EFFECTS OF DIFFUSION ON THE KINETICS OF MALTOSE HYDROLYSIS USING GLUCOAMYLASE IMMOBILIZED ON MACROPOROUS SILICA

EFFECTS OF DIFFUSION ON THE KINETICS OF MALTOSE HYDROLYSIS USING GLUCOAMYLASE IMMOBILIZED ON MACROPOROUS SILICA

L.R.B. Gonçalves, R.L.C. Giordano and R.C. Giordano

Departamento de Engenharia Química - Universidade Federal de São Carlos

C.P. 676 - CEP 13565-905-São Carlos - SP - Brazil

Fax number: [phone]; e-mail: [e-mail]

(Received: June 11, 1997; Accepted: October 30, 1997)

Abstract - In this work the effects of diffusion on the hydrolysis of maltose using glucoamylase immobilized on macroporous silica at 30^o C are studied. Two different kinds of experimental assays are carried out: one using free enzyme and the other using an enzyme covalently linked to macroporous silica, preactivated with glutaraldehyde. Free enzyme assays are used to estimate the kinetic parameters for hydrolysis of maltose at 30ºC, according to a Michaelis-Menten equation, with inhibition by the product. Runs with the immobilized enzyme enable us to estimate dextrin diffusivities in silica, assuming that the inherent kinetic parameters are equal to the intrinsic ones. The values of kinetic and mass transfer parameters are: K₃ = 0.90x10^-5 g/U.s, K_m = 0.61x10^-3 g/ml, K_i = 1.23x10^-1 g/ml, D_Ms = 0.50x10^-6 cm² /s and D_Gs = 0.55x10^-6 cm² /s.

Keywords: Maltose hydrolysis, dextrin diffusivity, kinetic parameters.

INTRODUCTION

This work is part of a research project that studies the process of ethanol production from liquefied starch, using glucoamylase immobilized in silica and baker’s yeast entrapped in pectin gel. In this process, the enzyme is covalently linked to silica with controlled porosity, after silanization (with g -aminopropiletoxisilane) and activation of the support with glutaraldhyde. The silica containing the enzyme is later coimmobilized with baker’s yeast in spherical pellets of pectin gel, 4 mm diameter. This biocatalyst may be used in a continuous fixed bed reactor (Giordano and Schmidell, 1992; Gonçalves et al., 1994).

To build a model to represent this bioprocess, it is necessary to estimate kinetic and mass transport parameters. The first step in the estimation of inherent kinetic parameters is to find experimental conditions that guarantee no resistance to mass transfer outside the biocatalyst (external mass transfer limitation). To prevent this external transport limitation, a batch system with vigorous agitation was used.

The main purpose of this work is to determine the diffusivities of maltose and glucose in macroporous silica with immobilized enzyme. It was necessary to perform preliminary assays with free glucoamylase to estimate the kinetic parameters for maltose hydrolysis under bioreactor operational conditions. The kinetic and mass transfer parameters were estimated by fitting mathematical models to experimental data of substrate and product concentration in the course of time.

MATERIALS E METHODS

Materials

Substrate: Maltose - Merck;

Enzyme: glucoamylase - a gift from Novo Nordisck do Brasil (activity: 180 U/ml, where 1 U = amount of enzyme that yields 1 g of glucose/h.l from 40 g/l of soluble starch at 60º C and pH = 4.2);

Support: high porosity silica, with an average diameter of 170 m m, a porosity equal to 0.57 and a mean pore diameter of 270 Å (measured by a N₂ desorption device, ASAP 2000, Micrometrics). All other reactants used are of different laboratory trademarks.

Methods

Enzyme Immobilization (Giordano and Schmidell, 1992):

Silica is silanized with a solution of g -aminopropiltrietoxisilano (0.5%v/v), pH = 3.3, 75º C, for 3 hours, and a liquid-solid ratio 3 ml/g. After that, it is washed with water and then

with acetone. It is later dried until its weight stops changing. The support is activated with glutaraldehyde (in a 2.5% sodium hydrogenophosphate buffer with pH = 7.0, 0.1M) for 1 h at 20 - 25ºC, with a liquid-solid ratio of 3 ml/g. It is washed again and allowed to react with the enzyme solution for 36 h at 20 - 25 ºC, under agitation.

Analytical Methods:

• Glucose: enzymatic method (glucose oxidase - GOD PAP).

• Maltose: Somogyi method.

• Enzyme: free and immobilized enzyme activity, according to Giordano and Schmidell, 1992.

Experimental Proceedure:

Free enzyme assays: Data on change of concentration in time are obtained by adding 0.16 or 0.32 ml (about 30 or 60 U) of glucoamylase solution to 69.5 ml of a 32.17 g/l maltose solution under agitation.

Immobilized enzyme essays: Data on change of concentration in time are obtained adding 0.50 g of silica (about 60 U) to 69.5 ml of a 36.02 g/l maltose solution.

In both assays, 0.1 ml samples are taken periodically. The agitation speed is fixed in order to eliminate the effects of external mass transport (increasing the speed in different experiments until a stationary point is reached).

Numerical Methods:

The solution of the foregoing partial differential equations is accomplished through discretization in the space subdomains of gel and silica (when appropriate), using orthogonal Jacobi polynomials, P^(0,1/2) (Villadsen and Michelsen, 1978). The resulting sets of ordinary differential equations are numerically solved in time. Tests indicate that five internal collocation points for the gel, and three for the silica, suffice to provide a precise response. The kinetic parameters are fitted using a maximum likelihood method (Anderson et al. 1978) that takes into account errors in all measured variables (except time, which is assumed to be error-free) considered to be random and to have normal distributions. The variances are: 9.0x10^-6 (g/ml)², for maltose concentration and 0.25x10^-6 (g/ml)² for glucose concentration in time. Because the maltose analytical method is less precise, only the glucose data are used to estimate the kinetic parameters.

MATHEMATICAL MODELS

Kinetic Model for Hydrolysis of Maltose

A steady-state kinetic model is used (assuming constant intermediate compositions), neglecting reverse reactions and the production of isomaltose, in view of the greater time constant of the last reaction. The kinetic assays, carried out with a batch reactor, endured at most two hours, and the appearance of isomaltose begins to be considerable only after 20 hours, under the conditions of the experiments (Adachi et al., 1984). A Michaelis-Menten equation, with product competitive inhibition, is fitted to the data:

(1)

where R_M = rate of hydrolysis (maltose consumption), g/ml/s; K3= kinetic constant, g/U.s; C_e = amount of enzyme, U/ml; Km= Michaelis-Menten constant, g/ml; C_M = substrate concentration, g/ml; C_G = product concentration, g/ml and K_i = product inhibition constant, ml/g.

The C_e value was obtained experimentally. It should be pointed out that the immobilization technique used in this work is unipunctual; only the amino group of the amino-terminal amino acid residue of the enzyme is reactive under the experimental conditions used here. Therefore, it is plausible to consider that the kinetic parameters for the immobilized enzyme are close to those for the free enzyme, since the enzyme molecule will not be considerably modified by immobilization. It is also known that isomaltose is formed during this reaction, but this formation is quite slow, becoming important only after many hours of reaction (Adachi et al., 1984), which is not the case in this work.

Mass balance for the substrate:

(2)

Initial condition: t = 0, C_S = C_S(0)

where: C_M = maltose concentration in the liquid phase, g/ml; t = time, s; and R_M = maltose consumption rate, g/ml/s.

The mass balance for the product is obtained in the same way as it is for the substrate.

Immobilized Enzyme

Mass balance for the substrate on the silica interface:

(3)

Initial condition: t=0, C_Ml= C_Ml (0)

Mass balance for the substrate inside the silica:

(4)

Initial condition: t=0, C_MS=0

Boundary condition 1: z = 0, =0

Boundary condition 2: z = 1, C_MS (z ) = C_Ml (z )

where e r= reactor porosity; e s= silica porosity; C_Ml= maltose concentration in the liquid, g/ml; CMS= maltose concentration in the silica, g/ml; C_Gs = glucose concentration, g/ml; D_MS = maltose diffusivity in the silica, cm²/s; r _S = silica density, g/cm³; R_S = silica radius, cm; and z = adimensional silica radius.

The mass balance for the product is obtained in the same way as it is for the substrate.

RESULTS AND DISCUSSION

Kinetic Parameters for the Hydrolysis of Maltose

The constants of equation (1) are estimated by fitting batch reactor data. Figure 1 depicts an example of the results. It should be emphasized that, although the transient experiments are run until hydrolysis is completed, the hypothesis concerning the reaction mechanism is consistent. The steady-state approach, which disregards changes in the intermediate complex concentrations, provides a good fit. On the other hand, all maltose is converted into glucose during the 2 hour assays, indicating that the formation of isomaltose has not yet begun, at least in measurable quantities. This behaviour is in accordance with the literature (Adachi et al., 1984). The estimated parameters and the respective confidence intervals, with a 95% significance level for maltose hydrolysis using glucoamylase, are presented in Table 1. These constants are used for describing the immobilized enzyme kinetic behaviour too. This assumption is justified, since immobilization is carried out at a pH of 4.0, and under this condition only one terminal amine of the enzyme is protonated and able to link covalently to the glutaraldehyde used in the activation of the silanized support (Giordano and Schmidell, 1992). Consequently, the changes at the glucoamylase active sites will be minimal.

The parameters estimated in this work, with the exception of K_i, are close to the ones in the literature. The comparison is not direct since the available data are not at the same temperature and it is not always for the same substrate. The K_i value is particularly larger than the values estimated by other authors for similar temperatures. However, even with the kinetic model frequently discussed in the literature (Swanson et al., 1977), a deviation from the Michaelis-Menten kinetics for maltose hydrolysis was found and a different model that takes into consideration the possibility of substrate linking in the four active sites of the enzyme was suggested.

Parameter In this work 30ºC - maltose (Zanin, 1989) 45º C – maltose (Giordano and Schmidell, 1992) 30ºC - soluble starch K3 (g/U/s) 0.90 x 10-5 ±0.2 x 10-7 3.89x10 -5 3.66 x 10-5 Km (g/ml) 0.61 x 10-3±0.8 x 10-4 1.0 x 10-3 0.5 x 10-3 Ki (g/ml) 1.23 x 10-1±0.2 x 10-2 7.2 x 10-4 3.64 x 10-4

Parameter	In this work 30ºC - maltose	(Zanin, 1989) 45º C – maltose	(Giordano and Schmidell, 1992) 30ºC - soluble starch
K3 (g/U/s)	0.90 x 10-5 ±0.2 x 10-7	3.89x10 -5	3.66 x 10-5
Km (g/ml)	0.61 x 10-3±0.8 x 10-4	1.0 x 10-3	0.5 x 10-3
Ki (g/ml)	1.23 x 10-1±0.2 x 10-2	7.2 x 10-4	3.64 x 10-4

Table 1: Estimated parameters and variances with a confidence interval of 95% significance for maltose hydrolysis using glucoamylase: K ₃ = product formation rate constant, such that V _max = K ₃ .C _e , and C _e = enzyme concentration in the reactor; K _m = Michaelis-Menten constant; K _i = product ¾ glucose ¾ inhibition constant

Maltose and Glucose Effective Diffusivities inside the Silica with Iimmobilized Enzyme

Silica particles are kept under agitation inside the reactor. A direct search procedure estimates the diffusivities (see Table 2). These low diffusivities can perhaps be explained by the presence of the enzyme inside the pores. It should be noticed that the mean pore diameter of silica is 270 Å and the effective molecular diameter of glucoamylase is 80 Å. If we consider that at a certain position inside the pore there can be more than one immobilized enzyme molecule, it can be inferred that a considerable restriction for diffusion of the species can be present.

Figure 2 shows the results of the fitting of the mathematical model to experimental data on changes in concentration of maltose and glucose in time during dextrin hydrolysis catalysed by glucoamylase immobilized in silica at 30ºC. A good fit of the model to the experimental data is observed when kinetic parameters for the free enzyme were used. This fitting gave values of maltose and glucose diffusivity in silica which were much smaller than in water, as can be seen in Table 2. However, the estimated values for maltose in silica of a nonspecified diameter (Lee et al., 1980) and for enzyme in silica of a pore diameter ten times larger than the one used in this work (Hossain & Do, 1988) are close to the parameter values estimated here.

Figure 1: Change in glucose concentrations in time, at 30º C with free glucoamylase.

Figure 2: Change in maltose and glucose concentrations in time during maltose hydrolysis using glucoamylase immobilized in silica at 30 º C.

Substance Diffusivity in water (cm2/s) Diffusivity in silica (cm2/s) Maltose - 0.50 x 10-6 * 0.78 x 10-6 (b) Glucose 6.70x 10-6 (a) 0.55 x 10-6 * 2.00 x 10-6 (b) Glucoamylase » 0.60 x 10-6 (a) 0.131 x 10-6 (c) 0.131 x 10-6 (c)

Substance	Diffusivity in water (cm2/s)	Diffusivity in silica (cm2/s)
Maltose	-	0.50 x 10-6 *	0.78 x 10-6 (b)
Glucose	6.70x 10-6 (a)	0.55 x 10-6 *	2.00 x 10-6 (b)
Glucoamylase	» 0.60 x 10-6 (a)	0.131 x 10-6 (c)	0.131 x 10-6 (c)

Table 2: Effective diffusivities for different substances in different media

* Values estimated in this work; (a) Tanaka et al., 1984; (b) Lee et al., 1980; (c) Hossain and Do, 1988

The experimental data at the beginning of the assay with immobilized enzyme present a higher reaction rate than that of the simulated data. In order to fit the model to this region, the immobilization should have to cause a large change in the kinetic parameters, which is not reasonable since there is no significant alteration of the spacial configuration of the enzyme molecule during this process.

CONCLUSIONS

In this work, kinetic parameters for maltose hydrolysis catalysed by free glucoamylase at 30 ºC and effective diffusivities of maltose and glucose in macroporous silica with immobilized enzyme are estimated. The estimated values agreed well with the ones available in literature, but the values obtained for the product inhibition constant and the dextrin diffusivities in silica suggest the need to validate these results by comparison with other experimental data.

ACKNOWLEDGEMENTS

The authors thanks CNPq for the sponsorship that made this work possible.

NOMENCLATURE

C_e Amount of enzyme, U/ml

K3 Kinetic constant, g/U.s

K_i Product inhibition constant

Km Michaelis-Menten constant, g/ml

C_Gs Glucose concentration, g/ml

C_G Product concentration, g/ml

C_M Substrate concentration, g/ml

CMl Maltose concentration in the liquid, g/ml

CMS Maltose concentration in the silica, g/ml

D_MS Maltose diffusivity in the silica, cm²/s

R_M Hydrolysis rate (maltose consumption), g/ml/s

R_S Silica radius, cm

t Time, s

Greek Symbols

e r Reactor porosity

e s Silica porosity

r _S Silica density, g/cm3

z Adimensional silica radius

REFERENCES

Adachi, S.; Ueda, Y. and Hashimoto, K., Kinetics of Formation of Maltose and Isomaltose through Condensation of Glucose by Glucoamylase - Biotechnology and Bioengineering, vol XXVI, pp. 121-127 (1984).

Anderson, T.F.; Abrams, D.S. and Grens, E.A., Evaluation of Parameters for Nonlinear Thermodynamic Models - AIChE Journal, vol 24 (1), pp. 20-29 (1978).

Giordano, R.L.C and Schimidell, N.W., Coimobilização de Enzima e Microrganismo em Gel de Pectina para a Produção de Etanol a Partir de Amido - Actas del XIII Simpósio Iberoamericano de Catalisis, Espanha, p. 643 - 46 (1992).

Gonçalves, L.R.B.; Giordano, R.L.C. and Giordano, R.C., Modelagem Matemática da Produção Contínua de Etanol a Partir de Amido Liqüefeito, Usando Enzima e Microrganismo Coimobilizados em Gel de Pectina - Anais do 10º Congresso Brasileiro de Engenharia Química, Vol. 2 - p. 1246. São Paulo (1994).

Hossain, MD. M. and Do, D.D., Determination of Intrinsic Parameters for Immobilization Reactions of Catalase and Amyloglucosidase in Porous Glass Supports - Biotechnology and Bioengineering, vol 31, pp. 730-736 (1988).

Lee, D.D.; Lee, G.K. and Reilly, P.J., Effect of Pore Diffusion Limitation on Dextrin Hydrolysis by Immobilized Glucoamylase - Biotechnology and Bioengineering, vol XXII, pp.1-17 (1980).

Petzold, L.R., DDASSL code, version 1989 - Computing and Mathematics Research Division, Lawrence Livermore National Laboratory (1989).

Swanson, S.J.; Emery, A. and Lim, H.C., Kinetics of Maltose Hydrolysis by Glucoamylase - Biotechnology and Bioengineering, vol XIX, pp. 1715-1717 (1977).

Tanaka, H.; Matsumura, M. and Veliky, I.A.,

Diffusion Characteristics of Substrates in Ca-Alginate Beads - Biotechnology and Bioengineering, vol 26, pp. 53-58 (1984).

Villadsen, J.V. and Michelsen, M.L., Solution of Differential Equation Models by Polynomial Approximation - Prentice Hall, Englewood Cliffs (1978).

Zanin, G.M., Sacarificação de Amido em Reator de Leito Fluidizado com Enzima Glucoamylase Imobilizada, PhD. Thesis, UNICAMP, (1989).

Publication Dates

• Publication in this collection
  06 Oct 1998
• Date of issue
  Dec 1997

History

• Accepted
  30 Oct 1997
• Received
  11 June 1997