Transient Kinetic Approach to the Study ofAcetylcholinesterase Reversible Inhibition by Eseroline

MARKO GOLICNIK* and JURE STOJAN

Institute of Biochemistry, Medical Faculty, University of Ljubljana, Vrazov trg 2, 1000 Ljubljana, Slovenia

(Received 19 June 2002)

The kinetic rate constants for interaction of (2)-esero-line-(3aS-cis)-1,2,3,3a,8,8a-hexahydro-1,3a,8-trimethyl-pyrrolo-[2,3-b]indol-5-ol with electric eelacetylcholinesterase (EC 3.1.1.7, acetylcholine acetylhy-drolase) were measured at a low substrate concentrationaccording to a transient kinetic approach by using a rapidexperimental technique. The measurements were carriedout on a stopped-flow apparatus where pre-incubatedsamples of enzyme with various inhibitor concentrationswere diluted with a buffer solution containing thesubstrate. The experimental data in the form of sigmoid-shaped progress curves were analysed by applying anexplicit progress curve equation that described the timedependence of product released during the reaction. Thekinetic parameters were evaluated by non-linearregression treatment and the values of the correspondingconstants showed approximately the equal affinities ofeseroline and eserine (cf. Stojan, J. and Zorko, M. (1997)Biochim. Biophys. Acta, 1337, 75–84.) for binding into theactive centre of the enzyme. On the other hand, thekinetic rates for association and dissociation of eserolinewere two grades of magnitude higher than those ofeserine. The explanation appears to be a substantionallyimpaired gliding of eserine into the active site gorge bythe great mobility of the carbamoyl tail as well as by itsnumerous possible interactions with the residues liningthe gorge. Additionally, a study of the dependence of thetransition phase information on the inhibitor concen-tration was carried out using our experimental data.

Keywords: Enzyme kinetics; Progress curves; Acetylchloinesterase;Easeroline; Stopped-flow

INTRODUCTION

Eserine (physostigmine) is a natural carbamateisolated and purified from the Calabar bean.Its inhibitory action on acetylcholinesterase (AChE)

was used in the treatment of glaucoma at the end of19th century. Recently, long chain analogs of eserinehave been studied as potential drugs againstsymptoms in Alzheimer’s disease.1,2 The three stepreaction mechanism for the inhibition of AChE byeserine has been investigated for many years and thecomplete kinetic characterization of the interactionhas recently been done by Stojan and Zorko.3 It wasfound in that work that the submicromolar affinity ofeserine is not so much a consequence of the fast initialcomplex formation but rather a consequence of itsslow dissociation. A similar affinity was measured forthe inhibition of AChE by eseroline4 (Ese), ahydrolytic derivative of eserine devoided of itsN-methyl carbamyl group. For this reason it seemsthat the interactions between the rigid tricyclic moietyof eserine and the enzyme active site are responsiblefor slow dissociation and consequently for highaffinity of eseroline-based carbamates. According toour knowledge, the determination of the rateconstants kon and koff for Ese had never been reportedand thus the interesting question on the backgroundof its efficient inhibition still remains. For this reasonthe comparison of kinetic constants for formation ofnon-covalent enzyme-inhibitor complexes of eserineand eseroline seemed meaningful.

There are two possible ways to determine theassociation and dissociation rate constants for fastequilibrating inhibitors, and both call for applyingrapid experimental techniques. Direct methods arebased on a system which contains only the enzymeand investigated ligand. The ligands are fluorescentprobes and the rate constants are determined using astopped-flow5,6 or a temperature-jump7 instrument

ISSN 1475-6366 print/ISSN 1475-6374 online q 2002 Taylor & Francis Ltd

DOI: 10.1080/1475636021000013920

*Corresponding author. Tel.: þ386-1-5437651. Fax: þ386-1-5437641. E-mail: golicnik@ibmi.mf.uni-lj.si

Abbreviations: AChE, acetylcholinesterase; ATCh, acetylthiocholine; DTNB, 5,50-dithio-bis-nitrobenzoic acid; Ese, eseroline

Journal of Enzyme Inhibition and Medicinal Chemistry, 2002 Vol. 17 (5), pp. 279–285

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with fluorescence detection. However, such methodsconsume much enzyme as well as ligand. On the otherhand, rapid hydrolysis of the substrate by enzymeslike AChEs together with fast and powerful detectionreactions, enables indirect absorbance basedmeasurements using relatively small amounts ofenzyme. The deviations in the shape of progresscurves, obtained by the system containing enzyme,inhibitor, and the substrate, provide information onkinetic rates of individual processes occurring duringthe reaction. Such an indirect method has beenexamined and extensively analysed in this study.

THEORY

Electric eel acetylcholinesterase catalyses thehydrolysis of acetylcholine at one of the highestrates known.8 It shows Michaelis–Menten likekinetic behaviour at substrate concentrations of upto 0.5 mM and negative pseudo-cooperativity abovethis concentration.8 The kinetic model of the AChEreaction mechanism at low substrate concentrationshas been described by the traditional reactionscheme9

where ES is the initial enzyme–substrate complex,EA is an acyl-enzyme intermediate, and P1, P2 are thetwo products of the reaction. Under classical steady-state conditions, the rate of hydrolysis v varieswith [S ] according to the Michaelis – Mentenequation10

v ¼d½P�

dt¼

Vmax½S�

½S� þ Kappð1Þ

where

Vmax

½E�T¼ kcat ¼

kþ2kþ3

kþ2 þ kþ3ð2Þ

and

Kapp ¼ðk21 þ kþ2Þ

kþ1·

kþ3

ðkþ2 þ kþ3Þð3Þ

Integration of Equation (1) when Kapp greatly exceeds[S ] give the following solution

½P�t ¼ ½S�0·ð1 2 ek obs ·½E�T ·tÞ ð4Þ

where

kobs ¼kcat

Kapp¼

kþ1kþ2

k21 þ kþ2ð5Þ

For acetylthiocholine, direct estimates of kþ2 andkþ3 for electric eel AChE, gave11 a kþ2/kþ3 ratio of 1.3.Inserting this ratio into Equation (2), where kcat hasbeen known for a long time,8 gives an estimation ofthe kþ2 constant higher than 3·104 s21: This value alsoexceeds8,12 k21 and from this point of view it can beassumed that at low substrate concentrations ð½S� !KappÞ; kobs in Equation (4) is app. kþ1 which meansthat the rate limiting step is the entry into the activecenter of AChE where every substrate molecule isalso metabolized.13 Following this explanation, thereaction mechanism for the inhibition of AChE byeseroline at sufficiently low substrate concentrationscan be represented by Scheme (2)

where EI is an AChE-Ese reversible complex, Irepresents Ese, and both hydrolytic products aredenoted as P1,2. The differential equations of time-dependent quantities shown in Scheme 2 are asfollows:

d½E�

dt¼ 2kon·½I�·½E� þ koff ·½EI�

¼ 2kon·½I�·½E� þ koff ·ð½E�T 2 ½E�Þ ð6Þ

d½S�

dt¼ 2kobs·½E�·½S� ð7Þ

Equation (6) is a separable ordinary first-orderlinear differential equation and is therefore simplysolved. It should be remembered that initialconditions are different (i) for case A where thereaction is started by the addition of enzyme into themixture containing the substrate and the inhibitorand (ii) for case B where the enzyme is preincubatedwith the inhibitor and the reaction is started by theaddition of substrate.Case A

½E�t¼0 ¼ ½E�T ð8Þ

Case B

½E�t¼0 ¼KI½E�T

ðKI þ R½I�Þð9Þ

where [E ]T and [I ] are total final enzyme andinhibitor concentrations, respectively. KI and Rare the equilibrium constant (koff/kon) and dilutionfactor.

SCHEME 1

SCHEME 2

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Solutions of Equation (6) for both cases are:Case A

½E�t ¼koff ½E�T

ðkon½I� þ koff Þ1 þ

½I�

KIe2ðkon½I�þkoff Þt

� �ð10Þ

Case B

½E�t ¼koff ½E�T

ðkon½I� þ koff Þ1 þ

½I�ð1 2 RÞ

ðKI þ R½I�Þe2ðkon½I�þkoff Þt

� �

ð11Þ

Inserting these two equations into Equation (7)gives final solutions describing the product for-mation during the reaction processCase A

ln 1 2½P�t½S�0

� �

¼ 2kobskoff ½E�Tðkon½I� þ koff Þ

£ t þ½I�

KIðkon½I� þ koff Þð1 2 e2ðkon½I�þkoff ÞtÞ

� �ð12Þ

Case B

ln 1 2½P�t½S�0

� �¼ 2

kobskoff ½E�T

ðkon½I� þ koff Þ

£ t þ½I�ð1 2 RÞ

ðKI þ R½I�Þðkon½I� þ koff Þ

�

£ 1 2 e2ðkon½I�þkoff Þt� ��

ð13Þ

For clarity, Equations (12) and (13) are given inlogarithmic form. It should be emphasized that bothequations hold only for classical inhibitors when freeand total inhibitor concentrations are assumed to beequal. Progress curves for case A (Equation 12) areconcave downward curves and often do not deviateobviously from the single exponential function(see Figure 1A). On the other hand, progress curvesfor case B (Equation 13) are sigmoid and thusprovide more reliably the information on the earlystages of the reaction. A special case is when ½I� ¼ 0where progress curves described by both Equations(12) and (13) reduce to Equation (4). Informationabout the kinetic rates of inhibitor action on anenzyme catalysed reaction is included in the shortperiod of time during the equilibration between theenzyme and inhibitor. Unfortunately, progresscurves obtained at various inhibitor concentrationsare not equally useful for the analysis. Sigmoidalityis inhibitor-dependent (see Figure 1B). Consequently,an interesting question arises: what might be thecriterion for the determination of the “quality” oftransient phase information? In practice, thereliability of the analysis would increase if the timeof the inflexion point (t*) as well as the change ofabsorbance were well within the range of the

detection method. Mathematically, the compromisebetween the two excluding demands can be achievedby maximizing a line integral L of the curvature kt

multiplied by [P ]t, along the curve connecting originðt ¼ 0Þ and the inflexion point ðt ¼ t* Þ: The curvatureof the progress curve at any point is a measure of thesigmoidality, while the amount of product formed([P ]t) is responsible for efficient and reliabledetection. Calculations of L can be obtained uponintegration of kt·½P�t along the path of integration (C):

L ¼

ðC

kt·½P�tds ð14Þ

where kt and [P ]t are the curvature and theconcentration of product at any time, while ds isthe linear element of the curve (reference14, see alsoAppendix).

EXPERIMENTAL PROCEDURES

Chemicals

Acetylcholinesterase (AChE, EC 3.1.1.7) from Elec-trophorus electricus, acetylthiocholine (ATCh) and

FIGURE 1 (A) Single exponential functions (lines) fitted onsimulated progress curves calculated according to Equation (4),Equation (12) and Equation (13) (dots) (ET ¼ 0:7 nM; kobs ¼3·108 M21 s21; kon ¼ 5·106 M21 s21; koff ¼ 0:5 s21; ½I� ¼ 0:5mM).(B) Simulated progress curves calculated according to Equation(13) at various inhibitor concentrations (the same parameters asunder (A) but ½I� ¼ 0; 0:5; 1:0; 1:5; 2:5 and 5.0mM ).

KINETIC RATES FOR ACHE-ESEROLINE INTERACTION 281

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5,50-dithio-bis-nitrobenzoic acid (DTNB, Ellman’sreagent) were purchased from Sigma Chemical Co.(St.Louis, U.S.A.). (2 )-Eseroline-(3aS-cis)-1,2,3,3a,8,8a-hexahydro-1,3a,8-trimethylpyrrolo-[2,3-b]indol-5-ol (Ese) fumarate was from Research BiochemicalInternational (Natick, U.S.A.).

Enzyme active sites concentration was indepen-dently estimated by pseudoirreversible titration,according to the procedure described previously.3

For prevention of eseroline oxidation to theo-quinone derivative, rubreserine, the stock solutionof the inhibitor was prepared freshly before theexperiments.4 All experiments were carried out at258C in a buffer solution prepared according toBritten and Robinson15 (a mixture of 25 mMphosphoric, acetic and boric acids and 75 mMsodium hydroxide) with a pH of 8.0 and a totalionic strength of 0.2 M, obtained by the addition ofNaCl. All reagents and salts were of analytical grade.

Kinetic Measurements

Rapid spectrophotometric measurements of acetyl-thiocholine hydrolysis catalysed by acetylcholine-sterase were carried out on a Hi-Tech (Salisbury, UK)PQ/SF 53 stopped-flow apparatus connected to aSU-40 spectrophotometer and Apple E-II microcom-puter. A theoretical dead time of 0.7 ms had beenstated by the manufacturer for the mechanical part ofthe apparatus.

The kobs value was independently determined byexperiments done in the absence of Ese. Briefly,aliquots of two solutions, one containing the enzymeand the other containing ATCh and DTNB, weremixed together in the ratio 1:15 in the mixingchamber of the instrument. The absorbance of thereaction mixture was recorded according to Ellmanet al.16 at 412 nm in a sweep from zero to 20 s and from20 s to 140 s. All progress curves reached the plateausduring that time. The time course of productformation was followed at various fixed finalconcentrations of the substrate (1mM–5mM ) atleast 10 times lower than Kapp.

For the determination of the kinetic constants kon

and koff, the experiments were carried out by asimilar procedure. The only difference was in thepreincubation of the enzyme with various concen-trations of Ese (0.5mM–5mM ) before mixing thesolution with the substrate and DTNB. The lattermeasurements were done in the presence of a 5mMsubstrate concentration. Final concentrations ofAChE active sites and DTNB were 0.69 nM and1 mM, respectively.

Data Analysis

Evaluation of the corresponding kinetic para-meters was carried out in two subsequent steps.

(i) The determination of kobs was done by fittingEquation (4) to the progress curves obtained at threedifferent substrate concentrations in the absence ofEse. (ii) The progress curve data in the presence ofEse were used to evaluate the two rate constants kon

and koff using Equation (15) (rearranged Equation 13,see Appendix). All computations were performedwith a modified non-linear regression computerprogram originally written by R.G. Duggleby.17

The values of evaluated kinetic parameters werecrosschecked by a numerical integration treatment.18

The relationships between the kinetic constants,experimental conditions, and the quality of theinformation on the transient phase in each individualprogress curve were also analysed. This was carriedout to check the suitability of individual chosenexperimental conditions ([I ]) under which theprogress curves were measured. The inhibitorconcentration dependence of t*, ½P�t¼t* and L werecalculated applying Equations (21), (15) (Appendix)and Equation (14), respectively. t* and ½P�t¼t* areexplicit analytical functions of [I ], whereas theintegral in Equation (14) has no general analyticalsolution. It was solved numerically using a Mathe-matica software package.19

RESULTS AND DISCUSSION

The time course of product formation in thehydrolysis of acetylthiocholine by AChE in theabsence of eseroline is shown in Figure 2A. It shouldbe emphasized that the measurements were per-formed at very low substrate concentrations (1mM–5mM ) while the concentration of DTNB was threetimes higher than in the original recipe for thecolorimetric determination of acetylcholinesteraseactivity described by Ellman et al.16 Under suchconditions, the progress curves in the absence ofinhibitor follow a single exponential function, asseen from the fitting of Equation (4) to theseexperimental data. On the basis of this informationwe can conclude the following: (i) the time course ofproduct formation at lower substrate concentrationrepresents the appropriate final portion of the curveobtained at the higher substrate concentration (usingup to 5mM initial substrate); (ii) the fact thatEquation (4) can be fitted to all curves in Figure 2Aindicates that the intermediates ES and EA do notaccumulate during the reaction with substrateconcentrations of up to 5mM. Scheme 2 is thusjustified. (iii) The non-sigmoidal shape of progresscurve(s) in the absence of inhibitor is evidence thatthe sigmoidality is introduced only by the additionof Ese and that the detection reaction does not distortthe effect of the inhibitor.20 The rate of the detectionreaction is DTNB dependent and for this reasonwe performed the experiments at 1 mM DTNB

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concentrations. The value of the evaluated rateconstant kobs ¼ ð3:43 ^ 0:04Þ·108 M21 s21; obtainedby the fitting of the data in Figure 2A to Equation(4) is in good agreement with the values foundpreviously.18,21,22

Figures 2B,C show progress curves for thehydrolysis of 5mM ATCh in the presence of variousEse concentrations. They were all obtained after 16fold dilution of Electric Eel AChE preincubated with0–5mM Ese. The uppermost, concave downwardcurve, is in fact the uppermost curve from Figure 2Awithout Ese, and the others were measured in thepresence of increasing Ese concentrations. They are

concave upwards up to the inflexion point andconcave downwards after the inflexion (see alsoExperimental Procedures). As mentioned, the reasonfor the sigmoidal shape is not a slow detectionreaction20 but the rather slow approach of theenzyme-inhibitor system from an initial equilibriumto a new one. Fortunately, this re-equilibration isslow enough to be detected on a stopped-flowapparatus. The fitting of Equations (4) and (13) to allmeasured data yielded both characteristic rateconstants from Scheme 2: an eseroline associationrate constant kon ¼ ð5:17 ^ 0:03Þ·106 M21 s21 anddissociation rate constant koff ¼ ð0:538 ^ 0:003Þ s21:The good agreement of the theoretical curves withthe experimental data also confirms the competitionbetween the substrate and the inhibitor at the activesite, as suggested by the model in Scheme 2. It is areasonable conclusion supported by the molecularmodel of eserine docked in the active site of Torpedocalifornica AChE which shows that the bulky rings ofeserine completely fill the space around the activecenter.23 Nevertheless, we tried to fit our experimen-tal data to other kinetic models proposing partialcompetition but they did not work.

The comparison of two rate constants with thevalues of the analogous constants for eserine revealsextremely interesting information: while the affi-nities of Electric Eel AChE for eseroline ðKI ¼

0:10mMÞ and eserine ðK1 ¼ 0:47mMÞ are very similar,the rates of association and dissociation are some twogrades of magnitude higher for eseroline thaneserine ðkon=kþ1 ¼ 135; koff=k21 ¼ 30Þ: This calls foran answer to the following question: what might bethe reason for the large difference in rate constantsfor eseroline and eserine but with only slightdifferences in the affinity constants for the twoenzyme-inhibitor complexes? In order to putforward an adequate explanation, one must takeinto account two points. First, from the structuralstudies it is known that eseroline and carbamoyl-eseroline derivatives accomodate at the acylation siteof cholinesterases;24 additionally, the shape and thesize of these ligands together with sub-micromolaraffinities appear to be indirect evidence. Second, thevery low ligand concentrations used in our experi-ments appear to exclude multiple binding in spite ofrelatively high ligand/enzyme ratios. All thesewould undermine the steric hindrance hypothesissimilar to the mechanistic interpretation of AChEinhibition by peripheral site ligands suggested bySzegletes et al.22 On the contrary, it seems that a smallN-methyl-carbamyl group plays an important role inthe gliding of eserine through the AChE’s active sitegorge and is only a minor obstacle in the aquisition ofthe Michaelis-Menten complex formation.25,26 Anonly slightly decreased affinity in the case of eserinepoints to a minimal difference between the transi-tion-state like binding pattern of eseroline and

FIGURE 2 Progress curves for the hydrolysis of acetylthiocholineby electric eel AChE: (A) at various substrate concentrations(1mM–5mM ) in the absence of eserolin, (B) at 5mM substrateconcentration and various inhibitor concentrations(0,0.5,1.2,1.8,3.0 and 5.0mM ), (C) the same as under (B) but atlower time/product ranges.

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the Michaelis–Menten complex in the case ofeserine. On the other hand, gliding is substantiallyimpaired by the great mobility of the carbamoyl tail(unpublished quantum mechanical computationdata) as well as by its numerous possible interactionswith the residues lining the gorge.

Finally, we would like to discuss the reliability ofthe evaluated kinetic parameters. Our analysisdemonstrates that progress curve measurements atoptimal conditions provide useful information on thetransient phase, from which kinetic parameters canbe evaluated. One of the most easily changedvariables is the inhibitor concentration and it shouldtherefore be chosen very carefully. Figure 3 showsvarious possible approaches for the optimization ofthe experimental design using the dependence ofparameters t*, ½P�t¼t* and the line integral L (seeTheory and Appendix) on the inhibitor concentrationas possible criteria. Each of them might be thecriterion for the reliability of progress curves inparticular situations. It is obvious from Figure 3 thatin the case of Electric Eel AChE and Ese, thenormalized parameter t* is poorly inhibitor concen-tration dependent. On the other hand, the normalizedparameters ½P�t¼t* and L possess more expressivepeaks. These peaks are optima which indicate atwhich inhibitor concentration the progress curveshave the most useful information of the transientphase. Indeed, the parameter L is more appropriatethan ½P�t¼t* but unfortunately cannot be expressed as

an analytical mathematical function. The arrows inFigure 3 show the inhibitor concentrations performedin our study. It can be seen that the lowest inhibitorconcentration used is also the optimal one. The samecan also be observed by inspecting diagram C inFigure 2 where the progress curve marked by thearrow displays the most pronounced sigmoidalshape and consequently gives the deepest insightinto the structure of the data.27

Finally, we must emphasize once again that ouranalysis is valid only for classical inhibitors ð½I�t ¼½I�TÞ and non-cooperative substrates. If these basicassumptions are violated, as with very potentinhibitors, a different treatment must be applied.28

For this reason the vertical line in Figure 3 indicatesthe inhibitor concentration where the ratio [I ]/[E ] is10. Above this ratio the inhibitor can be treated asclassical.

The introduced method for determining kineticrates of eseroline action on AChE seems perhapscomplex in view of data analysis but it does retainsome advantages in comparison to other directmethods that call for much higher enzymeconcentrations.

Acknowledgements

This work was supported by the Ministry ofEducation, Science and Sport of the Republic ofSlovenia (Grant P3-8720-0381 to J.S.).

FIGURE 3 Inhibitor concentration dependence of normalized parameters (A) t*=tmax* ; (B) ½P� t¼t*=½P�t¼t* ðmaxÞ and (C) L/Lmax. The arrowsshow inhibitor concentrations used in experiments. The vertical line inside the graph marks where the concentration equals 10·½E�T :

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APPENDIX

After the rearrangement of Equation (13), thefollowing equation describes the time course ofproduct formation:

½P�t ¼ ½S�0ð1 2 e2av

tþbvð12e2vtÞ

� �Þ ð15Þ

where

a ¼ kobskoff ½E�T ð16Þ

b ¼½I�ð1 2 RÞ

ðKI þ R½I�Þð17Þ

v ¼ kon½I� þ koff ð18Þ

It should be remembered again that Equation (15)holds only when the inhibitor acts by classicalmeans.

The second derivative of function [P ]t must bezero at the inflexion point. A rearranged equation½P�00t ¼ 0 gives the quadratic equation

a2

v2ð1 þ bxÞ2 þ abx ¼ 0 ð19Þ

where x ¼ e2vt* and t* is time at which the inflexionpoint occurs. Equation (19) gives two solutions but t*is positive:

e2vt* ¼2ð2aþ v2Þ þ v

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4aþ v2

p

2abð20Þ

or

t* ¼ 2ln 2ð2aþv 2Þþv

ffiffiffiffiffiffiffiffiffiffiffi4aþv 2

p

2ab

� �v

ð21Þ

The line integral given in Equation (14) can bewritten as

L ¼

ðt*

0

kt·½P�t·

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ ½P�

02t

qdt ð22Þ

where kt is defined as

kt ¼½P�00t

ð1 þ ½P�02t Þ

32

ð23Þ

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