A BIDISPERSE MODEL TO STUDY THE HYDROLYSIS OF MALTOSE USING GLUCOAMYLASE IMMOBILIZED IN SILICA AND WRAPPED IN PECTIN GEL

A BIDISPERSE MODEL TO STUDY THE HYDROLYSIS OF MALTOSE USING GLUCOAMYLASE IMMOBILIZED IN SILICA AND WRAPPED IN PECTIN GEL

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, a bidisperse model is built to represent the hydrolysis of maltose using immobilized glucoamylase. The experimental set is a mixed-batch reactor, maintained at 30ºC, with pectin gel spherical particles that contain enzyme immobilized in macroporous silica. The possibility of substrate adsorption on the pectin gel is also studied because this phenomenon may result in smaller values of diffusivity. Equilibrium assays are then performed for different substrates (maltose, lactose and glucose) at different temperatures and pHs. These assays show that adsorption on the pectin gel is not important for the three dextrins analysed. The bidisperse model presents a good fit with the experimental data, when using previously-estimated kinetic and mass transfer parameters (Gonçalves et al., 1997). This result shows that the methodology used (wrapping the silica in pectin gel) is appropriate for experimental studies with silica, since it allows a higher degree of agitation without causing shearing. Keywords: Mathematical models, maltose hydrolysis, process simulation.

INTRODUCTION

The reason to use starch as a raw material is to substitute cane sugar where the land and/or the climate is more appropriate for planting starch. However, the use of starch as a raw material requires a step before fermentation: hydrolysis or saccharification. Alternative processes have been studied to solve this problem; one of these is the Simultaneous Saccharification and Fermentation (SSF) process involving the use of immobilized glucoamylase and yeast (Giordano & Schmidell, 1992). In this process, glucoamylase is covalently immobilized in macroporous silica and wrapped in pectin gel.

A model to represent this bioprocess should consider two domains of reaction: hydrolysis inside the silica, with substrate and product mass transfer resistance, and fermentation inside the gel, where the yeast is located, also with mass transfer restrictions. The model construction, herein denominated a bidisperse model, will not only allow the process to be described but will also help to determine kinetic and mass transfer parameters inside the biocatalyst when operating the reactor under conditions which guarantee no external mass transport limitations.

The use of high agitation speed to eliminate this mass transport limitation may cause shearing and the use of fixed-bed reactors with recirculation may lead to a deviation from ideal flow. A batch system under agitation (Mattos et al., 1994) (possible due to the fact that the pectin gel protects the silica against the action of the mixer) will allow estimation of kinetic and diffusion coefficients when diffusivities of products and substrates in the gel phase are already known, as is the case in this work.

According to previous research, it is important to check whether there is adsorption of solute in the support because, if this phenomenon is relevant, it can lead to lower values of diffusion coefficients (Weisz, 1995). Pectin is formed by chains of poligalacturanic acid, with a pK about 4.0. The high methoxilation pectin forms a gel after the addition of sugar, which is more hydrophilic than the acid chain and attracts the water molecules, bringing together the acid chains and forming the gel phase. The pectin used here is a low methoxilation one, with higher hydrophilicity, requiring bivalent cations, like calcium, to bring together the acid molecules and form the gel. It can be seen that there is a fragile charge balance in the pectin gel, which can be changed due to the presence of dextrins, making adsorption possible. The methodology that is used in this work depends on reliable values of diffusion coefficients in the gel phase, which caused us to include initial studies on dextrin adsorption on the pectin gel.

MATERIALS AND METHODS

Materials

Dextrin: 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)

Supports: High porosity silica, with na average diameter of 170 m m, a porosity of 0.57 and a mean pore diameter of 270 Å (measured by a N₂ desorption device, ASAP 2000, Micrometrics); low methoxilation citric pectin, a gift from Braspectina do Brasil. Other reactants used are of different laboratory trademarks.

Methods

Pellet Preparation: A solution is prepared using 6 g of citric pectin added to 88 g of distillate water and 6 ml of acetate buffer 1M, pH = 4.2. A known amount of silica (0 or 0.5 g) containing the immobilized enzyme is then added. The resulting solution is dripped into a CaCl2 0.2 M solution under low agitation; the pellets so formed should remain in the refrigerator for 18 to 24 hours.

Enzyme Immobilization (Giordano and Schmidell, 1992): Silica is silanized with a g -aminopropiltrietoxisilano solution (0.5%v/v), pH = 3.3, at 75ºC for 3 hours, with a liquid-solid ratio of 3 ml/g. It is then washed, first with water and later with acetone. It is subsequently dried until its weight stops changing. The support is activated with glutaraldehyde (in 2.5% sodium hidrogenophosphate buffer, pH = 7.0, 0.1M) for 1 h, at 20 - 25ºC, with a liquid-solid ratio of 3 ml/g. It is then washed again and mixed with the enzyme solution for 36 h, at 20 - 25 ºC, under low agitation.

Analytical Methods:

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

• Maltose: Somogyi method.

• Pellets density: picnometry

• Pellets radius: an average radius is calculated after measuring the volume of 500 pellets, admitted of spherical shape.

• Pellets porosity: gravimetry.

Experimental Proceedure:

a) Equilibrium assays: 20 g of pure pellets, without silica, are added to 50 ml of a 50g/l solution of maltose, lactose or glucose. The experiments are done in different temperature (15, 30 and 50º C) and pH (3, 4.2 and 10) conditions.

b) Diffusion and reaction assays: Changes of concentration with the course of time are measured after adding 20g of pellets to 50 ml of a 50 g/l maltose solution under agitation (time 0). Samples of 0.1 ml are taken periodically. The agitation speed is set 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.

MATHEMATICAL MODELS

Kinetics of Maltose Hydrolysis Using Glucoamylase

A Michaelis-Menten equation with product inhibition is used to represent the hydrolysis of maltose by glucoamylase:

(1)

where R_M = hydrolysis rate (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.

Equilibrium Assays

Equation 2 is used to calculate the value of the solute partition coefficient between bulk and the gel phase (k_p).

(2)

where r _p = pellet density, g/ml; C⁰ = initial bulk solute concentration, g/ml; C^f = bulk solute concentration after reaching equilibrium, g/ml; V_l = liquid volume, cm³; m_g = amount of pellets; and e _p = pellet porosity.

Bidisperse Model

Mass balance for the substrate in the gel interface:

(3)

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

where C_Ml = maltose concentration in the bulk, g/ml; C_Mg = maltose concentration in the gel, g/ml; e _r = bed porosity, e _p = pellet porosity; R = pellet radius, cm; z = r/R = adimensional pellet radius; and D_Mg = maltose diffusivity in the gel, cm²/s.

Mass balance for the substrate in the gel:

(4)

Initial condition: t=0, C_Mg=0;

Boundary condition 1: z =0, ;

Boundary condition 2: z =1, C_Mg=k_p.C_Ml

where C_Mg = maltose concentration in the gel, g/ml; C_MS = maltose concentration in the silica, g/ml; e _gp = pure gel porosity; e _S = silica porosity; z _S = adimensional silica radius; and D_MS = maltose diffusivity in silica, cm²/s.

Mass balance for the substrate in the silica:

(5)

Initial condition: t=0, C_MS= 0;

Boundary condition 1: z _S =0, =0 ;

Boundary condition 2: z _S =1, C_MS (z _S) = k_p.C_Mg (z )

Equations (03) to (05) are solved numerically, using orthogonal collocation in two domains (silica and gel), with five (to the gel phase) and three (to the silica) internal collocation points after tests with 20 and 10 points. The differential ordinary equations are integrated using subroutine DASSL (Petzold, 1989). In all simulations, the sample volume is considered (0.1 ml).

RESULTS AND DISCUSSION

Dextrin Adsorption on Pectin Gel

Equilibrium assays for maltose, glucose and lactose with pellets of pectin gel are performed in order to verify the existence of adsorption of these sugars on the pectin gel. If there is no adsorption, the value of the partition coefficient would be equal to 1; in other words, the solute would be equally dissolved in the bulk water and in the water filling the gel pores. If adsortion is present, the change in the charge equilibrium, caused by different temperatures and pHs, will lead to different values of k_p. Because of that, the assays are performed at different temperature and pH conditions. Values of k_p, obtained after reaching equilibrium, can be seen in Table 1 and Table 2. The Student test (see Tables 1 and 2), with 90% significance, indicates that the k_p values are not significantly different from unity, except for two values.

The variations observed in the values of k_p were considered non-significant, specially in view of the empirical difficulties encountered, for example during gel humidity determination. So, we may conclude that dextrin adsorption on pectin gel is not important under the conditions studied in this work.

Temperature 15ºC 30ºC 50ºC t (calculated) t (table) Maltose 1.11 1.08 0.94 0.046 0.029 Glucose 1.05 1.07 0.97 0.032 0.050 Lactose 1.09 0.94 0.94 0.010 0.045

Temperature	15ºC	30ºC	50ºC	t (calculated)	t (table)
Maltose	1.11	1.08	0.94	0.046	0.029
Glucose	1.05	1.07	0.97	0.032	0.050
Lactose	1.09	0.94	0.94	0.010	0.045

Table 1: k _p values for maltose, glucose and lactose, different temperature values

Bidisperse Model Validation

The next step is a simulation using the bidisperse model. The simulation results are compared to experimental data for changes in maltose and glucose in time, obtained during maltose hydrolysis using glucoamylase immobilized in silica and wrapped in pectin gel. The kinetic and mass transfer parameters used in the simulation were obtained in previous work

(Mattos et al., 1994; Gonçalves et al., 1997). Table 3 depicts the parameters used. Figures 1 and 2 show the experimental data and simulated curves (obtained using the bidisperse model).

Two parameters in the bidisperse model are difficult to determine experimentally: particle porosity (e _p) and silica radius (R_s). Some sensitivity tests with respect to these parameters are therefore performed. The results can be seen in Figures 3 and 4.

PH Substance 3.0 4.2 10.0 t (calculated) t (table) Maltose 0.96 1.08 1.06 0.030 0.039 Lactose 1.03 1.07 1.12 0.076 0.046 Glucose 1.09 0.94 0.87 0.036 0.042

PH Substance	3.0	4.2	10.0	t (calculated)	t (table)
Maltose	0.96	1.08	1.06	0.030	0.039
Lactose	1.03	1.07	1.12	0.076	0.046
Glucose	1.09	0.94	0.87	0.036	0.042

Table 2: k _p values for maltose, glucose e lactose, different pH values

K3 (g/U/s) Km (g/ml) Ki (g/ml) DMS (cm2/s) DGS (cm2/s) DMg (cm2/s) DGg (cm2/s) 1.0 x 10-5 1.0 x 10-3 3.0 x 10-2 0.50 x 10-6 0.55 x 10-6 4.49 x 10-6 5.29 x 10-6

K3 (g/U/s)	Km (g/ml)	Ki (g/ml)	DMS (cm2/s)	DGS (cm2/s)	DMg (cm2/s)	DGg (cm2/s)
1.0 x 10-5	1.0 x 10-3	3.0 x 10-2	0.50 x 10-6	0.55 x 10-6	4.49 x 10-6	5.29 x 10-6

Table 3: Kinetic parameters of maltose hydrolysis with free glucoamylase, at 30 ^o C (Gonçalves et al., 1997): 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; and K _i = product inhibition constant – glucose. Difusivities of maltose and glucose in silica with immobilized enzyme (Gonçalves et al., 1997): D _MS , D _GS , and in pectin gel (Mattos et al., 1994): D _Mg , D _Gg

Figure 1: Changes in maltose and glucose concentrations in time; maltose hydrolysis; lucoamylase immobilized in silica and pectin gel, at 30 º C. C_e = 275 U/ml_silica. R_s = 94m m.

Figure 2: Changes in maltose and glucose concentrations in time; maltose hydrolysis; glucoamylase immobilized in silica and pectin gel at 30 º C, C_e = 108 U/ml_silica;R_s < 63m m..

Figure 3: Sensitivity test of the bidisperse model when changing the silica radius (R_s).

Figure 4: Sensitivity test of the bidisperse model when changing the particle porosity (e _p).

It can be noted that the model is not very sensitive to changes in the silica radius (see Figure 3); over a wide range of particle sizes (from 30 to 80m m) the model did not present significantly different responses. This is not true when we consider the particle porosity (e _p) (see Figure 4). For small changes in the porosity value (from 0.960 to 0.964), the model shows significant difference in its response. Changes in e _p, within the experimental error range, give slightly different responses. It is thus interesting to refine the value of e _p, based on its experimental value and using the model. To estimate this parameter some assays using the same pellets must be performed for different initial concentrations of substrate.

CONCLUSIONS

In observing the k_p values, we can say that there is no significant adsorption of the sugars studied here on the pectin gel. The maltose hydrolysis simulation, catalysed by glucoamylase immobilized in silica and wrapped in pectin gel, using the bidisperse model and parameter values previously estimated, gave a good response when compared to experimental data. These results validate the model and prove that wrapping in gel can be an adequate methodology for kinetic studies using supports that can undergo shearing.

This study also allowed the validation of the estimated parameters (kinetic parameters and dextrin diffusivities in silica) for maltose hydrolysis, using experimental conditions close to the ones that will be used in the ethanol production from starch with enzyme and yeast coimmobilized in pectin gel, the final aim of this work.

Sensitivity tests show, however, that the model is very sensitive to particle porosity (e _p). It is therefore recommended that this parameter be refined with the bidisperse model. The model can be validated using essays for the same pellets but for different initial concentrations of substrates.

ACKNOWLEDGEMENTS

Authors thanks CNPq for the sponsorship that made this work possible.

NOMENCLATURE

C⁰ Initial bulk solute concentration, g/ml

C_e Amount of enzyme, U/ml

C^f Bulk solute concentration after reaching equilibrium, g/ml

C_G Product concentration, g/ml

C_M substrate concentration, g/ml

C_Mg Maltose concentration in the gel, g/ml

C_Ml Bulk maltose concentration he, g/ml

C_MS Maltose concentration in the silica, g/ml

D_Mg Maltose diffusivity in the gel, cm²/s

D_MS Maltose diffusivity in silica, cm²/s

K3 Kinetic constant, g/U.s

K_i Product inhibition constant, ml/g

Km Michaelis-Menten constant, g/ml

m_g Amount of pellets

R Pellet radius, cm

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

V_l Liquid volume, cm³

Greek Symbols

e _gp Pure gel porosity

e _p Pellet porosity

e _r Bed porosity

e _S Silica porosity

z Adimensional pellet radius (r/R)

z _S Adimensional silica radius

r _p Pellet density, g/ml

• Giordano, R.L.C. and Schimidell, N.W., Coimobilizaçăo de Enzima e Microrganismo em Gel de Pectina para a Produçăo de Etanol a Partir de Amido - Atas del XIII Simpósio Iberoamericano de Catalisis, Spain, pp. 643 - 46 (1992).
• Gonçalves, L.R.B.; Giordano, R.L.C. and Giordano, R.C., Effects Of Diffusion On The Kinetics Of Maltose Hydrolysis Using Glucoamylase Immobilized On Macroporous Silica, Braz. J. Chem. Eng., in press (1997).
• Mattos, M.V.C.; Giordano R.C. and Giordano, R.L.C., Influęncia do Crescimento Celular nas Difusividades de Dextrinas em Gel de Pectina - Anais do IV Seminário de Hidrólise Enzimática de Biomassa, Maringá, PR (1994).
• Petzold, L.R., DDASSL code, version 1989 - Computing and Mathematics Research Division, Lawrence Livermore National Laboratory (1989).
• Villadsen, J.V. and Michelsen, M.L., Solution of Differential Equation Models by Polynomial Approximation - Prentice Hall, Englewood Cliffs (1978).
• Weisz, P.B. - Molecular Diffusion in Microporous Materials: Formalisms and Mechanisms - Ind. Chem. Res., vol 34 (8), pp. 2692-2699 (1995).

Publication Dates

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

History

• Accepted
  11 June 1997
• Received
  11 June 1997