Effect of nonlinear equilibrium on the mass transfer rate of α-amylase extraction by reversed micelles

Process Biochemistry Vol. 31, No. 3, pp. 249-252, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0032-9592/96 S 15.00 + 0.00 ELSEVIER

0032-9592(95)00053-4

Effect of Nonlinear Equilibrium on the Mass Transfer Rate of a-Amylase Extraction by Reversed Micelles Stefano Brandani,"* Vincenzo Brandani, a Gabriele Di Giacomo a & Loredana Spera b "Dipartimentodi Chimica,IngegneriaChimicae Materiali, Universithde L'Aquila,1-67040 Monteluco di Roio, L'Aquila,Italy hCRAB-Consorziodi RicercheApplicate alia Biotecnologia,1-67051 Avezzano(AQ), Italy (Received29 March 1995; accepted 11 June 1995)

The rate of mass transfer in the liquid-liquid extraction of a-amylase from an aqueous phase to a reversed micellar phase has been studied. A simple model for the mathematical representation of this system is discussed. Batch separation experiments at different total concentrations have been carried out. These show the effect of the nonlinear equilibrium on the mass transfer rate. The experimental results are used to obtain the time constant of the process.

temperature, surfactant concentration and protein concentration in the aqueous phase. Having characterized the equilibrium properties, the intent of this contribution is to propose a simple model for the mass transfer rate and to show the influence of the nonlinear equilibrium on the kinetics of the process.

INTRODUCTION Reversed micelles can be used for the recovery and concentration of proteins by traditional liquid-liquid extraction techniques. A reversed micelle can be considered a spherical aggregate of surfactant molecules in an apolar solvent with an inner core of water. These water pools enable idrophilic compounds, such as proteins, to be solubilized in organic solvents. In order to characterize the extraction process it is necessary to describe both equilibrium properties and mass transfer rate. The partition of a-amylase from an aqueous phase to an organic phase consisting of iso-octane, octanol (1% v/v) and a cationic surfactant trioctylmethyl ammonium chloride (TOMAC), has recently been studied in detail. 1-4 It has been possible to formulate a thermodynamic model 3 which is capable of representing the system. It has been shown that the partition coefficient is influenced by pH,

THEORY

In order to formulate a model for the transfer of a-amylase from an aqueous phase to a reversed miceUar system, some preliminary considerations are necessary. The transfer process can be schematically subdivided into the following steps: (1) migration of the protein from the bulk of the aqueous phase to the interface between the two phases; (2) interaction between the protein and the polar 'heads' of the surfactant for the formation of the reversed micelle; (3) migration of the reversed micelle in the bulk of the organic phase.

*To whomcorrespondence should be addressed. 249

S. Brandaniet al.

250

For this type of system it has been shown, 5 through a systematic study of the system, that the formation of the reversed micelle is quite rapid. Step 2 can therefore be considered at equilibirum and the overall process is controlled by the diffusion of a-amylase in the aqueous phase. Therefore, a linear driving force (LDF) can be used to represent the dynamics of the mass transfer process:

dq - VA ~t = koS(c_c,) Vo d--~=

(1)

at final equilibrium; and K is the partition coefficient defined as:

K =q~

(6)

cf

It has been shown experimentally3 that for this system the partition coefficient is dependent on the concentration of the protein in the aqueous phase. The concentration dependence can be expressed as: 3 A

K =1 +Bc*"

and VACo= VAC+ Voq

(2)

dq k ( c _ V o ) d--~= ~ o VA q--c* ,

(3)

or

where S = surface (m2); c----protein concentration in the aqueous phase (M); Co= initial concentration in aqueous phase (M); c* =equilibrium protein concentration in aqueous phase (M); k=koS/Vo

(7)

Equation (7) was based on the hypothesis that each reversed micelle can host one molecule of protein and that the number of micelles is proportional to the surfactant concentration. Clearly eqn (7) represents a Langmuir type of equilibrium isotherm. In this case the solution to eqn (3) is given by: (l-Q)"

( ; 1-q~q2Q

---exp ---~Akt ,

(8)

where

ql

Bco + AVo/VA + 1 - 4(Bco+ AVo/VA + 1)2-4ABco Vo/VA ---- q f ---2BVo/VA

(9)

Bco + AVo/ VA+ 1-4(Bco+AVo/VA+ 1)2-4ABco Vo/ VA q2 = 2BVo/VA time constant (s-1); ko = overall mass transfer rate coefficient, (m s- ~); q = protein concentration in the organic phase (M); t=time (s); /f"o and VA----organic and aqueous phase volumes (m3). When modelling this type of system5-7 the equilibrium concentration c* is considered to be proportional to the concentration in the organic phase q, i.e. a linear equilibrium isotherm is considered.

q =Kc*.

(4)

The solution to eqn (3) is given by:

where Q--reduced concentration in the organic phase; qf = protein concentration in organic phase

a=

A/B -ql q2

--

ql

;

fl=

(I0) q2 q2

-A/B --

ql

(11)

q~, q2, ct and fl can be calculated from the equilibrium properties. Figure 1 shows the comparison of the two models, eqns (5) and (8) (setting A=4.8678, B -- 468740 M-~ which are the values obtained for this system,3 and Vo/Vg-- 1), as a function of the parameter 2, defined as qf/qs (qs=A/B is the concentration at complete saturation, i.e. Co= oo ), which, in analogy with adsorption processes, a can be used as an index for nonlinearity. The two models are equivalent for 2 < 0.5, but at higher values the mass transfer is clearly influenced by the nonlinearity of the isotherm. In order to obtain an experimental validation of the proposed model we carried out transient batch experiments to evaluate the time constant of the process.

a-Amylase extraction using reversedmicelles

251

20 0.90.6"

18"

Co

i

16-

q(

!

14-

0.7-

~.~ 12

. . . .

0.60

¢~ 10"

0.5-

8

Linear

0.44

o.32

6 4

0.20

0.1~ 0

o

o12 o14 o16 o18 i

lla 114 1'6 1.6 a

kt

Fig. 1. Reduced organic phase concentration vs kt as a function of the nonlinearity parameter 2.

MATERIALS AND METHODS

Fig. 2. Equilibrium curves.

isotherm

and

total

concentration

fuged and the two phases separated. The experiment was considered to be complete when the centrifuge reached the speed of 1500 rpm

( 30s). Isooctane was purchased from Merck and was UV visible grade. 1-Octanol was obtained from Aldrich and has a purity greater than 99"5%. The quaternary ammonium salt TOMAC (trioctylmethyl ammonium chloride) was obtained from Merck, a-Amylase (1,4-a-D-glucan glucanohydrolase EC 3.2.1.1) from Bacillus species was purchased from Sigma and its molecular weight was 50 kDa. The quantity of protein was measured in aqueous phase by spectrophotometry at 280 nm. It was verified that the Lambert-Beer law was valid up to a concentration of 22/aM. The extinction coefficient was 110000 M-1 cm-i. All spectrometric measurements used a UNICAM PU 8730 spectrophotometer. Aqueous and organic phases were prepared separately. The initial aqueous phase contained the enzyme in a borate buffer (Na2B4OT. 10H20 / NaOH) at pH 9.9 and the best separation conditions were achieved at this pH value) The organic phase was a solution of TOIVIAC in isooctane-1octanol (0-1% v/v). The TOMAC concentration was fixed at 0.02 M. The experiments were performed at 25°C in a 20 c m 3 thermostatically controlled cell, by adding equal volumes, Vo= VA----5 c m 3, of the two phases. The cell was mixed with a magnetic stirrer at a fixed speed of 300 rpm. Under these conditions the organic phase appeared to be homogeneously dispersed. After stirring for fixed time intervals the mixtures were immediately centri-

RESULTS AND DISCUSSION Three experiments were carried out varying only the total concentration, Co, and maintaining all other conditions constant. With the simple experimental apparatus we used it was possible to monitor the transient of the a-amylase concentration. Since the process is controlled by the diffusion of the a-amylase in the aqueous phase, s the time constant of the process should be independent of the initial protein concentration. For this system the equilibrium constants are: 3 A -- 4.8678 and B = 468740 M-1. Three levels for co were chosen: 6, 12 and 20/~M. Figure 2 shows the equilibrium isotherm and the corresponding total concentration. This diagram can be used to read the final equilibrium value and also shows the difference between the Langrnuir isotherm and the corresponding linear approximation. As can be seen from Fig. 2 the first set of experiments are at concentration levels for which -- 0"43, therefore both models should be equivalent. For this reason we have used the runs for Co= 6 /ZM to obtain the time constant. Figure 3 shows the comparison between the experimental results and the curves calculated using the value of k = 0.002 s- ~. Figures 4, 2 = 0"69, and 5, A --- 0.84, show the comparison between the experimental results and the predictions obtained from the two models.

252

S. Brandani et al. 1

0.9 0.8' 0.7

0.6" 0

0.5"

Langmuir

0,4-

Linear

0.30.20.10

o

56o

1o6o

ISbO ~ t (s)

2sbo

~bo

35o0

It appears evident that the single time constant m o d e l is capable of representing the mass transfer process. T h e effect of the nonlinear equilibirum is also confirmed and indicates that especially in c o n c e n t r a t i o n units the approximation of a constant partition coefficient m a y be erroneous. If we consider as an index the time required to obtain 99% a p p r o a c h to equilibrium (Q = 0 " 9 9 ) f o r the third system, Co = 20/~M, the value obtained f r o m eqn (5) is 1000 s, while f r o m (8) is 450 s. T h e s e values w h e n c o m p a r e d to the experimental result o f 410 s clearly suggest the n e e d to check for the linearity of the equilibrium isotherm before adopting a constant partition coefficient model.

Fig. 3. Comparison between experimental data • and model calculations for total concentration co = 6/~M. CONCLUSIONS 1

A simple m o d e l for the interpretation of mass transfer process of a - a m y l a s e f r o m an aqueous phase to a reversed micellar phase has b e e n proposed. T h e single constant m o d e l is in good a g r e e m e n t with the experimental evidence. T h e effect of the nonlinearity of the equilibrium isot h e r m has b e e n shown, and for values of 2 > 0.5 the constant partition coefficient m o d e l is clearly inadequate.

0,9 0.8 0,7 0.6. o

0.5"

Langrnuir

0.4-

Linear

0.3" 0.20.1" 0

0

REFERENCES s6o

lobo

15bo

a~o

2~bo

~o

3soo

t (s)

Fig. 4. Comparison between experimental data • and model predictions for total concentration Co= 12 pM.

1 0.9 0.8 0.7 0.6 0

0.5

Langrnuir

0.4

Linear

0.3 0.2' 0.1' 0

56o

10bo

l~b0

a~o

2sbo

~obo

35oo

t (s)

Fig. 5. Comparison between experimental data • and model predictions for total concentration % = 20 pM.

1. Brandani, V., Di Giacomo, G. & Spera, L., Extraction of protein a-amylase by reverse micelles. Process Biochem., 28 (1993) 411-4. 2. Brandani, V., Di Gacomo, G. & Spera, L., Extraction of a-amylase protein by reverse micelles: II. Effect of pH and ionic strength. ProcessBiochem., 29 (1994) 363-7. 3. Brandani, S., Brandani, V., Di Giacomo, G. & Spera, L., A thermodynamic model for protein partitioning in reversed micellar systems. Chem. Eng. Sci., 49, (1994) 3681-6. 4. Brandani, V., Di Giacomo, G. & Spera, L., Recovery of a-amylase extracted by reverse micelles. Process Biochem., 31 (1995) 125-8. 5. Dekker, M., Van't Riet, K., Bijsterbosch, B. H., Fijneman, P. & Hilhorst, R., Mass transfer rate of protein extraction with reversed micelles. Chem. Eng. Sci., 45 (1990) 2949-57. 6. Dekker, M., Van't Riet, K., Weijers, S. R., Baltussen, J. W. A., Laane, C. & Bijsterbosch, B. H., Enzyme recovery by liquid-liquid extraction using reversed micelles. Chem. Eng. J., 33 (1986) B27-33. 7. Dekker, M., Van't Riet, K., Bijsterbosch, B. H., Wolbert, B. G. & Hilhorst, R., Modelling and optimization of the reversed micellar extraction of a-amylase. AiChE J., 35 (1989) 321-4. 8. Ruthven, D. M., Principlesof Adsorption and Adsorption Processes. Wiley, New York, 1984.