J . Chem. Tech. Biotechnol. 1990,48, 467482
Thermodynamics and Kinetics of Lipase Catalysed Hydrolysis of Oleyl Oleate Thomas Rostrup-Nielsen, Lars Saaby Pedersen & John Villadsen Instituttet for Bioteknologi, Danmarks tekniske H~jskole,2800 Lyngby, Denmark (Received 1 August 1988; revised version received 4 September 1989; accepted 30 September 1989)
ABSTRACT The kinetics of enzymatic hydrolysis of oleyl oleate in the boundary layer between stagnant organic and aqueous phases was studied using a commercial lipase preparation which was dissolved in the aqueous phase. Three aspects of the reaction were investigated. ( 1 ) The hydrolysis equilibrium in the organic phase cannot be expressed in terms of the concentrations of ester, alcohol and organic acid alone since the activity of the organic compounds changes dramatically with conversion, i.e. with the water content in the organic phase. An empirical correlation that accounts for the water activity and the unknown activity coefficients of the organic compounds is determined. (2)The influence of the interfacial area was examined, and it was found that the amount of ester converted per unit area of interjace is independent of the available interfacial area and of the amount of ester. (3)The inhibition of the reaction by the hydrolysis products and by n-alkanes was measured. Both acid and alcohol inhibit the hydrolysis reaction while the influence of long-chained alkanes is very small. I t is concluded that the reaction rate is determined by the interfacial concentrations, and that these concentrations differ from the bulk concentrations because of the different surface afinities of the components. Key words: lipase, oleyl oleate, kinetics, interfacial reactions, mathematical model. 1 INTRODUCTION
Lipases are enzymes of considerable industrial interest due to their capability to catalyse the reversible reaction between carboxylic acids and alcohols at low temperature. Typical industrial lipases are used in immobilised form for 467
J . Chem. Tech. Biotechnol. 0268-2575/90/$03.5001990Society of Chemical Industry. Printed in Great Britain
468
T. Rostrup-Nielsen. L.S. Pedersen, J . Villadsen
interesterification and for ester synthesis. A better understanding of the reaction mechanism, and hence a better basis for reactor design is, however, obtained by studying the enzyme in homogenous solution, as is done in a majority of the published investigations. The present investigation is not different in this respect, dealing with hydrolysis kinetics of oleyl oleate, and using a commercial lipase preparation dissolved in an aqueous phase in contact with the insoluble ester phase. Previous work by Benzonana and Desnuelle' and by Sarda and Desnuelle' demonstrated the importance of the interface and emphasized that the rates should be referred to the interfacial area rather than to the volumes of the bulk ester phase or aqueous phase. Their work showed that the reaction rate increases with increasing interfacial area and with increasing amounts of adsorbed lipase on the interface. It is assumed that lipases have two separate sites, a catalytic site and a site which binds the lipase at the i n t e r f a ~ e This . ~ . ~means that there exists an equilibrium between lipase E in the aqueous phase, and lipase bound at the interface Ed E+d=EB
(1)
where 0 is a free site on the interface. This elementary reaction has been used in a number of models to explain the kinetics of the lipase Mattson et aL6 have examined the influence of n-alcohol on the reaction rate. They found that n-alcohols inhibit the reaction-the reason being that they have a greater affinity to the interface than the ester. In their work they did not, however, take into account the influence of the alcohol concentration on the equilibrium. All or part of their observed effect could be explained by proper handling of the thermodynamic equilibrium in their rate expression. It is likely that other components could have a similar inhibiting effect on the reaction rate. Smith and Alford' found that fatty acids decrease the activity of lipase; and recently, Mukataka et af.' examined the effect of diluting the substrate with n-alkanes. In this work three aspects of the hydrolysis reaction were studied. (a) The equilibrium was carefully determined using excess amounts of oleic acid and oleyl alcohol added to the ester. The equilibrium constant, K , , is given by the activities of the components in the organic phase as
(2) can be written as
where Al, Ac, Es are concentrations of alcohol, acid and ester respectively and y the corresponding activity coefficients in the organic phase a, is the water activity in the organic phase. It is probably close to one since the organic phase is in contact with a large aqueous phase, but the activity coefficients of the organic compounds may be strongly dependent on the composition of the organic phase. We approximate f i n (3) by the empirical linear expression:
f - CA]AI+ C,,Ac
+ C,Es
(4)
Lipase-catalysed hydrolysis of oleyl oleate
469
in which CAI,CAc,CEsare constants to be determined by means of a large number of equilibrium experiments. (b) The rate of reaction was studied as a function of interfacial area A , of the ester amount M , and of ester concentration Es in the organic phase (using dilution with a longchain alkane). It is postulated that the conversion X of ester follows the rate law
where r ( X ) is expressed in units of moles converted per square metre per second. (c) r ( X ) includes a factor for the reverse reaction and inhibition terms for both alcohol and acid. The inhibition is studied by adding various amounts of alcohol and/or acid to the ester before start of reaction.
2 MATERIALS AND METHODS A lipase preparation from Mucor miehei with an activity of 10 000 lipase units g - ' ( L u g - ' ) was provided by Novo Industri A/S. The activity unit is based on
hydrolysis of tributyrine in a standardized procedure developed by Novo (AF 95/5GB). 1 LU is the amount of enzyme which liberates 1 pmol butyric acid min-' at 30"C, pH=7. Samples were prepared by dilution of the stock solution and all activities quoted in the present paper are relative values. The ester was synthesized from oleic acid and oleyl alcohol using immobilized lipase, also supplied by Novo Industri A/S. The reactants were all of technical grade quality (Merck 471 and Merck 820923). The synthesis was carried out at 70°C and 10 mm Hg using a total reaction time of 4 h. It proved difficult to obtain a pure ester. Starting with stoichiometric amounts of alcohol and acid, using different reaction times (up to 20 h), different total pressure (to 1 mm Hg) and organic acids (e.g. p-toluenesulfonic acid) instead of enzyme as catalyst,' various attempts to obtain a pure ester failed. It was also attempted to use an excess of either alcohol or acid and, as suggested previo~sly,~ separating ester from excess reagent at - 80"C, washing crystals of ester with hexane to remove acid and alcohol. This too was not successful. In all preparations about 2-3 % acid and alcohol remained mixed with the ester. In the rate experiments the initial conversion of the ester was, of course, determined by titrating the ester before using it in a hydrolysis experiment. The most likely explanation for the persistent acid impurity in ester preparations from equimolar quantities of alcohol and acid is that the reagents contain small amounts of other acids and alcohols (e.g. stearic acid) which do not react to completion." The presence of small amounts of non-identified alcohols and acids in addition to the oleyloleate were confirmed by both GC and TLC. 2.1 Experiments
All experiments were carried out at 44"C, and the enzyme concentration was 15.625 LU g-' if not otherwise stated. Most of the experiments were carried out in 100cm3 Ehrlenmeyer flasks. The amount of aqueous enzyme solution was
470
T. Rostrup-Niulsen, L. S . Pedersen. J . Villudseii
generally chosen such that the interfacial area between the ester phase and the water phase was 20.8 cm’. The interfacial area was determined by measuring the outer diameter of the flask and subtracting an assumed value for the glass thickness measured at the top of the flask. This gives an error of about 2% on the interfacial area. Larger and smaller interfacial areas were obtained by using flasks of different volume (5&1000cm3).
2.2 Procedure Enzyme solution (64 cm3 for 100 cm3 flasks) was poured into a flask, which was then placed in a thermostated waterbath (44°C). When the flask had equilibrated the appropriate amount of ester (e.g. 1.4 g for full coverage of 20.8 cm2 as found by visual inspection) was carefully layered on top of the aqueous phase and the flask was returned to the waterbath. After a specified time the contents of the flask were poured into a separating funnel. The aqueous phase was removed and the organic phase washed back into the flask with ethanol (50 cm3).The ethanol had previously been titrated using phenolphthalein as indicator. The amount of oleic acid in the organic phase was then determined by titration with (0.01 mol d m - 3 ) NaOH.
2.3 Accuracy Although the experimental procedure used was simple, reproducibility was good. (a) The Ehrlenmeyer flasks were carefully selected and the same set of about 20 flasks was used in randomized experiments. (b) A set of seven experiments was carried out using the same enzyme solution, amount of ester and reaction time (200 min). Another set ofexperiments was carried out at exactly the same conditions except that the enzyme solution had been subjected to the reaction temperature (44°C) for 20 h. No sign of deactivation of the enzyme was noticed, and the same conversion (to about 2 ”/, relative) was obtained in all 14 experiments. We conclude that the total experimental error is about 2 % relative and that the enzyme is stable at 44°C for at least 20 h. (c) CO, was carefully excluded from the flasks during the kinetic experiments (duration up to several days). Absorption of CO, during titration of the organic phase did not present a problem. The 14 above-mentioned experiments were titrated at different speed and sometimes left to stand for several minutes without any change in the titration end point. The same sharp and stable end points were obtained when the aqueous phase was titrated. (d)It is well known that the enzyme activity changes with pH, and since an acid is produced which to some extent is transported into the aqueous phase this might present a problem for the rate experiments. We have, however, found that the change in pH which might occur in the aqueous phase (at most 1 pH unit from 6.7 initially to 5.7 for about 65 cm3 aqueous phase and 1.4 g ester) is well within the limits of approximately constant enzyme activity.’ O
3 RESULTS 3.1 Reaction rate and conversion Figure 1 shows the conversion as a function of time at a total enzyme concentration = 15.625 LU g - solution. The curve starts at a conversion of 2.65 7;
Lipase-cutulysed hydrdysis oJ’ oleyl olrute
47 1
15
xeq
]fl V
X
- Verger - O u r model 4 Experimental
0
100
200
300
400
Time (rnin)
Fig. 1. Conversion X of ester as a function of reaction time for a lipase concentration of 15.625 LU g - ’. In all experiments the ester amount was 1.4 g and the interfacial area was 20.8 cm’. Full drawn curve is a best fit using the model eqn (24) with the constants C,=212, C3=647000, C,= 186500. and with K , = 15. Broken curve is a best fit using the model of Verger et d4( I I ) .
as determined by titration of the ester before staring the experiment-see Section 2. The full curve is drawn using the parameters of our final model-see Section 4.The broken curve on the figure is obtained by the best possible parameter fit to an earlier model.4
3.2 Reaction rate and lipase concentration Figure 2 shows reciprocal reaction rate as a function of reciprocal lipase concentration. The rates are obtained from plots such as Fig. 1, assuming that the rate is independent of conversion up to 4.5 ”/,. The initial conversion was 2.90% in all experiments. There are two curves (I and 11) on Fig. 2, and both are well approximated by straight lines. The upper curve (11) corresponds to an enzyme solution which has been kept for 4 days at room temperature before use, while the lower curve (I) corresponds to enzyme solution used directly after preparation by dilution of a concentrated enzyme sample. While no loss of activity in the concentrated solution was observed, the dilution (e.g. by a factor of 200 to give 50 LU g - solution) apparently introduced some enzyme instability. The linearity of the two curves permits calculation of K , (as the inverse of the intercept with the negative abscissa) and the maximum rate, rmax(as the inverse of the intercept with the ordinate axis). It can be seen that the K , value is independent of enzyme solution treatment-an observation which lends credibility to the statement that the difference between curves I and I1 is due only to enzyme deactivation.
T. Rosrriip-Nielsen, L. S . Pedersen, J . Villudsen
412
1
P
100-
?
--9
00-
1-
E
9
60-
E m
v 7
‘L
40-
20-
o
t
-80 (Lipase concentration)-’
( g LU-’) lo3
Fig. 2. Reciprocal reaction rate vs reciprocal enzyme concentration for two lipase preparations. Curve I : freshly prepared by dilution ofaconcentratedenzyme solution.Curve 11: thedilutedenzymesolution has been used 4 days after preparation. Ester amount. 1.4g; interhcial area. 20.8cm2.
3.3 Equilibrium constant A number of equilibrium experiments were carried out at 44°C and with a reaction time of 4-6 days. By adding different amounts of oleyl alcohol and oleic acid to the
ester, the equilibrium was established with different concentrations of the components. Since the equilibrium constant K , has, of course, the same value for all the experiments, experimental values can be obtained for the constants in the empirical expression (4). For the parameter estimation procedure we arbitrarily set C , , = l . Hence the f of eqn (4) will differ from the true f in eqn (3) by a proportionality constant 1, and K & can be calculated from AlAc
1
=(s), + ( + C,,Es A1 CAcAc
Based on the experimental results of Fig. 3, K & = O M 6 3 at 44°C. Since the true activities could not be measured by the experimental procedure used here, f , in (6) has to remain as an undetermined constant. This is, however, not a problem for the rate calculations since the approach to equilibrium is correctly predicted if the model predicts the correct variation of .f in the approximation (4) with changing composition of the organic phase. The deviation (in relative percentage) of the equilibrium constant from 0.0463 is shown in Fig. 3 as a function of the concentration of (a) oleic acid and (b) oleyl alcohol.
413
-
-f
10-
5
E" c
c 0
m
5
6.
8.
"# 2 m I 0 :......... o.Ps" ............... n
-2.
n
:
-4.
O
......................
6
D
71 6 2500
I
,
r
I
,
n I
0
0
0
_................__________
-2. a
0
0
-6.
3
I
0
-4.
c .(0
'
0
8I , " 0 ...............?~....Q
E
-2
na
I
;:
E
=
-6. -8. -101
B
6.
0 0
4-
X
10.
-
8.
-8. -101
I
I
I
I
I
I
I
I
X
3000
3500 AIM t
4000
4500
5000
5500
(s rn-2rnol-' ester)
Fig. 4.Conversion X as a function of AIM1 for different values of A, M and r
3.4 Influence of interfacial area To investigate eqn ( 5 ) a series of experiments were made with varying interfacial areas and varying amounts of ester as shown in Fig. 4. In all these experiments the amount of ester used was sufficient to cover the interfacial area, except for the experiment with 5 g oleyl oleate and 80.6 cm2 interfacial area. The reaction time was adjusted to give a conversion of 6 7 % in all experiments. Figure 4 shows the conversion as a function of A / M t . A much larger series of experiments was carried out with varying interfacial area A and varying amounts M of ester. The reaction time was 60min for all these experiments, and conversion was between 2.90%(initial) and up to about 6%. The
T. Rostrup-Nirlsm. L. S . Prdrrsen. J . Villadsrri
474
I
I
(a)
0
(b)
0.5
0
i
1
I
1.0 1.5 20 Amount of ester ( g )
I
I
2.5
3.0
I
I
I
I
I
I
0.5
10
1.5
2.0
2.5
3.0
I 3.5
i 3-5
Amount of ester (g)
Fig. 5. Reciprocal reaction rate vs reciprocal ester amount for four different values of geometrical interfacial area (four different flasks). The four straight lines are calculated from eqn (5). Reaction time 60 min for all experiments.
reaction rate which, as in Fig. 2, is taken to be independent of X in the conversion range 2*9&6%, was calculated as moles converted per unit time and available interfacial area. The reciprocal reaction rate l/r is shown in Fig. 5 as a function of 1/M with A as a discrete parameter.
Lipusr-curuly~rdhydrolysis of’ olegl oleutt.
475
Alcohol (g g-’ ester)
’
Fig.6. Conversion after 60min reaction time as a function of initially added alcohol (g g - ester).The full line is obtained from the model eqn (24) using C , =212, C3=647oOo, C4= 186500and K,= 15 as in Fig. I .
3.5 Inhibition by oleyl alcohol and oleic acid: Influence of dilution by n-alkane To determine whether the hydrolysis products inhibit the reaction, two series of experiments were made. The conversion after 60 min was measured with different amounts of oleyl alcohol and oleic acid added to the ester. Figure 6 shows the conversion as a function of the amounts of oleyl alcohol added. The experimental error in the experiments with added oleic acid was much larger than 2%, since in most of the experiments the NaOH amount needed to neutralize the added acid was much larger than the amount of NaOH needed to determine the conversion. Finally, the influence of ester concentration in the organic phase was investigated by diluting the ester with various amounts of n-hexadecane which is considered to be an inert for the reaction. The results are shown on Fig. 7-all for a reaction time of 60 min. An influence of concentration was only observed at extremely low ester concentrations. 4 DISCUSSION 4.1 Lipase adsorption at the interface
The adsorption equilibrium constant for the elementary reaction (1) is given by K,
=E x
BIE8
(7)
By assuming that the initial reaction rate r, is proportional to the adsorbed amount of enzyme r, =r,,,EB and by assuming4 that E B EB and that the total amount of sites, 8, is given by B,=B+EB one obtains
T. Rostrup-Nielsen, L. S. Pedersen, J . Villadsen
416
-
0.8
0 0
0
o
n I
--9 I
0
06-
I
m
0
0
N
E
5 E
W 0.4-
%
Y
. x
L
#
X
x i
-
0.2
-+ 1.Og ester -M-
-I
0
I
0.25
I
0.50
I
0.75
I
1.00
I
1.25
0.3g ester 1
1.50
I 1.75
Ester concentration (mmol dm-3)
Fig. 7. Reaction rate averaged over the first 60 min a s a function of ester concentration in n-hexadecane using 0 3 and 1,Og ester. Pure ester corresponds to 1.61 moldm-3.
which leads to
The good fit to a straight line (curve I or 11)in Fig. 2 confirms that the reaction rate is proportional to the adsorbed amount of lipase on the interface, and that the adsorption can be described by reaction (1). The value of K , is found from eqn (9) and Fig. 2 to be 15 LU g-' and rmaxOo=2.7x mol m - 2 s - ' . These values are based on experiments with conversion between 2.9 % (at t = 0) and 4.5 % (after 60 min). The increase of conversion is small enough, and the dependence of X on t sufficiently linear in the range (see Fig. 1) to ensure that the rates shown on Fig. 2 are good estimates of the initial rates.
4.3 Equilibrium constant To establish equilibrium in the experiments on which Fig. 3 is based, 4-6 days were used. This raises a problem because oleic acid may dissociate at the interface and slowly dissolve in the aqueous phase, especially in the presence of inorganic metal ions. Patil et al." investigated the kinetics of this reaction for a number of acids ' ~ the rate at which oleic acid dissolves including oleic acid. Scow et ~ 1 . measured into an aqueous phase containing 4 . 4 ~ m o l d m - albumin. ~ The rate was determined with a monlayer technique at different surface pressures (22-32 dyne cm-') and it was found to vary between 221 and 378. pmol cm-2 min-'.
Lipase-catalysed hydrolysis of oleyl oleate
477
TABLE 1 Transfer Rates of Oleic Acid into Aqueous Phase Measured by Equilibrium Experiments with Pure Ester (No Alcohol or Acid Added Initially)” Days
Moles acid found in aqueous phase (mol) lo3
4 4
3.94 3.52 4.45 5.60 6.52
4
5 6
Transfer rate (pmol cm-’ min-I)
329 294 371 375 363
‘Interfacial area 20.8 cm2 and 1.4 g ester.
TABLE 2 Transfer Rates of Oleic Acid from Ester Phase to Aqueous Phase as a Function of Initially Added Oleic Acid” Added acid (9)lo3
Moles acid found in aqueous phase (mol) 105
0 18 75 100 116 136 177 253 333
4.45
4.64 4.99 5.5 1 5.78 6.91 7.26 7.88 9.98
Transfer rate (pmol cm-’ min-’1
371 387 41 6 460 482 577 606 657 833
’All
experiments run to almost equilibrium of the hydrolysis reaction (4 days) using interfacial area 20.8 cm2 and 1.4 g ester.
Table 1 shows the amount of oleic acid found in the aqueous phase after 4-7 days as determined by titration with 0.01 N NaOH. It is seen that the transfer rate is constant at a level of about 346 pmol cm-’ min-’ which is in the range of Scow et al. Apparently, the bacterial lipase and the bovine serum albumin used by Scow et al. both produce some weak dissolution of oleic acid into the aqueous phase. The mol d m - 3 from final oleic concentration is, however, always small ( < 1.3 x Tables 1 and 2). The transfer of oleic acid to the aqueous phase takes place at a small but constant rate, and therefore a true chemical equilibrium for the ester phase cannot be established. Table 2 shows the amount of oleic acid found in the aqueous phase after 4 days as a function of increasing amounts of oleic acid added to the ester. Note that the transfer rate increases with increasing concentration of oleic acid in the organic phase. Figure 3 shows that within a factor 10 in theoleic acid concentration in the
T. Rostrup-Nii,lseti. L. S . Pederseti, J . Villudseti
478
organic phase at ‘equilibrium’,the equilibrium constant does not have a systematic variation with the oleic acid concentration. This means that the concentrations in the organic phase can be assumed to be close to their equilibrium values. Hence the equilibrium constant K L = 00463 together with the constants of the approximate expression (4) for f ’ have been determined without experimental bias. Since C,, was set at a value of unity in eqn (4)the true value of .f was not obtained from eqn (3) by the experimental procedure used. For calculations of the approach to equilibrium it is enough that the model predicts the correct variation of the approximation (4) to f’ with changing composition of the organic phase. Figure 3 also shows that for most of the observations the equilibrium constant varies less than 5 % from its mean value of KC =0.0463 at 44°C. Over the range of investigated compositions, f‘varies by about a factor of two which is far greater than the experimental error of about 2%. It must be concluded that the equilibrium model represents the data much better than an equilibrium model based solely on concentrations of organic reactants. An equilibrium constant of K & = 00463 corresponds to an equilibrium conversion of X, = 13.46%.
4.3 Interfacial area Equation (5) can be written as
Hence experiments run between the same initial conversion X, and the same final conversion X will give the same value of AIM t . Where approximately the same conversion X has been reached in a number of experiments with widely different A and M values, Fig. 4 shows that eqn (10) is satisfied. The three points obtained for the system with 5 g ester and 80.6 cm2 surface area show a smaller conversion than expected. The explanation is as shown in the following that the whole available geometrical interface area was not covered by the small quantity of ester used in these three experiments. Since the reaction rate is approximately constant between 6.5 and 7.5:4 conversion one obtains a linear relation between t and X in the experiments of Fig. 4. From the slope of the line one obtains r(X)=0.611 x lo-’ mol
s - ’ for X - 7 %
From Fig. 1, for X-7%, one obtains: MdX r(X)=--=0*600x A dt
m d m-’s-l
which agrees well with the above result. This is taken as an additional confirmation of the validity of the rate expression (5). The group of experiments shown in Fig. 5-with A as a parameter on the curves and M as abscissagives a final support of eqn (5). which appears to hold in a range of interfacial areas between 10 and 80cm2 and for M between 0.3 and 13 g. It should
Lipasr-cufalysrd hydrdysis q/’ o/ey/ oleate
479
be noted that whereas for all points on Fig. 4-except those at 5 g, 80.6 cm2-the total geometrical interface area is covered, this is not true for experiments in Fig. 5, where e.g. an ester amount of 1.4 g is necessary to cover 20.8 cm2 geometrical area. These results show a simple picture of the interfacial reaction. (1) The relation between reaction rate and A holds whether a small drop of ester is placed on a large surface of water ( e g experiments with 0.8 g ester on 80cm’ geometrical interface area) or a large amount of ester is deposited on a small water surface (e.g. 5 g on 20.8 cm2 geometrical interface area). (2) In Fig. 4 it is seen that 1.4,3 and 5 g ester on 20.8 cm2 surface all give the same rate. This last result shows that there is no transport restriction of the chemical reaction: a fully covered surface gives the same reaction rate whether the ester layer is thin (1.4 g on 208 cm2)or much thicker (5 g on 208 cm2).
4.4 Final reaction rate model An earlier model by Verger et ~ 1 was . tested ~ by making a best fit to the results in Fig. 1. This was done using an initial reaction rate corresponding to 2.65% conversion. Verger’s model is an initial reaction rate model, and the rate expression is given by
7 = k , E s / ( E s + k2(1 + k 3 / E ) )
(11)
where k , , k2 and k 3 are constants. To take the reverse reaction into account the rate expression is corrected as follows:
in which Q is the mass action fraction. Figure 1 clearly demonstrates that this model cannot describe the decrease in reaction rate observed at conversion above 6 %. This may be due to inhibition by the hydrolysis products, in a similar fashion as described by Mattson et aL6 for alcohols. In Verger’s model-eqn (11)-bulk concentrations are inserted. The results in Fig. 7 do, however, show that the reaction rate is independent of the bulk concentration over a wide range. Only at extremely low ester concentrations can an effect of Es be noticed. This indicates that the reaction rate depends on interfacial concentrations rather than on bulk concentrations. A new model was developed assuming that the reaction can be described by the following elementary reactions in terms of 0‘ which denotes surface sites, ‘activated’ by adsorption of an enzyme, e.g. O:, = EH of eqn (8),and which are not occupied by complexes with the reactants Es, Ac or Al. Es + 8‘= EsO
EsO
Ac+O’=AcO
(14)
Al+8’=AlO
(15 )
+ W+
(16)
A18
+ Ace
with adsorption constants KEarK,, and K , , , and with a rate constant k‘ for the
T. Rostrup-Nirlsm, L . S . Pedrrsen, J . Villudsetl
480
hydrolysis reaction (16). Assuming that this reaction is rate determining, the following rate expression for the hydrolysis reaction is obtained F= k’EsdW
(17)
By assuming that the water activity at the inre$ice is constant, eqn ( 1 7 ) is reduced to
(18)
7=kEsO
where k=k’W. The site balance is given by Ed = 0;
= 8‘
+ Esd + AcH + A10
(19)
Combining eqn (18) with eqn (19) and the adsorption equilibria, the following expression is obtained for the hydrolysis reaction (20)
Inserting 0: = EO and using eqn (8) for EU, we obtain: d
r=
Es C, E S C, +C,AC
+
+ C,Al
E X-
K,
+E
where C,, C2, C, and C, are constants which incorporate the unknown constant 8 , in eqn (8). As for Verger’s model, the overall reaction rate can be expressed as
r =7( 1 - Q / K : , )
(22)
where the mass action fraction Q is calculated similarly as K & in (6) i.e. as AlAc
1 Q=F A1 + CAc Ac X
+ CEsEs
In this fashion the unknown scalar factor ,L, cancels. It is true that j’(AI,Ac, Es) was determined from equilibrium experiments. Here j ’ is used also for compositions which may be very different from those found at equilibrium. It is considered that the functional relationship for j ’ which was determined by equilibrium experiments at widely different compositions of the organic phase is resilient enough to permit use of j a l s o to calculate Q.*A parameter estimation showed that the constant C2 is much smaller than the other constants. This means that there are very few free sites. Hence the constant is disregarded, and the expression for the forward rate of hydrolysis is reduced to 2
r=
Es C, Es+C3Ac+C4Al
X-
E K,+ E
(24)
In this expression the term EsC, is smaller than the other two terms in the denominator, but it cannot be removed, because it describes the initial reaction rate, where (for a pure ester) there is neither acid nor alcohol present. Since in all experiments there was an initial conversion of about 2-3 %, the value of the constant C, could not be determined with a satisfactorily low confidence interval. The values
Lipusr-curulvsrd hydrolysis
48 I
olryl olrutr
obtained by a parameter estimation are shown in the text to Fig. I . Figures 1 and 6 show that the model with the constants from the text to Fig. 1 gives a most satisfactory description of the results. The results obtained by dilution with alkane (Fig. 7) could be described by adding an additional elementary reaction to eqns (13)-( 15):
I
+ el = I e
(25)
This would result in the following rate expression +
r=
E
Es C , E s + C , A c + C,AI+C,I
X -
K,
+E
(26)
The results do, however, show that the influence of the alkane concentration I is small, and an eventual dependence on I could equally well be explained by a change of the physical properties of the interface, e.g. a change in the surface tension. Similar physical changes in the surface could also appear at high enough alcohol and acid concentrations. Our experiments do not, however, permit a more sophisticated explanation of the observed alcohol and acid inhibition than that expressed in eqn (24). 5 CONCLUSION
The design of industrial enzyme reactors should as far as possible be based on a quantitative understanding of the underlying physical and chemical processes. This makes an extrapolation from one operation mode to another (continuous vs batch or fluidized vs fixed bed) much easier. Our study is made with an ester of small industrial importance and with enzyme in homogeneous solution rather than on support particles. Still, the results concerning equilibrium, and the kinetic results (the simple relation between rate of change of conversion and available surface area, as well as the inhibition effect of products), are of immediate use in the scale-up of a lipase-catalysed reaction or in predictions of the effect of a change in contact pattern in the complex system of organic phase/immobilized enzyme and water.
REFERENCES 1. Benzonana, G. & Desnuelle, P., Kinetic study of the action of pancreatic lipase on triglycerides in emulsion. Enzyme action in a heterogeneous medium. Biochim. Biophys. Acts, 105 (1965) 121-36. 2. Sarda, L . & Desnuelle, P., Action de la lipase pancreatique sur les esters en emulsion. Biochim. Biophys. Acta, 30 (1958) 513-21. 3. Brockerhoff, H., A model of pancreatic lipase and the orientation of enzymes at interfaces. Chemistry Physics Lipids, 10 (1973) 215. 4. Verger, R., Mieras, C. E. & de Haas, G. H., Action of phospholipase A at interfaces. J . Biol. Chem., 248 (1973) 4023-34. 5. Brockman, H . L., General features of lipolysis: Reaction scheme, interfacial structure and experimental approaches. Lipases. Elsevier Science Publishers, Amsterdam (1984).
482
T. Rostrup-Nielsen, L. S . Pedersen, J . Villadsen
6. Mattson, F. H., Volpenhein, R. A. & Benjamin, L., Inhibition of lipolysis by normal alcohols. J . Biol. Chem., 245 (1970) 533540. 7. Smith, J. L. & Alford, J. A,, Inhibition of microbial lipases by fatty acids. Appl. Microbiology, 14 (1966) 699. 8. Mukataka, S., Kobayashi, T. & Takahashi, J., Kinetics of enzymatic hydrolysis of lipids in biphasic organic-aqueous systems. J . Ferment. Technol., 63 (1985) 461. 9. Swern, D., Billen, G . N. & Knight, H. B., Preparation of some polymerizable esters of oleic acid with unsaturated alcohols. J . Am. Chem. Soc., 69 (1947) 2439. 10. Novo Enzymes, The use of lipozyme for synthesis of esters. B 348b-GB 400 June, 1986. 1 1 . Patil, G. S., Matthews, R. H. & Cornwell, D. G.,Kinetics of the processes of desorption from fatty acid monolayers. J . Lipid Research, 14 (1973) 23. 12. Scow, R . O., Desnuelle, P. & Verger, R., Lipolysis and lipid movement in a membrane model. J . Bid. Chem., 254 (1979) 6456.
Thermodynamics and Kinetics of Lipase Catalysed Hydrolysis of Oleyl Oleate Thomas Rostrup-Nielsen, Lars Saaby Pedersen & John Villadsen Instituttet for Bioteknologi, Danmarks tekniske H~jskole,2800 Lyngby, Denmark (Received 1 August 1988; revised version received 4 September 1989; accepted 30 September 1989)
ABSTRACT The kinetics of enzymatic hydrolysis of oleyl oleate in the boundary layer between stagnant organic and aqueous phases was studied using a commercial lipase preparation which was dissolved in the aqueous phase. Three aspects of the reaction were investigated. ( 1 ) The hydrolysis equilibrium in the organic phase cannot be expressed in terms of the concentrations of ester, alcohol and organic acid alone since the activity of the organic compounds changes dramatically with conversion, i.e. with the water content in the organic phase. An empirical correlation that accounts for the water activity and the unknown activity coefficients of the organic compounds is determined. (2)The influence of the interfacial area was examined, and it was found that the amount of ester converted per unit area of interjace is independent of the available interfacial area and of the amount of ester. (3)The inhibition of the reaction by the hydrolysis products and by n-alkanes was measured. Both acid and alcohol inhibit the hydrolysis reaction while the influence of long-chained alkanes is very small. I t is concluded that the reaction rate is determined by the interfacial concentrations, and that these concentrations differ from the bulk concentrations because of the different surface afinities of the components. Key words: lipase, oleyl oleate, kinetics, interfacial reactions, mathematical model. 1 INTRODUCTION
Lipases are enzymes of considerable industrial interest due to their capability to catalyse the reversible reaction between carboxylic acids and alcohols at low temperature. Typical industrial lipases are used in immobilised form for 467
J . Chem. Tech. Biotechnol. 0268-2575/90/$03.5001990Society of Chemical Industry. Printed in Great Britain
468
T. Rostrup-Nielsen. L.S. Pedersen, J . Villadsen
interesterification and for ester synthesis. A better understanding of the reaction mechanism, and hence a better basis for reactor design is, however, obtained by studying the enzyme in homogenous solution, as is done in a majority of the published investigations. The present investigation is not different in this respect, dealing with hydrolysis kinetics of oleyl oleate, and using a commercial lipase preparation dissolved in an aqueous phase in contact with the insoluble ester phase. Previous work by Benzonana and Desnuelle' and by Sarda and Desnuelle' demonstrated the importance of the interface and emphasized that the rates should be referred to the interfacial area rather than to the volumes of the bulk ester phase or aqueous phase. Their work showed that the reaction rate increases with increasing interfacial area and with increasing amounts of adsorbed lipase on the interface. It is assumed that lipases have two separate sites, a catalytic site and a site which binds the lipase at the i n t e r f a ~ e This . ~ . ~means that there exists an equilibrium between lipase E in the aqueous phase, and lipase bound at the interface Ed E+d=EB
(1)
where 0 is a free site on the interface. This elementary reaction has been used in a number of models to explain the kinetics of the lipase Mattson et aL6 have examined the influence of n-alcohol on the reaction rate. They found that n-alcohols inhibit the reaction-the reason being that they have a greater affinity to the interface than the ester. In their work they did not, however, take into account the influence of the alcohol concentration on the equilibrium. All or part of their observed effect could be explained by proper handling of the thermodynamic equilibrium in their rate expression. It is likely that other components could have a similar inhibiting effect on the reaction rate. Smith and Alford' found that fatty acids decrease the activity of lipase; and recently, Mukataka et af.' examined the effect of diluting the substrate with n-alkanes. In this work three aspects of the hydrolysis reaction were studied. (a) The equilibrium was carefully determined using excess amounts of oleic acid and oleyl alcohol added to the ester. The equilibrium constant, K , , is given by the activities of the components in the organic phase as
(2) can be written as
where Al, Ac, Es are concentrations of alcohol, acid and ester respectively and y the corresponding activity coefficients in the organic phase a, is the water activity in the organic phase. It is probably close to one since the organic phase is in contact with a large aqueous phase, but the activity coefficients of the organic compounds may be strongly dependent on the composition of the organic phase. We approximate f i n (3) by the empirical linear expression:
f - CA]AI+ C,,Ac
+ C,Es
(4)
Lipase-catalysed hydrolysis of oleyl oleate
469
in which CAI,CAc,CEsare constants to be determined by means of a large number of equilibrium experiments. (b) The rate of reaction was studied as a function of interfacial area A , of the ester amount M , and of ester concentration Es in the organic phase (using dilution with a longchain alkane). It is postulated that the conversion X of ester follows the rate law
where r ( X ) is expressed in units of moles converted per square metre per second. (c) r ( X ) includes a factor for the reverse reaction and inhibition terms for both alcohol and acid. The inhibition is studied by adding various amounts of alcohol and/or acid to the ester before start of reaction.
2 MATERIALS AND METHODS A lipase preparation from Mucor miehei with an activity of 10 000 lipase units g - ' ( L u g - ' ) was provided by Novo Industri A/S. The activity unit is based on
hydrolysis of tributyrine in a standardized procedure developed by Novo (AF 95/5GB). 1 LU is the amount of enzyme which liberates 1 pmol butyric acid min-' at 30"C, pH=7. Samples were prepared by dilution of the stock solution and all activities quoted in the present paper are relative values. The ester was synthesized from oleic acid and oleyl alcohol using immobilized lipase, also supplied by Novo Industri A/S. The reactants were all of technical grade quality (Merck 471 and Merck 820923). The synthesis was carried out at 70°C and 10 mm Hg using a total reaction time of 4 h. It proved difficult to obtain a pure ester. Starting with stoichiometric amounts of alcohol and acid, using different reaction times (up to 20 h), different total pressure (to 1 mm Hg) and organic acids (e.g. p-toluenesulfonic acid) instead of enzyme as catalyst,' various attempts to obtain a pure ester failed. It was also attempted to use an excess of either alcohol or acid and, as suggested previo~sly,~ separating ester from excess reagent at - 80"C, washing crystals of ester with hexane to remove acid and alcohol. This too was not successful. In all preparations about 2-3 % acid and alcohol remained mixed with the ester. In the rate experiments the initial conversion of the ester was, of course, determined by titrating the ester before using it in a hydrolysis experiment. The most likely explanation for the persistent acid impurity in ester preparations from equimolar quantities of alcohol and acid is that the reagents contain small amounts of other acids and alcohols (e.g. stearic acid) which do not react to completion." The presence of small amounts of non-identified alcohols and acids in addition to the oleyloleate were confirmed by both GC and TLC. 2.1 Experiments
All experiments were carried out at 44"C, and the enzyme concentration was 15.625 LU g-' if not otherwise stated. Most of the experiments were carried out in 100cm3 Ehrlenmeyer flasks. The amount of aqueous enzyme solution was
470
T. Rostrup-Niulsen, L. S . Pedersen. J . Villudseii
generally chosen such that the interfacial area between the ester phase and the water phase was 20.8 cm’. The interfacial area was determined by measuring the outer diameter of the flask and subtracting an assumed value for the glass thickness measured at the top of the flask. This gives an error of about 2% on the interfacial area. Larger and smaller interfacial areas were obtained by using flasks of different volume (5&1000cm3).
2.2 Procedure Enzyme solution (64 cm3 for 100 cm3 flasks) was poured into a flask, which was then placed in a thermostated waterbath (44°C). When the flask had equilibrated the appropriate amount of ester (e.g. 1.4 g for full coverage of 20.8 cm2 as found by visual inspection) was carefully layered on top of the aqueous phase and the flask was returned to the waterbath. After a specified time the contents of the flask were poured into a separating funnel. The aqueous phase was removed and the organic phase washed back into the flask with ethanol (50 cm3).The ethanol had previously been titrated using phenolphthalein as indicator. The amount of oleic acid in the organic phase was then determined by titration with (0.01 mol d m - 3 ) NaOH.
2.3 Accuracy Although the experimental procedure used was simple, reproducibility was good. (a) The Ehrlenmeyer flasks were carefully selected and the same set of about 20 flasks was used in randomized experiments. (b) A set of seven experiments was carried out using the same enzyme solution, amount of ester and reaction time (200 min). Another set ofexperiments was carried out at exactly the same conditions except that the enzyme solution had been subjected to the reaction temperature (44°C) for 20 h. No sign of deactivation of the enzyme was noticed, and the same conversion (to about 2 ”/, relative) was obtained in all 14 experiments. We conclude that the total experimental error is about 2 % relative and that the enzyme is stable at 44°C for at least 20 h. (c) CO, was carefully excluded from the flasks during the kinetic experiments (duration up to several days). Absorption of CO, during titration of the organic phase did not present a problem. The 14 above-mentioned experiments were titrated at different speed and sometimes left to stand for several minutes without any change in the titration end point. The same sharp and stable end points were obtained when the aqueous phase was titrated. (d)It is well known that the enzyme activity changes with pH, and since an acid is produced which to some extent is transported into the aqueous phase this might present a problem for the rate experiments. We have, however, found that the change in pH which might occur in the aqueous phase (at most 1 pH unit from 6.7 initially to 5.7 for about 65 cm3 aqueous phase and 1.4 g ester) is well within the limits of approximately constant enzyme activity.’ O
3 RESULTS 3.1 Reaction rate and conversion Figure 1 shows the conversion as a function of time at a total enzyme concentration = 15.625 LU g - solution. The curve starts at a conversion of 2.65 7;
Lipase-cutulysed hydrdysis oJ’ oleyl olrute
47 1
15
xeq
]fl V
X
- Verger - O u r model 4 Experimental
0
100
200
300
400
Time (rnin)
Fig. 1. Conversion X of ester as a function of reaction time for a lipase concentration of 15.625 LU g - ’. In all experiments the ester amount was 1.4 g and the interfacial area was 20.8 cm’. Full drawn curve is a best fit using the model eqn (24) with the constants C,=212, C3=647000, C,= 186500. and with K , = 15. Broken curve is a best fit using the model of Verger et d4( I I ) .
as determined by titration of the ester before staring the experiment-see Section 2. The full curve is drawn using the parameters of our final model-see Section 4.The broken curve on the figure is obtained by the best possible parameter fit to an earlier model.4
3.2 Reaction rate and lipase concentration Figure 2 shows reciprocal reaction rate as a function of reciprocal lipase concentration. The rates are obtained from plots such as Fig. 1, assuming that the rate is independent of conversion up to 4.5 ”/,. The initial conversion was 2.90% in all experiments. There are two curves (I and 11) on Fig. 2, and both are well approximated by straight lines. The upper curve (11) corresponds to an enzyme solution which has been kept for 4 days at room temperature before use, while the lower curve (I) corresponds to enzyme solution used directly after preparation by dilution of a concentrated enzyme sample. While no loss of activity in the concentrated solution was observed, the dilution (e.g. by a factor of 200 to give 50 LU g - solution) apparently introduced some enzyme instability. The linearity of the two curves permits calculation of K , (as the inverse of the intercept with the negative abscissa) and the maximum rate, rmax(as the inverse of the intercept with the ordinate axis). It can be seen that the K , value is independent of enzyme solution treatment-an observation which lends credibility to the statement that the difference between curves I and I1 is due only to enzyme deactivation.
T. Rosrriip-Nielsen, L. S . Pedersen, J . Villudsen
412
1
P
100-
?
--9
00-
1-
E
9
60-
E m
v 7
‘L
40-
20-
o
t
-80 (Lipase concentration)-’
( g LU-’) lo3
Fig. 2. Reciprocal reaction rate vs reciprocal enzyme concentration for two lipase preparations. Curve I : freshly prepared by dilution ofaconcentratedenzyme solution.Curve 11: thedilutedenzymesolution has been used 4 days after preparation. Ester amount. 1.4g; interhcial area. 20.8cm2.
3.3 Equilibrium constant A number of equilibrium experiments were carried out at 44°C and with a reaction time of 4-6 days. By adding different amounts of oleyl alcohol and oleic acid to the
ester, the equilibrium was established with different concentrations of the components. Since the equilibrium constant K , has, of course, the same value for all the experiments, experimental values can be obtained for the constants in the empirical expression (4). For the parameter estimation procedure we arbitrarily set C , , = l . Hence the f of eqn (4) will differ from the true f in eqn (3) by a proportionality constant 1, and K & can be calculated from AlAc
1
=(s), + ( + C,,Es A1 CAcAc
Based on the experimental results of Fig. 3, K & = O M 6 3 at 44°C. Since the true activities could not be measured by the experimental procedure used here, f , in (6) has to remain as an undetermined constant. This is, however, not a problem for the rate calculations since the approach to equilibrium is correctly predicted if the model predicts the correct variation of .f in the approximation (4) with changing composition of the organic phase. The deviation (in relative percentage) of the equilibrium constant from 0.0463 is shown in Fig. 3 as a function of the concentration of (a) oleic acid and (b) oleyl alcohol.
413
-
-f
10-
5
E" c
c 0
m
5
6.
8.
"# 2 m I 0 :......... o.Ps" ............... n
-2.
n
:
-4.
O
......................
6
D
71 6 2500
I
,
r
I
,
n I
0
0
0
_................__________
-2. a
0
0
-6.
3
I
0
-4.
c .(0
'
0
8I , " 0 ...............?~....Q
E
-2
na
I
;:
E
=
-6. -8. -101
B
6.
0 0
4-
X
10.
-
8.
-8. -101
I
I
I
I
I
I
I
I
X
3000
3500 AIM t
4000
4500
5000
5500
(s rn-2rnol-' ester)
Fig. 4.Conversion X as a function of AIM1 for different values of A, M and r
3.4 Influence of interfacial area To investigate eqn ( 5 ) a series of experiments were made with varying interfacial areas and varying amounts of ester as shown in Fig. 4. In all these experiments the amount of ester used was sufficient to cover the interfacial area, except for the experiment with 5 g oleyl oleate and 80.6 cm2 interfacial area. The reaction time was adjusted to give a conversion of 6 7 % in all experiments. Figure 4 shows the conversion as a function of A / M t . A much larger series of experiments was carried out with varying interfacial area A and varying amounts M of ester. The reaction time was 60min for all these experiments, and conversion was between 2.90%(initial) and up to about 6%. The
T. Rostrup-Nirlsm. L. S . Prdrrsen. J . Villadsrri
474
I
I
(a)
0
(b)
0.5
0
i
1
I
1.0 1.5 20 Amount of ester ( g )
I
I
2.5
3.0
I
I
I
I
I
I
0.5
10
1.5
2.0
2.5
3.0
I 3.5
i 3-5
Amount of ester (g)
Fig. 5. Reciprocal reaction rate vs reciprocal ester amount for four different values of geometrical interfacial area (four different flasks). The four straight lines are calculated from eqn (5). Reaction time 60 min for all experiments.
reaction rate which, as in Fig. 2, is taken to be independent of X in the conversion range 2*9&6%, was calculated as moles converted per unit time and available interfacial area. The reciprocal reaction rate l/r is shown in Fig. 5 as a function of 1/M with A as a discrete parameter.
Lipusr-curuly~rdhydrolysis of’ olegl oleutt.
475
Alcohol (g g-’ ester)
’
Fig.6. Conversion after 60min reaction time as a function of initially added alcohol (g g - ester).The full line is obtained from the model eqn (24) using C , =212, C3=647oOo, C4= 186500and K,= 15 as in Fig. I .
3.5 Inhibition by oleyl alcohol and oleic acid: Influence of dilution by n-alkane To determine whether the hydrolysis products inhibit the reaction, two series of experiments were made. The conversion after 60 min was measured with different amounts of oleyl alcohol and oleic acid added to the ester. Figure 6 shows the conversion as a function of the amounts of oleyl alcohol added. The experimental error in the experiments with added oleic acid was much larger than 2%, since in most of the experiments the NaOH amount needed to neutralize the added acid was much larger than the amount of NaOH needed to determine the conversion. Finally, the influence of ester concentration in the organic phase was investigated by diluting the ester with various amounts of n-hexadecane which is considered to be an inert for the reaction. The results are shown on Fig. 7-all for a reaction time of 60 min. An influence of concentration was only observed at extremely low ester concentrations. 4 DISCUSSION 4.1 Lipase adsorption at the interface
The adsorption equilibrium constant for the elementary reaction (1) is given by K,
=E x
BIE8
(7)
By assuming that the initial reaction rate r, is proportional to the adsorbed amount of enzyme r, =r,,,EB and by assuming4 that E B EB and that the total amount of sites, 8, is given by B,=B+EB one obtains
T. Rostrup-Nielsen, L. S. Pedersen, J . Villadsen
416
-
0.8
0 0
0
o
n I
--9 I
0
06-
I
m
0
0
N
E
5 E
W 0.4-
%
Y
. x
L
#
X
x i
-
0.2
-+ 1.Og ester -M-
-I
0
I
0.25
I
0.50
I
0.75
I
1.00
I
1.25
0.3g ester 1
1.50
I 1.75
Ester concentration (mmol dm-3)
Fig. 7. Reaction rate averaged over the first 60 min a s a function of ester concentration in n-hexadecane using 0 3 and 1,Og ester. Pure ester corresponds to 1.61 moldm-3.
which leads to
The good fit to a straight line (curve I or 11)in Fig. 2 confirms that the reaction rate is proportional to the adsorbed amount of lipase on the interface, and that the adsorption can be described by reaction (1). The value of K , is found from eqn (9) and Fig. 2 to be 15 LU g-' and rmaxOo=2.7x mol m - 2 s - ' . These values are based on experiments with conversion between 2.9 % (at t = 0) and 4.5 % (after 60 min). The increase of conversion is small enough, and the dependence of X on t sufficiently linear in the range (see Fig. 1) to ensure that the rates shown on Fig. 2 are good estimates of the initial rates.
4.3 Equilibrium constant To establish equilibrium in the experiments on which Fig. 3 is based, 4-6 days were used. This raises a problem because oleic acid may dissociate at the interface and slowly dissolve in the aqueous phase, especially in the presence of inorganic metal ions. Patil et al." investigated the kinetics of this reaction for a number of acids ' ~ the rate at which oleic acid dissolves including oleic acid. Scow et ~ 1 . measured into an aqueous phase containing 4 . 4 ~ m o l d m - albumin. ~ The rate was determined with a monlayer technique at different surface pressures (22-32 dyne cm-') and it was found to vary between 221 and 378. pmol cm-2 min-'.
Lipase-catalysed hydrolysis of oleyl oleate
477
TABLE 1 Transfer Rates of Oleic Acid into Aqueous Phase Measured by Equilibrium Experiments with Pure Ester (No Alcohol or Acid Added Initially)” Days
Moles acid found in aqueous phase (mol) lo3
4 4
3.94 3.52 4.45 5.60 6.52
4
5 6
Transfer rate (pmol cm-’ min-I)
329 294 371 375 363
‘Interfacial area 20.8 cm2 and 1.4 g ester.
TABLE 2 Transfer Rates of Oleic Acid from Ester Phase to Aqueous Phase as a Function of Initially Added Oleic Acid” Added acid (9)lo3
Moles acid found in aqueous phase (mol) 105
0 18 75 100 116 136 177 253 333
4.45
4.64 4.99 5.5 1 5.78 6.91 7.26 7.88 9.98
Transfer rate (pmol cm-’ min-’1
371 387 41 6 460 482 577 606 657 833
’All
experiments run to almost equilibrium of the hydrolysis reaction (4 days) using interfacial area 20.8 cm2 and 1.4 g ester.
Table 1 shows the amount of oleic acid found in the aqueous phase after 4-7 days as determined by titration with 0.01 N NaOH. It is seen that the transfer rate is constant at a level of about 346 pmol cm-’ min-’ which is in the range of Scow et al. Apparently, the bacterial lipase and the bovine serum albumin used by Scow et al. both produce some weak dissolution of oleic acid into the aqueous phase. The mol d m - 3 from final oleic concentration is, however, always small ( < 1.3 x Tables 1 and 2). The transfer of oleic acid to the aqueous phase takes place at a small but constant rate, and therefore a true chemical equilibrium for the ester phase cannot be established. Table 2 shows the amount of oleic acid found in the aqueous phase after 4 days as a function of increasing amounts of oleic acid added to the ester. Note that the transfer rate increases with increasing concentration of oleic acid in the organic phase. Figure 3 shows that within a factor 10 in theoleic acid concentration in the
T. Rostrup-Nii,lseti. L. S . Pederseti, J . Villudseti
478
organic phase at ‘equilibrium’,the equilibrium constant does not have a systematic variation with the oleic acid concentration. This means that the concentrations in the organic phase can be assumed to be close to their equilibrium values. Hence the equilibrium constant K L = 00463 together with the constants of the approximate expression (4) for f ’ have been determined without experimental bias. Since C,, was set at a value of unity in eqn (4)the true value of .f was not obtained from eqn (3) by the experimental procedure used. For calculations of the approach to equilibrium it is enough that the model predicts the correct variation of the approximation (4) to f’ with changing composition of the organic phase. Figure 3 also shows that for most of the observations the equilibrium constant varies less than 5 % from its mean value of KC =0.0463 at 44°C. Over the range of investigated compositions, f‘varies by about a factor of two which is far greater than the experimental error of about 2%. It must be concluded that the equilibrium model represents the data much better than an equilibrium model based solely on concentrations of organic reactants. An equilibrium constant of K & = 00463 corresponds to an equilibrium conversion of X, = 13.46%.
4.3 Interfacial area Equation (5) can be written as
Hence experiments run between the same initial conversion X, and the same final conversion X will give the same value of AIM t . Where approximately the same conversion X has been reached in a number of experiments with widely different A and M values, Fig. 4 shows that eqn (10) is satisfied. The three points obtained for the system with 5 g ester and 80.6 cm2 surface area show a smaller conversion than expected. The explanation is as shown in the following that the whole available geometrical interface area was not covered by the small quantity of ester used in these three experiments. Since the reaction rate is approximately constant between 6.5 and 7.5:4 conversion one obtains a linear relation between t and X in the experiments of Fig. 4. From the slope of the line one obtains r(X)=0.611 x lo-’ mol
s - ’ for X - 7 %
From Fig. 1, for X-7%, one obtains: MdX r(X)=--=0*600x A dt
m d m-’s-l
which agrees well with the above result. This is taken as an additional confirmation of the validity of the rate expression (5). The group of experiments shown in Fig. 5-with A as a parameter on the curves and M as abscissagives a final support of eqn (5). which appears to hold in a range of interfacial areas between 10 and 80cm2 and for M between 0.3 and 13 g. It should
Lipasr-cufalysrd hydrdysis q/’ o/ey/ oleate
479
be noted that whereas for all points on Fig. 4-except those at 5 g, 80.6 cm2-the total geometrical interface area is covered, this is not true for experiments in Fig. 5, where e.g. an ester amount of 1.4 g is necessary to cover 20.8 cm2 geometrical area. These results show a simple picture of the interfacial reaction. (1) The relation between reaction rate and A holds whether a small drop of ester is placed on a large surface of water ( e g experiments with 0.8 g ester on 80cm’ geometrical interface area) or a large amount of ester is deposited on a small water surface (e.g. 5 g on 20.8 cm2 geometrical interface area). (2) In Fig. 4 it is seen that 1.4,3 and 5 g ester on 20.8 cm2 surface all give the same rate. This last result shows that there is no transport restriction of the chemical reaction: a fully covered surface gives the same reaction rate whether the ester layer is thin (1.4 g on 208 cm2)or much thicker (5 g on 208 cm2).
4.4 Final reaction rate model An earlier model by Verger et ~ 1 was . tested ~ by making a best fit to the results in Fig. 1. This was done using an initial reaction rate corresponding to 2.65% conversion. Verger’s model is an initial reaction rate model, and the rate expression is given by
7 = k , E s / ( E s + k2(1 + k 3 / E ) )
(11)
where k , , k2 and k 3 are constants. To take the reverse reaction into account the rate expression is corrected as follows:
in which Q is the mass action fraction. Figure 1 clearly demonstrates that this model cannot describe the decrease in reaction rate observed at conversion above 6 %. This may be due to inhibition by the hydrolysis products, in a similar fashion as described by Mattson et aL6 for alcohols. In Verger’s model-eqn (11)-bulk concentrations are inserted. The results in Fig. 7 do, however, show that the reaction rate is independent of the bulk concentration over a wide range. Only at extremely low ester concentrations can an effect of Es be noticed. This indicates that the reaction rate depends on interfacial concentrations rather than on bulk concentrations. A new model was developed assuming that the reaction can be described by the following elementary reactions in terms of 0‘ which denotes surface sites, ‘activated’ by adsorption of an enzyme, e.g. O:, = EH of eqn (8),and which are not occupied by complexes with the reactants Es, Ac or Al. Es + 8‘= EsO
EsO
Ac+O’=AcO
(14)
Al+8’=AlO
(15 )
+ W+
(16)
A18
+ Ace
with adsorption constants KEarK,, and K , , , and with a rate constant k‘ for the
T. Rostrup-Nirlsm, L . S . Pedrrsen, J . Villudsetl
480
hydrolysis reaction (16). Assuming that this reaction is rate determining, the following rate expression for the hydrolysis reaction is obtained F= k’EsdW
(17)
By assuming that the water activity at the inre$ice is constant, eqn ( 1 7 ) is reduced to
(18)
7=kEsO
where k=k’W. The site balance is given by Ed = 0;
= 8‘
+ Esd + AcH + A10
(19)
Combining eqn (18) with eqn (19) and the adsorption equilibria, the following expression is obtained for the hydrolysis reaction (20)
Inserting 0: = EO and using eqn (8) for EU, we obtain: d
r=
Es C, E S C, +C,AC
+
+ C,Al
E X-
K,
+E
where C,, C2, C, and C, are constants which incorporate the unknown constant 8 , in eqn (8). As for Verger’s model, the overall reaction rate can be expressed as
r =7( 1 - Q / K : , )
(22)
where the mass action fraction Q is calculated similarly as K & in (6) i.e. as AlAc
1 Q=F A1 + CAc Ac X
+ CEsEs
In this fashion the unknown scalar factor ,L, cancels. It is true that j’(AI,Ac, Es) was determined from equilibrium experiments. Here j ’ is used also for compositions which may be very different from those found at equilibrium. It is considered that the functional relationship for j ’ which was determined by equilibrium experiments at widely different compositions of the organic phase is resilient enough to permit use of j a l s o to calculate Q.*A parameter estimation showed that the constant C2 is much smaller than the other constants. This means that there are very few free sites. Hence the constant is disregarded, and the expression for the forward rate of hydrolysis is reduced to 2
r=
Es C, Es+C3Ac+C4Al
X-
E K,+ E
(24)
In this expression the term EsC, is smaller than the other two terms in the denominator, but it cannot be removed, because it describes the initial reaction rate, where (for a pure ester) there is neither acid nor alcohol present. Since in all experiments there was an initial conversion of about 2-3 %, the value of the constant C, could not be determined with a satisfactorily low confidence interval. The values
Lipusr-curulvsrd hydrolysis
48 I
olryl olrutr
obtained by a parameter estimation are shown in the text to Fig. I . Figures 1 and 6 show that the model with the constants from the text to Fig. 1 gives a most satisfactory description of the results. The results obtained by dilution with alkane (Fig. 7) could be described by adding an additional elementary reaction to eqns (13)-( 15):
I
+ el = I e
(25)
This would result in the following rate expression +
r=
E
Es C , E s + C , A c + C,AI+C,I
X -
K,
+E
(26)
The results do, however, show that the influence of the alkane concentration I is small, and an eventual dependence on I could equally well be explained by a change of the physical properties of the interface, e.g. a change in the surface tension. Similar physical changes in the surface could also appear at high enough alcohol and acid concentrations. Our experiments do not, however, permit a more sophisticated explanation of the observed alcohol and acid inhibition than that expressed in eqn (24). 5 CONCLUSION
The design of industrial enzyme reactors should as far as possible be based on a quantitative understanding of the underlying physical and chemical processes. This makes an extrapolation from one operation mode to another (continuous vs batch or fluidized vs fixed bed) much easier. Our study is made with an ester of small industrial importance and with enzyme in homogeneous solution rather than on support particles. Still, the results concerning equilibrium, and the kinetic results (the simple relation between rate of change of conversion and available surface area, as well as the inhibition effect of products), are of immediate use in the scale-up of a lipase-catalysed reaction or in predictions of the effect of a change in contact pattern in the complex system of organic phase/immobilized enzyme and water.
REFERENCES 1. Benzonana, G. & Desnuelle, P., Kinetic study of the action of pancreatic lipase on triglycerides in emulsion. Enzyme action in a heterogeneous medium. Biochim. Biophys. Acts, 105 (1965) 121-36. 2. Sarda, L . & Desnuelle, P., Action de la lipase pancreatique sur les esters en emulsion. Biochim. Biophys. Acta, 30 (1958) 513-21. 3. Brockerhoff, H., A model of pancreatic lipase and the orientation of enzymes at interfaces. Chemistry Physics Lipids, 10 (1973) 215. 4. Verger, R., Mieras, C. E. & de Haas, G. H., Action of phospholipase A at interfaces. J . Biol. Chem., 248 (1973) 4023-34. 5. Brockman, H . L., General features of lipolysis: Reaction scheme, interfacial structure and experimental approaches. Lipases. Elsevier Science Publishers, Amsterdam (1984).
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T. Rostrup-Nielsen, L. S . Pedersen, J . Villadsen
6. Mattson, F. H., Volpenhein, R. A. & Benjamin, L., Inhibition of lipolysis by normal alcohols. J . Biol. Chem., 245 (1970) 533540. 7. Smith, J. L. & Alford, J. A,, Inhibition of microbial lipases by fatty acids. Appl. Microbiology, 14 (1966) 699. 8. Mukataka, S., Kobayashi, T. & Takahashi, J., Kinetics of enzymatic hydrolysis of lipids in biphasic organic-aqueous systems. J . Ferment. Technol., 63 (1985) 461. 9. Swern, D., Billen, G . N. & Knight, H. B., Preparation of some polymerizable esters of oleic acid with unsaturated alcohols. J . Am. Chem. Soc., 69 (1947) 2439. 10. Novo Enzymes, The use of lipozyme for synthesis of esters. B 348b-GB 400 June, 1986. 1 1 . Patil, G. S., Matthews, R. H. & Cornwell, D. G.,Kinetics of the processes of desorption from fatty acid monolayers. J . Lipid Research, 14 (1973) 23. 12. Scow, R . O., Desnuelle, P. & Verger, R., Lipolysis and lipid movement in a membrane model. J . Bid. Chem., 254 (1979) 6456.
