BIOTECHNOLOGY AND BIOENGINEERING, VOL. XVII, PAGES 1421-1433 (1975)
Kinetic Studies on Insoluble Cellulose-Cellulase System ANDREW A. HUAKG,* IT. S . Army Salick Laboratories, Satick, Massachusetts 01760
Summary Enzymatic hydrolysis of insoluble amorphous cellulose by 'I'richoderma viride cellulase was investigated in a batch reactor a t several substrate concentrations and three enzyme levels. The reactions were carried out a t 50°C and pH 4.8. Enzyme was rapidly adsorbed onto solids on contact, then gradually returned to the liquid phase as the reaction proceeded. A kinetic model that considered the fast adsorption which was followed by the slow reaction, and subsequent product inhibition was developed to interpret the experimental observations. The resulting equation successfully correlated the data for up t o 707, conversion. The methods for determining the kinetic parameters are discussed.
INTRODUCTION Cellulose is abundant and renewable. One way of utilizing this readily available product is to hydrolyze it enzymatically into reducing sugar, which can be used as a source of food for human beings, as a substrate for single cell protein, and as a raw material for fermentation. It was reported1s2 that cellulase produced from a Trichoderma viride fungus was capable of extensive degradation of cellulosic materials and that this enzyme was very stable. Saccharification of pure cellulose by employing T . viride cellulase has been investigated.3-7 Using waste cellulose as a substrates*9has the added advantage of alleviating solid waste problems, and thus offers a promising economic utilization. The mode of cellulase action is complex and not fully understood. At least two enzymes, designated C1 and C,, are required to hydrolyze crystalline cellulose, although only one is needed for amorphous cellulose hydrolysis.lOJ1 Exactly which enzyme is necessary has *NAS/NRC Visiting Scientist a t the U. S. Army Natick Laboratories. Present address: 101 Cheng-Tu Road, 6th Floor, Tsu-Yun Building, Taipei, Taiwan, Republic of China. 1421 @ 1975 by John Wiley & Sons, Inc.
1422
HUANG
yet to be agreed upon. The final products such as cellobiose and glucose are shown to be the competitive inhibitors of cellulase action, with cellobiose being the stronger Little information is available in the literature concerning the kinetics of the cellulose-2'. viride cellulase system. 7 ~ * Present ambiguities concerning the exact mechanism of hydrolysis make the kinetic modeling more difficult. Prior to investigating the waste cellulose degradation, the kinetic study of a simpler system is desirable. Enzymatic hydrolysis of insoluble amorphous cellulose is in essence a one-substrate, one-enzyme catalyzed reaction and provides a simple system for analysis. However it requires a heterogeneous catalysis approach the same as the waste cellulose system does. This investigation should make possible more complete analysis when more practical substrates are employed.
EXPERIMENTAL Amorphous cellulose was prepared by swelling Solka Floc BW-200 (Brown Company, Berlin, N. H.) in 85% phosphoric acid according to the method of Walseth.'s The amorphous cellulose thus obtained was about 2% in suspension, and kept refrigerated a t 2°C with p H 4.8. Cellulase was produced in submerged fermentation using a mutant of T. viride (&;\I 9123); the crude culture filtrate was used directly as the enzyme solution.2 Reactions were carried out in a 2 liter batch reactor operated a t 50°C and pH 4.8, the optimal conditions reported for saccharification.2 The reactor configuration was essentially the same as that described by previous worker^.^ Preliminary experiments on the effect of agitation speed on the product concentration versus time curve were performed a t three agitation speeds, i.e., 60, 120, and 240 rpm. Little or no difference was noticed. This showed the insignificance of external mass-transfer as long as the solids were kept suspended. Agitation speed was thus chosen a t 120 rpm throughout this study. Samples withdrawn a t various contact times were quickly centrifuged and the supernatants were frozen for later analyses. The total reducing sugar was measured by a dinitrosalicylic acid (DNS) method.16 The amount of glucose was determined by the glucose oxidase method; the Glucostat (Worthington Biochemical Corp., Freehold, N. J.) used was found to be specific and suitable for rapid analyses. The difference in total reducing sugar and glucose in a given sample was cellobiose. Protein content was assayed by the phenol procedure.'?
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1423
THEORETICAL The cellulase used in this study contained high levels of C1 and endo-p-1,4 glucanases, but low levels of exo-P-1,4 glucanases and j3-glucosidases.2 The soluble hydrolysates were mainly cellobiose and glucose, with little if any higher glucose polymers. In constructing a kinetic model, it is stipulated that the enzyme I3 is adsorbed rapidly on the cellulose S to form complex Xl, which irreversibly proceeds to yield products P. The products (mixture of cellobiose and glucose) then reversibly combine with the enzyme to form inactive complexes X2. This reaction scheme can be depicted as follows.
It is assumed that adsorption occurs so fast that equilibrium is established a t all times, that the Langmuir adsorption modells
prevails, and that eq. ( 2 ) is the rate determining step. I n eq. (4), Xl and X1, are the amount and saturation amount of enzyme adsorbed per unit mass of substrate, ( E ) is the enzyme concentration, and K 1equals kl/k-l. Since substrate concentration is much greater than enzyme concentration, the steady-state assumption is va1id;'g in this case d(X2)/dt = 0. Thus, with conservation equation ( E ) o= ( E ) (XI) (X2),the rate of reaction v is
+
+
HUANG
1424
where parentheses denote concentrations based upon the unit volume of liquid phase, subscript zero denotes the initial condition, t is the contact time, and K 3 equals k3/k_,. Rearranging eq. (5) by assuming X1, >> X1 gives 1 _ -
-
1
V
If (S)
=
+ Kl(E)O + K3(P) . - 1 +- 1 k?XlmKl(E)O (S) k m o
(6)
(S)o - ( P ) is assumed, eq. (6) can be integrated to form
with (P)o = 0. Rearranging (7) to a linear form
or
reveals that a plot of l / e versus 1/(8) for the batch reactions a t a given (E)o but varying (S)o would yield a family of straight lines with the same intercept. The slope, however, is a function of AS)^. One way to evaluate the kinetic parameters in eq. (7) is to use initial rate data, vo. When ( P ) = 0, eq. (6) becomes
1
_ -VO
+
1 K1(E)o .-+1 hX,rnKl(E)O (S)o
1
k2(E)0
(10)
Therefore, plotting l / v o versus l/(S)o a t a given ( E ) o usually , referred to as the Lineweaver-Burk plot, should yield linear relationships. The rate constant k2 can be determined directly from the intercept, and the constants K1 and X1, are derived from the slopes of different ( E ) o . The value of K 3 can then be evaluated according to eq. (9) from either the slope or intercept. The use of one would serve as a check for the other. One of the best ways of obtaining vo is by fitting the product concentration-time data to a polynomial form.20 In this way, the notorious initial rate measurements’ reproducibility scatter was
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1425
avoided and a more reliable value obtained. Expansion of eq. (7) in a series gives
Thus, the coefficient of the ( P ) term directly gives the value of l/vo. It is obvious that all the polynomial coefficients in eq. (11) should be positive.
RESULTS AND DISCUSSION Batch reactions were carried out at several initial substrate concentrations and three initial enzyme levels, i.e., 0.38,0.25,and 0.15 mg protein/ml. The initial substrate concentration was determined from the sugar produced at 50 hr of reaction time; essentially, all of the amorphous cellulose was solubilized a t this prolonged contact with the enzyme. Since 10 mg/ml of cellulose would yield 11 mg/ml of reducing sugar, all of the glucose concentrations assayed by the DNS method were corrected accordingly before being fitted to eq. (9). As illustrated in Figure 1, a linear relationship prevailed up to 70y0conversion or higher when 1/0 was plotted against l/(S) for all cases. The slopes and the intercepts obtained are tabulated in Table I. It is TABLE I Experimental and Calculated Slopes and Intercepts According to Eq. (9) Experimental (El0
@)o
slope
intercept
Calculated slope ~
0.38
0.25
0.15
10.0 7.2 5.0 3.6 10.7 7.1 5.2 3.5 5.0 3.8
3.68 2.68 1.90 1.38 6.00 4.02 2.98 2.05 4.91 3.68
-0.33 -0.30 -0.32 -0.36 -0.50 -0.51 -0.51 -0.54 -0.88 -0.81
~~~
3.69 2.69 1.90 1.40 5.97 4.01 2.97 2.05 4.75 3.66
intercept ~
~~
-0.33 -0.33 -0.33 -0.33 -0.50 -0.50 -0.50 -0.50 -0.83 -0.83
1426
HUANG 0.6
0.4
I>
\
0.2
0.0
- 0.2
- 0.4 (a)
Fig. 1. (Continued).
evident that the intercept is inversely proportional to ( E )0, as expected from eq. (9). Figure 2 shows typical results of protein content in the liquid phase as a function of time. A sharp initial drop is indicative of the rapid adsorption process. As the reaction progressed, enzyme was released slowly back into the liquid phase due to the lesser substrate availability. Since it is reasonable to assume that the protein concentration in the liquid phase is proportional to the enzyme concentration, the only effect it has upon the protein concentration in the analysis is on the K 1 value (see eq. (4)). Also shown is the total reducing sugar and glucose produced as a function of time. The discrepancy between the total reducing sugar and glucose is due to the cellobiose. The cellobiose/glucose ratio was about 3 : l for a
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1427
0.5
I> \
-
0.0
- 0.5
(b) Fig. 1. (Continued)
time of .5 hr and was 7:3 for G hr. A t 24 hr, however, it was about 1 : l . The fact that this ratio was held reasonably constant for the experimental time period permitted the assumption of the validity of eq. (3). Progress curves ( P ) versus t were evaluated in accordance with eq. (7), using the slopes and intercepts shown in Table I. The calculated data were then matched by means of least-square-error analysis t o a third-order polynomial in ( P ) ,with a zero order coefficient set to be zero (see eq. (11)). At 40% conversion it was estimated to be only 6y0in error with the terms in (P)4and higher orders being ignored. Using the calculated data instead of the experimental data assured positive polynomial coefficients from the computer
HUANG
1428
-1.01 (C)
Fig. 1. Plot of l/V vs. l/(S) a t ( E ) o of (a) 0.38, (b) 0.25, and (c) 0.15 mg/ml. Parameters: (S)O. Arrows: 70% conversion.
output. The first-order coefficients ( l / v o ) were then used for the Lineweaver-Burk type plot. At two enzyme levels, l / v o versus l/(S)oplot showed linearity (Fig. 3). I t thus permitted the evaluation of kinetic parameters kz, K1, Xlm,and subsequently K S ;they were 80.3 (hr)-l, 1.68 (mg/ml)-l, 0.305 (mg/mg), and 5.61 (mg/ml)-l, respectively. The third enzyme level was not deemed appropriate for this plot since only two batch runs were performed. Nevertheless, it could serve to check the accuracy of the determined parameters. Of the slopes and intercepts calculated by using these parameters, all agreed satisfactorily with the experimentally determined values (see Table I). It was particularly gratifying in the case of (E)o =
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1429
T I M E , HRS.
Fig. 2. Sugar and enzyme levels as a function of the reaction time for (S)O= 10.0 mg/ml, ( E ) o = 0.38 mg/ml; (0) yo converted to reducing sugar; (0) yo converted to glucose; ( A ) % protein in the liquid phase.
0.15 inasmuch as they were predicted values. Progress curves generated from these kinetic constants are compared with the experimental results in Figure 4. In general, they overestimated for conversion beyond 70%. The discrepancy a t higher conversion is understandable. First, the assumption of X1, >> X1may not be valid in that region. Calculation of XI (from Fig. 2 ) a t 10 min and 4 hr of contact time, for example, gives 0.021 and 0.071 mg protein/mg cellulose. This is to be compared with the X1, value of 0.305. This invalid assumption would cause the model to overestimate the experimental results. Secondly, by not taking into account the enzyme heat denaturation and sugar adsorption on cellulose, in constructing the model there is a tendency to overestimate the actual data. However, the fact that the ratio of cellobiose to glucose decreased slightly during the first few hours of reaction should have the opposite effect.
1430
HUANG
o’2
0.0
t I
0.2
0.I
0.3
l/(s)o
Fig. 3. The Lineweaver-Burk plot for ( E ) o = 0.38 (0)and 0.25 ( A ) mg/ml; the slopes being 0.105, and 0.138, and the intercepts 0.032, and 0.052, respectively.
The parameter K Bdefined here is not an intrinsic kinetic constant, instead it is a function of individual sugar concentration. Ideally, eq. (3) should be further divided into two reactions, one reaction for each enzyme complexing with cellobiose and glucose. I n practice, since the cellobiose/glucose ratio was fairly constant up to several hours, combining these two inactivation reactions did not greatly affect the data analysis. Enzymatic degradation of waste cellulose such as newspaper would require a model consisting of two substrates (amorphous and crystalline cellulose) and a t least one inert material (lignin). Although lignin does not appear to interfere with the hydrolysis chemically, it does have adsorptive capacity for the enzyme molecules. A kinetic study of pure cellulose (containing both amorphous and crystalline states) and the knowledge of enzyme adsorption on lignin are necessary before waste cellulose hydrolysis modeling in pollution abatement and glucose producing schemes can be done.
INSOLUBLE CELLULOSE-CELLULASE KINISTICS
(D
t
N
1431
0
1 W /OW ‘HQOIW
(D
t v)
K
I
N
0
1432
HUANG
4
I 0
I
2
4
6
TIME, HRS (c)
Fig. 4. Comparison of experimental (points) and predicted (lines) progress curves for (E)o a t (a) 0.38, (b) 0.25, and.(c) 0.15 mg/ml. Parameters: (S)O. The author is grateful to Dr. Mary Mandels for her constant guidance and to Mr. Leo A. Spano for his continued interest throughout the investigation. He is indebted to Dr. E. T. Reese for his advice and to Dr. R. K. Andren, Mr. J. A. Kostick, and Mr. L. Hontz for their assistance during the various phases of the program. This research was conducted while the author was a National Research Council Visiting Scientist a t the U. S. Army Natick Laboratories, Natick, Massachusetts.
References 1. M. Mandels and E. T. Reese, Develop. Ind. Microbiol., 5, 5 (1964). 2. M. Mandels and J. Weber, Advan. Chem. Ser., 95, 391 (1969). 3. T. K. Ghose, Biotechnol. Bioeng., 11, 239 (1969). 4. T. K. Ghose and J. A. Kostick, Advan. Chem. Ser., 95, 415 (1969). 5. T. K. Ghose and J. A. Kostick, Biotechnol. Bioeng., 12, 921 (1970). 6. M. Mandels, J. A. Kostick, and It. Parizek, J. Polym. Sci., Part C, 36, 445 (1971). 7. B. H. Van Dyke, Doctoral Thesis, M. I. T., Cambridge Mass., 1972.
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1433
8. M. Mandels, L. Hontz, and D. Brandt, Disposal of Cellulosic Waste Materials by Enzymatic Hydrolysis, A r m y Sci. Conf. Proc., vol. 3, AD 750351, 1972, pp. 16-31. 9. D. Brandt, L. Hontz, and M. Mandels, Engineering Aspects of the EnzymaticConversion of WasteCellulose to Glucose, A I C H E S y m p . Ser., vol. 69, No. 133, 1973, pp. 127-133. 10. E. T. Reese, R. G. H. Siu, and H. S. Levinson, J . Bacteriol., 59, 485 (1950). 11. T. M. Wood and S. I. McCrae, Biochem. J., 128, 1183 (1972). 12. T. K. Ghose and K. Das, in Advances in Biochemical Engineering, vol. 1, T. K. Ghose and A. Fiechter, Eds., Springer-Verlag, New York, 1971, pp, 55-76. 13. M. Mandels and E. T. Reese, in Advances in Enzymic Hydrolysis of Cellulose amd Related Materials, E. T. Reese, Ed., Pergamon Press, New York, pp. 115-157. 14. M. Katz and E. T. Reese, Appl. Microbiol., 16, 419 (1968). 15. C. S. Walseth, Tappi, vol. 35, No. 5, May, 1952, pp. 228-233. 16. J. B. Sumner and G. F. Somers, Laboratory Experiments in Biological Chemistry, Academic Press, New York, 1944. 17. 0. H. Lowry, N. J. Rosebrough, A. L. Farr, and R. J. Randall, J . Biol. Chem., 193, 265 (1951). 18. I . Langmuir, J . Amer Chem. Soc., 38, 2267 (1916). 19. F. G. Heineken, H. M. Tsuchiya, and K. Ark, Math. Biosciences, 1, 95 (1965). 20. R. D. Philo and M. J . Selwyn, Biochem. J., 135, 525 (1973).
Accepted for Publication April 28, 1975
Kinetic Studies on Insoluble Cellulose-Cellulase System ANDREW A. HUAKG,* IT. S . Army Salick Laboratories, Satick, Massachusetts 01760
Summary Enzymatic hydrolysis of insoluble amorphous cellulose by 'I'richoderma viride cellulase was investigated in a batch reactor a t several substrate concentrations and three enzyme levels. The reactions were carried out a t 50°C and pH 4.8. Enzyme was rapidly adsorbed onto solids on contact, then gradually returned to the liquid phase as the reaction proceeded. A kinetic model that considered the fast adsorption which was followed by the slow reaction, and subsequent product inhibition was developed to interpret the experimental observations. The resulting equation successfully correlated the data for up t o 707, conversion. The methods for determining the kinetic parameters are discussed.
INTRODUCTION Cellulose is abundant and renewable. One way of utilizing this readily available product is to hydrolyze it enzymatically into reducing sugar, which can be used as a source of food for human beings, as a substrate for single cell protein, and as a raw material for fermentation. It was reported1s2 that cellulase produced from a Trichoderma viride fungus was capable of extensive degradation of cellulosic materials and that this enzyme was very stable. Saccharification of pure cellulose by employing T . viride cellulase has been investigated.3-7 Using waste cellulose as a substrates*9has the added advantage of alleviating solid waste problems, and thus offers a promising economic utilization. The mode of cellulase action is complex and not fully understood. At least two enzymes, designated C1 and C,, are required to hydrolyze crystalline cellulose, although only one is needed for amorphous cellulose hydrolysis.lOJ1 Exactly which enzyme is necessary has *NAS/NRC Visiting Scientist a t the U. S. Army Natick Laboratories. Present address: 101 Cheng-Tu Road, 6th Floor, Tsu-Yun Building, Taipei, Taiwan, Republic of China. 1421 @ 1975 by John Wiley & Sons, Inc.
1422
HUANG
yet to be agreed upon. The final products such as cellobiose and glucose are shown to be the competitive inhibitors of cellulase action, with cellobiose being the stronger Little information is available in the literature concerning the kinetics of the cellulose-2'. viride cellulase system. 7 ~ * Present ambiguities concerning the exact mechanism of hydrolysis make the kinetic modeling more difficult. Prior to investigating the waste cellulose degradation, the kinetic study of a simpler system is desirable. Enzymatic hydrolysis of insoluble amorphous cellulose is in essence a one-substrate, one-enzyme catalyzed reaction and provides a simple system for analysis. However it requires a heterogeneous catalysis approach the same as the waste cellulose system does. This investigation should make possible more complete analysis when more practical substrates are employed.
EXPERIMENTAL Amorphous cellulose was prepared by swelling Solka Floc BW-200 (Brown Company, Berlin, N. H.) in 85% phosphoric acid according to the method of Walseth.'s The amorphous cellulose thus obtained was about 2% in suspension, and kept refrigerated a t 2°C with p H 4.8. Cellulase was produced in submerged fermentation using a mutant of T. viride (&;\I 9123); the crude culture filtrate was used directly as the enzyme solution.2 Reactions were carried out in a 2 liter batch reactor operated a t 50°C and pH 4.8, the optimal conditions reported for saccharification.2 The reactor configuration was essentially the same as that described by previous worker^.^ Preliminary experiments on the effect of agitation speed on the product concentration versus time curve were performed a t three agitation speeds, i.e., 60, 120, and 240 rpm. Little or no difference was noticed. This showed the insignificance of external mass-transfer as long as the solids were kept suspended. Agitation speed was thus chosen a t 120 rpm throughout this study. Samples withdrawn a t various contact times were quickly centrifuged and the supernatants were frozen for later analyses. The total reducing sugar was measured by a dinitrosalicylic acid (DNS) method.16 The amount of glucose was determined by the glucose oxidase method; the Glucostat (Worthington Biochemical Corp., Freehold, N. J.) used was found to be specific and suitable for rapid analyses. The difference in total reducing sugar and glucose in a given sample was cellobiose. Protein content was assayed by the phenol procedure.'?
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1423
THEORETICAL The cellulase used in this study contained high levels of C1 and endo-p-1,4 glucanases, but low levels of exo-P-1,4 glucanases and j3-glucosidases.2 The soluble hydrolysates were mainly cellobiose and glucose, with little if any higher glucose polymers. In constructing a kinetic model, it is stipulated that the enzyme I3 is adsorbed rapidly on the cellulose S to form complex Xl, which irreversibly proceeds to yield products P. The products (mixture of cellobiose and glucose) then reversibly combine with the enzyme to form inactive complexes X2. This reaction scheme can be depicted as follows.
It is assumed that adsorption occurs so fast that equilibrium is established a t all times, that the Langmuir adsorption modells
prevails, and that eq. ( 2 ) is the rate determining step. I n eq. (4), Xl and X1, are the amount and saturation amount of enzyme adsorbed per unit mass of substrate, ( E ) is the enzyme concentration, and K 1equals kl/k-l. Since substrate concentration is much greater than enzyme concentration, the steady-state assumption is va1id;'g in this case d(X2)/dt = 0. Thus, with conservation equation ( E ) o= ( E ) (XI) (X2),the rate of reaction v is
+
+
HUANG
1424
where parentheses denote concentrations based upon the unit volume of liquid phase, subscript zero denotes the initial condition, t is the contact time, and K 3 equals k3/k_,. Rearranging eq. (5) by assuming X1, >> X1 gives 1 _ -
-
1
V
If (S)
=
+ Kl(E)O + K3(P) . - 1 +- 1 k?XlmKl(E)O (S) k m o
(6)
(S)o - ( P ) is assumed, eq. (6) can be integrated to form
with (P)o = 0. Rearranging (7) to a linear form
or
reveals that a plot of l / e versus 1/(8) for the batch reactions a t a given (E)o but varying (S)o would yield a family of straight lines with the same intercept. The slope, however, is a function of AS)^. One way to evaluate the kinetic parameters in eq. (7) is to use initial rate data, vo. When ( P ) = 0, eq. (6) becomes
1
_ -VO
+
1 K1(E)o .-+1 hX,rnKl(E)O (S)o
1
k2(E)0
(10)
Therefore, plotting l / v o versus l/(S)o a t a given ( E ) o usually , referred to as the Lineweaver-Burk plot, should yield linear relationships. The rate constant k2 can be determined directly from the intercept, and the constants K1 and X1, are derived from the slopes of different ( E ) o . The value of K 3 can then be evaluated according to eq. (9) from either the slope or intercept. The use of one would serve as a check for the other. One of the best ways of obtaining vo is by fitting the product concentration-time data to a polynomial form.20 In this way, the notorious initial rate measurements’ reproducibility scatter was
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1425
avoided and a more reliable value obtained. Expansion of eq. (7) in a series gives
Thus, the coefficient of the ( P ) term directly gives the value of l/vo. It is obvious that all the polynomial coefficients in eq. (11) should be positive.
RESULTS AND DISCUSSION Batch reactions were carried out at several initial substrate concentrations and three initial enzyme levels, i.e., 0.38,0.25,and 0.15 mg protein/ml. The initial substrate concentration was determined from the sugar produced at 50 hr of reaction time; essentially, all of the amorphous cellulose was solubilized a t this prolonged contact with the enzyme. Since 10 mg/ml of cellulose would yield 11 mg/ml of reducing sugar, all of the glucose concentrations assayed by the DNS method were corrected accordingly before being fitted to eq. (9). As illustrated in Figure 1, a linear relationship prevailed up to 70y0conversion or higher when 1/0 was plotted against l/(S) for all cases. The slopes and the intercepts obtained are tabulated in Table I. It is TABLE I Experimental and Calculated Slopes and Intercepts According to Eq. (9) Experimental (El0
@)o
slope
intercept
Calculated slope ~
0.38
0.25
0.15
10.0 7.2 5.0 3.6 10.7 7.1 5.2 3.5 5.0 3.8
3.68 2.68 1.90 1.38 6.00 4.02 2.98 2.05 4.91 3.68
-0.33 -0.30 -0.32 -0.36 -0.50 -0.51 -0.51 -0.54 -0.88 -0.81
~~~
3.69 2.69 1.90 1.40 5.97 4.01 2.97 2.05 4.75 3.66
intercept ~
~~
-0.33 -0.33 -0.33 -0.33 -0.50 -0.50 -0.50 -0.50 -0.83 -0.83
1426
HUANG 0.6
0.4
I>
\
0.2
0.0
- 0.2
- 0.4 (a)
Fig. 1. (Continued).
evident that the intercept is inversely proportional to ( E )0, as expected from eq. (9). Figure 2 shows typical results of protein content in the liquid phase as a function of time. A sharp initial drop is indicative of the rapid adsorption process. As the reaction progressed, enzyme was released slowly back into the liquid phase due to the lesser substrate availability. Since it is reasonable to assume that the protein concentration in the liquid phase is proportional to the enzyme concentration, the only effect it has upon the protein concentration in the analysis is on the K 1 value (see eq. (4)). Also shown is the total reducing sugar and glucose produced as a function of time. The discrepancy between the total reducing sugar and glucose is due to the cellobiose. The cellobiose/glucose ratio was about 3 : l for a
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1427
0.5
I> \
-
0.0
- 0.5
(b) Fig. 1. (Continued)
time of .5 hr and was 7:3 for G hr. A t 24 hr, however, it was about 1 : l . The fact that this ratio was held reasonably constant for the experimental time period permitted the assumption of the validity of eq. (3). Progress curves ( P ) versus t were evaluated in accordance with eq. (7), using the slopes and intercepts shown in Table I. The calculated data were then matched by means of least-square-error analysis t o a third-order polynomial in ( P ) ,with a zero order coefficient set to be zero (see eq. (11)). At 40% conversion it was estimated to be only 6y0in error with the terms in (P)4and higher orders being ignored. Using the calculated data instead of the experimental data assured positive polynomial coefficients from the computer
HUANG
1428
-1.01 (C)
Fig. 1. Plot of l/V vs. l/(S) a t ( E ) o of (a) 0.38, (b) 0.25, and (c) 0.15 mg/ml. Parameters: (S)O. Arrows: 70% conversion.
output. The first-order coefficients ( l / v o ) were then used for the Lineweaver-Burk type plot. At two enzyme levels, l / v o versus l/(S)oplot showed linearity (Fig. 3). I t thus permitted the evaluation of kinetic parameters kz, K1, Xlm,and subsequently K S ;they were 80.3 (hr)-l, 1.68 (mg/ml)-l, 0.305 (mg/mg), and 5.61 (mg/ml)-l, respectively. The third enzyme level was not deemed appropriate for this plot since only two batch runs were performed. Nevertheless, it could serve to check the accuracy of the determined parameters. Of the slopes and intercepts calculated by using these parameters, all agreed satisfactorily with the experimentally determined values (see Table I). It was particularly gratifying in the case of (E)o =
INSOLUBLE CELLULOSE-CELLULASE KINETICS
1429
T I M E , HRS.
Fig. 2. Sugar and enzyme levels as a function of the reaction time for (S)O= 10.0 mg/ml, ( E ) o = 0.38 mg/ml; (0) yo converted to reducing sugar; (0) yo converted to glucose; ( A ) % protein in the liquid phase.
0.15 inasmuch as they were predicted values. Progress curves generated from these kinetic constants are compared with the experimental results in Figure 4. In general, they overestimated for conversion beyond 70%. The discrepancy a t higher conversion is understandable. First, the assumption of X1, >> X1may not be valid in that region. Calculation of XI (from Fig. 2 ) a t 10 min and 4 hr of contact time, for example, gives 0.021 and 0.071 mg protein/mg cellulose. This is to be compared with the X1, value of 0.305. This invalid assumption would cause the model to overestimate the experimental results. Secondly, by not taking into account the enzyme heat denaturation and sugar adsorption on cellulose, in constructing the model there is a tendency to overestimate the actual data. However, the fact that the ratio of cellobiose to glucose decreased slightly during the first few hours of reaction should have the opposite effect.
1430
HUANG
o’2
0.0
t I
0.2
0.I
0.3
l/(s)o
Fig. 3. The Lineweaver-Burk plot for ( E ) o = 0.38 (0)and 0.25 ( A ) mg/ml; the slopes being 0.105, and 0.138, and the intercepts 0.032, and 0.052, respectively.
The parameter K Bdefined here is not an intrinsic kinetic constant, instead it is a function of individual sugar concentration. Ideally, eq. (3) should be further divided into two reactions, one reaction for each enzyme complexing with cellobiose and glucose. I n practice, since the cellobiose/glucose ratio was fairly constant up to several hours, combining these two inactivation reactions did not greatly affect the data analysis. Enzymatic degradation of waste cellulose such as newspaper would require a model consisting of two substrates (amorphous and crystalline cellulose) and a t least one inert material (lignin). Although lignin does not appear to interfere with the hydrolysis chemically, it does have adsorptive capacity for the enzyme molecules. A kinetic study of pure cellulose (containing both amorphous and crystalline states) and the knowledge of enzyme adsorption on lignin are necessary before waste cellulose hydrolysis modeling in pollution abatement and glucose producing schemes can be done.
INSOLUBLE CELLULOSE-CELLULASE KINISTICS
(D
t
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1 W /OW ‘HQOIW
(D
t v)
K
I
N
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HUANG
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I 0
I
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6
TIME, HRS (c)
Fig. 4. Comparison of experimental (points) and predicted (lines) progress curves for (E)o a t (a) 0.38, (b) 0.25, and.(c) 0.15 mg/ml. Parameters: (S)O. The author is grateful to Dr. Mary Mandels for her constant guidance and to Mr. Leo A. Spano for his continued interest throughout the investigation. He is indebted to Dr. E. T. Reese for his advice and to Dr. R. K. Andren, Mr. J. A. Kostick, and Mr. L. Hontz for their assistance during the various phases of the program. This research was conducted while the author was a National Research Council Visiting Scientist a t the U. S. Army Natick Laboratories, Natick, Massachusetts.
References 1. M. Mandels and E. T. Reese, Develop. Ind. Microbiol., 5, 5 (1964). 2. M. Mandels and J. Weber, Advan. Chem. Ser., 95, 391 (1969). 3. T. K. Ghose, Biotechnol. Bioeng., 11, 239 (1969). 4. T. K. Ghose and J. A. Kostick, Advan. Chem. Ser., 95, 415 (1969). 5. T. K. Ghose and J. A. Kostick, Biotechnol. Bioeng., 12, 921 (1970). 6. M. Mandels, J. A. Kostick, and It. Parizek, J. Polym. Sci., Part C, 36, 445 (1971). 7. B. H. Van Dyke, Doctoral Thesis, M. I. T., Cambridge Mass., 1972.
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8. M. Mandels, L. Hontz, and D. Brandt, Disposal of Cellulosic Waste Materials by Enzymatic Hydrolysis, A r m y Sci. Conf. Proc., vol. 3, AD 750351, 1972, pp. 16-31. 9. D. Brandt, L. Hontz, and M. Mandels, Engineering Aspects of the EnzymaticConversion of WasteCellulose to Glucose, A I C H E S y m p . Ser., vol. 69, No. 133, 1973, pp. 127-133. 10. E. T. Reese, R. G. H. Siu, and H. S. Levinson, J . Bacteriol., 59, 485 (1950). 11. T. M. Wood and S. I. McCrae, Biochem. J., 128, 1183 (1972). 12. T. K. Ghose and K. Das, in Advances in Biochemical Engineering, vol. 1, T. K. Ghose and A. Fiechter, Eds., Springer-Verlag, New York, 1971, pp, 55-76. 13. M. Mandels and E. T. Reese, in Advances in Enzymic Hydrolysis of Cellulose amd Related Materials, E. T. Reese, Ed., Pergamon Press, New York, pp. 115-157. 14. M. Katz and E. T. Reese, Appl. Microbiol., 16, 419 (1968). 15. C. S. Walseth, Tappi, vol. 35, No. 5, May, 1952, pp. 228-233. 16. J. B. Sumner and G. F. Somers, Laboratory Experiments in Biological Chemistry, Academic Press, New York, 1944. 17. 0. H. Lowry, N. J. Rosebrough, A. L. Farr, and R. J. Randall, J . Biol. Chem., 193, 265 (1951). 18. I . Langmuir, J . Amer Chem. Soc., 38, 2267 (1916). 19. F. G. Heineken, H. M. Tsuchiya, and K. Ark, Math. Biosciences, 1, 95 (1965). 20. R. D. Philo and M. J . Selwyn, Biochem. J., 135, 525 (1973).
Accepted for Publication April 28, 1975
