limitation may be extremely useful in enhancing an immobilized enzyme's operational characteristics. In particular 'designer' diffusion limitation can increase an immobilized enzyme's operational stability, decrease its sensitivity to pH fluctuations 6, and offset the effect of inhibitors (either products or contaminants of the substrate stream) 7. All of these effects are in essence brought about by the situation where diffusion (or mass transfer), rather than the enzyme reaction rate, is the rate limiting step of the process, and diffusion itself is unaffected by these parameters.

Operational stability The stability of an enzyme is not absolute and is governed by a number of factors. Of principal concern here is thermal denaturation. Many reports exist of enzymes' thermal stability being enhanced as a consequence of immobilization. In some cases this may be due to intrinsic stabilization of the enzyme's tertiary structure; however, in most instances it is a result of the presence of diffusion limitation 8. Consider the case of an immobilized enzyme particle in which severe diffusion limitation results in the substrate concentration being effectively zero over the middle 90% of the particle. The enzyme in this portion of the particle is unused. A reduction in the intrinsic activity of the enzyme by 50% as a result of thermal denaturation will be largely offset by increased penetration of the substrate into the particle, which in turn will increase the total quantity of enzyme with which the substrate comes into contact. Thus the effec-

TIBTECH - J A N U A R Y 1987 [Vol. 5]

tive catalytic rate of the whole particle may decrease by only a few per cent, if at all. In addition, the higher the temperature, the more likely diffusion limitation is to be present, because increasing the temperature by, say, 30°C will markedly increase the intrinsic activity of the enzyme, but only marginally increase diffusion rates. This also will result in reactor productivity remaining relatively constant despite temperature fluctuations. Thus an immobilized enzyme particle, the effective catalytic activity of which is kinetically controlled at low temperatures, may become diffusion controlled at high temperatures as the intrinsic activity of the enzyme outstrips the substrate diffusion rate. The end effect, however, is that the immobilized enzyme has a high operational stability, bringing an increase in the predictability and constancy of reactor productivity and a reduction in the frequency of enzyme replacement in the reactor.

Effect of inhibitors Most enzyme inhibitors of concern in this context will probably be competitive inhibitors, in particular the product. Competitive inhibitors are most effective at low substrate concentrations, precisely the condition in which the effective rate of an immobilized enzyme is likely to be diffusion rather than kinetically controlled, and thus the effect of a competitive inhibitor on an immobilized enzyme may be invisible (Fig. 3).

Designing diffusion limitation How, therefore, might one design diffusion limitation into an immobilized enzyme? Very simply by the p H fluctuations reverse of the procedures given above Similarly, enzyme reaction rates to limit its effect: high catalyst are often markedly influenced by loadings, larger immobilized enchanges in pH. The range of pH over zyme particles, and use of enzymes which many enzymes retain at least with intrinsically high Km values. 80% of their maximal activity may Entrapment of dead permeabilized be less than one unit and therefore, microorganisms in highly crossto retain full productivity of an linked, large polymer particles, or enzyme based process, pH must be alternatively crosslinking dead (flocaccurately controlled. In addition, culated) cells with glutaraldehyde the pH optimum of an enzyme may would be suitable methods; over half be dependent upon the prevailing of the large scale industrial applisubstrate concentration. Where sub- cations of immobilized enzymes use strate diffusion limitation is present, methods of this kind, whether by an immobilized enzyme will usually accident or design. Also of interest have a much broadened pH profile, in this respect are various reports of retaining 80% of maximal activity the economic potential of hollow over several pH units, or indeed may fibre enzyme reactors, known to be become essentially independent of subject to poor mass transfer. The pH. The reason for this is that work of Takata et al. 9 on the substrate flux rates are unlikely to be production of L-malic acid from pH sensitive. In such a system, if the Brevibacterium flavum makes parpH is taken far enough away from ticularly interesting reading. Thus the deliberate design of the intrinsic optimum for the enzyme, the intrinsic enzyme activity diffusion limited immobilized enwill be reduced so that the reaction zymes may be advantageous. The becomes kinetically controlled and criteria which have to be balanced in therefore sensitive to pH changes objective consideration of such an (Fig. 2). approach include the cost and in-

trinsic stability of the enzyme, the extent of product inhibition, the degree of control available on the reactor environment, and the cost and technical difficulty of the immobilization process. Thus to return to our starting question 'Diffusion limitation - friend or foe?': the answer is probably 'opportunistic ally'.

References 1 Levenspiel, O. (1972) Chemical Reaction Engineering (p. 5), J. Wiley & Sons 2 Thomas, W. J. (1979) in Chemical Engineering (Vol. 13, 2nd edn) (Richardson, J. F. and Readcock, D. G., eds), pp. 107 et seq., Pergamon 3 Weetall, H. H. (1985) Trends Biotechnol. 3,276-280 4 Goldman, R., Kedem, O. and Katchalski, E. (1968) Biochemistry 7, 4518-4513

5 Engasser, J-M. and Horvath, C. (1976) in Applied Biochemistry and Bioengineering Vol. 1: Immobilized Enzyme Principles (Wingard, L. B., Katchalski-Katzir, E. and Goldsmith, L., eds), p. 151, Academic Press 6 Trevan, M. D. (1985)-in Molecular Biology and Biotechnology (Walker, J.M. and Gingold, E.B., eds), pp. 217-221, Royal Society of Chemistry 7 Trevan, M. D. (1980) Immobilized Enzymes: An Introduction and Applications in Biotechnology, pp. 44-55, John Wiley & Sons 8 Klibanov, A. M. (1979) Anal. Biochem. 93, 1-25 9 Takata, I., Yamamoto, K., Tosa, T. and Chibata, I. (1980) Enzyme Microb. Technol. 2, 30-36 MICHAEL TREVAN

School of Natural Sciences, The Hatfield Polytechnic, PO Box 109, College Lane, Hatfield, Hefts ALIO 9AB, UK.