A General Treatment for Meaningful Comparison of RateParameters of Enzyme-Catalyzed Reactions in Aqueous

and Reverse Micellar Solutions

Eduardo A. Lissi and Elsa B. Abuin*

Universidad de Santiago de Chile, Facultad de Quımica y Biologıa, 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 reversemicellar 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 equalsubstrate activity. In the present work, it is proposed that this comparison can be carried out by employingthe activity of the substrate in bulk water solution as a thermodynamic concentration scale. In order tocarry out this comparison, the kinetic results obtained in the reverse micellar solution employing theanalytical substrate concentration must be corrected by the solute distribution between the micellarpseudophase and the external solvent and by the partitioning of the substrate between the external solventand an aqueous solution. The proposed methodology is applied to data previously reported for the oxidationof 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 efficiencyand selectivity of the enzyme is very similar in bulk aqueous solution and in the reverse microemulsion.

Many studies concerning the activity of enzymes inreverse micellar solutions (RMS) have been reported.1-24

In most systems, the enzyme (E) is totally associated withthe micelles, but the substrate (S) is distributed between

the micellar pseudophase and the external solvent. Apertinent question concerning enzyme efficiency is whetherthe ratio kcat/Km or the individual constants kcat and Km(see below for definitions) in the RMS are different fromthose in bulk aqueous solution. The answer requires akinetic treatment that includes two main factors: (i) thepartitioning of the substrate between the micellarpseudophase and the external solvent and (ii) the substrateconcentration scale to be employed for the evaluation ofthe concentration-dependent kinetic parameters, that is,kcat/Km and Km. These points have been partially addressedpreviously,6,10,19,22 but we consider that the general treat-ment introduced here does not require assuming specificsites for the enzyme or the substrate inside the micelles.In this work, we propose a substrate concentration scalethat allows for meaningful comparison of the kineticbehavior of enzymes in RMS and in bulk aqueous solution.

Let us consider a reaction catalyzed by a water-solubleenzyme which, in RMS, is totally associated to the micellarpseudophase. If a Michaelis-Menten mechanism (eq 1)applies,

the rate law given by eq 2 can be derived,

where V0 is the initial reaction rate (in M-1 s-1) and Kmis the Michaelis-Menten constant defined by eq 3.

Consider the factors controlling the rate of reaction intwo 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

* To whom correspondence should be addressed. E-mail: eabuin@lauca.usach.cl.

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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.

E + S {\}k1

k-1(ES) 98

kcatProducts + E (1)

V0 )kcat [E] [S]

Km + [S](2)

Km ) (k-1 + kcat)/k1 (3)

10084 Langmuir 2000, 16, 10084-10086

10.1021/la000788z CCC: $19.00 © 2000 American Chemical SocietyPublished on Web 11/28/2000

substrate concentration and the rate law is given by

where [E] is the analytical concentration of the enzyme.The value of the catalytic rate constant, kcat, is then givenby eq 5, and comparison of the kinetic behavior of theenzyme in RMS with that in bulk aqueous solution isstraightforward.

In this limit, the experimentally determined rateconstant is a first-order rate constant equal to kcat and,hence, the partitioning of the substrate and the methodof expressing its concentration are irrelevant.

(b) Very Low Substrate Concentration Limit, [S], Km. Under this condition, the rate of the process, perenzyme, is expressed as

where [S] is the substrate concentration and k is given byeq 7.

A meaningful comparison of the k values (and hence Kmvalues if kcat is known) obtained in bulk water and in RMSrequires a precise specification of the substrate concen-tration to be employed in eq 6. A rigorous comparison ofthe kinetic parameters obtained in RMS with thoseobtained in bulk water requires the rate law to beexpressed in terms of the thermodynamic substrateactivities and not in terms of substrate concentrations. Ifa dilute solution behavior is assumed (allowing so for theuse of concentration units instead of thermodynamicactivities), valid comparisons require that the samereference state be used in the RMS and in bulk water. Thesimplest approach is to compare the rate constants whenthe substrate in the RMS has the same thermodynamicactivity as that in the bulk aqueous solution. The centralproblem is making the correct comparison for specificanalytical substrate concentrations in RMS. In otherwords, how does one obtain a k value using the analyticalsubstrate concentrations in RMS that can be comparedwith k values obtained in bulk aqueous solution?

In RMS, the distribution of the substrate between themicellar pseudophase and the external organic solventcan be expressed in terms of a substrate partition constant,Kp:

where [Surf] is the concentration of micellized surfactant,[S]org is the concentration of the substrate in the organicexternal solvent, and [S]m is the (analytical) concentrationof the susbtrate in the micellar pseudophase (withoutspecifying its distribution within the micelles). The valueof [S]m is given by eq 9 and is related to the total analyticalconcentration of the substrate, [S]analyt, by

If the partition constant, Kp, of the substrate betweenthe micellar pseudophase and the external solvent isknown, the concentration of the substrate in the organicsolvent can be related to the analytical concentration

through eq 10, in which forg is the fraction of the substrateremaining in the external organic solvent at a givenconcentration of surfactant.

Otherwise, forg can be expressed in terms of Kp and thesurfactant concentration through eq 11.

If dilute solution behavior is assumed, the concentrationof the substrate in a bulk aqueous phase [S]bwater whoseactivity is equal to that in the organic solvent in the RMS(and hence in the micellar pseudophase) is given by eq 12

where K(water/org) is the partition constant of the substratebetween bulk water and the organic solvent in the absenceof micelles.

In turn, [S]bwater can be expressed in terms of theanalytical concentration of the substrate by substitutingin eq 10 to give

Equation 13 shows that k values obtained from eq 6 inRMS can be compared with those obtained in bulk wateronly if the substrate concentration [S] in RMS is taken as

and hence

In other words, second-order rate constants obtainedin RMS employing analytical substrate concentrationsmust be divided by the factor forgK(water/org) to be comparedwith second-order rate constants obtained in bulk aqueoussolution. This comparison, together with the comparisonof the kcat values, will reveal whether the efficiency of theenzyme is different in the micellar pseudophase than inbulk water. If kcat and k are obtained from classical doublereciprocal plots, the concentrations given by eq 15 shouldbe employed to directly obtain the correct kcat and k valuesand, from their ratio, the Km values; this proposedcorrection does not assume any particular distribution ofthe substrate inside the micelles, and it even can be appliedunder 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 pub-lished results for horse liver alcohol dehydrogenase (ADH)in RMS composed of sodium 1,4-bis(2-ethylhexyl) sulfo-succinate (AOT)/octane/water, relative to bulk aqueoussolution.7,8 This system is a classical example of the effectof reverse micelles on the enzyme turnover (kcat/Km)relative to bulk aqueous solution. ADH catalyses theoxidation of aliphatic alcohols to the correspondingaldehydes:

The maximum kcat/Km ratio in aqueous solution isobtained for octanol, whereas in RMS composed of AOT(0.1 M)/octane/water (0.05 buffer phosphate, pH ) 8.8) atH2O/AOT ) 49, butanol is the best substrate.7,8 Figure 1

V0 ) kcat [E] (4)

kcat ) V0/[E] (5)

V0/[E] ) k [S] (6)

k ) kcat/Km (7)

Kp )[S]m

[S]org [Surf](8)

[S]m ) [S]analyt - [S]org (9)

[S]org ) forg [S]analyt (10)

forg ) {1 + Kp [Surf]}-1 (11)

[S]bwater ) K(water/org) [S]org (12)

[S]bwater ) forgK(water/org) [S]analyt (13)

[S] ) forgK(water/org) [S]analyt (14)

[S] ) {K(water/org)/(1 + Kp [Surf])} [S]analyt (15)

CH3(CH2)nOH + NAD+ f

CH3(CH2)n-1COH + NADH + H+

Rate Parameters of Enzyme-Catalyzed Reactions Langmuir, Vol. 16, No. 26, 2000 10085

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 (obtainedby using the analytical concentrations of the alcohols).Note the difference in specificity of the enzyme for thesubstrate and the values of k for a given alcohol in bothmedia. This behavior may be the result of a true micellareffect on enzyme activity or the consequence of differentsubstrate concentrations used to express the rate of thereaction in both media. In previous works, we havereported 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)exporiginally obtained by using the analytical concentrationsof the alcohols are expressed in terms of the activity of thesolute in bulk water (eq 15), values of (kcat/Km)cor can beobtained:

Figure 2 shows the dependence of (kcat/Km)cor values onthe length of the hydrocarbon chain of the alcohol (n) in

the micellar solution and (kcat/Km) values in the homo-geneous aqueous phase. This figure shows that both thedependence of (kcat/Km)cor values on the length of the alkylchain and their absolute values are very similar when theenzyme catalyzes the process in bulk water or in thereverse micellar solution. This conclusively shows thatthe reverse micelle incorporated enzyme behaves as inbulk water and that all the differences observed whenkcat/Km is expressed in terms of the analytical substrateconcentration (Figure 1) are due to differences in thealkanol activities in the micellar solution.

The kinetic analysis proposed in this paper revealswhether the presence of the micellar interface and/or theconstraint of the enzyme to a limited water pool modifiesits catalytic behavior. Furthermore, it shows when therate of the process (measured in terms of the analyticalsubstrate concentration) will depend on the surfactantconcentration (see eq 16). Furthermore, a similar correc-tion must be applied to Km values obtained in reversemicellar solutions employing analytical substrate con-centrations in order to evaluate if the reverse micellemodifies the affinity of the enzyme for the substrate. Theproposed approach to compare the behavior of the enzymein bulk aqueous solutions and RMS does not make any apriori assumption regarding the location of the enzymeand/or the substrate within the micelles.

Acknowledgment. Financial support of this work byDicyt (USACH) and Fondecyt (Project No. 1980211) isacknowledged.

LA000788Z

(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 1. Dependence of the second-order rate constant (kcat/Km)exp for the oxidation of aliphatic alcohols catalyzed by ADHon the length of the hydrocarbon chain of the alcohol. (b) Reversemicellar solution composed of AOT (0.1 M)/octane/water (0.05M phosphate buffer, pH ) 8.8) at water/AOT ) 49. Values of(kcat/Km)exp are on the left ordinate. (2) Aqueous solution (0.05M phosphate buffer, pH ) 8.8). Values of (kcat/Km) are on theright ordinate. The data are taken from refs 7 and 8.

(kcat/Km)cor ) {(kcat/Km)exp (1 + Kp [Surf])}/K(water/org)

(16)

Figure 2. Dependence of the second-order rate constant (kcat/Km)cor for the oxidation of aliphatic alcohols catalyzed by ADHon the length of the hydrocarbon chain of the alcohol. (b) Reversemicellar solution composed of AOT (0.1 M)/octane/water (0.05M phosphate buffer, pH ) 8.8) at water/AOT ) 49. (2) Aqueoussolution (0.05 M phosphate buffer, pH ) 8.8).

10086 Langmuir, Vol. 16, No. 26, 2000 Lissi and Abuin