Kinetic characterization of all steps of the interaction between acetylcholinesterase and eserine

E L S E V I E R Biochimica et Biophysica Acta 1337 (1997) 75-84

BIO( 'HIMI( 'A ET BIOPt lYSICA ACIA

Kinetic characterization of all steps of the interaction between acetylcholinesterase and eserine

Jure Stojan *, Matja~ Zorko Institute of Biochemist~', Medical Faculty, UniL,ersity of Ljubljana, Vrazo~' trg 2, 61000 Ljubljana, Slovenia

Received 13 May 1996; revised 20 August 1996; accepted 3 September 1996

Abstract

The three-step carbamylenzyme mechanism of the action of eserine on acetylcholinesterase (acetylcholine acetylhydro- lase, EC 3.1.1.7) has been known for a long time, but its complete kinetic characterization has never been done. Some of our investigations indicated that the determination of missing kinetic parameters should include the inspection of the enzyme-eserine interaction in a very wide range of eserine concentrations. Therefore, the activity of acetylcholinesterase as a function of time in the presence of low concentrations of eserine comparable to the enzyme concentration was followed. The reaction mechanism was analysed by fitting numerically integrated differential equations that describe the time dependences of all reactants and reaction intermediates to these data. Additionally, the progress curve measurements at higher eserine concentrations were carried out on a stopped-flow apparatus. The corresponding progress curve equations were derived and the kinetic parameters evaluated by non-linear regression treatment. The complex analysis confirmed the three-step mechanism. The values of the constants showed that the very high affinity of eserine for binding into the active centre of the enzyme is not so much a consequence of the fast initial complex formation but rather a consequence of its slow dissociation. The subsequent covalent bonding of eserine is also slow, but faster than the dissociation of the initial complex. In this manner, the decarbamoylation is the only process responsible for the reactivation of acetylcholinesterase after removal of eserine.

Keywords: Acetylcholinesterase; Acetylcholinesterase-eserine interaction; Eserine; Kinetic analysis; Rate constant

1. In troduct ion

It is known that carbamates inhibit acetylcholinesterase (ACHE) by binding covalently to the serine residue in the esteratic site of the enzyme. The three step reaction mechanism which includes enzyme-

carbamate complex formation, carbamoylation, and subsequent decarbamoylation of the enzyme was pro- posed in the early 60's [1-3]:

C~ H20

Scheme A

" Corresponding author. Fa:~: +38661 1320016 In this reaction scheme, E and C are the free

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76 J. Stojan, . Zorko / Bioc'himic'a et Biophysica Acta 133 7 t 1997) 75- 84

enzyme and eserine, respectively, EC is the complex between enzyme and eserine, EC* is the carbamoylated enzyme and C t, C 2 are the hydrolytic products of eserine; k+~, k ~, k,~,_ and k+~ are the corresponding rate constants.

The reaction scheme, which has been proven to be appropriate for carbamates [4-6], is essentially analogous to the scheme for the reaction between AChE and the substrates (cf. [4]). However, the very small value of k+~ makes carbamates effective inhibitors of this enzyme. The decarbamoylation characterized by k+ 3 is slow enough that it can be independently investigated and is therefore the best clarified step in this interaction [2,7]. On the other hand, apparently strong and fast formation of the complex and its subsequent fast conversion into the carbamoylated enzyme makes the characterization of these two steps much less reliable, and the separation of the velocity constants difficult. This seems to be especially true for eserine, which is one of the most effective carbamates and has often been used as a diagnostic reagent for this enzyme [4]. Therefore, many studies of the interaction between eserine and AChE were performed (cf. [2,6,8,9]). In these studies, however, enzyme-carbamate complex formation was treated as an instantaneous step, characterized by K~ (K i repre- sents k i l k+ ~ in reaction scheme (A)). The determination of rate constants k+~ and k j has thus never been done for eserine nor for any of its analogues.

Some of our investigations on the action of various ligands on ACHE, as in the case of eserine, reveal that the determination of the missing kinetic parameters should include inspection of the enzyme-eserine interaction in a wide range of eserine concentrations. The experiments were performed with very low eserine concentrations - - i.e., under conditions in which the decrease of ligand concentration during the reaction with the enzyme is significant. In a separate experiment high eserine concentrations were used, which called for a rapid reaction technique. The consistent analysis of the experimental data obtained under all these different conditions is intricate. We present our experimental approach to the investigations under specified conditions and propose the corresponding analysis to quantitatively characterize all steps of the reaction between AChE and eserine. Such an approach can also be applied to other similar c a s e s .

2. Materials and methods

2.1. 7~tration experiments

To estimate the concentration of AChE active sites in the incubation mixture and to prove that this concentration is comparable to the concentration of eserine, the so-called pseudo-irreversible titration (Ackermann-Potter plot [10,1 !]) was used. Varying amounts, 10 to 150 /,tl. of AChE stock solution with the approximate activity of 200 /~mol/min per ml were incubated with eserine at fixed concentrations of 0, 50 nM, or 300 nM in a buffered solution in a total volume of 500 /xl (the incubation mixture). Alter the incubation periods in two parallel experiments for 30 or 45 min, an aliquot of the incubation mixture was tested for AChE residual activity.

2.2. Dilution experiments

The activity of the residual free enzyme portion after various times of incubation with eserine was measured as follows. Various amounts, between 10 to 60 ~1, of enzyme stock solution were incubated with concentrations of eserine from 8.3 nM to 300 nM in a buffered incubation mixture with a total volume of 500 p,l. After time intervals of zero to 180 min, aliquots of the incubation mixture were tested for AChE residual activity. The zero-time activity in the presence of eserine in each experiment was in fact measured after approx. 7 s of incubation due to technical manipulations. The activity, however, was always the same as in the control experiment without eserine, but the delay of 7 s became important with concentrations of eserine above ! /zM.

2.3. Progress curces measurement.s"

The effect of high eserine concentrations on the time-course of the product formation in the hydrolysis of ASCh by AChE was followed on a stopped-flow apparatus. Progress curves were recorded until the rate of increase in absorbance become constant. The final concentrations of eserine were, respectively, 0.5, 1, 2, 3, 4, 5, 10, 20, 30, 40 and 50 p,M.

J. Stojan, . Zorko / Biochimica et Biophysica Ac'ta 1337 (1997) 75-84 77

2.4. Enzyme actiL~ity determination

AChE activity was assayed photometrically by the method of Ellman et al. [12]. In titration and dilution experiments the reaction was started by the addition of 10 /zl of the incubation mixture to 3 ml of buffer solution containing ASCh and 5,5'-dithio-bis-nitro- benzoic acid (DTNB) in final concentrations of 0.5 mM and 0.33 mM, respectively. It took approx. 4 s to start measuring activity which was then recorded lk)r 30 s. In progress curves measurements equal amounts of the two solutions, one containing the enzyme and the other one eserine, ASCh and Ellman's reagent, were mixed together in a stopped-flow apparatus with the theoretical dead time of 0.7 millisecond. The final concentration of substrate was 0.1 mM, low enough to prevent substrate inhibition; the concentration of DTNB was 0.33 mM.

2.5. Materials

Experiments were done at 25°C in buffer solution prepared according to Britten and Robinson [13] with a pH of 8.0 and a total ionic strength of 0.2 M, obtained by addition of NaC1. The enzyme used was Electric Eel ACHE, purchased from Sigma, Poole, UK (Lot# 128F8040, 1580 uni ts /mg protein). ASCh iodide, DTNB (Ellman's reagent) and eserine were from BDH Biochemical.~,. All substances were reagent grade. Enzyme activity measurements were performed on a Beckman spectrophotometer DU 7500 and on a stopped-flow apparatus PQ-SF 53, manufac- tured by High-Tech, Salisbury, UK.

3. Theory and data analysis

Inspection of the shal~es of the experimental curves in the titration and dilution experiments proved our presumption that the concentrations of AChE and eserine in the incubation mixture were comparable. Therefore, the quantitative analysis of the experimental data in dilution experiments had also to take into account the depletion of eserine during the reaction with the enzyme.

The explicit solution of the system of non-linear differential equations a,zcording to reaction scheme

(A), is not possible; a numerical treatment of experimental data had to be applied. A modified non-linear regression computer program developed by Yamaoka and Nakagawa [14] was used. This program is able to fit the numerically integrated differential equations which yield the concentrations of the free enzyme portion as a function of time, to the time-course of the experimentally determined free enzyme activities. According to reaction scheme (A) the data from dilution experiments represent the time-course of AChE activity, reflecting alteration of the concentration of free enzyme after various times of incubation with eserine. It was important at this point to recog- nize from which enzyme species in reaction scheme (A) the free enzyme portion originated during the activity measurements in our experimental conditions. Depending on the relative magnitudes of the corresponding rate constants, three cases are possible: first, if the complex EC dissociates fast enough, both E and EC are included; second, if EC dissociates very slowly, only E is included; and finally, the intermedi- ate situation is possible, where the dissociation of EC is in progress during the activity measurement.

The only way to discover which of the three cases is appropriate is to test all of them. The first two were tested by fitting numerically integrated differential equations yielding (E) or (E) + (EC), respectively, as the concentration of free enzyme portion to the experimentally determined residual enzyme activities in dilution experiments. In addition to the four rate constants, k+ ~, k_ ~, k+2, and k+3, there was also the initial concentration of the enzyme, (E) o, in each dilution experiment which was set as a fitting parameter. (E) 0 must be well established for two reasons: (i) the residual activities after various times of incubation with eserine depend strongly on the total amount of the enzyme and (ii) it also serves as a cross proof that the initial concentrations of AChE obtained by fitting correspond to their ratios according to the dilutions used. Since we used an iterative fitting procedure, the initial estimates for each initial concentration of the enzyme active sites were determined in two independent ways. The first used the active-site activity (given by [4] as 12000 s - I ) and the specific activity (1580 U / m g protein) and the second the analysis of pseudo-irreversible titration experiments. The other boundary conditions at t = 0 were always set to ( E C ) = 0, ( E C * ) = 0, (C n) = 0,

78 J. Stojan. . Zorko / Biochimica et Biophysica Acta /337 ( 19971 7.5-84

(C 2) = 0. (C)() was set to the initial concentration of eserine.

The third case was also considered; this by the evaluation of the shapes of progress curves obtained in the activity measurements. If the dissociation of the complex EC is in progress during the activity measurement, upward concave curves are expected; otherwise the measured product formation should be linear in time.

Since the results of the above analysis suggested that complex EC in dilution experiments does not accumulate to a significant extent, the obtained values for the rate constants k ,. j, k_ t, and k, ~ appear uncertain. To verify the assumption that EC does not accumulate, the mechanism in reaction scheme (A) was reduced as tbllows:

E÷C ~ B~' - - -~ E+Cz H20

Scheme B

k i in this scheme can be expressed by the rate constants from reaction scheme (A) (of. [15,16]):

k+jk,2 k i= k_, +k+~ (1)

The values of k i and k,3 were determined by simultaneous fitting numerically integrated differential equations of the reduced mechanism (reaction scheme (B)) to the experimentally determined enzyme activities obtained in dilution experiments.

The reaction in the presence of higher eserine concentrations, however, can only be accomplished by using a rapid reaction method such as stopped- flow. In this case the progress curves are measured in the presence of substrate which, of course, must be introduced into reaction scheme (B).

p + E ,~k--k ES K~-~,~S + E + C - ~ EC"[,~E+C2 C, H~O

Scheme C

S and P represent the substrate and the product, ES is the instantaneously formed complex between AChE and ASCh, K~ is Michaelis constant for ASCh under

the equilibrium assumption and k is overall rate constant for the transition of ES into E and P.

Under such conditions the concentration of eserine always greatly exceeds the concentration of the enzyme. If the reaction is measured where no substrate depletion is observed, the following explicit progress curve equation is valid (of. [15]):

AV,,(S) P,= [Ks+(S)]B2(1-e-m) +

V.(S)k, 3 [ K s + ( s ) ] g t

(2)

(C)oKs a = k i Ks + (S) (2a)

B = A + k+3 (2b)

However, in the case of EC accumulation at high eserine concentrations the experimental data should deviate from the theoretical curves of Eq. (2) but not from those curves calculated from an analogous equation derived (cf. [15,17]) from a system which allows for the accumulation of the EC complex:

C, H20

Scheme D

Vo(S)[PQ(C + k+ 3) - k, 3C(P + Q)] Pt =

[Ks+(S)]p2Q 2

Vo( S)k+ 3C + t

[K s + (S)] PQ

Vo(S)[P~-- P(C + k+ 3) + k+ 3C]

[ K s + ( S ) I P 2 [ P - Q ] - P t

e

+ V0(S)[Q2 _ Q(C + k+3) + k+3C] e -0 '

[Ks+ (S)]Q2[ P - QI

C=k_ l +k+ 2

( C)o Ks D=k+l Ks+(S)

P = C + D + k + 3

Q = ( k 4 2 "q- k + 3 ) O .-.{- ( k _ l Jr" k + 2 ) k + 3

(3)

(3a)

(3b)

(3c) (3d)

J. Stojan, . Zorko / Biochimica et Biophysica Acta 1337 (1997) 75-84 79

The evaluation of kinetic parameters was performed in three subsequent steps. In the first, the four parameters in Eq. (2) - - V o, K s , k i, and k 3 - were determined by simultaneous fitting of Eq. (2) to the experimental progress curves in the absence and in the presence of lower eserine concentrations using a modified non-linear least-squares regression computer program developed by Duggleby ([18]). In the next step the progress curves in the presence of higher eserine concentrations were fitted to Eq. (3). Here there are six kinetic parameters to be estimated but the previously determined K s, k+ 3, and k i w e r e

set as constants, k, was actually used to express k+2 by rearranging Eq. (1). Thus, only three parameters, k , ~, k_ I, and V 0 remained to be evaluated. General criteria for the goodness of fit were used throughout the analysis ([19]). Finally, the obtained values of all four rate constants from reaction scheme (A) were used to simulate the theoretical curves in dilution experiments by numerical integration.

In this way we evaluated the unique set of kinetic parameters which corresponded to all our experimental data.

4. Results

4.1. Estimation of the concentration of AChE active sites

Varying concentrations of enzyme were incubated with eserine in different fixed concentrations until an apparently constant residual activity of AChE was achieved. It is important to emphasise that the progress curves (not shown) from which the residual activities of AChE were determined were always linear. The corresponding plot of the obtained residual activity expressed as a function of the total enzyme concentration is shown in Fig. 1.

It can be seen from this figure that the residual

¢

c

,D

>

E N C

2.0

1.0

B

C

- - / / I I I

0 50 tO0 15_o

E n z y m e c o n c e n t r a t i o n [ I J L of s tock s o l . / 5 0 0 U L1 I I ! I

0 5 0 100 150 2 0 0

E n z y m e c o n c e n t r a t i o n I N N ' ]

Fig. I. The dependence of the residual activity of acetylcholinesterase in the absence and presence of eserine as a function of the total enzyme concentration. A, without eserine; B, 50 nM eserine + incubation time 30 min; C, 50 nM eserine + incubation 45 rain; D, 300 nM eserine + incubation time 30 min; E, 300 nM eserine + incubation time 45 min. Note that all activity measurements were carried out in Ellman's solution after a 300-fold dilution of the incubation mixture.

80 Y. St~jan. . Zorko / Biochimica et Biophysica Acta 1337(1997) 75-84

activity of AChE in the presence of eserine increases nonlinearly with the increasing total enzyme concentration. In general, such shapes of the curves are diagnostic of tight-binding conditions [10] here prov- ing that the enzyme and eserine in the incubation mixture are present in comparable concentrations. More precisely, the linear extrapolations of curves B and C through the two last points (dashed line) parallel line A. Their intersections with the x-axis represent equimolar concentrations of eserine and AChE active sites [10,11]. Thus, we can estimate that approx. 40 p,l of stock solution diluted to the final volume of 500 p,l corresponds to the concentration of AChE active sites of 50 nmol / l in the incubation mixture, as seen from the x-axis double notation in Fig. I. The obtained value is in good agreement with the value calculated from active-site activity and the specific activity of the enzyme used. So in all further

experiments the initial estimate of the enzyme initial concentration, (E) o, was set according to this value and the dilution used (Fig. 2). Note that from double notation of the x-axis and from the slope of line A in Fig. 1, the enzyme active-site concentration can be estimated directly from the enzyme activity measurement performed under conditions specified in Section 2.4, the section on enzyme activity determination.

4.2. Time-dependent residual actiL'ity studies

The results of dilution experiments are summarised in Fig. 2. It is evident from this figure that maximal inhibition is achieved after approx. 30 min and that with low eserine concentrations (A-D) a progressive recovery of enzyme activity can be observed. It is important to remember that the points in each picture are experimental but the curves are theoretical. It

o

0

~ cO~ .q ........ o .... "

- ~ o ......... --- -'"

o • ¢ ¢ ..+e~

B

o o . . • • "a-.~ + .r. ~"+. ~:" .y , s " " " ~ ' ,~" -9 .+ * . . " r '+-" , ' " • - " .

p

o

%

~ o , ..+~ r ~o

C:

F

I I

0 7200 t Es'l

Fig. 2. Time-course of the residual activity of different concentrations of acetylcholinesterase after various times of incubation with eserine in various concentrations. The concentrations of eserine and acetylcholinesterase active centres were: A, 8.3 riM, 23.8 riM; B, curve a: 16.7 nM, 22.5 nM and curve b: 16.7 nM, 5.6 nM; C, 33.3 nM, 17 riM; D, 50 nM, 9.3 nM; E, 100 nM, 3.8 nM; F, 300 riM, 9.1 riM, respectively. The curves in each diagram are theoretical, calculated by numerical integration of differential equations for the system in reaction scheme (A), yielding (E) as a free enzyme portion; the values of k + l, k I, k_ 2, and k + s from Table I were used in the simulation. Note the effect of enzyme concentration on the time-course of the residual activity in diagram 2.

J. Stojan. . Zorko / Biochimica et Biophysica Acta 1337 (1997) 75-84

Table 1 Characteristic rate constants for the interaction of eserine with acetylcholinesterase

81

Data from k, x 1 0 - 4 M - t s I k_l X 1()-4 M - i s - ~ k _ l x 102s i k+2X 102 s - i k_3 X 1()4 s - t

Dilution experiments 2.67 + 0.14 " 3.80 + 0.22 " Progress curves (low eserine) 2.66 _- 0.41 b 6.05 + 0.13 h Progress curves (high eserine) 3.81 + 0.03 ~ 1.80 -4- 0.14 " 4.18 ,t

Listed are the values obtained by the analysis of data in dilution experiments and from progress curve measurements at low and high eserine concentrations.

Obtained by fitting numerically integrated differential equations for the system in reaction scheme (B), yielding (E) as a free enzyme portion to the experimental points in Fig. 2. b Obtained by fitting the Eq. (2) to all experimental data in Fig. 3 simultaneously.

Obtained by fitting the Eq. (3) to all experimental data in Fig. 4 simultaneously. o k. _~ was set as a non-fitting parameter expressed by rearranging Eq. (1). using the previously determined value of k,.

must be emphasized that almost identical curves can be obtained with different sets of rate constants k+ ~, k_~, and k+2 and with lhe unique value of k+3. The

same result was also found if in the fitting of numerically integrated differential equations for reaction scheme (A), (E) or (E) + (EC) was set as a concentra-

6.250

A

=E - '1

qD o Q.

A /" B

C

E - I

0 Time (sec.) 4 8 0

Fig. 3. Time-course of the pr,~uct formation in the hydrolysis of acetylthiocholine by acetylcholinesterase in the absence and presence of low eserine concentrations. Concentrations of eserine were: A, zero: B, 0.5 /.tM; C, I /xM; D. 2 /.tM; E, 3 /zM; F, 4 /xM; G, 5 /xM; H. 10 /zM; I. 20 p,M. The concentration of acetylthiocholine was 0.1 mM. Dotted curves are reproductions from the original hardcopies of the experimental data obtained by a stopped-flow apparatus. The curves are shifted to give a common origin at P¢t=0~ = O. Solid curves are theoretical, obtained by fitting Eq. (2) to all experimental data simultaneously.

~2 J. St~?jan, . Zorko / Biochimica et Bi~q~hysica Acta 1337(1997) 75-84

tion of the free enzyme portion. On the other hand, the values of (E) o, also the fitting parameters, were in all cases practically the same as their initial estimates which were calculated as described above.

All of these strongly indicate that the EC complex in dilution experiments does not accumulate, thus making the values of the three rate constants k+~, k_~, and k 4 ~ uncertain. Moreover, the analogous analysis of the reduced system (reaction scheme (B)) resulted in very reliable determination of k i and k~ 3 (see Table 1).

4.3. Progress curt'es studies

The results of the progress curve measurements are summarised in Figs. 3 and 4. In both figures it can be

seen that all progress curves have the same initial slope. The fitting of Eq. (2) to the experimental points in Fig. 3 yielded the following values for the kinetic parameters: k~ = 2.67 + 0.41 × 104 M -~ s - t , k~3 = 6 . 0 5 + 0 . 1 3 × 10 -4 S l and K s = 134_+48 /xM. Note that the values of k~ and k+, are the same as the corresponding values from dilution experiments (Table !). Progress curves obtained with much higher eserine concentrations in the same procedure (Fig. 4) failed to give a good fit of Eq. (2) to the experimental data. Introducing Eq. (3), however, a very reliable fit was obtained (see Table 1). Another graphical presentation of the adequateness of these four constants and that according to reaction scheme (A) can be seen in simulated theoretical curves through the experimental points in dilution experiments (Fig. 2).

0.735

A :E

"o o a.

0 "

~ q

0

0

t • C

* D

0 T ime (sec.) 20

Fig. 4. Time-course of the product formation in the hydrolysis of acetylthiocholine by acetylcholinesterase in the absence and presence of high eserine concentrations. Concentrations of eserine were: A, zero; B, 10 ~M; C, 20 /zM; D, 30 gM; E, 40 gM; F, 50 /xM. The concentration of acetylthiocholine was 0.1 mM. Dotted curves are reproductions from the original hardcopies of the experimental data obtained by a stopped-flow apparatus. The curves are shifted to give a common origin at P(,= o~ = 0. Solid curves are theoretical, obtained by fitting Eq. (3) to all experimental data simultaneously.

J. Stojan, . Zorko / Biochimica et Biophysica Acta 1337 (1997) 75-84 83

5. Discussion

In order to monitor all steps of the interaction between eserine and ACHE, the time-course of this interaction should be followed until the conversion of eserine into its hydrolytic products is almost com- pleted. Therefore, relatively low concentrations of eserine as well as relattvely high concentrations of AChE were applied. Under such conditions the non- linearity of the pseudo-irreversible titration plot (Fig. 1) confirmed that the enzyme and the ligand are in comparable concentrations, resulting in the depletion of both free enzyme and eserine. Additionally, the depletion of eserine is enhanced by its enzymatic degradation (see reaction scheme (A)). The shapes of the curves A - D in Fig. 2 show that stable residual enzyme activity is not achieved. The ascending parts of the curves are a direct demonstration of eserine degradation. On the other hand, curves E and F in Fig. 2 show that at higher eserine concentrations a steady state is achieved. The absence of the ascending parts in these curves indicates that the degradation of eserine does not influence the achieved steady-state during the experimental time used. Of course, the ascending pattern had to be observed at longer incubation times but the time-dependent insta- bility of AChE [20] prevents its detection. Numerical simulation of curve F from Fig. 2 (not shown), using the values of rate constants from Table 1, reveals the ascending pattern only after about 20 h. A similar shift of the ascending part of the curve toward longer incubation times, however, can also be accomplished by using a lower enzyme concentration when eserine is present in the same initial concentration. Such a shift can be clearly seen when comparing both curves in Fig. 2B.

As pointed out previously, the results of the fit- tings based on (E) or (E) + (EC) as the free enzyme portion yielded practically the same values for all kinetic constants in reaction scheme (A). Having this in mind the most reasonable explanation is that during the time-course of the reaction only a very small portion of enzyme is in EC form. Further proof for this explanation is the successful analysis of the data in dilution experiments using the reduced reaction mechanism (reaction scheme (B)). Besides, it is evident from Table 1 that the same result in terms of rate constants was obtair~ed by the analysis of progress

curves in Fig. 3. It must be stressed that both types of experiments were performed under essentially different conditions (see Section 2). Such a finding could lead to the conclusion that in both cases the system represented in reaction scheme (B) is operating, thus indicating that the carbamoylation of AChE by eserine is a single step process. The experimental data in progress curves with very high eserine concentrations (Fig. 4) show, however, that this is not the case. The simplest model which corresponds to these data re- quires a three step reaction mechanism according to reaction scheme (A). As a matter of fact, reaction scheme (B) can be used for each individual progress curve, but the obtained values of the rate constants, except k+ 3, are dependent on the eserine concentration. On the other hand, the values of the four rate constants according to reaction scheme (A) and Eq. (3) are eserine concentration independent (cf. [21]), and the obtained set is in full agreement with the experimental data in dilution experiments (see theo- rctical curves in Fig. 2).

To some extent unexpected is that the binding of eserine to AChE - - i.e., the k+~ step - - is so slow. The second-order rate constant is on the order of 10 4

M-~ s-n, which is four to five orders of magnitude slower than the estimated binding rate constant for the natural substrate and for some reversible inhibitors [22]. If eserine were to act with a comparably fast rate, an instantaneous inhibition phase should be observed even when if the experiments had been performed on a high-performance stopped-flow apparatus with a dead time of less than 1 millisecond. Figs. 3 and 4 prove that this is not the case. The observed relatively slow action might be explained by the shape and the dimensions of the eserine molecule [23] which are comparable with the dimensions of AChE gorge [24]. In this way a diffusion rate limited accommodation of eserine in the gorge cannot be achieved. An instantaneous phase, however, was observed with butyrylcholinesterase, a similar enzyme with wider gorge [25].

In conclusion, let us try to describe the interaction of eserine with AChE in terms of the magnitudes of the four obtained rate constants according to the three step reaction mechanism (reaction scheme (A)). In spite of unexpectedly slow complex formation (k+l) in the first step, the affinity of eserine for the binding into the active centre is very high (K i = k _ ~ / k + i).

84 J. Sto.jan. . Zorko / Biochimica et Biophy~ica Acta 1337 (1997) 75-84

The small 0.43 /zM K~ is predominantly a consequence of very slow dissociation of the EC complex ( k ~). The second step, the covalent bonding of eserine to AChE (k, 2), is also slow. It is, however, faster then the dissociation of EC, thus being responsible for the prompt conversion of EC into the carbamoylated form E C ' . In this way, the third step (k+3) is practically the only process which accounts lbr the reactivation of AChE after the removal of eserine.

Acknowledgements

This work was supported by the Ministry of Sci- ence and Technology of the Republic of Slovenia, grant No.: P3-5298-0381, 1995. The authors are in- debted to Mrs. Klavdija Makovec and Mrs. Nevenka

v

Klenovgat-Spat for their valuable technical assistance.

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