Polygalacturonic acid/endo-polygalacturonase system: a kinetic study in batch reactors

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Biotechnol. Prog. 2004, 20, 1430−1436

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Polygalacturonic Acid/endo-Polygalacturonase System: A Kinetic Study in Batch Reactors Alberto Gallifuoco,* Maria Cantarella, Paolo Viparelli, and Mariagrazia Marucci Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universita` degli Studi di L’Aquila, 67040 Monteluco di Roio (AQ), Italy

The enzymatic depolymerization of the pectic substance polygalacturonic acid (PGA) is studied in batch reactor. The number-average molecular weight of native substrate is estimated, using a simple and quick technique, to be approximately 11.1 kDa, the polymeric chains consisting on average of 63 galacturonic acid units. The effect of enzyme concentration was studied varying biocatalyst loading from 6 to 242 mg/L. The experiments were repeated at substrate concentrations ranging from 0.5 to 5 g/L. Data obtained at both short reaction time (20 min) and prolonged enzyme action (up to 350 min) are correlated using different kinetic equations, and the parameter values are discussed.

Introduction Pectic substances, polysaccharides contained in plant cell wall and fruit lamella, represent a potentially interesting resource, abundantly present in agro-food industry wastes. In particular, polygalacturonic acid (PGA), a homopolymer of up to 200 units of 1,4-R-Dgalactosyluronic acid, could be exploited as a source of valuable oligogalacturans, which play an important role in plant growth and development, plant-microbe interactions, and fruit ripening (1). Oligomers sized above three units are not commercially available, and there could be interest in isolating large quantities of oligogalacturans with a degree of polymerization within a narrow range above 9 units. These molecules could help in identifying and studying receptors for oligosaccharides in plants or be used as substrates for pectin-modifying enzymes and as analytical standards (2). The need to control macromolecule degradation could be achieved by an enzymatic process that ensures high yields of selected classes of oligomers and reduces byproduct formation. This possibility has been explored extensively in the literature, and a study of general applications appeared recently (3). The large amounts of feedstock available suggest the possibility of designing a continuous bioprocess, and our preliminary results on the controlled enzymatic degradation in a laboratory-scale UF-membrane CSTR have been already reported (4). These findings encourage the development of an industrial process for enzymatic PGA degradation. The industrial exploitation of pectin-modifying enzymes has been well assessed during the past decades. Pectinases account for 10% of the total food enzyme market (5). Till now, these enzymes have been employed mostly as clarifying agents in the agro-food industry. For these applications, a complete understanding of the mode of action of biocatalysts is not strictly required. This could explain why only recently have the fundamental biochemical aspects of pectic depolymerases been examinated (6, 7). The hydrolysis of polygalacturonic acid is catalyzed by the * To whom correspondence should be addressed. E-mail: [email protected]. Fax: ++39-0862-434203. 10.1021/bp049853b CCC: $27.50

enzyme endopolygalacturonase (EC 3.2.1.15) according to a multistep endo-breaking mechanism (8). The main evidence in the literature indicates that the enzyme action causes a rapid breakdown of the macromolecules, producing a mixture of oligomers whose molecular weight range is of industrial interest. However, these moieties are further on hydrolyzed, with a slower kinetics, and unwanted products are formed. To design the optimal bioprocess, it is very important to monitor continuously or at close time intervals the mean molecular weight evolution of the reaction mixture. The analysis is traditionally performed with expensive and complex techniques. Methods have been proposed that use highperformance size exclusion (9) or anion exchange (10) chromatography. The authors also proposed an alternative method for a more cheap and easy analysis (11). On the other hand, understanding the mechanism of action of pectinases requires kinetic descriptions of the time course of enzymatic depolymerization. These constitutive equations are of the utmost importance for designing industrial processes based on the controlled degradation of the polysaccharide. This paper reports on a more in-depth kinetic study performed in batch reactors. The effect of substrate and enzyme concentration on the biodegradation rate is investigated and some constitutive equations fitting the experimental data are discussed. The experimental results reported are opening studies in continuous membrane reactors that are presently in progress in our laboratory.

Materials and Methods All experiments were performed with reagent grade, commercially available chemicals. PGA (Fluka, Germany), average molecular weight 30 kDa, was previously characterized for molecular weight distribution using a cascade of ultrafiltration steps according to a procedure detailed elsewhere (12). Polygalacturonase was an enzymatic complex from Aspergillus japonicus (Pectolyase Y23, Sheisin Corp., Japan). This commercial preparation also contains pectin-lyase and pectin-esterase, but because their respective substrates are absent in the PGA used for the experiments, these activities do not interfere

© 2004 American Chemical Society and American Institute of Chemical Engineers Published on Web 09/17/2004

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with the determinations here described. The kinetic runs were performed in Pyrex vessels of 25 mL working volume. The temperature was controlled by submerging the reactors into a thermostatic water bath. The mixing was assured by magnetic bars (D ) 0.5 cm, L ) 1.5 cm) rotating at 250 rpm. The reaction medium was buffered (25 mM sodium citrate pH 5.6) and modified by the addition of 10 mg/L of sodium ethylmercurithiosalicylate (SIGMA, St. Louis, USA) to inhibit occasional microbial contamination that could invalidate long time runs by superimposing an extraneous macromolecule degradation. Samples were withdrawn at regular time intervals from batch reactors and assayed for reducing groups according to the Nelson-Somogyi method (13, 14). The product concentration is evaluated as galacturonic acid equivalent, i.e., the reducing power is referred to a calibration curve obtained using the monomer galacturonic acid (GA) as standard. Mixtures of differently sized polymeric chains are usually characterized through the mean molecular weight, generally defined according to the following: number-average molecular weight:

M hn)

∑iniMi ) ∑iwi ∑ini ∑i wi

(1)

Mi

weight-average molecular weight:

M hw)

∑iwiMi ) ∑iniMi2 ∑iwi ∑iniMi

(2)

where i labels the generic species, Mi is the molecular weight, and ni and wi, respectively, are the number of hw moles and the weight of each species. The ratio M h n/M is the polydispersity of the polymer mixture and is equal to 1 when all of the chains are equally sized.

Results and Discussion Preliminary Characterization of the Substrate and Mathematical Modeling. The analytical procedure adopted in this study allows the evaluation of the overall concentration of polymeric chains (in terms of reducing groups concentration) but does not give any information about the molecular weight distribution of the mixture. Differently sized PGA chains are lumped into a unique “product”, and the extent of polymer degradation produced by the enzymatic action is measured by the overall reducing power in the batch reactor. The native substrate solution itself possesses a certain “reducing power” (defined in Materials and Methods): as the enzymatic hydrolysis proceeds, the substrate molecular weight distribution evolves from the initial one (highest main molecular weight, lowest total concentration) to the ultimate state (minimum main molecular weight, maximum overall concentration). The end-point state represents the asymptotic value of the reaction time course in a given condition and has to be determined preliminarily in order to explain correctly the experimental batch data. Figure 1 illustrates the characterization of PGA solution as reducing power concentration versus mass concentration. The results were obtained by adding to substrate solutions, ranging from 0.5 to 5 g/L, a large excess of enzyme (1.21 g/L, roughly 50 times the amount used in standard kinetic runs) in order to accomplish the

Figure 1. Reducing group calibration of PGA: (- - -) native solutions; (s) end-point solutions.

bioconversion till the end-point. The reducing power of the mixtures was assayed prior to enzyme addition (dashed line) and after 24 h of incubation (full line) and reported as a function of substrate mass concentration. In both cases, the response is in good accordance with a linear variation with the initial PGA concentration. These results can be used either for estimating the mass concentration of native substrate solutions or to predict the total conversion of a batch reactor performed at any initial concentration internal to the explored range. The slope of the lines is m0 ) 0.091 mM/(g/L) and me ) 3.137 mM/(g/L), respectively, for native substrate and end-point solutions. It is worth mentioning that the reciprocal of these slopes is dimensionally a molecular weight (g/mol). Provided that the adopted analytical method is, as usually assumed, equally sensitive to the reducing end of chains regardless of their length, it is easily seen that 103/m0 ) 11 100 (g/mol) directly gives an estimate of the number-average molecular weight of the native substrate solution. Furthermore, whenever the total reducing power and the mass concentration of a sample are known, its M h n can be easily calculated. Data reported in Figure 1 deserve further discussion. The biosynthesis of the PGA chain occurs, as for other carbohydrate macromolecules, by condensation of the monomers (galacturonic acid, MW ) 194 g/mol) with water molecule elimination. Thereby, if U0 is the number of monomeric units that originate the polymer chain, U0 - 1 water molecules are eliminated. The chain molecular weight is then given by

MW ) 194U0 - 18(U0 - 1) ) 176U0 + 18

(3)

This implies that the native substrate solution consists of polymeric chains whose average size is given by the degree of polymerization:

U0 )

(11100 - 18) = 63 176

(4)

When the enzymatic action breaks down substrate MW to the final value (end-point), the residual species have reached the smallest possible size, and the number of monomeric units is Ue. A solely endo-attack would give at the end-point Ue g 2, whereas a pure exo-attack would produce a final solution of the only monomer (Ue ) 1). During the hydrolytic reaction, each catalytic event introduces one water molecule. The average number of

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cleavages is then

c)

U0 -1 Ue

(5)

Consequently, the enzyme activity provokes the increase of both overall molarity and mass concentration of the mixture. The end-point mass concentration can be easily evaluated by the following equation:

We ) W0 +

(

)

18CR CR c ) W0 1 + 0.018 c 1000 W0

(6)

where CR is the reducing group concentration (mM) of the native substrate solution, and W0 and We are the initial and end-point mass concentrations, respectively. As a consequence of the mass increase, the abscissa of each point of the full line in Figure 1 should be, respectively, multiplied and divided by a fixed quantity. The slope of the end-point line (me) is corrected according to

m′e )

(

me

)

CR 1 + 0.018 W0c

(7)

Equation 7 contains two unknowns, namely, Ue and m′e. However, it can be solved, since a relationship between these two variables is experimentally available through the measured slope of the line that correlates the end-point data. The following relationship holds:

103 ) 176Ue + 18 m′e

(8)

Equations 7 and 8 can be solved simultaneously to give

Ue ) 1.78 m′e ) 3.02

(9)

[ ] mMR g/L

This calculated value of Ue clearly indicates that the end-point mixture should predominately contain the dimer and the monomer, respectively, 78% and 22%, which in turn implies the possible existence of small amounts of exo-activity in the commercial enzymatic preparation. Effect of Enzyme Concentration. Figure 2 shows the effect of enzyme concentration on the depolymerization rate. Biocatalyst loading was varied from 6 to 242 mg/L, while all the other parameters were kept constant: substrate concentration 5 g/L, temperature 25 °C, pH 5.6 (Na citrate/phosphate buffer, 25 mM), reaction volume 20 mL, stirring 250 rpm. The inspection of the plots clearly indicates that as the initial amount of enzyme in the reactor is increased, “product” concentration increases according to an initial apparent linearity, but as the time proceeds, the reaction rate progressively slows down. Besides, the higher the enzyme concentration, the earlier the rate depression. The highest concentration measured in these experiments is roughly 8.5 mM of galacturonic acid equivalent, which represents 54.2% of the end-point for the 5 g/L PGA solution. Here too, as pointed out previously, the enzymatic attack causes the increase of reducing power, as well as a variation in MW distribution. More molecules are thus

Figure 2. PGA (5 g/L) hydrolysis as a function of enzyme concentration (mg/L): (]) 6.0; (4) 24.2; (0) 48.4; (O) 121.1; (3) 242.3. Inset: initial reaction rate as a function of enzyme loading.

available as substrate, the kinetics is modified, and the reaction rate is magnified. To evaluate solely the effect of enzyme concentration, only data obtained during the very first reaction time should be considered, when a constant MW distribution may be assumed. Consequently, only data encompassed in the first 10 min of hydrolysis were interpolated linearly, and the resulting slopes were assumed as a measure of the “initial” reaction rate, r0. These latter are plotted as a function of enzyme concentration in the picture in Figure 2. A good linear relationship is obtained (R ) 0.9998), and here the slope represents the specific activity, whose value is 6.568 EU/ mg. For longer reaction time, data of Figure 2 deviate from the linearity. Indeed, the accumulation of intermediate oligomers in the reactor enhances the reaction rate. The slope consequently increases, passes through a maximum (point of inflection), and then progressively tends to vanish, as the breakdown proceeds and the driving force for the bioreaction dissipates. The total reducing power detected in the batch reactor represents the highest level of lumping, which explains the complex evolution occurring in the MW distribution with the time course of a unique species. The analysis of the data here discussed is not straightforward because of the difficulty in finding a kinetic equation totally satisfactory for data interpolation. For example, the model originally proposed by Sendra and Carbonell for glucan hydrolysis catalyzed by endo-β-glucanase and the subsequent simulation procedure (15, 16) was adopted as one of the more suitable. According to this model, the kinetic equation for the time course of the reducing power CR(t) would be

CR(t) ) (CR,e - CR,0)[1 - e-bt(1 + bt)] + CR,0

(10)

where CR,0 and CR,e are, respectively, the initial and final value of the reducing group concentration and b is a characteristic reaction frequency; 1/b represents the time of appearance of the inflection point. Solid and dashed lines in Figure 3 represent typical results of modeling predictions obtained with the experimental data here discussed. Correlations curves were performed with a nonlinear fitting procedure adopting the initial condition t ) 0, CR(t) ) 0.448, which corresponds to the reducing power of the native 5 g/L substrate solution utilized in the kinetic runs. As a general rule, eq 10 predicts an

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CR,e, µmol/L

b, min-1

R2

6.0 24.2 48.4 121.1 242.3

7.892 7.544 7.543 7.569 6.919

0.0261 0.0867 0.1440 0.3430 0.6710

0.98 0.98 0.96 0.95 0.95

equation can be arranged to give a complete mathematical equivalence with the allosteric equation:

(t/t1/2)n CR(t) - CR,0 [S′]n r ) w ) CR,e - CR,0 1 + (t/t1/2)n vmax 1 + [S′]n Figure 3. Typical data correlation according to model eq 10 at different enzyme concentration (mg/L): (O) 48.4; (0) 121.1. Inset: characteristic reaction frequency as a function of enzyme loading.

initial increase in product concentration slower than that experimentally observed. The fittings show an “induction period”, i.e., the time needed for the hydrolysis to produce substantially more high MW “substrate molecules”, and thereby the increase in low MW products is small. Since in the batch reactor there is no possibility to discriminate between molecules with different MW, the experimental data (overall concentration) show a faster initial increase of the reducing power. The discrepancy between experimental data and fitting curves is also evident for longer reaction time, when correlations tend to an asymptotic value of product concentration. This predicted value is systematically lower than that actually observed: the experimental data present an increasing trend while the correlation has already attained its highest value. Similar results were obtained with all the other enzyme concentrations investigated (data not shown) and confirm the trend illustrated in Figure 3. Therefore the model eq 10 does not appear totally satisfactory to represent data from batch reactor experiments. The correlation parameters are reported in Table 1 and show, as expected, rather unsatisfactory regression coefficients. Nevertheless, by inspection of b values (which represent the observed reaction frequencies) a certain internal coherence appears evident. Indeed, at the adopted experimental conditions, b should be proportional to the enzyme loading in the reactor and, as the picture inside Figure 3 illustrates, the linearity is fair (regression coefficient R2 ) 0.9998). A possible approach to improve the model could be the search for a more complex kinetic equation that includes as a part of it the relationship of eq 10. This latter should weigh more during the intermediate reaction time and less during the initial and final ones. Generally, using different kinetic equations, better fittings can be achieved, but these correlations suffer from the lack of a physical meaning directly connected to the system under study. As an example, the logistic equation is strictly related to the Hill equation, which describes enzyme kinetics with allosteric effects (17):

CR(t) - CR,0 CR,e - CR(t)

)

( ) t

t1/2

p

(11)

where t is the current reaction time. When t ) t1/2 the bioconversion has accomplished 50% of the polymer endpoint degradation. It can be easily seen that the kinetic

(12)

where [S′] ) [S]/KS is the dimensionless substrate concentration. It is worth mentioning that a similar equation is widely employed in pharmacology to describe the dose-response of tissue, where time t is replaced by drug bulk concentration (driving force) and CR(t) is replaced by drug (ligand) concentration internal to the tissue. In this latter case, the exponent n is related to the binding behavior of drug to the cellular receptor and is generally known as the Hill coefficient. The scenario of enzymatic depolymerization is obviously quite different from that of drug response or a pure allosteric one-substrate reaction, and the analogies between these systems are not immediately evident. The accordance of eq 11 to the experimental data here discussed is, however, very good. Figure 4 shows the regression curve for a typical run, and similar results were obtained with all experimental sets, as illustrated by Table 2, which reports the correlation parameters as a function of enzyme loading in the reactors. For each enzyme concentration, the regression coefficient is better than the corresponding one obtained with eq 10. The asymptotic CR,e values vary slightly between the runs and, as in the case of eq 10, are below the endpoint. This could be well explained by the following considerations. Since experimental evidence exists that the enzyme is still active at the end of the kinetic runs, the apparent asymptote cannot be attributed to biocatalyst deactivation. The theoretical values lower than the end-point could be explained if we take into account the possible presence of trace amounts of exo-activity. This continues producing monomers at a lesser rate once the endo-activity ends because of substrate depletion. The relative importance of this endo-activity is negligible with respect to that of the exo-polygalacturonase as long as the MW of the reacting mixture is sufficiently high to ensure the driving force for the main bioreaction. As the degradation proceeds, the endo-activity is depressed, but consistent amounts of low MW products are still recognized as substrate by the exo-enzyme. The enzyme in excess employed in the end-point experiments ensures a fast kinetics for both activities, and the biodegradation is totally accomplished within the observation time. The values of parameter p are greater than unity with the only exception of the run performed at the highest enzyme concentration (242.3 mg/L). In the case of the Hill equation, this would indicate a cooperative binding of the enzyme to the substrate. This cannot be transferred directly to the case of PGA degradation, when a pool of different, time evolving substrate molecules is present. A more in-depth investigation is advisable, aiming to assess a model reaction mechanism that could account

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Figure 4. Typical data correlation according to model eq 11. Enzyme loading 24.2 mg/L. Inset: characteristic reaction frequency as a function of enzyme loading. Table 2. Parameters of the Logistic Equation as a Function of Enzyme Loading [E], mg/L

CR,e, µmol/L

t1/2, min

p

R2

6.0 24.2 48.4 121.1 242.3

8.889 7.779 8.478 8.300 7.779

71.454 24.233 12.906 4.841 2.375

1.486 1.203 1.283 1.289 0.911

0.996 0.985 0.996 0.995 0.985

for the observed mathematical analogies between the two different phenomena. The parameter t1/2 also deserves special attention. According to the logistic model, it represents a characteristic time, i.e., the time required to accomplish 50% of the total degradation. The picture inside Figure 4 reports 1/t1/2 as a function of enzyme concentration. The data are very well fitted by a straight line, thus indicating that the inverse proportionality holds. This is related to enzyme loading: the higher the biocatalyst amount, the faster the kinetics and consequently the shorter the characteristic time. Effect of Substrate Concentration. The effect of PGA concentration on the reaction rate was studied using substrate solutions from 0.5 to 5 g/L while keeping the biocatalyst loading constant. The range of substrate concentration was determined by the macromolecule solubility, which becomes critical above 5 g/L, and by the sensitivity of the analytical procedure. To accurately determine the effect on the initial reaction rate, product concentration was assayed for a time up to 16 min, withdrawing from the reactors, every 2 min, samples sufficiently small to avoid consistent changes of reaction volume. Figure 5 reports the results obtained using 24.2 mg/L of enzyme preparation. Since the range of observed product concentration increases with PGA concentration, the diagram is split to enhance the readability. Data at low substrate concentration deviate from linearity early, and the sigmoidal shape is evident. The autocatalytic behavior of the system is more pronounced under conditions of low substrate concentration, when the driving force has to increase before the reaction rate becomes significant. At higher substrate concentrations, the kinetics are faster, the induction period falls within the very first sampling intervals, and the inflection point does not appear. The small plot in the upper left corner reports the linear relationship between the reaction rate and substrate concentration, thus indicating that the overall initial reaction rate obeys an apparent first order. The

Figure 5. Short-time hydrolysis at different PGA concentrations. Enzyme loading 24.2 mg/L. Substrate concentration (g/ L): (]) 5; (right open triangle) 4; (3) 3; (0) 2; (O) 1; (4) 0.5. Inset: initial reaction rate as a function of substrate concentration.

slope of the linear plot is 0.0466 mmol of reducing groups per minute and per gram of PGA. Taking into account the previous estimate of the substrate mean MW, this corresponds to an apparent first-order constant equal to 0.518 min-1. These experiments were repeated, varying only the enzyme loading, which was five times higher (121 mg/L). The obtained results are reported in Figure 6, which is organized similarly to Figure 5. As a consequence of reaction rate enhancement due to the higher enzyme loading, the sigmoidal shape disappears, the inflection points being located quite close to the origin. For the same reason, the deflection from linearity is evident at each substrate concentration. Consequently, to estimate the initial reaction rates (reported in the inserted diagram), data were interpolated by polynomials and the initial derivatives were calculated. Despite the different correlation procedure adopted, the linearity between initial reaction rate and substrate concentration still holds. The estimated value of the first-order constant is 2.533 min-1, which is almost exactly five times that previously calculated at 24.2 mg/L of enzyme concentration, thus indicating that all of the runs were also performed, as far as enzyme concentration is concerned, under linear assay conditions. These latter data fit fairly well the model eq 10 as shown by the computed solid lines depicted in Figures 5 and 6, which refer to the lower enzyme loading (24.2 mg/

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Figure 7. Second correlation for parameters of eq 10). Asymptotic concentration CR,e (left-hand y-axis, open symbols) and characteristic reaction time 1/b (right-hand y-axis, closed symbols) as a function of substrate concentration. Enzyme loading (mg/L): (O,b) 24.2; (4,2) 121.1.

Figure 6. Short-time hydrolysis at different PGA concentration. Enzyme loading 121.1 mg/L. Substrate concentration (g/L): (]) 5; (right open triangle) 4; (3) 3; (0) 2; (O) 1; (4) 0.5. Inset: initial reaction rate as a function of substrate concentration. Table 3. Parameters of the Model by Sendra and Carbonell as a Function of Substrate Concentration [PGA] (g/L) 0.5

1.0

2.0

3.0

4.0

5.0

[E] ) 24.2 mg/L CR,e (mmol/L) 5.563 4.589 3.028 1.842 0.792 0.353 b (min-1) 0.151 0.158 0.183 0.245 0.287 0.34 R2 0.9924 0.9970 0.9970 0.9963 0.9954 0.9967 CR,e (mmol/L) 6.607 b (min-1) 0.438 R2 0.992

[E] ) 121 mg/L 4.416 2.885 2.025 0.312 0.409 0.592 0.970 0.973 0.995

0.952 0.681 0.987

0.38 0.569 0.993

L) and the higher one (121 mg/L), respectively. Interestingly, as the hydrolysis time is quite short, it can be assumed that the system is still under “recycle conditions”, which means that molecules produced by the hydrolysis are large enough to undergo the subsequent catalytic acts with unchanged affinity between substrate and enzyme. These assumptions correspond to the ground hypotheses for the model depicted by Sendra and Carbonell (15); hence data are in good accordance with the fit. The corresponding correlation parameters are reported in Table 3. Data obtained using the lower enzyme amount are better represented by the model curves than those obtained using more enzyme. This was somewhat expected, since the increase of the enzyme amount in the reaction medium enhances the characteristic reaction

frequency and thus shortens the induction period, i.e., the time interval of model holding. This affects the second-step correlations as well. Regressions of model parameters with the PGA concentration are shown in Figure 7. Obviously, the higher the substrate concentration, the higher the final value of product concentration predicted by the model, no matter if this latter, for the reasons previously pointed out, does not correspond to the end-point experimentally determined. By inspection of Figure 7 (left-hand y-axis, open symbols) it can be observed that CR,e, as a function of PGA concentration, is quite well represented (R2 > 0.99) by a straight line through the origin. Besides, data tend to line up on the same fitting irrespectively of the enzyme loading, thus confirming that the asymptotic values were attained in all the experiments. Adapting the model of Sendra and Carbonell to this case, the reciprocal of b should depend linearly on substrate initial concentration (right-hand y-axis, full symbols) and the corresponding lines should intercept the x-axis in a point whose abscissa represents the value of a lumped affinity parameter (pseudo-Km) of the enzyme toward the polymeric mixture. As previously pointed out, the elaboration adapts better to data with 24.2 mg/L of enzyme. The linear fitting is quite fair (R2 ) 0.987, pseudo-Km equal to 2.96 g/L,), whereas data with 121 mg/L scatter more widely and the estimate is worse (R2 ) 0.735, pseudo-Km equal to 5.35 g/L). These latter experiments further on confirm that the biocracking, which appears to be under first-order conditions with respect to substrate concentration, should be described by a more complex kinetic equation. It is necessary to use a model capable of accounting for how the reaction proceeds out of the recycle time period. In addition, the characteristic time of contact between enzyme and substrate solution should be varied in order to maximize the yield of requested oligomers. This could be well performed using a continuous reactor, as our preliminary results already pointed out. Experimental evidence reported in this paper gave more valuable information to perform a guided campaign of tests in continuous reactors, which has already been carried out.

Conclusions The system polygalacturonic acid/endo-polygalacturonase was characterized in a batch reactor. The average

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size of native biopolymer (roughly 11.1 kDa) was easily estimated with the simple procedure illustrated in the paper, which makes use only of a colorimetric assay and of the macromolecular mixture breakdown performed with the same enzyme used in the kinetic tests. Initial reaction rate obeyed linear conditions with respect of either enzyme or substrate concentration. Specific activity was 6.568 EU/mg, and a small amount of exo-activity was detected. The hydrolysis was monitored up to 350 min, measuring the total reducing power of the mixture. This lumped parameter was correlated to both a theoretical and an empirical model. The former proved to be more confident when using a low enzyme amount and especially up to the first 20 min of reaction. The latter has been found to agree very well with data of the entire time course and deserves more in-depth attention, since a valid explanation of its success in describing the data is not yet available.

Notation b c CR KS MW M h m m′ n p r R [S′] t t1/2 U

model parameter (1/min) number of catalytic cleavages reducing group concentration (mM) substrate affinity constant (mM) molecular weight (g/mol) average molecular weight (g/mol) slope of regression line (mM/(g/L)) corrected slope of regression line (mM/(g/L)) number of moles (mol) model parameter reaction rate (µmol/min) regression coefficient substrate dimensionless concentration reaction time (min) model parameter (min) number of monomeric units

Subscripts 0 e i n w

initial end-point (final) label index number-averaged weight-averaged

Acknowledgment The authors wish to acknowledge the Italian Ministry of University and Research, MIUR, for funding this work. Accepted for publication July 8, 2004.

References and Notes (1) Grassin, C.; Fauquembergue P. In Industrial Enzymology, 2nd ed.; Godfrey T., West, S., Eds.; MacMillan: London, 1996; pp 227-262. (2) Hotchkiss, A. T. Jr; Lecrinier, S. L.; Hiks, K. B. Isolation of Oligogalacturonic Acids up to DP 20 by Preparative High

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