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Enzyme reaction kinetics in organic solvents: A theoretical kinetic model and comparison with experimental observations
JOURNAL
OF FERMENTATION
Vol. 79, No. 5, 479-484.
AND BIOENGINEERING 1995
Enzyme Reaction Kinetics in Organic Solvents: A Theoretical Kinetic Model and Comparison with Experimental Observations SUN BOK LEE Department
of Chemical Engineering, Pohang University of Science and Technology, Pohang 790-784, Korea Received 12 December
1994IAccepted
10 February
San 31, Hyoja Dong,
1995
A theoretical kinetic model has been developed in order to describe the enzyme reaction in organic solvents. In this model the hydration of the enzyme molecule was examined and the equilibrium kinetic constants expressed in terms of thermodynamic activity. Analysis of a proposed kinetic model shows that the enzyme reaction rate in organic solvents is determined by two factors: substrate solvation and enzyme hydration, which are determined by the activity coefficient of the substrate and the water activity of the reaction media, respectively. The activity coefficient of the substrate and the water activity have been calculated using the UNIFAC equation to analyze the effects of organic solvents on the rate of enzyme reaction, and the results were compared with experimental data. Predictions of the proposed model were found to be in good agreement with previous experimental observations. [Key words:
enzyme
kinetics,
nonaqueous
enzyme
reaction,
substrate
solvation,
enzyme
hydration,
UNIFAC]
In a preceding paper (l), the effects of thermodynamic water activity on enzyme hydration and enzyme reaction rate in organic solvents were analyzed. These analyses provided valuable information on enzyme behavior in organic solvents. For a more comprehensive understanding of nonaqueous biocatalysis, however, there is a need for development of a kinetic model that can properly describe enzyme action in the solvent. In this paper, a theoretical kinetic model has been proposed and analyzed in detail. The proposed model successfully explains the phenomena observed in an earlier report (1). One of the most important findings of this study may be that the enzyme reaction rate in organic media is determined by two factors: substrate solvation and enzyme hydration. Earlier studies have focused on the role of water in nonaqueous biocatalysis (2-4), while little attention has been paid to changes in the activity coefficient of the substrate in organic media. THEORETICAL
denotes the apparent order of the enzyme hydration tion. Mass balance on enzyme species yields (C)t,t=Q+(E5)+(ESQ) =(E”){ l++&+$e]
and from Eqs. 4 and 5
(6) The activity coefficients of the enzyme species in Eq. 6 are difficult to assess. We will here presume that
MODEL
El- nH,O &+ E@
(1)
E@+SAES(BLE@+P
(2)
~sJr~=&=constant,
_
KM=
aEoaS aESe
rEB r& _
IEdS YES@
kG%,,(S) ‘= (a/ys>~l+(~/K)(l/a~)}K,+(~
69 0
' (W(s) (ES@)
~sSe/yse=~=constant
(7)
If the structure or chemical nature of the hydrated enzyme molecule and the enzyme-substrate complex is not altered by the reaction medium, then it may be reasonable to assume that the ratios of the activity coefficients of enzyme species (E and u) are constant, independent of the medium composition. There is some direct or indirect experimental evidence supporting this assumption (5-8). With the presumption of Eq. 7, Eq. 6 can now be simplified to:
The hydration equilibrium constant and the Michaelis constant in Eqs. 1 and 2 can be expressed by: aEa%
(4)
With the assumption that the hydrated enzyme molecule follows Michaelis-Menten kinetics, the reaction velocity is given by
A simple kinetic model was developed based on the following assumptions: hydration of the enzyme is a prerequisite step for the catalytic action of the enzyme (Eq. 1) and the hydrated enzyme molecule follows Michaelis-Menten kinetics (Eq. 2).
K=---- aEe
reac-
k3(E),,,(S)
(8)
= Pdp+(g
Equation 8 indicates that the apparent Michaelis constant can be changed depending on the reaction medium while the maximum reaction rate is independent of the medium composition. Rearrangement of Eq. 8 gives the following relationship between the apparent kinetic
(3)
where ai and Ti represent the activity and the activity coefficient of the component i, respectively, and n 479
480
J. FERMENT.BIOENG.,
LEE
parameters
and the intrinsic
kinetic
parameters:
(9) Usually we do not know the value of the intrinsic parameters. Hence, it is more convenient to use the parameter obtained in an aqueous solution as a reference value. At aw= 1.0 (i.e. aqueous solution) Eq. 8 becomes
activity coefficient of the substrate. In many cases the initial reaction rate (a), instead of the kinetic parameters (k,/K,), is determined from the experiments. Although the ratio of the initial reaction rate in organic media to aqueous solution (rj/fj”) can be easily derived from Eqs. 8 and 10, it is rather difficult to evaluate the value of fl/rl” because the intrinsic Michaelis constant is usually unknown. However, if the substrate concentration is sufficiently low (i.e. enzyme reaction follows first order reaction kinetics), then t,/r1° is given by II
7=
where v”, ~9, and flM are the corresponding parameters obtained in an aqueous solution. From Eqs. 8 and 10, the ratio of the apparent rate constants in organic media to the rate constants in an aqueous solution can be expressed as:
and Eq. 17 can be rewritten log (rJ/rJO)= log (r&8)
= log (r&8)
+ logf(a,)
ESTIMATION
(12)
(13)
Equation 12 implies that both the activity coefficient of the substrate and the water activity determine the rate of enzyme reaction in organic solvents. Equation 12 can be further simplified for the limiting cases. When a!,$<< l/K, Eq. 12 reduces to the following linear form: i0g
{c~~/KP)~~,/K~)I = c+ log (ys/j+) + n log a,
(15)
In the case that ab>>l/K’,
Eq. 12 becomes
log {G’G/K%~)/(~JK$)
= log (rJr8)
(18)
ACTIVITY
PREDICTIONS
Effect of organic solvent on the activity coefficient of substrate In order to examine the effect of organic solvents on the activity coefficient of the substrate and the rate of enzyme reaction, methyl butyrate and heptanol, which have been used for lipase-catalyzed transesterification reactions (12), were chosen as model substrate molecules. In this paper, the results obtained for water-alcohol binary solvent systems will be presented as a case study (Similar calculations for several other model substrate compounds and solvent systems have been carried out using the UNIFAC method, and it was found that the general trends are not much different
(14)
(1 +K)
+ log&w)
OF THERMODYNAMIC
MODEL
where c=log
as:
The activity coefficient of the substrate and the water activity were calculated using the UNIFAC equation (9) as described in a companion paper (1). The volume and surface parameters, and binary interaction parameters for each pair of functional groups were obtained from the literature (10). The activity coefficient of the substrate was estimated at a fixed value of substrate mole fraction (xs= 0.001) and constant temperature (T= 25’C). The log P values were calculated using the hydrophobic fragment method (11).
where
f(aw)=at~[l+(l~~)l~~a~++(1~~~1~
(17)
Equation 18, which is equivalent to Eq. 12, may be used as an approximate expression for the enzyme reaction rate in organic media (at low substrate concentration).
In Eq. 11, u was canceled out and K/E was left as constant, K’, based on Eq. 7. By taking the logarithm of Eq. 10 we can obtain the following expression: log {(kJK%‘p)/(kJK!$)}
(l/r;){ 1+(1/K’): (l/ys){lf(l/K’)(l/ab)i
(16)
In Eq. 16, log{1 +(1/K’)} has been omitted since l/K’ is much smaller than 1 (1 >>l/K’, if a$.,>>l/K’ (Olaw I 1)). Equation 16 indicates that even at higher levels of water activity the reaction rate can be influenced by the
3.5
3.5 I (a) 3.0
3.0
2.5
2.5
2.0
2.0
7.5
$
7.0
7.0
0.5
0.5
0.0
0.0 -0.5
-0.5 0.0 FIG. butyrate
1. Dependence (b) heptanol.
7.5
0.2
0.4
0.6
0.8
7.0
of the activity coefficient of two model substrates Symbols in (a) and (b): (‘i) methanol, (0) ethanol,
(JJIII0.2
0.0
0.4
0.6
0.8
on water activity in water-alcohol (A) n-propanol, (A) n-butanol, (0)
7.0
binary systems: (a) methyl n-pentanol, ( n ) n-hexanol.
VOL. 79, 1995
ENZYME 7
0.0 (a)
0.0
0.4
0.6
0.8
7.0
0.0
0.2
0.4
SOLVENTS
481
0.6
0.8
7.0
x,
a, FIG. 2. Example of enzyme hydration
IN ORGANIC
.,,,............_.* 7 +......‘. *,........ _... /
(b)
0.2
REACTION
of water-miscible solvent (methanol). (a) Dependence of reaction rate on water activity as a function of the apparent order (n). Reaction rate was calculated using Eq. 18 at K= 1. (b) Dependence of log (r&P) (-_) and log a, (.....,) on xW.
from that presented in this paper). In Fig. 1, the logarithm of the activity coefficient (log ys) of the two model substrates is depicted as a function of water activity (aw) for n-alcohol-water binary systems. First, it should be noticed that the activity coefficient of the substrate in organic media is significantly different from that in aqueous solution. The activity coefficient in anhydrous solvent medium (aw=O) is about lOO- and 1000-fold lower than that in an aqueous solution (aw= 1) for methyl butyrate and heptanol, respectively (Depending on the substrate and solvent properties the changes in log rs can be more remarkable). However, the patterns of changes in log ys with aw are not much different: as the water activity is decreased, the activity coefficient of both model substrates is reduced in a similar way. Other features of the UNIFAC calculation results presented in Fig. 1 are: (i) the changes in the activity coefficient of the substrate are much more significant at higher water activity than at lower water activity; (ii) the activity coefficient of the substrate is lower in the solvents of greater hydrophobicity (or lower polarity) at a given water activity; (iii) in water-immiscible organic solvents (closed symbols in Fig. l), the activity coefficient of the substrate is almost constant if the water content of the medium is lower than the solubility of water in the solvent. In the next, more detailed analyses will be provided for two solvents (methanol and n-butanol) as
-0.0
examples of water-miscible and water-immiscible solvents. Effect of organic solvent on the enzyme reaction rate To analyze the effects of organic solvent on the enzyme reaction rate, Eq. 18 was employed for calculating the reaction rate (in a strict sense, Eq. 18 is applicable only to the case of low substrate concentration as mentioned earlier). The model calculation results for methyl butyrate are presented in Figs. 2 and 3 (shown is the case for K’= 1; the sensitivity of log (u/uO) to K’ is relatively small). In Fig. 2a, as an example of water-miscible solvent, the dependence of the reaction rate on the order of the enzyme hydration reaction (n) is shown for a methanol-water system. At higher n values, the log (u/v”) values become linear with a,. In Fig. 2b the contribution of the substrate activity coefficient term {log (rs/r$91 and the water activity term (log aw) is compared as a function of the mole fraction of water (xw). At higher xw the activity coefficient of the substrate is changed markedly while at lower xw the changes in water activity are more significant. The results for a butanol-water system are shown in Fig. 3 as an example of water-immiscible solvent. The dependence of log (u/uO) on water activity is rather complex due to phase equilibrium between water and the solvent (Fig. 3a). In the case of a water-immiscible solvent, there are three distinct regions (A, B and C in Fig. 3)
L.”
0.2
0.4 a,
FIG. 3. Example of water-immiscible order of enzyme hydration (n). Reaction
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
&V
solvent (n-butanol). (a) Dependence of reaction rate on water activity as a function of the apparent rate was calculated using Eq. 18 at R= 1. (b) Dependence of log (rs/rQ) (-) and log a, (......) on x,.
482
J. FERMENT. BIOENG.,
LEE
-0.8
-7
0
Log P
1
2
-1.0 -7
FIG. 4. Dependence of (a) log (~~1~8)and (b) log aw on log P (solvent) at various x0: (0)
I
0
I
Log P
7
2
0.05, (0) 0.1,(0) 0.2,(+) 0.3,(0 )0.4,(n )0.5,
(n)0.6, (~)0.7; (+) 0.8,(*) 0.9. due to liquid-liquid phase separation: in region A, the equilibrium state is a single liquid phase with a high water content (this will be called the aqueous singlephase region); in region B, phase separation occurs and two phases will form (two-phase region); and region C is a single liquid phase where the water content is lower than the solubility limit of water in the solvent (this will be called the organic single-phase region). It should be noted that in the two-phase region the thermodynamic activity of water (and the solvent) is identical in each phase due to liquid-liquid phase equilibrium (see Fig. 3). The features of the results shown in Fig. 3 may be summarized as follows: (i) in the aqueous single-phase region log (u/uO) is, with little dependence on n, linearly related with aw; in the two-phase region a, is constant, but log (u/uO) decreases as xw decreases; in the organic single-phase region the relationship between log (u/r/O) and a,,, becomes linear as n becomes higher; (ii) due to phase separation the values obtained by extrapolating the data in the organic single-phase region to aw= 1 can be significantly different from the reaction rate in an aqueous solution; (iii) the log (rs/r8) value of the solvent-saturated water (point ~1)in Fig. 3b) is significantly higher than that of water-saturated solvent (point L:i in Fig. 3b) (but, the water activity is the same for both cases); and (iv) the changes in log (ys/yg) and log a, with x, are greater compared to that for water-miscible solvent. Relationship between reaction rate and log P The log P parameter is currently widely used to correlate biocatalytic activity and solvent properties (13). To investigate the relationship between the reaction rate and the hydrophobicity of the solvent, the dependence of log (rs/r4) and log a, on log P of the solvent has been examined at various mole fractions of organic solvent (x0). Figure 4 shows the model calculation results obtained for methyl butyrate in n-alcohol-water systems (It is worth mentioning that the values of log (rs/ry) and log aw of the solvents having the same log P value can be very different depending on the nature of the solvent. The results shown in Fig. 4 therefore should be regarded as one typical example showing a general trend). Consider the implications of Fig. 4. When x0 is low (for example, x,=0.1), the reaction rate is determined mainly by the changes in log rs (Fig. 4a) since the water activity is close to 1.0 (Fig. 4b). As a consequence, the
reaction rate is lower in solvents with greater hydrophobicity. On the other hand, at higher x0 (for example, x0=0.9) the dependence of water activity (log aw) on log P becomes significant, being higher in more hydrophobic solvents (Fig. 4b). The changes in log ys are relatively small in this case (Fig. 4a). When the water content of the solvent is low, therefore, the reaction rate is higher in more hydrophobic solvents. COMPARISON WITH EXPERIMENTAL OBSERVATIONS Relationship between enzyme hydration and reaction rate It has been found that the logarithms of the reaction rate both in water-miscible and in water-immiscible solvents are linearly related to water activity (1). The results shown in Figs. 2a and 3a indicate that the relationship between log (u/uo) and aw becomes linear (within certain ranges) if the reaction order of enzyme hydration (n) is high. Let us consider the reaction order of enzyme hydration (n) by relating it to the reaction rate. Based on the theoretical analysis presented in the previous section, it is possible to estimate an approximate value of n from the data. Since the log rs values of water-immiscible solvents are not appreciably changed with a, in the organic single-phase region (see Fig. l), the log (r.Jrp) term may be considered to be a constant in this case. The approximate value of n can then be calculated from the plot of log u against log a, (cf. Eq. 14). Using the data of Zaks and Klibanov (14) obtained in the organic single-phase region, we obtain: log~~=8.6810gaw+0.74
R2=0.827
(19)
(cf. Ref. 1). Equation 19 indicates that the apparent order of enzyme hydration is about 8-9 in the case of alcohol oxidase used by Zaks and Klibanov (14). It may be interpreted that n represents the number of water molecules required for proper interaction between the hydrated enzyme and the substrate (to form the ES complex at the active site). If this interpretation is correct, then the following can be inferred. First, the amount of water that takes part in the reaction is quite different from the amount of water bound to the enzyme molecule. The value of n (8-9) is much lower than the amount of the monolayer water bound to the enzyme, even if the uncertainties in the estimation of n are taken
VOL. 19. 1995
into account. As analyzed in a preceding paper (l), the value of the BET monolayer water of alcohol oxidase has been estimated to be 0.052 g water/g protein, a value which corresponds to about 900 water molecules per enzyme molecule (assuming MW=300 kD). Thus, the actual number of water molecules that directly participate in the reaction is much smaller than may be postulated. Second, enzymes that require less water molecules will have a higher reaction rate in organic media. As shown in Figs. 2a and 3a, the reaction rate at a given water activity is lower as n is increased, especially at a low level of water activity. It would be interesting to examine the relationship between the chemical nature of the enzyme and the reaction order of protein hydration using engineered enzyme molecules or enzymes obtained from different sources. In this regard, it is worth noting that porcine pancreatic lipase prepared by acetone drying showed a higher reaction rate than Candida cylindracea lipase and Mucor lipase in most organic solvents (12). Relationship between reaction rate and water activity It has also been found that in water-immiscible solvents the log I) values at a given water activity were not significantly dependent on the nature of the solvent, while in water-miscible solvents the slope of log u vs a, plot was very much dependent on the solvent (1). This observation can also be explained based on the relationship between log rs and a, shown in Fig. 1. In water-immiscible solvents (closed symbols in Fig. l), the dependence of the log ys value on the solvent is relatively small so that the effect of the log (rs/# term in Eq. 12 is largely insensitive to the properties of the solvent. Hence, the variations in the reaction rate due to differences in solvent properties may be relatively small if the reaction rate is compared at the same water activity. In water-miscible solvents (open symbols in Fig. l), on the other hand, the dependence of log ys on a, is remarkable and at a given water activity the log rs is lower in the solvents of lower polarity. This may be the case for horseradish peroxidase data (15). Previous analysis of this data has shown that the reaction rate at a given water activity was ethanediol> methanol > DMF > THF, and this order was in good accordance with the solvent polarity scale, Ey, showing a lower reaction rate in less polar solvents (1). According to Eq. 12, the difference in the log I) values at a given water activity reflects the difference in log ys since the water activity term in Eq. 12 is constant. One more previous experimental observation will be examined. During work on the thermolysin-catalyzed peptide synthesis reaction it was found that the initial reaction rate in buffer solution saturated with ethyl acetate (10.1 mM/h) was much higher than that in ethyl acetate saturated with buffer solution (1.2mM/h) (Hwang, K.A. et al., Biotechnol. Lett., in press 1995). In both cases the water activity was identical due to phase equilibrium. This observation can be explained by the results shown in Fig. 3b: log rs is significantly higher in solvent-saturated water (point 0 in Fig. 3b) than in water-saturated solvent (point 0 in Fig. 3b). As can be deduced from Eq. 12, it is the difference in log ys that determines the reaction rate in this particular case since the water activity is the same for both reaction media. Relationship between reaction rate and solvent hydrophobicity It has been observed that penicillin-acylase reaction rates in the presence of solvent are lower in sol-
ENZYME REACTION IN ORGANIC SOLVENTS
483
vents with higher log P values (Kim, M. G., MS thesis, POSTECH, Korea, 1992): that is, the initial reaction rates were inversely related to the hydrophobicity of the solvent. In this experiment, only 2% (v/v) solvent was added and the deactivation of the enzyme during the reaction was negligible. A plausible reason for this phenomenon may be provided by the results presented in Fig. 4 which show that the dependence of the reaction rate on solvent hydrophobicity can be different depending on the mole fraction of organic solvent (xo). At low x0 the major factor that determines the reaction rate is ys and thus the rate can be lower in solvents with greater hydrophobicity (Details of the penicillin-acylase reaction will be reported elsewhere). When x0 is high, on the other hand, the reaction rate is largely governed by the water activity and the rate becomes higher in less polar solvents. The latter case has been reported by many workers (2-4, 13). It should however be noted that the dependence of the reaction rate on the log P of the solvent can also be affected by n and K’ in addition to log (~~1~8) and log a, (see Eq. 12 or Eq. 14). Effect of organic solvent on kinetic parameters The proposed model indicates that the apparent Michaelis constant (KM) changes as the reaction medium composition changes, while the maximum reaction rate ( VM= k,(E),,,) is independent of the reaction medium, as was observed by Martinek et al. (16) and Nakajima et al. (17). One thing which should be remembered is that the kinetic parameter required for the rate expression in Eq. 12 is not V, or KM, but the ratio V,/K,. The desirable features of V,/K, will be illustrated using the data of Zaks and Klibanov (12). As shown in Table 1, the values of V, and KM are very different for the same substrate (e.g. tributyrin and heptanol). By contrast, consistencies in V,/K, for the same substrate can be readily found (VM/KM (tributyrin)-0.228, I/,/K, (heptanol)=0.374). Thus, it is recommended that the ratio VM/KM be used rather than individual parameters (V, or KM) when comparing enzyme efficiency. Additional comments on the proposed kinetic model Development of the kinetic model proposed in this paper was initiated in order to answer questions that were addressed in previous papers (1; Hwang, K.-A. et al., Biotechnol. Lett., in press, 1995; Lee, S. B. et al., Abstr. 9th Int’l Biotechnol. Symp., Crystal City, USA, No. 441, 1992). As has already been discussed, the kinetic model developed in this study can now provide answers to these questions. However, the proposed model may not sufficiently explain all experimental observations reported in the literature. Simple Michaelis-Menten kinetics were assumed, and the inhibition and/or denaturation of the enzyme due to organic solvents was not considered in the model. Should the mechanisms of inhibition and/or denaturation of the enzymes become available, however, such additional factors can easily be incorporated into the model. Another assumption of the proposed model was that the ratios of the activity coefficients of enzyme species (E and a) are constant, independent of the reaction medium. Although there is some direct or indirect experimental evidence which supports this assumption (58), further experimental proof may be required. Finally, it should be mentioned that other kinetic models have been used to analyze enzyme reactions in polar organic solvents. Laidler and his coworkers formulated rate expressions using the Debye-Huckel theory for electrolyte activity coefficients (see Laidler and Bunting
484
J. FERMENT. BIOENG.,
LEE
1. Kinetic parameters
TABLE Substrate Ester Tributyrin Tributyrin Tributyrin TCEBb a Experimental b Trichloroethyl
of pancreatic
Experimental Alcohol
KM (ester)
Methanol Heptanol Dodecanol Heptanol
42 20 83 39
data (Khl, mM; butyrate.
V,,
pmol/h
KM (alcohol) 33 13 5.2 4.5
mg enzyme)
were taken
(18) and the references therein). Comparison with this model will be discussed elsewhere. It has been shown in this Concluding remarks study that enzyme reactions in nonaqueous media-ranging from aqueous solution to anhydrous organic media -can be successfully described by a simple kinetic model. Most existing controversial observations on enzyme reaction in organic solvents can be explained by the proposed model. The expressions which relate the reaction rate to thermodynamic parameters (ys and aw) have also been derived (Eqs. 12 and 18). Since the thermodynamic parameters are related to the free energy changes, Eq. 12 can be rewritten as: Acreaction= AGsubstratesalvation + AGenzymehydration where
AGreaction=RT
In
{W~~p>4W~~~
A%IM~~v.
(20) salvation
R T In (rs/y$)) and AGenzymehydration=RT In f(f+,). Therefore, it may be stated that the rate of enzyme reaction in organic media is mainly determined by two factors: substrate solvation and enzyme hydration. This simple but significant principle can be applied to the rational design of the reaction medium, which is of most interest to researchers. The general conclusions obtained from the model calculation can most likely be applied to other substrates and solvent systems. This may be true for nonelectrolyte molecules to which the UNIFAC method can be applied. Further testing of the model’s predictions and extension of the proposed model need to be studied in the future. =
ACKNOWLEDGMENT The author thanks his students who provided valuable experimental data and calculation results in previous papers (K. A. Hwang, K.-J. Kim, and M. G. Kim) and for their help with preparing this paper (J. C. Jeong, M. G. Kim, and C. B. Park). This work was supported in part by the Korean Ministry of Science and Technology and BioProcess Engineering Center.
REFERENCES Lee, S. B. and Kim, K.-J.: Effect of water activity on enzyme hydration and enzyme reaction rate in organic solvents. J. Ferment. Bioeng., 79, 473-478 (1995). Dordick, J. S.: Enzyme catalysis in monophasic organic solvents. Enzyme Microb. Technol., 11, 194-211 (1989). Laane, C. and Tramper, J.: Tailoring the medium and reactor
porcine
lipase in hexane” Calculated
data VM
VM/KM (ester)
10 4.8 17 1.7
0.238 0.240 0.205 0.044
from Zaks and Klibanov
V&K,
(alcohol) 0.303 0.369 3.269 0.378
(12).
for biocatalysis. CHEMTECH, 20, 502-506 (1990). B. and Adlercreutz, P.: Tailoring the microenviron4. Mattiason, ment of enzymes in water-poor systems. Trends Biotechnol., 9, 394-398 (1991). P. A., Steinmetz, A. C. U., Ringe, D., and 5. Fitzpatrick, Klibanov, A.M.: Enzyme crystal structure in a neat organic solvent. Proc. Natl. Acad. Sci. USA, 90, 8653-8657 (1993). A. M.: Solid-state 6. Burke, P. A., Griffin, R. G., and Klibanov, NMR assessment of enzyme active center structure under nonaqueous conditions. J. Biol. Chem., 267, 20057-20064 (1992). 7. Adams, K. A. H., Cbung, S.-H., and Klibanov, A. M.: Kinetic isotope effect investigation of enzyme mechanism in organic solvents. J. Am. Chem. Sot., 112, 9418-9419 (1990). W. W., and Klibanov, 8. Burke, P. A., Smith, S. O., Bachovchin, A.M.: Demonstration of structural integrity of an enzyme in organic solvents by solid-state NMR. J. Am. Chem. Sot., 111, 8290-8291 (1989). 9. Fredenslund, A., Jones, R. L., and Prausnitz, J. M.: Groupcontribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J., 21, 1086-1099 (1975). J., Rasmussen, P., and Fredenslund, A.: 10. Tiegs, D., Gmehling, Vapor-liquid equilibria by UNIFAC group contribution. IV. Revision and extension. Ind. Eng. Chem. Res., 26, 159-161 (1987). fragmen11. Rekker, R. F. and de Kort, H. M.: The hydrophobic tal constant; an extension to a 1000 data point set. Eur. J. Med. Chem., 14, 479-488 (1979). A. M.: Enzyme-catalyzed processes in 12. Zaks, A. and Klibanov, organic solvents. Proc. Natl. Acad. Sci., 82, 3192-3196 (1985). C., Boeren, S., Vos, K.. and Veeger, C.: Rules for 13. Laane, optimization of biocatalysis in organic solvents. Biotechnol. Bioeng., 30, 81-87 (1987). 14. Zaks, A. and Klibanov, A. M.: The effect of water on enzyme action in organic media. J. Biol. Chem., 263. 8017-8021 (1988). 15. Epton, R.. Hobson, M. E., and Marr, G.: Catalytic activity of poly(acryloy1 morpholine)-immobilized horseradish peroxidase in organic/aqueous solvent mixtures. Enzyme Microb. Technol., 1, 37-40 (1979). K., Levashov. A. V., Klyachko, N. L., Pantin, V. I., 16. Martinek, and Berezin, I. V.: The principles of enzyme stabilization. VI. Catalysis by water-soluble enzyme entrapped into reversed micelles of surfactants in organic solvents. Biochim. Biophys. Acta, 657, 277-294 (1981). 17. Nakajima, H., Suzuki, K., and Imahori, K.: Effects of various organic solvents on the activity of thermolysin. Agric. Biol. Chem. (Japan), 49, 317-323 (1975). The chemical kinetics of 18. Laidler, K. J. and Bunting, P.S.: enzyme action, 2nd ed., p. 49-59. Clarendon Press, Oxford (1973).
OF FERMENTATION
Vol. 79, No. 5, 479-484.
AND BIOENGINEERING 1995
Enzyme Reaction Kinetics in Organic Solvents: A Theoretical Kinetic Model and Comparison with Experimental Observations SUN BOK LEE Department
of Chemical Engineering, Pohang University of Science and Technology, Pohang 790-784, Korea Received 12 December
1994IAccepted
10 February
San 31, Hyoja Dong,
1995
A theoretical kinetic model has been developed in order to describe the enzyme reaction in organic solvents. In this model the hydration of the enzyme molecule was examined and the equilibrium kinetic constants expressed in terms of thermodynamic activity. Analysis of a proposed kinetic model shows that the enzyme reaction rate in organic solvents is determined by two factors: substrate solvation and enzyme hydration, which are determined by the activity coefficient of the substrate and the water activity of the reaction media, respectively. The activity coefficient of the substrate and the water activity have been calculated using the UNIFAC equation to analyze the effects of organic solvents on the rate of enzyme reaction, and the results were compared with experimental data. Predictions of the proposed model were found to be in good agreement with previous experimental observations. [Key words:
enzyme
kinetics,
nonaqueous
enzyme
reaction,
substrate
solvation,
enzyme
hydration,
UNIFAC]
In a preceding paper (l), the effects of thermodynamic water activity on enzyme hydration and enzyme reaction rate in organic solvents were analyzed. These analyses provided valuable information on enzyme behavior in organic solvents. For a more comprehensive understanding of nonaqueous biocatalysis, however, there is a need for development of a kinetic model that can properly describe enzyme action in the solvent. In this paper, a theoretical kinetic model has been proposed and analyzed in detail. The proposed model successfully explains the phenomena observed in an earlier report (1). One of the most important findings of this study may be that the enzyme reaction rate in organic media is determined by two factors: substrate solvation and enzyme hydration. Earlier studies have focused on the role of water in nonaqueous biocatalysis (2-4), while little attention has been paid to changes in the activity coefficient of the substrate in organic media. THEORETICAL
denotes the apparent order of the enzyme hydration tion. Mass balance on enzyme species yields (C)t,t=Q+(E5)+(ESQ) =(E”){ l++&+$e]
and from Eqs. 4 and 5
(6) The activity coefficients of the enzyme species in Eq. 6 are difficult to assess. We will here presume that
MODEL
El- nH,O &+ E@
(1)
E@+SAES(BLE@+P
(2)
~sJr~=&=constant,
_
KM=
aEoaS aESe
rEB r& _
IEdS YES@
kG%,,(S) ‘= (a/ys>~l+(~/K)(l/a~)}K,+(~
69 0
' (W(s) (ES@)
~sSe/yse=~=constant
(7)
If the structure or chemical nature of the hydrated enzyme molecule and the enzyme-substrate complex is not altered by the reaction medium, then it may be reasonable to assume that the ratios of the activity coefficients of enzyme species (E and u) are constant, independent of the medium composition. There is some direct or indirect experimental evidence supporting this assumption (5-8). With the presumption of Eq. 7, Eq. 6 can now be simplified to:
The hydration equilibrium constant and the Michaelis constant in Eqs. 1 and 2 can be expressed by: aEa%
(4)
With the assumption that the hydrated enzyme molecule follows Michaelis-Menten kinetics, the reaction velocity is given by
A simple kinetic model was developed based on the following assumptions: hydration of the enzyme is a prerequisite step for the catalytic action of the enzyme (Eq. 1) and the hydrated enzyme molecule follows Michaelis-Menten kinetics (Eq. 2).
K=---- aEe
reac-
k3(E),,,(S)
(8)
= Pdp+(g
Equation 8 indicates that the apparent Michaelis constant can be changed depending on the reaction medium while the maximum reaction rate is independent of the medium composition. Rearrangement of Eq. 8 gives the following relationship between the apparent kinetic
(3)
where ai and Ti represent the activity and the activity coefficient of the component i, respectively, and n 479
480
J. FERMENT.BIOENG.,
LEE
parameters
and the intrinsic
kinetic
parameters:
(9) Usually we do not know the value of the intrinsic parameters. Hence, it is more convenient to use the parameter obtained in an aqueous solution as a reference value. At aw= 1.0 (i.e. aqueous solution) Eq. 8 becomes
activity coefficient of the substrate. In many cases the initial reaction rate (a), instead of the kinetic parameters (k,/K,), is determined from the experiments. Although the ratio of the initial reaction rate in organic media to aqueous solution (rj/fj”) can be easily derived from Eqs. 8 and 10, it is rather difficult to evaluate the value of fl/rl” because the intrinsic Michaelis constant is usually unknown. However, if the substrate concentration is sufficiently low (i.e. enzyme reaction follows first order reaction kinetics), then t,/r1° is given by II
7=
where v”, ~9, and flM are the corresponding parameters obtained in an aqueous solution. From Eqs. 8 and 10, the ratio of the apparent rate constants in organic media to the rate constants in an aqueous solution can be expressed as:
and Eq. 17 can be rewritten log (rJ/rJO)= log (r&8)
= log (r&8)
+ logf(a,)
ESTIMATION
(12)
(13)
Equation 12 implies that both the activity coefficient of the substrate and the water activity determine the rate of enzyme reaction in organic solvents. Equation 12 can be further simplified for the limiting cases. When a!,$<< l/K, Eq. 12 reduces to the following linear form: i0g
{c~~/KP)~~,/K~)I = c+ log (ys/j+) + n log a,
(15)
In the case that ab>>l/K’,
Eq. 12 becomes
log {G’G/K%~)/(~JK$)
= log (rJr8)
(18)
ACTIVITY
PREDICTIONS
Effect of organic solvent on the activity coefficient of substrate In order to examine the effect of organic solvents on the activity coefficient of the substrate and the rate of enzyme reaction, methyl butyrate and heptanol, which have been used for lipase-catalyzed transesterification reactions (12), were chosen as model substrate molecules. In this paper, the results obtained for water-alcohol binary solvent systems will be presented as a case study (Similar calculations for several other model substrate compounds and solvent systems have been carried out using the UNIFAC method, and it was found that the general trends are not much different
(14)
(1 +K)
+ log&w)
OF THERMODYNAMIC
MODEL
where c=log
as:
The activity coefficient of the substrate and the water activity were calculated using the UNIFAC equation (9) as described in a companion paper (1). The volume and surface parameters, and binary interaction parameters for each pair of functional groups were obtained from the literature (10). The activity coefficient of the substrate was estimated at a fixed value of substrate mole fraction (xs= 0.001) and constant temperature (T= 25’C). The log P values were calculated using the hydrophobic fragment method (11).
where
f(aw)=at~[l+(l~~)l~~a~++(1~~~1~
(17)
Equation 18, which is equivalent to Eq. 12, may be used as an approximate expression for the enzyme reaction rate in organic media (at low substrate concentration).
In Eq. 11, u was canceled out and K/E was left as constant, K’, based on Eq. 7. By taking the logarithm of Eq. 10 we can obtain the following expression: log {(kJK%‘p)/(kJK!$)}
(l/r;){ 1+(1/K’): (l/ys){lf(l/K’)(l/ab)i
(16)
In Eq. 16, log{1 +(1/K’)} has been omitted since l/K’ is much smaller than 1 (1 >>l/K’, if a$.,>>l/K’ (Olaw I 1)). Equation 16 indicates that even at higher levels of water activity the reaction rate can be influenced by the
3.5
3.5 I (a) 3.0
3.0
2.5
2.5
2.0
2.0
7.5
$
7.0
7.0
0.5
0.5
0.0
0.0 -0.5
-0.5 0.0 FIG. butyrate
1. Dependence (b) heptanol.
7.5
0.2
0.4
0.6
0.8
7.0
of the activity coefficient of two model substrates Symbols in (a) and (b): (‘i) methanol, (0) ethanol,
(JJIII0.2
0.0
0.4
0.6
0.8
on water activity in water-alcohol (A) n-propanol, (A) n-butanol, (0)
7.0
binary systems: (a) methyl n-pentanol, ( n ) n-hexanol.
VOL. 79, 1995
ENZYME 7
0.0 (a)
0.0
0.4
0.6
0.8
7.0
0.0
0.2
0.4
SOLVENTS
481
0.6
0.8
7.0
x,
a, FIG. 2. Example of enzyme hydration
IN ORGANIC
.,,,............_.* 7 +......‘. *,........ _... /
(b)
0.2
REACTION
of water-miscible solvent (methanol). (a) Dependence of reaction rate on water activity as a function of the apparent order (n). Reaction rate was calculated using Eq. 18 at K= 1. (b) Dependence of log (r&P) (-_) and log a, (.....,) on xW.
from that presented in this paper). In Fig. 1, the logarithm of the activity coefficient (log ys) of the two model substrates is depicted as a function of water activity (aw) for n-alcohol-water binary systems. First, it should be noticed that the activity coefficient of the substrate in organic media is significantly different from that in aqueous solution. The activity coefficient in anhydrous solvent medium (aw=O) is about lOO- and 1000-fold lower than that in an aqueous solution (aw= 1) for methyl butyrate and heptanol, respectively (Depending on the substrate and solvent properties the changes in log rs can be more remarkable). However, the patterns of changes in log ys with aw are not much different: as the water activity is decreased, the activity coefficient of both model substrates is reduced in a similar way. Other features of the UNIFAC calculation results presented in Fig. 1 are: (i) the changes in the activity coefficient of the substrate are much more significant at higher water activity than at lower water activity; (ii) the activity coefficient of the substrate is lower in the solvents of greater hydrophobicity (or lower polarity) at a given water activity; (iii) in water-immiscible organic solvents (closed symbols in Fig. l), the activity coefficient of the substrate is almost constant if the water content of the medium is lower than the solubility of water in the solvent. In the next, more detailed analyses will be provided for two solvents (methanol and n-butanol) as
-0.0
examples of water-miscible and water-immiscible solvents. Effect of organic solvent on the enzyme reaction rate To analyze the effects of organic solvent on the enzyme reaction rate, Eq. 18 was employed for calculating the reaction rate (in a strict sense, Eq. 18 is applicable only to the case of low substrate concentration as mentioned earlier). The model calculation results for methyl butyrate are presented in Figs. 2 and 3 (shown is the case for K’= 1; the sensitivity of log (u/uO) to K’ is relatively small). In Fig. 2a, as an example of water-miscible solvent, the dependence of the reaction rate on the order of the enzyme hydration reaction (n) is shown for a methanol-water system. At higher n values, the log (u/v”) values become linear with a,. In Fig. 2b the contribution of the substrate activity coefficient term {log (rs/r$91 and the water activity term (log aw) is compared as a function of the mole fraction of water (xw). At higher xw the activity coefficient of the substrate is changed markedly while at lower xw the changes in water activity are more significant. The results for a butanol-water system are shown in Fig. 3 as an example of water-immiscible solvent. The dependence of log (u/uO) on water activity is rather complex due to phase equilibrium between water and the solvent (Fig. 3a). In the case of a water-immiscible solvent, there are three distinct regions (A, B and C in Fig. 3)
L.”
0.2
0.4 a,
FIG. 3. Example of water-immiscible order of enzyme hydration (n). Reaction
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
&V
solvent (n-butanol). (a) Dependence of reaction rate on water activity as a function of the apparent rate was calculated using Eq. 18 at R= 1. (b) Dependence of log (rs/rQ) (-) and log a, (......) on x,.
482
J. FERMENT. BIOENG.,
LEE
-0.8
-7
0
Log P
1
2
-1.0 -7
FIG. 4. Dependence of (a) log (~~1~8)and (b) log aw on log P (solvent) at various x0: (0)
I
0
I
Log P
7
2
0.05, (0) 0.1,(0) 0.2,(+) 0.3,(0 )0.4,(n )0.5,
(n)0.6, (~)0.7; (+) 0.8,(*) 0.9. due to liquid-liquid phase separation: in region A, the equilibrium state is a single liquid phase with a high water content (this will be called the aqueous singlephase region); in region B, phase separation occurs and two phases will form (two-phase region); and region C is a single liquid phase where the water content is lower than the solubility limit of water in the solvent (this will be called the organic single-phase region). It should be noted that in the two-phase region the thermodynamic activity of water (and the solvent) is identical in each phase due to liquid-liquid phase equilibrium (see Fig. 3). The features of the results shown in Fig. 3 may be summarized as follows: (i) in the aqueous single-phase region log (u/uO) is, with little dependence on n, linearly related with aw; in the two-phase region a, is constant, but log (u/uO) decreases as xw decreases; in the organic single-phase region the relationship between log (u/r/O) and a,,, becomes linear as n becomes higher; (ii) due to phase separation the values obtained by extrapolating the data in the organic single-phase region to aw= 1 can be significantly different from the reaction rate in an aqueous solution; (iii) the log (rs/r8) value of the solvent-saturated water (point ~1)in Fig. 3b) is significantly higher than that of water-saturated solvent (point L:i in Fig. 3b) (but, the water activity is the same for both cases); and (iv) the changes in log (ys/yg) and log a, with x, are greater compared to that for water-miscible solvent. Relationship between reaction rate and log P The log P parameter is currently widely used to correlate biocatalytic activity and solvent properties (13). To investigate the relationship between the reaction rate and the hydrophobicity of the solvent, the dependence of log (rs/r4) and log a, on log P of the solvent has been examined at various mole fractions of organic solvent (x0). Figure 4 shows the model calculation results obtained for methyl butyrate in n-alcohol-water systems (It is worth mentioning that the values of log (rs/ry) and log aw of the solvents having the same log P value can be very different depending on the nature of the solvent. The results shown in Fig. 4 therefore should be regarded as one typical example showing a general trend). Consider the implications of Fig. 4. When x0 is low (for example, x,=0.1), the reaction rate is determined mainly by the changes in log rs (Fig. 4a) since the water activity is close to 1.0 (Fig. 4b). As a consequence, the
reaction rate is lower in solvents with greater hydrophobicity. On the other hand, at higher x0 (for example, x0=0.9) the dependence of water activity (log aw) on log P becomes significant, being higher in more hydrophobic solvents (Fig. 4b). The changes in log ys are relatively small in this case (Fig. 4a). When the water content of the solvent is low, therefore, the reaction rate is higher in more hydrophobic solvents. COMPARISON WITH EXPERIMENTAL OBSERVATIONS Relationship between enzyme hydration and reaction rate It has been found that the logarithms of the reaction rate both in water-miscible and in water-immiscible solvents are linearly related to water activity (1). The results shown in Figs. 2a and 3a indicate that the relationship between log (u/uo) and aw becomes linear (within certain ranges) if the reaction order of enzyme hydration (n) is high. Let us consider the reaction order of enzyme hydration (n) by relating it to the reaction rate. Based on the theoretical analysis presented in the previous section, it is possible to estimate an approximate value of n from the data. Since the log rs values of water-immiscible solvents are not appreciably changed with a, in the organic single-phase region (see Fig. l), the log (r.Jrp) term may be considered to be a constant in this case. The approximate value of n can then be calculated from the plot of log u against log a, (cf. Eq. 14). Using the data of Zaks and Klibanov (14) obtained in the organic single-phase region, we obtain: log~~=8.6810gaw+0.74
R2=0.827
(19)
(cf. Ref. 1). Equation 19 indicates that the apparent order of enzyme hydration is about 8-9 in the case of alcohol oxidase used by Zaks and Klibanov (14). It may be interpreted that n represents the number of water molecules required for proper interaction between the hydrated enzyme and the substrate (to form the ES complex at the active site). If this interpretation is correct, then the following can be inferred. First, the amount of water that takes part in the reaction is quite different from the amount of water bound to the enzyme molecule. The value of n (8-9) is much lower than the amount of the monolayer water bound to the enzyme, even if the uncertainties in the estimation of n are taken
VOL. 19. 1995
into account. As analyzed in a preceding paper (l), the value of the BET monolayer water of alcohol oxidase has been estimated to be 0.052 g water/g protein, a value which corresponds to about 900 water molecules per enzyme molecule (assuming MW=300 kD). Thus, the actual number of water molecules that directly participate in the reaction is much smaller than may be postulated. Second, enzymes that require less water molecules will have a higher reaction rate in organic media. As shown in Figs. 2a and 3a, the reaction rate at a given water activity is lower as n is increased, especially at a low level of water activity. It would be interesting to examine the relationship between the chemical nature of the enzyme and the reaction order of protein hydration using engineered enzyme molecules or enzymes obtained from different sources. In this regard, it is worth noting that porcine pancreatic lipase prepared by acetone drying showed a higher reaction rate than Candida cylindracea lipase and Mucor lipase in most organic solvents (12). Relationship between reaction rate and water activity It has also been found that in water-immiscible solvents the log I) values at a given water activity were not significantly dependent on the nature of the solvent, while in water-miscible solvents the slope of log u vs a, plot was very much dependent on the solvent (1). This observation can also be explained based on the relationship between log rs and a, shown in Fig. 1. In water-immiscible solvents (closed symbols in Fig. l), the dependence of the log ys value on the solvent is relatively small so that the effect of the log (rs/# term in Eq. 12 is largely insensitive to the properties of the solvent. Hence, the variations in the reaction rate due to differences in solvent properties may be relatively small if the reaction rate is compared at the same water activity. In water-miscible solvents (open symbols in Fig. l), on the other hand, the dependence of log ys on a, is remarkable and at a given water activity the log rs is lower in the solvents of lower polarity. This may be the case for horseradish peroxidase data (15). Previous analysis of this data has shown that the reaction rate at a given water activity was ethanediol> methanol > DMF > THF, and this order was in good accordance with the solvent polarity scale, Ey, showing a lower reaction rate in less polar solvents (1). According to Eq. 12, the difference in the log I) values at a given water activity reflects the difference in log ys since the water activity term in Eq. 12 is constant. One more previous experimental observation will be examined. During work on the thermolysin-catalyzed peptide synthesis reaction it was found that the initial reaction rate in buffer solution saturated with ethyl acetate (10.1 mM/h) was much higher than that in ethyl acetate saturated with buffer solution (1.2mM/h) (Hwang, K.A. et al., Biotechnol. Lett., in press 1995). In both cases the water activity was identical due to phase equilibrium. This observation can be explained by the results shown in Fig. 3b: log rs is significantly higher in solvent-saturated water (point 0 in Fig. 3b) than in water-saturated solvent (point 0 in Fig. 3b). As can be deduced from Eq. 12, it is the difference in log ys that determines the reaction rate in this particular case since the water activity is the same for both reaction media. Relationship between reaction rate and solvent hydrophobicity It has been observed that penicillin-acylase reaction rates in the presence of solvent are lower in sol-
ENZYME REACTION IN ORGANIC SOLVENTS
483
vents with higher log P values (Kim, M. G., MS thesis, POSTECH, Korea, 1992): that is, the initial reaction rates were inversely related to the hydrophobicity of the solvent. In this experiment, only 2% (v/v) solvent was added and the deactivation of the enzyme during the reaction was negligible. A plausible reason for this phenomenon may be provided by the results presented in Fig. 4 which show that the dependence of the reaction rate on solvent hydrophobicity can be different depending on the mole fraction of organic solvent (xo). At low x0 the major factor that determines the reaction rate is ys and thus the rate can be lower in solvents with greater hydrophobicity (Details of the penicillin-acylase reaction will be reported elsewhere). When x0 is high, on the other hand, the reaction rate is largely governed by the water activity and the rate becomes higher in less polar solvents. The latter case has been reported by many workers (2-4, 13). It should however be noted that the dependence of the reaction rate on the log P of the solvent can also be affected by n and K’ in addition to log (~~1~8) and log a, (see Eq. 12 or Eq. 14). Effect of organic solvent on kinetic parameters The proposed model indicates that the apparent Michaelis constant (KM) changes as the reaction medium composition changes, while the maximum reaction rate ( VM= k,(E),,,) is independent of the reaction medium, as was observed by Martinek et al. (16) and Nakajima et al. (17). One thing which should be remembered is that the kinetic parameter required for the rate expression in Eq. 12 is not V, or KM, but the ratio V,/K,. The desirable features of V,/K, will be illustrated using the data of Zaks and Klibanov (12). As shown in Table 1, the values of V, and KM are very different for the same substrate (e.g. tributyrin and heptanol). By contrast, consistencies in V,/K, for the same substrate can be readily found (VM/KM (tributyrin)-0.228, I/,/K, (heptanol)=0.374). Thus, it is recommended that the ratio VM/KM be used rather than individual parameters (V, or KM) when comparing enzyme efficiency. Additional comments on the proposed kinetic model Development of the kinetic model proposed in this paper was initiated in order to answer questions that were addressed in previous papers (1; Hwang, K.-A. et al., Biotechnol. Lett., in press, 1995; Lee, S. B. et al., Abstr. 9th Int’l Biotechnol. Symp., Crystal City, USA, No. 441, 1992). As has already been discussed, the kinetic model developed in this study can now provide answers to these questions. However, the proposed model may not sufficiently explain all experimental observations reported in the literature. Simple Michaelis-Menten kinetics were assumed, and the inhibition and/or denaturation of the enzyme due to organic solvents was not considered in the model. Should the mechanisms of inhibition and/or denaturation of the enzymes become available, however, such additional factors can easily be incorporated into the model. Another assumption of the proposed model was that the ratios of the activity coefficients of enzyme species (E and a) are constant, independent of the reaction medium. Although there is some direct or indirect experimental evidence which supports this assumption (58), further experimental proof may be required. Finally, it should be mentioned that other kinetic models have been used to analyze enzyme reactions in polar organic solvents. Laidler and his coworkers formulated rate expressions using the Debye-Huckel theory for electrolyte activity coefficients (see Laidler and Bunting
484
J. FERMENT. BIOENG.,
LEE
1. Kinetic parameters
TABLE Substrate Ester Tributyrin Tributyrin Tributyrin TCEBb a Experimental b Trichloroethyl
of pancreatic
Experimental Alcohol
KM (ester)
Methanol Heptanol Dodecanol Heptanol
42 20 83 39
data (Khl, mM; butyrate.
V,,
pmol/h
KM (alcohol) 33 13 5.2 4.5
mg enzyme)
were taken
(18) and the references therein). Comparison with this model will be discussed elsewhere. It has been shown in this Concluding remarks study that enzyme reactions in nonaqueous media-ranging from aqueous solution to anhydrous organic media -can be successfully described by a simple kinetic model. Most existing controversial observations on enzyme reaction in organic solvents can be explained by the proposed model. The expressions which relate the reaction rate to thermodynamic parameters (ys and aw) have also been derived (Eqs. 12 and 18). Since the thermodynamic parameters are related to the free energy changes, Eq. 12 can be rewritten as: Acreaction= AGsubstratesalvation + AGenzymehydration where
AGreaction=RT
In
{W~~p>4W~~~
A%IM~~v.
(20) salvation
R T In (rs/y$)) and AGenzymehydration=RT In f(f+,). Therefore, it may be stated that the rate of enzyme reaction in organic media is mainly determined by two factors: substrate solvation and enzyme hydration. This simple but significant principle can be applied to the rational design of the reaction medium, which is of most interest to researchers. The general conclusions obtained from the model calculation can most likely be applied to other substrates and solvent systems. This may be true for nonelectrolyte molecules to which the UNIFAC method can be applied. Further testing of the model’s predictions and extension of the proposed model need to be studied in the future. =
ACKNOWLEDGMENT The author thanks his students who provided valuable experimental data and calculation results in previous papers (K. A. Hwang, K.-J. Kim, and M. G. Kim) and for their help with preparing this paper (J. C. Jeong, M. G. Kim, and C. B. Park). This work was supported in part by the Korean Ministry of Science and Technology and BioProcess Engineering Center.
REFERENCES Lee, S. B. and Kim, K.-J.: Effect of water activity on enzyme hydration and enzyme reaction rate in organic solvents. J. Ferment. Bioeng., 79, 473-478 (1995). Dordick, J. S.: Enzyme catalysis in monophasic organic solvents. Enzyme Microb. Technol., 11, 194-211 (1989). Laane, C. and Tramper, J.: Tailoring the medium and reactor
porcine
lipase in hexane” Calculated
data VM
VM/KM (ester)
10 4.8 17 1.7
0.238 0.240 0.205 0.044
from Zaks and Klibanov
V&K,
(alcohol) 0.303 0.369 3.269 0.378
(12).
for biocatalysis. CHEMTECH, 20, 502-506 (1990). B. and Adlercreutz, P.: Tailoring the microenviron4. Mattiason, ment of enzymes in water-poor systems. Trends Biotechnol., 9, 394-398 (1991). P. A., Steinmetz, A. C. U., Ringe, D., and 5. Fitzpatrick, Klibanov, A.M.: Enzyme crystal structure in a neat organic solvent. Proc. Natl. Acad. Sci. USA, 90, 8653-8657 (1993). A. M.: Solid-state 6. Burke, P. A., Griffin, R. G., and Klibanov, NMR assessment of enzyme active center structure under nonaqueous conditions. J. Biol. Chem., 267, 20057-20064 (1992). 7. Adams, K. A. H., Cbung, S.-H., and Klibanov, A. M.: Kinetic isotope effect investigation of enzyme mechanism in organic solvents. J. Am. Chem. Sot., 112, 9418-9419 (1990). W. W., and Klibanov, 8. Burke, P. A., Smith, S. O., Bachovchin, A.M.: Demonstration of structural integrity of an enzyme in organic solvents by solid-state NMR. J. Am. Chem. Sot., 111, 8290-8291 (1989). 9. Fredenslund, A., Jones, R. L., and Prausnitz, J. M.: Groupcontribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J., 21, 1086-1099 (1975). J., Rasmussen, P., and Fredenslund, A.: 10. Tiegs, D., Gmehling, Vapor-liquid equilibria by UNIFAC group contribution. IV. Revision and extension. Ind. Eng. Chem. Res., 26, 159-161 (1987). fragmen11. Rekker, R. F. and de Kort, H. M.: The hydrophobic tal constant; an extension to a 1000 data point set. Eur. J. Med. Chem., 14, 479-488 (1979). A. M.: Enzyme-catalyzed processes in 12. Zaks, A. and Klibanov, organic solvents. Proc. Natl. Acad. Sci., 82, 3192-3196 (1985). C., Boeren, S., Vos, K.. and Veeger, C.: Rules for 13. Laane, optimization of biocatalysis in organic solvents. Biotechnol. Bioeng., 30, 81-87 (1987). 14. Zaks, A. and Klibanov, A. M.: The effect of water on enzyme action in organic media. J. Biol. Chem., 263. 8017-8021 (1988). 15. Epton, R.. Hobson, M. E., and Marr, G.: Catalytic activity of poly(acryloy1 morpholine)-immobilized horseradish peroxidase in organic/aqueous solvent mixtures. Enzyme Microb. Technol., 1, 37-40 (1979). K., Levashov. A. V., Klyachko, N. L., Pantin, V. I., 16. Martinek, and Berezin, I. V.: The principles of enzyme stabilization. VI. Catalysis by water-soluble enzyme entrapped into reversed micelles of surfactants in organic solvents. Biochim. Biophys. Acta, 657, 277-294 (1981). 17. Nakajima, H., Suzuki, K., and Imahori, K.: Effects of various organic solvents on the activity of thermolysin. Agric. Biol. Chem. (Japan), 49, 317-323 (1975). The chemical kinetics of 18. Laidler, K. J. and Bunting, P.S.: enzyme action, 2nd ed., p. 49-59. Clarendon Press, Oxford (1973).