kinetic studies on the enzyme (s)-hydroxynitrile lyase from hevea brasiliensis using initial rate...

Kinetic Studies on the Enzyme(S)-Hydroxynitrile Lyase from Heveabrasiliensis Using Initial Rate Methodsand Progress Curve Analysis

Michael Bauer,1 Herfried Griengl,2 Walter Steiner1

1Institute of Biotechnology, Enzyme-Technology Group, SFB Biocatalysis,Technical University Graz, Petersgasse 12, 8010 Graz, Austria; telephone:+43 316 873-8408; fax: +43 316 873-8434; e-mail:[email protected] of Organic Chemistry, SFB Biocatalysis, Technical UniversityGraz, Stremayrgasse 16, 8010 Graz, Austria

Received 30 March 1998; accepted 19 June 1998

Abstract: (S)-Hydroxynitrile lyase (EC 4.1.2.39) from He-vea brasiliensis (rubber tree) catalyzes the reversiblecleavage of cyanohydrins to aldehydes or ketones andprussic acid (HCN). Enzyme kinetics in both directionswas studied on a model system with mandelonitrile,benzaldehyde, and HCN using two different methods—initial rate measurements and progress curve analysis.To discriminate between possible mechanisms with theinitial rate method, product inhibition was studied. Benz-aldehyde acts as a linear competitive inhibitor againstmandelonitrile whereas HCN shows S-linear I-parabolicmixed-type inhibition. These results indicate an OrderedUni Bi mechanism with the formation of a dead-end com-plex of enzyme, (S)-mandelonitrile and HCN. Prussic acidis the first product released from the enzyme followed bybenzaldehyde. For progress curve analysis, a kineticmodel of an Ordered Uni Bi mechanism including adead-end complex, enzyme inactivation, and the chemi-cal parallel reaction was set up, which described the ex-perimental values very well. From the reaction rates ob-tained the kinetic constants were calculated and comparedwith the ones obtained from the initial rate method.Good agreement could be achieved between the twomethods supporting the suggested mechanism. © 1999John Wiley & Sons, Inc. Biotechnol Bioeng 62: 20–29, 1999.Keywords: enzyme kinetics; hydroxynitrile lyase; Heveabrasiliensis; progress curve analysis

INTRODUCTION

The function of hydroxynitrile lyases (Hnls) from plants innature is to catalyze the cleavage of cyanohydrins fromcyanogenic glycosides into the corresponding aldehydes orketones and HCN (Conn, 1981). In the reverse reaction,hydroxynitrile lyases can be used for the synthesis of enan-tiomerically pure cyanohydrins (Effenberger, 1994; Grienglet al., 1997; Kruse, 1992). Cyanohydrins can be converted

into a wide range of chiral compounds, which are importantfor the production of fine chemicals, pharmaceuticals, andagrochemicals. Therefore, hydroxynitrile lyases have be-come of growing industrial interest during the last years.

The biochemistry of Hnls, in general, has been reviewedin literature (Hickel et al., 1996; Wajant and Effenberger,1996). Hydroxynitrile lyases have been isolated and puri-fied from different plant families and can be classified ac-cording to their substrate specificity in(R)- or (S)-specific,or if they contain flavoprotein (FAD) or not.

Hydroxynitrile lyases fromHevea brasiliensis(HbHnl),whose natural substrate is acetone cyanohydrin, has beenpurified and characterized by Schall (1996), Selmar et al.(1989), and Wajant and Fo¨rster (1996). HbHnl is a ho-modimer (Schall, 1996), a homotrimer, or homotetramer(Wajant and Fo¨rster, 1996) with a molecular weight of itssubunit of 29–30 kDa. It has an isoelectric point of 4.1(Schall, 1996) and a pH optimum of 5.5–6.0 (Schall, 1996)and 5.3–5.7 (Wajant and Fo¨rster, 1996) is reported. Theenzyme contains no FAD and is not glycosylated. Kineticconstants have been determined for acetone cyanohydrinand for racemic mandelonitrile (Schall, 1996; Selmar et al.,1989; Wajant and Fo¨rster, 1996). Enzyme stability has beeninvestigated in detail in various aqueous buffers (Hickel etal., 1997).

The crystal structure of HbHnl has been determined to 1.9Å resolution. It belongs to thea/b hydrolase superfamilywith an active site which is deeply buried within the proteinand connected to the outside by a narrow tunnel (Wagner etal., 1996). The proposed mechanism of enzyme catalysis isstill under discussion (Hasslacher et al., 1997a; Wagner etal., 1996). HbHnl has been cloned and expressed inEsch-erichia coli, Saccharomyces cerevisiae,andPichia pastoris.Highest yields were obtained in a high cell density batchfermentation of aPichia pastoris transformant that ex-pressed HbHnl to about 50% of the cytosolic protein (Has-slacher et al., 1997b).

Correspondence to:Michael BauerContract grant sponsors: SFB Biocatalysis Project; European Union

ProjectContract grant numbers: F001/D13; BI04 CT960112

© 1999 John Wiley & Sons, Inc. CCC 0006-3592/99/010020-10

HbHnl is a versatile tool for the synthesis of opticallyactive cyanohydrins as it accepts aliphatic, aromatic, andheterocyclic aldehydes (Klempier et al., 1993, 1995;Schmidt et al., 1996). To use this enzyme on an industrialscale, knowledge of the enzyme kinetics is of great impor-tance. To study the kinetics of HbHnl, the cleavage andsynthesis of mandelonitrile was chosen as a model system(Fig. 1). Besides the enantioselective enzymatic reaction, achemical parallel reaction has to be considered which in-creases strongly with pH and does not discriminate betweenthe two enantiomers (Selmar et al., 1987). On the contrary,HbHnl loses its activity below pH 5 very quickly (Hickel etal., 1997). Therefore, it is necessary for kinetic investiga-tions to find reaction conditions where the enzyme is rela-

tively stable and the chemical reaction can be mostly sup-pressed.

In this work we investigated the kinetics of the HbHnlwith two different methods: initial rate measurements andprogress curve analysis. The strategies are quite different.For the traditional initial rate method, many experimentalsets at the beginning of the reaction are necessary, whereasfor progress curve analysis fewer experiments close to equi-librium and a lot of computation has to be performed. It willbe shown that both methods may be used for kinetic studiesand that good correspondence between the two approachescan be achieved.

Models for the Enzymatic Mechanismand Computation

Initial Rate Method

The model reaction investigated can be described as an UniBi/Bi Uni reaction. There are two main categories of pos-sible mechanisms: ordered and random mechanisms. For

hydroxynitrile lyase fromPrunus amygdalusan OrderedUni Bi mechanism has been proposed in which HCN is thefirst product released from the enzyme followed by benz-aldehyde (Jorns, 1980). For this mechanism the velocityequation has been derived and the product inhibition patterndetermined (Cleland, 1963a,b). As the experimental resultsin this work did not correlate with this mechanism (seeResults), the model was extended to an Ordered Uni Bimechanism with the formation of a dead-end complex ofenzyme,(S)-mandelonitrile and HCN (Fig. 2). According toJorns (1980), the same order of product release was as-sumed. The rate equations for this system have been derivedaccording to the rules of King and Altman (1956). Theoverall velocity equation in the form of the kinetic constants

can be expressed as:

The kinetic constants expressed in the form of reaction ratescan be found in the Appendix. For initial rate studies, thisvelocity equation can be simplified. For the forward reac-tion, the cleavage of racemic mandelonitrile, the productconcentrations can be set to 0 and Eq. (1) can be simplifiedto a Henri-Michaelis-Menten equation. For product-inhibition studies with benzaldehyde, Eq. (1) can be reducedto an equation for a linear-competitive inhibition:

v

Vmax,f=

@MN#

Km,MN ? S1 +@BA#

Ki,BAD + @MN#

(2)

If HCN is the inhibitor, a more complex equation resultsfrom Eq. (1):

Figure 2. Reaction scheme for an Ordered Uni Bi mechanism(a), in-cluding a dead-end complex of enzyme,(S)-mandelonitrile and HCN(b),notation according to Cleland (1963a).

v =Vmax,f? @MN# −

Vmax,r ? Ki,MN

Ki,HCN ? Km,BA? @BA# ? @HCN#

Km,MN+ @MN# +Ki,MN

Ki,HCN? @HCN# +

Km,MN

Ki,BA? @BA# +

Ki,MN

Ki,HCN ? Km,BA? @BA# ? @HCN# +

+@MN# ? @HCN#

Ki,HCN+

@MN# ? @HCN#

K9dead+

1

Ki,HCN ? K8dead? @MN# ? @HCN#2 +

Ki,MN

Ki,HCN ? Km,BA? K8dead? @BA# ? @HCN#2

(1)

Figure 1. Model reaction for the investigation of the enzyme mechanism.

BAUER, GRIENGL, AND STEINER: KINETICS OF A HYDROXYNITRILE LYASE FROM HEVEA BRASILIENSIS 21

Eq. (3) can be transformed in the double-reciprocal form ofLineweaver-Burk:

No intersection point of all lines with varying HCN con-centration can be found in the Lineweaver-Burk plot be-cause of the square term in the equation. The slope term inEq. (4) is linear resulting in a linear-slope replot. The in-tercept term in Eq. (4) can be expressed in the form of aparabola [Eq. (5)]. A replot of the intercept is, therefore,parabolic.

intercept= a + b@HCN# + c@HCN#2 (5)

HCN acts as aS-linear I-parabolic mixed-type inhibitor inthis mechanism. In Table I, the inhibition pattern for pos-sible Uni Bi mechanisms are summarized (Cooper and Ru-dolph, 1996; Rudolph, 1979; Segel, 1975; this work).

For the back reaction, the formation of(S)-mandelonitrilefrom benzaldehyde and HCN, a simple Ordered Bi Unimechanism was assumed as the concentration of the product

is very low at initial rate conditions and therefore, the backreaction with the formation of a dead-end complex was not

considered. Analyzing a two-substrate kinetics, one sub-strate is varied whereas the other one is kept constant atdifferent concentrations. The kinetic constants can be cal-culated from the slope and intercept replots of the Line-weaver-Burk plots (Segel, 1975) or by nonlinear leastsquares fitting to the proper rate equations (Cleland, 1979).If Lineweaver-Burk plots are used for the determination ofkinetic parameters a weighting scheme has to be establishedto circumvent the errors resulting from double reciprocalplots (Cleland, 1979; Henderson, 1992).

Progress Curve Analysis

Progress curve analysis is another approach for the inves-tigation of enzyme kinetics (Duggleby and Morrison, 1977).For this purpose a model following an Ordered Uni Bi

Table I. Comparison of the inhibition pattern of different Uni Bi mechanisms (Cooper andRudolph, 1996; Rudolph, 1979; Segel, 1975; this work).

Mechanism Inhibitor Inhibition Slope replotIntercept

replot

Ordered Uni Bi HCN Mixed-type Linear LinearBA Competitive Linear —

Ordered Uni Bi HCN Mixed-type Linear ParabolicWith dead-end complexa BA Competitive Linear —

Random Uni Bi HCN Mixed-type Hyperbolic HyperbolicBA Mixed-type Hyperbolic Hyperbolic

Rapid Equilibrium HCN No inhibition — —Ordered Uni Bi BA Competitive Linear —

Rapid Equilibrium HCN Competitive Linear —Random Uni Bi BA Competitive Linear —

Rapid Equilibrium Random HCN Mixed-type Nonlinear LinearUni Bi with dead-end complexa BA Competitive Linear —

aComplex: E-(S)-MN-HCN.

v

Vmax,f=

@MN#

Km,MN ? S1 +Km,BA

Ki,BA ? Km,HCN? @HCN#D + @MN# ? S1 +

@HCN#

Ki,HCN+

@HCN#

K9dead+

@HCN#2

K8dead? Ki,HCND (3)

1

v=

Km,MN

Vmax,f? S1 +

Km,BA

Ki,BA ? Km,HCN? @HCN#D

slope

?1

@MN#+

1

Vmax,f? S1 +

@HCN#

Ki,HCN+

@HCN#

K9dead+

@HCN#2

K8dead? Ki,HCND

intercept

(4)

22 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 62, NO. 1, JANUARY 5, 1999

mechanism including a dead-end complex, the chemicalparallel reaction and enzyme inactivation was developed(Fig. 3).

The differential equations for this system can be found inthe Appendix. Simulations for this model were done withMatlabt and Simusolvt. For numerical integration, theGear’s BDF algorithm was used (Gear, 1971). For fittingthe model parameters to the experimental values the LogLikelihood Function (LLF) implemented in Simusolvt wasused to judge whether a set of parameter values is ‘‘thebest’’ (Bard, 1974). To ensure that the best values for thereaction rates have been determined contour plots of theLLF for the model parameters against each other were plot-ted. A sensitivity analysis was applied with Simusolvt tostudy the relationship between the input parameters and themodel responses. From a plot of the normalized sensitivitycoefficient against time the importance of each reaction ratefor the proposed model can be seen.

In addition, a model for a Random Uni Bi mechanismincluding enzyme inactivation and the chemical reactionwas set-up to discriminate between different mechanismswith progress curve analysis.

MATERIALS AND METHODS

Chemicals and Enzyme

Purified racemic mandelonitrile was a gift from DSM-Chemie Linz (Lint, Austria). Benzaldehyde was purchasedfrom Aldrich (Steinheim, Germany) and distilled under ni-trogen before use to remove benzoic acid which is a stronginhibitor (Schall, 1996). Freshly distilled HCN was pro-vided by the Institute of Organic Chemistry, Technical Uni-versity Graz. All other chemicals were of p.a. quality.

Purified (S)-hydroxynitrile lyase fromHevea brasiliensiswas provided by the Genetic Engineering Group, Depart-

ment of Biotechnology, Technical University Graz. The en-zyme was expressed inPichia pastorisand purified by ionexchange chromatography (Hasslacher et al., 1996,1997a,b).

Hydroxynitrile Lyase Activity Test

Enzyme activity was measured following the cleavage ofracemic mandelonitrile into benzaldehyde and HCN, at asubstrate concentration of 12 mM and at an enzyme con-centration of 0.74mg/mL. The assay was performed in 20mM glutamate buffer at pH 5 and 25°C and the formation ofbenzaldehyde was monitored spectrophotometrically at 280nm. Besides the enzymatic reaction a chemical parallel re-action takes place which has to be measured separately. Thereaction was monitored for 2 min. From the slopeDE vs.time, enzyme activity was calculated. One InternationalUnit (IU) is defined as the amount of enzyme that cleavesonemmol mandelonitrile per minute.

Enzyme Stability

To investigate enzyme inactivation under the experimentalconditions the enzyme solution was incubated in 20 mMglutamate buffer, pH 5.0 at 25°C. At distinct intervalssamples were taken up to 10 h, and activity was determined.From the first order inactivation, the inactivation constantwas calculated and used for modeling.

Enzyme Kinetics with Initial Rate Experiments

All initial rate measurements are based on the standard ac-tivity test. At low substrate concentrations the assay timewas shortened to measure in the linear region of the reac-tion. To study product inhibition for the cleavage reactionthe products were added at different fixed concentrations(benzaldehyde: 0.3 to 1.3 mM, HCN: 10 to 40 mM) to thesubstrate mandelonitrile, which was varied between 0.4 and12 mM. The inhibition type of the products was determinedfrom Lineweaver-Burk plots and their replots. For the syn-thesis reaction, one substrate was varied while the other waskept constant at fixed concentrations and vice versa (benz-aldehyde: 0.05 to 6 mM, HCN: 3 to 200 mM). The kineticconstants for all initial rate experiments were determined bynonlinear least squares fitting to the appropriate equationsusing Origint.

Enzyme Kinetics with Progress Curve Analysis

For progress curve analysis the same experimental condi-tions were applied as for the standard activity test. Com-pletely filled cuvettes were closed with stoppers to avoid theevaporation of HCN. All reactions were monitored spectro-photometrically at 280 nm close to equilibrium. At distinctintervals samples were taken to determine the enantiomericexcess of(R)- or (S)-mandelonitrile. For the cleavage reac-tion the starting concentration of racemic mandelonitrile

Figure 3. Model of an Ordered Uni Bi mechanism(a), including a dead-end complex of enzyme,(S)-mandelonitrile and HCN(b), enzyme inacti-vation (c), and the chemical parallel reaction(d).


was varied between 1 and 6 mM. For the synthesis reactionthe starting concentrations for benzaldehyde were variedbetween 0.5 and 3 mM and for HCN between 5 and 50 mM.The resulting ratio of HCN to benzaldehyde varied between1.3 and 100. The chemical cleavage and formation of man-delonitrile was measured separately.

Determination of the Enantiomeric Excess of (S)-and (R)-Mandelonitrile

The enantiomeric excess of(S)-and(R)-mandelonitrile wasdetermined by gas chromatography from the ratio of theacetylated derivatives. The aqueous mandelonitrile solutionwas extracted with one volume equivalent of dibutyl ether,and the organic phase was removed. Ten mol equivalentpyridine, 10 mol equivalent acetic acid anhydride, and 0.1mol equivalent of 4-N,N-dimethyl aminopyridine wereadded to the organic phase, and the mixture was incubatedat 40°C for 2 h. The derivatized samples were analyzed ona b-cyclodextrin column (Chrompack CP Chirasil Dex CB25 m × 0.32 mm) with nitrogen as the carrier gas at aconstant flow of 3.1 mL/min. The temperature was first keptconstant at 80°C for 4 min, was then increased with 5°C/min up to 145°C and then kept constant for 1 min. Theretention times for benzaldehyde,(R)-mandelonitrile, and(S)-mandelonitrile were 5.7, 15.0, and 16.3 min, respec-tively.

RESULTS

Initial Rate Method—Mechanism of the HbHnl

The kinetics of the enzymatic cleavage of racemic mande-lonitrile obeys a Michaelis-Menten kinetics (data notshown). The kinetic parametersKm,MN andVmax,f were de-termined by nonlinear least squares fitting (Table II). En-zymatic cleavage and synthesis of(R)-mandelonitrile was

not observed. Addition of(R)-mandelonitrile did not inhibitthe enzyme (data not shown).

The addition of benzaldehyde as a product inhibitor de-creases enzymatic activity with increasing concentrations ofbenzaldehyde. In the weighted Lineweaver-Burk plotstraight lines are obtained (Fig. 4a). The slope increaseswith increasing concentrations of benzaldehyde. One com-mon point of intersection can be found on the ordinate in-dicating a competitive inhibition. From a replot of the slopefrom the Lineweaver-Burk plot against the inhibitor con-centration, the inhibition constant for benzaldehyde (Ki,BA)can be determined as the point of intersection with the ab-scissa (Fig. 4b, Table II). Benzaldehyde consequently actsas a linear competitive inhibitor and is, therefore, the secondproduct released from the enzyme.

Enzyme activity also decreases with increasing concen-tration of HCN, but very high concentrations of inhibitor arenecessary to see a pronounced effect. Slope, as well as

Table II. Comparison of the kinetic constants from the initial rate method and progress curve analysis.

Initial rate method Progress curve analysis

Kinetic constants Kinetic constants Reaction rate [ l? mmol−1 ? s−1 ] [s−1]

Vmax,f4 132 ± 2 IU? mg−1 Vmax,f4 271 ± 6 IU? mg−1 k1 504.3 ± 0.4kcat,f 4 64 ± 1 s−1 kcat,f 4 131 ± 1 s−1 k2 2122 ± 2

Vmax,r4 7100 ± 50 IU? mg−1 Vmax,r4 4386 ± 3 IU? mg−1 k3 207.1 ± 0.2kcat,r 4 3436 ± 24 s−1 kcat,r 4 2111 ± 2 s−1 k4 7.91 ± 0.01

Km,MN4 3.1 ± 0.1 mM Km,MN4 2.93 ± 0.01 mM k5 357.9 ± 0.5Ki,MN 4 3.3 ± 0.2 mMa Ki,MN 4 4.21 ± 0.01 mM k6 470.8 ± 0.1Km,BA4 5.2 ± 0.3 mM Km,BA4 4.51 ± 0.01 mM k7 n.d.Ki,BA 4 1.18 ± 0.02 mM Ki,BA 4 0.76 ± 0.001 mM k8 n.d.

Km,HCN4 350 ± 45 mM Km,HCN4 294.8 ± 0.5 mM k9 3.52? e − 5 ± 0.15? e − 5Ki,HCN 4 150 ± 14 mMa Ki,HCN 4 71.5 ± 0.2 mM k10 2.402? e − 5 ± 5? e − 8

k11 9.34? e − 6 ± 2? e − 8

Keq 4 3.2 ± 0.2 mmol? l−1 a Keq 4 4.73 ± 0.02 mmol? l−1 Keq 4 2.57 ± 0.01 mmol? l−1 (chemical reaction)

aCalculated from the Haldane equations (A7, A8).

Figure 4. Lineweaver-Burk plot for the product inhibition of benzalde-hyde (BA) (a), slope replot from the Lineweaver-Burk plot(b).


intercept, increases with increasing inhibitor concentrationin the Lineweaver-Burk plot indicating a mixed-type inhi-bition (Fig. 5). Consequently, HCN is the first product re-leased from the enzyme. The families of straight lines do notintersect at a common point, indicating that HCN does notonly show mixed-type inhibition but also dead-end inhibi-tion (Segel, 1975). The slope replot of the Lineweaver-Burkplot is linear, while the intercept replot is parabolic (Figs.6a,b). Applying the rules of Cleland (1963b) for product-inhibition pattern, this observation can be explained prop-erly. Only one point of HCN addition in the reaction se-quence (Fig. 2) predicts slope effects leading to a linearslope replot. On the contrary, HCN combines at two pointsin the reaction sequence that are reversibly connected, andcombination at both points predicts intercept effects result-ing in a parabolic intercept replot. Consequently, HCN canbe described as anS-linear, I-parabolic mixed-type inhibi-tor. The inhibition constant for HCN (Ki,HCN) was calcu-lated according to the Haldane equation (A7).

Enzymatic synthesis of(S)-mandelonitrile also followsMichaelis-Menten kinetics (data not shown). To determinethe kinetic constants for the synthesis reaction, one substrate(benzaldehyde or HCN) was varied, while the other was

kept constant at different concentrations. The constantswere calculated by nonlinear least squares fitting (Table II).For the synthesis reaction, no inhibition experiments withmandelonitrile were performed because the cleavage ofmandelonitrile which takes place in parallel to the synthesiswould make isotope-exchange studies necessary.

The inhibition pattern observed for benzaldehyde andHCN corresponds well with an Ordered Uni Bi mechanismincluding the formation of a dead-end complex of enzyme,(S)-mandelonitrile and HCN (Table I). HCN is the firstproduct released from the enzyme followed by benzalde-hyde while in the synthesis reaction, benzaldehyde is thefirst substrate bond to the enzyme followed by HCN.

Enzyme Kinetics with Progress Curve Analysis

The reaction rates for the chemical reaction (k10, k11) inFigure 3d were determined separately by fitting the progresscurves for four different starting concentrations of racemicmandelonitrile and for six different HCN/benzaldehyde ra-tios simultaneously to the chemical reaction model. Goodagreement could be achieved between the experimental val-ues and simulated curves for the chemical decompositionand synthesis (data not shown). The decomposition of ra-cemic mandelonitrile follows first-order kinetics, while theformation obeys second-order kinetics. The equilibriumconstant was calculated from the reaction rates (Table II).

For the simulation of the enzymatic reaction the wholemodel from Figures 3a–d was used. As for the chemicalreaction four different starting concentrations of racemicmandelonitrile and six different HCN/benzaldehyde ratioswere used simultaneously for optimizing the model param-eters to the experimental values. For cleavage and synthesisthe simulated curves fit well to the measured values forracemic mandelonitrile and benzaldehyde as well as to theenantiomeric excess (Figures 7, 8).

In the cleavage reaction half of the mandelonitrile iscleaved within 1 h at a lowstarting substrate concentration(1 mM), while at a higher starting substrate concentration (6mM) only one third of the substrate is cleaved within the

Figure 5. Lineweaver-Burk plot for the product inhibition of HCN.

Figure 6. Slope(a) and intercept(b) replot from the Lineweaver-Burk plot for the product inhibition of HCN.


same time (Fig. 7a). This fact is due to the inhibition bybenzaldehyde. At a high starting substrate concentration thebenzaldehyde concentration rises fast, resulting in a stronginhibition of the HbHnl. If the benzaldehyde concentrationis equal to its inhibition constant (Ki,BA 4 1.1 mM) theapparentKm,MN is already doubled, and HbHnl activity issignificantly decreased. The inhibition effect of benzalde-hyde also contributes to the low enantiomeric excess for(R)-mandelonitrile at a high starting concentration of thesubstrate (Fig. 7b). Enzyme activity drops due to the inhi-bition of benzaldehyde, and the chemical parallel reactionincreases relative to the enzymatic reaction, which lowersthe enantiomeric excess. Simulations over some hours showthat the maximum of the enantiomeric excess is reachedafter about 1 h and then the chemical reaction decreases theenantiomeric excess due to racemization.

In the synthesis reaction an increase of the HCN/benzaldehyde ratio increases the reaction rate drastically buthas no significant influence on the enantiomeric excess

(Figs. 8a,b). At the beginning of the reaction the enzymaticconversion is fast resulting in a high enantiomeric excess.When the reaction approaches equilibrium the enantiomericexcess decreases due to the chemical reaction which againincreases relatively to the enzymatic reaction.

The kinetic constants for progress curve analysis (TableII) were calculated from the optimized reaction rates ac-cording to Eqs. A1–A6 (see Appendix). It was not possibleto determine the rate constants for the formation of thedead-end complex (k7, k8) because their values are not sen-sitive enough for the shape of the progress curve. Sensitivityanalysis showed that the rate constants for the Ordered UniBi mechanism (k1–k6) are most sensitive for the proposedmodel. The sensitivity coefficients for enzyme inactivationand the chemical parallel reaction (k9–k11) are about onetenth of the ones for the Ordered Uni Bi mechanism,whereas the sensitivity coefficients for the formation of thedead-end complex (k7, k8) are 5 orders of magnitudesmaller; consequently, the values of these two rate constants

Figure 8. Progress curves for the enzymatic synthesis of(S)-mandeloni-trile (MN), concentrations of benzaldehyde (BA) and mandelonitrile(a),and enantiomeric excess(b) in the course of the reaction at differentstarting concentrations of benzaldehyde ([BA]0) and HCN. +: HCN/BA4

1.7, [BA]0 4 3.0 mM; o: HCN/BA 4 3.3, [BA]0 4 3.0 mM; *: HCN/BA4 10, [BA]0 4 3.0 mM; —: simulated curves; symbols: measured values.[E]t 4 2.56? e − 5 mM.

Figure 7. Progress curves for the enzymatic cleavage of racemic man-delonitrile (MN), concentrations of benzaldehyde (BA) and mandelonitrile(a), and enantiomeric excess(b) in the course of the reaction at differentstarting concentrations of racemic mandelonitrile ([MN]0). +: [MN]0 4 1mM; o: [MN]0 4 2 mM; *: [MN] 0 4 4 mM; x: [MN]0 4 6 mM; —:simulated curves; symbols: measured values. [E]t 4 2.56? e − 5 mM.


cannot be determined with progress curve analysis and can,therefore, be neglected in the model.

In addition, the Random Uni Bi mechanism was alsofitted to the experimental values. But no good agreementbetween the simulated curves of this mechanism and theexperimental values could be achieved. The reaction ratesfor the formation of an enzyme-HCN complex go towards 0during the optimization routine, indicating that the proposedenzyme-HCN complex in this mechanism does not exist.

DISCUSSION

Comparison Between the Initial Rate Method andProgress Curve Analysis

In general, good correspondence between the two differentmethods could be achieved (Table II). The differences in themaximum velocity for the reverse reaction is due to thedifficulty in determining the constant with initial rate mea-surements as the chemical and the enzymatic reaction areboth very fast. The different values for the Michaelis-Menten and inhibition constant for HCN can be contributedto the very low affinity of HCN for the enzyme.

The consistency of the kinetic parameters from progresscurve analysis was checked with the Haldane equation (A7).The equality for Eq. A7 (4.74 5.0 4 4.8) is satisfactory.Also, for a new Haldane equation (A8) found for OrderedUni Bi mechanisms by Straathof and Heijnen (1996) theagreement was excellent (0.714 0.71). For initial rate stud-ies, no consistency check was possible asKeq, Ki,MN, andKi,HCN were determined from the Haldane equations.

The equilibrium constants for the chemical reaction canbe compared with values reported by Ching et al. (1978,Keq

4 3.8–4.7 mmol? l−1) and Young et al. (1979,Keq 4 3.6

mmol ? l−1). Moreover, its value is close to the equilibriumconstants obtained for the enzymatic reaction. The equilib-rium is on the side of benzaldehyde and HCN, which has anegative influence on organic synthesis. Product recoveryduring the reaction would enhance the conversion.

Comparison of the Enzyme Kinetics of DifferentHydroxynitrile Lyases

Hydroxynitrile lyases are, in general, intensively studied,but the kinetics of cyanohydrin synthesis and cleavage wasdetermined only for Hnl fromPrunus amygdalus(PaHnl)(Jorns, 1980; Niedermeyer, 1990). This enzyme also fol-lows an Ordered Uni Bi mechanism, but no dead-end com-plex of enzyme, cyanohydrin and HCN has been detected(Table III). The kinetic constants determined by Jorns are,in general, 1 order of magnitude lower than the ones fromHbHnl. This could be due to the fact that mandelonitrile, thenatural substrate for PaHnl, has a higher affinity to thisenzyme than to HbHnl whose natural substrate is acetonecyanohydrin.

For Hnl from other sources not many kinetic data can befound (Table III). Selmar et al. (1989) pointed out thatHbHnl is more active towards the natural substrate acetonecyanohydrin than towards mandelonitrile as the enzymeshowed a higher reaction velocity and a lowerKm value foracetone cyanohydrin. TheKm value for racemic mandelo-nitrile is of the same order as in this work. Surprisingly,Wajant and Fo¨rster (1996) found a very highKm value foracetone cyanohydrin for HbHnl. In general, differentsources for Hnl show similarKm values for mandelonitrile,which was shown by different authors (Niedermeyer, 1990;Schall, 1996; van Scharrenburg et al., 1993; Wajant et al.,1995).

Table III. Comparison of the kinetic data for Hnl from different plants.

Enzyme pH Substrate Kinetic constants Reference

(S)-HbHnl 3.7 Rac. mandelonitrile Km 4 3.4 mM, Vmax4 0.058 mM/min Wajant and Fo¨rster (1996)(S)-HbHnl 5.4 Acetone cyanohydrin Km 4 115 mM Wajant and Fo¨rster (1996)(S)-HbHnl 5.5 Acetone cyanohydrin Km 4 0.7 mM, Vmax4 21.2 IU/mg Selmar et al. (1989)

Rac. mandelonitrile Km 4 1.2 mM, Vmax4 3.7 IU/mg(S)-MeHnl 5.0 Acetone cyanohydrin Km 4 110 mM Hughes et al. (1994)(R)-PaHnl 5.5 Rac. mandelonitrile Km 4 0.59 mM, kcat 4 630 s−1 Jorns (1980)

Benzaldehyde Km 4 0.15 mM, Ki 4 0.12 mM, kcat 4 1700 s−1

HCN Km 4 57 mM, Ki 4 18 mM, a ? Ki 4 63 mM(R)-PaHnl 3.75 Rac. mandelonitrile Km 4 1.05 mM, Vmax4 76 IU/mg Niedermeyer (1990)

Benzaldehyde Km 4 0.46 mM, Ki 4 0.37 mM, Vmax4 527 IU/mgHCN Km 4 711 mM, Ki 4 72 mM

(R)-PaHnl 5.5 Rac. mandelonitrile Km 4 0.7 mM, Vmax4 280 IU/mg van Scharrenburg et al. (1993)(S)-SbHnl 5.5 Rac. mandelonitrile Km 4 6.7 mM, Vmax4 15 IU/mg van Scharrenburg et al. (1993)(S)-SbHnl 3.75 p-hydroxybenz. cyanoh. Km 4 1.74 mM, Vmax4 48 IU/mg Niedermeyer (1990)

p-hydroxybenzaldehyde Km 4 0.61 mM, Ki 4 0.32 mM, Vmax4 153 IU/mgHCN Km 4 264 mM, Ki 4 17 mM

(S)-XaHnl 5.5 Rac. mandelonitrile Km 4 0.53 mM, Vmax4 1030 IU/mg van Scharrenburg et al. (1993)(R)-PhaHnl 6.0 Rac. mandelonitrile Km 4 0.83 mM Wajant et al. (1995)(R)-LuHnl 5.5 Acetone cyanohydrin Km 4 2.5 mM Xu et al. (1988)

Hb: Hevea brasiliensis;Me: Manihot esculenta;Pa: Prunus amygdalus;Sb: Sorghum bicolor;Xa: Ximenia americana;Pha:Phlebodium aureum;Lu: Linum usitatissimum.


It can be seen in this work that both methods—initial ratestudies and progress curve analysis—can be used to eluci-date an enzymatic reaction mechanism. The initial ratemethod needs a high experimental effort, but the determi-nation of the kinetic constants is rather simple. In progresscurve analysis only a few experiments have to be per-formed, but a lot of computation has to be done. The modelfrom progress curve analysis offers the possibility of pre-dicting conversion and enantiomeric excess depending ontime and substrate concentrations. Optimized reaction con-ditions can now be achieved by simulations—not only byexperiments. Simulations are, therefore, a powerful tool anda clever way to save substrates, enzyme, and time (Dugglebyand Morrison, 1978; Frieden, 1994; Rakels et al., 1993).

NOMENCLATURE

[E]t total enzyme concentration[BA] concentration of benzaldehyde[HCN] concentration of prussic acid[MN] concentration of mandelonitrilekcat,f turnover number for the cleavage of mandelonitrilekcat,r turnover number for the synthesis of mandelonitrileKm,BA–Ki,BA Michaelis-Menten and inhibition constant for benzal-

dehydeKm,HCN–Ki,HCN Michaelis-Menten and inhibition constant for prussic

acidKm,MN–Ki,MN Michaelis-Menten and inhibition constant for mande-

lonitrileK8dead–K9dead constants for the dead-end complex of enzyme-(S)-

mandelonitrile-HCNKeq equilibrium constantv reaction rateVmax,f maximum rate for the cleavage of mandelonitrileVmax,r maximum rate for the synthesis of mandelonitrile

APPENDIX

The derivation of Eq. (1) is available from the authors uponrequest. The kinetic constants in Eq. (1) can be expressed inthe form of the rate constants:

Vmax,f=k3 ? k5

k3 + k5? @E#t Vmax,r= k2 ? @E#t (A1 a, b)

Km,MN=k5 ? ~k2 + k3!

k1 ? ~k3 + k5!Ki,MN =

k2

k1

(A2 a, b)

Km,BA=k2

k6Ki,BA =

k5

k6(A3 a, b)

Km,HCN=k2 + k3

k4Ki,HCN =

k3 + k5

k4(A4 a, b)

K8dead=k8

k7K9dead=

K8dead? ~k3 + k5!

k5(A5 a, b)

Keq =k1 ? k3 ? k5

k2 ? k4 ? k6(A6)

The equilibrium constant can be expressed as a combinationof the kinetic constants. This relationship is known as theHaldane equation:

Keq =Vmax,f? Ki,BA ? Km,HCN

Vmax,r ? Km,MN=

Vmax,f? Ki,HCN ? Km,BA

Vmax,r ? Ki,MN(A7)

A new Haldane equation for Ordered Uni Bi mechanismshas been recently found by Straathof and Heijnen (1996),which can be used to check the consistency of the kineticconstant:

Km,MN

Ki,MN= 1 +

Vmax,f

Vmax,r? S1 −

Km,BA

Ki,BAD (A8)

The system of differential equations for Figure 3 can bewritten as:

d@E#

dt= k2 ? @E − ~S!MN# − k1 ? @E# ? @~S!MN#

− k6 ? @E# ? @BA# + k5 ? @E − BA# − k9 ? @E# (A9)

d@E − ~S!MN#

dt= −k2 ? @E − ~S!MN# + k1 ? @E# ? @~S!MN#

+ k4 ? @E − BA# ? @HCN# − k3 ? @E − ~S!MN#(A10)

d@E − ~S!MN − HCN#

dt= k7 ? @E − ~S!MN# ? @HCN# −

k8 ? @E − ~S!MN − HCN#(A11)

d@E − BA#

dt= k3 ? @E − ~S!MN# − k4 ? @E − BA# ? @HCN#

+ k6 ? @E# ? @BA# − k5 ? @E − BA# (A12)

d@~S!MN#

dt= k2 ? @E − ~S!MN# − k1 ? @E# ? @~S!MN#

− k10 ? @~S!MN# + 0.5 ? k11 ? @BA# ? @HCN#(A13)

d@~R!MN#

dt= −k10 ? @~R!MN# + 0.5 ? k11 ? @BA# ? @HCN#

(A14)

d@BA#

dt= k5 ? @E − BA# − k6 ? @E# ? @BA# + k10 ? @~S!MN#

+ k10 ? @~R!MN# − k11 ? @BA# ? @HCN# (A15)

d@HCN#

dt= k3 ? @E − ~S!MN# − k4 ? @E − BA# ? @HCN#

+ k10 ? @~S!MN# + k10 ? @~R!MN#

− k11 ? @BA# ? @HCN# + k8 ? @E − ~S!MN − HCN#

− k7 ? @E − ~S!MN# ? @HCN# (A16)

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kinetic studies on the enzyme (s)-hydroxynitrile lyase from hevea brasiliensis using initial rate...

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