J. Phys. Chem. 1987, 91, 5755-5760 TABLE 111: Sulfur Radical Reaction Rate Coefficients
reaction S + NO2 SO + NO HS + NO2 HSO + NO CH3S + NO2 products SO + NO2 SO2 + NO HSO + NO2 products S + O3 SO + O2
--- + + + - + + +
HS
so
HSO
0 3 0 3
O3
HSO
so2
0 2 0 2
products
rate coeff (298 K), cm3 molecule-' s-I 6.0 X lo-" (ref 26) 6.7 X lo-" (ref 8) 8.0 x lo-" (ref 37) 1.4 X lo-" (ref 26) 9.6 X (this work) 1.2 X lo-" (ref 26) 3.2 X (ref 6) 9.0 X (ref 26) 1.0 X lo-" (ref 6)
will not be important in the atmosphere because of the rapid competing reactions involving 02.These oxygen reactions, (10) and (15), both produce H02. The role of ozone in the sequence requires further study. The effect of the reaction of ozone with HS is similar to that of NOz since it also produces an H S O product. An interesting ozone influence may occur in the reaction with HSO. There are a number of possible reaction pathways and no definitive product analysis has been performed. HSO + O3 AH298 = -22 kcal mol-' OH SO O2 (17a)
--
+ + HS + 2 0 2 AHzss = 1 kcal mol-' A H 2 9 8 = -52 kcal mol-' H + O2+ SO2
+ O2 H 0 2 + SOz HS02
(17b) (17c)
AH298
= -86 kcal mol-'
(1 7 4
AH298
= -101 kcal mol-'
(17e)
Reactions 17b and 2 represent a catalytic cycle for O3destruction as discussed by Fried1 et aL6 This cycle would be interrupted by
5755
other loss channels for HSO and HS. HSO removal by reaction with NOz is thus the only established path for HSO oxidation. Prior to the availability of kinetic data for HS, its reactivity was often predicted to be similar to OH. However, recent results indicate that this is not a good analogy and other comparisons, particularly with Br,6 have been discussed. With regard to trends in reactivity, it is interesting to note the similarities among the homologues of the two sets of sulfur radicals: S/HS/CH3S and SO/HSO. The rate coefficients for the reactions of these species with NOz and O3are presented in Table 111. Each set of reactions appears to proceed by a similar mechanism and the homologues exhibit similar reactivities at room temperature. It is interesting to note that the mechanism of 0 atom transfer to the sulfur is consistent with HS02 production via reaction 9. When there is not an analogous exothermic channel available, the homologue reactivities vary. For example, the reaction
s+0 2
- so +
0
(18)
is reasonably fast (k18= 2.3 X cm3 molecule-l s-')~~ but the similar reactions of HS and CH3S are endothermic and are not cm3 molecule-' s - ' ) , ~ , ~ ' observed ( k C 2 X
Acknowledgment. This work was supported by NOAA as part of the National Acid Precipitation Assessment Program. We are grateful to Dr. T. J. Sears for assistance with the LMR spectroscopy of HSO and to Dr. A. R. Ravishankara for his useful comments on the manuscript. Registry No. HSO, 62470-71-7; NO2, 10102-44-0;NO, 10102-43-9; 0 2 , 7782-44-7. (37) Balla, R. J.; Nelson, H. H.; McDonald, J. R. Chem. Phys. 1986, 109,
101.
Effects of Pressure on the Sucrose Inversion over an Immobilized Invertase Catalyst Masanori Sato, Sentaro Ozawa, and Yoshisada Ogino* Department of Chemical Engineering, Faculty of Engineering, Tohoku University, Aramaki-Aoba, Sendai 980, Japan (Received: February 9, 1987; In Final Form: May 19, 1987)
Kinetics of the sucrose inversion over an invertase catalyst immobilized by porous glass particles has been studied under high pressures up to 127 MPa and at a temperature of 30 f 0.1 OC. The rate equation derived by using the Michaelis-Menten type kinetic model well represents reaction rates observed for E + S + ES EF + G E + F and E + G + EG, where E, S, ES, F, G, EF, and EG denote enzyme, substrate, Michaelis complex, fructose, glucose, enzyme-fructose complex, and enzyme-glucose (inhibitor) complex, respectively. Utilizing the rate equation, one can evaluate kinetic parameters such as the maximum reaction rate V-, the Michae1i:constant K,, and the inhibitor constant Ki as a function of pressure. The activation volume (AVJ), the volume change (AV,) for the dissociation of the Michaelis complex, and the volume change (AVJ for the dissociation of the inhibitor complex have been determined to be -29 f 3 mL/mol, +20 f 3 mL/mol, and +1 f 0.1 mL/mol, respectively, at 0.1 MPa. A strong polarity induced by the enzyme upon the transition state together with an incorporation of one water molecule into the transition state would account for the fairly large negative activation volume.
-
Introduction Little information about the effect of pressure upon the beterogenmus a&lysis in solution is available in the literature, though numerous papers reporting the pressure effects upon chemical reactions in solutions have hitherto been published.'+ Considering (1) Hamann, S. D. Physico-Chemical Effects ofpressure; Butterworths: London, 1951. ( 2 ) Weale, K. E. Chemical Reactions at High Pressures; E.& F.N. SPN: London, 1967. (3) Kelm, H., Ed. High Pressure Chemistry; D. Reidel: London, 1978.
0022-3654/87/2091-5755$01.50/0
-
this situation, the present authors have attempted to make a series of high-pressure studies on solid-liquid interfacial phenomena, andtar€' ofthe results have already been The Present (4) Isaacs, N. S . Liquid Phase High Pressure Chemistry; Wiley: New York, 1981. ( 5 ) Noguchi, H.; Uchiyama, G.; Ozawa, S . ; Ogino, Y. Nippon Kagaku Kaishi 1980, 1195. ( 6 ) Ozawa, S.; Gotoh, M.; Kimura, K.; Ogino, Y. J. Chem. SOC.,Faraday Trans. 1 1984, 80, 1049. (7) Ozawa, S.; Kawahara, K.; Yamabe, M.; Unno, H.; Ogino, Y. J . Chem. SOC.,Faraday Trans. I 1984, 80, 1059.
0 1987 American Chemical Society
Sat0 et al.
5756 The Journal of Physical Chemistry, Vol. 91. No. 22, 1987
@
@
50
c
QQ 40 ,P
Q
.3 0 x 20
10
0 0
2
4 Time
6 I
8 h
Figure 2. Relations between the sucrose conversion ( X ) and the reaction period ( t ) for different initial sucrose concentrations (in mol/L) at 0.1MPa pressure: 0 , 0.06; 0 , 0.09; 8 , 0.12; 0, 0.15. Error bars indicate
maximum deviations.
Figure 1. Schematic drawing of the reactor assembly: 1, electric lead wire; 2, Teflon tube; 3, top closure; 4, top cover; 5, stainless steel plug (pressure transmitter); 6 , opening with filter; 7, high-pressure shell; 8, glass cell; 9, stirrer; 10, outer magnet; 11, motor; 12, bottom closure; 13, bottom cover; 14, O-ring seals; 15, reaction mixture. study aims at extending the above-mentioned series to biological fields, particularly to heterogeneous enzymic problems. With the purpose mentioned above, the rate of sucrcse inversion has been measured at high pressures up to 127 MPa with an immobilized invertase catalyst. Taking account of the stability against chemical and mechanical destruction, the invertase has covalently been immobilized onto porous glass. As described in the text, the use of this catalyst gives good reproducibilities in rate measurements, allowing a derivation of useful information concerning the pressure effects. High-pressure studies on catalysis by immobilized enzymes are scarce in the literature, though there is abundant information'^^ about the pressure effects upon homogeneous enzymic reactions. For the sucrose inversion reaction, previous researchers have studied only the effects of pressure upon homogeneous reaction systems. For instance, Whalley et aL8 have studied the pressure effects upon the sucrose inversion using a homogeneous acid catalyst. Eyring et a1.: Laidler,lo and Ludwig et al." have studied the pressure effects upon the sucrose inversion in a homogeneous solution containing native invertase. Although Venkatasubramanian et al.12 have studied the same reaction with invertase immobilized onto collagen under pressures up to -2 MPa, no physicochemical information about the pressure effects has been obtained.
Experimental Section Immobilized Enzyme and Substrates. An invertase (p-Dfructofuranoside fructohydrolase, EC 3.2.1.26) was commercially obtained (Wako Pure Chemicals Ind., Ltd.) and immobilized onto porous glass (Electro-Nucleonic Inc.; 0.13-0.1 8-mm particles with the specific surface area of 40.7 m2/g and mean pore diameter of 52.2 nm). The method reported by Mason13 was used in the immobilization: the enzyme/glass ratio was 0.05 by weight. The immobilized enzyme was stored in a refrigerator, keeping wet (8) Whalley, E. Trans. Faraday SOC.1959, 55, 198. (9) Eyring, H.; Johnson, F. H.; Gender, R. L. J . Phys. Chem. 1946, 50, 453. (10) Laidler, K. J. Arch. Biochem. 1951, 30, 226. (11) Ludwig, H.; Greulich, K. 0. Biochemistry 1978, 8, 163. (12) Venkatasubramanian, K.; Vieth, W. R. Biolechnol. Bioeng. 1973, 15, 583. (13) Mason, R. D.; Weetall, H. H. Biotechnol. Bioeng. 1972, 14, 631.
conditions at about 3 "C. Repeated preliminary experiments showed that the enzyme thus stored maintained constant activity, within 4~2%deviation on average. Sucrose was mainly used as a substrate, though D-glucose and D-fructose were also used in order to study inhibition effects. All these materials were commercially obtained (Guaranteed grade reagent) and used without further purification. Apparatus and Procedures. A schematic drawing of the reactor assembly used in the present study is given in Figure 1. The assembly consists of an outer high-pressure shell and an inner glass cell, A movable stainless steel plug with two O-rings is inserted into the glass cell and serves as a pressure transmitter: two O-rings always hold the plug in a right position, and the lower O-ring seal prevents the reacting solution in the cell from mixing with the pressurizing fluid (2-propanol) surrounding the cell. A Teflon tube with an i.d. of 0.5 mm is passed through the center of the plug. One end of the Teflon tube opens in the cell, and the opening is covered with a filter which separates the catalyst powder from the sampling solution. The other end of the Teflon tube is connected to the sampling valve. The Teflon tube extends from the glass cell to the sampling valve, passing through the inside of the high-pressure tubing. In addition, the glass cell contains a small bar magnet covered with Teflon. This magnet serves as a stirrer which is driven by the rotation of another magnet held on the shaft of a small motor placed outside the bottom of the glass cell. In the rate measurement, 50 mL of a sucrose solution of a predetermined concentration and 50 mg (dry base) of the immobilized invertase were introduced into the glass cell. After placing the glass cell in the high-pressure cell, we connected the assembly to a pressurizing system equipped with a plunger pump and a calibrated pressure gauge. During the reaction, the magnet stirrer was driven and the reactor assembly was immersed in a water bath maintained at a constant temperature of 30 f 0.1 O C . Samplings of the reaction solution were made at about 2-h intervals, and the analysis was carried out using a digital polarimeter (Union Giken PM-101). The sucrose conversion ( X ) was calculated by using the polarimetric data and plotted against the reaction period ( t ) . Since the ratio of the volume of the reaction system to the amount of the catalyst added varies on sampling, the reaction period was corrected by using the following relation t = t'+ A t ~ o / [~~ o ( -n l ) ]
(1)
where t is the corrected reaction period for the nth sampling, t' is the corrected reaction period for the (n - 1)th sampling, At is the interval between the ( n - 1)th and nth samplings, uo is the initial volume of the reaction system, and u is the volume of the sample solution. The rate measurements mentioned above were carried out under the following conditions: sucrose concentration, (6-1 5 ) X lo-*
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5151
Sucrose Inversion over an Invertase Catalyst
0
-1
C, I
t
x
1 1 o6 I
2 mol.l-'.S-'
Figure 5. Linear plots for rate data obtained under 0.1-MPa pressure (keys as in Figure 2). 0
2
4
6
8 Time
0 I
2
4
6
8
h
Figure 3. Relations between the sucrose conversion ( X ) and the reaction period ( t ) at different pressures (in MPa) for different initial sucrose concentrations: A, 20; B, 49; C, 98; D, 127 (keys as in Figure 2).
30
I I
.-"
-
,I 20
not show any inhibition as we can see in the figure. In contrast to this, addition of D-glUcoSe (the same amount as in M) brought about a reduction in the sucrose conversion. It can be seen in the figure that the degree of inhibition of M is almost equivalent to that of D-glucose. It is evident, therefore, that the product inhibition is due to the glucose produced. The inhibition effects revealed here are of great significance in discussing the reaction mechanism. Rate Equation and Kinetic Parameters. Taking into account the paper of Ludwig et al." and the present experimental results, in particular the inhibition results, we assumed the following reaction scheme:
X
10
G
(3)
E+G=E G Ki
0 0
2
4 6 8 Time I h Figure 4. Results of inhibition experiments at 0.1 MPa and the initial sucrose concentration of 0.15 mol/L: -, original conversion; A,addition of D-fructose (0.1 mol/L); 0,addition of equimolar (0.1 mol/L) mixture of D-fructose and D-glucose; 0 , addition of D-ghCOSe (0.1 mol/L).
mol/L; amount of catalyst, 50 mg (dry base, constant); pressure, 0.1-127 MPa; temperature, 30 f 0.1 OC (constant). Although no buffer solution was used, the pH of the reaction solution was within 5.2-5.4.
Results and Discussion Qualitative Behavior of Reaction. The sucrose conversions ( X ) for the different initial sucrose concentrations are plotted in Figure 2 and Figure 3A-D as a function of the reaction period ( t ) . The conversion becomes lower as the initial concentration of sucrose increases, and each X-t curve is convex-upward. The reproducibility of the experimental results was better than *2% so long as the immobilized enzyme stored in the refrigerator was used: extents of experimental errors determined by four separate measurements under a given condition are shown with error bars in Figure 2 and Figure 3A-D. In addition, it was proved that more than 5-h standing of the immobilized enzyme in water at 30 O C did not impair the activity. This indicated that the reaction temperature of 30 f 0.1 O C was sufficiently below the denaturation temperature of the enzyme. Furthermore, a separation of the solid catalytic phase from the reacting solution resulted in an interruption of the reaction. This proved that the dissolution of enzyme from the glass surface into the solution did not take place under the reaction conditions. Presented in Figure 4 are the results of the experiments concerning inhibition effects. Addition of an equimolar mixture (M) of D-glucose and D-fructose to the reaction mixture reduced the conversion, indicating a product inhibition. An addition of Dfructose (the same amount as in M) to the solution, however, did
where E, F, G, S, E,EF, EG, kj 0' = +1, -1, 2, 3), and Ki denote the enzyme, fructose, glucose, the substrate, the Michaelis complex, the enzyme-fructose complex, the enzyme-glucose complex (inhibitor complex), the rate constant of thejth step shown above, and the inhibitor constant (the reciprocal of the equilibrium constant of the inhibition step (3)), respectively. Although the reaction scheme mentioned above is a Michaelis-Menten type which has originally been proposed for the catalysis of the native enzyme in a homogeneous solution,'J4 the following discussion proves that it is applicable to the catalysis of the immobilized enzyme. The reaction schemes (2) and (3) together with the stationary-state approximation enable us to derive the following differential rate equation14 rate = V,,,Cs/[(l
+ CG/Ki)Km + Cs]
(4)
where V, is the maximum reaction rate defined by V , = kcC, = k2k3CEO/(k2k,) which defines the composite rate constant k, (= k 2 k 3 / ( k 2 k3)), K, is the Michaelis constant defined by K m = (k-1 + k 2 ) k c / k + , k = ~ i(k-1 + k2)/k+ll[k3/(k2+ k3)1*Ki = CECG/CEG,and C, denotes the concentration of the subscripted species ( J = E, G, S;JO = initial value for of 4..The differential rate equation (4) has a concise form, and it is seemingly convenient for evaluating the kinetic parameters. Unfortunately, however, this method needs precise measurements of the initial rates, while an assembling of the high-pressure reaction system hinders the initial rate measurements. Thus, the integral rate equation ( 5 )
+ +
(14) Segel, I. 112.
H.Enzyme Kinetics; Wiley: New York,
1975; pp 59-60,
5758 The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 TABLE I: Kinetic Parameters for Sucrose Inversion” Dress., MPa VmarX lo6, mol/(L s) K, X lo2, mol/L 0.1 3.12 f 0.4 3.15 f 0.4 2.79 f 0.3 20 3.72 f 0.5 49 3.85 f 0.5 2.72 f 0.3 98 3.64 f 0.3 2.67 f 0.4 4.84 f 0.6 127 3.62 f 0.4
Sat0 et al.
Ki X lo2, mol/L 0.74 f 0.1 0.74 f 0.1 0.75 f 0.1 0.89 f 0.1 1.90 f 0.2
AVO*,mL/mol -29 f 3 -12 f 3 O f 3 +5 f 3 +5 f 3
ATm, mL/mol +20 f 3 +12 f 3 +1 f 3 -18 f 3 -29 f 4
AK, mL/mol +1 f 0.1 + I f 0.1 -1 f 0.1 -26 f 3 -110 f 13
“Volume changes AV:, Arm, and A K were evaluated with equations given in the text.
2.0
-
1.0
-
Y)
2 X c
m
0-
V
5 10 15 CsoX102/moI I“ Figure 7. An example of the linear relationship between 1/B and Cso. Data for 0.1 MPa are shown. 0
-2
-1
0
1
2
3 - 2 - 1
0
1
2
3
c G / t x 106 / mol I-’ S-’ Figure 6. Linear plots for rate data obtained under different pressures (in MPa): A, 20; B, 49; C , 98; D, 127 (keys as in Figure 2).
was used in the present discussion. The integral rate equation (5) was proved to be applicable to the experimental rate data obtained in the present study. This is best understood by the plots shown in Figure 5. As we can see in the figure, the plots of In (Cso/Cs)/t against CG/tare linear within the experimental error indicated in the figure. Furthermore, every straight line representing the In (Cso/Cs)/t - Cc/t relationships with different Csovalues converge to one point located on the abscissa. All these characteristics satisfy the requirements of the rate equation (5). The agreement between the theory and experiments was satisfactory at every pressure studied, as shown in Figure 6A-D. Thus, it can be said that, at least within the conditions of the present study and within the experimental error observed, the kinetics of the sucrose inversion is described in the framework of the Michaelis-Menten type f ~ r m a l i s m . ’ ~ , ’ ~ Kinetic parameters necessary for further discussion on the reaction characteristics can be evaluated by utilizing the linear plots shown in Figures 5 and 6. Firstly, the rate equation (5) predicts that the reciprocal (1/B) of the intercept (B) of the straight line with the ordinate should be equal to K,Cs0/Vma,Ki K,V,. Hence, the plot of 1/B against C, should be a straight line with a slope of K m / V , K iand with an intercept at the ordinate of Km/Vmax. Indeed, the relation between 1/B and Csowas a straight line, as exemplified in Figure 7. It is easy to evaluate the inhibitor constant from the slope and intercept of this straight line. Secondly, the rate equation (5) indicates that the slope ( A ) of any straight line shown in Figures 5 and 6 should have the following relation with K, (the Michaelis constant) and Ki (the inhibitor constant):
+
K, = Ki/ [ 1 - A(Ki
+ Cso)]
(6)
Therefore, we can evaluate K, from the values of Ki, A , and CsQ Finally, the rate equation ( 5 ) indicates that the maximum reaction rate V,,, is given by Vmax = BKm(Ki + C S O ) / K ~
(7)
This relation enables us to evaluate V, after evaluating K , and Ki. Values for kinetic parameters thus obtained are summarized in Table I. (1 5) Laidler, K . J. The Chemical Kinetics of Enzyme Action; Clarendon: Oxford, 1958.
Pressure Dependences of Kinetic Parameters. The kinetic parameters V,,, K,,and K, as well are pressure-dependent as we can see in Table I. According to the high-pressure chemistry,14 such pressure dependences as above are reasonably represented by the following formulas: d(ln V,,,)/ap
= -AV,*(obsd)/RT
(8)
d(ln K,)/ap = -AV,‘/RT
(9)
a(ln K,)/ap = -AV,’/RT (10) The quantity AV,f(obsd) on the right-hand side of (8) is an apparent activation volume. If we take into account the definition that V,,, is the product of the rate constant k, (= k2k3/(k2+ k , ) ) and the enzyme concentration CEO,the following relation results: AV,f(obsd) = AV: PRT, where AV: is the activation volume defined by a In k,/dp = -AV,‘/RT and p is the compressibility of the solvent (water). The quantity AV,‘ on the right-hand side of (9) represents the apparent volume change on dissociation of the enzymeinhibitor complex into enzyme and inhibitor. The quantity AV,’ on the right-hand side of (10) represents the pressure dependence of the composite rate constant ratio [(k.., + k2)/k+J [k3/(k2+ k,)], and its meaning is not simple in general. -However, when the rate-determining step is ES E F G, AV,’ represents the apparent volume change on dissociation of the Michaelis complex ES into the enzyme and the substrate. Although the activation volume as well as any volume change on reaction is a function of pressure, their values at zero pressure (p = 0; essentially equal to the ordinary pressure) are of significance in discussing the reaction mechanism. In the present study, the volume changes at p = 0 were evaluated by the following procedures. Namely, AVcv(p=O) was obtained by the linear plot of In [( 1/ p ) In ( Vmax(p)/ Vmax(p=O)]against p shown in Figure 8A : the intercept aI at the ordinate represents -AV,p(p=O)/RT provided that -AV,v(p)/RT is approximated by (1 bg)exp(al + b,p) where bl is the slope of the straight line plot. The value of AV,’p=O) was obtained from the linear plot of (l/p) In [K,(p)/K,(p=O)] againsrp shown in Figure 8B : the intefcept u2 at the ordinate gives -AV,’(p=O)/RT, provided that -AV,,,’(p)/RT is approximated by a2 + b2p16 where b2 is the slope of the straight line plot. The value of AV/(p=O) was obtained by extrapolating a linear plot similar to Figure 8A as shown in Figure 8C. Values of AVc*(p=O),AV,(p=O), AK(p=O) thus obtained are also given
+
-
+
+
(16) Kelm, H.; Palmer, D. A. In ref 3, p 296.
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5759
Sucrose Inversion over an Invertase Catalyst
*:
0
50
100
I
Pressure
MPa
Figure 8. Graphical extrapolations of kinetic parameters t o p = 0: A, for Vmx;B, for K,; C,for Ki.
I
F
-
I
1
site
G
-
site
Figure 9. A transition-state model.
in Table I; apparent values for Av,’(p=O) and Av,‘@-0) have also been corrected for the compressibility of wattr, in order to obtain the corresponding intrinsic values for AV,(p=O) and AK(p=O). Activation Volume and Transition State around p = 0. Considering the sucrose inversion mechanism reported in the l i t e r a t ~ r e , ~ ~itJis’ likely that the rate-determining step at low EF G, Le., k-l, k+,, k3 >> k2. In this case presures is ES we can write that k , = k2. Thus, AV>(p=O) can be regarded as the intrinsic activation volume for the above-mentioned rate-determining step. It is possible, therefore, to discuss the transition-state model on the basis of the AVct(p=O) value. The transition-state model shown in Figure 9 best accounts for the experimental results obtained around p = 0. The polar structure of the transition-state model proposed would explain the larger part of the negative activation volume of -29 f 3 mljmol. It is well-known that a polar transition state attracts solvent molecules around it. The solvent molecules thus bound by the transition state are compressed by an electrostriction, causing a negative activation volume. Although the electrostriction mentioned above sometimes brings about a large negative activation volume of -20 mL/mol or more, the activation volume of -29 f 3 mL/mol appears unlikely to be accounted for only by the polar transition state. Perhaps incorporation of a water molecule into the transition state is also contributing to reduce the activation volume. This is not unlikely since one molecule of water is required for the conversion of one mole of sucrose to the equivalent glucose and fructose. A negative activation volume for the ester hydrolysis
-
+
by a-chymotrypsin” has also been explained by the water incorporation mechanism as above. It must be added here that the enzyme part of the transitionstate model shown in Figure 9 has been drawn by taking into account Bowski’s modells for the pH range of the present study. The fructose-oxygen cleavage has been considered by taking account of the result of the sucrose inversion carried out by Koshland and Steini9using H2I80as a solvent. The result of the inhibition experiment suggests that the G site (Figure 9) is capable of adsorbing a glucose molecule from the bulk of the solution. This appears plausible since the G site is considered to be less specific than the F site.I9 The large negative activation volume discussed above suggests an easy access of a substrate molecule to the enzyme site of the immobilized invertase. In other words, the enzyme site is supposed to be located outside the enzyme molecule, as suggested by Eyring et aL9 It is hard to consider that the enzyme site is located inside the enzyme molecule. For this model, an extension of the enzyme molecule is required in forming the transition state because otherwise the substrate molecule cannot approach the enzyme site. The activation volume for such a molecular extension has been estimated by Laidlerlo to be +60 mL/mol or more. This clearly contradicts the present result. Pressure Dependences of K , and K, around p = 0. The positive value of AV,@=O) = +20 f 3 mL/mol obtained in the present study means that high-pressure conditions are unfavorable to the dissociation equilibrium of the Michaelis complex ES E S. At low pressures where we can consider that k+l, k-], k3 >> k Z , the Michaelis constant K , is given by k_,/k+] and hence represents the equilibrium constant of the above-mentioned dis_sociation reaction. Therefore, the interpretation for the positive A V , is easy and straightforward. Namely, it is obvious that two molecules are formed from one molecule in the above-mentioned dissociation reaction. LeChatelier’s law predicts that the equilibrium of this sort of reaction would be shifted by pressure toward the left-hand side. Considering the fact that the dissociation of the Michaelis complex simply obeys this law, no significant polarity change would be involved in this dissociation reaction. The dissociation of the enzyme-inhibitor (glucose) complex EG ==E + G is also classified into the type in which one molecule produces two molecules. Thus, a positive value is expected for AK(p=O). However, the experimental result shown in Table I indicates that the AV,@=O) value is close to zero, Le., 1 f 0.1 mL/mol. This suggests that any unknown factors capable of resulting negative volume changes are competing with the dissociation. If a slight molecular extension of glucose and/or a little desolvation take place on forming the enzyme-glucose complex, the small volume change AV,,(P=O) could result. Behaviors of Kinetic Parameters at High Pressure. The primary intention of this study is to discuss the enzymic mechanism at low pressures by obtaining kinetic parameters, in particular the activation volume at p = 0. However, experimental results shown in Table I have required additional discussion about behaviors of kinetic parameters at high pressures beyond 50 MPa. The experimental data (Table I) show that the V,,, value exhibits a maximum around 49 MPa and the K , value exhibits a minimum at 49-98 MPa. Furthermore, the K , value tends to increase at 49-98 MPa. Corres onding to these behaviors, the volume changes AV>@) and A $ , @ ) change their signs and increments of AC@) against pressure become steeper, as we can see in Figure 10A-C. Since V,,, is defined by = CEok, = CEOk2k3/(k2 k , ) , we have to discuss the pressure dependence of k,k3/(k2 k,) in order to explain the above-mentioned behavior of V,,,. As mentioned in the preceding section, we have considered that k2
