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Product Inhibition Influence on Immobilized Cell Biocatalyst Performance Gregory D. Sayles and David F. Ollis* Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905
T h e potential steady-state influence of product inhibition on the performance of immobilized cell cultures is thoroughly explored with the aid of a simple unstructured reactiondiffusion model. Production inhibition was assumed to diminish the specific growth rate directly. T h e range of product sensitivity explored corresponds directly with the observed range of ethanol sensitivity of Clostridium thermocellum, Clostridium acetobutylicum, Saccharomyces uvarum, Zymomonas mobilis, and Saccharomyces cerevisiae. T h e consequent influence on the immobilized cell growth rate, thickness of steady-state viable cell layer, formation of growth-associated product, and global performance of the immobilized cell particle is explored by simulated variation of both the external bulk solution product level and the cell intrinsic sensitivity t o the inhibitory product. Thus, both the thickness of the steady-state viable cell layer and the consequent biomass loading of the bead are predicted variables of the model; these are variables due t o the adaptive growth and biomass redistribution which occur in porous supports. T h e calculated influences are appreciable and even dramatic under some circumstances; the implications for packed-bed reactor operations for ethanol and solvent production are discussed.
Introduction Some cellular products depress the specific growth rate of the producer organism. For example, ethanol inhibits the growth of the bacterium Zymomonas mobilis (1) and the yeast Saccharomyces cerevisiae (2);butanol, acetate, ethanol, acetic acid, and butyric acid inhibit the growth of the bacterium Clostridium acetobutylicum (3), and lactate (4) and ammonium (5) inhibit the growth of mammalian cells. The quantitative influence of product ethanol concentration on bacteria and yeast kinetics has been well studied (1-3,6) and the impact of product inhibition on continuous suspension culture performance has been investigated (7). The performance of an immobilized cell biocatalyst, in which viable cells are entrapped in a gel matrix, depends on the coupled phenomena of cellular reaction kinetics and solute diffusion within the available carrier porosity. The performance of uninhibited immobilized cell cultures exhibiting Monod kinetics was reviewed by Venkatasubramian (8), Karel et al. (9),and Mavituna (10) and has been analyzed by using structured kinetics by Monbouquette and Ollis (11, 12). Luong (13) and Monbouquette, Sayles, and Ollis (14) have investigated the performance of an immobilized cell particle using substrate and product inhibition kinetics without exploring the influence of the inhibition in detail. The steady-state analysis of the influence of product inhibition on immobilized cell system performance is more complex than the corresponding earlier analyses of product inhibition on immobilized enzyme performance (1517) for several reasons: (i) The maximum density to which immobilized biomass may grow in the bead directly influences the effective diffusivity of the nutrient(s) and product(s) (1822); this ultimate biomass density will depend both on
the support porosity (total pellet void volume) and on the pore size distribution (fraction of pores large enough to accommodate living cells of finite size) (11, 12). (ii) The steady-state thickness of the viable cell layer is a n intrinsic variable of the adaptive culture. The microenvironmental condition that exists a t steadystate at the inner boundary of this layer is that the cells are a t a stationary state where synthesis just replaces degradation (11, 12). In a product-inhibited culture, therefore, the product effective diffusivity will be modified by biomass presence, and product concentration will influence metabolic kinetics and thus the locations of the inner boundary position or, equivalently, the thickness of the viable cell layer. The present paper analyzes the performance of an i"obilized cell catalyst particle operating at steady state under t h e influence of growth inhibition by a growthassociated product (such as ethanol). The performance will be evaluated by calculating substrate, product, and specific growth rate profiles, the thickness of the steadystate viable cell layer (which gives in turn the total biomass loading), the total biocatalytic productivity, the total particle productivity per unit immobilized biomass, and the biocatalyst particle effectiveness. The model system will be a single spherical gel bead entrapping viable microbial cells, with known constant bead surface nutrient and product concentrations.
Methods The apparent steady-state behavior of immobilized cell systems has been observed experimentally (23-31) and is typically associated with the formation of a region of high cell density of relatively uniform viable cell concentration that extends from the bead surface to a distinct radial position inside the bead.
8756-7938/90/3006-0153$02.50/0 0 1990 American Chemical Society and American Institute of Chemical Engineers
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Table I. Steady State Model (Dimensionless)
Table 11. Model Parameter Values $s = 88.7
&, = 27.4 K = 0.0023 S, = 0.565 a = 0.12
where
As before (11, 12) it is assumed that a t steady state a uniform biomass distribution extends from the bead surface to a radial position where the lack of substrate and/ or the abundance of inhibitory product allows no net cell growth. There are thus no growing cells at greater depths. In theory, maintenance metabolism of any cells more deeply located will have reduced the substrate concentration so low as to yield negative net growth; the steadystate outcome is that all such deeper cells are theoretically dead. The steady state is maintained despite continuous cell growth by constant leakage of cells from the bead and/or exudation of cells further into the bead where they are assumed to die (for lack of essential nutrient or abundance of inhibitory product). For lack of any detailed model, cell lysis is not considered here. These assumptions were employed previously in a structured steadystate immobilized cell model (11). The inner boundary of the viable cell layer (VCL) is the position of zero net growth where cell growth is slow enough to just balance the combined effects of natural cell death and biomass turnover due to endogenous metabolism. In terms of the dimensionless radial coordinate, R , where 0 IR 5 1, biomass extends from R = 1 (the bead surface) to R = R* such that pnet(R=R*)= 0, where pnet is the dimensionless net specific growth rate of the cells and is a function of the local substrate (S) and product ( P ) concentrations. The net specific growth rate is defined by eq 1, where p is the dimensionless specific
growth rate arising directly from substrate consumption and CY is the dimensionless combined specific death and endogenous metabolism rates, taken here to be constant. The value of R* depends on all catalyst parameters and external boundary conditions. The dimensionless form of the steady-state model is presented in Table I (eqs Tl-T7). A t steady state, no separate biomass concentration equation is needed because a uniform, fully loaded biomass layer has been assumed for R* IR I1. This outcome is also predicted from the long-time asymptotic behavior of a transient simulation of immobilized gel bead activation (14). In addition to substrate and product concentrations, R* is also a dependent variable. Therefore, in addition to the substrate equation (Tl) and the product equation (T2),a third equation (T3), which defines the inner edge
of the viable cell layer, is included. With use of a trial value for R*, eqs T1 and T2 are solved simultaneously, subject to boundary conditions T4 and T5. With this trial solution, satisfaction of eq T 3 is checked. If eq T 3 is not satisfied, an updated R* is used to solve the system again. Eventually, eqs T1-T5 are satisfied yielding S ( R ) ,P ( R ) ,and R*. The parameter values used in the present study (Table 11) are those employed for a previous kinetic simulation of glucose-limited calcium aliginate immobilized 2. mobilis growth and ethanol production (14). The functionality of the previous (14) specific growth rate was simplified for this analysis (eqs T6 and T7). It continues to include a term for inhibition by product. This linear form of product inhibition (1 - Kip),where Ki is a constant, has been used to describe inhibition by ethanol (2). It is a particular case of the generalized inhibition models proposed by Levenspiel (32) [ (1- P/P,,)"] and by Luong (33) [ l - (P/P,,,)"]. Values of Ki for several ethanolproducing organisms are presented in Table I11 along with the corresponding dimensional maximum ethanol concentration. The dimensionless Thiele moduli & and &., defined in Table IV, are composed of parameters used previously (14). One kinetic parameter and one environmental variable will be altered to simulate various levels of inhibition. The product inhibition kinetics parameter, Ki, will be varied to simulate the influence of intrinsic product sensitivity on the specific growth rate and on the overall biocatalyst particle performance. Product concentration at the bead surface, P,, will be varied to simulate various reactor conditions. For example, an increase in P, can simulate (a) a decrease of the dilution rate for a steady-state slurry or fluidized bed, (b) an increased time in a (pseudosteady) batch reactor, or (c) a location further downstream in a packed-bed column reactor.
Simulation Results and Discussion Intraparticle Results. Figure 1 shows the calculated steady-state substrate (S) and product ( P )concentrations within the immobilized cell carrier as a function of radial position ( R ) for several values of the inhibition rate constant Ki and for a moderate product surface concentration of P, = 0.1. The curves A for Ki= 0 correspond to an uninhibited culture. Figure 1 shows that employing organisms of increasing sensitivity to product (increasing K i values) yields higher residual substrate levels and lower product levels throughout the particle: the overall conversion of substrate is always lowered by inhibition. Increasing K idepresses the growth rate throughout the particle and thus the stoichiometrically corresponding substrate consumption and product formation rates. This behavior is clearly seen from calculations of the net specific growth rate profile, pnet, within the carrier using Figure 1 and eqs T6 and T7 for Ps = 0.1. The plot of pnet versus K iin Figure 2 shows that increasing Ki depresses pnet nonuniformly throughout the immobilized culture. The pnet profiles extend across the viable cell layer, i.e., from the carrier surface ( R = 1) to the position ( R = R*) where pnet = 0, as discussed in Meth-
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Table 111. Ethanol Inhibition Constants max ethanol corresponding organism concn P,,, g/L Ki = pb/Pmu C. thermocellum 25 7.1 C. acetobutylicum 41 4.3 S. uvarum 60 3.0 2.mobilis 86 2.1 S. cerevisiae 90 2.0
ref 34
3 2 1 2
Table IV. Dimensionless Quantities
0
0.7
0.8
0.9
1 .o
R Figure 2. Specific rate functions g et, gs, and pp as functions of radial position (R),for K . = 0 (A?, 1.0 (B),2.5 (C), 3.5 (D), 5.0 (E),and 8.0 (F) and forb, = 0.1.
n
LT
W
m
This behavior of L can be seen more clearly if the functionality is examined. The function p is the product of its substrate-dependent portion, p,, and its product-dependent portion, pp, where
,
? or
I
I
I
I
I
t
1 I
0.7
I
I
I
0.8
I
0.9
I
1 .o
R Figure 1. Substrate (S) and product (P) concentrations within the immobilized cell particle as a function of radial position (R),for K, = 0 (A), 1.0 (B), 2.5 (C), 3.5 (D), 5.0 (E), and 8.0 (F) and for P, = 0.1.
ods. The figure also reveals that increasing Ki first increases the VCL thickness L (decreases R*)in which cells can grow, but that later increases in Ki eventually lead to diminution of the VCL. Thus, L, the viable cell layer thickness, exhibits a maximum with respect to Ki.
r(S,P) = CLs(S)Pp(P)
(2)
and
pp(P) E 1- KiP (4) The calculated functions ps and pp are also plotted in Figure 2 as functions of R for several K i , for Ps = 0.1. Comparison of the plots in Figure 2 reveal that (i) a t Ki = 0, p (and therefore L ) varies with ps (and therefore S), (ii) for K i greater than approximately 3.5, p varies with pLp(and therefore P), and (iii) for 0 < Ki < 3.5, p is determined jointly by variations of ps and pp. At low K i , the drop in pnet,and therefore in substrate uptake rate, allows greater penetration of substrate into the carrier thereby allowing a thicker viable cell layer. As Ki approaches 3.5, however, the substrate consumption rate is decreased by the increasing local product level. Further increase in Ki nearly causes substrate uptake to cease, and S approaches the surface concentration S,. Now, increases in Kidecrease L because p is now determined by pp only, and pp decreases with increased product sensitivity, Ki (Figure 2). The trade-off in the influence of ps and pp on the VCL thickness is shown in Figure 3. Here, the functions ps
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I
I
I
I
I
I
I
I
I
I
v1
W +
0 E
.-'cV
:t \ I c
\
/
i 4
V
W
Q
fn 0
Ki Figure 3. Functions ps and pp evaluated at R = R* (ps* and pp*) as a function of Ki, for Ps = 0.1. and .up evaluated at the inner edge of the viable cell layer , plotted versus Ki.The (at R = R*), ps* and F ~ * are transition from substrate-dominated behavior (K, I0.5) to product-dominated behavior (K,> 3.5) is evident. The value of Kia t which the viable cell layer thickness L is a maximum, where product concentration begins to be the dominant influence on L, will be called the turning point (TP) (at Ki= 3.5 in Figure 3). Figure 4 shows that the VCL thickness, L , is a function of the product surface concentration, P,, as well as a function of Ki.At low Ki, L increases with respect to Ps. However, for values of K , above the turning point (TP),an increase in P, decreases L, as expected considering the results associated with Figures 1-3. Particle Performance. The intraparticle results of Figures 1-4 can be used to calculate the overall biocatalyst performance measures. In Figure 5, the dimensionless steady-state particle production rate (PR) and the total productivity per unit of immobilized biomass, Le., the average specific activity (SA), are plotted versus the inhibition rate constant, K,, for various particle surface concentrations, P,. The quantities PR and SA are defined mathematically in Table IV. The plotted quantities have been normalized to the uninhibited immobilized culture values, i.e., P R and SA for K , = 0. Known K ivalues of several organisms (Table 111) are indicated with arrows in Figure 5. Figure 5 shows that P R and SA, relative to uninhibited immobilized cultures, decrease markedly with moderate increases of K , and Ps. For example, operation with immobilized 2. mobilis or S. cereuisiae for which Ki= 2, a t the moderate value of Pi= 0.1, leads to a 20% loss in P R and a 40% drop in SA, relative to uninhibited immobilized cell cultures. Note that the change in slope of each SA curve in Figure 5 occurs at the corresponding turning point. Figure 5 clearly demonstrates that the particle production (PR) always decreases more slowly than SA as K ifirst increases; this is due to the partially offsetting increase of biomass particle loading (Figure 4). At higher K ivalues, the converse occurs, since both SA and biomass loading decrease with increasing Ki. As shown in Figures 4 and 5, there exists a critical external product level above which no steady-state biocatalytic activity is predicted. The domain of operational safety (guaranteed activity) with respect to the parameters K iand Ps can be determined by noting that the inequality pn,,(R=l) > 0 or p ( R = l ) > a ensures the presence of an active culture. Rearranging the inequality yields
Equation 5 gives the surface product concentration oper-
0
2
4
6
10
8
Ki Figure 4. Viable cell layer thickness Parameter: Ps. N c
I
I
I
I
I
I
1
I
I
(L)as a function of Ki. I
I
I
I
I
I
n
-U -
.-Q,
N 0
E
L
0 C W
CY
a
n
-0 0, N ..
.L
0
c
W
U
v,
I
0
2
6
4
I
8
I
10
Ki Figure 5. Particle production rate (PR) and particle specific activity (SA), normalized to the same quantities calculated for uninhibited cultures (Ki= 0), as a function of Ki.Parameter: Ps. The arrows correspond to known Kivalues for several ethanol-producing organisms (Table 111). Dotted line: Example progression from entrance (top, Ps = 0) to the end of a (viable cell) packed-bed reactor (Ps = 0.2) for K i= 4.3 (C. acetobutylicum example).
ating regime, which guarantees some biomass activity (viability), given K iand the surface substrate concentration, S,. [Some killed, immobilized cell cultures exhibit limited ethanol production. This case is not considered here; we have assumed that product is always growth associated.] Equation 5 and Figure 4 imply that a very dramatic loss of particle activity will occur in a packed-bed reactor as P, approaches this critical value (Perit) at an intermediate position along the column. Performance as a function of axial position in a packed bed can be visualized by using Figure 4 or 5 by following a vertical path at the desired K , beginning from the P, = 0 curve (reactor entrance), as the dotted line in Figure 5 demon-
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9 7
xt
i
x4 a 0
2
4
6
10
culture since intraparticle product levels must be higher that external solution conditions. The presence of product inhibition lowers the specific growth rate of the culture pointwise in the carrier, thus diminishing the particle conversion of substrate to product and the total productivity a n d specific activity of t h e biocatalyst. Counterintuitively, perhaps, increased sensitivity to product inhibition results a t first in an increased viable biomass loading of each carrier particle; then at still higher sensitivities a decreased loading and eventual extinction of viable cells is predicted. The application of these calculations for packed-bed reactor design is suggested and constitutes a portion of our ongoing studies.
Ki Figure 6. Particle effectiveness (E) as a function of Ki. Parameter: Ps.
strates for Ki= 4.3 (C.acetobutylicum example). Figure 6 summarizes the variation of the VCL effectiveness ( E ) versus Kifor several values of the surface product concentration, Ps. Effectiveness is d e f i e d (Table IV) as the ratio of the total productivity of the immobilized cell culture to the total productivity of the same biomass quantity referred to the bead surface conditions. The effectiveness first decreases with increasing K ibecause the immobilized cells are exposed to product levels higher than the surface conditions, thereby depressing their activity relative to suspension cultures. However, for Kigreater than the turning point value, the effectiveness E increases with Kibecause the VCL thickness is also decreased, thereby lowering the resistance to diffusion. Production Reactor Design. Figures 4-6 indicate that, due to both the inhibition by product and the interactive redistribution of viable immobilized cells, the biomass loading per bead (reflected in the variable viable cell layer thickness, Figure 4), the averaged specific biomass activity (Figure 5, bottom), and the biomass effectiveness (Figure 6) all vary as a function of external nutrient (S,) and product (P,) levels. For a packed-bed reactor design, using a feed stream containing no product and a simple plug flow design equation, the local S and P bulk fluid profiles would be given by eqs 6 and 7. CU
Greek Letters
dS + (1- t)f$sp(S,P)(l-R*3(S,P))E(S,P)/3 = 0 dz
Notation Cx,max maximum attainable and the steady-state viable cell layer biomass concentration [M/L3] effective diffusivity of product [Lz/Z'l D;l effective diffusivity of substrate [L*/Z'l Dff E effectiveness of the biocatalyst (dimensionless, defined in Table IV) K Monod saturation constant (dimensionless) product inhibition constant (dimensionless) Ki thickness of the viable cell layer, equal to 1 - R* L (dimensionless) P product concentration (dimensionless) product concentration at the carrier surface ( R = PS 1) (dimensionless) PR particle product formation rate (Table IV, dimensionless) R radial coordinate (dimensionless) radial position of the inner edge of the steadyR* state viable cell layer (dimensionless) radius of the immobilization particle [ L ] rP S substrate concentration (dimensionless) substrate concentration at the carrier surface (R SS = 1) (dimensionless) SA particle specific activity of biomass (Table IV, dimensionless) yield coefficient for product [M/M] YP yield coefficient for substrate [M/M] YS a
(6)
(7)
Thus, for a simple axial integration, one would substitute eq 7 into 6, solve at each step for the resulting p(S,P),R*(S,P), and E(S,P), integrate to find S in the next bead layer, calculate a new P, and then repeat the evaluations and integrations. The model developed here will clearly predict axial variations of easily accessible experimental quantities: viable cell layer thickness, total viable cell loading per bead, and variation of reactor productivity with inlet substrate and solvent concentrations. Experiments and reactor simulations to test the applicability of the present model to reactor design are currently underway.
Summary These model calculations indicate that product inhibition can very significantly influence the performance of immobilized cell particles. Immobilization alone necessarily increases the impact of product inhibition on the
P
Pmax
4P 4s pb
specific endogenous maintenance and death rate (dimensionless) specific growth rate (dimensionless) maximum specific growth rate [ 1/r ] reaction-diffusion modulus for product (defined in Table IV, dimensionless) reaction-diffusion modulus for substrate (defined in Table IV, dimensionless) biomass intrinsic density, dry weight per biotic volume [ M I L 3 ]
Literature Cited (1) Rogers, P. L.; Lee, K. J.; Smith, G. M.; Barrow, K. D. In Alcohol Toxicity in Yeasts and Bacteria; van Uden, N., Ed.; CRC Press: Boca Raton, FL, 1988; Chapter 10. (2) Pamment, N. B. In Alcohol Toxicity in Yeasts and Bacteria; van Uden, N., Ed.; CRC Press: Boca Raton, FL, 1988; Chapter 1. (3) Linden, J. C.; Kuhn, R. H. In Alcohol Tonicity in Yeasts and Bacteria; van Uden, N., Ed.; CRC Press: Boca Raton,
FL, 1988; Chapter 12. Glacken, M.; Fleischaker, R.; Sinskey, A. Biotechnol.
(4)
Bioeng. 1986, 28, 1376. Butler, M. Dev. Biol. Stand. 1985, 40, 269.
(5)
Biotechnol. Prog., 1990, Vol. 6, No. 2
(6) Mulchandani, A.; Luong, J. H. T. Enzyme Eng. 1989, 1 1 , 66. (7) Schugerl, K. Bioreactor Engineering; John Wiley and Sons: New York, 1985; Vol. 1, Section 2.3.6. (8) Venkatasubramnian, K.; Karkare, S. B.; Vieth, W. R. Appl. Biochem. Bioeng. 1983,4, 312. (9) Karel, S. F.; Libicki, S. B.; Robertson, C. R. Chem. Eng. Sci. 1985, 40, 1321. (10) Mavituna, F. Process Engineering Aspects of Immobilized Cell Systems; The Institution of Chemical Engineers: Rugby, Warwickshire, England, 1986; Chapter 9. (11) Monbouquette, H. G.; Ollis, D. F. Ann. N.Y. Acad. Sci. 1985,469, 230. (12) Monbouquette, H. G.; Ollis, D. F. In Bioreactor Immobilized Enzymes and Cells, Moo-Young, M., Ed.; Elsevier Applied Science: New York, 1988; pp 9-33. (13) Luong, J. H. T. Biotechnol. Bioeng. 1985,27, 1652. (14) Monbouquette, H. G.; Sayles, G. D.; Ollis, D. F. Biotechnol. Bioeng., submitted for publication. (15) Engasser, J.-M.; Horvath, C. Appl. Biochem. Bioeng. 1976, I , 128. (16) Bailey, J. E.; Chow, M. T. C. Biotechnol. Bioeng. 1974,16, 1345. (17) Ollis, D. F.; Carter, R. Enzyme Eng., 1974, 2, 271. (18) Klein, J.; Manecke, G. Enzyme Eng., 1982, 6 , 181. (19) Furui, M.; Yamashita, K. J . Ferment. Technol. 1985, 63, 167.
(20) Sakaki, K.; Nozawa, T.; Furusaki, S. Biotechnol. Bioeng. 1988. 31. 603. (21) Chresand, T. J.; Dale, B. E.; Hanson, S. L.; Gillies, R. J. Biotechnol. Bioeng. 1988,32, 1029. (22) Libicki, S. B.; Salmon, P. M.; Robertson, C. R. Biotechnol. Bioeng. 1988,32, 68. (23) Shinmyo, A.; Kimura, H.; Okada, H. Eur. J . Appl. Microbiol. Biotechnol. 1980, IO, 275. (24) Wada, M.; Kato, J.; Chibata, I. Eur. J. Appl. Microbiol. BiotechnoL 1980, 10, 275. (25) Linko, Y.-Y.; Linko, P. Biotechnol. Lett. 1981, 3, 21. (26) Krouwel, P. G.; Groot, W. J.; Kossen, N. W. F. Biotechnol. Bioeng. 1983,25, 281. (27) Osiga, J.; Mori, A.; Kato, J. J . Ferment. Technol. 1984, 62, 139. (28) Wada, M.; Uchida, T.; Kato, J.; Chibata, J. Biotechnol. Bioeng. 1980, 22, 1175. (29) Klein, J.; Kressdorf, B. Biotechnol. Lett. 1983, 5, 497. (30) Prevost, H.; Divies, C.; Rousseau, E. Biotechnol. Lett. 1985, 7, 247. (31) Sato, K.; Tosa, K. J. Ferment. Technol. 1983, 61, 239. (32) Levenspeil, 0. Biotechnol. Bioeng. 1980, 22, 1671. (33) Luong, J. H. T. Biotechnol. Bioeng. 1985,27, 280. (34) Kundu, S.; Ghose, T. K.; Mukhopadhyay, S. N. Biotechnol. Bioeng. 1983, 25, 1109. Accepted February 28, 1990.
