NORMAN C. CRAIGAND G. B. KISTIAKOWSKY [CONTRIBUTION FROM THE
VOl. 80
GIBBSCHEMICAL LABORATORY O F HARVARD UNIVERSITY]
Kinetics of Ester Hydrolysis by Horse Liver Esterase.
I1
BY NORMAN C. CRAIGAND G. B. KISTIAKOWSKY RECEIVED OCTOBER 2, 1967 T h e hydrolysis of methyl n-butyrate was studied by the pH-stat technique over a pH range from 3.5 t o 10 and a concentration range of 1.5 t o 58 mJf or less. Ethyl n-butyrate was studied over a narrower PH range. The substrate dependence of the rates lvas studied a t pH 6 and 8 with methyl propionate, ethyl propionate, n-propyl propionate, methyl isobutyrate and ethyl isobutyrate. T h e dependence of Vmkxof methyl (and ethyl) n-butyrate on PH between 6 and 9 is very slight. 9 t lower p H the activity decreases but is detectable even at p H 3.5, the activity-pH curve approaching sigmoid shape. The Michaelis constant increases with decreasing pH by more than a n order of magnitude. No direct evidence of a twosite mechanism was obtained. The data on other esters also fit the simple Michaelis-Menten mechanism, the ICm?*being larger at the lower of the two pH investigated and Vmimaxt. being essentially the same. Inhibition b y the products of the reactions, particularly butyric acid, was observed, which increases with the lowering of pH. These d a t a are compared with the results of previous work on horse liver esterase and some of the inconsistencies resolved. T h e pH dependence of V,,, agrees with that derived from the assumption that the active group undergoes acidic ionization, b u t the pH dependence of does not agree completely with this treatment. A requirement of the general Michaelis-Menten mechanism for the pH dependence of V,.,/KM is found to be obeyed only approximately in the series of esters investigated. Also, if an acylenzyme intermediate is formed, its rate of decomposition cannot be the rate determining step.
V’ork was begun in this Laboratory on the kinetics of the non-specific enzyme liver esterase’ to complement studies of the specific enzyme urease.2 These studies of the hydrolysis of methyl 77,-butyrate and ethyl n-butyrate, over a thousandfold concentration range a t pH 10.2, were interpreted with a two-site or two-enzyme mechanism. For the same substrates Schwert and Glaid3 found simple Michaelis-Alenten behavior over a fivefold concentration range a t pH 8. Both of these studies were conducted in unbuffered solutions a t very low ionic strength, with a purified horse liver esterase preparation.4 Conners, er a1.,4 also found Michaelis-Menten kinetics for the action of their enzyme preparation on methyl $2-butyrate in strongly buffered solutions a t pH 7.3. Christiansen and G ~ - a a eusing , ~ an extract from horse liver acetone powder, followed the hydrolysis of methyl valerate a t pH 8 to nearly 100% reaction. They interpreted their findings in terms of an activated enzyme mechanism, much like that proposed by bIedwedew,6 adding a step involving the combination of the substrate with two molecules of enzyme. H ~ f s t e e ,also ~ using an extract of horse liver acetone powder, found deviations from RIichaelisArenten kinetics a t $11 5 for the hydrolysis of hydroxybenzoic acid esters of aliphatic acids. For the PH dependence of liver esterase activity Connors, et al.,4 found a bell-shaped curve with an optimum a t pH 8, supporting previous work on liver esterases.8 They used a single methyl nbutyrate concentration, 0.1 -If,and a borate buffer concentration of 0.02 JI. In contrast, K. and 11.’ suggested an activity Berms pH curve with no maximum but of a sigmoid shape. There is clearly (1) G . B Kistiakowsky and P . C . Mangelsdorf, Jr., THISJ O U R N A L , 78, 2 9 0 4 (1956). ( 2 ) G. B . Kistiakowsky and W. E. Thompson, i b i d . , 78, 4821 (1956). (3) G. T. Schwert and A . J . Glaid. J . Bioi. Cizem., 199, 613 (1952). (4) W IfConnors, 4. Pihl, A. L. Dounce and E . Stotz, i b i d . , 184, 20 (1950). (J) J . A . Christiansen and J . Graae, Acta Chem. Scnnd., 10, 1258 (1956). (6) G. Medwedcw, ElzZy?noiogin. 3, 1, 31, 53 (1937). ( 7 ) R . H . J. Hofstee, J . Bioi. Chcm., 207, 211, 219 (1954). ( 8 ) K. Amon and M. Jaarma, “ T h e Enzymes,” Vol. I, P a r t 1, ed. J . B . Sumner and K. Myrback, Academic Press, New York, N. Y., 1950.
a great deal of uncertainty about the substrate and
pH dependences of liver esterase activity.
Since Boursnell and Webbg have shown that horse liver esterase is irreversibly inhibited by antiesterases such as diisopropyl fluorophosphate, just as are acetyl cholinesterase, a-chymotrypsin and trypsin, it is reasonable to look for similarities in the kinetics. 1X7ilson1Ohas proposed a detailed, two-intermediate mechanism for acetylcholinesterase action. d similar mechanism has been proposed for a-chymotrypsin by Gutfreund and Sturtevant. l1 These mechanisms involve an acylenzyme compound as the second intermediate. The present study with a series of aliphatic esters, chosen for their water solubility and similarity in structure, was undertaken in an attempt to resolve the inconsistencies in the substrate and pH dependences of liver esterase activity, to examine the applicability of the two-intermediate mechanism and to compare the enzymatic catalysis with the well-understood acid and base catalysis.
Experimental Details Although the conductometric method, which was previously used in this Laboratory, has evcellent sensitivity in unbuffered, low ionic strength solutions, i t is inconveniently non-linear at pH’s near neutrality and is limited t o low ionic strengths. It was therefore replaced for this research by a manual pH-stat method,b whereby the pH was maintained constant throughout a n experiment by continuously adding standard alkali from a micrometer buret. The amount of titrant added measured the extent of the reaction. -4 p H meter, having a sensitivity and stability of better than 0.003 p H unit, was constructed from a Type K potentiometer and a DuBridge-Brorwl typeI2 d .c. amplifier. The amplifier, used with a galvanometer as a null detector, employed a FP 54 electrometer tube and served as a current amplifier with a gain of about 105. I t s grid resistance was inserted between the glass electrode and the potentiometer, the output being fed t o a Type E, L. and N. galvanometer. The electrometer tube was housed in a dehumidified brass case. Storage batteries were used as the power source. The Beckman glass electrode (1190-80) was employed. Calomel electrodes with leak-type junctions gave fluctuating potentials in the rapidly stirred, low ionic strength solutions. An agar gel junction in a n electrode design similar t o one of (9) J . C . Boursnell and E , C . Webb, Nnlurc, 164, 875 (1949). (10) I . B. Wilson, Disc. F U Y Q ~SOL., Q Y 30, 119 (1965). (11) H. Gutfreund and J. M. Sturtevant, Proc. S a t . A c a d . Sci. u . s.,43, 719 (1956). (12) L. A. DuBridge and H. Brown; Rev. Sci. I n s f v . , 4 , 532 (1933).
April 5, 1958
KINETICSOF ESTERHYDROLYSIS BY HORSELIVERESTERASE
Linganel3 proved satisfactory. It was contained in a Pyrex tube of 12 mm. diameter which was closed at the bottom with sintered glass of medium porosity. Above i t was a plug of 37G agar saturated with potassium chloride, and above the agar was saturated potassium chloride solution. T h e reaction vessel was a 200-ml. tall-form beaker fitted with a rubber stopper in which were mounted the glass and calomel electrodes. Holes were provided for a nitrogen line, the micrometer buret, a microburet and a pipet to in. troduce the enzyme. The 150-ml. reaction mixtures were stirred with a Teflon-covered magnet bar. The water-filled thermostat was regulated to 1k0.02’ a t 25.0”. -1Gilmont micrometer buret (Manostat G 15401) of 1ml. total capacity and 0.0002-ml. minimum scale division was used t o deliver 0.01 ?i standard sodium hydroxide manually. Solutions were prepared with COZ-free water and stored in a Con-free box. Glassdistilled water was freed from carbon dioxide by purging with nitrogen until i t had a PH of 7.0 +C 0.2 units. Two enzyme preparations (no. 1 and 2 ) were made by the method of Connors, et u Z . ~ Their procedure was followed except in the last step, where concentration by evaporation from a dialysis bag was substituted for pressure filtration. The relative activity a t each step agreed quite well with their report. The concentrated stock solution was stored at 1’. ( A similar preparation made four years ago’ and stored at 1’ has retained nearly full activity.) Dilute enzyme stocks usually were prepared by diluting 0.10 ml. of the concentrated stock to 50 ml. with water equilibrated with atmospheric COa and were stored at room temperature. The enzymatic activity of these solutions changed less than 2YG in ten days. d unit of enzyme mas defined as t h a t amount which hydrol>-zed 10 micromoles of ester per minute in a solution 0.010 X in potassium chloride and 14.5 m M in methyl n-butyrate a t pH 8 and 25’. The substrates, methyl-n-butyrate, ethyl n-butyrate, methyl propionate, ethyl propionate and n-propyl propionate were Eastman Kodak White Label reagents. Ethyl isobutyrate was obtained from the Verona Chemical Company. Methyl isobutyrate was synthesized by a standard procedure from IVhite Label propionic acid and Merck absolute methanol. Where necessary, the esters were extracted with dilute sodium bicarbonate to remove acid, then dried with anhydrous magnesium sulfate and distilled. nPropyl propionate was fractionally distilled t o remove an unidentified impurity. The final purity of the esters was checked by refractive index, titration and gas chromatography. The refractive indices were within 0.0002 unit of the published values,14 except for ethyl isobutyrate and npropyl propionate which were within 0.0004 unit. Titration showed that acid was less than 0.05% for all the esters. As determined by gas chromatography, water mas less than 0.170 for all the esters, and contaminating esters were less than 0.3% except in wpropyl propionate, where the impurity was less than 0.5y0. Stock substrate solutions were prepared daily volumetrically. Special care was taken to prevent loss of ester by evaporation. The extent of the hydrolysis of the esters in the stock solutions was less than 0.17, per day. The 0.01 N standard alkali mas prepared from COZ-free water and COz-free sodium hydroxide, stored in a paraffinlined bottle and standardized against Merck potassium acid phthalate. All other reagent solutions were prepared by weight from either Mallinckrodt or Merck analytical grade reagents. Beckman buffers were used to standardize the p H meter. Rates were obtained graphically from the slopes of plots of ml. of base consumed versus time. The scatter of points, taken every 20 to 30 seconds, was such t h a t initial slopes generally could be determined t o better than 1% in individual runs a t rates of the order of one micromole/minute.
Results The influence of buffer ions and ionic strength was investigated briefly. Since Schwert and Glaid’s3measurements were made in the presence of dilute phosphate buffer (apparently 0.0003 to (13) J . J . T h g a n e , “Electroanalytical Chemistry,” Interscience Pnblishers, h’ew York, N , Y..1954, p. 209. (14) 4.I . Vogel, J . Chcm. Soc., 624 (1948).
1575
0.001 JV),a series of enzymatic activity measurements were made with 42 mill methyl n-butyrate a t pH 8 with phosphate concentrations varying from 0.005 to 0.008h?. No significant eITect on the enzymatic rate was observed. Also, the presence of the equilibrium concentration of COz was shown to be without effect since 0.001 111 carbonate-bicarbonate did not aTect the rate. No significant influence on the enzymatic activity was observed due to changes in the ionic strength from 0.001 to 0.018 M potassium chloride a t pH 9 with 14.5 m M methyl n-butyrate. Thus, since the effect of 0.01 A4 ionic strength on the maxirrium rate appeared to be negligible and to define better the reaction conditions, all the measurements reported below were made in the presence of 0.010 -Ifpotassium chloride. The concentration and CH dependence of the rate of enzymatic hydrolysis of methyl n-butyrate was studied over a wide range of pH. Figure 1 gives the
P H.
Fig. l.--pH dependence of the rate of enzymatic hydrolysis of methyl b-butyrate: (1) enzyme preparation no. 1; (M) four year old preparation of Mangelsdorf; ( I ) dependence proposed by Kistiakowsky and Mangelsdorf ; (11) curve proposed by Connors, et al. Curves (1) and (AI) have been displaced downward for better clarity.
pH dependence measured a t 42 mJ4 ester for the authors’ first enzyme preparation and a t 42 and 4 mM ester for Mangelsdorf’s preparation. Since, as shown below, the authors’ second enzyrne preparation has the same pH dependence of activity, it is believed to be characteristic of liver esterase. A similar, nearly pH independent activity was observed for 18 mJ4 ethyl n-butyrate between pH G and 9.5. Included on the graph in dotted lines are the bell-shaped curve reported by Connors, et u I . , ~ and the sigmoid-shaped curve suggested by K. and 1LI.l The results of the study of methyl n-butyrate hydrolysis by our second enzyme preparation a t pH’s 5 , 6, 7, 8 and 9 are presented in Fig. 2 as a graph of the reciprocal of the initial rate ( l l v ) versus the reciprocal of the substrate concentration (l/S). Each point is an average of two or more determinations. They have been corrected for the hydroxide-catalyzed hydrolysis but have not been corrected for incomplete dissociation of product acid a t low pH’s. The substrate dependence of the enzymatic ac-
NORMAN C. CRAIGAND G. B. KISTIAKOWKY
1576
TABLE I CONCENTRATION DEPENDENCE OF LIVERESTERASE-CATALYZED HYDROLYSIS FOR Initial ester concn. mAl Rate,“ PH 6.06 Rate, PH 8.06 Initial ester concn. in mM Rate, PH 6.06 Rate, PH 8.06 Initial ester concn. in mJi Rate, PH 6.06 Rate, pH 8.06
0.307
..
2.28 2.31
..
6.06
0.611
..
3.47
Ethyl n-butyrate 1.22 1.84 3 . 0 3 .. . . 2.83 4.00 3.97 4.17
8.64 6.27 8.93
Methyl isobutyrate 14.4 20.1 28.7 7.35 7.92 3.23 ‘3.48 . . f0.X
0.917
..
2.98 5.77 5.20 8.02
..
..
..
2.21
2.87
3.09
12thyl isubutyratc I .20 2. 10 :;.oo 2:c 3:11 3,711 :;:I Methyl propion:itr 10.3 17.1) 17.2
0.302 0.601
0.902
Initial ester concn. in niM Rate, PH 6.06 Rate, pH 8.06
2.70
5.45
6.83
..
..
..
0.89i
..
1.5l iwbittl rate arid 0 304 m h l n-propyl propionate.
.. ..
tivity with the other esters was studied a t pH (i and S. At PH 5 the inhibitioii by product acid and incomplete dissociation of the acid obscure even initial rate determinations; a t PH 9 the hy-
/%H6
i
/
Y”
i
PH
7A
droxide-catalyzed hydrolysis interferes with the c117yrnaticcatalysis. Table I summarizes the results. Slost of the data in the table are averages of several determinations. Corrections for alkaline hydrolysis were calculated from published values. -1s with methyl n-butyrate, the enzymatic hydrolysis of these esters effectively followed Michaelis-Menten kinetics. Graphs of reciprocal rate ueysus reciprocal ester concentration were linear, except for ethyl propionate which showed substrate inhibition a t high substrate concen trations. hlaximum rates and Michaelis constants for t h e esters a t pH G arid S are summarized in Table TI. They have been corrected for incomplete dissociation of the product acid a t PH 6 and hydroxide catalysis a t pH 8. The usual linearization of the Michaelis-Meriten type kinetic expression l/v
o.2
Y
/
t XS,
=-’,
Fig. 2.--The dependence on concentration of the rate uf hydrolysis of methyl n-butyrate at several pH.
=
(Ru/Vm’m)1/(S)
+ l/Vm
was used. Figure 3 displays the corrected constants for methyl n-butyrate a t several pH. The constants for ethyl n-butyrate, methyl isobutyrate and ethyl propionate were evaluated by a weighted least squares procedure, with v / I’, as the weighting factor. For the other esters the constants were obtained graphically. Accelerating initial rates or induction periods, which decreased in duration with increasing substrate concentration, were observed for methyl propionate hydrolysis a t pH S. Extrapolated to the time axis they extended to 30 seconds. No in-
KINETICSO F ESTERHYDROLYSIS BY HORSELIVERESTERASE
April 5, 1955
duction periods were observed at pH 6. T h e observations a t p H 8 could not be satisfactorily explained by the presence of a n ester impurity since such would produce induction periods which increase in duration with increasing substrate concentration. They also could not be explained as initial, non-steady state kinetics since Schwert and Glaid’s3 estimate of the absolute rate constant for the breakdown of the enzyme-substrate complex predicts an induction period of less than 0.02 second. The rates obtained after the induction periods fitted, however, Michaelis-Menten kinetics.
FOR THE
AND
MICHAELISCONSTANTS, KM.
SERIES OF ESTERSAT p H 6 pH 606
Esters
Methyl n-butyrate Ethyl n-butyrateb Methyl isobutyrate* Ethyl isobutyrate Methyl propionate Ethyl propionateb n-Propyl propionate
Cor
,c
c
I
/‘A
I
/ /
TABLE I1 MAXIMUM RATES, Vm,
XI
1577
KM,
V m
mM
11.6 4.66 10.6 3.31 8.55 2.06 5.30
6.24 1.575 5.37 0.749 70.6 6.48 1.94
AND
,
8 pH 8.06
V,‘
11.2 4.96 10.97 4.03
5.53 2.44 5.50
K M,
mM
1.72 0.371 1.96 0.257 9.06 1.310 0.313
0 Enzymatic rate in micromoles/liter-minute-unit enzyme. bThe constants for these esters were obtained by least squares analysis. Corrected for incomplete dissociation of product acid.
The observable activity of the enzyme a t PH 3.5 raised the possibility of studying the esterification reaction. Consideration of the equilibrium constants for esterification (K’ = 0.048)15 and the dissociation of the acid shows that the pH change accompanying esterification above pH 3.5, where the enzyme is active, is given approximately by the product (K’)(Alcohol). Thus, the sensitivity of the measurement is nearly independent of ;bH. For 5 M alcohol a total PH change of about 0.24 unit is t o be expected. An attempt was made to observe this change at “pH” 5.9 with 5 M methanol, 0.1 hf n-butyrate and five times the enzyme concentration usually employed in the hydrolysis experiments. No significant pH change was observed in 4 hr., and a precipitate indicated that the enzyme was probably not completely soluble in the 20% alcohol: Strong inhibition by products was observed a t p H 6 ana below for all of the esters. For example, a noticeable decrease in rate was observed a t pH G with 5.7 mllf methyl n-butyrate after only 0.8470 decomposition, and a 26y0decrease in rate was observed with 2.9 m M ester after 2.57, decomposition. Larger decreases were observed a t p H 5 for the same concentrations and per cent. decompositions. At p H 6 and 2.0 m M ester, the addition of 0.5 m;ll sodium butyrate caused a 25y0decrease in rate whereas 0.5 m M methanol caused a 9y0decrease in rate. Thus, a t pH 6 the butyratebutyric acid is the more potent inhibitor. From the least squares analysis of the rates of hydrolysis of ethyl n-butyrate, methyl isobutyrate and ethyl propionate the average standard devia(15) “International Critical Tables,” Vol. 11, McGraw-Hill. Inc., New York, N . Y.,1930, p. 139.
Fig. 3.--pH dependence of Vmsx and Km for methyl nbutyrate: units of V,,,, p M L - 1 rnin.-‘ enzyme unit-’; p M 1.-1 enzyme unit-] units of Vmax/Km,
tion in the rate measurements and in the maximum rates was found to be 2.2%, including the measurements of enzyme activity units. The standard deviation in the Michaelis constant ( K M ) ranged from 3.0 to 6,870 with an average of 5.37;. The relative pH was known to better than 0.02 unit, being limited primarily by the standard buffers. An empirically determined pH correction of 0.06 unit was applied because of the difference in liquid junction potential in the standard buflers and the reacting solutions, due to stirring. Some of the maximum rates and Michaelis constants for methyl n-butyrate and ethyl n-b’utyrate are compared in Table 111 with previous results in which a horse liver esterase prepared by the method of Connors, et al., also was used. Weighted mean values are given for the previous measurements from this Laboratory. The differences a t PH 5 between the results of this research and t.hose of Schwert and Glaid may be due to the limited substrate concentration range investigated b!7 them, to ionic strength effects, particularly on K M ,undisclosed by the present cursory ionic strength study a t high substrate concentration, or to nonuniformity of the enzyme preparation. ’To test the possibility of such non-uniformity, the liver esterase preparation made four years ago‘ was investigated a t p H 9 and 0.910 M ionic strength. The K M of 1.83 mM, given in the table, was obtained. This differs significantly from the K M of the more recent preparation. Evidently the enzyme preparation is not uniform; it may be a mixture of two enzymes, as suggested by the .two-site hypothesis. The extremely divergent result of 22 m M for K M obtained by Connors, et a1.,4may be due, in part, to inhibition and/or ionic strength effects of the 0.025 M bicarbonate buffer used. I t is noteworthy that the present results are the lowest values for K M , indicating maximum freedom from inhibitors.
Discussion As shown in Figs. 1 and 3 there is a marked contrast between the pH dependence observed in this
1.578
?;ORMAN
c. CRAIGAND G . B. KISTIAKOWSKY
versus time, the curves are superimposable within
TABLE 111
KM’SO F
SEVERaL RESEARCHES K M for methyl w h u t y r a t e gH 7 . 4 pH 8 pIr 9 p i i 10.2
COMPARISOX O F
Mangelsdorf .... ...... ...... Schwert and Glaid . . . . 3 . 1 4 mdf ...... Connors, et al. 22 m J I ...... ...... This research Preparation 2 2.7 1.i 2 1 . 3 0 m.11 hlangelsdorf’s preparation(M). . . . . . . . . . 1.83 K M for ethyl n-butyrate Mangelsdorf Schwert and Glaid This research Preparation 2
2.46111,l.l
...... ......
...... ......
pH 8
gH 10.2
.......
0.685rnM
0.683 m-If
.......
0.371
....... PH 8 This S. and G. research
Ratio
Vm(methyl n-butyrate) Vm(ethyl n-butyrate)
Vol. 80
1.93
2.26
research and the bell-shaped dependence found by Connors, et aL4 There is also a significant difference between the location of the inflection point of the sigmoid-shaped curve presently observed and of the partly extrapolated curve reported earlier from this Laboratory. This latter discordance is not real, being the result of an improper assumption in the earlier work. The run a t pH 5.9, on which the extrapolation was based, was made a t a methyl nbutyrate concentration of 2.5 mM, which is of the order of the Michaelis constant. The present investigation of pH dependence shows that, although the maximum rate ( Vm) is nearly constant from pH 10 to 5.9, the Michaelis constant ( K M )is a strong function of pH. Thus, the extrapolation which assumed K M to be constant was unjustified. The marked contrast with the bell-shaped pH dependence reported by Connors, et al., and others8 may be the result of a t least two factors. First, their activity-pH curve was not based on VmvS but on the activity a t a single substrate concentration, 0.1 JI, where a pH-dependent substrate inhibition may be active as has now been observed for ethyl propionate. Second, their measurements were carried out in the presence of borate and mannitol buffers, which may have influenced the rate. The unusual mechanism proposed by Christiansen and Graae5 for the action of horse liver esterase on methyl valerate is not necessary to interpret their data. They fitted the results of four runs a t the same enzyme concentration but different ester concentrations and four runs a t nearly the same ester concentration but different enzyme concentrations, to an empirical equation
the apparent experimental error. This procedure indicates that the d l / ( E ) ~ dependence is not called for by the data. In addition, if their data for the four different ester concentrations are plotted as (S)oa/tversus [ln(l - a ) ] / t ,straight lines are obtained within the scatter of the experimental points. The slopes of these lines depend linearly on the initial ester concentration. Thus, the integrated -Michaelis-Menten equation, which can be rearranged toI6
-
(S)aa - C I n ( 1 t
0)
t
+D
fits their data. The linear dependence of C on initial substrate concentration suggests product inhibition, presumably by the valerate. This fitting of their data to the conventional mechanism reduces the area of disagreement about liver esterase kinetics. The hypothesis of a two-enzyme or two-site mechanism suggested by the earlier study’ remains unsettled by the present research. The kinetic expression for a two-site Xchaelis-Menten mechanism approaches a linear Lineweaver-Burk form a t high substrate concentrations since i t expands to
where subscripts 1 and 2 characterize the two sites. Because the pH-stat measurements were limited by lower sensitivity to higher ester concentrations, i t may be that only the limiting, linear behavior of a two-site mechanism was resolved. The lack of quantitative agreement between the Michaelis constants determined for enzyme preparations ( 2 ) and ( A I ) a t pH 0 (Table 111) suggests that a mixture of esterases is involved, rather than a single enzyme with two sites. This uncertainty about the uniformity of the enzyme must be borne in mind throughout the following discussion. The concentration and pH dependence for methyl n-butyrate hydrolysis can be fitted to a simple Michaelis-Menten mechanism, including an acidic ionization of the active site. For the mechanism’6
s + E H ~kiE I I S + E H + P k7
(1)
22
and where A and B are adjustable parameters and CY is the degree of reaction. Their data can be fitted, however, to a simple Michaelis-Menten mechanism involving competitive inhibition by a product. If the four runs a t nearly the same ester concentration are adjusted to the same enzyme concentration by multiplying the observed times by the enzyme concentration and then plotted as cy
In Fig. 3 the dotted portion of the Ir, curve is a theoretical extrapolation based on K a m = 2.0 X lov5. It coincides with the experimental curve be(16) R . A. Alberty, “Enzyme Kinetics,” “Advances in Enzymology,” Vol. X V I I , ed. F. F . Nord, Interscience Publishing Co., N e w York, N. Y., 1956.
April 5 , 1958
KINETICS OF ESTERHYDROLYSIS BY HORSELIVERESTERASE
1579
TABLE IV COMPARISONS OF pH DEPENDENCE OF ESTERASE CATALYSIS OF SEVERAL ESTERSAND
ACID-BASECATALYSIS
kolr (MeBu) kolr ( x )
Ester
Methyl n-butyrate Ethyl n-butyrate Methyl isobutyrate Ethyl isobutyrate Methyl propionate Ethyl propionate n-Propyl propionate
OF
3.51 4.52 2.84 3.55 5.04 5.89 6.43
.. 7.9 8.6
.. 8.4
..
..
tween p H 5 and 7. The low pH extrapolation is supported by the less detailed rate measurements (Fig. 1) in this pH region. The downward curvature of the Vm plot above flH 7 is probably an evidence of the involvement of a second acidic ionization in the active site. It is not possible, however, to fit as well a function G [ ( H + ) ] to the K M / l / m curve. The dotted line in Fig. 3 represents the best possible fit, obtained with K a = ~ 6.3 X The deviation could be attributed to a more complex mechanism (e.g., two-intermediate mechanism),non-uniformity of theenzyme or a p H dependent ionization constant due to an electrostatic effect, as was discussed in conjunction with urease.2 The weakening of the implicated basic group, upon binding of the substrate, ( K a E S > K a E ) fits with the interpretation that this group attracts the positive end of the carbonyl dipole of the ester in the initial complex. Any mechanism such as that given in equation 1 involving several ionizations affecting the active site, if it can be fitted by a kinetic expression of the Michaelis-Menten form, has a pH dependence for V , and Kni~of the forms16
(1.00) 2.26 1.02 2.78 2.03 4.59 2.04
(1.00) 1.96 1.28 3.31 0.613 1.13 1.38
K__H (IZeBu) kx ( A )
(1.00) 0.925 1.05 1.04 0 . E82 ,601
.E 8 l
to the data. However, the variation in C; is only a factor of two, while the kinetic constants involved spread over a much wider range. This suggests that there is no gross error in the application of the simple theory, and, if we are dealing with an enzyme mixture, that perhaps one enzyme predominates. No kinetic evidence for an acyl-enzyme intermediate postulated by Wilson has been obtained, since if such were formed in a single step or if its breakdown were the rate determining step in a two-intermediate mechanism, then V , would be the same for the various esters of the same acid. Reference to Table I1 shows that this is not so, except for methyl and n-propyl propionate. If it is assumed that K L a~t PH 8 is essentially independent of pH (or has approximately the same pH dependence for the various esters studied as was observed for methyl n-butyrate), then the data can be examined in two further respects. A comparison with the well-understood non-enzymatic hydrolysis is included in Table 111, where the maximum enzymatic rates a t p H 8, relative to methyl n-butyrate, are comDared with the relative of hydroxide and h$drogen ion catalysis. v, = vt,/F[(H+)] and KM= KrnrG[(H+)]/F[(H+)] ratesThere is no correlation of the maximum rates with Thus, for a such as horse the latter which is essentially independent of the liver esterase, regardless of the substrate alcohol moiety of the ester. On the other hand, (vm/Kif)$H~ - G K H a = qH+lI2 there is qualitative correlation between the maxi(vm/Kni)fim G[(H+)lpm mum enzymatic rate and hydroxyl ion catalysis for where G is characteristic only of the ionization of methyl and ethyl esters of
