Theoretical and experimental studies on the influence of ultrasound on immobilized enzymes

Theoretical and Experimental Studies on the Influence of Ultrasound on Immobilized Enzymes

Peter Schmidt, Eike Rosenfeld, and Rudolf Millner lnstitut fur Angewandte Bioph ysik, Bereich Medizin, Martin Luther Universitat Halle, DDR-4014 Halle, StK d. DSF 81, FRG

Regina Czerner Organisations und Rechenzentrum der Martin Luther Universitat Halle, DDR-4020 Halle, Weinbergweg 77, FRG

Alfred Schellenberger Wissenschafisbereich Biochemie, Sektion Biowissenschafien, Martin Luther Universitat Halle, DDR-4020 Halle, Domplatz 1, FRG

Accepted for publication November 3, 1986

Experimental investigations on a-amylase and glucoamylase bound to porous polystyrene show that the activity of immobilized enzymes can be raised in the presence of an ultrasonic field. The maximum activity increase in a flow cuvette at 7.6 MHz and a sound intensity of 5 k W h 2 amounts to more than 200% under the given experimental conditions. A mathematical model based on the differential equation for the interior and exterior substrate transport is set up and solved numerically. From the theoretical considerations and the experiments it is evident that the mechanism of the ultrasonic effect can be explained in terms of a reduction of the unstirred diffusion layer around the matrix particles.

INTRODUCTION

Investigations on enzymes immobilized at insoluble carrier matrices have shown that diffusion limitations can greatly reduce the efficiency of the enzyme carrier complex.I4 Es- pecially in the case of porous carrier material characterized by its large inner surface and consequently by its enzyme binding capability, the diffusion limitation plays an important part. In that case, the diffusion of the substrate and product molecules can be distinguished by an inner and an outer component. Exterior diffusion effects are accom- panied by a substrate concentration gradient between the matrix surface and the bulk volume. The thickness of this diffusion layer is on the order of 100 pm for the unstirred systems. The measurement can be achieved directly by means of laser interferometry' or by means of appropriate microelectrodes.6

The surrounding diffusion layer can be reduced by stirring or streaming of the substrate solution, however, up to a

Biotechnology and Bioengineering, Vol. 30, Pp. 928-935 (1987) 0 1987 John Wiley & Sons, Inc.

residual unstirred layer only. To determine the thickness, 6 , of this layer, empirical formulas were published for columns by Engasser7 and for batch reactors by Kasche.* These re- lations permit the calculation of S as a function of the relative velocity between particles and the suspending liq- uid. Assuming the viscosity of the substrate solution is equal to that of water and the particle diameter is 4 X m, 6 is 5 pm (column) and 10 pm (batch) for a relative velocity as high as 1 m/s. This velocity has no practical relevance, neither in stirred batch reactors nor in flow systems.

On the other hand, others have reported that diffusion increases in an ultrasonic field. This effect has been shown with membranes,' photographic layers, lo electrode surfaces in electrolytes,'' and in connection with immobilized enzymes, too. Ishimori found an ultrasonically induced increase in activity of a-chymotrypsin when bound to ag- arose.I2 The increase for casein as substrate was more than 200%. With N-acetyl-L-tyrosin-ethylester as substrate, no effect due to ultrasound was demonstrated. As cause for this activity, enhancement/diffusion effects were discussed again. Finally, Rosenfeld and Schmidt l3 showed that different enzymes fixed at a solid porous carrier can be stimulated by an ultrasonic field which resulted in an activity increase.

Starting from these findings, l3 the present study first presents a theoretical basis to interpret the experimental results in terms of an ultrasonic effect on the diffusion layer thickness and then presents experimental results obtained at a -amylase and glucoamylase bound to porous polystyrene for comparison. For this aim, numerical solutions of the diffusion equation of the outer and inner substrate transport under consideration of the reaction of the immobilized en-

CCC 0006-3592/87/080928-08$04.00

zyme are discussed. The experimental part of the work presents results on the ultrasonic effect on the enzymatic activity obtained at a -amylase and glucoamylase bound to porous polystyrene.

MATHEMATICAL MODEL

For a porous spherical carrier particle the mass transport outside and inside of the matrix can be described by the diffusion equation. With regard to the enzymatic reaction inside the carrier matrix this equation has been modified to the following set of differential equations, a model which is based on Michaelis-Menten kinetics:

Ro < r 5 Ro + 6 The boundary conditions are

with the initial condition: SF(Ro + S , t ) = So (2)

(3) SF(r,O) = So; Ro < r 5 Ro + (+

(4) with the boundary conditions:

( 5 )

.S(r,O) = 0; 0 5 r 5 Ro (6)

as S(R0, t ) = SF(R0, t, 1 (0,t) =

and the initial condition:

Further assumptions are: 1) the diffusion within the carrier body can be described by an effective diffusion coefficient, Deff, which is independent on space and time; 2) a single carrier sphere is considered and the diffusion layers are not disturbed by neighboring particles; 3) the reaction is isothermal; and 4) the enzymatic activity on the outer surface of the matrix can be neglected relative to the inner surface.

The solution of this nonlinear, partial, second-order differential equation results in a substrate concentration profile, S(r), across the particle cross section including the adjoining diffusion layer.

The concentration profile allows for steady-state conditions the calculation of the reaction rate, v, according to the following equation^'^:

(7) v = Ah(& - S,)

The differential equation system has been solved numerically using finite differences.” The type of the difference scheme can be controlled by a weighting parameter. The space and time discretization points are determined as a function of the bounds given for the local trunction errors.

Computations were carried out on a ES 1040 computer. The system of equations [eqs. (1)-(6)] can be solved for the stationary as well as for the instantaneous case. The non- linearity of the Michaelis-Menten term has been treated by Newton’s Method.I6 The system of eqs. (1)-(8) allows, by varying the corresponding parameters, to examine the influence of the kinetic constants and/or the diffusion coef- ficients. Especially, the influence of the outer diffusion parameter is of interest, because the quantity is assumed to be sensitive to the action of ultrasonic waves.

THEORETICAL RESULTS

The following results are based on the reaction of glucoamylase and maltose. The kinetic constants used were the same as those for the reaction in solution. Possible alter- ations of V,, and K, due to the immobilization are neglected. The diffusion coefficient in the diffusion layer is D = 1,6 x lo-’’ m2/s l7 and the coefficient of the inner diffusion has been estimated, according to the relation by Engasser’ and Satterfield,” to be Deff = lo-’’ m’/s.

Figure 1 shows the calculated substrate concentration profile, S(r) , as a function of the particle radius, r, including the adjoining diffusion layer for. the steady state [eqs. ( l) , (2), (4), and (5)J. For big particles (R, = 4 x m), the substrate concentration has fallen off nearly to zero at half of the particle radius (r/Ro = 0.5); i.e., only the outer region of the matrix is involved in the chemical reaction. Furthermore, a steep concentration drop from the bulk volume to the carrier surface can be observed.

Depending on the bulk concentration, the true concentration on the surface is 53.7% for So = 1.5 mmol/L, 64% for So = 15 mmol/L, and 87% for So = 150 mmol/L of the total concentration. The corresponding calculated activities are 1.15, 8.8 , and 32.3 pmol/cm3/min, respectively. Figure 2 shows the effect of the exterior diffusion on the enzymatic reaction. By varying the diffusion layer thickness from 100 to 5 pm, the reaction rate, v,,, increases. This is also dependent on the substrate concentration. Rate v,] re- fers to the true reaction rate for S = 100 pm, being unity. Whereas vE1 reaches a maximum of 200% for a substrate concentration of S = 1.5 mmol/L, the corresponding value is only 106% for S = 150 mmol/L. This means that the diffusion effects within the adjacent region of the carrier can strongly reduce the reaction rate. At substrate concentrations below 150 mmol/L, the diffusion influences can be neglected.

MATERIALS AND METHODS

The experiments were carried out with a -amylase (Novo A/S, Denmark)(E.C.3.2.1.1.) and glucoamylase (Merck, Darmstadt, FRG) (E.C.3.2.1.3.) covalently bound to porous polystyrene beads (type Y 58, VEB Chemiekombinat Bitterfeld).I9 As substrates, Zulkowsky starch (Merck, Darmstadt, FRG) and maltose (VEB Laborchemie Apolda) were used. The protein fixation procedure via benzoquinone and the enzyme activity determination for a-amylase and

SCHMIDT ET AL.: INFLUENCE OF UNTRASOUND ON IMMOBILIZED ENZYMES 929

I I

+ , Q2 0.3 0.4

Figure 1. Calculated substrate concentration profile, S(r) , as a function of the radius, r, of the carrier particle including the diffusion layer. Material is glucoamylase/maltose; constants used are S = 15 mmol/L; Vm.x = 0.06 mmol/L/min; K, = 3 . 5 mmol/L; Ro = 0.4 mm; 6 = 50 p m ; D = 1.6 X lO-"/m*/s; and Den = 10-"/m2/s.

glucoamylase with starch solution are described else- where. 16,20

The glucose formed in the course of the hydrolysis reaction of maltose was estimated by the glucoseoxidase/ peroxidaselo-dianisidine method.20*21 For the sonification procedure, a flow cuvette of ca. 1 mL, volume was used.13 The carrier matrix beads form a loosly packed bed. The cell is cylindrically shaped. Both end faces, 20 mm in diameter, are made of thin plastic sheets operating as sound windows. Plane continuous ultrasonic waves penetrate the reactor volume axially, the ultrasonic frequency is 7.6 MHz. The spa- tial and time averaged sound intensity, J, is varied up to 5 kW/m2. Transducer and cuvette are positioned in a temperature-controlled water bath and the temperature was kept constant at 37 2 0.2"C. A hydrophone was positioned near the reactor volume. No subharmonic or harmonic sig- nals could be detected within the intensity range applied in

our measurements, indicating that cavitation did not occur. For details to the experimental arrangement, see ref. 22.

EXPERIMENTAL RESULTS

Figure 3 shows the dependence of the reaction rate on the sound intensity in the reaction volume for the glucoamylase/maltose system. The activity increase is propor- tional to the intensity, resulting in a maximum gain factor of 2.1 for the acoustic and chemical conditions given in our experiments. The least-squares fit gives a correlation coefficient of 0,999. The linearity also seems to extend to low intensity values. A threshold of the effect, as frequently observed if cavitation occur, could not be found within the intensity range under consideration here.

Similar results were obtained for glucoamylase with starch and maltose as substrates (Fig. 4). The relative reac-

930 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 30, DECEMBER 1987

20

1.8

1.6

T >

f.4

t2

1.0

1

3

20 40 60 m Do

&Pm) Figure 2. Calculated reiative reaction rate, vet, as a function of the diffusion layer thickness, 6, of the unstirred layer for various substrate concentrations. Material is glucoamylase/maltose.. The curves show (1) S = 1.5 mmol/L; (2) S = 15 mmol/L; and (3) S = 150 mmol/L. The constants used are R , = 0 .4 mm; D = 1.6 x lo-'' m2/s ; DCtr = lo- ' ' m2/s; Vm,x = 0.06 mmol/L/min; and k,,, = 3.5 mmol/L.

tion rate, vXl, that is the quotient of the reaction rate in presence of ultrasound and the control value, increases with rising sound intensities. A tendency to a saturation can be seen as intensity increases.

The influence of the substrate concentration on the sonic effect is demonstrated in Figure 5 . For maltose an increase of v,, of 1.82 is attained, decreasing to 1.3 for substrate concentration higher than 100 mmol/L. For starch, the equivalent values are 2.5 (S = 5 g/L) and 1.7 (S = 50 g/L), respectively. The relative reaction rate declines when the flow velocity of the substrate solution through the reaction vessel increases as shown for glucoamylase/ maltose in Figure 6.

DISCUSSION

The numerical solution of the differential equation system [eqs. (1)-(6)] shows that the influence of the chemical and physical conditions on the heterogeneous catalyze in spherical porous carrier particles as well as the dynamic behavior

of the reaction system can be studied. It is evident that after ca. 10 s the substrate concentration profile is established, and further change is less than 1%.

The mathematical treatment allows the simultaneous and separate consideration of exterior and interior diffusion processes. The former can be suppressed by omitting eqs. (1)-(3) and setting S(R,) = So in eq. (5). The results obtained in this way are in accordance with those of ReganZ3 for the interior diffusion.

The exterior diffusion control is taken into consideration by the variation of the diffusion layer thickness and the diffusion coefficient of the substrate molecules in this region. The theoretical results show evidently that the diffusion limitation in the unstirred layer around the carrier body is a very essential quantity with respect to the total reaction rate of the enzyme carrier complex. By suppressing the exterior diffusion limitation theoretically, an activity enhancement for the low-molecular-weight substrate by 100% is possible (Fig. 2). In the case of a polymer substrate (starch), still higher activity enhancement are to be ex-

SCHMIDT ET AL.: INFLUENCE OF ULTRASOUND ON IMMOBILIZED ENZYMES 931

* I I 1 1

0 1 2 3 4 5 J ( kW.rn-2)

Figure 3. particle diameter is 0.60.8 mm; S = 10 g/L; and Q = 48 mL/h.

Reaction rate, v, of a-amylase/starch as function of the sound intensity, J , obtained experimentally. The carrier is Y58; the

pected. Our experimental results show that heterogeneous enzyme reactions can be decisively accelerated in an ultrasonic field. Resulting from the preceding theoretical considerations, this effect can be attributed to the sound influence on the exterior diffusion of the substrate and product molecules.

The hydrodynamic situation around small bodies in a sound field is treated by Nyborg" in detail. According to this theory, the suspended bodies in a sound field are sur- rounded by a layer of microeddies characterized by a quantity with the dimension of the acoustic boundary layer and dependent on the kinematic viscosity and the sound frequency. Strictly speaking, for the theoretical prediction of the ultrasonic effect on the enzyme activity, the micro- streaming near the matrix surface must be included into the total mass transportation. This should be achieved by adding a convectional term, vo, in eq. (1). Since vo is a function of space and time, it is obvious that the differential equation system becomes very complicated. Furthermore it is likely that the prerequisite of hydrodynamically independent single carrier spheres assumed in our model will not hold exactly: Thus another term regarding the interaction should be included. The resulting differential equation system is no

longer solvable on the basis of the algorithm used in this work. However, the experimental results furnish a number of arguments which support the hypothesis of an ultrasonically aided diffusion enhancement:

1) The ultrasonic effect depends on the molecular weight of the substrate (Fig. 4). For a smaller molecule (maltose) with a higher diffusion coefficient, the effect is less pro- nounced than that for a bigger molecule (starch), since the diffusion effect is less important. 2) The bigger carrier particles show a more distinct sound effect, which is obvious since the activity of the carrier complex strongly depends on the particle diameter. Re- cently, Mansfeld2' could show for a invertase-polystyrene and sucrose as substrate that the activity increases by a factor of 5 if the particle diameter is varied between 0.8 and 0.05 mm. 3) The ultrasonic effect increases with decreasing substrate concentration (Fig. 5). 4) The ultrasonic effect decreases with increasing flow rate (Fig. 6). 5) In the ultrasonic field, a decrease of the apparent K , values and the apparent activation energies were found."

932 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 30, DECEMBER 1987

3.c

2.6

22

3 >

1.8

1

;i 2

J ikW.m-2)

Figure 4. Relative reaction rate, v,,, as a function of the sound intensity, J , for glucoamylase and starch (S = 5 g/L) and maltose (S = 1.46 mmoI/L), respectively, as substrates at different particle diameters d, with Q = 42 mL/h. The curves show (1) 0.6 < d < 0.8 mm starch; (2) 0.15 < d < 0.2 mm starch; (3) 0.6 < d < 0.8 mm maltose; and (4) 0.15 < d < 0.2 mm maltose.

6) The ultrasonic effect increases with the square of the sound frequency and decreases with the viscosity of the medium, indicating acoustic streaming.” Further phenomena responsible for the experimentally

found activity change could be internal diffusion effects, a temperature rise within the matrix, and a direct influence on the chemical properties of the enzyme. Internal diffusion effects should not directly be influenced by ultrasound because the matrix body is assumed to be rigid and the mean pore radius is less than 70 nrn (for comparison the sound wave length is ca. 0.15 mm for a sound frequency of 10 MHz).

The matrix material itself is resistent against the sound waves as long as transient cavitation is avoided. At much higher intensities ultrasonic erosion occurs at the carrier

surface which might affect the activity of the carrier- enzyme complex, too.’’ This effect is irreversible and can unambifuously be excluded under experimental conditions given here.

The temperature rise was estimated theore t i~a l ly .~~*~~ Ac- cording to this calculation and to the experimental results the maximum activity increase is less than 12% for the maximum sound intensity and the lowest flow velocity through the cuvette. A direct influence of the sound waves on the catalytic mechanism of the enzyme molecules can not be excluded totally. It would result in a change of V,, in the Michaelis-Menten equation which, however, we coulti not detect. On the other hand, several authors tried to show a stimulative effect on solved enzymes and got negative results .26,27


934

25 -

23.

21 - e >

1.9 -

1.7 -

Figure 5. Relative reaction rate, vml, as a function of the substrate concentration, S, for giucoamylase and (a) maltose and (b) starch, with Q = 54 mL/h and J = 2.6 kW/m2.

Figure 6. Relative reaction rate, vSl, as a function of the substrate flow rate, Q, for giucoamyiase/ maltose with S = 1.5 mmol/L; 0.6 < d < 0.8 m, and J = 2.6 kW/m2.

BIOTECHNOLOGY A N D BIOENGINEERING, VOL. 30, DECEMBER 1987

CONCLUSIONS References

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3. L. Goldstein, Methods Enzymol., 44, 397 (1976). 4. L. B. Wingard, Jr., E. Katchalslu-Katzir, L. Goldstein, Eds., Applied

Biochemistry and Bioengineering, Volume 1 : Immobilized Enzyme Principles (Academic, New York, 1976) pp. 127-219.

5. D. Lerche, “Untersuchungen zum zeitlichen Verhalten des Kon- zentrationsprofils in Diffusionsschichten in Membranen,” dissertation, Humboldt-Universit , Berlin, 1974.

6. V. Kasche and G. Kuhlmann, Enzyme Microbiol. Technol., 2 , 309 ( 1980).

7. J. -M. Engasser, Biochem. Biophys. Acta, 526, 301 (1978). 8. V. Kasche, A. Kapune, and H. Schwegler, Enzyme Microb. Technol.,

9. J. Mendez, B. Franklin, and J. Kollias, Biomedicine, 25, 121 (1976). 10. M.E. Arkhangel’skii and Yu. G. Statnikov, “Diffusion in Hetero-

geneous Systems,’’ in Physical Principles of Ultrasonic Technology, Volume 2, L. D. Rosenberg, Ed. (Plenum, New York, 1973),

1 1 . E. Yeager, T. S. Dey, and F. Hovorka, J . Phys. Chem., 57(3), 268

12. Y. Ishimori, J. K m b e , and S . Suzuki, J. Mol. Catal., 12,253 (1981). 13. E. Rosenfeld and P. Schmidt, Arch. Acoust., 9(1/2), 105 (1984). 14. V. Kasche, Enzyme Microb. Technol., 5, 2 (1983). 15. R. Czemer, Wiss. Z. Univ. Halle, 34(5), 113 (1985). 16. R. Ulbrich, W. Damerau, and A. Schellenberger, Biotechnol. Bioeng.,

28, 511 (1986). 17. D. A. Sirotti and A. H. Emery, Appl. Biochem. Biotechnol., 9 , 27

(1984). 18. C. N. Satterfield, Mms Transfer in Heterogeneous Catalysis (MIT

Press Cambridge, MA, 1970), pp.129-134. 19. R. Kaufmann, K. Haupke, J. Fischer, A. Schellenberger, Acra Poly-

mer., 31, 739 (1980). 20. P. Schmidt, “Zum Einfluss von Ultraschall auf heterogene En-

zymkatalysen,” dissertation Martin Luther Universitat Halle, 1985. 21. J. Mansfeld and A. Schellenberger, Biotechnol. Bioeng., 29, 72

(1987). 22. P. Schmidt, E. Rosenfeld, R. Millner, and A. Schellenberger, Ultra-

sonics, in press. 23. D. L. Regan, M. D. Lilly, and P. Dunnill, Biotechnol. Bioeng., 16,

108 1 (1974). 24. W. L. Nyborg, “Acoustic Streaming,” in Physical Acoustics,

Volume I t , W. P. Mason, Ed. (Academic, New York, 1965), part B, pp. 265-331.

25. T. J. Cavicchi and W. D. O’Brien, Jr., IEEE Trans. Sonics Ultrason.,

26. R. M. Macleod and F. Dunn, J . Acoust. SOC. Am., 44, 932 (1968). 27. E. P. Chetverikova, T. N . Pashovkin, N. A. Rosanova, A.P.

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(1973).

1, 41 (1979).

pp. 322-347.

(1953).

SU-32(1), 17 (1985).

The results of our theoretical investigations show that the activity of immobilized enzymes is decisively dependent on the transport processes in the vicinity of the porous carrier particles. Because of the complicated hydrodynamic situation within the reactor bed and the uncertainties as to the physical and chemical constants used in the com- putation, solution of the diffusion equation can be regarded as a semiquantitative description of the mass transport only. Nevertheless, the theory provides values that reasonably correspond to those experimentally found for (Y -amylase and glucoamylase. Hence, theory and experiments support the hypothesis that ultrasound-aided enzyme activity enhancement can be attributed to a reduction of the unstirred diffusion layer around the carrier bodies.

The authors are obliged to W. D. O’Brien, Jr., University of Illi- nois, Bioacoustics Research Laboratory, for helpful discussions and his kind support during the preparation of the manuscript for this article.

NOMENCLATURE

sum of the spherical surfaces of the carrier particles, included in I-cm3 reactor volume (A = 86 cmz for Y58 and a particle diameter 0.6 < d < 0.8 m) diffusion coefficient of the bulk substrate solution substrate diffusion coefficient within the carrier matrix = (D/6) substrate transport coefficient in the diffusion layer

( 4 s ) sound intensity (kW/mz) Michaelis constant of the soluble enzyme flow rate of the substrate solution through the cuvette (mL/h) radius coordinate particle radius substrate concentration substrate concentration in the diffusion layer initial substrate concentration substrate concentration at the carrier surface time reaction rate of the enzyme carrier complex (pmol product/cm’ carrier material/min) relative reaction rate (quotient of the reaction rate with and without ultrasound) maximum reaction rate of the enzyme thickness of the diffusion layer


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Theoretical and experimental studies on the influence of ultrasound on immobilized enzymes