THE CHEMICAL KINETICS OF THE ENOLASE REACTION WITH … · 658 ENOLASE KINETICS in speed and reproducibility to that of fitting the data to an empirical cubic equation, as previously

THE CHEMICAL KINETICS OF THE ENOLASE REACTION WITH SPECIAL REFERENCE TO THE USE OF

MIXED SOLVENTS

BY E. W. WESTHEAD* AND BO G. MALMSTRiiM

(From the Institute of Biochemistry, University of Uppsala, Uppsala, Sweden)

(Received for publication, February 5, 1957)

A recent review by Alberty (1) shows that a number of enzymes have now been studied extensively from a kinetic point of view. It is apparent that certain aspects of enzymic catalysis, such as the general applicability of the Michaelis-Menten or Briggs-Haldane equations, have been well established, but that the specific courses of such reactions have been determined in only a few instances. While important information may be derived from non-kinetic sources (a), “intermediates” found by such means may have no direct role in the catalytic mechanism (cf. (3)); there- fore kinetic measurements will always be a necessary part of the investiga- tion.

As a means of increasing the information obtainable through the kinetic approach, the addition of organic solvents to the reaction medium would seem promising. The advantages to be gained would be as follows: first, a lowering of the freezing point of the solution and, second, an increased range of other physical properties, thereby allowing the experimenter to vary kinetic parameters which are fixed in purely aqueous solution. The depression of the freezing point is important with respect to hitherto un- explained peculiarities of many enzyme systems at low temperatures, such as a rapid fall off in the Arrhenius plot (4, 5) and frequent irreproducibility of the rate constant in the neighborhood of 0” (4, 6). Another, hitherto unexplored, possibility is the use of very low temperatures to slow up the attainment of the steady state. In this way it may be possible to study the transient state kinetics of enzyme reactions (7) without the use of the relatively complicated rapid reaction techniques of Roughton and Chance (8).

The second possible advantage to be derived from the use of solvent mixtures, i.e. a continuous variation of the reaction medium, has been investigated only recently despite the fact that it has been a well established tool in physical organic research (cf. (9, 10)). Undoubtedly the possibility of denaturation or other special effects on the protein has caused

* Successive support by the American-Scandinavian Foundation, New York, and the National Science Foundation, Washington, D. C., as a postdoctoral research fellow is gratefully acknowledged.

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ci56 ENOLASE KINETICS

hesitation on the part of research workers to apply the technique to enzyme problems. On the other hand, when organic solvents have been used to reduce the freezing point of enzyme solutions, the tacit assumption seems to have been made that. no such special effects exist (5). In general no background experiments to test this assumption have been reported.

As part of a program of research on the mechanism of enzyme action, the work described in the present communication is a relatively detailed study of the kinetics of the enolase reaction with special regard to the effect of organic solvents. This work is also intended t’o serve as a background for low temperature kinetic studies now in progress. Enolase was chosen t,o be the first enzyme investigated because certain aspects of its behavior have been thoroughly studied by one of the authors (11, 12), because it is a rather stable enzyme, and because it can be readily purified (13).

The data presented here elucidate several effects observed earlier, such as inhibition by high concentrations of substrate or activating metal ion (1 I), and, furthermore, show interesting and important effects of buffer ions. These latter data support in part t’he suggestion of Kistiakowsky and Lumry (4) that “breaks” in Arrhenius plots are due to experimental conditions and are not inherently part of the enzymic mechanism. The complexity of the effects of species present in the reaction media described here points to the desirability of fairly thorough studies on a given enzyme and shows the danger of making deductions from the effects of organic solvents without a sufficiently extensive study of such effects. Special attention has been given, in this study, to the accurate inspection and control of all factors likely to influence the rate measurements, and the kinetic information has been complemented by centrifugal sedimentation studies. Finally, on the basis of the kinetic studies in mixed solvents, a somewhat more detailed mechanism has been suggested.

EXPERIMENTAL

Material and Methods

Pu$cation of Bnolase-The enolase used in these studies was obtained from yeast as previously described (11)) but t’he final purification of some samples was made by electrophoresis and chromatography (13). No differences in kinetic behavior were detected among the various preparations.

Substrate Preparation-DL-2-Phosphoglyceric acid (PGA) was synthe- sized and purified as previously described (11).

Metal Solutions-Weighed amounts of MgO mere dissolved in standard I-ICI solution to give an approximately neutral, 2.27 M solution of MgCl?, \&ich was stored and diluted with met’al-free Hz0 as needed for experiments.

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E. W. WESTHEAD S&W B. G. MALMSTRiiM 657

Organic Solvents-Methanol and glycerol were Merck’s (Darmstadt) pro analysi grade reagents. Dioxane was technical grade, which was refluxed with sodium under a slow stream of nitrogen for about 2 days or until the metal beads appeared bright. It was then distilled under nitrogen within a range of 0.1”. The bulk of the material was stored frozen under nitrogen, while quantities for immediate use were stored in the re- frigerator as 50 per cent (by weight) aqueous solutions. 06 per cent ethanol of pharmaceutical grade, which was distilled in a glass apparatus prior to use, was employed; its boiling range was less than 0.1”.

Buffer Solutions-Phosphate and tris(hydroxymethyl)aminomethane (Tris)-HCl buffers of ionic strength 0.050 were used. Phosphate buffers were prepared from KHZ04 and Na2HP04. Solutions of Tris-HCl buffers were prepared by titrating a 0.20 N solution of NC1 to pH 7.8 with a more concentrated solution of Tris, at the temperature at which the buffer was to be used. This was then diluted with water, in a volumetric flask, to make the solution 0.10 N in chloride ion. Buffer to be used at - 7” was prepared according to an extrapolation of a plot of the temperature at which pH 7.8 was attained versus the volume of Tris solution added.

Buffer solutions to be used in 0.50 M KC1 solution were prepared in the presence of 0.50 M KCl, then diluted to the correct buffer concentration in a volumetric flask containing sufficient KC1 to make the resulting solution 1.00 M in potassium ion. The measured pH values of four solutions containing the highest concentrations of organic solvents used were in each case less than one-tenth of a pH unit away from pH 7.8. The pH used (7.8) is the optimal pH of enolase under the conditions employed (unpublished experiments of Malmstrijm and WestJund) ; the rate is there- fore relatively insensitive to minor variations in pH.

Extraction and Storage of Xolutions-Combined solutions of KCl, Tris buffer, and MgC12 were prepared at double strength and then extracted with dithizone reagent (14)) which does not remove Mg++. PGA solutions were extracted and stored frozen. PGA was not combined with the metal solutions until shortly before use, since prolonged contact (several days to weeks) between these two species leads to reaction and eventual precipitation.

Activity Measurements-The activity measurements were based on the change of optical density (D) with time, measured in a Beckman DU spectrophotometer as previously described (15), except that a lower wave length (230 mp) was used to increase the sensitivit’y. All activities are in terms of initial velocities, AD per minute (00). The estimation of initial velocities in the case of low substrate concentration was made with the aid of a mirror and straight edge t’o fit a tangent to t#he curve at the origin as described by Livingston (16). This method was found to be superior

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658 ENOLASE KINETICS

in speed and reproducibility to that of fitting the data to an empirical cubic equation, as previously done (15).

Reactions that were too rapid for manual rate determination were recorded on a 10 mv. Leeds and Northrup recorder, with a chart speed of 0.5 inch per 10 seconds and a response time of 1 second for full scale de- flections.

Normal mixing was performed by adding 25 ~1. of enzyme solution to the substrate in the cuvette, by using a plastic plunger described by Boyer and Segal (17). For faster reactions, and measurements below O”, a two chamber, “stopped flow” mixing device, similar to that of Beers (18), was used.

Temperature Control-For measurements between O-40”, the Beckman cell compartment was temperature-controlled by means of the “thermo- spacer” arrangement; the temperature was read on a thermometer in- serted into a cell half filled with water before and after each set of three measurements. Below O”, a 30 liter glycol-water bath, refrigerated and temperature-controlled, was used as temperature controller and stabilizer for the “stopped flow” mixer. Temperature was measured with a thermo- couple and recorded automatically. Fuller details will be given in a sub- sequent publication.

The absorption spectrum of phosphoenolpyruvic acid from 220 to 244 rnp was found not to be significantly temperature-dependent under the conditions of our experiments.

Determination of Substrate-Metal Interaction-The determinations of the dissociation constant for the complex between the substrates and Mg++ were based on the difference in molar extinction coefficients between the free and metal-complex forms of phosphoenolpyruvic acid, as discussed by Malmstrijm (19).

Ultracentrifugal Studies-The ultracentrifugal behavior of enolase in aqueous solution was compared with that in some mixed solvents in a Spinco model E ultracentrifuge.

Results

Buffer E$ects-Fig. 1 shows the temperature dependence of the enolase reaction under four different conditions. The two lower curves (Curves c and d) were obtained by using phosphate buffer at pH 6.8, while the two upper ones (Curves a and b) were obtained by using Tris-HCl buffer at pH 7.8. Both pairs of curves were recorded under comparable conditions, i.e. at optimal concentrations of substrate and Mg++. The pH values of the solutions were the same at all temperatures. The rates shown for Curves b and d were determined in the presence of 27 per cent glycerol (by weight), while those shown for Curves a and c were determined in purely aqueous

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E. W. WESTHEAD AND 33. G. MALMSTRiiM 659

solution. There are two significant differences between the pair of curves obtained in phosphate buffer and the pair obtained in Tris-HCl buffer. The first difference is that the two phosphate curves, Curves c and d, show a distinct deviation from linearity at the low temperature side of the plot,, while the other two curves are linear throughout the temperature range measured. An experiment similar to that recorded for Curve b was per-

2.5

32 33 36 35 36 1 O&x T-'

FIG. 1. Arrhenius plots for the enolase reaction under different experimental conditions. Curve a, Tris-HCl buffer, 0.050 N, pH ‘7.8; [Mg++] = 1F2 M; [PGA] = 4.1 X 10V3 M, aqueous solution; enzyme concentration = 2 t.o 3 y per m.l. Curve b, Tris-HCl buffer, 0.050 N, pH 7.8; [Mg++] = 1OW _nl; [PGA] = 4.1 X 10W3 ;M; 27 per cent (weight) glycerol solution; enzyme concentration = 2 to 3 y per ml. Curve c (cf. (6)), phosphate buffer, p = 0.05, pH 6.75; [Mg++] = 8 X lo+ 11, [PGA] = 2.4 or 3.6 X 10V3 M, aqueous solution; enzyme concentration = approximately 10 y per ml. Curve d, phosphate buffer, p = 0.05, pH 6.8; [Mg++] = low2 SI; [PGA] = 3.6 X 10e3 M; 27 per cent (weight) glycerol solution; enzyme concentration = approximately 5 y per ml.

formed in the presence of 0.500 M HCl, but carried to -7.5”. The two rates recorded at this temperature also fell on the straight line.

The second difference to be noted is that, although there is a distinct difference in slope bet’ween Curves c and d, no such difference exists between the upper two curves. The Arrhenius “activation energy” calculated from the slopes of Curves a and b is 12,720 calories, with a probable error for Curve a of 75 calories and a probable error for Curve b of 140 calories. Arrhenius plots for two intermediate concentrations of glycerol in phosphate buffer were also obtained; both these curves manifested the drop in rate near O”, and they had slopes intermediate between those of Curves c and d. The scatter is appreciably less in phosphate buffer, pre-

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sumably owing to the metal-buffering action of the phosphate ion, which can damp effects of traces of inhibitory metal ions (13).

Table I shows a further difference between results in phosphate buffer and those in Tris-HCl. Ax previously reported by Malmstrdm (6), there is a difference in the activation energies between the reaction catalyzed by Zn++-activated enolase and that catalyzed by the Mg++-activated enzyme. Those results were obtained in phosphate buffer, pH 6.8. In the Tris-HCl-buffered solutions, pH 7.8, this difference remains, but it is of a considerably lower magnitude. In the earlier work referred to, it was shown that the difference in activation energy was 3 times as large as the difference in rates would have led one to predict, indicating an appreciable difference in entropy factors. In the Tris-buffered system, however, the difference in activation energy is approximately that which

TABLE I

Comparison of Kinetic Parameters at 20” for Mg++- and Zn++-Activated Enolase

Activator BUl33

Mg++ Zn++ Mg++ Zn++

Phosphate “

Tris-HCI “

Activation energy, calories per mole

14,600 15,100 14,270 14,860

Ratio of rates zn++ - Mg++

0.34

0.32

Difference in activation energy, calories per mole

- Calculated* Found

600 1900

670 590

* Calculated with the assumption that there is no difference in entropy terms.

would account for the difference in activity. These effects will be considered further under “Discussion.”

Inhibition by Substrate and Activating Metal Ion; Effect of Added Xalt- Plots of activity as a function of either substrate or activating metal ion concentration show considerable deviation from the Michaelis-Menten type of kinetics in either of the two buffers used in this study. This deviation is especially marked in Tris-HCl buffer, as shown in Fig. 2, which records the change of activity with substrate concentration at two different concentrations of Mg++. The form of the upper curve is typical of plots of activity as functions of either metal ion or substrate when the concentration of the other species is near its optimum; i.e., in the case of the upper curve the metal ion is at the concentration at which maximal activity can be obtained. When the concentration of metal ion is raised to a markedly inhibitory level, however, the curve of activity versus substrate concentration shows a distinctly different form (Fig. 2, lower curve), and a Lineweaver-Burk plot (20) of the data does not approximate a straight

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E. W. WESTHEAD AND B. G. MALMSTRijM 661

line over any reasonable portion of the plot. The exact shape of these curves is influenced by both the metal ion used and the buffer. In phosphate buffer, for example, the metal-buffer effect of the phosphate ion makes the maximum of a curve of activity versus [Mg++] much less sharp in addition to displacing it to higher metal ion concentrations.

x- Methanol

25-

I I I 8 I I I I I 2

[PG$X103 6 8 12 3 4 5

[PGPj x10’

FIG. 2 FIG. 3

FIG. 2. Enolase activity as a function of [PGA] in Tris-HCl buffer, 0.050 N, pH 7.8; in aqueous solution at 20”; enzyme concentration = approximately 10 y per ml. Upper curve, [Mg++] = 1OF M; lower curve, [Mg++] = 1OW M.

FIG. 3. Enolase activity as a function of [PGA] at 20”; in Tris-HCl buffer, 0.050 N,

pH 7.8; [KC11 = 0.500 M; [Mg++] = 5 X 10-a M. Upper curve, aqueous solution; middle curve, 20 per cent (volume) methanol; bottom curve, 22.5 per cent (volume) dioxane. Enzyme concentration for upper curve, approximately 5 y per ml.; middle and lower curves, 30 y per ml.

In the absence of added salt, the change of ionic strength with changing concentration of metal ions or substrate (triply charged) is large, and the effect of this on the rate of reaction is unpredictable. To reduce the effect of ionic strength changes, the reaction solutions were made 0.500 M in KCl. This change made a great difference in the plots of activity versus substrate concentration, as seen from the top curve in Fig. 3; over the substrate concentration range 2.5 X 1O-3 to 5.0 X 10e3 M, no change in activity could be detected, and below 2.5 X 10e3 M the data yield a good straight line when plotted according to the method of Lineweaver and Burk.

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On the other hand, a plot of activity versus metal ion concentrat,ion at high salt concentration, while approaching much more closely the form of the “ideal” curve, still shows a maximum instead of a plateau region. An experimental determination of the dissociation constant (Kd) for the Mg++ complex of PGA gave a value of 0.10 mole per liter for I<, in 0.500 M KC1 solution. This value for Kd means that at a total substrate concentration of 3 X 10V3 and a Mg++ concentration of 5 X 10-3, the concentration of the complex is only 1 X 1O-4 M; thus the amount of substrate “removed” from the system in this way cannot cause a significant lowering of the activity.

Solvent E$ects-In all of the experimenk involving organic solvents, a standard set of conditions was used with regard to buffer, Mg++, and substrate concentrations, except when there is an explicit indication to the contrary, e.g. in a plot of vg as a function of substrate concentration. These standard concentrations were for PGA, 3 X 1O-3 M; Mg++ (as chloride), 5 X 1O-3 M; KCl, 0.500 M; Tris-HCl buffer, pH 7.8, 0.05 N in positive ion. In purely aqueous solution under these conditions experiments showed that the substrate concentration is on the plateau of a Michaelis-Menten plot, that the Mg++ activation is at its maximum, and that the concentration of the Mg++ complex of PGA is well below a significant level (c-f. previous section). To be sure that this situation was not affected by the presence of organic solvents, it was necessary to determine v. as a function of both PGA and Mg++ concentrations in the solutions containing these solvents. Fig. 3 illustrates the variation of v. with PGA concentration in solutions containing dioxane and methanol, in comparison with the curve obtained in purely aqueous solution. Although the Michaelis constant (K,) is obviously reduced in the presence of the solvents, the plateau region is extensive enough to insure that, at a concentration of 5 X low3 M PGA, there is no danger of substrate inhibition affecting the rate. Less complete experiments with ethanol and glycerol showed that the same situation prevails in the presence of those solvents. The values of K, are so low in the presence of these solvents that it was not practicable to determine t.his constant as a function of solvent concentration.

The plots of activity as a function of Mg++ concentration (Fig. 4) con- tinue, in the presence of the organic solvents, to show the same broad maximum as in aqueous solution, and, at 5 X 1O-3 M Mg++, the curve is so flat that even a 10 per cent change in metal ion concentration would not lead to an important change in the rate of reaction. The curves shown in Figs. 3 and 4 are satisfactory evidence that, at the concentrations of Mg++ and PGA used in our experimenk, the addition of the organic solvents does not significantly increase the formation of the metal-substrate complex. Similarly, the curves of Fig. 4 are satisfactory evidence

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E. W. WESTHEAD AND R. G. MALMSTRBM 663

that the extent of metal ion inhibition is not appreciably affected by the presence of these solvents. In addition, control experiments showed that the concentrations of substrate and Mg++ were such that no appreciable change in activity was caused by the temperature dependence of the dissociation constants of the respective complexes.

80-

10 60-

40-

20-

-603

ii -40 s

3

-20.s

--Y 0

9

I I I I I I

2 4 6 8 10 90 80 70 60 50 [Mg++]x103 Grams H,O per 100 ml solution

FIG. 4 FIG. 5

FIG. 4. Enolase activity as a function of [Mg++] at 20”, in water and in the presence of organic solvents, in Tris-HCl buffer, 0.050 N, pH 7.8; [KC11 = 0.500 M; [PGA] = 3 X 10-a M. Solutions contained dioxane, 20 per cent (volume); methanol, 20 per cent (volume); glycerol, 18 per cent (weight); ethanol, 20 per cent (volume). Enzyme concentration, dioxane and methanol solution, approximately 8 y per ml.; glycerol and ethanol solution, approximately 4 y per ml.

FIG. 5. Relative activity of enolase as a function of water concentration at 20” in the presence of four organic solvents. Ordinate for glycerol mixtures on the right- hand side of the figure. Tris-HCl buffer, 0.050 N, pH 7.8; [Mg++] = 5 X 1OF M;

[KC11 = 0.500 M; [PGA] = 3 X 1OV M; enzyme concentrations = approximately 10 y per ml.

Fig. 5 shows the effect of organic solvents on vo, which, according to the experiments just described, represents maximal velocities. Although a single curve is fitted to the combined data for ethanol, methanol, and dioxane, a closer inspection of Fig. 5 reveals that separate curves might well be fitted to the data for each of the three solvents, with a somewhat better fit resulting. However, the importance of these data lies not in the small differences, but rather in the striking similarities of the effects of the various solvents. The significance of this will be considered under “Discussion.”

Fig. 6 shows Arrhenius plots for reactions run in water and in the pres-

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ence of three solvents. I’;0 data are shown for ethanol solutions because denaturation occurred rapidly in the presence of this solvent at the high-

3.20 3.30 3.40 350 360 1000/T

FIG. 6 FIG. 7 FIG. 6. hrrhenius plots for the enolase reaction in H&J and in the presence of or-

ganic solvents. Tris-HCl buffer, 0.050 N, pH 7.8; [KCl] = 0.500 M; [Mg++] = 5 X IO-3 &5\1; [PG$] = 3 X 10m3 M; enzyme concentration = approximately 5 y per ml. Di- oxane, 20 per cent (volume) ; methanol, 20.5 per cent (volume) ; glycerol, 33.1 per cent (weight). The values of log vo for diosane solut.ions have been increased by 0.01 to separate them from the methanol data.

FIG. 7. Sedimentation patterns of enolase and of dioxane solution without protein. Protein concentration in (a), (b), and (d) approximately 1.5 per cent, but varying slightly from run to run. All the solutions contain 0.05 N Tris-HCl buffer, pH 7.8, and 0.500 ;\I KCl. The average temperature during the runs was 20”. Speed, 59,780 r.p.m. In (a), enolase in aqueous solution; (5)) enolase in 10 per cent (volume) methanol; (c), 10 per cent (volume) dioxane solution, no protein; (d), enolase in 10 per cent (volume) dioxane. The time (in minutes after speed equilibration) and base angles are as follows: (a) and (d), 19 minutes, 60’; 35 minutes, 60”; 51 minutes, 60”; 67 minutes, 50”; (b), 16 minutes, 63”; 48 minutes, 60”; 64 minutes, 60”; 80 minutes, 60”; (c), 1,33, 49, and 65 minutes, all 60”.

est temperatures measured (38”). That no denaturation occurred in the other solvents was shown by the fact that the plots of optical density versus time remained linear to as high an optical density as at the lower temperatures.

In view of the effect of organic solvent on rate, we had to consider the

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E. W. WESTHEAI) AND B. G. MALMSTRijM 665

possibility that the concentration of active protein was being decreased either by permanent denaturation or by reversible association into inactive aggregates such as must occur prior to precipitation by higher concentrations of these same organic solvents. The former of these possibilities was readily ruled out, since enzyme solutions containing high concentrations of the organic solvents showed full activity, when assayed in the absence of solvent, even after several hours storage.

The second possibility was eliminated by investigating the effect of solvent additions on the sedimentation behavior of enolase. Exposures from four runs under different conditions are shown in Fig. 7. Since there is a possibility that a concentration gradient is set up owing to differences in density between water and the added solvent, a run without protein was included (Fig. 7, c). The relative sedimentation constants in water, methanol, and dioxane, corrected to the same density and viscosity (al), were found to be 1.00: 1.03:0.98. The significance of these results will be discussed later.

DISCUSSION

Bu$er Bffects-To explain the effect of temperature on the enolase reaction in phosphate buffer, it has been postulated (6) that the active site on the enzyme can exist in two forms, one being found in the Mg++-enzyme at temperatures above approximately 5”, the other in the Zn++- or Mn++- enzyme and in the Mg ++-enzyme at low temperatures. However, the data in Fig. 1 and Table I show that the low temperature “inhibition” and the differences in entropies of activation upon which the hypothesis was based disappear when the rate measurements are carried out in Tris- HCI buffer. This suggests strongly that the different forms of the enzyme are due to binding of HPO,= at the active site, the effects of the activating ions being explained by the higher affinity of Zn++, as compared with Mg++, for this ion. Since the addition of glycerol has no effect on the activation energy in Tris-HCI, it appears probable that the difference between Curves c and d is due to an effect of the solvent on the inhibition by HPOd. Unfortunately, for reasons of buffering capacity and solu- bility of metal phosphates, t)he measurements in the two buffers could not be carried out at the same H30+ concentration; thus complicating pH effects cannot be excluded. However, the addition of HPOJ= to the Tris buffer caused a distinct change in the slope of the Arrhenius plot of the Mg++-enzyme, measured at the same concentration of free Mg++, showing that t’his ion must be involved in the observed effects.

The interpretation of the temperature effects given here is analogous to the findings of Kistiakowsky and Lumry (4), who showed that the ion t,emperature “inhibition” of urease is due t,o int,eractions bet,ween the

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enzyme and components of the reaction system. Thus, the alternative interpretation of Kavanau (22), invoked also by Maier et al. (5) and by Hultin (23), viz. the formation of intramolecular hydrogen bridges, can be excluded in these two cases. With enolase, as has already been pointed out (6), the entropy factors are, in addition, too small to be due to a major conformation change. It may well be that ion effects are involved in all reported cases of low temperature “inhibitions” of enzymes, and a detailed study of such systems is now in progress.

Inhibition by Substrate and Activating Metal Ion-Earlier studies (11, 12) have shown that the kinetic formulation of Warburg and Christian (24) is partly incorrect, since the rate as a function of substrate concentration was shown to go through a maximum. Furthermore, high concentrations of metal ions were found to inhibit the enzyme; hence the simple mass action law of Warburg and Christian is not applicable. Various possible explanations of these effects have been advanced (11, 15), but most of these can be eliminated by the present data which, as will be seen, are best accounted for by assuming that the inhibition by substrate is due to removal of activating ion by complex formation, while the metal ion inhibition is caused by direct interaction with the enzyme. The following reaction sequence is postulated :

KG E+MBEM

Ki E+M C EM' (inactive)

(1)

(2)

kl EMfS ___L EMS

kz (3)

Kd SSM - SM (4)

EMS h - EM+P (5)

where E, M, S, and P represent enzyme, metal ion, substrate, and product, respectively, while the K symbols indicate dissociation constants and the lc ones rate constants. On the basis of this mechanism, the following rate law can be derived (cf. (15)) :

ka Ki Kd ~ EMS

vo - & + 8

(Km + 8) Kcz + j&M d >(

Ki + Kd

(6) -M & + 8 >

where E and M stand for the total concentrations of enzyme and metal ion, respectively, while S represents the concentration of free substrate,

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E. W. WESTHEAD AND B. G. MALMSTR8M 667

and K, is assumed to equal kz/kl, as indicated by previous studies (12). Equation 6 can be shown to describe the type of rate curves shown in Fig. 2. However, when S and M are small compared to Kd, no appreciable decrease in activity due to removal of M should be possible. In such a case, at a constant value of M, which is high compared to K, but low compared to K;, Equation 6 reduces to

k, ES

vo = K,+s

i.e., Michaelis-Menten kinetics should be followed. Fig. 3 shows that this is the case in 0.50 M KCl, where Ka = 0.10 mole per liter (see under “Results”) ; hence the condition for the applicability of Equation 7 is ful- filled.

In contrast to this, the metal ion inhibition does not disappear in 0.50 M KCI, as seen in Fig. 4, indicating that this cannot be wholly explained as a removal of S owing to the reaction in Equation 4. This is also demonstrated by the fact that this inhibition is found even in the case of Zn+f (11) which has an activating concentration negligible compared to that of S. The most probable explanation of the metal ion inhibition will be given in conjunction with the solvent effects.

The applicability of Equation 7 under certain experimental conditions has made it possible to measure separately the effect on k3 and Km of such extrinsic factors as temperature and solvent concentration, as described under “Results.” The measured kS is, of course, only the rate constant for the slowest step. Since several elementary reactions, in addition to the ones shown in Equations 3 and 5, must be involved in the formation and breakdown of EMS, it cannot be assumed that kg always refers to the same step, as variations in conditions may cause a shift in relative rates, making another step the slowest one. Such changes have been implicated in the case of papain kinetics (25), but, as will be shown, they are appar- ently not involved in the present case.

Solvent E$ects-As seen from Fig. 5, all organic solvents used in this study have a marked inhibitory effect on the enolase reaction. Under the conditions of the measurements, this can be due to a decrease in k~ or in the concentration of active enzyme. An explanation in terms of a lowering of kt can immediately be ruled out, since the solvent additions have no significant effect on the activation energies, as shown in Fig. 6.

The most obvious may in which a decrease in E could occur would be through an association of protein molecules such as must occur prior to precipitation by the organic solvents. In such a case (see Fig. 5), at a concentration of 10 per cent dioxane or methanol, it would be expected that only 70 per cent of the enzyme would be unassociated and hence active. However, no evidence of association could be found in the ultra-

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centrifugal experiments, since no decrease in the area under the peak was observed and there was no sedimentation of larger particles during the entire experiment, including the acceleration phase.

A very striking feature of Fig. 5 is the fact that three of the four solvents used have nearly identical effects on the rate despite great differences in dielectric constant, the physical property most commonly invoked to explain solvent effects. This suggests that the rate decrease is due to the displacement of water rather than to a specific effect of the solvents. Such an effect could readily be understood by a comparison with the mechanism for the analogous fumarase reaction, for which Alberty (1) has demonstrated t.he involvement of a proton donor and a proton acceptor on the enzyme surface. The decreased water concentration, at a constant pH, would affect the degree of dissociation of the proton-transferring groups, and this would result in a lowered rate. If this interpretation is correct, the group being affected would most likely be an amino or imidazole and not a carboxyl group,l since the dissociation of the latter, but not of the former, would be strongly dependent on the dielectric constant. In connection with this mechanism, it also seems likely that the inhibition caused by an excess of activating metal ion is due to an interaction of the metal with one of the groups of the enzyme necessary for catalysis.

It should be noted in Fig. 5 that the activity approaches zero at still very high concentrations of water. This may be due to the water concentration in the neighborhood of protein complex being much lower than that in the bulk of the solution (cf. (26)). Differences in solvent distribu- tion may also explain the fact that glycerol is a somewhat less effective inhibitor than the other three solvents (Fig. 5).

As was previously mentioned, the experiments described herein are intended partially as a background to low temperature studies. Since the interpretations offered here indicate that solvent additions do not change the mechanism of the reaction, there appears to be no formal ob- jection to the use of the suggested low temperature technique for the study of transient state kinetics.

The work presented in this paper shows that, while useful information may be obtained from the use of solvent mixtures in studying enzyme kinetics, the situation may be very complex. Results obtained from limited experiments may easily be subject to gross errors in interpretation. At the present time, only a few investigators have actually applied such

1 In principle, it should be possible to test this hypothesis by determining the maximal initial velocity (o”~:,~) as a function of pH (l), but in practice it has been impossible to arrive at the true urnal at all pH values, since both the metal ion activation and inhibition change with pH in a way in which it is difficult to make correc- tions (unpublished data of Malmstriim and Westlund).

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E. W. WESTHEAD AND B. G. MALMSTRiiM 669

methods to the study of enzymic catalysis, but in each case the results have been discussed in terms of dielectric constant effects. However, data in the literature (27, 28) make it apparent that factors other than dielectric constant changes must play a major role.

The danger in the interpretation of results obtained from the use of a single organic solvent became apparent to us when it was found that our dioxane data, when plotted as log rate versus (dielectric constant)-‘, fit a good straight line over most of the range of measurement. When the results on all four solvents were plotted in a similar way, it became quite apparent that no such correlation exists between rate and dielectric constant. The several papers by Laidler et al. (29-31), in which is discussed the application of concepts of dielectric constant effects derived from reactions of smaller molecules to enzyme kinetics, thus seem to be of limited practical significance, at least in the general case.

It is not very surprising that activity changes do not show a good correlation with dielectric constant changes in enzymic catalysis. The theory of dielectric constant effects is based on the concept of a continuous medium of changing dielectric constant; this is, of course, not strictly applicable in the best of instances, but in enzyme catalysis, occurring at the surface of a very large body of unchanging dielectric constant, it is cer- tainly far from reality. It is easy to see, then, that any other effect of the organic solvent may easily overshadow the very reduced effect due to the changing dielectric constant, although these other effects may well give valuable information themselves when properly understood.

SUMMARY

1. The effect of substrate and activator concentration, as well as of temperature, on the rate of the enolase reaction has been measured under a variety of experimental conditions. These include the use of different buffers and the addition of inorganic salt and of organic solvents (dioxane, methanol, ethanol, and glycerol). Conditions have been devised allowing separate estimation of the effect of these extrinsic factors on the rate constant for the slow step (ks) and on the Michaelis constant (K,).

2. The differences in low temperature fall off in the Arrhenius plot and in steric factors between the Mg ++- and Zn++-activated enzyme, observed in phosphate buffers (6), disappear when the rate measurements are carried out in tris(hydroxymethyl)aminomethane-HCl. Because of this, it is suggested that the different forms of the enzyme, postulated previously (6)) involve binding of HPOb= at the active site rather than an intramolecular rearrangement.

3. The inhibition by high substrate concentrations has been shown to be due to removal of activating metal ion through complex formation.

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670 ENOLAST” KINETICS

At high salt concentrations (0.50 at KCI), at which the metal-substrate interaction is weak, this effect disappears, and Michaelis-Menten kinetics are followed. The inhibition by high activator concentrations, on the other hand, cannot be entirely accounted for in terms of removal of substrate, and it is postulated that the metal ion interacts with a proton acceptor or donor necessary for the reaction on the enzyme surface.

4. All solvents added decrease both iY, and the maximal velocity of the reaction. Ultracentrifugal measurements have shown that the diminished rate is not due to protein association. The activation energy is not changed by the addition of solvent. The four solvents studied have very similar effects which bear no relation to the bulk dielectric constant. It is suggested that a displacement of water is mainly involved. This is inter- preted as affecting the dissociation of an amino or imidazole group of the enzyme.

The authors would like to thank Professor A. Tiselius for helpful discussions and, in the case of the first author, for his hospitality. We are also indebted to Dr. Kai 0. Pedersen for helpful consultations on the per- formance and interpretation of the ultracentrifugal experiments. This work has been supported by grants from the Rockefeller Foundation and the Knut and Alice Wallenberg Foundation.

BIBLIOGRAPHY

1. Alberty, R. A., Advances in Enzymol., 17, I (1956). 2. Koshland, D. E., Jr., in McElroy, W. D., and Glass, B., The mechanism of en-

zyme action, Baltimore, 608 (1954). 3. Chance, B., in Friess, S. L., and Weissberger, A., Investigations of rates and

mechanisms of reactions, New York, 627 (1953). 4. Kistiakowsky, G. B., and Lumry, It., J. Am. Chem. Sot., ‘71, 2006 (1949). 5. Maier, V. P., Tapper, A. L., and Volman, D. H., J. Am. Chem. Sac., 77, 1278

(1955). 6. Malmstrom, B. G., Biochim. et biophys. acta, 18, 285 (1955). 7. Gutfreund, H., Discussions Faraday Sot., 20, 167 (1955). 8. Roughton, F. J. W., and Chance, B., in Friess, S. L., and Weissberger, A., In-

vestigations of rates and mechanisms of reactions, New York, 669 (1953). 9. Amis, E. S., Kinetics of chemical change in solution, New York (1949).

10. Hammett, L. P., Physical organic chemistry, New York (1940). Il. Malmstrom, B. G., Arch. Biochem. and Biophys., 46, 345 (1953). 12. Malmstriim, B. G., The mechanism of metal-ion activation of enzymes; studies on

enolase, Uppsala (1956). 13. Malmstriim, B. G., Arch. Biochem. and Biophys., 70, 58 (1957). 14. Malmstrom, B. G., in Glick, D., Methods of biochemical analysis, New York, 3,

327 (1956). 15. Malmstrom, B. G., and Westlund, L. E., Arch. Biochem. and Biophys., 61, 186

(1956). 16. Livingston, R., in Friess, S. L., and Weissberger, A., Investigations of rates and

mechanisms of reactions, New York, 169 (1953).

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E. W. WESTHEAD AND B. G. MALMSTRGM 671

17. Boyer, P. D., and Segal, H. L., in McElroy, W. D., and Glass, B., The mechanism of enzyme action, Baltimore, 520 (1954).

18. Beers, R. F., Jr., Biochem. J., 62, 492 (1956). 19. Malmstriim, B. G., Arch. Biochem. and Biophys., 58, 381 (1955). 20. Huennekens, F. M., in Friess, S. L., and Weissberger, A., Investigations of rates

and mechanisms of reactions, New York, 535 (1953). 21. Svedberg, T., and Pedersen, K. O., The ultracentrifuge, London (1949). 22. Kavanau, J. L., J. Gen. Physiol., 34, 193 (1950). 23. Hultin, E., Acta them. Stand., 9, 1700 (1955). 24. Warburg, O., and Christian, W., Biochem. Z., 310, 384 (1941-42). 25. Smith, E. L., Finkle, B. J., and Stockell, A., Discussions Faraday Sot., 20, 96

(1955). 26. Lumry, R., and Eyring, H., J. Phys. Chem., 58, 110 (1954). 27. Lumry, R., and Smith, E. L., Discussions Faraday Sot., 20, 105 (1955). 28. Kaufman, S., and Neurath, H., J. Biol. Chem., 180, 181 (1949). 29. Barnard, M. L., and Laidler, K. J., J. Am. Chem. Sot., 74, 6099 (1952). 30. Laidler, K. J., and Ethier, M. C., Arch. Biochem. and Biophys., 44. 338 (1953). 31. Laidler, K. J., Discussions Faraday Sot., 20, 83 (1955).

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