Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
401
Optimization of Polysaccharide Carriers for Immobilized Glucoamylase Reactors Steven J. Swanson, Henry C. Lim, and Alden Emery" School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
Glucoamylase was immobilized to dextran and agarose and the effects of the conditions of immobilization on the activity and stability of the catalyst were measured. Activity bound to dextran is a strong function of the concentration of the cyanogen bromide used, reaching a limiting value at a rather high concentration. Activity bound to agarose increases with increasing solid content of the agarose, showing that the customary 4 % agarose may be too low a concentration for optimal reactors. Enzymic activity and carrier capacity decrease with time, and in use a catalyst must be regenerated periodically and eventually replaced. Equations were developed giving optimum cycle time and number of uses of carrier as a function of two cost parameters. Reactors designed using the data showed that carrier stability is a crucial factor and that increased agarose concentration is probably advisable.
Introduction The immobilized enzyme reactors used in commercial applications so far appear to have involved simple methods of immobilization, namely trapping and adsorption (Chibata and Tosa, 1976; Smiley, 1974). Covalent bonding, however, offers the possibility of enhanced stability over simpler preparations, and this, in turn, demands a carrier of good characteristics. The polysaccharides dextran and agarose have shown their usefulness in considerable chromatographic work, and having apparent uniformity and a range of porosities from which to draw for a given application, would seem reasonable candidates for the immobilization of enzymes. There are, in fact, several reports of enzymes being immobilized to dextran (Beeley and McCairns, 1972; Lasch et al., 1972; Marshall and Rabinowitz, 1976) and many articles dealing with the immobilization of various enzymes to agarose (Caldwell et al., 1976; Chung and Middleditch, 1972; Coughlan and Johnson, 1973; Gurne and Shemin, 1973; Sjoberg and Holmgren, 1973; Zaborsky and Ogletree, 1972), most of which appear to have scientific objectives. For industrial reactors transforming feeds of high concentration, such as the proposed use of immobilized glucoamylase in the production of glucose from starch, catalysts of high activity and stability will be needed. In addition, such reactors must be carefully designed and optimized. The objectives of the work reported here were to probe conditions of preparation and determine the properties of the catalysts formed by immobilizing the enzyme glucoamylase to dextran and agarose, and to develop design procedures and optimize the design of reactors using these catalysts. Experimental Work Methods. Glucoamylase from Aspergillus oryzae was used in a preparation obtained from Sigma Chemical Co. The dextran used was Sephadex G-10, a designation of Pharmacia indicating that the dry polymer will imbibe about an equal volume of water. The pore size formed is very small, large enough to allow free access to small ligands such as tyrosine, but too small to allow the enzyme to penetrate into the interior of the bead. Agarose beads are manufactured with several different concentrations of polysaccharide in the bead. The most popular carrier in chromatography work is Sepharose 4B, which contains about 4% polysaccharide in a bead. The void fraction in a bead is thus about 96%, and the best 0019-7882/78/1117-0401$01 .OO/O
visualization of the bead would seem to be a few wisps of linear polymer sparingly dispersed in space. While this may be good for chromatography, reactors require porous catalysts with high activity, and agarose of higher concentration and higher binding capacity seemed called for. For this reason, we studied the properties of agarose beads of higher concentration, using 4% agarose manufactured by Pharmacia and 6 and 10% agarose from Bio-Rad Laboratories. In addition, a 12% agarose special preparation was generously donated by Pharmacia Fine Chemicals. Agarose was cross-linked with epichlorohydrin by the technique of Porath et al. (1971), who found that this greatly improved the flow characteristics of packed beds of agarose. This it does, but in addition, we found that it is essential to cross-link the gel for stability of activity of enzyme-carrier complexes; otherwise reactors operated at 40 "C and above lost their activity in a very short time. Sipe and Schaeffer (1973) studied the amount of globular protein bound to agarose as a function of the concentration of cyanogen bromide in the activating solution. They found that the curve reached a plateau a t about 240 g/L of cyanogen bromide, for which reason this value was used in all immobilizations to agarose reported here. Free glucoamylase was assayed by obtaining initial rate data in batch reactions at 40 OC. The reactant was maltose a t a concentration of 40 mg/mL, roughly ten times the value of the Michaelis constant, in 0.05 M acetate buffer at pH 4.5. Enough enzyme was used so that no more than a few percent of the maltose was consumed during the period of the 20-30 min assay. The slope of a straight line through the points on a plot of glucose concentration against time yielded the activity of the preparation. Glucoamylase immobilized to dextran was assayed in a small batch stirred-tank reactor, using the same conditions as for the free enzyme. Glucoamylase immobilized to agarose was assayed at 40 "C in small packed-bed reactors containing about 1 mL volume of bed, using as feed the same solution as for the free enzyme. This concentration of maltose is well above that at which diffusional resistance can be detected, as shown by the constancy of activity when concentration is increased. Extent of reaction was below 10% in all cases, enabling analysis by the differential reactor model. The enzyme immobilization technique was essentially that of Axen et al. (19671, modified as noted below for the 0 1978 American
Chemical Society
402
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
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study of the effects of time of activation with cyanogen bromide, the time of reaction with ligand, and the amount of cyanogen bromide. The quantity of enzyme used was in all cases several times that which disappeared from the solution. The degree to which the amount of ligand attached was sensitive to the time of activation of dextran with cyanogen bromide and the time of reaction with the ligand was studied using tyrosine as a model ligand. Time of activation at pH 11.5 and 20-25 " C was varied from 6 to 18 min, each sample was washed in a standard fashion, combined with the tyrosine at 0-5 "C, and samples of the liquid were withdrawn periodically and analyzed in a spectrophotometer. The effect of the amount of cyanogen bromide used on the glucoamylase activity bound to dextran was studied using from 0.1 to 1 g cyanogen bromide per gram of dry carrier, conditions otherwise being standard.
Results The amount of glucoamylase bound to dextran and the retention of activity on binding were averaged over nine immobilizations. The amount bound did not differ significantly from an estimate of that which would be found in a monolayer on perfect spheres the size of the dextran beads, which were indeed perfect spheres. The estimate was based on an enzyme molecular weight of 80000, a spherical volume occupied by the enzyme containing 73 70 solids, and a triangular arrangement of enzyme molecules on the surface. The retention of activity on immobilization was 42%. The study of the effect of time of activation with cyanogen bromide gave the results shown in Figure 1. The amount of tyrosine bound to dextran is not sensitive to the time of activation in the range studied. A single test of much longer duration (not shown) gave a significantly lower result. Thus the number of sites active for binding ligands does not decrease perceptibly in the times needed for preparation of the activated carrier. An activation time of 6 to 12 min was used in further work, the value recommended by Axen et al. (1967). A secondary result shown in Figure 1is that the amount of binding of tyrosine appears to have leveled off in about 3 h. Since tyrosine penetrates to the interior of the dextran bead, this represents the time needed to diffuse into the interior and react. The enzyme does not penetrate, and later work showed that reaction of the activated dextran with the enzyme leveled off in about an hour, suggesting that the reaction is rapid and the limiting process is
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TIME OF TYROSINE RERCTION. HOURS Figure 1. Tyrosine bound to dextran as a function of the time of activation with cyanogen bromide and the time of reaction with tyrosine. Time of activation: 0, 6 min; +, 9 min; 0, 12 min; and A, 16 min. Tyrosine bound is per gram of dry carrier.
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Figure 2. Enzymic activity bound to dextran as a function of the amount of cyanogen bromide used in the activation.
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diffusion of the ligand to the solid surface. The study of the enzymic activity bound to dextran as a function of the amount of cyanogen bromide used in the activation yielded the data shown in Figure 2. The curve reaches a plateau near 1.0 g of cyanogen bromide per gram of carrier, the value recommended by Axen et al. (1967). This quantity of cyanogen bromide is incredible when compared to the maximum possible productive use made of it. For instance, if ten bonds are imagined per enzyme molecule, the total cyanogen bromide fed to the reaction is three orders of magnitude larger. Such a low efficiency of use may be acceptable in the preparation of analytical columns, but it contributes to unacceptable costs in the preparation of industrial catalysts, as noted below. The Sipe and Schaeffer study (1973) of the protein bound to 4% agarose as a function of the concentration of cyanogen bromide yielded a similar curve which reached a plateau at about 240 g/L of cyanogen bromide, which is difficult to reconcile with the results reported here for dextran. The situation is undoubtedly confused by a competing degradation of the cyanogen bromide by hydrolysis. The study of the activity bound to agarose as a function of the solid content of the agarose produced the results shown in Figure 3. As hypothesized, the gels with higher solids content did bind more activity. While the increase could be approximately linear below the range studied, it here falls off from a linear functionality. An unfortunate simultaneous variation was the decrease in stability of the enzyme-carrier complex with increasing solid content, as shown in Figure 4. The reason is not known, but re-
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 403
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membering the poor stability shown by uncross-linked gel, it may be that epichlorohydrin is not capable of producing enough cross-links in the gels with higher solid content. An important question in the economics of immobilized enzymes is whether the carrier can be used repeatedly. As a preliminary test of this possibility, several batches of dextran containing active immobilized glucoamylase were combined at the completion of their usefulness in the work and, without any previous treatment, exposed to the standard immobilization procedure involving activation with cyanogen bromide at pH 11.5,washing, and reaction with fresh enzyme. The activity of the resulting preparations was not significantly different from what would be expected with fresh carrier. Insignificant carrier was lost in reactivation, at least during this one single extra cycle.
Reactor Design and Optimization The activity of immobilized-enzyme catalysts decays with time, and after a certain time of running, fresh activity must be supplied. It is imperative to be able to use high-quality carriers repeatedly, so we will imagine that fresh activity is bound to the same carrier, and it is put on stream again. To avoid the excessive variation of output concentration with time than can be experienced with constant flow rate operation as the activity decays, N modules of varying ages will be placed in series, and one extra module will be off stream in the process of regeneration. The capacity of a carrier will not be maintained indefinitely, but will gradually decay with time, and after a certain number of cycles, to be determined economically, the carrier must be thrown away and replaced with fresh carrier. These two variables, the cycle time, 8, and the number of cycles of use of one charge of carrier, n, are to be determined in the design and optimization. Two limiting modes of degradation of the carrier may be delineated, one in which the carrier capacity degrades during the time on stream, such as might be experienced by polymers which hydrolyze, friable solids subjected to large pressure drop in a packed bed, or particles in a fluidized bed, and one in which the carrier degrades during the process of regeneration, such as the application of strong chemicals or heat. The first mode is treated here, degradation only during the time on stream. Reactor Design. Reactor design involves calculating the volume of a module in terms of 8, n, and the desired yearly production, P. When both the carrier and the immobilized enzyme are fresh, the maximum activity of the catalyst per unit volume of reactor is V,,. Decay of activity of the immobilized enzyme is assumed to follow
first-order kinetics (as our data show it to be for the case studied above) with a rate constant k , and decay of the binding capacity of the carrier is similarly taken to be first order with a rate constant k,. For most enzymes currently immobilized commercially, equilibrium in the reaction of interest lies far to the right and the value of the Michaelis constant is small, for which reasons the reaction rate assumes its maximum value throughout almost the entire reactor and is not influenced by reactant concentration. Reaction rate will be assumed here to be the maximum value in the entire reactor. When both carrier and enzyme are fresh, the rate of production of product in one module is VV,, where V is the volume of the module. A t the beginning of the ith cycle, the rate of production is VV,, exp[-(i - l ) k , 8 ] ,and thus the total production by this module during the entire ith cycle, Pi is given by
Pi
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Total production during all n cycles for this charge of carrier in this module, P,, is
Total production for the year for this module is Pnh/n%, and total production for all modules is N times this. Thus the volume of one module is
Optimization. The costs considered here are for enzyme, immobilization reagent, carrier, and reactor housing. Other costs are important in venture decisions, but for a study of the effects of the variables and an indication of future direction, these suffice. In terms of activity, the quantity of enzyme required in the immobilization for the ith cycle in VV,,, exp(-(i l)k,B), and the quantity required all year for all N modules is
(4) The quantity of immobilization reagent needed is presumed to vary with the binding capacity of the carrier. The total cost of the operation per year, C, including only the four costs noted above, is
Two cost parameters are defined rl = (CEV,,, 7.2
+ CRR)ks/C3
= CSkJC3
(6)
(7)
where
C3 = CHD(N + 1)/A Nh The optimization results which follow are determined by
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Ind. Eng. Chern. Process Des. Dev., Vol. 17, No. 4, 1978
Table I. Parameters Used in Design Calculations
CE,cost of enzymic activity
$0.6/106 units of immobilized activity CR,cost of cyanogen bromide $60/kg Cs, cost of carrier $6O/L CH,cost of installed reactor housing $ 2 0 0 0 0 / m of length D,rate of charging capital costs 0.3Iyear against production h, days of operation per year 300 N , number of series modules o n 10 stream A , cross section of module 0.66 m a
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Figure 5. Relation between cost parameter rl, cycle time, and rate constants which must be met in the optimization.
the values of these two parameters. Using these and the volume given by eq 3, total yearly cost is
cycle time
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n, number o f reuses of one charge of carrier 10 n e , total life of one charge of carrier 1.5 years V, volume of one module C, total annual cost percentage breakdown of costs enzyme cyanogen bromide carrier re actor housing
410 L $360000
0.1 44 45 11
The partial derivative of C with respect to n leads to the expression r2 = enkd - nk,d - 1
(9)
and the partial derivative with respect to d leads to
Simultaneous numerical solution of these equations leads to optimum values of n and 8. Substitution of these two equations into eq 8 gives C = PC3h exp(nk,d kd)/Vma, (11)
+
and this is the total cost when the optimum values of n and 8 are used. Equation 9 gives r2 as a unique function of the compound variable nk,8. Equation 10, however, is more difficult to appreciate. The family of curves obtained by numerical solution is brought together by noting that as k, approaches zero, the equation approaches the limit rle-nkcO = e k 0 - kfl - 1 (12) Numerical solutions of eq 10 for several values of k/kc are shown in Figure 5 plotted as k8 against the left side of eq 12, a form suggested by the limit as k, approaches zero. The limiting curve for k/k, = 00 is eq 12. It can be seen in Figure 5 that eq 12 is a good approximation to the more rigorous solution for the other values of k, also. Economic Effects of the Variables To find the consequences of the observations, reactors were designed to produce 10' lb/year of glucose (dry weight) from a 50 wt 70 solution of maltose at 95% conversion. The saccharification of liquefied starch by immobilized glucoamylase will probably have as its most expensive portion the final stages of the reaction, involving hydrolysis of maltose, so that the optimization of a reactor fed pure maltose serves as a first pass at the broader problem. Stability of the carrier, porosity of the agarose beads, and concentration of cyanogen bromide were singled out for study. In each case several values of the parameter
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were picked and the optimum values of cycle time, 8, and number of regenerations of a batch of carrier, n, were calculated using eq 9 and 10 and the cost was obtained from eq 11. Values of the parameters used are shown in Table I. Carrier Stability. To find the effect of carrier stability, optimum reactors were designed for the catalyst formed from 4% agarose using a number of different values for the first-order rate constant describing the degradation of the carrier. Results are shown in Figure 6. It is clear that the stability of the carrier has an important impact on the cost of the operation. This impact is heightened by the comparatively high cost of this particular carrier, but the conclusion will be substantially the same for any of the several carriers now being proffered by vendors for immobilization of enzymes. A summary of the results for the case klk, = 4 is given in Table 11. For the other studies presented below, the value of k / k c was arbitrarily set at 4, giving a half-life of carrier of 120 days. Agarose Concentration. Optimum reactors for the four concentrations of agarose studied were designed. Using the stability of each preparation as measured, the top line in Figure 7 was obtained. This shows that the
Ind. Eng. Chern. Process Des. Dev., Vol. 17, No. 4, 1978 405
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production cost goes up with increasing agarose concentration, contradicting the hypothesis with which the work started. However, the stability of the preparations decreased drastically with agarose concentration, as shown in Figure 4,and since this unreasonable result is probably caused by an imperfection in the cross-linking procedure developed for the 4% agarose, we also calculated optimum design and cost assuming that the stability of the catalyst remained constant a t the value for the 4% agarose. This gave the lower line in Figure 7, showing that cost could be decrease by using higher concentration agarose, provided the stability did not suffer. Cyanogen Bromide Concentration. The calculation was made for 4% agarose using the data of Sipe and Schaeffer (1973) on protein bound as a function of cyanogen bromide concentration. Results are shown in Figure 8. Least cost occurs a t a concentration of 160 g/L, about 60% of that a t which maximum activity was attained. Production cost is about 10% less than that a t maximum loading. Conclusions In the dextran work: (1)time needed for the reaction of the activated dextran with a small ligand that diffused into the interior was 3 h, whereas with a large ligand that did not, it was 1 h; (2) the amount of enzyme bound is a
strong function of the concentration of cyanogen bromide used in the activation; (3) roughly a monolayer of enzyme was bound; (4) finally, it appears that used enzymedextran can be put through the immobilization reactions with no previous treatment to get a catalyst with properties not different from the original. In the agarose work: (1) activity of glucoamylaseagarose reactors per unit volume of reactor increases with increasing content of agarose in the bead, confirming the original hypothesis; (2) however, stability decreases with agarose content, suggesting that the cross-linking procedure needs development. The design work yielded expressions giving optimum values of cycle time, 0, and number of reuses of carrier, n, as functions of two compound cost parameters. Designs of reactors based on the experimental data showed that: (1)carrier stability is crucial to success of an immobilized glucoamylase reactor; (2) agarose concentration is important, and offers the possibility of lowered expense of operation a t the higher concentrations; (3) cyanogen bromide concentration makes a small difference in costs. Nomenclature A = cross section of module C = total cost of production per year, $ CE = cost of enzymic activity CH = cost of installed reactor housing C R = cost of cyanogen bromide Cs = cost of carrier D = rate of charging capital costs against production h = days of operation per year k = first-order decay constant for activity, day-' k , = first-order decay constant for carrier capacity, day-' k , = sum of k and k , n = number of reactivations of a charge of carrier N = number of series modules on stream P = total production per year, lb of dry glucose rl, rz = cost parameters defined by eq 6 and 7 R = amount of cyanogen bromide used, kg/L of packed catalyst V = volume of one module, L V,, = activity of fresh catalyst, units/L of packed catalyst (the unit is 1 pmol/min of glucose produced) Greek L e t t e r 0 = time of operation before reactivating catalyst, days Literature Cited Axen, R., Porath, J., Ernback, S.,Nature (London),214, 1302 (1967). Beeley, J. G., McCairns, E., Biochim. Biophys. Acta, 271, 204 (1972). Caldwell, K. D., Axen, R., Porath. J., Biotechnol. Bioeng., 18, 433 (1976). Chibata, I., Tosa, T., in "Immobilized Enzyme Principles", L. Wingard, E. Katchalski-Katzir, and L. Goldstein, Ed., Academic Press, New York, N.Y., 1976. Chung, A. E., Middleditch, L. E., Arch. Biochem. Biophys.. 152, 539 (1972). Coughlan, M. P., Johnson, D. B., Biochim. Biophys. Acta, 302, 200 (1973). Gurne, D., Shernin, D., Science, 180, 1188 (1973). Lasch, J., Iwig, M., Lapidot, Y., Barziiay, I., J . Chromatogr., 71, 275 (1972). Marshall, J. J.. Rabinowitz, M. L., Biotechnol. Bioeng., 18, 1325 (1976). Porath, J., Janson, J.-C., Laas, T.. J . Chfornatogr., 60, 167 (1971). Sipe, J., Schaeffer, F., Appl. Microbial., 29,880 (1973). Sjoberg, 8.-M., Holmgren, A., Biochim. Biophys. Acta. 315 (1973). Smiley, K. L., Presentation at ACS Chemical Engineering Symposium, Purdue University, Jan 1974. Zaborsky, 0. R., Ogletree, J., Eiochirn. Siophys. Acta, 289, 68 (1972).
Received for review June 9, 1977 Accepted April 19, 1978
This work was supported by Grant GI-34919 from the Applied Research Directorate of the National Science Foundation, for which the authors express their appreciation.
