Damped oscillatory hysteretic behaviour of butyrylcholinesterase with benzoylcholine as substrate Patrick Masson 1 , Boris N. Goldstein 2 , Jean-Claude Debouzy 3 , Marie-The ´ re ` se Froment 1 , Oksana Lockridge 4 and Lawrence M. Schopfer 4 1 Centre de Recherches du Service de Sante ´ des Arme ´ es (CRSSA), De ´ partement de Toxicologie, Unite ´ d’Enzymologie, La Tronche, France; 2 Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Moscow, Russia; 3 CRSSA, Unite ´ de Biophysique, La Tronche, France; 4 University of Nebraska Medical Center, Eppley Institute, Omaha, NE, USA Steady-state kinetics for the hydrolysis of benzoylcholine (BzCh) and benzoylthiocholine (BzSCh) by wild-type human butyrylcholinesterase (BuChE) and by the peripheral anionic site mutant D70G were compared. k cat /K m for the hydrolysis of BzSCh was 17-fold and 32-fold lower than that for hydrolysis of BzCh by wild-type and D70G, respectively. The rate-limiting step for hydrolysis of BzCh was deacyla- tion, whereas acylation was rate-limiting for hydrolysis of BzSCh. Wild-type enzyme and the D70G mutant were found to reach steady-state velocity slowly with BzCh as the substrate. At pH 6, the approach to steady-state for both enzymes consisted of a mono-exponential acceleration upon which a set of damped oscillations was superimposed. From pH 7 to 8.5, the approach to steady-state consisted of a simple exponential acceleration. The damped oscillations were analyzed by both a numerical approximation and simulation based on a theoretical model. BuChE-catalyzed hydrolysis of the thiocholine analogue of BzCh showed neither lags nor oscillations, under the same conditions. The frequency and amplitude of the damped oscillations decreased as the BzCh concentration increased. The appar- ent induction time for the exponential portion of the lag was calculated from the envelope of the damped oscillations or from the smooth lag. Wild-type BuChE showed a hyperbolic increase in induction time as the BzCh concentration increased (s max ¼ 210 s at pH 6.0). However, the induction time for D70G was constant over the whole range of BzCh concentrations (s max ¼ 60 s at pH 6.0). Thus, the induction time does not conform to a simple hysteretic model in which there is a slow conformational transition of the enzyme from an inactive form E to an active form E¢.No pH-dependence of the induction time was found between pH 6.0 and 8.5 in sodium phosphate buffers of various concentrations (from 1 m M to 1 M ). However, increasing the pH tended to abolish the oscillations (increase the damping factor). This effect was more pronounced for D70G than for wild-type. Although the lyotropic proper- ties of phosphate change from chaotropic at pH 6.0 to kosmotropic at pH > 8.0, no effect of phosphate con- centration on the oscillations was noticed at the different pH values, suggesting that the oscillations are not related to a pH-dependent Hofmeister effect of phosphate ions. Simulation and theoretical analysis of the oscillatory behaviour of the approach to the steady-state for BuChE led us to propose a model for the hysteresis of BuChE with BzCh. In this model, the substrate-free enzyme is present as an equilibrium mixture of two forms, E and E¢. Substrate binds to E and E¢, but only E¢ S makes products. It is proposed that oscillations originate from a time-dependent change in the local concentration, solvation and/or con- formation of substrate in the bulk solution. 1 H-NMR measurements provided evidence for a slow equilibrium between two BzCh conformers. Binding of the conforma- tionally preferred substrate conformer leads to products. Keywords: benzoylcholine; butyrylcholinesterase; damped oscillations; hysteresis; slow conformational change. Butyrylcholinesterase (BuChE, EC 3.1.1.8) is a serine esterase closely related to acetylcholinesterase (AChE, EC 3.1.1.7). AChE plays a central role in the cholinergic system by terminating the action of acetylcholine in synapses, but so far no clear function has been assigned to BuChE. However, several lines of evidence indicate that BuChE could be involved in the development of the nervous system and in neurodegeneratives diseases [1]. In addition, studies on the tissue distribution of BuChE combined with the fact that AChE knock-out mice survive in the complete absence of AChE suggest that BuChE may function in cholinergic nerve signal transmission as a surrogate esterase for acetylcholine [2,3]. It is also a toxicologically and pharmacologically relevant enzyme because it hydrolyzes Correspondence to P. Masson, CRSSA, De ´ partement de Toxicologie, Unite ´ d’Enzymologie, BP 87, 38702 La Tronche cedex, France. Fax: + 33 4 76 63 69 62, Tel.: + 33 4 76 63 69 59, E-mail: pymasson@compuserve.com and pmasson@unmc.edu Abbreviations: AChE, acetylcholinesterase; BuChE, butyrylcho- linesterase; BuSCh, butyrylthiocholine; BzCh, benzoylcholine; BzSCh, benzoylthiocholine; NMIA, N-methylindoxyl acetate; PAS, peripheral anionic site. Enzymes: butyrylcholinesterase (EC 3.1.1.8); acetylcholinesterase (EC 3.1.1.7). (Received 14 September 2003, revised 7 November 2003, accepted 14 November 2003) Eur. J. Biochem. 271, 220–234 (2004) Ó FEBS 2003 doi:10.1046/j.1432-1033.2003.03924.x various ester-containing drugs (e.g. cocaine, heroin, succi- nylcholine, aspirin) [4], and scavenges poisonous carbamyl and organophosphate esters [5]. A truncated, monomeric form of human BuChE was recently crystallized [6]. Reso- lution of its X-ray crystallographic structure at 2 A ˚ [7] confirmed that its structure is very close to that of AChE [8,9]. In addition, unexpected electronic density attached to the catalytic serine (S198) of native BuChE was modelled as a bound butyrate. Cholinesterases have been known for a long time as enzymes that do not follow Michaelis–Menten kinetics with positively charged substrates such as choline and thiocholine esters. Both enzymes display inhibition and/or activation by excess substrate, depending on the pH [10–12] or medium conditions [13]. There is evidence that a conformational change induced by transient binding of substrate on a peripheral anionic site (PAS) causes these catalytic com- plexities. Additional kinetic complexities such has a nonlin- ear temperature dependence have also been shown [14,15]. Moreover, human BuChE [16] was found to reach steady- state velocity (v ss ) slowly with the neutral ester N-methyl- indoxyl acetate (NMIA) as substrate. The time course for release of product P 1 throughout the lag phase was described by the simple, mono-exponential, integrated-rate equation (Eqn 1): ½P 1 ¼½v ss t Àðv ss À v i Þð1 À e Àkt Þ=k ð1Þ 1 where v i is the inititial velocity and k the induction rate constant. The maximum induction time, s ¼ 1/k, for wild- type BuChE was found to be 15 min [16]. This transient is too slow to be involved in establishing the Michaelis– Menten steady-state. Indeed, the transient pre-steady-state half-time for hydrolysis of NMIA can be estimated to be less than 0.38 ls (Appendix 1). Thus, the BuChE induction period was interpreted in terms of hysteresis. The concept of hysteresis in enzymology was developed by Frieden [17], Neet & Ainslie [18] and Kurganov et al. [19]. The hysteresis of BuChE with NMIA can be described by Scheme 1. In Scheme 1, E and E¢ aretwostatesoftheenzyme,whichare in slow equilibrium; k 0 and k )0 are the first-order rate con- stants for the reversible transition E !  E¢. K¢ s ¼ k )1 /k 1 is the dissociation constant for substrate binding to E¢ (assu- ming that k 1 [S] + k )1 ) k 0 + k )0 ). E¢Sistheenzyme– substrate complex that makes products P (P 1 and P 2 ,cf. Appendix 1) through acylation k 2 (E¢S fi E¢A+P 1 ), and deacylation k 3 (EA fi E¢ +P 2 ). The substrate depend- ence of the hysteretic rate constant is described by Eqn (2): k ¼ k 0 þ k À0 =ð1 þ½S=K 0 s Þð2Þ In Scheme 1, it is assumed that only E¢ canbindsubstrate and make products and that the resting enyzme is essentially all in the E form. These assumptions derive from the fact that hysteresis with NMIA starts at zero activity [in Eqn (1), v i ¼ 0]. Slow transient kinetics of BuChE with NMIA were therefore interpreted in terms of a slow conformational transition from an inactive form E to an active form E¢ preceding substrate binding [16]. This scheme provides a good description of the behaviour of BuChE with NMIA. However, substrates such as butyrylthiocholine (BuSCh) show no hysteresis. This observation can be accommodated ifbothEandE¢ have the same affinity for BuSCh and make products at the same rate; then the two enzyme forms would be indistinguishable and no hysteresis would appear in product accumulation curves. The existence of two, active, interconvertible forms of the enzyme may also explain nonlinearity in Arrhenius plots of BuChE-catalyzed reactions [14] and thermal inactivation kinetics [20] with wave-like transitions around the break point [20,21]. Complex progressive inhibition processes may also be explained by an equilibrium between two enzyme forms. For example, photo-induced carbamoylation of BuChE by N-methyl-N-(2-nitrophenyl)carbamoyl chloride was found to follow biphasic kinetics. However, X-ray diffraction data revealed that the active site serine was the sole target of N-methyl-N-(2-nitrophenyl)carbamoyl chlor- ide [22]. A similarscenario appears to exist forAChE. Results from several groups indicate that this enzyme is composed of two discrete forms in slow conformational equilibrium and that ligands of the PAS bind only to one form [23,24]. Hysteresis of BuChE was accompanied by large negative values of activation entropy and activation volume [25]. We have provided evidence that hysteresis is not a property of the PAS [16]. However, the hysteretic behaviour of the enzyme can be altered by mutation in the PAS and by hydrostatic pressure and lyotropic salts. These observations suggest that the hydration status of the catalytic gorge modulates the slow conformational transition that leads to hysteresis. Hysteresis may originate from isomerization of the free enzyme (E to E¢) and/or the enzyme–substrate complex (ES to E¢S). Formation of E¢S by either pathway triggers the catalytic cycle. Hysteresis of wild-type BuChE and certain mutants has also been observed with other substrates [16,25]. In this report, the catalytic properties of human BuChE with benzoylcholine (BzCh) and benzoylthiocholine (BzSCh) are compared. The wild-type enzyme and its D70G mutant display hysteretic behaviour with BzCh but not with BzSCh. A careful analysis of the hysteretic kinetics of BzCh hydrolysis showed that for certain conditions of pH, salt concentration, and substrate concentration, an oscilla- tory lag (up to 4 min) precedes establishment of the steady- state. Under these conditions, the induction process cannot be described by a simple, mono-exponential kinetic model; rather, the approach to steady-state follows an exponential acceleration which is overlaid with damped oscillations. Materials and methods Chemicals Benzoylcholine chloride (BzCh) was purchased from Sigma France (Saint-Quentin-Fallavier, France). Benzoylthiocho- Scheme 1. Ó FEBS 2003 Oscillations in butyrylcholinesterase hysteresis (Eur. J. Biochem. 271) 221 line iodide (BzSCh) was from NCI (Tokyo, Japan). Chlorpyrifos-oxon was obtained as standard grade from Cluzeau (Sainte-Foy-la-Grande, France). Heavy water (D 2 O; 99.998 atom 2 H) was from Eurisotope (Saint-Aubin, France). Other chemicals were of biochemical grade. Enzyme sources Wild-type human BuChE was from plasma or was expressed in CHO K 1 cells [26]. Recombinant wild-type enzyme and the PAS mutant, D70G, were made and expressed in stably transfected CHO K 1 cells, as previously described [26]. Tetrameric forms of natural and recombin- ant wild-type enzyme and D70G mutant enzymes were highly purified by ion-exchange chromatography and affinity chromatography on procainamide gel, as described [26]. Kinetic measurements Hydrolysis of BzCh. BuChE-catalyzed hydrolysis of BzCh was assayed at 25 °C in sodium phosphate buffer of various molarities (from 1 m M to 1 M ) and different pH values (from 6.0 to 8.5). The BzCh concentration ranged from 1 to 150 l M . The active site enzyme concentration in the assay was 31.5 n M for wild-type enzyme and 25 n M for D70G. The hydrolysis kinetics were followed by recording the decrease in A 240 (De ¼ 6700 M )1 Æcm )1 in phosphate) for 5–10 min. Preliminary analysis showed that the induction time, s, with BzCh as substrate was much shorter than with NMIA [16]. Moreover, with NMIA and BuSCh, it was found that s increased with decreasing pH [25]. Therefore, to make s observable for a longer period, most assays were carried out in 67 m M phosphate, pH 6.0. Hydrolysis of BzSCh. BzSCh hydrolysis by wild-type enzyme and its D70G mutant was assayed at 25 °Cin sodium phosphate (10, 67, 100 and 500 m M )atdifferentpH values (6.0, 7.0, 7.4 and 8.0). The BzSCh concentration range was 1 l M to 10 m M . Hydrolysis of BzSCh was followed by the method of Ellman et al.[27]with0.33m M 5,5¢-dithiobis(2-nitrobenzoic acid) as the chromogenic rea- gent. The increase in A 420 due to the appearance of 5-thio- 2-nitrobenzoate was recorded. 5-Thio-2-nitrobenzoate is the product of reduction of 5,5¢-dithiobis(2-nitrobenzoic acid) by thiocholine, the hydrolysis product P 1 .Themolar absorption coefficient (e) of 5-thio-2-nitrobenzoate at 420 nm is 12 500 M )1 Æcm )1 at pH 6.0, 13 200 M )1 Æcm )1 at pH 7.0, and 13 300 M )1 Æcm )1 at pH 8.0. Determination of steady-state catalytic parameters. As described in the Introduction, BuChE-catalyzed hydrolysis of positively charged substrates such as BzCh and BzSCh does not follow Michaelis–Menten kinetics. There is inhibition or activation by excess substrate, depending on the pH [11]. Steady-state kinetics of positively charged substrates can be conveniently described by Scheme 2 and Eqn (3). In Scheme 2, the complex S p E corresponds to S bound to the PAS. When the first substrate molecule is bound to the catalytic binding site, a second substrate molecule can bind to the PAS to form the ternary complex S p ES. v ¼ k cat ½E 1 þ K m =½S 1 þ b½S=K ss 1 þ½S=K ss  ð3Þ with k cat ¼ k 2 k 3 ðk 2 þ k 3 Þ ð3 0 Þ and K m ¼ K s k 3 ðk 2 þ k 3 Þ ð3 00 Þ K s is the dissociation constant of the ES complex, k 2 is the acylation rate constant, and k 3 is the deacylation rate constant. In Eqn (3), K ss is the dissociation constant of complexes S p E and S p ES(K ss > K m ). The parameter b reflects the efficiency by which S p ES forms products. Substrate activation occurs when b >1;whenb <1there is substrate inhibition; the enzyme obeys the Michaelis– Menten model if b ¼ 1. The steady-state catalytic parameters, K m , K ss , k cat and b factor for hydrolysis of BzCh and BzSCh were determined by nonlinear computer fitting of Eqn (3) using the SIGMA PLOT 4.16 program (Jandel Scientific, San Raphael, CA, USA). The enzyme active site concentration, [E], was determined by titration by the residual activity method, using chlorpyrifos-oxon as titrant [28]. Analysis of transient kinetics for BuChE-catalyzed hydro- lysis of BzCh. The transient kinetics of substrate hydrolysis were analyzed by following the slow exponential increase in product P 1 release over 20–90 min. The induction rate constant, k, was determined by nonlinear regression fitting of the progress curves to Eqn (1), using the SIGMA PLOT 4.16 software. Induction time s ¼ 1/k. The asymptote of the curves, i.e. when the steady-state was reached, is [P 1 ] ¼ v ss (t ) s). The effect of substrate concentration, pH and the molarity of the buffer salts on the induction time was investigated at 25 °C. The pH was varied from 6.0 to 8.5. The phosphate concentration in the buffers varied from 1m M to 1 M . The BzCh concentration in the assays varied from 2.5 to 125 l M ; and the concentration in BzSCh varied from 5 l M to 1 m M . As the approach to the steady-state could not be explained by the simple mono-exponential process described by Eqn (1), under certain conditions of pH, substrate concentration and buffer salt concentration, a numerical method was used to fit the curves. The method is described in Appendix 2. In addition, a kinetic analysis of the enzyme oscillatory regimen was performed using the graph–theory method [29]. This method allowed us to predict oscillatory behaviour by inspecting the structure of the kinetic scheme [30]. Scheme 2. 222 P. Masson et al.(Eur. J. Biochem. 271) Ó FEBS 2003 Nonlinearity in the system was necessary for oscillatory behaviour to occur. A computer solution of the differential kinetic equations was used to simulate the experimental data. NMR measurements 1 H-NMR spectra of BzCh solutions (BzCh was in 0.1 M phosphate buffer prepared in D 2 O, pD ¼ 6.4; pH ¼ pD ) 0.4) were recorded at 25 °ConanAM400Brukerspectro- meter with presaturation of the solvent. A total of 32 000 data points were acquired on a 10 p.p.m. spectral width. The number of acquisition scans (% 2 s per scan) was increased with dilution (from 32 for the 10 m M solution to 12 000 for the 10 l M solution). Results and discussion Steady-state hydrolysis of BzCh vs. BzSCh BzCh has long been known as a good, positively charged substrate for BuChE [4]. Steady-state kinetic analysis carried out in 67 m M phosphate buffer, pH 7.4, at 25 °Cgave K m ¼ 3 l M , k cat ¼ 245 s )1 for wild-type enzyme, and K m ¼ 21 l M , k cat ¼ 250 s )1 for the D70G mutant (Table 1). These values are in accordance with previously reported data determined under similar conditions [26]. The values of K m for BzSCh (2.8 l M for wild-type and 59 l M for D70G) were very similar to those for BzCh. However, BzSCh was hydrolyzed at a much lower rate than BzCh: k cat ¼ 13.3 s )1 for wild-type and 21.6 s )1 for D70G (Table 1). Thus, compared with BzCh, BzSCh appears to be a poor substrate. This conclusion is supported by the specificity constants, k cat /K m ¼ k 2 /K s , for wild-type and D70G hydrolysis of BzSCh, which are smaller than those for BzCh by 17-fold and 32-fold, respectively. These ratios are similar to the ratio (k cat /K m ) ester/thioester of 52 for the hydrolysis of (–)-cocaine [31] and (–)-thiococaine [32] by wild-type enzyme, at 25 °C. The cocaine esters are the bulkiest benzoyl ester and thioester compounds hydrolyzed by this enzyme. At pH 7.4, wild-type BuChE is inhibited by excess BzCh and BzSCh (b < 1). However, at pH < 7.0, both sub- strates show substrate activation (b > 1) (Table 2). This shift from substrate inhibition to substrate activation was also seen by Kalow for the hydrolysis of BzCh by wild-type human enzyme (Fig. 2 in [33]). Hydrolysis of BuSCh by the human BuChE mutant A328W also showed this pH-dependent shift [11], as did hydrolysis of acetylthiocho- line by AChE from both human and Bungaras fasciatus [10]. Taken together, these observations support the idea that a pH-dependent shift between substrate activation and sub- strate inhibition is a general property of positively charged substrates reacting with cholinesterases. Rate-limiting step of BzCh and BzSCh hydrolysis Krupka [34] and Froede & Wilson [35] have shown that for AChE, the hydrolytic rate of good substrates is limited by deacylation whereas that of poor substrates is limited by acylation. This can also be demonstrated for BzCh and BzSCh reacting with BuChE, as follows. BzCh and BzSCh lead to the same benzoyl–enzyme intermediate (EA), there- fore deacylation for both reactions occurs with the same rate constant (k 3 ). BzCh is the better substrate of the pair, based on its better specificity constants (Table 1). Glaubiger [36] has shown that deacylation is partly rate-limiting for hydrolysis of BzCh by wild-type enzyme (k 3 ¼ k 2 ) and fully rate-limiting (k 3 << k 2 ) for D70G, as predicted for a good substrate. Indeed, with BuSCh, deacylation is partly rate limiting for wild-type and fully rate-limiting for D70G [37]. With BzSCh, k cat is much lower than k cat for BzCh (18-fold with wild-type and 12-fold with D70G). As k 3 did not change, the decrease in k cat must reflect a decrease in k 2 . From the large decreases in k cat , it follows that the rate- limiting step has become acylation (k 2 << k 3 ) for both enzymes, and, therefore, k cat ¼ k 2 for BzSCh hydrolysis with both enzymes, as expected for a poor substrate. Table 1. Steady-state catalytic parameters and apparent induction times for hydrolysis of BzCh and BzSCh by wild-type human BuChE and its D70G mutant in 67 m M sodium phosphate pH 7.4 at 25 °C. Values are mean ± SE from three independent determinations. BzCh BzSCh Wild-type D70G Wild-type D70G K m (l M ) 3.00 ± 0.3 21.1 ± 4.9 2.84 ± 0.3 59.2 ± 2.4 k cat (s )1 ) 245 ± 7 250 ± 16 13.3 ± 1.3 21.6 ± 0.83 10 6 · k cat /K m ( M )1 Æs )1 ) 81.6 ± 10.3 11.8 ± 3.5 4.7 ± 0.9 0.366 ± 0.03 b 0.4 ± 0.1 1 0.3 ± 0.1 1 K ss (m M ) 0.5 ± 0.1 – 3.7 ± 0.5 – s max (s) a 210 ± 15 60 ± 15 0 b 0 b < DG à E fi E¢ > (kJÆmol )1 )86 83 – – [BzCh]-dependence of k Decrease No – – a s max ¼ 1/k lim for [BzCh] > 40 m M ; b Induction time was not detectable under current experimental conditions. Table 2. pH-dependence of k cat and b factor for hydrolysis of BzCh and BzSCh by wild-type BuChE in 0.1 M sodium phosphate at 25 °C. pH BzCh BzSCh k cat (s )1 ) bk cat (s )1 ) b 6 83 1.8 2.2 2.5 7 250 a 0.46 a 10.2 1.15 8 367 0.4 16.3 0.25 8.5 ND ND 23.3 0.1 a Experimental values were taken from [26]. Ó FEBS 2003 Oscillations in butyrylcholinesterase hysteresis (Eur. J. Biochem. 271) 223 Values of k 2 and k 3 were calculated for the reactions of BzCh with wild-type and D70G. These calculations used Eqns (3¢)and(3¢¢) together with measured values for K m and k cat , and estimated values for K s .AsestimatesofK s ,theK i values for benzoylcholine amide, a competitive inhibitor and steric analogue of BzCh, taken from Glaubiger [36] (K i ¼ 14.1 l M and 556 l M for wild-type and D70G, respectively) were used. The resultant values were k 2 ¼ 980 s )1 and k 3 ¼ 330 s )1 for wild-type and k 2 ¼ 5830 s )1 and k 3 ¼ 270 s )1 for D70G (Table 3). These values are similar to those obtained by Glaubiger and support the statement that k 3 is partially rate-limiting in the wild-type enzyme reaction and completely rate-limiting in the D70G reaction. Next, values of k 2 , k 3 ,andK s for the reactions of BzSCh with wild-type and D70G were determined. The k 3 values were taken to be the same as those for BzCh, as both substrates generate the same benzoyl–enzyme intermediate. The k 2 values were taken to be the same as k cat ,ask cat was much smaller than k 3 , and the decreases in k cat between BzCh and BzSCh could only have resulted from decreases in k 2 . Using these values for k 2 and k 3 , along with the measured values for K m ,Eqn(3¢¢) was used to calculate reasonable estimates of K s . Calculated values of K s , k 2 and k 3 for hydrolysis of BzCh and BzSCh by both enzymes are giveninTable3. Lower limit estimates for k 1 were also calculated. It was assumed that substrate binding was rapid, therefore k )1 ) k 2 .AsK s ¼ k 1 /k )1 , it followed that k 1 > k 2 /K s . Using values of k 2 and K s from Table 3, estimates of k 1 for BzCh were determined for wild-type enzyme, k 1 >70· 10 6 M )1 Æs )1 and for D70G, k 1 >10.5· 10 6 M )1 Æs )1 (Table 3). Similar calculations were made for BuSCh. The actual values of k 1 have to be higher than the respective k cat / K m values (Table 1). The minimum value of k 1 is about 7–10-fold higher for wild-type than for D70G. k 1 for wild- type is high because of an initial interaction of substrate with the functional PAS. The lower k 1 for D70G reflects the absence of that interaction in this mutant. Moreover, k -1 for D70G is thought to be faster than for wild-type because the gorge entrance is larger and the conformational plasticity of the gorge is better in the absence of a functional PAS [16,44]. The limiting values for k 1 and k )1 are consistent with the current understanding of the structure of the active-site gorge of cholinesterases and with the mechanism of binding of positively charged ligands/substrates by these enzymes [7,8,26]. The large decrease in the k 2 /k 3 ratio on going from BzCh to BzSCh is unprecedented. Earlier reports by Hillman & Mautner [38], Bretskin 2 et al. [39], and Froede & Wilson [35] have demonstrated that substituting sulfur for oxygen in the ethereal position of acetylcholine, propionylcholine, and butyrylcholine will cause the k 2 /k 3 ratio to decrease, but to a much lower extent. The reported decrease becomes larger as the size of the substrate increases [39], and is further enhanced if selenium is substituted for oxygen instead of sulfur [38]; but in none of the reported instances, does k 2 become rate limiting. It seems evident that the sulfur (selenium) imposes constraints on the formation of the acylation tetrahedral intermediate, and that those con- straints become more restrictive as the size of the substrate increases. With BzSCh, it would seem that the substrate is large enough to reduce k 2 to the point where acylation finally becomes rate limiting. It is likely that acylation is also rate limiting in the formation of (–)-thiococaine, which is even larger than BzSCh. This prediction is supported by the large ratio of (k cat /K m ) ester/thioester for the (–)-cocaine/(–)- thiococaine couple. What properties of sulfur might contribute to a decrease in the acylation rate? The size of the sulfur atom is larger than that of the oxygen atom: van der Waals radii are 0.18 nm and 0.14 nm, respectively. This should introduce a steric constraint into the formation of the acylation transition state. The Pauling electronegativity of sulfur is less than that of oxygen: 2.5 and 3.4, respectively. Thus the energy needed to break a C–O bond is % 350 kJÆmol )1 compared with 260 kJÆmol )1 for a C–S bond. This factor should actually make acylation easier. Still, overall, the atomic properties of sulfur are thought to slow down the reactions leading to acylation of BuChE by BzSCh. This can be attributed to the following factors: (a) steric factors may radically affect the conformation of the BzSCh molecule compared with that of BzCh; (b) steric and electronic effects of the ethereal sulfur will perturb adjustment and hydrogen- bonding of the carbonyl oxygen in the oxyanion hole (NH groups of residues G115, G116 and G117 in human enzyme), thus increasing the acylation reaction barrier. (For more information on the role of the cholinesterase oxyanion hole, see [40,41]; (c) both the tetrahedral transition state and the tetrahedral adduct would be less stabilized. Computational modelling of the acylation transition state by quantum mechanical calculations should verify or disprove these contentions. Hysteresis with BzCh but not with BzSCh As with NMIA, BuChE-catalyzed hydrolysis of BzCh was found to present a slow hysteretic phase preceding the steady- state. Thus, hysteresis of the enzyme is not restricted by neutral substrates such as NMIA. The lag (s)withBzChwas long enough to be seen under standard assay conditions. However, the transient phase was more complex than with NMIA. At selected substrate concentrations and/or pH values, lags overlaid with damped oscillations replaced the simple lags normally seen. When oscillations were seen, there were typically three to four damped oscillations with increas- ing period (T ) over the whole induction time (Figs 1 and 2) 3 . No lags or oscillations were seen for hydrolysis of the homologous thioester, BzSCh, by either wild-type or the Table 3. Estimates of constants involved in the hydrolyic turnover of BzCh and BzSCh by wild-type BuChE and D70G mutant. BzCh BzSCh Wild-type D70G Wild-type D70G K s (l M ) 14.1 a 556 a 3.3 67 k 2 (s )1 ) 980 5800 13 22 k 3 (s )1 ) 330 270 330 270 10 6 · k 1 ( M )1 Æs )1 ) b ) 70 ) 10.5 ) 4 ) 0.3 a Values taken from Glaubiger [36]. b Substrate binding was reduced to a single step and assuming k )1 ) k 2 . 224 P. Masson et al.(Eur. J. Biochem. 271) Ó FEBS 2003 D70G mutant, under the same conditions. It is also noteworthy that BuChE-catalyzed hydrolysis of neither butyrylcholine nor BuSCh presented a lag. However, hysteresis was reported for hydrolysis of BuSCh by some mutants of the active site [25]. This indicates that the hysteretic behaviour of BuChE depends on both the structure of the enzyme and the chemical structure of the substrate. Modulation of hysteresis Mutation in the peripheral anionic site. The PAS mutant, D70G, displayed hysteretic behaviour with BzCh, which was similar to that found with wild-type. However, at saturating substrate concentration, s max was about threefold shorter for D70G than for wild-type (Table 1). These results show that hysteresis does not require interaction of the substrate with the PAS, but that mutation of that site can affect the rate constants for hysteresis. This corroborates previous results obtained from the hysteretic behaviour of wild-type and PAS mutants with NMIA [16]. In general, disruption of the PAS architecture by mutation tends to increase the rate, k, of the hysteretic transition (k is the reciprocal of s), probably by increasing the conformational plasticity of the active-site gorge. pH. The induction time of the hysteresis for BzCh with wild-type and D70G mutant displayed no pH-dependence between pH 6.0 and 8.5. This contrasts with the behaviour of active-site mutants E197Q and A328C with BuSCh and NMIA, which showed increases in induction time as the pH was reduced to pH 4.0 [25]. The absence of effects in this pH range implies that hysteresis of BzCh with wild-type does not depend on ionization of a histidine. Increasing the pH damped the oscillations; this effect was more pronounced for D70G than for the wild-type enzyme. Oscillations in the hysteresis of D70G were almost undetectable at pH > 7, but still detectable with wild-type enzyme. Concentration of buffer salts. We suggested previously that the hysteretic behaviour of BuChE might be related to the structure of water at the enzyme–solvent interface [16]. Indeed, high hydrostatic pressure and highly concentrated, strong kosmotropic salts (water-structure makers) caused decreases in the induction time for hysteresis with NMIA. In addition, a large negative change in the entropy of activation associated with the conversion E fiE¢was calculated (DS „ ¼ )31.5 JÆK )1 Æmol )1 at 25 °C), which may reflect the dominating contribution of a solvation change (increase in local order and local density) to enzyme ÔisomerizationÕ [25]. Additional hydrodynamic changes have been reported for various dynamic processes involving cholinesterases. Molecular dynamics simulations indicated that water mole- cules are displaced from the active-site gorge of cholinest- erases during the catalytic cycle [42,43]. A change in water structure both around amino-acid residues lining the gorge and around substrate/ligand molecules moving down the gorge has been demonstrated using hydrostatic and osmotic Fig. 1. Typical pre-steady-state kinetics curves of wild-type BuChE with BzCh. Reactions were performed at pH 6.0 and 25 °Catdifferentsubstrate concentrations and at different buffer concentrations; (A) [BzCh] ¼ 3.5 l M ,67m M phosphate; (B) [BzCh] ¼ 25 l M ,0.2 M phosphate; (C) [BzCh] ¼ 50 l M ,10m M phosphate; (D) [BzCh] ¼ 100 l M ,0.75 M phosphate. Ó FEBS 2003 Oscillations in butyrylcholinesterase hysteresis (Eur. J. Biochem. 271) 225 methods [44]. Furthermore, motion of water molecules along the pathway of different BuChE-catalyzed reactions has been shown in high-pressure experiments [16,44,45]. To probe the effect of changes in water structure on the hysteresis of BuChE-catalyzed hydrolysis of BzCh, we varied the concentration and pH of the phosphate buffer salts and monitored the hysteretic behaviour of the wild- type enzyme and the D70G mutant. The lyotropic proper- ties of phosphate ions change with the pH. At pH 6.0, 94% of phosphate ions are H 2 PO 4 – , whereas at pH 8.0, 86% of phosphate ions are HPO 4 2– .HPO 4 2– , a large doubly charged anion with high charge density, is one of the strongest kosmotropic salts known, whereas H 2 PO 4 – is a large singly charged anion with low charge density, which has chao- tropic properties (water-structure breaker). The counterion in the buffer, Na + , is considered to be a lyotropically neutral cation. The pH was varied from 6.0 to 8.5, and the phosphate concentration was varied from 0.001 to 1.0 M . There was no significant effect of phosphate concentration on the induction times, the frequency of the oscillations, or the amplitude of the oscillations at any pH between 6 and 8.5. Thus, there were no stabilizing or destabilizing effects on the hysteresis that could be related to a change in the structure of water in the hydration shell of the enzyme active surface. This indicates that the hysteretic behaviour of BuChE with BzCh is not sensitive to changes in the chemical potential of the medium. Dependence of hysteresis on substrate concentration A complete study of the dependence of the hysteretic lags on BzCh concentration was carried out in 67 m M phosphate, pH 6.0. Induction times were calculated from Eqn (1) or Eqn (15) in Appendix 2. In Eqn (15), e –t/a 1 is the envelope of the damped oscillations and the coefficient a 1 is approxi- mately equal to s (Fig. 2). As seen in Fig. 3A, s for wild-type BuChE increased with substrate concentration to a maxi- mum value of 3.5 min (210 s). However, s for D70G appeared to be independent of BzCh concentration (s ¼ 1 min). Owing to uncertainties in the measurement of s for D70G at BzCh concentrations less than 20 l M ,we were unable to determine whether a decrease in s occurred at these concentrations. Scheme 1 adequately describes the hysteretic behaviour of wild-type BuChE with NMIA [16]. However, in Scheme 1, the equilibrium between E and E¢ is the sole determinant of the kinetics of hysteresis. This predicts that all substrates will show hysteresis. Furthermore, Eqn (2) predicts that the limiting rates at high and low substrate concentrations will be k 0 and k 0 + k )0 , respectively, for all substrates. When these predictions were tested by studying additional substrates, the expected results were not obser- ved. For example, results from the current study showed that the hysteretic rate constants for BzCh with wild-type were larger (k 0 ¼ 0.0048 s )1 , k 0 + k )0 % 0.033 s )1 than those for NMIA (k 0 ¼ 0.001 s )1 , k 0 + k )0 % 0.003 s )1 [16]). This is contrary to the prediction. The values at low substrate concentration (k 0 + k )0 ) are not reliable, because of the steepness of the curve in that region, which makes extrapolation to zero substrate concentration difficult. Fig. 2. Damped oscillations in the approach to steady-state for D70G. Thereactionwasperformedin0.2 M phosphate, pH 6.0, [BzCh] ¼ 25 l M . The damped oscillation curve fits the equation: Y ¼ )55 (e )t/53 ) 0.02e )t/1000 ){cosp[(t + 10)/(53.4 ) t/18)]}. d [P] is the differ- ence in progress curves between steady-state and pre-steady-state for the formation of choline, the product P 1 of BzCh hydrolysis. dOD is the change in A 240 . The two exponential cuves are the envelopes of damped oscillation curve. Fig. 3. Dependence of the induction time and rate on the BzCh con- centration for wild-type BuChE and the D70G mutant. (A) Dependence of the induction time (s ¼ k )1 ) on the BzCh concentration for wild- type BuChE (d) and the D70G mutant (m)in67m M sodium phos- phate, pH 6.0, at 25 °C and (B) dependence of the induction rate constant k on the BzCh concentration for wild-type BuChE (d)and the D70G (m)mutant. 226 P. Masson et al.(Eur. J. Biochem. 271) Ó FEBS 2003 However, the values at high substrate concentration (k 0 )are well established. This finding argues that the model in Scheme 1 is too simple to explain all of the hysteretic properties of BuChE. Support for this conclusion comes from BuSCh hydrolysis, which showed no hysteresis at all withthewild-typeenzyme.Thusthehystereticrate constants for BuChE are dependent on the structure of the substrate. To accommodate this fact, alternative mech- anisms have to be considered. The next more complicated hysteretic model is the general model proposed by Frieden [17], which is shown in Scheme 3. According to Scheme 3, different substrates may bind exclusively to form E or E¢, or may bind to both forms with equal or different affinities. This model provides sufficient flexibility to accommodate all of the observations for hysteresis with BuChE, as will be described below. First, the Frieden model will be slightly modified to better reflect the situation with this enzyme. In the original Frieden model, substrate bound rapidly to E and E¢. As both ES and E¢S were taken to be catalytically active, some degree of product formation was predicted immediately on mixing substrate with the enzyme. It has already been shown that there is essentially no product formed from NMIA, immediately after mixing [16]. This was attributed to a selective binding of NMIA to the E¢ form, when most of the resting enzyme was in the E form. Thus most of the enzyme would have to undergo the slow, hysteretic transition before becoming catalytically competent. It has also been shown that there is essentially no product formation from BzCh immediately after mixing [16]. However, exclusive binding of BzCh to form E¢ is not consistent with the observed hysteretic rate constants. It follows that BzCh must bind, at least in part, to form E. If the ES complex were catalytically active, this would predict a nonzero rate of product formation immediately after mixing. This was not seen, which indicates that ES is not catalytically active. If it is assumed that only the E¢ form is catalytically active, then Scheme 3 reduces to Scheme 4. k ¼ k 0 þ k es K S ½S 1 þ ½S K S 0 @ 1 A þ k À0 þ k Àes K 0 S ½S 1 þ ½S K 0 S 0 @ 1 A ð4Þ Scheme 4 is described by Eqn (4), which indicates that hysteresis depends on the rate constants of equilibria E !  E¢ and ES !  ¢S. With the use of Eqn (4), the hysteretic observations on BuChE reacting with NMIA [16], BuSCh [25] and BzCh (present work) can all be accommo- dated. For example (a) if substrate binds only to E¢,thenES would not form and hysteresis would be controlled by rate constants k 0 and k )0 . This is the situation described in Scheme 1. Hysteresis of BuChE with NMIA is consistent with this model. (b) If substrate binds exclusively to E, and the transition ES to E¢S is fast, then there would be no hysteresis. This could be the case when wild-type enzyme reacts with BuSCh and BzSCh. It is important to note here that,astheEStoE¢S transition involves an enzyme form in complex with substrate, the rate constants for this transition may vary from substrate to substrate. (c) If substrate binds exclusively to E, and if the ES to E¢S transition is slow, then there would be hysteresis. And, the hysteretic behaviour would be consistent with the previously proposed model that incoporates an Ôinduced fitÕ step [26]. Under such conditions, an increasing dependence of k on substrate concentration from 0 to k ¼ k es + k )es would be expected. So far, such a dependence of k on substrate concentration has only been observed for the A328C mutant with NMIA (unpublished). (d) If substrate binds to both forms E and E¢, thentherewouldbehysteresisandthedependenceofk on substrate concentration would vary with the relative rates of the transitions E to E¢ andEStoE¢S. At low substrate concentrations, the apparent rate constant would approach k 0 + k )0 , and at high substrate concentration the rate constant would approach k es + k )es .Ifk 0 + k )0 > k es + k )es , there would be a positive, hyperbolic dependence; if k 0 + k )0 < k es + k )es , there would be a negative, hyper- bolic dependence. Hysteresis of wild-type with BzCh could be described by this latter condition. If k 0 + k )0 ¼ k es + k )es , there would be no dependence of k on substrate concentration. The latter condition could describe the hysteresis of the D70G mutant with BzCh. Having established Scheme 4 as the hysteretic model for BuChE, analysis of BzCh hysteresis can be undertaken. Figure 3B shows the dependence of the induction rate constants (k ¼ 1/s) on BzCh concentration. Analysis of the wild-type data according to Eqn (4) yields: k 0 + k )0 % 0.033 s )1 and k es + k )es ¼ 0.0042 s )1 .ForD70G,k 0 + k )0 ¼ k es + k )es % 0.016 s )1 . K¢ s values should corres- pond to K s taken from Glaubiger [32], which in Table 3 is 14.1 l M for wild-type and 556 l M for D70G. In the simplest case, if K s ¼ K¢ s , it follows from Eqn (4) that k ¼ (k 0 + k )0 + k es + k )es )/2 when [S] ¼ K s ¼ K¢ s ; then for wild- type, k ¼ 0.019 s )1 and the dissociation constant of ES and E¢S can be estimated graphically from Fig. 3B to be % 5 l M . Analysis of damped oscillations in the approach to the steady-state Oscillations in kinetic behaviour of isolated enzymes have been known for a long time (for reviews see [46,47]). Although damped oscillations in the approach to Scheme 3. Scheme 4. Ó FEBS 2003 Oscillations in butyrylcholinesterase hysteresis (Eur. J. Biochem. 271) 227 the steady-state of single-enzyme systems have been predic- ted and theoretically analyzed by several investigators [29,46–49], so far there are only two experimental reports of such behaviour: acid phosphatase [50] and horseradish peroxidase [51]. Reports of sustained oscillations in enzyme reactions, e.g. peroxidases [51,52], and of oscillatory beha- viour in complex systems are more common: glycolysis, photosynthesis, mitochondrial ion transport, and synthesis of cAMP (see [56] and references therein). The sparsity of experimental observations of damped oscillatory beha- viour makes the current study on BzCh/BuChE relatively unique. We used two methods to analyze the complex hysteretic behaviour of BuChE with BzCh as substrate: numerical approximation and simulation. Numerical approximation. This method was used to determine parameters, e.g. s, of the approach to steady- state and of the damped oscillations (see Appendix 2). For example, Fig. 2 shows damped oscillations in the approach to the steady-state for D70G. The frequency of the first oscillation m 1 (m ¼ x/2p; x is the pulsation factor 2p/T)was 0.012 s )1 for wild-type and 0.019 s )1 for D70G ([BzCh] ¼ 25 l M ,in67m M phosphate, pH 6.0). Interestingly, oscilla- tions were maximal at % 20–25 l M BzCh for both wild-type and D70G. This concentration is approximately equal to K m for D70G and eightfold higher than K m for wild-type. The frequency and amplitude of the oscillations decreased with increasing substrate concentration. Thedifference(d) in progress curves between steady-state and pre-steady-state for the formation of product P 1 (d[P 1 ]) is described by Eqn (15) in Appendix 2. A more convenient form of this equation can be made by removing the constants A, b, K¢ and u: d½P 1 ¼ðe Àt=a 1 À ue Àt=a 2 Þcosp½t=ðc À t=dÞ ð5Þ This facilitates the analysis of the different contributions to this equation. As shown in Fig. 2, the envelopes of the curve can be fitted by the exponential term ± e )t/a 1 .This term was often sufficient to fit the envelope during the 0–400 s preceding establishment of the steady-state and to estimate induction times at different substrate concentra- tions (Fig. 3A). The second contribution deals with later times, where the intensity decreases become smoother, and a partial corrective term, ue )t/a 2 (0<u<1), is required. The significance of this second term remains puzzling. The third contribution cosp(t/c) is related to the periodic oscillation in lineshape. However, the overall lengthening of the oscillation period (T) with time required the introduction of a time-dependent factor (– t/d). The possible significance of the increase in T is discussed in the next sections. Simulation of kinetic models describing damped oscilla- tions. The transient kinetics for hysteretic enzymes are usually described by models using the rapid equilibrium supposition for enzyme–substrate interaction, with slow conformational transitions between the other enzyme forms. These kinetic models predict a simple exponential time-dependence for the transient approach to steady-state. Moreover, these models usually assume that substrate in solution exists as a single species, at approximately constant concentration. The oscillations that overlay the exponential time course for the hysteresis of BzCh reacting with wild-type BuChE induced us to modify the latter assumption. This is because a nonlinearizing factor must appear in the model for oscillations to be observed, and one method of introducing such nonlinearity is to control the rate at which substrate enters the reaction [51]. As substrate molecules in solution can be expected to exist in a variety of conformations, only one of which is suitable for binding to a given enzyme, we reasoned that a slow transition from an unsuitable confor- mation to a suitable one would constitute slow introduction of the substrate into the reaction. Therefore, we modified Scheme 4 to include two different states of the substrate, SandS¢, as shown in Scheme 5. This model is similar to the models proposed by Roussel [51], but differs with regard to the openness conditions for substrate and product, and the presence of two enzyme forms that bind substrate. Substrate form S¢ is assumed to be a minor fraction of the total substrate concentration in the bulk solution. The rate of its appearance in the reaction is controlled by the rate constant k s . We solved the kinetic equations, corresponding to Scheme 5. The following differential equations correspond to the four independent concentration variables: d½E dt ¼Àk 0 ½Eþk À0 ½E 0 Àk 1 ½S 0 ½Eþk À1 ½ES 0  d½E 0  dt ¼ k 0 ½EÀk À0 ½E 0 Àk 0 1 [S 0 ½E 0 þðk cat þk 0 À1 Þ½E 0 S 0  d½E 0 S 0  dt ¼ k 0 1 [S 0 ½E 0 Àðk cat þk 0 À1 Þ½E 0 S 0 Àk Àes [E 0 S 0 þk es ½ES 0  d½S 0  dt ¼Àk 1 ½S 0 ½Eþk 0 À1 ½ES 0 Àk 0 1 [S 0 ½E 0 þk 0 À1 [E 0 S 0  þk s [SÀk Às ½S 0  ð6Þ Eqns (6) were solved with additional equality for the total enzyme concentration E tot ¼½E 0 þ½E 0 S 0 þ½Eþ½ES 0 ð7Þ Eqns (6) and (7) were variously normalized to have fewer parameters by dividing all concentrations by E tot .Inthe Scheme 5. 228 P. Masson et al.(Eur. J. Biochem. 271) Ó FEBS 2003 normalized equations, all parameters are the same as in Eqn (6) but k 1 and k¢ 1 are changed to k 1 E tot and k¢ 1 E tot , correspondingly. Other normalizations were obtained by dividing concentrations of all enzyme forms by E tot and all substrate forms by [S]. Concentration [S] is assumed to be in excess and therefore to remain constant. All relative concentrations were calculated with the same equations. Normalization by dividing all substrate forms by [S] was used for estimation of k s and k )s ; normalization by dividing all concentrations by E tot wasusedtoinvestigatethe dependence of oscillations, i.e. [E¢S¢], on substrate concen- tration. The concentration of E¢S¢ is proportional to the reaction rate. Figure 4 shows the dependence of [E¢S¢]/E tot on time, calculated according to Eqns (6) and (7). The number of periods observed is enhanced, if we diminish the rates of enzyme isomerization. The simulation procedure was per- formed by computer solution of the differential Eqn (6) with parameter values taken as close as possible to the experi- mentally found values. The calculations yield three to four periods of damped oscillations similar to the experimental observation (Figs 1 and 2). During the simulation we constrained the parameter values using the principle of detailed balance, i.e. the products of the parameters in both directions of enzyme isomerization cycle are equal: k 0 k 0 1 k Àes k À1 ¼ k À0 k 1 k es k 0 À1 ð8Þ Curve a in Fig. 4 shows a simulation using concentrations and kinetic constants similar to experimental values. Curves b and c in Fig. 4 show the effect on [E¢S¢]/E tot of increasing k )s to 0.01 s )1 and 0.05 s )1 , respectively, while keeping the other parameters constant. It is noteworthy that oscillations tend to vanish as k )s is increased. Analysis of the pre-steady- state kinetics showed that damping increased with substrate concentration. Thus, simulations were carried out at various substrate concentrations. Curves a, b, c and d in Fig. 5 show the dependence of the oscillatory behaviour on substrate concentration, using k )s ¼ 0.006 s )1 and variable k s .Itcan be seen that at high [S], or high k s as equivalent (as seen in the non-normalized equation), there is a smooth lag, but damping is so high that there are no oscillations. The oscillation period changes slightly over the time course (Figs 1A, B and 2) if we allow the substrate con- centration [S] to change with time. It should be mentioned that various types of period changes could be obtained, if we introduced additional substrate states with different local concentrations into Scheme 5. Substrate transition S !  S¢ As predicted by Strickland and Ackerman [48], any cyclic reaction, e.g. enzymatic turnover, involving two or more enzyme–substrate complexes as time-dependent variables can theoretically exhibit damped oscillations if the kinetic constants and substrate concentration satisfy certain condi- tions. However, in a linear reaction system, e.g. a hysteretic approach to steady-state such as Scheme 5, oscillations damp out very rapidly and cannot be observed. Yet, damped oscillations can be seen in the simplest hysteretic mechanism if an additional time-dependent variable is branched in the reaction path (S !  S¢ in Scheme 5). Such a situation was theoretically predicted [51]. Simulations of Scheme 5 showed that the damping and period of the oscillations can be modulated by tuning the different rate constants of the equilibria. Oscillations are favoured if enzyme–substrate complex formation is irreversible. The existence of several enzyme–substrate complexes formed along the descent of substrate to its final position on the active site [26] would thus favour oscillations. The principal requirements for oscillations are that k 0 must be sufficiently slow, that k s [S] be less than the turnover capacity k cat [E] [51], and that k )s be less than 0.05 s )1 . The existence of multiple equilibria between substrate states S  ! S¢  ! S¢¢  ! … can change (decrease or increase) the period of damped oscillations with time. To simulate the observed oscillations in the hysteretic portion of the turnover time course, we introduced a model that contained two populations of substrate, where the form of the substrate capable of binding to the enzyme was produced at a low rate. However, a physical description of the nature of the transition between populations was puzzling. Earlier work using molecular mechanics and spectroscopic methods had shown that acetylcholine is Fig. 4. Simulation of damped oscillations in the approach to steady-state for hydrolysis of BzCh by human BuChE. Reaction rate (proportional to [E¢S¢]/E tot ) dependence on time calculated according to Scheme 5 andEqn(6)withparametervaluessetas[E] 0 /E tot ¼ 0.98, [E¢] 0 / E tot ¼ 0.02, [S¢] 0 /E tot ¼ 30, [S] 0 /[S¢] ¼ 1 and the following kinetic constants: k 0 ¼ 0.0015 s )1 ; k )0 ¼ 0.145 s )1 ; k es ¼ 0.006 s )1 ; k )es ¼ 0.005 s )1 ; k 1 ¼ 0.4 s )1 ; k )1 ¼ 140 s )1 ;k¢ 1 E tot ¼ 40 s )1 ;k¢ )1 ¼ 120 s )1 : k cat ¼ 250 s )1 , k s [S]/E tot ¼ 50 s )1 , E tot ¼ 30 n M . Parameter k )s varied: a, k )s ¼ 0.002 s )1 ;b,0.01s )1 ;c,0.05s )1 . Fig. 5. Dependence of damped oscillations on substrate concentration. Parameters are as in Fig. 4 with fixed k )s ¼ 0.006 s )1 and variable k s ¼ 160, 80, 40, 20 s )1 in curves a, b, c, and d, respectively. Ó FEBS 2003 Oscillations in butyrylcholinesterase hysteresis (Eur. J. Biochem. 271) 229 [...]... thioester: synthesis, kinetics of base hydrolysis, and application to the assay of cocaine esterases Chem Res Toxicol 11, 895–901 Kalow, W (1964) The influence of pH on the hydrolysis of benzoylcholine by pseudocholinesterase of human plasma Can J Physiol Pharmacol 42, 161–168 Krupka, R.M (1966) Chemical structure and function of the active center of acetylcholinesterase Biochemistry 6, 1988– 1997 Froede,... be described by a box scheme such as Scheme 5 The complex oscillatory hysteretic behaviour observed with BzCh can be reproduced by introducing a branched equilibrium involving substrate into the hysteretic model This substrate equilibrium has the effect of controlling the rate at which substrate converts between various unproductive forms and the specific form capable of binding to the enzyme Several... Bolger, M.B & Taylor, P (1979) Kinetics of association between bisquaternary ammonium ligands and acetylcholinesterase Evidence for two conformational states of the enzyme from stopped-flow measurements of fluorescence Biochemistry 18, 3622–3629 Masson, P., Froment, M-T., Nachon, F., Lockridge, O & Schopfer, L.M (2004) Hysteretic behavior of butyrylcholinesterase: kinetic curiosity or catalytically and... Yakovlev, V.A (1976) The theoretical analysis of kinetic behaviour of hysteretic allosteric enzymes J Theor Biol 60, 247–269 Masson, P & Laurentie, M (1988) Stability of butyrylcholinesterase: thermal inactivation in water and deuterium oxide Biochim Biophys Acta 957, 111–121 Masson, P., Adkins, S., Gouet, P & Lockridge, O (1993) Recombinant human butyrylcholinesterase G390V, the fluoride-2 variant, expressed... (2003) Unmasking tandem site interaction in human Ó FEBS 2003 232 P Masson et al (Eur J Biochem 271) 13 14 15 16 17 18 19 20 21 22 23 24 25 4 26 27 28 29 30 31 acetylcholinesterase Substrate activation with a cationic acetanilide substrate Biochemistry 42, 5438–5452 Levitsky, V., Xie, W., Froment, M.-T., Lockridge, O & Masson, P (1999) Polyol-induced activation by excess substrate of the D70G butyrylcholinesterase. .. the result of a combination of steric constraints and impaired electronic effects of the ethereal sulfur atom on stabilization of the acylation transition state The enzyme displays a hysteretic approach to steady-state with BzCh but not with BzSCh This behavioral difference may be related to binding of BzSCh to both enzyme states, E and E¢ The presence or absence of hysteresis in BuChE has been found... nature of the substrate, the concentration of the substrate, the structure of the enzyme, and the composition of the medium Although numerous studies have demonstrated the conformational plasticity of BuChE [45,60] and AChE [61], the molecular mechanisms underlying this plasticity, and therefore hysteresis are not yet known The differences between the E and E¢ enzyme states appeared to be the result of. .. Hormonal regulation of 6-phosphofructo-2-kinase/fructose-2,6-biphosphatase: kinetic models FEBS Lett 217, 212–215 Xie, W., Varkey-Altamirano, C., Bartels, C.F., Speirs, R.J., Cashman, J.R & Lockridge, O (1999) An improved cocaine 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 hydrolase: the A328Y mutant of human butyrylcholinesterase is 4-fold more efficient Mol Pharmacol 55, 83–91 Cashman, J.R.,... general conformational diversity of proteins Indeed, the Ônew viewÕ of proteins assumes that they exist in an equilibrium between pre-existing conformers of discrete and similar free energy, and that binding of ligands shifts the equilibrium in favour of the functional conformer [62] If this view is correct, the hysteretic behaviour of enzymes must be more common than has so far been reported The steady-state... P.-L (1999) Hydration changes during the aging of phosphorylated human butyrylcholinesterase: importance of residues aspartate-70 and glutamate-197 in the water network as probed by hydrostatic and osmotic pressures Biochem J 343, 361–369 Masson, P & Balny, C (1990) Conformational plasticity of butyrylcholinesterase as revealed by high pressure experiments Biochim Biophys Acta 1041, 223–231 Hess, B & . Damped oscillatory hysteretic behaviour of butyrylcholinesterase with benzoylcholine as substrate Patrick Masson 1 , Boris N. Goldstein 2 ,. induction time, s, with BzCh as substrate was much shorter than with NMIA [16]. Moreover, with NMIA and BuSCh, it was found that s increased with decreasing pH [25].