New Experimental Procedure for Monitoring Molecular Weight

membrane molecular weight cutoff (30 kDa) were kept constant. The time course of the oligomeric product concentration in the output solution was corre...
0 downloads 0 Views 91KB Size
Download PDF
Ind. Eng. Chem. Res. 2003, 42, 3937-3942

3937

New Experimental Procedure for Monitoring Molecular Weight Breakdown during Enzymatic Degradation of Polygalacturonic Acid in Continuous Membrane Reactors Alberto Gallifuoco,* Francesco Alfani, Maria Cantarella, and Paolo Viparelli Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universita` degli Studi di L’Aquila, 67040 Monteluco di Roio (AQ), Italy

The enzymatic depolymerization of polygalacturonic acid was studied in a continuous stirred UF membrane reactor. Experimental data were obtained in different runs with varying amounts of biocatalyst from 0.25 to 1.35 mg. The residence time (1.7 h), temperature (25 °C), and membrane molecular weight cutoff (30 kDa) were kept constant. The time course of the oligomeric product concentration in the output solution was correlated with a model equation, that was originally developed for batch reactions and modified for the continuous system. A new experimental method was used to detect the instantaneous mean molecular weight. Evidence was obtained that the enzymatic breakdown was almost complete within 2-3 h from the startup of the bioreaction. The proposed method proved to be sufficiently accurate and easy to employ for rapid on-line control of the industrial bioprocess. 1. Introduction Pectic substances, such as pectin and polygalacturonic acid, are widely contained in several fruits and vegetables and are particularly abundant in wastes. As an example, pectin represents roughly 6% by dry weight of oranges, but the peel alone contains this biopolymer up to 30 wt %. Only a minor fraction of pectic substances is currently recovered and recycled as additives for the agro-food industry. To improve the workability of the native biopolymers, treatments are required that modulate some physical and chemical properties (viscosity of the solutions, gelling properties, etc.) through partial degradation. Biological treatments could ensure a more precise control of the degradation than chemical treatments, and consequently, enzymatic purification of the macromolecules from the raw materials and their biotreatment have already been assessed and widely described in the literature.1 The total availability of pectic substances is much higher than the demand, and the surplus represents a waste material that could be exploited. Specifically, polygalacturonic acid (PGA) could represent an important resource for high-value-added products. This biopolymer is required at selected degrees of polymerization and polydispersities both as a native macromolecule and as a derivative for diagnostic and pharmaceutical applications.2,3 In these cases, monitoring of the molecular weight distribution during biological treatment is of paramount importance, and quite sophisticated analytical techniques have been proposed, such as highperformance size-exclusion chromatography3 and spectrofluorimetry coupled with flow injection analysis.4 The almost complete biodegradation of the macromolecule could also be of industrial interest, as some galacturonic oligomers can be used in the synthesis of new surfactants5 or as molecular tools for studying physiological mechanisms of plant host defense.6 Oligomers above * To whom correspondence should be addressed. E-mail: [email protected]. Fax: ++39-0862-434203.

three units are not commercially available. Only preparative-scale separations and isolations (milligram quantities) up to 20 units have been proposed.7 The biological depolymerization is catalyzed by endo-polygalacturonase (E.C. 3.2.1.15), which acts on the macromolecules through random endo-cleavages. Detailed knowledge of the kinetic mechanism of enzyme action would facilitate the development of constitutive kinetic equations that accurately describe the reaction progress and the development of these high-value-added processes. Different models are available in the literature for biopolymer degradation, and some predict fairly well the time course of the bioreaction in batch reactors. The control of the selectivity toward some classes of oligomers could be doubtful in batch reactors, where the only true degree of freedom to design is the reaction time. Moreover, to reduce process costs, the enzyme should be recovered at the end of the batch, and this could be satisfactorily achieved employing a continuous stirred reactor equipped with an ultrafiltration membrane (CSMR). This reactor, fed with fresh substrate according to an optimal policy, could theoretically operate at steady state and ensure the continuous recovery of oligomers of selected molecular weight with the permeate solution. A long optimal process time could be assured with a reasonable enzyme stability, a balance between the reaction rate and the feed rate, an appropriate choice of membrane molecular weight cutoff (MWCO), and an optimal retention time. With these conditions satisfied, the output stream of the continuous reactor should consist of a high-concentration mixture with a narrow molecular weight distribution. Such a continuous system is rather complex, and its optimization is possible only if the effects of each parameter on PGA degradation kinetics and product distribution are well understood. Our earlier study8 demonstrated the possibility of modifying models originally developed for batch reactor to describe the time course of enzymatic depolymerization in CSMR reactors. This study presents a more indepth investigation of the bioreaction. The experiments

10.1021/ie0210208 CCC: $25.00 © 2003 American Chemical Society Published on Web 07/29/2003

3938

Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003

were performed at constant temperature and residence time in a continuously operating stirred reactor equipped with an ultrafiltration (UF) membrane with an MWCO of 30 kDa. The amount of catalyst was varied from 0.25 to 1.35 mg to modulate the size of the oligomers leaving the reactor. The new experimental data are also well fitted using the model previously selected as the more suitable.8,9 A procedure was developed for detecting the time course of the average molecular weight in the permeate solution. The method is quite simple, does not require the use of sophisticated analytical techniques, and could easily be employed in industrial settings for the economical on-line control of the process. 2. Materials and Methods Reagents. All experiments were performed with reagent-grade, commercially available chemicals. PGA (Serva Fenbiochemica, Heidelberg, Germany), average molecular weight 30 kDa, was previously characterized for molecular weight distribution according to a procedure detailed elsewhere.6 The enzymatic complex was from Aspergillus japonicus (Pectolyase Y23, Sheisin Corp., Tokyo, Japan). The commercial preparation also contains pectin lyase and pectin esterase, but because their respective substrates were absent in PGA, these enzymes did not interfere with the determinations described herein. The kinetic runs were performed in 25 mM sodium citrate buffer, pH 5.6, modified by the addition of 10 mg L-1 of sodium ethylmercurithiosalicylate (Sigma, St. Louis, MO) to inhibit microbial contamination. Bioreactor Runs. The reactor was a stirred cell (35mL volume, magnetic bar, 250 rpm) equipped with a flat ultrafiltration membrane (YM30, Amicon Grace, Beverly, MA). The membrane molecular weight cutoff was selected at 30 kDa, thus ensuring complete retention of the enzyme and permeation of the oligomeric product solution. The flow rate was controlled at 20 mL h-1 with a peristaltic pump (Gilson Minipuls 2, Villiers le Bel, France). The reactor was loaded with 35 mL of a 5 g L-1 PGA solution (total substrate amount ) 175 mg). The device was flushed overnight with buffer to remove the low-molecular-weight fractions already present in the native substrate and previously estimated as 47.9 wt % of the total.8 When no more reducing groups were detected in the outlet solution, the kinetic run was started with a small volume (15-60 µL) of enzyme solution, injected through a multi-port valve (Whitey Co., Highland Heights, OH) without releasing the flow. The injection procedure was tested, and the system response turned out to be very close to that of an ideal impulse with a transportation lag time (10 min) due to the distance between the port and the reactor inlet. This delay was taken into account in the data analysis. The whole system, reactor and buffer reservoir, was maintained at 25 °C by immersion in a thermostatic water bath (Haake, Karlsruhe, Germany). Assay Procedure. The permeate solution was collected in small fractions by means of a fraction collector (LKB, Piscatawy, NJ). The volume of each fraction was measured, and a sample was assayed for reducing groups according to the Nelson-Somogyi method.10,11 The product concentration P is evaluated as galacturonic acid equivalents, i.e., the reducing power is referred to a calibration curve obtained using the monomer as the standard. Successively, an aliquot of 980 µL from each fraction was mixed with 20 µL of fresh enzyme (30 mg/mL), and

the mixture was left overnight at room temperature to achieve complete conversion. The large excess of enzyme (roughly 40 times the amount present in the membrane reactor) ensured that the depolymerization proceeded to completion: the mean molecular weight was continuously decreased to the end point, where no more cleavage could occur. The reducing groups were then again assayed. Experimental Data Elaboration. The total number of moles of oligomers produced (N) is calculated at each time from k

N)

ViPi + VRPk ∑ i)1

(1)

where Vi and Pi are the volume and product concentration of the ith fraction, respectively; VR is the reactor volume; and k labels the current fraction. The mathematical procedure underlying eq 1 is detailed elsewhere.8 Because each oligomer contributes one reducing group independently of its molecular weight, the reducing power of the specimen after the end-point treatment (E) is always greater than that assayed after the enzymatic breakdown occurred into the continuous reactor (P). The fractional increase (X) is calculated according to the formula

X)

E-P P

(2)

The X value is directly related to the mean molecular weight of the collected fraction. As a result, the higher the X value, the higher the number of further cleavages necessary to reach the end point. This is true regardless of the size of the oligomer recognized as the “end point” by the enzyme. For example, the monomer (molecular weight ) 194 g/mol) cannot be obtained by an endocleavage because the minimum size of a molecule, still degradable by the enzyme, is four units. Whatever the end point, each cleavage introduces a molecule of water, and the molecular weight of a generic polymeric chain (MW) is given by

MW ) 194U - 18(U - 1)

(3)

where U is the number of monomer units of the chain. One can easily see that X should be directly proportional to an integer number given by

(

X ∝ int

)

U -1 Ue

(4)

where Ue is the number of units of the end-point oligomer. According to the above analysis, the time course of X should vary similarly to the instantaneous mean molecular weight of the mixture outflowing the reactor and, consequently, monitoring of this quantity is easy. 3. Results and Discussion The kinetic runs hereafter discussed were performed in a CSMR at standard operating conditions with 175 mg of PGA but varying enzyme loadings from 250 to 1350 µg. The reactor was operated in two modes: batchwise with respect to the biocatalyst and the polymeric substrate, which are both retained by the membrane, but continuously with respect to the oligo-

Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 3939

Figure 1. Output product concentration as a function of dimensionless time. Enzyme loading (µg): 4, 250; 0, 750; O, 1050; ], 1350. Solid lines: data correlation. Dotted line: locus of maxima. Dashed lines: model simulations for 150 µg (lower line) and 2500 µg (upper line) of enzyme.

Figure 2. Values of model correlation parameters as a function of enzyme loading. Left y axis, ξ (0); right y axis, W (b). Solid lines represent second-step correlations.

mers, smaller than the MWCO of the membrane that are produced by the enzymatic reaction. The characteristic time of contact between enzyme and oligomers, set constant at 1.7 h for all experiments, is given by the mean retention time (τ), i.e., the ratio of the reactor volume to the buffer volumetric flow rate. The characteristic time of reaction, in contrast, depends on the enzyme specific activity and is inversely proportional to the amount of biocatalyst loaded into the reactor. Certainly, one might expect substantial variations in the system response and in the molecular weight distribution of products collected, if the enzyme concentration were varied and all other operational parameters were kept constant. The experimental data obtained in this series of experiments are reported in Figures 1 and 2. The data in Figure 1 refer to the instantaneous product concentration (P) detected in the output solution

as a function of dimensionless process time (θ ) t/τ). The autocatalytic behavior of the system appears evident as the signal tends initially to increase as a consequence of oligomer accumulation in the reactor. The intermediates produced during the bioreaction are, in turn, recognized as substrate by the enzyme and undergo further degradation. As the reaction proceeds, however, the mean molecular weight of the mixture decreases, and more oligomers can permeate through the membrane and leave the system. This tends to depress the substrate concentration in the reactor, and consequently, the reaction rate decreases. Asymmetrical bell-shaped curves are therefore expected. The solid lines in Figure 1 represent the correlation curves calculated using the model of Sendra and Carbonell.8 The model represents the experimental data quite well. Some minor discrepancies between the calculated curves and the response of the bioreactor can be observed, mainly in the vicinity of the peaks, thus indicating that some modification of the model is required to improve the agreement. Nevertheless, for the data discussed here, the fit is satisfactory, and one can assume that the time course of the product concentration in the permeate solution follows the model equation

(ξ -ξ 1) {e 2

P(t) ) W

] }

t / - 1 + (ξ - 1) e-ξt/τ τ

-t τ

[

(5)

where ξ is a lumped parameter equal to Rτ and R is a characteristic reaction frequency. W is directly related to the highest concentration of oligomers that can be achieved when the whole amount of substrate initially present into the reactor has been converted to products with molecular weights lower than the membrane cutoff. It does not represent the end-point value of the product concentration, which can be only attained in a batch reactor (τ f ∞), where, by definition, all of the intermediates remain available for further cleavage. In the membrane reactor, oligomers that can permeate tend to leave the system, and W is expected to depend on the relative values of the reaction rate and the output rate. The two correlation parameters, W and ξ, were calculated using the model equation (eq 5), and their numerical values for the kinetic runs are reported in Figure 2 as a function of the mass of enzyme loaded into the reactor (ME). Both parameters appear to increase almost linearly with biocatalyst loading. However, this trend cannot be valid for any mass of enzyme, because both parameters must be zero in the absence of biocatalyst. Imposing this condition, the best fits were calculated using hyperbolas (full lines) that asymptotically tend to the straight lines according to the following relationships

ξ)

A1ME + A3ME A 2 + ME

W)

A1ME + A3ME A 2 + ME

(6)

where A1, A2, and A3 are the correlation parameters. To improve the confidence of these latter regressions, more experimental data are required, especially with small amounts of enzyme. Unfortunately, kinetic runs with such low amounts of biocatalyst are hampered by the sensitivity limit of the experimental measuraments. On the other hand, a potential industrial process will

3940

Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003

Figure 3. Instantaneous product concentration (b, left y axis) and variable X (O, right y axis) as a function of dimensionless time. Enzyme loading ) 750 µg.

never operate at low enzyme concentration because of the unsatisfactory productivity. Thus, the range of biocatalyst mass explored here is sufficient for design purposes. The data in Figure 1 also show that the time of appearance of the maximum overall concentration in the solution (t*) depends on the amount of biocatalyst loaded into the reactor: the higher the enzyme concentration, the shorter the time. The locus of maxima was calculated using the W and ξ values estimated by the correlations of Figure 2 and is also plotted in Figure 1. This curve is very close to that joining the experimental maxima and hence predicts the data quite well. In addition, as an estimate to verify the correctness of our model, two further curves were generated simulating enzyme loadings outside the range explored experimentally (namely, 150 and 2500 µg). These simulations are reported in Figure 1 (dashed lines) and agree well with the trend of the experimental curves, with the maximum even falling perfectly on the locus of maxima. Therefore, the conclusion was reached that this kind of experiment and data organization allows for the prediction of the process time that maximizes the overall productivity for a given amount of biocatalyst loaded in the reactor. In fact, to sustain the reaction for a long time in a continuous process, the feed rate of fresh substrate should be adjusted to obtain τ/t* ≈ 1. Complete optimization of the bioconversion to give products of designed molecular weight requires more knowledge about the rate of the degradation reaction and the time course of the molecular weight of the mixture. As mentioned in the Introduction, in many industrial processes, control of product molecular weight would be advantageous. The membrane reactor would not operate at the optimal productivity, but a high selectivity toward valuable classes of oligomers could be assured. To explore this possibility, the end-point concentration of each fraction collected was evaluated following the procedure detailed in the Materials and Methods section. Figure 3 reports typical results and refers to a run with 750 µg of enzyme. The diagram shows the time course of the product concentration (P) and, superimposed, that of X (as evaluated by eq 2). In

Figure 4. Synopsis of the value of variable X at different times (min) of hydrolysis as a function of enzyme loading (µg). Lower plot, short reaction time ([, 40; 9, 70; b, 100; 2, 130). Middle plot, intermediate reaction time (], 160; O, 190; 4, 220; 3, 250). Upper plot, long reaction time (2, 280; b, 310; 9, 340; [, 370).

this experiment, the parameter X is as high as 11 in the initial time of reaction and tends to decrease monotonically to roughly 3. According to our analysis, this would correspond to a decrease by a factor of 4 of the mean molecular weight of the products during the entire run. Quite interestingly, the product concentration is at its maximum value after roughly 2 h, when the breakdown seems to be almost completely achieved. These results support those reported in the literature on the biodegradation of pectic substances in batch reactors. In these earlier studies, the most widely adopted technique for following the time course of the breakdown is based on the loss of solution viscosity.12,13 Generally, the observed decrease in viscosity is faster than the increase in reducing power. This obviously means that viscosity is very sensitive to the length of the polymeric chains, which drops rapidly in a narrow range without contributing significantly to an increase in the concentration of reducing units of the solution. The rapid decrease of X was reproduced in all runs, independently of the amount of enzyme loaded into the bioreactor. This is well illustrated in Figure 4, which reports the values of X observed at fixed reaction time (from 40 to 370 min) as a function of enzyme mass. The dependence of X on the amount of enzyme appears to be qualitatively different at various extents of reaction. For relatively short reaction times (40-130 min, lower plot), the data appear widely spread. The trend of data at intermediate reaction times (160-250 min, middle plot) is almost linear, and X varies over a much smaller range. A similar behavior is observed at longer times of hydrolysis (280-370 min, upper plot). For intermediate reaction times (70-100 min), X decreases at an almost constant rate, and the data representative of 70 min of reaction are distributed practically along a straight line. As a tentative mathematical description of the time decay of X, two different models were explored for data

Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 3941

Figure 5. Time course of variable X for runs at different enzyme loadings (µg): 9, 250; O, 750; 2, 1050; 3, 1350. Solid lines represent data correlation according to eq 7.

Figure 6. Time course of variable X for runs at different enzyme loadings (µg): 9, 250; O, 750; 2, 1050; 3, 1350. Solid lines represent data correlation according to eq 8.

correlation. The first model is represented by the equation

Table 1. Correlation Parameters for the Variable X

X ) X∞ + (X0 - X∞)e

-kt

(7)

and the second model by the equation

X ) X∞ +

X0 - X∞ 1 + kt

(8)

Both eqs 7 and 8 are purely phenomenological laws that describe decay curves. X0 represents an “initial” value, i.e., the value of X extrapolated to time zero, corresponding to the appearance in the output solution of the first product whose molecular weight is close to the highest possible, i.e., closest to the membrane MWCO. X∞ is the asymptotic value that occurs at long reaction time, i.e., the X value associated with the oligomers prevalently contained in the output solution at the end of the process. It is noteworthy that both E and P tend to zero for long reaction time, and consequently, eq 2 gives an indeterminate form. Nevertheless, it can be demonstrated that the mathematical limit of X for t f ∞ is finite. The parameter k represents the characteristic frequency of the decay time; accordingly, the time at which X has decreased to the arithmetic average between the initial and final values (tMW) is ln(2)/k in eq 7 and 1/k in eq 8. The complete time course of X for all experiments carried out at different amounts of biocatalyst was measured experimentally and is reported in Figures 5 and 6. The solid lines are the predictions of the model equations. The trends obeying eq 7 and 8 are illustrated in Figures 5 and 6, respectively. Table 1 reports the values of the correlation parameters of both models as a function of the amount of enzyme loaded in each run. The agreement of the experimental data with the fits is satisfactory, although, by inspection of Figures 5 and 6, it is not possible to choose between the two models. In fact, the fits of the models are not yet explained physically as this could be only done when a completely suitable kinetic consti-

k t MW (min-1) (min)

ME (µg)

X∞

eq 7 X ) X∞ + (X0 - X∞)e-kt

250 750 1050 1350

2.79 11.12 0.0126 55.01 2.66 12.83 0.0244 28.41 1.03 6.86 0.0129 53.73 1.29 8.54 0.0217 31.94

eq 8 X ) X∞ + (X0 - X∞)/(1 + kt)

250 1.65 15.86 0.0311 32.15 750 1.74 15.84 0.0569 17.57 1050 ∼0 7.49 0.0187 53.48 1350 0.45 10.18 0.043 23.26

model

X0

tutive equation is available. Identifying such an equation is rather difficult, as the system is complex, and more experiments at different operating conditions are required. The underlying model assumption that enzyme affinity toward different species does not vary with the molecular weight is critical. Kinetic patterns of biological chain degradations usually exhibit a KM spectrum over the length of substrate, and this holds true for a system similar to the one studied here.14 Consequently, future research will be directed at ascertaining the importance of this phenomenon and developing a kinetic equation that could take it into account. Moreover, some oligomers might act as inhibitors, which could lead to the necessity of adding nonlinear terms to the kinetic equation. The approach of lumping oligomers into a few different species appears to be the more promising. In our opinion, the use of a continuous system could provide a valuable tool for discriminating among different kinetic models. 4. Conclusions The CSMR reactor can be employed to study the kinetics of the enzymatic degradation of polygalacturonic acid, a pectic substance largely contained in wastes of the agro-food industry. The progress of the reaction can be more easily controlled in a membrane reactor than in a batch apparatus. Suitable combinations of molecular weight cutoff, biocatalyst amount, and residence time can be selected to maximize the productivity

3942

Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003

of the reactor and the selectivity of the bioreaction toward valuable classes of oligomers. The experimental responses obtained by varying the mass of enzyme loaded into the reactor fitted quite well to the adopted kinetic model. The proposed experimental procedure, based on an evaluation of the end-point reducing group to determine the instantaneous mean degree of polymerization downstream of the reactor, was applied to the performed runs. The mean molecular weight of the output mixtures was monitored using the variable X, which was expressly defined as the relative increase in the reducing power concentration after an end-point degradation. The time course of this latter experimental variable was correlated with two different equations. The time course of X fitted well to both decay models. The results achieved suggest a need to improve the kinetic model to obtain a constitutive equation with more significant lumped parameters. Research is in progress aiming to attain this end through both experiments performed at different operating conditions and the development of a more complete model that could conveniently simulate the dynamic behavior of the continuous reactor. The influence of concentration polarization phenomena and of the ionic strength of the solution on retention time, membrane cutoff, and overall UF membrane performance might also be considered in the development of the research. Acknowledgment The Authors wish to acknowledge the Italian Ministry of University and Research MIUR for funding this work. Nomenclature A1 ) dummy correlation parameter A2 ) dummy correlation parameter A3 ) dummy correlation parameter E ) end-point reducing group concentration, mmol dm-3 k ) characteristic frequency, min-1 ME ) mass of enzyme loaded in the reactor, µg MW ) mean molecular weight of oligomers, g mol-1 N ) total number of moles of oligomers produced, mol P ) instantaneous output reducing group concentration, mmol dm-3 Pi ) output reducing group concentration in the ith fraction, mmol dm-3 tMW ) time at which the initial molecular weight is halved, min t* ) time of appearance of the maximum product concentration, min U ) number of monomeric units Ue ) end-point value of U Vi ) volume of the ith fraction, dm3 VR ) reactor volume, dm3

W ) highest theoretically obtainable product concentration theoretically obtainable, mmol dm-3 X ) relative increase inof concentration Greek Letters R ) reaction frequency, min-1 θ ) dimensionless time τ ) residence time, min ξ ) model parameter

Literature Cited (1) Micard, V.; Renard, C. M. G. C.; Thibault, J. F. Enzymatic Saccharification of Sugar-Beet Pulp. Enzyme Microb. Technol. 1996, 19, 162. (2) Unger, E. C. U.S. Patent 465431 950605, 1995. (3) White, G. W.; Katona, T.; Zodda, J. P. The Use of HighPerformance Size Exclusion Chromatography (HPSEC) as a Molecular Weight Screening Technique for Polygalacturonic Acid for Use in Pharmaceutical Applications. J. Pharm. Biomed. Anal. 1999, 20, 905. (4) Batle, N.; Carbonell, J.; Sendra, J. Determination of Depolymerization Kinetics of Amylose, Amylopectin, and Soluble Starch by Aspergillus oryzae R-Amylase Using a Fluorimetric 2-p-Toluidinylnaphthalene-6-Sulfonate/Flow-Injection Analysis System. Biotechnol. Bioeng. 2000, 70, 544. (5) Petit, S.; Ralainirina, R.; Favre, S.; De Baynast, R. EU Patent 93/0209, 19932 (6) Dinnella, C.; Stagni, A.; Lanzarini, G.; Alfani, F.; Cantarella, M.; Gallifuoco, A. Pectin Degradation in UF Membrane Reactors with Commercial Pectinases. In Pectin and Pectinases; Visser, J., Voragen, A. G. J., Eds.; Elsevier Science: New York, 1996; p 153. (7) Hotchkiss, A. T., Jr; Lecrinier, S. L.; Hicks, K. B. Isolation of Oligogalacturonic Acids up to DP 20 by Preparative HighPerformance Anion-Exchange Chromatography and Pulsed Amperometric Detection. Carbohydr. Res. 2001, 334, 135. (8) Gallifuoco, A.; Alfani, F.; Cantarella, M.; Viparelli, P. Studying Enzyme-Catalyzed Depolymerizations in Continuous Reactors. Ind. Eng. Chem. Res. 2001, 23, 5184. (9) 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. (10) Nelson, L. A Spectrophotometric Adoption of the Somogyi Method for the Determination of the Glucose. J. Biol. Chem. 1944, 153, 375. (11) Collmer, A.; Ried, J.; Mount, M. Assay Method for Pectic Enzymes. Methods Enzymol. 1988, 161, 327. (12) Arslan, N. Extraction of Pectin from Sugar-Beet Pulp and Intrinsic Viscosity-Molecular Weight Relationshiops of Pectin Solutions. J. Food Sci. Technol. 1995, 32, 381. (13) Voragen, A. G. J.; Schols, H. A.; De Vries, J. A. Pilnik, W. High-Performance Liquid Chromatographic Analysis of Uronic Acids and Oligogalacturonic Acids. J. Chromatogr. 1982, 244, 327. (14) Sakai, T.; Protopectinase from Yeasts and a Yeastlike Fungus. Methods Enzymol. 1988, 161, 335.

Received for review December 13, 2002 Revised manuscript received June 9, 2003 Accepted June 12, 2003 IE0210208