- Email: [email protected]
Modelling thermal stability and activity of free and immobilized enzymes as a novel tool for enzyme reactor design
Bioresource Technology 98 (2007) 3142–3148
Modelling thermal stability and activity of free and immobilized enzymes as a novel tool for enzyme reactor design A.M.P. Santos a, M.G. Oliveira b, F. Maugeri b
b,*
a Laboratory Devices and Nanostructure/DES/UFPE, 50711-970, Recife, Brazil Food Engineering Department, Universidade Estadual de Campinas, UNICAMP, CEP – 13083-970 Campinas, SP, CP 6121, Brazil
Received 4 November 2005; received in revised form 26 October 2006; accepted 28 October 2006 Available online 24 January 2007
Abstract In this work, a novel method is proposed to establish the most suitable operational temperature for an enzyme reactor. The method was based on mathematical modelling of the thermal stability and activity of the enzyme and was developed using thermodynamic concepts and experimental data from free and immobilized inulinases (2,1-b-D fructan frutanohydrolase, EC 3.2.1.7) from Kluyveromyces marxianus, which were used as examples. The model was, therefore, designed to predict the enzyme activity with respect to the temperature and time course of the enzymatic process, as well as its half-life, in a broad temperature range. The knowledge and information provided by the model could be used to design the operational temperature conditions, leading to higher enzyme activities, while preserving acceptable stability levels, which represent the link between higher productivity and lower process costs. For the inulinase used in this study, the optimum temperature conditions leading to higher enzyme activities were shown to be 63 C and 57.5 C for the free and immobilized inulinases, respectively. However, according to the novel method of approach used here, the more appropriate operating temperatures would be 52 C for free and 42 C for immobilized inulinases, showing that the working temperature is not necessarily the same as the maximum reaction rate temperature, but preferably a lower temperature where the enzyme is much more stable. 2006 Elsevier Ltd. All rights reserved. Keywords: Enzyme reactor; Enzyme activity; Enzyme half-life; Mathematical modelling; Working temperature design
1. Introduction The thermal stability of enzymes is a very important parameter in enzyme reactor designs, as it determines the limits for use and reuse of the enzyme, and therefore process costs. Given the considerable concern about thermal conditions, many reports emphasize enzyme stability (Matsumoto and Ohashi, 2003; Albayrak and Yang, 2002; Yoon et al., 2002). However, a simple and reliable method, such as the one described in this work, leading not only to knowledge of the effect of temperature on enzyme activity
*
Corresponding author. Tel.: +55 19 3788 4052; fax: +55 19 3788 4024. E-mail address: [email protected] (F. Maugeri).
0960-8524/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2006.10.035
and stability, but also to the most convenient working temperature, has not yet been reported. Inulinase from Kluyveromyces marxianus var. bulgaricus was taken as a model enzyme to develop the methodology. Inulinases (2,1-b-D fructan frutanohydrolase, EC 3.2.1.7) are hydrolytic enzymes classified as endo or exo-inulinases according to their action on inulin, producing oligomers of fructose or only fructose, respectively. Microbial inulinases are an important class of industrial enzymes that have received much attention recently. Inulinases can be produced by host microorganisms, including fungi, yeast and bacteria (Pandey et al., 1999). Yeasts of the genus Kluyveromyces are used for the industrial production of b-galactosidase (EC 3.2.1.23) and also for the production of heterologous proteins (Van den Berg et al., 1990). Furthermore, these yeasts have the GRAS (generally regarded as
A.M.P. Santos et al. / Bioresource Technology 98 (2007) 3142–3148
3143
Nomenclature [E] E0 Ea Ed K K0
active enzyme concentration (lmols ml1) initial active enzyme concentration (lmols ml1) activation energy constant (kcal/mol) activation energy constant for enzyme denaturation (kcal/mol) kinetic constant (min1) constant (min1)
safe) status, which makes them particularly suitable for the production of pharmaceutical and food grade proteins ¨ ngen-Baysel and Sukan, 1996). (Hensing et al., 1994; O Many purified microbial inulinase enzymes show remarkable invertase activity, but studies carried out with inulinase have shown that the enzyme has both hydrolytic and transfructosylation activities (Santos and Maugeri, 2002). This latter property may lead to new approaches for the industrial application of inulinases, such as oligosaccharide synthesis from sucrose, increasing the economic and scientific importance of this enzyme.
Kd Kd0 R T s v v0
denaturation constant (min1) constant (min1) gas constant (1.9872) (cal mol1 K1) absolute temperature (K1) half-life (h) reaction rate (lmols ml1 min1) constant (lmols ml1 min1)
tion for the free enzyme, and per ml of particle volume for the immobilized enzyme. 2.3. Effect of pH and temperature on inulinase activity The effects of pH and temperature on the activity of free and immobilized inulinases were studied with 0.1 M sodium acetate buffer, incubating the enzyme solution under different conditions. The pH values ranged from 3.6 to 5.6 and temperature from 20 to 70 C. 2.4. Immobilization in calcium alginate
2. Methods 2.1. Enzyme Inulinase was produced by Kluyveromyces marxianus var. bulgaricus ATCC 16045 in shaken flasks. The fermentation medium was composed of 30 g sucrose l1, 20 g yeast extract l1, 20 g peptone l1 and 5 g K2HPO4 l1. All fermentations were carried out at pH 3.5 and 30 C for 72 h. The extracellular enzyme was recovered by precipitation, adding ethanol to the enzyme solution at 4 C up to a concentration of 70% alcohol. The precipitate was recovered by centrifugation, re-dissolved in 0.05 M acetate buffer at pH 5.0, and then stored in small portions at freezing temperature. 2.2. Enzyme activity
Inulinase was immobilized by adding 10 ml of enzyme solution to 10 ml of a 7% (w/v) sodium alginate solution. This solution was then dripped into a 0.2 M calcium chloride solution with agitation, forming spheres that were maintained in this solution for 2 h. They were then washed and stored in a 0.05 M calcium chloride solution. 2.5. Modelling Enzymatic activity, or reaction rate, can be expressed by Eq. (1), where K is the kinetic constant and E the active enzyme concentration. Additionally, K varies with temperature, so that it can be expressed by an Arrhenius type equation (Eq. (2)): v ¼ KE K ¼ K0 e
Inulinase activity was measured according to the concentration of reducing sugars released from sucrose, as fructose equivalents, after incubation of 9.0 ml of sucrose solution (2% w/v in 10 mM sodium acetate buffer pH 5.0) with 1.0 ml of enzyme solution or 1 ml of particles for the immobilized enzyme, at 50 C. In the latter case, the volume of particles was measured considering the equivalent volume of water displaced in a graduated tube. Reducing sugars were measured according to the DNS acid method (Miller, 1959). One unit of inulinase activity was defined as the amount of enzyme hydrolysing 1.0 lmol of sucrose per minute. The volumetric activity (lmol min1 ml1) was defined as the enzyme activity per ml of enzyme solu-
ð1Þ Es RT
ð2Þ
At high temperatures however, enzymatic denaturation becomes a relevant factor, so an additional term must be included in the equation, which will predict enzyme decay. Assuming that inulinase denaturation is a first order process, enzyme decay can be expressed by the following equations: dE ¼ K d :E dt E ¼ E0 eK d t
ð3Þ ð4Þ
where E0 is the active enzyme concentration at the starting point, usually zero time.
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Since the denaturation constant, Kd, is a kinetic parameter and temperature dependent, it may also be represented by an Arrhenius-type equation. Ed
K d ¼ K d0 eRT
ð5Þ
The final model representing enzyme activity as a function of temperature and reaction time can be expressed by the set of relationships represented in the following equations: v ¼ KE Ea
K ¼ K 0 eRT E ¼ E0 eK d t
ð6Þ
Ed
K d ¼ K d0 eRT
The final expression for m as a function of temperature and reaction time is obtained by combining the expressions in Eq. (6), leading to Ea Ed v ¼ v0 exp exp K d0 exp t ð7Þ RT RT This equation represents, therefore, two major phenomena in the enzyme reaction process: the activation process, represented by the first part of the right-hand side of the equation, the K part, which is significant at the lowest temperatures; and the inactivation process, expressed by the second term, the E part, which is significant at the highest temperatures. Since K0 and E0 are constants, they were lumped into a constant nominated v0. Another important parameter in enzyme reactor design is the thermal enzyme stability, which can be expressed by its half-life as shown in Eq. (8), which is obtained from Eq. (4) by substituting E by E0/2 and Kd by its respective expression from Eq. (6). E0 =2 ln ¼ K d s E0 0:69 ð8Þ s¼ Ed K d0 eRT The parameters in Eq. (7) are better determined by nonlinear regression. However, an important issue involved in good and reliable parameter fitting, is having a set of biochemically significant initial values, which requires prior determination, such as by linear regression of the experimental data. Therefore, the initial value for the activation energy, Ea, can be obtained from linearisation of Eq. (2) and by plotting the Ln of the experimental initial activity data, v, at different temperatures, against 1/T. The values for Kd at different temperatures are obtained by linearisation of Eq. (4) and by plotting the Ln of the experimental initial activities against time, whereas values for Ed and Kd0 are estimated by plotting the Ln of Kd at different temperatures against 1/T. The parameters E0 and K0, or v0, cannot be estimated directly from the experimental data and are therefore estimated by non-linear regression. Additionally,
for fitting proposals, the variable t in Eq. (7) should be very small, 1 min or less, since only initial rates are being considered. 3. Results and discussion 3.1. Effects of pH The effects of pH on the hydrolytic activities of sucrose were studied for free and immobilized inulinases. The optimum pH was shown to be 4.8 and 4.4 for free and immobilized inulinases, respectively (Fig. 1). This small difference was probably due to the anionic characteristic of the alginate, which attracts cations, changing the microenvironment around the immobilized enzyme. Coincidently, the same pH values were found to be the most appropriate for enzyme stability (Fig. 2). Ettalbi and Baratti (2001) obtained similar results for free (pH 4.7) and immobilized (5.0) inulinase from Aspergillus niger. Both preparations were fairly stable in acidic pH (pH 4.5–5.5), while there was a rapid decrease in stability at higher pH values. Inulinase from K. marxianus CDBB-L-278 was shown to have an optimum at pH 5.0 (Cruz-Guerrero et al., 1995) and inulinase from Penicillum rugulosum at pH 5.5–5.6, a value close to that of commercial inulinase (Barthomeuf et al., 1991). 3.2. Effects of temperature Thermal stability was studied at different temperatures and estimated for both immobilized and free enzymes. The maximum temperatures for activity were shown to be 63 C and 57.5 C for free and immobilized inulinases, respectively (Fig. 3). Since the maximum temperature was higher for the free enzyme, this means that free enzyme should be more stable than the immobilized form. This was confirmed by the inactivation energy constants and
Fig. 1. Enzymatic activity as a function of pH at 50 C in 0.1 M sodium acetate buffers, for free and immobilized inulinases.
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half-life values obtained in the present study. Kato et al. (1999) showed that free inulinase from Bacillus stearothermophilus KP1289 had an optimum at 60 C, while CruzGuerrero et al. (1995) verified that inulinase from K. marxianus CDBB-L-278 achieved greatest activity and good stability at 50 C. Similar results were found for the inulinase from fungi, where the enzyme was stable for 2 h at 50 C, but losing 12% activity after 2 h at 55 C and being totally inactivated after 30 min at 60 C (Barthomeuf et al., 1991). Such data, although similar to those obtained in the present work, are not appropriate for enzyme reactor designs, since they cannot predict enzyme behaviour according to the temperature. Only data dealing simultaneously with enzyme activity and half-life can fulfil this task, as shown in the present study. However it must be mentioned that a relatively high temperature is particularly interesting in industrial processes, because it inhibits bacterial contamination and allows for greater concentration of the sugars, an ideal condition for fructooligosaccharide production by inulinases (Santos and Maugeri, 2002). 3.3. The activation energy constant The activation energy constants, Ea, were first determined by linear regression according to Fig. 4, and then more finely by non-linear regression, using the software Statisca 5.5 from Statsoft InCo, obtaining values of 10.77 kcal/mol and 10.04 kcal/mol for the free and immobilized inulinases, respectively. Therefore, the catalytic potential of inulinase is not affected by immobilization, as the activation energies for the free and immobilized enzymes were quite similar. Ettalbi and Baratti (2001) also found similar activation energy constants for free (29.4 kJ/mol) and immobilized (26 kJ/mol) inulinase from A.niger. Fig. 2. Inulinase stability as a function of time and pH at 50 C in 0.1 M sodium acetate buffers for (a) free and (b) immobilized inulinases.
Fig. 3. Enzymatic activity as a function of temperature at pH 4.5 in 0.1 M sodium acetate buffer, for free and immobilized inulinases.
Fig. 4. Estimation of the activation energy constants (Ea) for the free and immobilized enzymes.
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3.4. The denaturation energy constant The denaturation constants, Kd, were determined at different temperatures by plotting Ln(v) against time for the free and immobilized enzymes (Fig. 5). The denaturation energy constants, Ed, were determined using the same method as for Ea, by first plotting Ln(kd) against temperature (Fig. 6) and then using non-linear regression, obtaining values of 126.75 kcal/mol and 71.33 kcal/mol for the free and immobilized inulinases, respectively. Since Ed represents the energy necessary to start the denaturation reaction, and since Ed for the immobilized enzyme was shown to be lower than for the free enzyme, it becomes clear that the immobilized enzyme was less stable as compared to the free enzyme, when using this immobilization method. This can be better seen in Table 2, where the half-lives of both types of enzyme are shown as a function of the temperature. In regions near the maximum activity temperature, the immobilized enzyme stability was very low. Similar results were found for the free inulinase from B. stearothermophilus KP1289, with a half-life at 60 C of about 10 min (Barthomeuf et al., 1991), and for the free inulinase from K. marxianus CDBB-L-278, with half-lives of 180 min at 50 C and 30 min at 60 C (Cruz-Guerrero et al., 1995).
Fig. 5. Determination of the denaturation constants (Kd,) at different temperatures for (a) free and (b) immobilized inulinases.
Fig. 6. Estimation of the denaturation energy constants (Ed) for free and immobilized inulinases.
3.5. Fitting to the mathematical model The values predicted by the model and the experimental data were plotted in Fig. 7. In this figure, the ordinates were normalized, represented by the relative activity (v/ vmax) and inverse relative half-live (smax/s), where vmax is the maximum activity and smax is the half-live at the temperature corresponding to vmax. The model was used with
Fig. 7. Estimation of the process temperature for (a) free and (b) immobilized inulinases, using the relative enzymatic activity for the experimental data (symbols) and for the model (Eq. (7)) predictions (solid lines). 100% absolute activities were 21.6 U/ml of solution for free and 1.2 U/ml of particles for immobilized inulinases.
A.M.P. Santos et al. / Bioresource Technology 98 (2007) 3142–3148 Table 1 Model (Eq. (7)) parameters for free and immobilized inulinases 1
Ea (kcal mol ) Ed (kcal mol1) v0 (lmols ml1min1) Kd0 (min1)
Free
Immobilized
10.70 121.65 1.97 · 108 5.69 · 1079
10.04 71.33 8.86 · 104 2.71 · 1047
the fitted parameters from Table 1. It can be seen that the model predicted the enzyme activity quite well according to the changes in temperature, for both the free and immobilized enzymes. The R2 correlation coefficients were determined by the Statistica Software (Statsoft Inc.) and their values were higher than 0.98, with 95% of confidence. Therefore, the model represented by Eq. (7) can be used for prediction proposals, as well as for the reactor design. 3.6. Half-lives for free and immobilized inulinases The enzyme half-lives were estimated by Eq. (8), for both the immobilized and free enzymes, and presented together with the experimental data in Table 2. In this case the R2 correlation coefficients were higher than 0.97, with 95% of confidence, despite some important deviation between the model prediction and experimental half-lives. However, as shown in Fig. 7, the fit was quite acceptable in the operational zone, as discussed later in this article. 3.7. Working temperature In industrial processes, finding a working temperature that gives high enzyme activity with good stability represents a compromise between lower process costs and higher productivities. This temperature can first be estimated from a double normalized plot of the enzyme half-life and the enzymatic activity against temperature, as shown in Fig. 7. As can be seen in this plot, the process temperatures are not necessarily those corresponding to maximum enzyme activity, since at this point the denaturation rate of the enzyme is very high. Therefore, the process temperature must be somewhat lower then that giving maximum activity in order to increase the enzyme lifetime, but to
3147
an extent that will not affect process productivity as a whole. This temperature may be determined from the interception of the lines, as shown by the arrows in Fig. 7. At this point, enzyme stability is significantly higher, which means that the loss of enzyme is greatly diminished. On the other hand, the reaction rate is lowered, which can be circumvented by a proportional increase in the enzyme concentration in the reaction medium, so that productivity will be less affected. However, since half-lives decrease very rapidly with temperature increases, the selection of an even lower temperature may improve enzyme stability without any considerable loss of activity. For example, if we choose 50 C as the operating temperature for free enzymes instead of 51 C, the half-live increases from 126 to 226 h, while the relative activity only decreases from 0.58 to 0.50. Therefore it is possible that the double intercept plot methodology described above may need a complementary assay, such as, for example, a target function involving the costs of the enzyme and the production, subsequently using standard optimisation calculations to find the optimum point. Also, the mathematical modelling of both activity and half-life was shown to be a very useful procedure in order to obtain the optimum conditions to operate the enzyme reactor, mainly when an objective function was to be determined. The results were quite similar if the model predictions were used as an alternative to the experimental data, since the models fitted the experimental points quite well in the operational zone, as shown in Fig. 7. In addition, the modelling procedure is less time demanding, and with only about five suitable experimental points it is possible to obtain a reliable model. As can be seen by the arrows in Fig. 7, the operational temperatures could be defined as about 51 C and 42 C, with half-lives of approximately 130 h and 80 h for the free and immobilized inulinases, respectively. 4. Conclusions The inulinase from K. marxianus var. bulgaricus showed higher activities and stabilities at pH 4.4 and 4.8, and maximum temperature activities at 63 C and 57.5 C, for the
Table 2 Experimental data and model predictions for the free and immobilized inulinase half-lives Temperature (C)
40.0 42.5 45.0 47.5 50.0 52.5 55.0 57.5 60.0
Half-life (h)
Half-life (h)
Free (experimental)
Free (model)
Deviation (%)
Immobilized (experimental)
Immobilized (model)
Deviation (%)
– – – – 228.8 10.0 5.5 1.6 0.3
– – – – 226.7 52.9 12.6 3.0 0.7
– – – –
138.0 74.2 47.6 9.4 7.2 1.9 – – –
153.7 62.0 25.4 10.5 4.5 1.9 – – –
11.3 16.4 46.6 11.7 37.5 0 – – –
Experimental data not available.
0.9 429 129 87 133
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free and immobilized inulinases, respectively. The activation energy constants were shown to be 10.77 kcal/mol and 10.04 kcal/mol, and the denaturation energy constants, 126.75 and 71.33 kcal/mol, for the free and immobilized inulinases, respectively. As shown in this study, according to the method using a double normalized plot, using either the experimental results or model predictions for the activities and half-lives, it is possible to determine the most appropriate operational temperature for an enzyme reactor. For the enzyme used, the values obtained were: 52 C for free and 42 C for immobilized inulinases. It was also shown that modelling of both the activity and half-lives as a function of temperature could be a valuable tool in enzyme reactor design. Acknowledgement The authors acknowledge FAPESP for their financial support. References Albayrak, N., Yang, S.T., 2002. Immobilization of Aspergillus oryzae bgalactosidase on tosylated cotton cloth. Enzyme Microb. Technol. 31 (4), 371–383. Barthomeuf, C., Regenerat, F., Purnrat, H., 1991. Production on inulinase by new mold of Penicillum rugulosum. J. Ferment. Bioeng. 72 (6), 491– 494. Cruz-Guerrero, A., Garcia-Pen˜a, I., Barzana, E., Garica-Garibay, M., Go´mez-Ruiz, L., 1995. Kluyveromyces marxianus CDBB-L-278: a wild
inulinase hyperproduction strain. J. Ferment. Bioeng. 80 (2), 159– 163. Ettalbi, M., Baratti, J.C., 2001. Sucrose hydrolysis by thermostable immobilized inulinase from Aspergillus ficcum. Enzyme Microb. Technol. 28, 596–604. Hensing, M., Vrouwenvelder, H., Hellinga, C., Baartmans, R., Van Dijken, H., 1994. Production of extracellular inulinase in high-cell density fed-batch cultures of Kluyvermyces marxianus. Appl. Microbiol. Biotechnol. 42 (4), 516–521. Kato, K., Araki, T., Kitamura, T., Morita, N., Moori, M., Suzuki, Y., 1999. Purification and properties of a thermostable inulinase (b-dFructan Fructohydrolase) from Bacillus stearothermophilus KP1289. Starch–Starke 51 (7), 253–258. Matsumoto, M., Ohashi, K., 2003. Effect of immobilization on thermostability of lipase from Candida rugosa. Biochem. Eng. J. 14, 75–77. Miller, G.L., 1959. Use of dinitrosalicylic acid reagent for determination of reducing sugar. Anal. Chem. 31 (3), 426–428. ¨ ngen-Baysel, G., Sukan, S.S., 1996. Production of inulinase by mixed O culture of Aspergillus niger and Kluyveromyces marxianus. Biotechnol. Lett. 18 (12), 1431–1434. Pandey, A., Soccol, C.R., Selvakumar, P., Soccol, V.T., Krieger, N., Fontana, J., 1999. Recent developments in microbial inulinase: its production, properties, and industrial application. Appl. Biochem. Biotechnol. 18, 35–52. Santos, A.M.P., and Maugeri, F., 2002. Production of sugar syrup contend fructose and glucose, enriched or not with fructooligosaccharides, from sucrose. Patent, PI 0202.602-3 (Brazil office). Van den Berg, J.A., Van der Laken, K.J., Van Ooyen, A.J.J., Renniers, T.C.H.M., Rietveld, K., 1990. Kluyveromyces as a host for heterologous gene expression: expression and secretion of prochymosin. Bio/ Technol. 8, 135–139. Yoon, S.Y., Noh, H.S., Kim, E.H., Kong, K.H., 2002. The highly stable alcohol dehydrogenase of Thermomicrobium roseum: purification and molecular characterization. Comp. Biochem. Physiol. Part B: Biochem. Mol. Biol. 132 (2), 415–422.
Modelling thermal stability and activity of free and immobilized enzymes as a novel tool for enzyme reactor design A.M.P. Santos a, M.G. Oliveira b, F. Maugeri b
b,*
a Laboratory Devices and Nanostructure/DES/UFPE, 50711-970, Recife, Brazil Food Engineering Department, Universidade Estadual de Campinas, UNICAMP, CEP – 13083-970 Campinas, SP, CP 6121, Brazil
Received 4 November 2005; received in revised form 26 October 2006; accepted 28 October 2006 Available online 24 January 2007
Abstract In this work, a novel method is proposed to establish the most suitable operational temperature for an enzyme reactor. The method was based on mathematical modelling of the thermal stability and activity of the enzyme and was developed using thermodynamic concepts and experimental data from free and immobilized inulinases (2,1-b-D fructan frutanohydrolase, EC 3.2.1.7) from Kluyveromyces marxianus, which were used as examples. The model was, therefore, designed to predict the enzyme activity with respect to the temperature and time course of the enzymatic process, as well as its half-life, in a broad temperature range. The knowledge and information provided by the model could be used to design the operational temperature conditions, leading to higher enzyme activities, while preserving acceptable stability levels, which represent the link between higher productivity and lower process costs. For the inulinase used in this study, the optimum temperature conditions leading to higher enzyme activities were shown to be 63 C and 57.5 C for the free and immobilized inulinases, respectively. However, according to the novel method of approach used here, the more appropriate operating temperatures would be 52 C for free and 42 C for immobilized inulinases, showing that the working temperature is not necessarily the same as the maximum reaction rate temperature, but preferably a lower temperature where the enzyme is much more stable. 2006 Elsevier Ltd. All rights reserved. Keywords: Enzyme reactor; Enzyme activity; Enzyme half-life; Mathematical modelling; Working temperature design
1. Introduction The thermal stability of enzymes is a very important parameter in enzyme reactor designs, as it determines the limits for use and reuse of the enzyme, and therefore process costs. Given the considerable concern about thermal conditions, many reports emphasize enzyme stability (Matsumoto and Ohashi, 2003; Albayrak and Yang, 2002; Yoon et al., 2002). However, a simple and reliable method, such as the one described in this work, leading not only to knowledge of the effect of temperature on enzyme activity
*
Corresponding author. Tel.: +55 19 3788 4052; fax: +55 19 3788 4024. E-mail address: [email protected] (F. Maugeri).
0960-8524/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2006.10.035
and stability, but also to the most convenient working temperature, has not yet been reported. Inulinase from Kluyveromyces marxianus var. bulgaricus was taken as a model enzyme to develop the methodology. Inulinases (2,1-b-D fructan frutanohydrolase, EC 3.2.1.7) are hydrolytic enzymes classified as endo or exo-inulinases according to their action on inulin, producing oligomers of fructose or only fructose, respectively. Microbial inulinases are an important class of industrial enzymes that have received much attention recently. Inulinases can be produced by host microorganisms, including fungi, yeast and bacteria (Pandey et al., 1999). Yeasts of the genus Kluyveromyces are used for the industrial production of b-galactosidase (EC 3.2.1.23) and also for the production of heterologous proteins (Van den Berg et al., 1990). Furthermore, these yeasts have the GRAS (generally regarded as
A.M.P. Santos et al. / Bioresource Technology 98 (2007) 3142–3148
3143
Nomenclature [E] E0 Ea Ed K K0
active enzyme concentration (lmols ml1) initial active enzyme concentration (lmols ml1) activation energy constant (kcal/mol) activation energy constant for enzyme denaturation (kcal/mol) kinetic constant (min1) constant (min1)
safe) status, which makes them particularly suitable for the production of pharmaceutical and food grade proteins ¨ ngen-Baysel and Sukan, 1996). (Hensing et al., 1994; O Many purified microbial inulinase enzymes show remarkable invertase activity, but studies carried out with inulinase have shown that the enzyme has both hydrolytic and transfructosylation activities (Santos and Maugeri, 2002). This latter property may lead to new approaches for the industrial application of inulinases, such as oligosaccharide synthesis from sucrose, increasing the economic and scientific importance of this enzyme.
Kd Kd0 R T s v v0
denaturation constant (min1) constant (min1) gas constant (1.9872) (cal mol1 K1) absolute temperature (K1) half-life (h) reaction rate (lmols ml1 min1) constant (lmols ml1 min1)
tion for the free enzyme, and per ml of particle volume for the immobilized enzyme. 2.3. Effect of pH and temperature on inulinase activity The effects of pH and temperature on the activity of free and immobilized inulinases were studied with 0.1 M sodium acetate buffer, incubating the enzyme solution under different conditions. The pH values ranged from 3.6 to 5.6 and temperature from 20 to 70 C. 2.4. Immobilization in calcium alginate
2. Methods 2.1. Enzyme Inulinase was produced by Kluyveromyces marxianus var. bulgaricus ATCC 16045 in shaken flasks. The fermentation medium was composed of 30 g sucrose l1, 20 g yeast extract l1, 20 g peptone l1 and 5 g K2HPO4 l1. All fermentations were carried out at pH 3.5 and 30 C for 72 h. The extracellular enzyme was recovered by precipitation, adding ethanol to the enzyme solution at 4 C up to a concentration of 70% alcohol. The precipitate was recovered by centrifugation, re-dissolved in 0.05 M acetate buffer at pH 5.0, and then stored in small portions at freezing temperature. 2.2. Enzyme activity
Inulinase was immobilized by adding 10 ml of enzyme solution to 10 ml of a 7% (w/v) sodium alginate solution. This solution was then dripped into a 0.2 M calcium chloride solution with agitation, forming spheres that were maintained in this solution for 2 h. They were then washed and stored in a 0.05 M calcium chloride solution. 2.5. Modelling Enzymatic activity, or reaction rate, can be expressed by Eq. (1), where K is the kinetic constant and E the active enzyme concentration. Additionally, K varies with temperature, so that it can be expressed by an Arrhenius type equation (Eq. (2)): v ¼ KE K ¼ K0 e
Inulinase activity was measured according to the concentration of reducing sugars released from sucrose, as fructose equivalents, after incubation of 9.0 ml of sucrose solution (2% w/v in 10 mM sodium acetate buffer pH 5.0) with 1.0 ml of enzyme solution or 1 ml of particles for the immobilized enzyme, at 50 C. In the latter case, the volume of particles was measured considering the equivalent volume of water displaced in a graduated tube. Reducing sugars were measured according to the DNS acid method (Miller, 1959). One unit of inulinase activity was defined as the amount of enzyme hydrolysing 1.0 lmol of sucrose per minute. The volumetric activity (lmol min1 ml1) was defined as the enzyme activity per ml of enzyme solu-
ð1Þ Es RT
ð2Þ
At high temperatures however, enzymatic denaturation becomes a relevant factor, so an additional term must be included in the equation, which will predict enzyme decay. Assuming that inulinase denaturation is a first order process, enzyme decay can be expressed by the following equations: dE ¼ K d :E dt E ¼ E0 eK d t
ð3Þ ð4Þ
where E0 is the active enzyme concentration at the starting point, usually zero time.
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Since the denaturation constant, Kd, is a kinetic parameter and temperature dependent, it may also be represented by an Arrhenius-type equation. Ed
K d ¼ K d0 eRT
ð5Þ
The final model representing enzyme activity as a function of temperature and reaction time can be expressed by the set of relationships represented in the following equations: v ¼ KE Ea
K ¼ K 0 eRT E ¼ E0 eK d t
ð6Þ
Ed
K d ¼ K d0 eRT
The final expression for m as a function of temperature and reaction time is obtained by combining the expressions in Eq. (6), leading to Ea Ed v ¼ v0 exp exp K d0 exp t ð7Þ RT RT This equation represents, therefore, two major phenomena in the enzyme reaction process: the activation process, represented by the first part of the right-hand side of the equation, the K part, which is significant at the lowest temperatures; and the inactivation process, expressed by the second term, the E part, which is significant at the highest temperatures. Since K0 and E0 are constants, they were lumped into a constant nominated v0. Another important parameter in enzyme reactor design is the thermal enzyme stability, which can be expressed by its half-life as shown in Eq. (8), which is obtained from Eq. (4) by substituting E by E0/2 and Kd by its respective expression from Eq. (6). E0 =2 ln ¼ K d s E0 0:69 ð8Þ s¼ Ed K d0 eRT The parameters in Eq. (7) are better determined by nonlinear regression. However, an important issue involved in good and reliable parameter fitting, is having a set of biochemically significant initial values, which requires prior determination, such as by linear regression of the experimental data. Therefore, the initial value for the activation energy, Ea, can be obtained from linearisation of Eq. (2) and by plotting the Ln of the experimental initial activity data, v, at different temperatures, against 1/T. The values for Kd at different temperatures are obtained by linearisation of Eq. (4) and by plotting the Ln of the experimental initial activities against time, whereas values for Ed and Kd0 are estimated by plotting the Ln of Kd at different temperatures against 1/T. The parameters E0 and K0, or v0, cannot be estimated directly from the experimental data and are therefore estimated by non-linear regression. Additionally,
for fitting proposals, the variable t in Eq. (7) should be very small, 1 min or less, since only initial rates are being considered. 3. Results and discussion 3.1. Effects of pH The effects of pH on the hydrolytic activities of sucrose were studied for free and immobilized inulinases. The optimum pH was shown to be 4.8 and 4.4 for free and immobilized inulinases, respectively (Fig. 1). This small difference was probably due to the anionic characteristic of the alginate, which attracts cations, changing the microenvironment around the immobilized enzyme. Coincidently, the same pH values were found to be the most appropriate for enzyme stability (Fig. 2). Ettalbi and Baratti (2001) obtained similar results for free (pH 4.7) and immobilized (5.0) inulinase from Aspergillus niger. Both preparations were fairly stable in acidic pH (pH 4.5–5.5), while there was a rapid decrease in stability at higher pH values. Inulinase from K. marxianus CDBB-L-278 was shown to have an optimum at pH 5.0 (Cruz-Guerrero et al., 1995) and inulinase from Penicillum rugulosum at pH 5.5–5.6, a value close to that of commercial inulinase (Barthomeuf et al., 1991). 3.2. Effects of temperature Thermal stability was studied at different temperatures and estimated for both immobilized and free enzymes. The maximum temperatures for activity were shown to be 63 C and 57.5 C for free and immobilized inulinases, respectively (Fig. 3). Since the maximum temperature was higher for the free enzyme, this means that free enzyme should be more stable than the immobilized form. This was confirmed by the inactivation energy constants and
Fig. 1. Enzymatic activity as a function of pH at 50 C in 0.1 M sodium acetate buffers, for free and immobilized inulinases.
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half-life values obtained in the present study. Kato et al. (1999) showed that free inulinase from Bacillus stearothermophilus KP1289 had an optimum at 60 C, while CruzGuerrero et al. (1995) verified that inulinase from K. marxianus CDBB-L-278 achieved greatest activity and good stability at 50 C. Similar results were found for the inulinase from fungi, where the enzyme was stable for 2 h at 50 C, but losing 12% activity after 2 h at 55 C and being totally inactivated after 30 min at 60 C (Barthomeuf et al., 1991). Such data, although similar to those obtained in the present work, are not appropriate for enzyme reactor designs, since they cannot predict enzyme behaviour according to the temperature. Only data dealing simultaneously with enzyme activity and half-life can fulfil this task, as shown in the present study. However it must be mentioned that a relatively high temperature is particularly interesting in industrial processes, because it inhibits bacterial contamination and allows for greater concentration of the sugars, an ideal condition for fructooligosaccharide production by inulinases (Santos and Maugeri, 2002). 3.3. The activation energy constant The activation energy constants, Ea, were first determined by linear regression according to Fig. 4, and then more finely by non-linear regression, using the software Statisca 5.5 from Statsoft InCo, obtaining values of 10.77 kcal/mol and 10.04 kcal/mol for the free and immobilized inulinases, respectively. Therefore, the catalytic potential of inulinase is not affected by immobilization, as the activation energies for the free and immobilized enzymes were quite similar. Ettalbi and Baratti (2001) also found similar activation energy constants for free (29.4 kJ/mol) and immobilized (26 kJ/mol) inulinase from A.niger. Fig. 2. Inulinase stability as a function of time and pH at 50 C in 0.1 M sodium acetate buffers for (a) free and (b) immobilized inulinases.
Fig. 3. Enzymatic activity as a function of temperature at pH 4.5 in 0.1 M sodium acetate buffer, for free and immobilized inulinases.
Fig. 4. Estimation of the activation energy constants (Ea) for the free and immobilized enzymes.
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3.4. The denaturation energy constant The denaturation constants, Kd, were determined at different temperatures by plotting Ln(v) against time for the free and immobilized enzymes (Fig. 5). The denaturation energy constants, Ed, were determined using the same method as for Ea, by first plotting Ln(kd) against temperature (Fig. 6) and then using non-linear regression, obtaining values of 126.75 kcal/mol and 71.33 kcal/mol for the free and immobilized inulinases, respectively. Since Ed represents the energy necessary to start the denaturation reaction, and since Ed for the immobilized enzyme was shown to be lower than for the free enzyme, it becomes clear that the immobilized enzyme was less stable as compared to the free enzyme, when using this immobilization method. This can be better seen in Table 2, where the half-lives of both types of enzyme are shown as a function of the temperature. In regions near the maximum activity temperature, the immobilized enzyme stability was very low. Similar results were found for the free inulinase from B. stearothermophilus KP1289, with a half-life at 60 C of about 10 min (Barthomeuf et al., 1991), and for the free inulinase from K. marxianus CDBB-L-278, with half-lives of 180 min at 50 C and 30 min at 60 C (Cruz-Guerrero et al., 1995).
Fig. 5. Determination of the denaturation constants (Kd,) at different temperatures for (a) free and (b) immobilized inulinases.
Fig. 6. Estimation of the denaturation energy constants (Ed) for free and immobilized inulinases.
3.5. Fitting to the mathematical model The values predicted by the model and the experimental data were plotted in Fig. 7. In this figure, the ordinates were normalized, represented by the relative activity (v/ vmax) and inverse relative half-live (smax/s), where vmax is the maximum activity and smax is the half-live at the temperature corresponding to vmax. The model was used with
Fig. 7. Estimation of the process temperature for (a) free and (b) immobilized inulinases, using the relative enzymatic activity for the experimental data (symbols) and for the model (Eq. (7)) predictions (solid lines). 100% absolute activities were 21.6 U/ml of solution for free and 1.2 U/ml of particles for immobilized inulinases.
A.M.P. Santos et al. / Bioresource Technology 98 (2007) 3142–3148 Table 1 Model (Eq. (7)) parameters for free and immobilized inulinases 1
Ea (kcal mol ) Ed (kcal mol1) v0 (lmols ml1min1) Kd0 (min1)
Free
Immobilized
10.70 121.65 1.97 · 108 5.69 · 1079
10.04 71.33 8.86 · 104 2.71 · 1047
the fitted parameters from Table 1. It can be seen that the model predicted the enzyme activity quite well according to the changes in temperature, for both the free and immobilized enzymes. The R2 correlation coefficients were determined by the Statistica Software (Statsoft Inc.) and their values were higher than 0.98, with 95% of confidence. Therefore, the model represented by Eq. (7) can be used for prediction proposals, as well as for the reactor design. 3.6. Half-lives for free and immobilized inulinases The enzyme half-lives were estimated by Eq. (8), for both the immobilized and free enzymes, and presented together with the experimental data in Table 2. In this case the R2 correlation coefficients were higher than 0.97, with 95% of confidence, despite some important deviation between the model prediction and experimental half-lives. However, as shown in Fig. 7, the fit was quite acceptable in the operational zone, as discussed later in this article. 3.7. Working temperature In industrial processes, finding a working temperature that gives high enzyme activity with good stability represents a compromise between lower process costs and higher productivities. This temperature can first be estimated from a double normalized plot of the enzyme half-life and the enzymatic activity against temperature, as shown in Fig. 7. As can be seen in this plot, the process temperatures are not necessarily those corresponding to maximum enzyme activity, since at this point the denaturation rate of the enzyme is very high. Therefore, the process temperature must be somewhat lower then that giving maximum activity in order to increase the enzyme lifetime, but to
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an extent that will not affect process productivity as a whole. This temperature may be determined from the interception of the lines, as shown by the arrows in Fig. 7. At this point, enzyme stability is significantly higher, which means that the loss of enzyme is greatly diminished. On the other hand, the reaction rate is lowered, which can be circumvented by a proportional increase in the enzyme concentration in the reaction medium, so that productivity will be less affected. However, since half-lives decrease very rapidly with temperature increases, the selection of an even lower temperature may improve enzyme stability without any considerable loss of activity. For example, if we choose 50 C as the operating temperature for free enzymes instead of 51 C, the half-live increases from 126 to 226 h, while the relative activity only decreases from 0.58 to 0.50. Therefore it is possible that the double intercept plot methodology described above may need a complementary assay, such as, for example, a target function involving the costs of the enzyme and the production, subsequently using standard optimisation calculations to find the optimum point. Also, the mathematical modelling of both activity and half-life was shown to be a very useful procedure in order to obtain the optimum conditions to operate the enzyme reactor, mainly when an objective function was to be determined. The results were quite similar if the model predictions were used as an alternative to the experimental data, since the models fitted the experimental points quite well in the operational zone, as shown in Fig. 7. In addition, the modelling procedure is less time demanding, and with only about five suitable experimental points it is possible to obtain a reliable model. As can be seen by the arrows in Fig. 7, the operational temperatures could be defined as about 51 C and 42 C, with half-lives of approximately 130 h and 80 h for the free and immobilized inulinases, respectively. 4. Conclusions The inulinase from K. marxianus var. bulgaricus showed higher activities and stabilities at pH 4.4 and 4.8, and maximum temperature activities at 63 C and 57.5 C, for the
Table 2 Experimental data and model predictions for the free and immobilized inulinase half-lives Temperature (C)
40.0 42.5 45.0 47.5 50.0 52.5 55.0 57.5 60.0
Half-life (h)
Half-life (h)
Free (experimental)
Free (model)
Deviation (%)
Immobilized (experimental)
Immobilized (model)
Deviation (%)
– – – – 228.8 10.0 5.5 1.6 0.3
– – – – 226.7 52.9 12.6 3.0 0.7
– – – –
138.0 74.2 47.6 9.4 7.2 1.9 – – –
153.7 62.0 25.4 10.5 4.5 1.9 – – –
11.3 16.4 46.6 11.7 37.5 0 – – –
Experimental data not available.
0.9 429 129 87 133
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free and immobilized inulinases, respectively. The activation energy constants were shown to be 10.77 kcal/mol and 10.04 kcal/mol, and the denaturation energy constants, 126.75 and 71.33 kcal/mol, for the free and immobilized inulinases, respectively. As shown in this study, according to the method using a double normalized plot, using either the experimental results or model predictions for the activities and half-lives, it is possible to determine the most appropriate operational temperature for an enzyme reactor. For the enzyme used, the values obtained were: 52 C for free and 42 C for immobilized inulinases. It was also shown that modelling of both the activity and half-lives as a function of temperature could be a valuable tool in enzyme reactor design. Acknowledgement The authors acknowledge FAPESP for their financial support. References Albayrak, N., Yang, S.T., 2002. Immobilization of Aspergillus oryzae bgalactosidase on tosylated cotton cloth. Enzyme Microb. Technol. 31 (4), 371–383. Barthomeuf, C., Regenerat, F., Purnrat, H., 1991. Production on inulinase by new mold of Penicillum rugulosum. J. Ferment. Bioeng. 72 (6), 491– 494. Cruz-Guerrero, A., Garcia-Pen˜a, I., Barzana, E., Garica-Garibay, M., Go´mez-Ruiz, L., 1995. Kluyveromyces marxianus CDBB-L-278: a wild
inulinase hyperproduction strain. J. Ferment. Bioeng. 80 (2), 159– 163. Ettalbi, M., Baratti, J.C., 2001. Sucrose hydrolysis by thermostable immobilized inulinase from Aspergillus ficcum. Enzyme Microb. Technol. 28, 596–604. Hensing, M., Vrouwenvelder, H., Hellinga, C., Baartmans, R., Van Dijken, H., 1994. Production of extracellular inulinase in high-cell density fed-batch cultures of Kluyvermyces marxianus. Appl. Microbiol. Biotechnol. 42 (4), 516–521. Kato, K., Araki, T., Kitamura, T., Morita, N., Moori, M., Suzuki, Y., 1999. Purification and properties of a thermostable inulinase (b-dFructan Fructohydrolase) from Bacillus stearothermophilus KP1289. Starch–Starke 51 (7), 253–258. Matsumoto, M., Ohashi, K., 2003. Effect of immobilization on thermostability of lipase from Candida rugosa. Biochem. Eng. J. 14, 75–77. Miller, G.L., 1959. Use of dinitrosalicylic acid reagent for determination of reducing sugar. Anal. Chem. 31 (3), 426–428. ¨ ngen-Baysel, G., Sukan, S.S., 1996. Production of inulinase by mixed O culture of Aspergillus niger and Kluyveromyces marxianus. Biotechnol. Lett. 18 (12), 1431–1434. Pandey, A., Soccol, C.R., Selvakumar, P., Soccol, V.T., Krieger, N., Fontana, J., 1999. Recent developments in microbial inulinase: its production, properties, and industrial application. Appl. Biochem. Biotechnol. 18, 35–52. Santos, A.M.P., and Maugeri, F., 2002. Production of sugar syrup contend fructose and glucose, enriched or not with fructooligosaccharides, from sucrose. Patent, PI 0202.602-3 (Brazil office). Van den Berg, J.A., Van der Laken, K.J., Van Ooyen, A.J.J., Renniers, T.C.H.M., Rietveld, K., 1990. Kluyveromyces as a host for heterologous gene expression: expression and secretion of prochymosin. Bio/ Technol. 8, 135–139. Yoon, S.Y., Noh, H.S., Kim, E.H., Kong, K.H., 2002. The highly stable alcohol dehydrogenase of Thermomicrobium roseum: purification and molecular characterization. Comp. Biochem. Physiol. Part B: Biochem. Mol. Biol. 132 (2), 415–422.