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Langmuir 2000, 16, 10084-10086
A General Treatment for Meaningful Comparison of Rate Parameters of Enzyme-Catalyzed Reactions in Aqueous and Reverse Micellar Solutions Eduardo A. Lissi and Elsa B. Abuin* Universidad de Santiago de Chile, Facultad de Quı´mica y Biologı´a, Casilla 40, Correo 33, Santiago, Chile Received June 5, 2000. In Final Form: October 3, 2000 A relevant question concerning the kinetics of reactions catalyzed by water-soluble enzymes in reverse micellar solutions is whether the efficiency of the enzyme is different from that in bulk aqueous solution. The comparison can be carried out only if the rates of the processes are compared under conditions of equal substrate activity. In the present work, it is proposed that this comparison can be carried out by employing the activity of the substrate in bulk water solution as a thermodynamic concentration scale. In order to carry out this comparison, the kinetic results obtained in the reverse micellar solution employing the analytical substrate concentration must be corrected by the solute distribution between the micellar pseudophase and the external solvent and by the partitioning of the substrate between the external solvent and an aqueous solution. The proposed methodology is applied to data previously reported for the oxidation of aliphatic alcohols catalyzed by alcohol dehydrogenase in a sodium 1,4-bis(2-ethylhexyl) sulfosuccinate/ isooctane/water microemulsion. It is shown that when properly treated, the data indicate that the efficiency and selectivity of the enzyme is very similar in bulk aqueous solution and in the reverse microemulsion.
Many studies concerning the activity of enzymes in reverse micellar solutions (RMS) have been reported.1-24 In most systems, the enzyme (E) is totally associated with the micelles, but the substrate (S) is distributed between * To whom correspondence should be addressed. E-mail: eabuin@ lauca.usach.cl. (1) Menger, F. M.; Donohue, J. A.; Williams, R. F. J. Am. Chem. Soc. 1973, 95, 286. (2) Menger, F. M.; Yamada, K. J. Am. Chem. Soc. 1979, 101, 6731. (3) Martinek, K.; Levashov, A. V.; Klyachko, N. L.; Pantin, V. I.; Berezin, I. V. Biochim. Biophys. Acta 1981, 657, 277. (4) Barbaric, S.; Luisi, P. L. J. Am. Chem. Soc. 1981, 103, 4239. (5) Hilhorst, R.; Spruijt, R.; Laane, C.; Veeger, C. Eur. J. Biochem. 1984, 144, 459. (6) Fletcher, P. D. I.; Robinson, B. H.; Freedman, R. B.; Oldfield, Ch. J. Chem. Soc., Faraday Trans. 1 1985, 81, 2667. (7) Martinek, K.; Levashov, A. V.; Klyachko, N. L.; Khmelnitsky, Yu. L.; Berezin, I. V. Eur. J. Biochem. 1986, 155, 453. (8) Martinek, K.; Klyachko, N. L.; Kabanob, A. V.; Khmelnitsky, Yu. L.; Levashov, A. V. Biochim. Biophys. Acta 1989, 981, 161. (9) Bru, R.; Sa´nchez-Ferrer, A.; Garcı´a-Carmona, F. Biochem. J. 1989, 259, 355. (10) Verhaert, R. M. D.; Hilhorst, R.; Vermue¨, M.; Schaafsma, T. J.; Veeger, C. Eur. J. Biochem. 1990, 187, 59. (11) Verhaert, R. M. D.; Tyrakowska, B.; Hilhorst, R.; Schaafsma, T. J.; Veeger, C. Eur. J. Biochem. 1990, 187, 73. (12) Tyrakowska, B.; Verhaert, R. M. D.; Hilhorst, R.; Schaafsma, T. J.; Veeger, C. Eur. J. Biochem. 1990, 187, 81. (13) Bru, R.; Sa´nchez-Ferrer, A.; Garcı´a-Carmona, F. Biochem. J. 1990, 268, 679. (14) Bru, R.; Walde, P. Eur. J. Biochem. 1991, 199, 95. (15) Larsson, K. M.; Adlercreutz, P. A.; Mattiasson, B. J. Chem. Soc., Faraday Trans. 1991, 87, 465. (16) Sarcar, S.; Jain, T. K.; Maitra, A. Biotechnol. Bioeng. 1992, 39, 474. (17) Miyake, Y.; Owari, T.; Matsuura, K.; Teramoto, M. J. Chem. Soc., Faraday Trans. 1993, 89, 1993. (18) Stamatis, H.; Xenakis, A.; Menge, U.; Kolisis, F. Biotechnol. Bioeng. 1993, 42, 931. (19) Miyake, Y.; Owari, T.; Ishiga, F.; Teramoto, M. J. Chem. Soc., Faraday Trans. 1994, 90, 979. (20) Stamatis, H.; Xenakis, A.; Dimitriadis, E.; Kolisis, F. N. Biotechnol. Bioeng. 1995, 45, 33. (21) Setti, L.; Ferreiro, P.; Melo, E. P.; Piferri, P. G.; Cabral, J. M. S.; Aires-Barros M. R. Appl. Biochem. Biotechnol. 1995, 55, 207. (22) Miyake, Y. Colloids Surf., A 1996, 109, 255. (23) Das, P. K.; Srilakshmi, G. V.; Chaudhuri, A. Langmuir 1999, 15, 981. (24) Das, P. K.; Chaudhuri, A. Langmuir 2000, 16, 76.
the micellar pseudophase and the external solvent. A pertinent question concerning enzyme efficiency is whether the ratio kcat/Km or the individual constants kcat and Km (see below for definitions) in the RMS are different from those in bulk aqueous solution. The answer requires a kinetic treatment that includes two main factors: (i) the partitioning of the substrate between the micellar pseudophase and the external solvent and (ii) the substrate concentration scale to be employed for the evaluation of the concentration-dependent kinetic parameters, that is, kcat/Km and Km. These points have been partially addressed previously,6,10,19,22 but we consider that the general treatment introduced here does not require assuming specific sites for the enzyme or the substrate inside the micelles. In this work, we propose a substrate concentration scale that allows for meaningful comparison of the kinetic behavior of enzymes in RMS and in bulk aqueous solution. Let us consider a reaction catalyzed by a water-soluble enzyme which, in RMS, is totally associated to the micellar pseudophase. If a Michaelis-Menten mechanism (eq 1) applies, k1
kcat
E + S {\ } (ES) 98 Products + E k -1
(1)
the rate law given by eq 2 can be derived,
V0 )
kcat [E] [S] Km + [S]
(2)
where V0 is the initial reaction rate (in M-1 s-1) and Km is the Michaelis-Menten constant defined by eq 3.
Km ) (k-1 + kcat)/k1
(3)
Consider the factors controlling the rate of reaction in two limiting situations, very high (a) and very low (b) substrate concentrations. (a) Very High Substrate Concentration Limit, [S] . Km. Under this condition, the reaction is zero order in
10.1021/la000788z CCC: $19.00 © 2000 American Chemical Society Published on Web 11/28/2000
Rate Parameters of Enzyme-Catalyzed Reactions
Langmuir, Vol. 16, No. 26, 2000 10085
substrate concentration and the rate law is given by
V0 ) kcat [E]
(4)
where [E] is the analytical concentration of the enzyme. The value of the catalytic rate constant, kcat, is then given by eq 5, and comparison of the kinetic behavior of the enzyme in RMS with that in bulk aqueous solution is straightforward.
kcat ) V0/[E]
through eq 10, in which forg is the fraction of the substrate remaining in the external organic solvent at a given concentration of surfactant.
[S]org ) forg [S]analyt
Otherwise, forg can be expressed in terms of Kp and the surfactant concentration through eq 11.
forg ) {1 + Kp [Surf]}-1
(5)
In this limit, the experimentally determined rate constant is a first-order rate constant equal to kcat and, hence, the partitioning of the substrate and the method of expressing its concentration are irrelevant. (b) Very Low Substrate Concentration Limit, [S] , Km. Under this condition, the rate of the process, per enzyme, is expressed as
(10)
(11)
If dilute solution behavior is assumed, the concentration of the substrate in a bulk aqueous phase [S]bwater whose activity is equal to that in the organic solvent in the RMS (and hence in the micellar pseudophase) is given by eq 12
[S]bwater ) K(water/org) [S]org
(12)
where [S] is the substrate concentration and k is given by eq 7.
where K(water/org) is the partition constant of the substrate between bulk water and the organic solvent in the absence of micelles. In turn, [S]bwater can be expressed in terms of the analytical concentration of the substrate by substituting in eq 10 to give
k ) kcat/Km
[S]bwater ) forgK(water/org) [S]analyt
V0/[E] ) k [S]
(6)
(7)
A meaningful comparison of the k values (and hence Km values if kcat is known) obtained in bulk water and in RMS requires a precise specification of the substrate concentration to be employed in eq 6. A rigorous comparison of the kinetic parameters obtained in RMS with those obtained in bulk water requires the rate law to be expressed in terms of the thermodynamic substrate activities and not in terms of substrate concentrations. If a dilute solution behavior is assumed (allowing so for the use of concentration units instead of thermodynamic activities), valid comparisons require that the same reference state be used in the RMS and in bulk water. The simplest approach is to compare the rate constants when the substrate in the RMS has the same thermodynamic activity as that in the bulk aqueous solution. The central problem is making the correct comparison for specific analytical substrate concentrations in RMS. In other words, how does one obtain a k value using the analytical substrate concentrations in RMS that can be compared with k values obtained in bulk aqueous solution? In RMS, the distribution of the substrate between the micellar pseudophase and the external organic solvent can be expressed in terms of a substrate partition constant, Kp:
Kp )
[S]m [S]org [Surf]
(8)
where [Surf] is the concentration of micellized surfactant, [S]org is the concentration of the substrate in the organic external solvent, and [S]m is the (analytical) concentration of the susbtrate in the micellar pseudophase (without specifying its distribution within the micelles). The value of [S]m is given by eq 9 and is related to the total analytical concentration of the substrate, [S]analyt, by
(13)
Equation 13 shows that k values obtained from eq 6 in RMS can be compared with those obtained in bulk water only if the substrate concentration [S] in RMS is taken as
[S] ) forgK(water/org) [S]analyt
(14)
[S] ) {K(water/org)/(1 + Kp [Surf])} [S]analyt
(15)
and hence
In other words, second-order rate constants obtained in RMS employing analytical substrate concentrations must be divided by the factor forgK(water/org) to be compared with second-order rate constants obtained in bulk aqueous solution. This comparison, together with the comparison of the kcat values, will reveal whether the efficiency of the enzyme is different in the micellar pseudophase than in bulk water. If kcat and k are obtained from classical double reciprocal plots, the concentrations given by eq 15 should be employed to directly obtain the correct kcat and k values and, from their ratio, the Km values; this proposed correction does not assume any particular distribution of the substrate inside the micelles, and it even can be applied under conditions in which a “free” water may not exist (i.e., at low values of the [water]/[surfactant] ratio). The proposed kinetic treatment was tested with published results for horse liver alcohol dehydrogenase (ADH) in RMS composed of sodium 1,4-bis(2-ethylhexyl) sulfosuccinate (AOT)/octane/water, relative to bulk aqueous solution.7,8 This system is a classical example of the effect of reverse micelles on the enzyme turnover (kcat/Km) relative to bulk aqueous solution. ADH catalyses the oxidation of aliphatic alcohols to the corresponding aldehydes:
CH3(CH2)nOH + NAD+ f
(9)
CH3(CH2)n-1COH + NADH + H+
If the partition constant, Kp, of the substrate between the micellar pseudophase and the external solvent is known, the concentration of the substrate in the organic solvent can be related to the analytical concentration
The maximum kcat/Km ratio in aqueous solution is obtained for octanol, whereas in RMS composed of AOT (0.1 M)/octane/water (0.05 buffer phosphate, pH ) 8.8) at H2O/AOT ) 49, butanol is the best substrate.7,8 Figure 1
[S]m ) [S]analyt - [S]org
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Langmuir, Vol. 16, No. 26, 2000
Lissi and Abuin
Figure 1. Dependence of the second-order rate constant (kcat/ Km)exp for the oxidation of aliphatic alcohols catalyzed by ADH on the length of the hydrocarbon chain of the alcohol. (b) Reverse micellar solution composed of AOT (0.1 M)/octane/water (0.05 M phosphate buffer, pH ) 8.8) at water/AOT ) 49. Values of (kcat/Km)exp are on the left ordinate. (2) Aqueous solution (0.05 M phosphate buffer, pH ) 8.8). Values of (kcat/Km) are on the right ordinate. The data are taken from refs 7 and 8.
shows the dependence of the catalytic efficiency k ) (kcat/ Km )exp on the length of the hydrocarbon chain of the alcohol (n) in aqueous buffer and in the micellar solution (obtained by using the analytical concentrations of the alcohols). Note the difference in specificity of the enzyme for the substrate and the values of k for a given alcohol in both media. This behavior may be the result of a true micellar effect on enzyme activity or the consequence of different substrate concentrations used to express the rate of the reaction in both media. In previous works, we have reported the data required to test our proposal, that is, the partitioning of the alcohols in the micellar solutions, (Kp),25,26 and the water/heptane partition constants, Kwater/org.27 When the experimental values of (kcat/Km)exp originally obtained by using the analytical concentrations of the alcohols are expressed in terms of the activity of the solute in bulk water (eq 15), values of (kcat/Km)cor can be obtained:
(kcat/Km)cor ) {(kcat/Km)exp (1 + Kp [Surf])}/K(water/org) (16) Figure 2 shows the dependence of (kcat/Km)cor values on the length of the hydrocarbon chain of the alcohol (n) in (25) Lissi, E. A.; Engel, D. Langmuir 1992, 8, 452. (26) Silber, J. J.; Biasutti, A.; Abuin, E.; Lissi, E. Adv. Colloid Interface Sci. 1999, 82, 189. (27) Lissi, E. A.; Abuin, E. B. SBJC 1994, 2, 71.
Figure 2. Dependence of the second-order rate constant (kcat/ Km)cor for the oxidation of aliphatic alcohols catalyzed by ADH on the length of the hydrocarbon chain of the alcohol. (b) Reverse micellar solution composed of AOT (0.1 M)/octane/water (0.05 M phosphate buffer, pH ) 8.8) at water/AOT ) 49. (2) Aqueous solution (0.05 M phosphate buffer, pH ) 8.8).
the micellar solution and (kcat/Km) values in the homogeneous aqueous phase. This figure shows that both the dependence of (kcat/Km)cor values on the length of the alkyl chain and their absolute values are very similar when the enzyme catalyzes the process in bulk water or in the reverse micellar solution. This conclusively shows that the reverse micelle incorporated enzyme behaves as in bulk water and that all the differences observed when kcat/Km is expressed in terms of the analytical substrate concentration (Figure 1) are due to differences in the alkanol activities in the micellar solution. The kinetic analysis proposed in this paper reveals whether the presence of the micellar interface and/or the constraint of the enzyme to a limited water pool modifies its catalytic behavior. Furthermore, it shows when the rate of the process (measured in terms of the analytical substrate concentration) will depend on the surfactant concentration (see eq 16). Furthermore, a similar correction must be applied to Km values obtained in reverse micellar solutions employing analytical substrate concentrations in order to evaluate if the reverse micelle modifies the affinity of the enzyme for the substrate. The proposed approach to compare the behavior of the enzyme in bulk aqueous solutions and RMS does not make any a priori assumption regarding the location of the enzyme and/or the substrate within the micelles. Acknowledgment. Financial support of this work by Dicyt (USACH) and Fondecyt (Project No. 1980211) is acknowledged. LA000788Z
