Dipole formation and solvent electrostriction in subtilisin catalysis

Article abstract of DOI:10.1021/ja9713892

The transition state for subtilisin-catalyzed transesterification was probed by high-pressure kinetic studies in solvents spanning a wide range of dielectric constants. The electrostatic model of Kirkwood described the solvent effects and gave a lower lim

Full text of DOI:10.1021/ja9713892

VOLUME 119, NUMBER 40
OCTOBER 8, 1997
© Copyright 1997 by the
American Chemical Society
Dipole Formation and Solvent Electrostriction in Subtilisin
Catalysis
Peter C. Michels,†,‡ Jonathan S. Dordick,*,§ and Douglas S. Clark*,†
Contribution from the Department of Chemical and Biochemical Engineering, UniVersity of Iowa,
Iowa City, Iowa, 52242, and Department of Chemical Engineering, UniVersity of California,
Berkeley, California 94720
ReceiVed May 1, 1997X
Abstract: The transition state for subtilisin-catalyzed transesterification was probed by high-pressure kinetic studies
in solvents spanning a wide range of dielectric constants. The electrostatic model of Kirkwood described the solvent
effects and gave a lower limit of 31 ( 1.5 Debye for the dipole moment of the transition state. This value remained
constant in a wide range of polar and apolar solvents, indicating that the catalytic triad of subtilisin is remarkably
robust. Despite the highly polar transition state, substantial rate enhancements relative to the uncatalyzed reaction
were measured in highly apolar solvents such as hexane; this is the first report of such an extreme disparity between
transition-state and solvent polarities. Moreover, the solvent dependence of the activation volume implies a low
effective dielectric of the polypeptide chain in the active site and substantial penetration of the active site by solvent.
Kirkwood’s model was also used to quantify the effect of an active-site mutation on the transition-state dipole moment.
These results illustrate that the electrostatic model combined with high-pressure kinetics can provide unique information
on the basic properties of enzyme reaction processes and can be useful in predicting solvent effects on enzyme
reaction rates.
Introduction
particular, kinetic isotope effects observed for transesterifcations
catalyzed by subtilisin Carlsberg indicated that the transition
state structure was independent of the organic solvent.4 Pres-
ervation of the transition state was also suggested by solid-state
MAS 15N-NMR spectra of a serine protease from Lysobacter
enzymogenes, which revealed that the unique tautomeric struc-
ture and hydrogen bonding interactions essential for function
of the catalytic triad were identical in water, acetone, and
octane.1,2 In addition, the crystal structure of cross-linked
subtilisin in acetonitrile was essentially identical to the structure
of the enzyme in water.6,7 Despite these results, molecular
details on the reaction mechanisms of proteases and other
enzymes in nonaqueous media remain scarce.
The structure and function of serine proteases in nonaqueous
media have recently been examined by a variety of techniques.
For example, solid-state NMR,1,2 ESR,3 deuterium isotope
analysis,4 and crystallographic studies5-7 on serine proteases
suggest that the structure and catalytic mechanism of these
enzymes is retained in a wide variety of organic solvents. In
* To whom correspondence should be addressed.
† University of California.
‡ Present address: EnzyMed Inc., Iowa City, Iowa 52242.
§ University of Iowa.
X Abstract published in AdVance ACS Abstracts, September 15, 1997.
(1) Burke, P.; Griffin, R. G.; Klibanov, A. M. J. Am. Chem. Soc. 1989,
111, 8290.
(2) Burke, P. A.; Griffin, R. G.; Klibanov, A. M. J. Biol. Chem. 1992,
267, 20057.
(3) Affleck, R.; Xu, Z.-F.; Suzawa, V.; Focht, K.; Clark, D. S.; Dordick,
J. S. Proc. Natl. Acad. Sci. U.S.A. 1992, 89, 1100.
(4) Adams, K. A. H.; Chung, S., et al. J. Am. Chem. Soc. 1990, 122,
9418.
(5) Yennawar, N. J.; Yennawar, H. P.; Farber, G. K. Biochemistry 1994,
33, 7326.
(6) Fitzpatrick, P. A.; Steinmetz, A. C. U.; Ringe, D.; Klibanov, A. M.
Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 8653.
(7) Fitzpatrick, P. A.; Rings, D.; Klibanov, A. M. Biochem. Biophys.
Res. Comm. 1994, 198, 675.
S0002-7863(97)01389-9 CCC: $14.00 © 1997 American Chemical Society

9332 J. Am. Chem. Soc., Vol. 119, No. 40, 1997
Michels et al.
High-pressure kinetic studies, although not widely utilized,
can be very valuable for investigating the mechanisms of
enzymatic reactions in aqueous solution, especially when other
methods of mechanistic analysis prove insufficient.8-10 The key
parameter governing the effect of pressure on the rate of a
chemical reaction is the activation volume, ∆Vq. In general,
bond formation, charge development, and steric hindrance during
the rate-controlling step make negative contributions to the
activation volume,11,12 whereas the reverse processes have the
opposite effect. In reactions that proceed through a charged or
partially charged transition state, the resulting electric field
induces electrostriction of the solvent, causing a reduction in
volume. Solvent effects have thus been used to infer transition-
state properties of many organic reactions.11-17 With one
exception, however, solvent effects on activation volumes of
enzyme reactions have not been explored.18
Metshutkin reactions,15 Diels-Alder reactions,16,22 SN1 substi-
tiutions,17 and many other classes of organic reactions.13,14
Because of the limiting assumptions inherent in the derivation
(most notably the exclusion of nonelectrostatic interactions, e.g.,
van der Waals forces and hydrogen bonding), deviations from
the theory for some solvents are not unusual.15,16 However,
recent molecular dynamics simulations23 have revealed that the
Born-Kirkwood dielectric continuum representation of the
reaction solvent agrees much more closely with microscopic
models than previously thought, although its application to
enzyme reactions has not been considered previously. This is
the focus of the current study.
Kirkwood Analysis of Enzymatic Reactions
The activation volume for an enzymatic reaction can be
related to its catalytic efficiency, kcat/Km, through an expression
analogous to eq 2
Underlying Theory
kcat
The interpretation of charge formation in reaction pathways
has been greatly aided by the fundamental analyses of Born19
and Kirkwood.20 In particular, Kirkwood generalized Born’s
original treatment of charge solvation to systems containing
arbitrary distributions of charge centers. From this work, the
electrostatic Gibbs energy upon transfer of a mole of dipoles
of moment µ from a vacuum (i.e., ꢀ ) 1) into a spherical cavity
of radius r, inside an isotropic continuum of dielectric constant
ꢀ, can be evaluated (eq 1):
∂ ln
( )
µ2 ∂q
Km
(
)
-RT
) ∆Vq ) ∆Vq0 - NA∆
(3)
(
)( )
r3
∂P
T
∂p
where
µ2ES
µ2S µ2E
-
µ2
( )
q
∆
)
-
(4)
3
3
(
)
r
rES
r3S r3E
q
µ2
(ꢀ - 1)
(2ꢀ + 1)
and ΕSq, S, and E denote the enzymic transition state, substrate,
and enzyme, respectively. From eq 3, plotting the experimental
∆Vq versus (∂q/∂P) for various solvents should yield a straight
line, with a slope of -NA∆(µ2/r3) and a y-intercept of ∆Vq0.
This intercept consists of the intrinsic structural contributions
to ∆Vq0, such as changes in bonding and bond lengths during
formation of the transition state as well as nonelectrostrictive
solvent contributions that are common among all the solvents
used. Neglected from this description are pressure effects
arising from any specific contributions from a given solvent,
such as hydrogen bonding, solvent participation in the transition
state, or solvophobic effects. These omissions are difficult to
evaluate independently and often result in deviations from the
Kirkwood plot, underscoring the approximate nature of this
analysis. Nevertheless, a strong solvent dependence of the
activation volume signals a highly polar transition state and, in
the absence of strong specific solvent effects, provides the basis
for estimating the transition-state dipole moment.
∆GE ) -NA
(1)
( )
r3
[
]
The quantity in brackets is the dielectric constant factor q.
Equation 1 can also be used to evaluate the electrostatic Gibbs
energy of activation for a chemical reaction,21 e.g., the reaction
S f P that proceeds through the transition state Sq. Further-
more, the pressure derivative of eq (1) describes the electros-
triction caused by the net dipole moment of the transition state
and represents the electrostatic contribution to the activation
volume of the reaction.14 The total activation volume, ∆Vq,
can thus be expressed as a combination of nonelectrostrictive
and electrostrictive terms (eq 2), as presented in ref 14:
2
µS2
µS
q
∂q
∆Vq ) ∆Vq0 - NA
-
(2)
3
3
( )
[
]
∂p
rS
rS
q
In eq (2) ∆Vq0 represents the activation volume in the absence
of electrostriction, and the term in brackets contains the dipole
‡
moment of the transition state µs . Kirkwood’s electrostatic
Materials and Methods
model has been useful in high-pressure mechanistic studies of
Catalytic efficiencies were determined for subtilisin-catalyzed trans-
esterification in various organic solvents. Twice-crystallized and
lyophilized subtilisin Carlsberg (Sigma Chemical, St. Louis, MO), and
subtilisin BPN′ (wild-type and the active-site mutant, G166N, gener-
ously provided by Dr. Thomas Graycar at Genencor International, S.
San Francisco, CA) were activated for catalysis in organic solvents by
freeze-drying from a 10 mg/mL aqueous solution (10 mM phosphate
buffer, pH 7.8) for 42 h at 40 mTorr. All organic solvents were of the
highest grade commercially available and were dehydrated by storing
over 3 Å molecular sieves (Linde) for at least 24 h immediately prior
to use. Water concentrations of the solvent were measured prior to
each set of reactions by Karl Fischer titration.
(8) Rodgers, K. K.; Pochapsky, T. C.; Sligar, S. G. Science 1988, 240,
1657.
(9) Rasper, J.; Kauzmann, W. J. Am. Chem. Soc. 1962, 84, 6835.
(10) Chryssomallis, G. S.; Torgerson, P. M.; Drickamer, H. G.; Weber,
G. Biochemistry 1982, 20, 3955.
(11) van Eldik, R.; Asano, T.; le Noble, W. J. Chem. ReV. 1989, 89,
549.
(12) Weale, K. E. Chemical Reactions at High Pressures; Spon: London,
1967; pp 1-349.
(13) Brower, K. R.; Chen, J. S. J. Am. Chem. Soc. 1965, 87, 3396.
(14) Eckert, C. A. Ann. ReV. Phys. Chem. 1972, 23, 239.
(15) Hartmann, H.; Brauer, H. D.; Kelm, H.; Rinck, G. Z. Physik Chem.
1968, 61, 53.
(16) Greiger, R. A.; Eckert, C. A. Trans. Faraday Soc. 1970, 66, 2579.
(17) Kotowsky, R.; Palmer, D. A.; Kelm, H. Inorg. Chem. 1970, 18,
2555.
(18) Kim, J.; Dordick, J. S. Biotechnol. Bioeng. 1993, 42, 772.
(19) Born, M. Z. Phys. 1920, 1, 45.
In a typical reaction, 925 µL of a 0.27 mg/mL suspension of subtilisin
in the reaction solvent was added to a stainless steel type 316 pressure
bomb (internal volume, 1.5 mL) and preheated to 30.0 °C in a forced
(22) McCabe, J. R.; Eckert, C. A. Ind. Eng. Chem. Fundam. 1974, 13,
168.
(23) Roux, B.; Yu, H.-A.; Karplus, M. J. Phys. Chem. 1990, 94, 4683.
(20) Kirkwood, J. G. J. Chem. Phys. 1934, 2, 351.
(21) Stearn, A. E.; Eyring, H. Chem. ReV. 1941, 29, 509.

Dipole Formation/SolVent Electrostriction in Subtilisin Catalysis
J. Am. Chem. Soc., Vol. 119, No. 40, 1997 9333
air oven (Blue M Corp, Blue Island, IL). The suspension was
maintained by sonication during sampling of the stock enzyme solution.
The transesterification reaction of acetyl-L-phenylalanine ethyl ester
(APEE) was then initiated by adding 75 µL of a freshly prepared stock
solution of APEE in n-propanol. The final concentrations of the
substrates were 1 M n-propanol and 5-40 mM APEE in a 1 mL total
liquid volume. Pressurization was achieved with oxygen-free helium
and was complete within 20-30 s of the substrate being added to the
pressure bomb. In a control experiment to investigate potential heating
upon pressurization, pressurization of the water-filled bomb to 500 atm
over 5 s caused a temperature rise of less than 1 °C, measured with a
high-pressure thermocouple.
Samples were periodically withdrawn from the reactor, and the
formation of acetyl-L-phenylalanine propyl ester was followed by GC-
MS using a 25 m, 95% methyl-5% biphenyl capillary column (Hewlett-
Packard). There was no measurable reaction in hexane in the absence
of enzyme and hence no detectable product. Therefore, a lower limit
of the enzymatic rate enhancement relative to the uncatalyzed reaction
Figure 1. Catalytic efficiency of subtilisin Carlsberg measured for
transesterification in hexane as a function of pressure. The curve
represents a quadratic fit to the data. The activation volume was
calculated from the slope of the quadratic at 1 bar.
at room temperature was determined by dividing kcat/Km (4.6 M-1 s-1
)
APEE are plotted against (∂q/∂P) in Figure 2.28 Values of (∂q/
∂P) were calculated from literature data for the dependence of
the solvent dielectric constant on pressure.29-32 As shown by
the plot, pressurization of subtilisin Carlsberg significantly
increased or decreased catalytic efficiencies for transesterifica-
tion, depending on the solvent. For example, kcat/Km in propyl
ether increased from 0.44 M-1‚s-1 at ambient pressure to 4.6
M-1‚s-1 at 1000 bar (i.e., ∆Vq) -55 mL/mol), a factor of
greater than 10. In contrast, the apparent activation volume in
acetone is 58 mL/mol, which corresponds to a 10-fold reduction
in kcat/Km at 1000 bar.
The good linear correlation between ∆Vq and (∂q/∂P) for the
various solvents demonstrates the strong participation of
electrostatic effects during the formation of the transition state.
From eq 3, the slope of the line equals -NA∆(µ2/r3). Estimating
the value of r from the known geometry of the transition state
thus enables one to calculate the apparent change of polarity
for the formation of the transition-state acyl-enzyme complex
(eq 4). The most likely source of this polarity change, based
on the widely accepted charge-transfer mechanism of serine
proteases in water, is the developing charge on both His64 and
the substrate carboxyl group during formation of the transition
state.
by the rate constant for the uncatalyzed reaction estimated from the
measured detection limit of the gas chromatograph for acetyl-L-
phenylalanine propyl ester (2.2 × 10-10 M-1 s-1). The estimated lower
limit of the rate enhancement was thus ca. 2.1 × 1010.24
The initial rates increased linearly with substrate concentration,
indicating that the reaction followed first-order kinetics over the
substrate range tested (5-40 mM). To convert the reaction velocities
into the kinetic parameter kcat/Km, the fraction of active sites available
in the suspended subtilisin powders (which were prepared exactly the
same way for all experiments) was assumed to be 15%, independent
of pressure. This value is based upon our previous active-site titration
measurements for this enzyme in a variety of solvents and is in
agreement with the results of Affleck et al.3 for the same lyophilization
procedure. The relatively low fraction of competent active sites is
reportedly due to the irreversible (in organic solvents) partial unfolding
of the native enzyme structure during the lyophilization process.25,26
Once the sonicated powders are suspended in organic solvent, no
treatment, including pressurization, has been shown to induce irrevers-
ibly denatured enzyme to refold to the native and active form. Hence
the assumption that the competent active-site concentration is inde-
pendent of pressure.
Because the kcat/Km values are reported in pressure-dependent units
of M-1‚s-1, compression of solvent must be accounted for by correcting
the calculated activation volumes by RTâT, where âT is the isothermal
compressibility of the solvent.27 For subtilisin-catalyzed transesteri-
fication in organic solvents, this adjustment typically resulted in a
correction of 3-4 cm3/mol.
In eq (4), the term µs2/rs3 can be calculated for the substrate
in its ground state using standard computational methods.33 For
APEE in organic solvents, a radius of 3.9 Å was calculated
from a van der Waals volume of 184 Å3.34 Optimizing the
structure of APEE by molecular simulation in a low dielectric
and calculating its dipole moment using the method of Pullman
Results and Discussion
Figure 1 plots the catalytic efficiencies in hexane versus
pressure. As is often the case, this plot exhibits slight curvature,
which is typically described by a quadratic series in pressure.12
The value for ∆Vq in hexane was obtained from Figure 1 by
evaluating the slope of this quadratic at 1 bar.12,13 The
uncatalyzed reaction was very slow at room temperature (no
measurable product in hexane after 48 h). However, cursory
rate measurements of the uncatalyzed reaction in hexane at 150
°C provided an upper limit for the reaction rate of ∼0.4 µM/h
and showed very little effect of pressure (∆Vq∼ -5 mL/mol at
100 °C based on a comparison of the uncatalyzed reaction rates
at 1 and 500 bar).
(28) We did not compare ester hydrolysis in aqueous solution to
transesterification in organic solvents for two primary reasons. First, the
two types of reactions have different rate-limiting steps. The rate-controlling
step for subtilisin-catalyzed ester hydrolysis is deacylation (Bonneau, P.
R.; Graycar, T. P.; Estell, D. A.; Jones, B. J. J. Am. Chem. Soc. 1991, 113,
1026), whereas the rate-controlling step for transesterification in organic
solvents is acylation (Wangikar, P. P.; Graycar, T. P.; Estell, D. A.; Clark,
D. S.; Dordick, J. S. J. Am. Chem. Soc. 1993, 115, 12231. Chatterjee, S.;
Russell, A. J. Biotechnol. Bioeng. 1992, 40, 1069.) Moreover, water differs
in its mechanism of electrostatic solvation compared with more apolar
solvents (Whalley, E. J. Chem Phys., 1963, 38, 1400.) and commonly
engages in nonelectrostrictive interactions. These effects often cause
deviations from the Kirkwood model for electrostriction (Isaacs, N. Liquid
Phase High Pressure Chemistry; John Wiley & Sons: Chichester, 1981 pp
181-343. Hamann, S. D. Mod. Asp. Electochem. 1972, 9, 47.).
(29) Brazier, D. W.; Freeman, G. R. Canadian J. Chem. 1969, 47, 893.
(30) Owen, B. B.; Stuart R. Brinkley, J. Phys. ReV. 1943, 64, 32.
(31) Schornack, L. G.; Eckert, C. A. J. Phys. Chem. 1970, 74, 3014.
(32) Skinner, J. F.; Cussler, E. L.; Fuoss, R. M. J. Phys. Chem. 1968,
72, 1057.
Effective activation volumes for the transesterification of
(24) This estimate, while only approximate, is comparable to the value
reported previously for a similar transesterification reaction catalyzed by
subtilisin in octane (Zaks, A.; Klibanov, A. M. J. Biol. Chem. 1988, 263,
3194).
(25) Desai, U. R.; Osterhout, J. J.; Klibanov, A. M. J. Am. Chem. Soc.
1994, 116, 9420.
(33) Clark, M.; Cramer, R. D.; van Opdenbosch, N. J. Comput. Chem.
1989, 10, 982.
(34) Cox, P. J. J. Chem. Educ. 1982, 59, 275.
(26) Desai, U. R.; Klibanov, A. M. J. Am. Chem. Soc. 1995, 117, 3940.
(27) le Noble, W. J. ReV. Phys. Chem. Jpn. 1980, 50, 207.

9334 J. Am. Chem. Soc., Vol. 119, No. 40, 1997
Michels et al.
Figure 2. Kirkwood plot for the apparent activation volumes of
subtilisin-catalyzed transesterification in organic solvents.
and Berthod35 gave µs ) 5.99 Debye. Based on these values,
µs2/rs3 ) 6.05 × 10-13 ergs. Furthermore, the dipole of the
catalytic triad in the ground state of subtilisin is expected to be
negligible in comparison to the dipole of the charged transition
state; hence, the ground-state dipole of the active site has been
Figure 3. Hypothetical transition state for transesterification of APEE
catalyzed by subtilisin Carlsberg, with the 9.3 Å charge separation of
the effective dipole indicated by the arrow. The dashed arc represents
the average position of hydrogen bonds from Asn155 that delocalize
the charge of the oxyanion group of the transition state. For further
details, see text.
neglected. Neglecting this term in the right-hand side of eq
‡
(4) leads to a lower limit for the value of µES
.
simulation of electrostatic potential integrals on the quantum
level. These calculations showed that generation of the
electrostatic field centered around the protonated active-site His64
and the electrophilic “oxyanion hole” created between the
backbone NH of the catalytic Ser221 and the side-chain amide
group of Asn115. The formation of charge was promoted by
the interaction of at least 10 additional residues in a 7 Å sphere
around the active site. This illustrates the dramatic cooperativity
of residues in proximity to the catalytic serine, leading to the
high catalytic efficiency of the enzyme macromolecule. Inter-
estingly, the inclusion of 25 solvent (water) molecules in the
active site had little effect on charge development in the
transition state, suggesting that water plays no direct role in
the formation of the transition state. That the inclusion of water
molecules in the calculations of Lamotte-Brassuer et al.37 had
little effect on the maximum amplitude of the local electrostatic
potential supports our contention that water need not be present
for significant charge to be generated in the active site of
subtilisin during catalysis.
If electrostatic damping was the only role played by the
solvent in subtilisin catalysis, the integrated form of eq (3)
predicts that a plot of ln(kcat/Km) versus q for various solvents
should yield a straight line of slope (NA/RT)∆(µ2/r3). As
illustrated in Figure 4, this is not the case.38 The dashed line
in Figure 4 represents the theoretical effect of simple electrostatic
solvation on the reaction rate, assuming a transition-state dipole
of 31 Debye. The line was forced through the value of kcat/Km
determined for the hydrolysis of APEE in subtilisin’s native
solvent, water. The apparently random scatter of data for the
organic solvents suggests that a nonelectrostrictive solvent
effect(s) influences catalysis in these solvents. In addition, the
linear correlation of activation volumes with (∂q/∂P) in Figure
2 indicates that these additional solvent effects are independent
of pressure. These observations highlight the inherent limita-
tions of the Kirkwood model and provide strong evidence that
nonelectrostrictive effects can have a profound influence on
catalytic function. In this case, there are nonelectrostrictive
contributions to the activation free energy, which do not affect
the activation volume.
The separation of charge in the transition state can be
approximated as the distance between the Nδ1 atom of His64
and the average position of hydrogen bonds from Asn155 that
delocalize the charge of the oxyanion group of the transition
state. Based on the X-ray crystal structure of subtilisin Carlsberg
inhibited by the transition-state analog N-tert-butoxycarbonyl-
ala-pro-phe-O-benzoylhydroxylamine,36 this charge separation
is 9.3 ( 0.3 Å (Figure 3). The error range of (0.3 Å represents
the accuracy to which atoms can be located, given the 1.8 Å
resolution of the crystal structure.36 Although this crystal
structure was obtained for the enzyme in aqueous solution, the
crystal structures of cross-linked subtilisin Carlsberg in nearly
anhydrous acetonitrile and in water are essentially identical to
within the limits of their resolution.6,7 Likewise, the crystal
structure of the serine protease chymotrypsin in hexane exhibits
only minor perturbations from the crystal structure in aqueous
solution.5 Thus, an aqueous structure can be assumed to
describe the structure of subtilisin in hexane. Therefore, in terms
of the Kirkwood model, the separation of charge in the transition
state can be viewed as a dipole consisting of positive and
negative charges of 0.7 charge units each separated by a distance
of 9.3 Å (1 charge unit ) 4.8029 × 10-10 esu).
A charge separation of 9.3 ( 0.3 Å leads to a value of 31 (
‡
1.5 Debye for µES , which represents a lower limit for the dipole
moment of the transition-state acyl-enzyme complex. Note
that eq 3 predicts that for a line of constant slope, the dipole
moment varies with r raised to the 3/2 power. Thus, varying
the charge separation from 8 to 10 Å (i.e., r from 4 to 5 Å)
leads to a range of dipole moments from 25 to 35 Debye.
However, the linearity of Figure 2 illustrates that the transition
state dipole moment is independent of the solvent. Moreover,
the charge separation of 9.3 Å is based on current knowledge
of the enzyme’s transition state structure and recent crystal-
lographic data for the protein in aqueous and organic solvents.
‡
This value of µES determined from the Kirkwood plot is
comparable to the value of 35 Debye calculated for subtilisin
in aqueous solution by Lamotte-Brasseur et al.37 using computer
(35) Berthod, H.; Pullman, A. J. Chem. Phys. 1965, 62, 942.
(36) Steinmetz, A. C. U.; Demuth, H.-U.; Ringe, D. Biochemistry 1994,
33, 10535.
(37) Lamotte-Brassuer, J.; Dive, G.; Dehareng, D.; Ghuysen, J. M. J.
Theor. Biol. 1990, 145, 183.
(38) Essential data on the effect of pressure on the dielectric constant
(∂ꢀ/∂P) were available for a limited number of solvents; hence, more solvents
were included for the modeling in Figure 4 than in Figure 2.

Dipole Formation/SolVent Electrostriction in Subtilisin Catalysis
J. Am. Chem. Soc., Vol. 119, No. 40, 1997 9335
Figure 4. Catalytic efficiencies of subtilisin BPN′ versus the dielectric
constant factor, q, of the solvent. Note that the values (excluding the
value for water) span at least two orders of magnitude. The dashed
line represents the theoretical prediction based on the integrated form
of eq 3, assuming a transition-state dipole of 31 Debye. The deviation
of the data from the prediction is evidence that nonelectrostrictive effects
have a strong influence on subtilisin catalysis in most if not all of these
solvents. Solvents (q, kcat/Km in M-1‚s-1) are as follows: hexane (0.186,
0.43); toluene (0.236, 0.030); propyl ether (0.300, 0.44); isopropyl ether
(0.329, 0.26); tert-amyl alcohol (0.381, 0.60); 2-heptanone (0.439,
0.018); 3-heptanone (0.444, 0.0064); cyclohexanone (0.459, 0.016);
acetone (0.464, 0.95); and water (0.49, 2800).
Figure 5. Catalytic efficiency of the active-site mutant G166N,
normalized by that of wild-type subtilisin BPN′, as a function of the
dielectric constant factor. The solid line represents the theoretical
prediction of the integrated form of eq 3, assuming that the transition-
state dipole of G166N is 5.0 Debye less than that of the wild-type.
description of electrostriction effects in the transition state of
subtilisin.
From the slope of the plot in Figure 5, the effect of the active-
site mutation on transition-state dipole formation can be
estimated. The slope of Figure 5 indicates that mutation of
Gly166 to the more polar Asn166 results in a decrease of roughly
5 Debye in the transition-state dipole strength. This change is
consistent with improved catalytic efficiency of the polar mutant
relative to the wild-type subtilisin BPN′ in low dielectric solvents
due to a reduction in the electrostatic energy of dipole formation.
The results reported here support a transition-state model in
which the concerted action of several amino acid residues
specifically oriented in the active site of subtilisin enables the
formation of a strong net dipole during catalysis in organic
media. The marked dependence of the activation volume on
the solvent suggests solvent penetration of the active site in the
Vicinity of the transition state. The magnitude of the transition-
state dipole moment is independent of the bulk solvent, however,
indicating that the separation and charge in the transition state
remain constant, and solvent does not penetrate the dipole sphere
defined by a diameter of 9.3 Å (Figure 3).
In the absence of an enzyme catalyst, reactions that occur
through an activated intermediate with a dipole moment greater
than 3-6 Debye are very uncommon in apolar solvents. For
instance, the rate of the Diels-Alder cycloaddition reaction,
which has a transition state dipole moment of between 3-7
Debye, is ∼100 times slower in isopropyl ether (ꢀ ) 3.8) than
in acetone (ꢀ ) 20.6).31 Metschutkin reactions are a dramatic
example of a charge-generating organic reaction proceeding
through a highly polar (∼11 Debye) transition state, but the
rate in solvents of dielectric below that of toluene (ꢀ ) 2.4) is
almost negligible, even at high pressures32 (which accelerate
the reaction). Considering the µ2 dependence of the electrostatic
solvation energy, that enzyme catalysis can proceed through a
highly polar transition state (∼31 Debye) in extremely apolar
solvents such as hexane, with catalytic enhancements relative
to the uncatalyzed reaction on the order of 1010, is indeed
remarkable and highlights the robustness of the enzyme in
maintaining the cooperativity among active-site groups necessary
to effect catalysis.
If nonelectrostrictive effects of the solvent on the enzyme
could be implicitly accounted for, the agreement of the activation
free-energy data with the Kirkwood model should improve. This
postulate can be examined by replotting the data of Xu et al.39
for the transesterification activity of the active-site mutant of
subtilisin BPN′, G166N. (Gly166 is located at the far end of
the open cleft of the S1 acyl binding pocket of the enzyme40).
Because the data for the active-site mutant in various solvents
can be normalized by the catalytic efficiency of the wild type,
solvent effects distinct from the active site can be factored out.
Such a plot (Figure 5) exhibits good agreement with the
predicted linear dependence of ln(kcat/Km) versus q. That the
mutant differs from the wild type only in the active site implies
that the solvent effects on the activation volume (Figure 2) and
reaction rate (Figure 5) do indeed arise from active-site
polarization during catalysis for the enzyme-catalyzed reaction.
Furthermore, the agreement of the normalized data with theory
indicates that nonelectrostrictive effects act almost exclusively
at regions distinct from the enzyme’s active site.
The extent to which nonelectrostrictive effects influence
subtilisin catalysis warrants further consideration in view of
Figures 4 and 5. The Kirkwood model clearly fails to describe
the data plotted in Figure 4, where kcat/Km values vary over
several orders of magnitude and exhibit no discernable depen-
dence on q. Thus, whereas the electrostriction model explains
reasonably well the pressure dependence of catalysis, it is too
simplistic to predict the free energy change during catalysis.
However, if nonelectrostrictive effects removed from the active
site are accounted for, as they are in the normalized data plotted
in Figure 5, the accuracy of the model improves substantially.
This indicates that the Kirkwood model offers a reasonable
(39) Xu, Z.-F.; Affleck, R; Wangikar, P.; Suzawa, V.; Dordick, J. S.;
Clark, D. S. Biotechnol. Bioeng. 1994, 43, 515.
(40) Based on the x-ray crystal structure of subtilisin BPN′, the distance
between the Oγ atom of serine 221 and the CR atom at position 166 is 10.6
Å (41). The distance from the CR atom to the Nδ2 atm of asparagine is ca.
3.5 Å.
(41) Bott, R.; Ultsch, M. ; Kosiakoff, A.; Graycar, T. Katz, B.; Power,
S. J. Biol. Chem. 1988, 263, 7895.
Acknowledgment. We thank Joseph O. Rich for assistance
in preparing the manuscript. This work was supported by the
Army Research Office (DAAH04-94-G-0307).
JA9713892