Studying Enzyme-Catalyzed Depolymerizations in Continuous

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Studying Enzyme-Catalyzed Depolymerizations in Continuous Reactors Alberto Gallifuoco,* Francesco Alfani, Maria Cantarella, and Paolo Viparelli Department of Chemistry, Chemical Engineering, and Materials, University of L’Aquila, 67040 Monteluco di Roio (AQ), Italy

The models of Ohmine et al. and Sendra and Carbonell for the enzymatic breakdown of polymers in batch reactors were modified to describe the depolymerization in continuous reactors. The model equations give the time course of the product concentration in the reactor permeate and that of the total product. The model predictions were compared with the experimental results for the hydrolysis of polygalacturonic acid in ultrafiltration membrane reactors. The amount of enzyme in the reactor varied from 0.18 to 1.80 mg. The residence time (100 min), temperature (25 °C), and membrane molecular cutoff (30 kDa) were maintained constant in the experiments. The system response was sensitive to the kinetic pattern of the enzymatic attack and was in reasonable agreement only with the predictions of the model based on the kinetic assumption made by Sendra and Carbonell. An induction period and an asymptotic amount of product were detected, which cannot be explained by the model of Ohmine et al. 1. Introduction Native biopolymers constitute an abundant and cheap feedstock in well-established processes. For example, starch, pectin, and cellulose have been employed in the agro-food industry and in other innovative processes. A partial depolymerization of the native macromolecules is generally important in improving their workability and reaching the required organoleptic quality of the final products. Processes are under development that require the complete hydrolysis of the cellulose and the production from pectin of high added-value oligomers (selected molecular weight). Chemical methods do not adequately ensure the control of the degradation mechanism, the high selectivity toward an expected category of oligomers, and the absence of undesired byproducts. In contrast, the enzymatic depolymerization is a very promising strategy, but the technology requires effort for its improvement. In the literature, models are available that simulate the mode of action of enzymes in depolymerization kinetics. The conversion process can involve more than one enzyme acting simultaneously. In addition, the biocatalyst activity can be very sensitive to the presence of several compounds, including intermediate and final reaction products that can be source of potential inhibition. At the same time, the adsorption of the enzyme on the substrate and its desorption from the exhausted biomass (hydrolyzed cellulose) can affect the overall rate of the process. Both physical phenomena and biocatalysis, therefore, control the productivity and yield of bioconversion. A comprehensive process development is complex to describe, and optimization of the simulation procedures is still required. Kinetic equations that aim to describe the time course of the molecular weight distribution in oligomer mixtures generated by enzymatic cleavage are difficult to use for reactor design and process optimization. The models contain a large number of parameters. Gener* To whom correspondence should be addressed. E-mail: [email protected]. Fax: 39-0862-434203.

ally, this ensures a good fit of the experimental data but also an unsatisfactory accuracy in process design. A reduction of the model variables can partly limit the problem. The simulation procedure involves lumped kinetics and continuous reactant distributions. This approach was originally developed for chemical reactions and relatively simple kinetics.1 More recently, the method was extended to complex reaction mechanisms2 and was also applied to the case of Langmuir-type catalytic processes, where nonlinear (hyperbolic) constitutive equations hold. The algebraic similarity of these kinetic equations to Michaelis-Menten kinetics suggested, in a previous study, that the same procedure be applied to a simple biocracking process.3 An adequate description of the biodegradation mechanism gave rise to very a concise and formally elegant model. However, integration of the differential equations generated “stiff” mathematical difficulties. An alternative approach would be to use empirical rate equations that introduce parameters devoid of physical significance. The pertinent models become poorly predictive and suffer from a lack of generality. However, these models show several interesting features, including (i) good agreement between model predictions and experimental results and (ii) simple use of the model equations. A paradigm of this model category is the equation originally adopted to describe the batch hydrolysis of cellulosic substrates with cellulase, where a rapid decay of biopolymer degradation rate is generally observed.4 This approach was recently employed with success in a study on the effect of the accumulation of exhausted biomass on the bioprocess rate.5 The bioconversion of pretreated wood to glucose and reducing oligomers was predicted with reasonable accuracy. The empirical model depicts fairly well the bioprocess dynamics, even though several phenomena, such as enzyme deactivation, end-product inhibition, and biocatalyst adhesion to the biomass surface, contribute to determine the effective rate of hydrolysis. This evidence justifies the interest in extending the use of this approach to the hydrolysis of other biopolymers. A third type of model has been developed. Such

10.1021/ie001053s CCC: $20.00 © 2001 American Chemical Society Published on Web 06/09/2001

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models represent a compromise between those of the previous two types. A discrete description of all of the species is made, but it is lumped over a selected range of oligomers. A theoretical analysis has recently been published.6 The study was undertaken for the case of a single-step, random attack on the macromolecule, which is the most common mechanism for endo-acting enzymes. The technique is very interesting because the time course concentration of oligomers below a threshold molecular weight can be predicted. All of the different models referred to above predict the results of experiments performed in batch reactors. In this study, the models were modified to describe the time course of enzymatic depolymerization in continuous reactors. The analysis was performed to characterize the continuous and stirred ultrafiltration membrane reactor (CSMR). This reactor configuration has proven to be a helpful tool for studying simple (one substrate) reaction kinetics.7 The CSMR was selected because the residence time and membrane cutoff represent two important additional process variables that affect the product distribution. The model was tested in the hydrolysis of polygalacturonic acid with a commercial enzymatic preparation. The reactor worked according to a semicontinuous configuration in that the liquid phase flowed continuously whereas the substrate was confined. 2. Materials and Methods All of the chemicals were reagent-grade and commercially available. Serva Fenbiochemica (Heidelberg, Germany) supplied polygalacturonic acid, with an average molecular weight (MW) of 30 kDa. The molecular weight distribution was determined before use following a procedure detailed elsewhere.8 The weight percentage of the fraction with MW > 30 kDa was 52.1%. The enzyme was a commercial preparation from Aspergillus japonicus (Pectolyase Y23, Sheishin Corp., Tokyo, Japan) and was used without purification. The enzymatic complex was not previously purified from pectin-lyase and pectin-esterase activities, because they cannot act on the substrate present in the reaction medium. All of the experiments were run in 25 mM sodium citrate buffer, pH 5.6. The reaction medium was modified by the addition of sodium ethylmercurithiosalicylate (10 mg L-1) to prevent microbial contamination. Experiments were carried out in a stirred CSMR (35 mL volume, 250 rpm) equipped with YM30 ultrafiltration membranes (30 kDa molecular weight cutoff, MWCO) from Amicon Grace (Danvers, MA). The cell was continuously fed with buffer using of a peristaltic pump (Gilson Minipuls 2, Villiers-le-Bel, France) that ensured the flow rate. The entire system was maintained at 25 °C by immersion in a thermostatic water bath. The reactor was loaded with a 5 g L-1 solution of polygalacturonic acid. Before the kinetic run, the system was flushed for roughly 20 h with buffer to remove the low-MW fractions from the substrate, which could be erroneously attributed to enzymatic breakdown. At the adopted conditions, when 400 mL of buffer were flowed, reducing groups were no longer detected in the reactor permeate, and the reaction was initiated by the addition of enzyme. A small volume (15 ÷ 60 µL) was injected through a multiport valve (Whitey, Highland Heights, OH) without releasing the flow. The total dead volume between the injection point and the reactor inlet was measured to calculate the transport lag phase and to determine the real initial

Figure 1. Diagram of the experimental apparatus: fraction collector (FC), reactor (Re), multiport valve (V), buffer reservoir (BR), peristaltic pump (P).

time of the reaction. Samples of reactor permeate were collected in a fraction collector (LKB, Piscatawy, NJ). The fraction time interval was sufficiently low (10 min) to assume that the measured mixing-cup product concentration was very close to the instantaneous concentration. The volume of each fraction was measured, and the reducing groups in the samples were determined by the Nelson-Somogyi method.9 A diagram of the experimental apparatus is shown in Figure 1. As the system operated under unsteady-state conditions during the entire hydrolysis period, the volume and the reducing group concentration of the different fractions do not allow for evaluation of the instantaneous rate of reaction because the product can also accumulate in the reactor. At any time, t, the following mass balance of product over the reactor provides the total amount of oligomers with MWs below the MWCO

VRr ) VR

dP + QP dt

(1)

where VR is the reactor volume, r is the reaction rate, P is the product concentration in the reactor permeate, and Q is the volumetric flow rate. For constant VR and Q, eq 1 can be manipulated into the integral form t dt + Q∫0 P dt ∫0t(VRr) dt ) VR∫0t dP dt

(2)

where the left-hand term of eq 2 represents the total amount of product, Np,tot, generated during the hydrolysis period. The two integrals on the right-hand side of eq 2 can be converted into discrete form and evaluated using the experimental curve of product concentration versus process time. 3. Model Equations The following empirical equation for the depolymerization rate was proposed for cellulosic substrates by Ohmine et al.4

dr ) -kr dX

(3)

where X is the substrate conversion (ratio of the instantaneous concentration of soluble oligomers, P, to the initial concentration of biopolymer substrate, S0) and k is an empirical proportionality factor that lumps the effects of all of the rate-depressing phenomena. The substrate mass balance over the batch reactor can be integrated with the initial condition, r ) r0 at t ) 0 to give

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P(t) )

(

)

S0 r0 log 1 + k t k S0

(4)

Equation 4 describes the buildup of the product concentration in the batch bioreactor. The rate of product generation in the CSMR can be obtained from the derivative of this equation with respect to time. The product mass balance in the continuous system can be written as

dP P + ) dt τ

r0

(5)

r0 1+k t S0

where τ is the residence time in the reactor. The two dimensionless variables θ ) t/τ and γ ) P/τr0 can be conveniently introduced, where γ represents the steadystate dimensionless concentration of product in the reactor permeate. The introduction of these dimensionless variables into the differential equation reduces the product mass balance to

dγ 1 +γ) dθ 1 + Aθ

(6)

where A is given by kr0τ/S0. Equation 6 has to be solved with the initial condition γ ) 0 at θ ) 0. Solving the integral of eq 6 requires knowledge of the incomplete gamma special function and would be of little use. In contrast, numerical integration readily yields the response curves as a function of the lumped parameter A. The term Aθ in eq 6 has an important meaning: it is the ratio of the retention time to the characteristic reaction time. Therefore, A determines the system response. The total amount of product generated during the hydrolysis period can be calculated from eq 2. Simple algebraic manipulations give the expression

1 Γtot ) log(1 + A) ) A

∫0tr dt r0τ

(7)

where Γtot is the dimensionless total product formed during the enzymatic depolymerization. A second depolymerization model was considered in this study. Sendra and Carbonell6 proposed a kinetic expression that describes the time course of oligomers with a selected range of MWs in batch reactors. Those authors tested the model with the experimental results for β-glucan depolymerization catalyzed by (1f3)(1f4)-β-D-glucan 4-glucanhydrolase (commercial licheninase). The reaction mixture was assayed with an analytical technique that allows for detection of the total amount of product above a threshold MW. In this study, we adopted an alternative technique for the separation and recovery of a selected fraction that is based on the use of a CSMR. This reactor configuration represents a simple tool for the separation of a reaction mixture into two fractions, one below and one above the MWCO of the membrane. The model of Sendra and Carbonell6 was adapted to describe the behavior of the continuous reactor. The time-course equation of the product concentration in batch reactors6 is

P ) P0[1 - e-Rt(1 + Rt)]

(8)

where P0 is the highest concentration of oligomers that

Figure 2. Model results (Ohmine et al.6) for polymer breakdown in a CSMR: product concentration in the reactor permeate (solid lines), total product (dashed lines).

can be achieved for complete depolymerization and R is a lumped kinetic parameter, a characteristic reaction frequency, that is defined by

k3E0 R ) MWt Km + P0

(9)

In eq 9, MWt is the threshold value, k3 is the catalytic constant, E0 is the total amount of enzyme, and Km is an overall Michaelis-Menten constant. Of course, this analysis is correct if the rate of reaction is mechanisticly independent of the product concentration. Taking the derivative with respect to time of eq 8 and substituting it into the product mass balance, eq 2, yields an expression for the dimensionless product concentration, ω, in the CSMR

ω)

ξ 2 -θ P ) {e - [1 + θ(ξ - 1)]e-ξθ} P0 ξ-1

(

)

(10)

where ξ is equal to Rτ and θ is the previously defined time ratio. The system response depends on the lumped parameter ξ, which is the ratio of the retention time in the reactor, τ, to the characteristic reaction time (1/R). The introduction of the new variables into eq 2 gives the following dimensionless equation for the time course of the total amount of product in a continuous reactor

Ωtot ) 1 - eξθ(1 + ξθ) )

∫0tPP0dt τ

(11)

4. Results and Discussion Figure 2 shows some model results for polymer depolymerization in the CSMR calculated with the kinetic assumption of Ohmine et al.4 The time courses of the dimensionless instantaneous concentration of product in the reactor permeate, γ, and of the dimensionless total amount of product are plotted as functions of the lumped model parameter A. The concentration in the reactor permeate, γ, tends asymptotically to 0 for θ f ∞, as the substrate initially loaded into the reactor is completely consumed. A ) 0 depicts the case of a constant depolymerization rate. It is notable that A )


Figure 3. Model results (Sendra and Carbonell6) for polymer breakdown in a CSMR: product concentration in the reactor permeate (solid lines), total product (dashed lines).

0 is the condition leading to the highest value of the dimensionless product concentration, γ ) 1. The results show the interrelationship between A and product formation. The higher the value of A, the lower the maximum product concentration in the reactor permeate and the time at which it appears. The total product formed (total oligomers) was calculated through eq 7. Γtot does not reach an asymptotic value, regardless of the value of the lumped parameter A. This finding is in agreement with the behavior reported in the literature for a batch reactor.4 In fact, the algebraic expression obtained in our study for the CSMR is similar to that reported in the literature for a batch reactor substituting the reaction time, t, with θ ) t/τ. The response of the continuous system, therefore, suffers from the same inaccuracy as the batch reactor. Clearly, the amount of product collected in the permeate fractions cannot exceed the amount of substrate initially charged in the reactor. The above analysis indicates that the model curves cannot fit the experimental data in the continuous reactor for long depolymerization periods. For very short process times, the hydrolysis behaves as an autocatalytic reaction. The first cleavages of the biopolymer molecule generate other high-molecularweight substrates that can be further attacked by the enzyme. The production of low-MW compounds is rather limited. This ensures that the enzyme does not operate under conditions of limited substrate concentration. The model response should predict this “induction period”. This result cannot be obtained with the Ohmine model. By contrast, this evolution time is well predicted by the model of Sendra and Carbonell6 in batch reactors. The latter model also takes into account the fact that, for long reaction times, the total concentration of oligomers available for enzymatic attack is reduced because the number of cleavages decreases to a very low level and the depolymerization kinetics tends to slow. Consequently, the second part of the simulation study was devoted to a modification of the model developed by Sendra and Carbonell6 to the case of the CSMR. Figure 3 shows the simulated evolution of the dimensionless instantaneous concentration of product, ω, and total product, Ωtot, versus depolymerization time. As can be seen, the system response was very similar to that reported in Figure 2. At the early stages of the reaction, the product concentration increases and reaches a

maximum. The value and the time at which the maximum occurs depend only on ξ. The higher the value of ξ (reaction time smaller than retention time), the earlier the appearance of the maximum, and the higher its value. At long reaction times, the product concentration tends to vanish because the depolymerization of the substrate initially loaded in the reactor is almost complete. The simulated evolution of the system response is described by sigmoids. Thus, the presence of an induction period is detected. The abscissa of the inflection point depends on ξ and is coincident with the time at which the maximum occurs in the corresponding curve for the product concentration. Another part of this study was devoted to a test of the fit between the experimental and simulated curves. The hydrolysis of polygalacturonic acid was performed with a commercial preparation of pectolytic enzyme. Polygalacturonic acid was chosen as the model substrate, because this native polymer has a purely linear chain and its breakdown is catalyzed by only one enzyme. The depolymerization of other native macromolecules (pectin, cellulose, hemicellulose) would be interesting to model, but the presence of hairy regions (pectin), the low solubility of the substrates, and/or the action of multienzyme complexes (pectinases and cellulases) discouraged their use in this study focused on a comparison between batch and continuous reactors. The mathematical simulation and the experiments of the hydrolysis of other biopolymers that are largely employed in industrial processes could represent the next step of this investigation. On the other hand, oligomers obtained from the degradation of polygalacturonic acid are interesting for the production of new surfactants. In addition, a partial and controlled degradation is important for the improvement of the industrial filtration of clouded juices.10 It is worth emphasizing that, in addition to the kinetic pattern, several process parameters, i.e., retention time, membrane cutoff, enzyme-to-substrate ratio, and initial substrate concentration, could affect the bioconversion in the continuous reactor. Consequently, the experiments should be planned to determine the effect of each variable on the bioconversion and to test the model simulation of the enzymatic breakdown with the individual results. In this work, the predictions of the two models were compared with data from the depolymerization of polygalacturonic acid to ascertain the kind of kinetic equation that is likely to apply. To produce a consistent set of data, the experiments were performed with different amounts of enzyme in the reactor (from 0.18 to 1.80 mg). All other process parameters were kept constant. Figure 4 gives a typical plot of the product concentration in the reactor permeate as a function of bioconversion time. The retention time was kept constant at about 100 min in all of the experiments. This is an optimization between the need to recover a sufficient specimen during the collection time while avoiding the enzyme deposition onto the membrane surface (polarization) that occurs at higher liquid flow rates. The reaction was initiated by the addition of 0.90 mg of the enzymatic preparation. The product concentration was assayed as molar concentration of the reducing groups. The model of Ohmine et al.4 assumes a kinetic equation based on the hypothesis of a progressive decay of the reaction rate from its initial highest value to zero.

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Figure 4. Experimental time courses of product concentration (2) and total product (4). Mathematical simulation with Ohmine et al.4 model (dashed lines) and with Sendra and Carbonell6 model (solid lines).

In contrast, the equation of Sendra and Carbonell6 predicts that an autocatalytic reaction occurs at short depolymerization times. An increase in the rate of oligomer production is followed by a progressive decline. Simulation curves of product concentration in the reactor permeate and of the total product can provide a clear interpretation of the true mechanism. The solid lines in Figure 4 are the results of the Sendra and Carbonell6 model simulation, which show reasonable agreement with the experimental data. In contrast, the dashed lines are the results for the Ohmine et al.4 model, which show a poor fit to the experimental data (both r0 and k determined by data fitting). The following discussion aims to elucidate the observed shape of the curves. At very short process times, the product concentration increases because the rate of product generation is higher than the rate of product removal from the reactor. The characteristic reaction time being smaller than the residence time, the product tends to accumulate in the reactor. As the experimental conditions assure the presence of a well-mixed liquid phase, the product concentration in the permeate flux also increases. At long process times, the substrate in the reactor is almost completely converted, and the previous condition on the characteristic times no longer holds. Therefore, the product concentration in the permeate tends to zero. The two opposite phenomena, product generation and product removal, provide bell-shaped curves for different sets of the parameters. The locus of the maximum depends on the reactor volume, the flow rate, the initial substrate concentration, the enzyme concentration, and the other physicochemical parameters of enzyme kinetics, i.e., temperature, pH, and Michaelis-Menten constant. Equation 2 was used to evaluate the total product formed as a function of the depolymerization time. As can be seen, the Np,tot curve is depicted well by a sigmoid. This confirms that the hydrolysis of polygalacturonic acid occurs in reasonable agreement with the model of Sendra and Carbonell6 and not with that of Ohmine et al.4 In fact, the latter model cannot explain the sigmoidal behavior or the observed asymptotic limit of product formation. In Figure 5, the diagram of Ωtot refers to four enzyme amounts of 0.18, 0.45, 0.90, and 1.80 mg in the reactor. The asymptotic values of the total product, Np,∞, were

Figure 5. Experimental time course of total product. Mathematical simulation with Sendra and Carbonell model.6 Enzyme amount in the reactor: O, 1.80 mg; 4, 0.90 mg; 0, 0.45 mg; ∇, 0.18 mg. Table 1. Model Predictions and Experimental Values of Lumped Parameter ξ E0 (mg)

ξexp

ξexp/ξ0.45

ξmod/ξ0.45

0.18 0.45 0.90 1.80

0.48 0.95 1.63 1.81

0.51 1.00 1.72 1.91

0.40 1.00 2.00 4.00

determined from the experimental data at each enzyme concentration, and the ratio of Np,tot to Np,∞ was calculated. As the above discussion noted, only the model of Sendra and Carbonell6 is in reasonable agreement with the curves of Np,tot, the values of Np,tot/Np,∞ were compared with Ωtot values predicted by the simulation of their model. The experimental profiles of total product versus time indicate that the model must predict an induction period. This observation, therefore, is a further confirmation that the model of Ohmine et al.4 cannot be adopted for describing the enzymatic depolymerization of polygalacturonic acid. As expected, ω attained a maximum within the range 4 < θ < 7 depending on the biocatalyst concentration (data not shown). As the volumetric flow rate was constant while the reaction rate varied, the higher the amount of enzyme, the lower the duration of the phenomenon. The time of the inflection point of each sigmoid (coincident with the abscissa of maximum in the ω curve) depended on the enzyme amount loaded in the reactor. This result is predicted by the model of Sendra and Carbonell6 (see Figure 3), which states that the inflection time is inversely proportional to the lumped parameter ξ and, hence, to the enzyme amount, E0. The model results are listed in Table 1. Column 2 reports the value of ξexp, which was estimated through the fitting of the data. Column 3 reports the ratio of ξexp to ξ0.45 (reference experiment) calculated from the values of column 2. The bioconversion run with 0.45 mg of enzyme was selected as the reference experiment because the model prediction showed the best fit of the experimental data for this run. Column 4 reports the same ratio, ξexp/ξ0.45 determined on the basis of the enzyme concentrations in the different runs and the model assumption. The results in Table 1 and the curves in Figure 5 show that the kinetic assumption made in the model of


Sendra and Carbonell6 can be considered valid and that the mathematical simulation indicates biopolymer breakdown in continuous enzymatic reactors. The most important deviations of the model predictions from the experimental data were observed at the smallest (0.18 mg) and largest (1.80 mg) enzyme amounts in the reactor (see Figure 5 and Table 1). An exact interpretation is not yet possible; however, the following discussion aims to provide a rather plausible analysis. In experiments at high enzyme concentrations, a partial segregation of the biocatalyst on the membrane can occur in well-stirred reactors. Aliquots of enzyme remain free in solution and can catalyze polymer breakdown. This could explain why the curves in Figure 5 for E0 ) 0.90 mg and E0 ) 1.80 mg are almost superimposable and why the time of the inflection point of the sigmoid (Table 1) does not vary with changes in the enzyme amount. Another partial inaccuracy could be related to the product assay. The adopted colorimetric method allows for detection of the reducing power of the mixtures irrespective of the molecular weight of the molecules. In contrast, the experimental results showed that the MWs of the oligomers varied in the fractions collected using different reaction periods. At very short process times, the MW was higher than that in the last stages of the degradation. This was demonstrated through the addition of a large amount of enzyme (0.75 mg) to the fractions collected at θ ≈ 2 and θ ≈ 5. Complete depolymerization of the oligomers occurred. The increase in the reducing power of the first fraction (θ ≈ 2) was 2.6 times higher than that of the second fraction (θ ≈ 5), thus indicating that a larger amount of smallmolecular-weight oligomers was produced. Finally, inspection of eq 11 gives a further explanation of the observed discrepancy between the experimental results and the model predictions. The dimensionless total product apparently depends only on the parameter ξ because the asymptotic value is theoretically equal to 1; of course, this is the same for all of the curves. In batch reactors, the mass balance can predict the asymptotic amount of generated product because the initial amount of substrate in the reactor is known. In contrast, this is not the case in continuous reactors. The initial amount of substrate in the reactor is still known, but the total product collected in the reactor permeate does not represent a true end-point value. In fact, molecules with MWs lower than the membrane cutoff can leave the system at any time and no longer react in the collector volumes. These oligomers, therefore, increase the signal with the contribution of only one reducing group, regardless of the number of monomeric units in the molecule. At the end of the run, the total reducing power depends on the balance between the residence time of degradable molecules in the reactor and the characteristic reaction time, which is determined by both the enzyme concentration and the instantaneous substrate concentration. Therefore, at any reaction time, the system appears to operate at different values of the expected final amount of product. 5. Conclusions Enzymatic depolymerization can be successfully studied in a continuous reactor equipped with an ultrafiltration membrane. This reactor configuration has been shown to be suitable for detecting the time course of a selected range of oligomers, i.e., those with molecular weights smaller than the cutoff of the membrane.

Models already present in the literature for enzymatic depolymerization in batch reactors can be modified for simulation of the behavior of continuous reactors. Overwhelming mathematical difficulties are not generated. The simulation can be also applied to the modeling of bioconversion in semicontinuous reactors (continuous for the liquid phase and discontinuous for the solid substrate). The system response in the CSMR is sensitive to the kinetic pattern of enzymatic attack and detects the presence of an induction time due to the initial accumulation of oligomers capable of undergoing further hydrolysis. Experimental results for the depolymerization of a model substrate (polygalacturonic acid) are in reasonable agreement with the predictions of the model based on the kinetic assumption made by Sendra and Carbonell6 in their mathematical simulation. The effect of the enzyme concentration on the time evolution of the product concentration in the reactor permeate and the total product confirms the dependence of the model lumped parameters on the amount of enzyme in the reactor. There is a need for improvement of the model. The asymptotic amount of generated product must be related to the operating conditions. It is crucial that the variation of the product end point during process evolution be introduced. The new development has to be preceded by further experiments performed by varying the residence time in the reactor, the cutoff of the membrane, and the initial amount of substrate in the reactor. Acknowledgment Funding was provided by the Ministry of Research for Science and Technology (MURST-PRIN/98). Paolo Viparelli received a research fellowship from the University of L’Aquila, L’Aquila, Italy. Nomenclature A ) lumped model parameter E0 ) enzyme concentration, kg m-3 k ) empirical kinetic constant k3 ) catalytic constant, s-1 Km ) overall Michaelis-Menten constant, kg m-3 MWt ) threshold molecular weight, kg kmol-1 Np,∞ ) end point of total generated product, mol Np,tot ) total generated product, mol P ) product concentration, kg m-3 P0 ) end point of product concentration, kg m-3 Q ) volumetric flow rate, m3 s-1 r ) generic reaction rate, kg m-3 s-1 r0 ) initial reaction rate, kg m-3 s-1 S0 ) substrate initial concentration, kg m-3 VR ) reactor volume, m3 X ) substrate conversion Greek Letters R ) model regrouping, s-1 γ ) product concentration in Ohmine model Γtot ) total product in Ohmine model θ ) process time τ ) retention time, s ω ) product concentration in the Sendra model Ωtot ) total product in the Sendra model ξ ) model regrouping

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Literature Cited (1) Aris, R.; Gavalas, G. R. On the Theory of Reactions in Continuous Systems. Philos. Trans. R. Soc. 1966, A260, 351. (2) Astarita, G.; Ocone, R. Lumping Nonlinear Kinetics. AIChE J. 1988, 34, 1299. (3) Cicarelli, P.; Astarita, G.; Gallifuoco, A. Continuous Kinetic Lumping of Catalytic Processes. AIChE J. 1992, 38, 1038. (4) Ohmine, K.; Ooshima, H.; Harano, Y. Kinetic Study on Enzymatic Hydrolysis of Cellulose by Cellulase from Trichoderma viride. Biotechnol. Bioeng. 1983, 25, 2041. (5) Desai, S. G.; Converse, A. O. Substrate Reactivity as a Function of the Extent of Reaction in the Enzymatic Hydrolysis of Lignocellulose. Biotechnol. Bioeng. 1997, 56, 650. (6) Sendra, J. M.; Carbonell, J. V. A Theoretical Equation Describing the Time Evolution of the Concentration of a Selected Range of Substrate Molecular Weights in Depolymerization Processes Mediated by Single-Attack Mechanism Endo-Enzymes. Biotechnol. Bioeng. 1998, 57, 387.

(7) Alfani, F.; Cantarella, L.; Gallifuoco, A.; Cantarella, M. Membrane Reactors for the Investigation of Product Inhibition on Enzyme Activity. J. Membr. Sci. 1990, 52, 339. (8) Dinnella, C.; Stagni, A.; Lanzarini, G.; Alfani, F.; Cantarella, M.; Gallifuoco, A. Pectin Degradation in UF-membrane Reactors with Commercial Pectinases. Pectin and Pectinases; Visser, J., Voragen, A. G. J., Eds.; Elsevier Science: New York, 1996; p 439. (9) Nelson, L. A Photometric Adoption of the Somogyi Method for the Determination of the Glucose. J. Biol. Chem. 1944, 153, 375. (10) Thomas, L.; Hohn, A. As cited in Todisco, S.; Calabro`, V.; Iorio, G. A kinetic model for the pectin hydrolysis using an endoacting pectinase from Rhizopus. J. Mol. Catal. 1994, 92, 333.

Received for review December 4, 2000 Accepted April 23, 2001 IE001053S

Studying Enzyme-Catalyzed Depolymerizations in Continuous

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