We present a model for the molecular traffic of ligands,
substrates, and products through the active site of cholinesterases (ChEs). First, we describe a common treatment of the diffusion to a
buried active site of cationic and neutral species. We then explain the
specificity of ChEs for cationic ligands and substrates by introducing
two additional components to this common treatment. The first module is
a surface trap for cationic species at the entrance to the active-site
gorge that operates through local, short-range electrostatic
interactions and is independent of ionic strength. The second module is
an ionic-strength-dependent steering mechanism generated by long-range
electrostatic interactions arising from the overall distribution of
charges in ChEs. Our calculations show that diffusion of charged
ligands relative to neutral isosteric analogs is enhanced ~10-fold by
the surface trap, while electrostatic steering contributes only a 1.5- to 2-fold rate enhancement at physiological salt concentration. We
model clearance of cationic products from the active-site gorge as
analogous to the escape of a particle from a one-dimensional well in
the presence of a linear electrostatic potential. We evaluate the
potential inside the gorge and provide evidence that while contributing
to the steering of cationic species toward the active site, it does not appreciably retard their clearance. This optimal fine-tuning of global
and local electrostatic interactions endows ChEs with maximum catalytic
efficiency and specificity for a positively charged substrate, while at
the same time not hindering clearance of the positively charged products.
 |
INTRODUCTION |
Cholinesterases (ChEs) are a family of enzymes
that fall broadly into two types: acetylcholinesterase (AChE) and
butyrylcholinesterase (BChE). They are distinguished primarily by their
substrate specificity: AChE hydrolyzes the natural neurotransmitter
acetylcholine (ACh) faster than choline esters with bulkier acyl
chains; thus it is much less active on the synthetic substrate,
butyrylcholine (BCh). In contrast, BChE displays similar activity
toward the two substrates (Chatonnet and Lockridge, 1989
).
Vertebrates contain both AChE and BChE, which probably originate from
the duplication of a single ChE gene (Massoulié et al., 1993
).
Insects possess a single ChE gene coding for an enzyme with a
specificity intermediate between those of AChE and BChE (Massoulié et al., 1993
; Taylor and Radic, 1994
), while in
certain nematode species, up to four ChE genes have been identified
(Grauso et al., 1998
). The principal physiological function of AChE has long been known to be termination of impulse transmission at
cholinergic synapses by rapid hydrolysis of ACh, but the biological
role of BChE is still an open question (Chatonnet and Lockridge, 1989
).
ChEs are able to catalyze the rapid breakdown of a variety of esters,
both cationic and neutral (Quinn, 1987
). The highest catalytic rate is
displayed by AChE hydrolysis of ACh, at a rate approaching the
diffusion-controlled limit (Rosenberry, 1975b
; Hasinoff, 1982
;
Bazelyansky et al., 1986
). This efficiency is a common characteristic
of ChEs. A tally of the bimolecular rate constants
(kcat/KM) among ChEs for
their best substrates shows a spread of less than an order of
magnitude. Values range from 1.6 × 108
M
1 s
1, for hydrolysis of ACh by
Electrophorus electricus AChE (EeAChE) (Rosenberry, 1975a
), to 4.0 × 107 M
1
s
1 for BChE hydrolysis of both ACh and BCh (Vellom et
al., 1993
).
Catalytic efficiency of ChEs for neutral substrates is also very high.
Values of kcat/KM for
hydrolysis by AChE of ACh and of its neutral isoster
3,3-dimethylbutylacetate (DBA) do differ by ~40-fold at physiological
salt concentration (Hasan et al., 1981
), but there is evidence that the
hydrolysis of the thio analog of DBA is also diffusion-controlled
(Bazelyansky et al., 1986
). Moreover, it has been shown that BChE turns
over o-nitrophenyl butyrate (o-NPB) faster than
it breaks down butyrylthiocholine (Masson et al., 1997
).
Studies of the pH and charge dependence of catalytic hydrolysis of
substrates and of binding of reversible inhibitors suggested that the
active site of ChEs contains two major subsites, the "esteratic"
and the "anionic" (Wilson and Bergmann, 1950
), corresponding, respectively, to the catalytic machinery and the choline-binding pocket
(Froede and Wilson, 1971
). The high bimolecular association constants
for cationic ligands and their ionic strength dependence suggested a
high charge density in the active site. This led to the prediction that
up to nine negative charges were present in the "anionic" site
(Rosenberry and Neumann, 1977
; Nolte et al., 1980
). A second
"anionic" site, which became known as the "peripheral" anionic
site (PAS), was proposed based on binding of bis-quaternary ammonium
compounds (Bergmann et al., 1950
). Binding of ligands to the peripheral
anionic site causes inactivation of the enzyme, though the mechanism of
inhibition is not clear. It has been speculated that the PAS is
involved in the phenomenon of substrate inhibition and activation
through binding of a second substrate molecule. Its function may
involve either allosteric modification of the active site (Radic et
al., 1991
; Shafferman et al., 1992
; Barak et al., 1995
) or alteration
of the traffic of substrate and products by blocking access to the
catalytic machinery (Berman and Nowak, 1992
; Haas et al., 1992
; Schalk
et al., 1992
). In addition, there is evidence for an involvement of the
PAS in functions distinct from catalysis. Recent studies have presented
evidence for a role of the PAS of AChE in neurite regeneration and
outgrowth (Layer et al., 1993
; Willbold and Layer, 1994
; Jones et al.,
1995
; Srivatsan and Peretz, 1997
) and in the growth and differentiation
of spinal motor neurons (Bataillé et al., 1998
).
Catalysis by ChEs occurs by a mechanism similar to that of the serine
proteases, via an acyl-enzyme intermediate. It is assumed to involve a
tetrahedral transition state produced by nucleophilic attack on the
substrate by a serine, followed by general-base catalysis assisted by a
histidine. The transition state subsequently collapses to the
acyl-enzyme by general-acid-catalyzed expulsion of choline (Quinn,
1987
). Solution of the three-dimensional (3D) structure of AChE from
Torpedo californica (TcAChE) (Sussman et al.,
1991
) was followed by determination of the crystal structures of
several complexes of AChE with specific inhibitors (Harel et al., 1993
,
1995
, 1996
). Analysis of these structures, taken together with
systematic site-directed mutagenesis studies (Radic et al., 1991
, 1993
;
Shafferman et al., 1992
; Barak et al., 1995
), has permitted
identification of the key functional residues in the active site and
contributed to clarification of their role in recognition of substrates
and inhibitors. (A comprehensive and updated list of references for
cholinesterase mutants can be obtained through the ESTHER server,
http://meleze.ensam.inra.fr/cholinesterase (Cousin et al., 1997
).) It
has thus been possible to construct a picture of the structural factors
governing both the mechanism and specificity of ChEs. At the same time
the data obtained have given rise to a new set of still unanswered questions.
The structure/function relationships that have emerged over the past
seven years paint a picture of a family of rapid enzymes specific for
cationic substrates that have evolved to very high catalytic efficiency
by adopting some rather counterintuitive solutions. The active-site
serine of TcAChE, S200, was unexpectedly found to be located
near the bottom of a 24-Å-deep gorge, ~4.4 Å wide at its narrowest
point and 8.0 Å wide at its mouth. This serine forms a catalytic triad
with H440 and E327. [Residue numbers follow the guidelines established
at the 1992 OHOLO meeting, Eilat (Massoulié et al., 1993
). The
numbering used is that of the sequence of TcAChE. When
species-specific numbers are employed, the homologous position in
TcAChE will follow, printed in italics and appearing in
parentheses.] Contrary to the assumption of a concentration of
negative charges within the active site (Nolte et al., 1980
), no more
than two formal negative charges were found near the active site serine
(E199 and E443). In fact, the walls of the gorge were found to be lined
by the side-chains of 14 conserved aromatic residues (Sussman et al.,
1991
). In analogy to studies of ACh binding to model hosts (Dougherty
and Stauffer, 1990
), it was suggested that the binding of ACh to the
sites within the gorge involved in substrate recognition is stabilized
by interactions between the quaternary ammonium group of ACh and the
electrons of some of the conserved aromatic residues of AChE. This
hypothesis was confirmed by inspection of the structures of complexes
of AChE with various quaternary inhibitors (Harel et al., 1993
). Analysis of the 3D structure of the complex of AChE with the
transition-state analog, m-trimethylammonium
trifluoroacetophenone (TFK+), has highlighted the specific
intermolecular interactions between the substrate and the active site
that are responsible for the catalytic efficacy of AChE. These
structural data suggest that the particular active-site configuration
of AChE allows the enzyme to efficiently sequester the acylation
transition state in a preorganized polar environment formed by the
oxyanion hole, consisting of the main-chain N-H dipoles, G118, G119,
and A201, and the side chains of key aromatic residues such as W84 and
F330 (Harel et al., 1996
). This environment is able to stabilize the
catalytic transition state by providing it with larger electrostatic
stabilization than in the solvent and is the basis of the catalytic
power of the ChEs (Fuxreiter and Warshel, 1998
).
Inspection of the overall 3D structure of TcAChE revealed a
marked asymmetrical surface distribution of charged residues. These
residues were shown to segregate roughly into a "northern" negative
hemisphere, considering the mouth of the gorge as the north pole, and a
"southern" positive one, giving rise to a large "dipole moment"
roughly oriented along the axis of the active-site gorge (Ripoll et
al., 1993
; Tan et al., 1993
; Antosiewicz et al., 1994
; Felder et al.,
1997
). The magnitude of this "dipole moment" was estimated, by
electrooptical measurements on Bungarus fasciatius AChE
(BfAChE), to be ~1000 Debyes (Porschke et al., 1996
). The biological significance of these unusual electrostatic properties has
been the subject of much controversy. It has been suggested that the
"macrodipole" might act to steer cationic ligands to the mouth of
the gorge (Sussman et al., 1991
; Tan et al., 1993
), where they would
bind to the aromatic residues lining it and subsequently be committed
to moving down the gorge, toward the active site, in a fashion similar
to that of an affinity column (Sussman et al., 1991
). Calculations of
the rates of encounter of charged ligands and substrates based on
Brownian dynamics (BD) simulations predicted that the electrostatic
properties of AChE would be responsible for a rate enhancement of up to
240-fold (Zhou et al., 1996
). The possibility of a large electrostatic
steering effect on positively charged substrates has raised the
question of the route of clearance of choline (Ch), the cationic
product of enzymatic hydrolysis, which would seem to be trapped at the
bottom of the gorge by a strong electric field.
Molecular dynamics (MD) simulations have suggested that an alternative
route of access to the active site might open via the concerted
movement of residues W84, V129, and G441 (Gilson et al., 1994
), while a
more recent MD study has identified a number of "side entrances" to
the gorge, all involving concerted movements of a number of side chains
in the
loop (C67-C92) of AChE (Wlodek et al., 1997b
). As yet, no
simple and predictive model for the clearance of the products of
hydrolysis of ACh or BCh has been introduced into the treatment of the
molecular traffic of substrates and ligands through the active site of ChEs.
The importance of electrostatic interactions in the steering of
cationic substrates to the active site of ChEs was challenged by a
study of a series of mutants of human recombinant AChE (hAChE), in
which up to seven negative residues around the outer rim of the gorge
were neutralized, thus substantially reducing the magnitude of the
"macrodipole," without producing large changes in the second-order hydrolysis rate constant (Shafferman et al., 1994
). The contradiction between data documenting the electrostatic properties of ChEs and the
apparent lack of correlation between their experimental modification
and a major catalytic effect has been the topic of various studies.
Antosiewicz and co-workers (Antosiewicz et al., 1994
, 1995a
,b
, 1996
;
Antosiewicz and McCammon, 1995
) have attempted to correlate the
electrostatic properties of AChE with the on rates for charged ligands
and the second-order hydrolysis rate constants. The picture emerging
from their work supports the existence of an electrostatic steering
effect in ChEs. Moreover, calculations performed by the same group, on
structural models of the mutants analyzed kinetically by Shafferman et
al. (1994)
, account for the small changes in catalytic rates observed.
This reconciles the hypothesis of a role for electrostatics in
accelerating the encounter between the enzyme and reactive species with
experimental data that seemed to argue against it (Antosiewicz et al.,
1995b
). Nevertheless, these studies were unable to strongly correlate experimental results with any one particular aspect of the
electrostatic properties of the ChEs, since neither the total charge
nor the dipole moment fully accounted for the electrostatic steering of ligand to the active site.
Calculations of the potential gradient along the axis of the gorge and
of its dependence on salt concentration have been performed both for
wild-type (WT) AChE of different species and for a series of surface
and active-site mutants (Antosiewicz et al., 1995b
; Wlodek et al.,
1997a
; Felder et al., 1997
). These calculations have revealed that
AChEs display a similar negative potential gradient, beginning several
angstroms outside the gorge entrance, and continuing down the gorge
toward the active site. This potential is not correlated with ChE
surface charge distribution, but is due to a combined effect of the
overall charge distribution in the ChE molecule, including the effect
of several
-helix dipoles. The results of these studies suggest the
existence of a long-range electrostatic interaction, attributable to
this potential gradient, that contributes to both the enhancement of
encounter rates between cationic ligands and the catalytic machinery
buried at the bottom of the active-site gorge of ChEs. Radic et al.
(1997)
have performed a detailed analysis of the influence of
electrostatics on the kinetics of ligand binding to AChE. This study
focused on the ionic-strength dependence of the binding of reversible
inhibitors to AChE after neutralization, by site-directed mutagenesis,
of anionic side chains in the surface area around the entrance to the
active-site gorge, in the PAS and in the active center. Comparison of
the experimental data to BD simulations of the on rates of the ligands
revealed good agreement for surface mutants, while predictions were
less accurate when some key residues in the PAS were neutralized. The
results were interpreted in the framework of two distinct types of
electrostatic interactions: the first, dependent on salt concentration,
causing acceleration of the initial encounter rates of cationic ligands
with the enzyme, and the second, independent of salt concentration,
resulting in trapping of these ligands by specific residues in the PAS
or within the active site. The presence of a trap for cationic ligands
in AChE and BChE has been proposed in several other studies (Rosenberry
and Neumann, 1977
; Hasinoff, 1982
; Hosea et al., 1996
; Masson et al.,
1996
, 1997
), but no analytical and quantitative treatment of the effect of a trapping surface on the encounter rate of cationic ligands with
the ChEs has been advanced until now.
In the following sections we will present a model for the molecular
traffic of neutral and cationic ligands, substrates, and products
through the active site of ChEs, and we will evaluate the contributions
of electrostatic interactions to the traffic of cationic species.
First, we will illustrate a common treatment for the diffusion of both
neutral and cationic ligands toward an enzyme characterized by a buried
active site. Subsequently, we will show how the specificity of ChEs for
cationic ligands and substrates can be treated by introducing two
additional modules to this common treatment:
| 1. |
A module that incorporates the effects of short-range and
ionic strength independent interactions between key residues
in the area of the entrance to the active-site gorge and the quaternary ammonium moiety of cationic substrates and ligands. This local module
will be shown to describe the effects of a putative trapping mechanism
for cationic species. The effect of this surface trap on the
enhancement of encounter rates between cationic ligands and ChEs will
be analyzed quantitatively by correlating the electrostatic potentials
in the area surrounding the entrance to the active-site gorge with the
experimentally measured encounter rates of cationic ligands with ChEs.
|
| 2. |
A module that incorporates the effects of long-range and
ionic-strength dependent interactions. This global module,
which is shown to describe the steering of cationic substrates and
ligands to the gorge floor, can be analyzed quantitatively by
evaluating the overall electric potential around the entrance and
within the active-site gorge and its dependence on ionic strength.
|
The clearance of positively charged products and ligands from the
active-site gorge will be considered as analogous to the Brownian
migration of a charged particle out of a one-dimensional box against an
electrostatic potential linear in distance along the length of the box.
For neutral molecules, the value of this potential will be set to zero,
while for charged species we will introduce values of the gorge
potential either derived from experimental data or calculated with the
Poisson-Boltzmann equation (PB).
This modular approach will enable us to rationalize the apparent
paradox of electric fields, which act to steer cationic species toward
the active site while at the same time not hindering the clearance of
positively charged products. The results obtained will be used to
discuss the mechanisms involved in the emergence of the specificity of
ChEs for cationic substrates from the framework of an already very
efficient catalytic machinery for the hydrolysis of small esters.
 |
METHODS: ELECTROSTATIC CALCULATIONS AND HOMOLOGY MODELS |
We calculated the electrostatic potential along the active-site
gorge of ChEs, by solving the PB equation, to study the influence on
gorge electrostatic potentials of salt concentration and of the
neutralization of a number of key residues in the area of the surface
cationic trap and in the active-site gorge. The electrostatic calculations were performed on the following enzymes (where
crystallographic coordinates are available, the PDB ID code will follow
in parentheses): AChE from the following species: Torpedo
californica (TcAChE-PDB ID: 2ACE), mouse (mAChE-PDB ID
1MAH), Bungarus fasciatus (BfAChE),
Drosophila melanogaster (DmAChE), and human
(hAChE); and human BChE (hBChE). Where the crystallographic coordinates were not available, homology models were constructed. The residues to
be mutated were chosen on the basis of their presumed involvement in
the recognition of cationic substrates and in the contribution to the
steering of cationic ligands toward the active site of ChEs (Shafferman
et al., 1992
, 1994
; Radic et al., 1993
, 1995
; Barak et al., 1995
;
Masson et al., 1996
; Ordentlich et al., 1996
). Three classes of mAChE
mutants, as shown in Table 1, were
generated by homology modeling from the respective WT structures. The
positions of these mutations on the 3D fold of ChE are illustrated in
Fig. 1. In the first class, based on the
studies of Shafferman et al. (1994)
and Radic et al. (1997)
, we
generated five mutant structures in which up to seven acidic residues
on the enzyme surface near the gorge entrance were neutralized. In the
second and third classes, the mutations focused on the modification of
residues in the area of the cationic trap and at the bottom of the
gorge, respectively, to analyze the correlation between local and
overall electrostatic potentials and the encounter rates of cationic
ligands and substrates.

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FIGURE 1
Ribbon diagram of AChE showing the relative positions
of the mutated residues. The axis of the gorge is indicated by the
yellow bar; the side chains of the surface mutants are colored in red;
E199, at the bottom of the gorge, is in green; and D72, the main
component of the cationic trap, is in purple.
|
|
Construction of homology models
In brief, models were constructed by use of the automated
knowledge-based model-building tool resident on the Swiss-Model Server
(Peitsch, 1996
) (http://www.expasy.ch/swissmod/SWISS_MODEL.html), employing 3D structures of TcAChE (PDB ID 2ACE, 1ACJ, 1FSS) and mAChE (PDB ID 1MAH) as templates. The automatic procedure involved
alignment of the sequence to be modeled with the template sequences, by
application of the BLAST algorithm (Altschul et al., 1990
). Regions of
sequence similarity were automatically selected and employed to build a
framework for the model structure. Missing loops were automatically
constructed by searching the PDB database, employing either the best
fitting fragment corresponding to the sequence or a framework
constructed by the average of the five best fragments. The last step of
the procedure involved automated rebuilding of side chains,
verification of the quality of the model, and refinement of the final
structure by energy minimization and molecular dynamics. The models
were then checked again manually, and any missing part that was not
successfully built automatically was added manually as described
previously (Felder et al., 1997
).
Calculation of electrostatic potentials along the active-site gorge
The electrostatic potential along the active-site gorge was
calculated by generating a string of dummy atoms at 1-Å intervals along the gorge axis (Fig. 1) and evaluating the electric potential for
the position of each dummy atom. The axis of the active-site gorge in
the structures examined was defined as extending from atom I444-CD
(gorge bottom) to the center of mass of atoms E73-CA, N280-CB, D285-CG,
and L333-O (gorge entrance) (Antosiewicz and McCammon, 1995
). The
portion of the gorge extending from the bottom to S200-OG was defined
as the binding region (~4 Å long), and the remainder as the transit
region (~20 Å long). The width of the gorge mouth was measured by
taking the average of the values of gorge radii originating from the
center of mass of atoms E73-CA, N280-CB, D285-CG, and L333-O and
intersecting the gorge rim at the CB atoms of residues D72, W279, D273,
and D365. To study the local electrostatic potentials generated in the
gorge by the residues involved in the cationic trap, we defined a
region of the gorge extending from its mouth (as defined above) to a
depth of 6 Å. The value of the electrostatic potential along this
portion of the axis was then averaged and taken as a measure of the
local potential in the trap region.
The PB equation was solved by the finite-difference method (Warwicker
and Watson, 1982
), using the QDIFFXS algorithm of version 3.0 of DelPhi
(Gilson and Honig, 1988
; Honig and Nicholls, 1995
). A grid of up to 90 Å3 was used. Calculations were performed, using an initial
coarser grid with a 35-Å border and 1.45-Å grid spacing and
subsequently focusing onto a second grid with a 10-Å border and
0.89-Å spacing. The internal and external dielectric constants were
fixed at values of 2 and 80, respectively. Calculations were performed
for salt concentrations of 5, 145, and 670 mM. The Stern ion exclusion layer was set at 2 Å, and the dielectric boundary between protein and
solvent was constructed using a probe radius of 1.4 Å. Calculations were performed at 298.15 K and pH 7.0, using the Parse partial atomic
charge and radius set (Sitkoff et al., 1994
). The protonation states of
the ionizable amino acids were assigned by examination of the solvent
accessibility of their side chains in the 3D structure. On the basis of
this analysis, all Glu, Asp, Lys, and Arg residues were set to be fully
ionized, and the average charge on the active-site H440 and on all
other histidines was set to zero (M. K. Gilson, personal
communication). Potential values are expressed in kT/e units
(1 kT/e = 25.6 mV = 0.593 kcal/mol/e).
 |
RESULTS AND DISCUSSION |
Because our study focuses on providing a model for the diffusive
and binding events occurring before and after the bond rearrangement and cleavage steps of catalysis, the experimental parameters best suited for comparison with our model are the on rates and binding constants (kon and Ki) of
transition-state analogs, whose magnitudes are dependent only on the
processes of diffusion and binding to the active site of ChEs. The
contributions of both long- and short-range electrostatic interactions
to the stability of the complex formed between a charged
transition-state analog and AChE (or BChE) and to the on rate of the
ligand can be evaluated by comparing the values of
Ki and kon for the
charged species with those for a neutral isosteric ligand. These
results can then be used to segregate the contributions of
electrostatic interactions to molecular traffic from their effect on
the chemical steps of catalysis.
Peptidyl trifluoromethyl ketones have been used extensively as
transition-state analogs of various serine hydrolases (Imperiali and
Abeles, 1986
; Takahashi et al., 1988
; Allen and Abeles, 1989b
; Brady et
al., 1989
). In particular, they have been employed to assess the role
of global electrostatic interactions in the stabilization of the
catalytic transition state of subtilisin BPN' (Jackson and Fersht,
1993
). A large body of kinetic evidence demonstrates that another
series of trifluoromethyl ketones serves as transition-state analogs of
ChEs (Allen and Abeles, 1989a
; Nair et al., 1993
, 1994
). The structure
of the complex of the phenyl trifluoromethyl ketone, TFK+,
with TcAChE has been solved by x-ray crystallography,
illustrating in detail the structural interactions responsible for the
tight binding of this particular transition-state analog (Harel et al., 1996
). The effect of salt concentration and of the mutation of residues
D72, E199, and several negatively charged surface residues on the
Ki of both TFK+ and its isosteric
neutral analog, m-tertbutyltrifluoroacetophenone (TFK0) (Quinn et al., 1995
; Radic et al., 1995
, 1997
; Hosea
et al., 1996
), have been measured.
Accordingly, the results of our calculations, presented in the
following sections, will be compared to experimental data collected for
TFK+, TFK0, and another ligand,
N-methylacridinium (NMA), which has been employed to study
the role of electrostatic properties in ChE catalysis (Nolte et al.,
1980
).
Part I: Molecular traffic
diffusion
A common treatment for the diffusion of cationic and neutral
isosteric ligands to a buried active site points toward two different
limits for diffusion to the active site of ChEs
In treating the diffusion of ligands and substrates toward ChEs,
we will employ the model described by Samson and Deutch (1978)
. In this
model, the enzyme is approximated as a sphere, and the active site by a
spherical cap. It focuses on the effect of burying a reactive site on
the inside of an enzyme, away from the surface and at the bottom of a
conical duct. The rest of the spherical surface, including the walls of
the duct, is considered to be inert. The relationship between the
actual 3D structure of AChE and the model is shown in Fig.
2. The entrance to the active-site gorge
constitutes a cap on the surface of a sphere of radius R. The gorge is modeled as a conical duct, characterized by an opening angle,
. The bottom of this duct is delimited by a spherical cap of
radius
, the surface of which includes the catalytic machinery of
the enzyme. We will ignore complications arising from hydrodynamic interactions and dynamic conformational changes of the enzyme. BD
simulations of the diffusion of a ligand to the active site of AChE
indicate that the influence of these effects on the diffusive process
is not very significant (Antosiewicz et al., 1995a
; Antosiewicz and
McCammon, 1995
).

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FIGURE 2
Schematic diagram of the model for diffusion of neutral
and cationic ligands and substrates to the active site of ChE. The
spherical model is superimposed on a slab view of TcAChE
showing the active-site gorge and the positions of D72 and of the
catalytic serine, S200. The inner and outer spherical caps are colored
in red. The inner cap includes the catalytic machinery of AChE, as can
be seen by the position of S200.
|
|
The following expressions should permit evaluation of the upper limit
for the encounter rates of charged and neutral ligands without
postulating any special diffusive mechanism for cationic species.
According to Samson and Deutch (1978)
, the rate constant for the
encounter of a ligand with the active site buried at the bottom of the
conical duct can be expressed as
|
(1)
|
where s is given by
/R, D is the
diffusion coefficient of the ligand, and the function
(cos
) is
given by the following expression:
|
(2)
|
where P(l) is the Legendre polynomial of
order l.
Let us then introduce numerical values for diffusion to the active site
of AChE of TFK+, of TFK0, and of NMA, a charged
ligand characterized by essentially the same diffusion coefficient as
TFK+ and TFK0 (Fig.
3 A).

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FIGURE 3
(A) Molecular structure of the
transition-state analogs, TFK+ and TFK0, and of
NMA. (B) Molecular structures of ACh, BCh, and some neutral
substrates of the ChEs.
|
|
A value of 32 Å for the hydrodynamic radius, R, of AChE is
taken from the study of Antosiewicsz et al. (1995a)
. The value of
can be estimated by subtracting the transit region of the gorge (as
defined in Methods) from the value of R, and the value of
can be estimated by taking arctan (r/g), where
r is the radius of the gorge mouth as defined in Methods,
and g is the total gorge length. Inspection of the
crystallographic 3D structure of TcAChE and mAChE yields
values of 8 Å for r and 24 Å for g (of which 4 Å constitute the binding region and 20 Å the transit region). These
figures result in a value of ~18° for
and 0.38 for s
(for an active site buried ~20 Å deep in the center of a protein of 32-Å radius). If we assume that TFK+, TFK0,
and NMA are characterized by diffusion constants similar to that of
ACh, we can employ the value of D = 61.2 × 10
7 cm2 s
1 (Antosiewicz et
al., 1995a
).
Introducing the values for R,
,
, s, and D
into Eq. 1 yields a value of k = 0.21 × 109 M
1 s
1 for diffusion of
these ligands to the active site of AChE buried ~60%
(
/R = s = 0.38) of the way down a conical duct
of aperture
= 20°. Values for k were calculated
using the program MATLAB (Version 5.1, 1998, Mathworks, Inc.). The
values tabulated in Table 2 reveal a good
agreement with experimental values gathered for TFK0; but
values for the charged ligands, TFK+ and NMA, are between
10- and 80-fold larger (depending on whether the data were collected at
very high or very low ionic strength, respectively).
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TABLE 2
Experimental inhibition constants and on rates of
TFK+, TFK0, and NMA and comparison with
theoretical values
|
|
Our guiding assumption for explaining the faster diffusion of cationic
species relative to their isosteric counterparts is that positively
charged ligands and substrates will diffuse in 3D until they reach a
negatively charged area at the entrance to the active-site gorge. This
area will act as a perfect sink for positively charged ligands, which
will undergo a reduction in dimensionality of diffusion from 3D to 1D
(Adam and Delbrück, 1968
) and be committed to travel to the
bottom of the gorge by a negative potential gradient. Because each
encounter with this trap will be productive, in effect "raising"
the buried active site to the surface, it can be modeled as a spherical
patch on the surface of the enzyme. In the case of neutral isosteric
ligands, which should neither interact with the trapping surface nor be influenced by the gorge potential gradient, an encounter will be
considered productive only if the ligand hits the spherical cap at the
bottom of the gorge. Thus, even though the gorge may restrict the
mobility of neutral species, they can effectively be considered to
be searching for the buried active site as if diffusion were taking
place in 3D, because their diffusion is not facilitated by a surface
trap or by the negative potential gradient.
If we then assume a surface trap around the gorge area of
a ChE molecule for cationic ligands, s = 1, and the
model gives the following expression for the rate constant:
|
(3)
|
Introducing the appropriate numerical values, we get 1.5 × 109 M
1 s
1 as the limit of
diffusion for TFK+ (or NMA) toward a molecule of AChE
characterized by a surface trap with
= 20°. As can be seen
by comparing this result with the values in Table 2, agreement with
experimental data is very good for on rates measured at high ionic
strength. The additional acceleration of diffusion that is observed at
very low ionic strengths is best explained by a steering mechanism
produced by long-range electrostatic interactions arising from the
global asymmetrical distribution of surface charges in ChEs (Ripoll et
al., 1993
; Antosiewicz et al., 1996
; Felder et al., 1997
).
On the basis of these observations, we can conclude that there are two
separate limits for the diffusion toward ChEs of neutral and charged
isosteric ligands. In the absence of a steering mechanism generated by
long-range electrostatic interactions (as is the case when on rates for
ligands are measured at high salt concentration), cationic substrates
are characterized by a diffusion limit about one order of magnitude
larger than that for neutral isosters, and this effect is achieved by
means of a trapping surface at the entrance to the gorge. As can be
seen from the data in Table 2, at physiological salt concentration
steering effects contribute only a 1.5-2-fold acceleration.
Significant steering is present only at very low salt concentrations,
when long-range contributions are strongest. Even then, the steering
effect is responsible for an additional increase in encounter rates for
cationic ligands of only one order of magnitude, which is much lower
than the 240-fold enhancement calculated on the basis of BD simulations
(Zhou et al., 1996
).
We can extend this treatment to the diffusion of cationic and neutral
isosteric substrates (Fig. 3 B). At high salt concentration, in the absence of any steering effect, the
kcat/KM values for ACh
and BCh are 10-15-fold larger than those for the neutral substrates, DBA, phenyl acetate (PhAC), and o-NPB (Tables
3 and
4, column 6), and both are about one
order of magnitude smaller than the respective upper diffusion limits
for cationic and neutral ligands. If we take the values of
kcat/KM as reflecting the
catalytic efficiency of ChEs toward these two classes of substrates, we
can say that the hydrolysis of both cationic and neutral substrates
approaches their specific limits of diffusion.
These findings lead us to conclude that ChEs are as efficient in
catalyzing the hydrolysis of neutral substrates as they are in
catalyzing the hydrolysis of their isosteric cationic counterparts. The
emergence of specificity for cationic substrates thus seems to arise
via a mechanism geared to speed up the diffusion of positively charged
substrates toward an already optimally efficient catalytic active site.
This enhancement of diffusion is accomplished primarily via a surface
trap whose effectiveness is independent of salt concentration, and
secondarily through a salt-dependent steering effect. The manner in
which they operate will be the subject of the following sections.
Module I: a surface trap for cationic species operating via
short-range local interactions
Experimental evidence for the presence of a trapping surface on
ChEs and for a reduction in the dimensionality of diffusion for charged
reactive species comes also from a study of the influence of viscosity
on the catalytic efficiency of EeAChE (Hasinoff, 1982
), in
which the dependence of
kcat/KM on
2/3 was interpreted as evidence for a reaction governed
by nonspecific binding of ACh to the enzyme, followed by surface
diffusion to the active site. A measure of the radius of the trapping
surface can be calculated by introducing the value for the on rate of a
ligand into the following equation (Hasinoff, 1982
):
|
(4)
|
where Reff is the effective trap radius,
N is Avogadro's number, and D is the diffusion
coefficient of the ligand.
If we introduce into Eq. 4 the value for the diffusion coefficient of
TFK+ or NMA, and the on rates measured for these ligands
and AChE from various species at high salt concentration, we get an
average value for the trap radius of ~7.5 Å, which is similar both
to the mean radius of ~9 Å estimated in recent MD studies (Wlodek et
al., 1997b
) and to our own estimate of ~8 Å derived from the crystallographically determined structure of TcAChE (Sussman
et al., 1991
).
Recent studies have suggested that a particular residue, D72 (D74 in
mAChE and hAChE, D70 in hBChE), might contribute to the specificity of
ChEs for cationic ligands by a trapping mechanism (Hosea et al., 1996
;
Masson et al., 1996
, 1997
). This residue is strategically placed near
the top of the active-site gorge (Fig. 1) and was identified as a
crucial component of the PAS (Shafferman et al., 1992
; Barak et al.,
1995
). Strong evidence in support of our model comes from the
observation that in mutant enzymes in which the putative cationic trap
has been removed by neutralizing the charge on D72, on-rate values for
cationic ligands fall to the theoretical values for neutral ones (Table
2). In addition, at physiological salt concentration,
kcat/KM values for
cationic substrates closely approach the values for neutral substrates
when the negative charge on the side chain of residue D72 is
neutralized (Table 3, column 6). These findings point to D72 as the
major component of a cation-specific trap at the entrance to the
active-site gorge of ChEs. Previous calculations comparing the D72N
mutant to WT AChE revealed a small contribution of the negative charge
of the side chain of D72 to the overall potential gradient within the
active-site gorge (Felder et al., 1997
). This small contribution does
not correlate with the drastic reductions in both catalytic efficiency
and in on rates for cationic ligands produced by mutations in this
position. BD simulations of the on rates of cationic ligands have been
found to be in good agreement with experimental data, but their
predictions were significantly less accurate when residue D72 was
neutralized (Radic et al., 1997
). However, we find a good correlation
between on rates for TFK+ and the average potential in the
gorge region corresponding to the cationic trap, both for WT AChE and
for a series of mutants in which the charge on D72 was neutralized
along with the charges on a number of surface residues, particularly
D82 and D278 (Radic et al., 1997
) (Fig. 4
A). Moreover, we also find a good correlation between on
rates for TFK+ and overall gorge potentials for surface
mutants and for the E199Q mutant, whose side chain is shown to
contribute significantly to the overall gorge potential (Felder et al.,
1997
; Wlodek et al., 1997a
) (Fig. 4 B). These findings
provide supporting evidence for our treatment of the acceleration of
diffusion of cationic species as being composed of the additive effects
of a surface trap operating through local short-range interactions,
constituted by the side chains of a few key residues, primarily D72,
D82, and D278, and of a long-range steering effect generated by the overall gorge potential.

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FIGURE 4
(A) Correlation between average potentials
in the trap region and encounter rates for TFK+ at high
(600 mM), physiological (145 mM), and low (2 mM) salt concentrations.
The potential values are calculated for WT mAChE and for the following
mutants (the abbreviations used in the list on the right of the figure
are given in parentheses): D72N (D72N); D72N/D275V/D278N (72/275/278);
E82Q/E89Q/D275V/D278N (4m); E82Q/E89Q/D275V/D278N/D365N (5m);
E82Q/E89Q/D275V/D278N/E285Q/D365N (6m). (B) Correlation
between overall gorge potential and encounter rates for
TFK+ at high (600 mM), physiological (145 mM), and low (2 mM) salt concentrations. The potential values are calculated for WT
mAChE and for the following mutants (the abbreviations used in the list
on the right of the figure are given in parentheses): D275V (D275V);
D275V/D278N (275/278); E82Q/E89Q/D275V/D278N (4m);
E82Q/E89Q/D275V/D278N/D365N (5m); E82Q/E89Q/D275V/D278N/E285Q/D365N
(6m); E199Q (E199Q).
|
|
If we want to uncouple the effects of local short-range interactions
from the effect produced by long-range interactions on diffusion rates,
we must resort to systems in which the mechanism necessary for the
recognition of positively charged substrates is maintained, while the
contribution of the negative charge on D72 to the gorge potential has
been eliminated. It so happens that in all insect species studied so
far, the amino acid at the position equivalent to residue 72 in
TcAChE is a tyrosine (Toutant, 1989
; Anthony et al., 1995
;
Zhu and Clark, 1995
). Site-directed mutagenesis studies on
DmAChE in which Y109 (equivalent to D72 in
TcAChE) was mutated to a glycine or a lysine showed that
such a mutation increased the KM for ACh by 10- and 100-fold, respectively, whereas mutation to glutamate had no effect
on KM (Mutero et al., 1992
). We interpret these
results as evidence for a trapping mechanism for cationic substrates
and ligands mediated, in insect ChEs, by the aromatic side chain of
Y109 via local cation-
interactions. The predictions made by our
model are supported by a comparison of the 3D structure of
DmAChE, recently solved in our laboratory (Harel et al.,
1999
) and that of TcAChE, which shows the position of
residue Y109 to be almost identical to that of D72. We thus predict
that the D72Y mutant in Torpedo or other vertebrate ChEs should retain most of its catalytic efficiency, and that any reduction in catalytic efficiency resulting from the D72Y mutation should be
correlated with the corresponding small decrease in gorge potential. Our assumption that an aromatic residue can be as efficient as a
negatively charged one in the recognition of cations is corroborated by
the following data:
| 1. |
Cation- interactions are predominantly electrostatic,
involving the interaction of the cation with the large, permanent
quadrupole moment of the aromatic ring (Dougherty, 1996 ).
|
| 2. |
Gas-phase measurements of binding energy of cations to benzene
and to toluene have shown that in this phase a cation would preferentially bind to an aromatic compound rather than to water (Sunner et al., 1981 ).
|
| 3. |
In an aqueous environment, a pocket lined with the side chains
of amino acids such as Trp, Phe, and Tyr can efficiently compete with
full water solvation for the stabilization of a positive charge,
because of the sizable quadrupole moment of the rings of aromatic
residues (Luhmer et al., 1994 ). The importance of cation-
interactions in the catalytic function of ChEs has been confirmed by a
large body of structural (Sussman et al., 1991 ; Harel et al., 1993 ,
1996 ) and kinetic (Ordentlich et al., 1993 ; Radic et al., 1993 ; Nair et
al., 1994 ; Barak et al., 1995 ) data.
|
Modeling of the D72Y mutant of TcAChE shows that the
hydroxyl moiety of the tyrosine at position 72 is capable of forming a
hydrogen bond with Y121. It has been hypothesized that the hydrogen bond between Y121 and D72 in WT AChE is required for maintaining the
"functional cross-talk" postulated for the transduction of allosteric signals from the PAS to the catalytic center (Shafferman et
al., 1992
; Barak et al., 1995
). These considerations also provide us
with a rather straightforward test for the presence of such cross-talk,
because replacing tyrosine with phenylalanine, i.e., generating the
D72F mutant, should have a disruptive effect on signal transduction and
reduce catalytic efficiency significantly. Analysis of the kinetic
properties of these mutants is under way, and preliminary results show
that the KM values of both D72Y and D72F mutants
of TcAChE are not significantly different from those of
WT-TcAChE, thus providing strong supportive evidence for our hypothesis. A complete analysis of the catalytic properties of these
mutants, along with other mutants generated to study the role of
aromatic and charged residues inside the active-site gorge of ChEs, is
currently under way (S. A. Botti, E. Krejci, S. Bon, D. M. Quinn, J. L. Sussman, I. Silman, and J. Massoulié,
manuscript in preparation).
Module II: the potential gradient along the active-site gorge is
responsible for steering cationic species to the active site of ChE
We now turn our attention to the second module of our treatment:
the long-range electrostatic steering effect. We will discuss how this
effect arises from the potential gradient along the gorge axis, which
arises from the combined effect of the overall charge distribution in
the ChE molecule and the contribution of several
-helix dipoles.
Kinetic studies have revealed both a marked reduction in the affinity
of AChE for cationic substrates and inhibitors (Mendel and Rudney,
1943
) and an increase in kcat (Nolte et al., 1980
; Smissaert, 1981
; Hofer et al., 1984
), upon the addition of
inorganic salts such as sodium or magnesium chloride. The dependence upon salt concentration has been ascribed to the binding of inorganic cations to anionic sites (Taylor and Lappi, 1975
; Smissaert, 1981
), to
conformational changes resulting from occupation of the PAS by metal
ions (Changeux, 1966
), and to the screening of favorable electrostatic
interactions between the cationic substrate and the "anionic"
subsite in the active site of the enzyme (Dawson and Crone, 1973
; Nolte
et al., 1980
; Hofer et al., 1984
). Comparison of the effects of
monovalent and divalent ions on the activity of AChE suggests a general
screening effect of monovalent cations, while it has been proposed that
divalent cations interact specifically with carboxylate groups present
in the active site (Hofer et al., 1984
). The identification of a
putative binding site for Zn2+ in hBChE (Bhanumathy and
Balasubramanian, 1996
) supports the notion of specific binding sites
for divalent cations in ChEs.
The potential gradient along the gorge axis and its dependence on salt
concentration have been calculated both for WT TcAChE and
for a series of surface and active-site mutant models (Antosiewicz et
al., 1995b
; Felder et al., 1997
; Wlodek et al., 1997a
). On the basis of
these results, it has been suggested that enhancement of encounter
rates between cationic ligands and the catalytic machinery buried near
the bottom of the active-site gorge is due to long-range electrostatic
interactions, attributable to the potential drop along the length of
the active-site gorge. Radic et al. (1997)
recently analyzed in detail
the influence of electrostatics on the kinetics of ligand binding
to AChE. Their study focused on the ionic-strength dependence of the
binding of ligands to AChE after neutralization, through site-directed
mutagenesis, of the negative charges of residues in the active site, in
the PAS, and within a surface area around the entrance to the gorge. Comparison of experimental on rates for TFK+ gathered on
the surface and active-site mutants revealed good agreement with BD
simulations. However, prediction of on rates after neutralization of
the negative charge of D72, which is considered to be a major component
of the PAS, was considerably less accurate. Radic et al. (1997)
interpreted their results by assuming two distinct types of
electrostatic interaction: one interaction, dependent on salt
concentration, brings about acceleration of the initial encounter rates
of cationic ligands with the enzyme, and a second one, independent of
salt concentration, results in trapping of these ligands by specific
residues within the PAS.
Fig. 5 shows that the
ionic-strength-dependent decrease in electrostatic potential inside
(and outside) the active-site gorge is rather well correlated with the
corresponding decrease in encounter rates of both NMA and
TFK+ with EeAChE, TcAChE, and mAChE
(Nolte et al., 1980
; Berman et al., 1991
). It thus seems reasonable to
argue that this correlation corresponds to the contribution to
molecular traffic of salt-dependent long-range interactions arising
from the global asymmetrical distribution of charges in ChEs.

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FIGURE 5
Correlation between overall gorge potentials of WT
AChEs and encounter rates of TFK+ and NMA as a function of
salt concentration. The potential values were calculated for
TcAChE for salt concentration values varying from 2 to 600 mM.
|
|
This argument is reinforced by the observation that neutralization of
seven negatively charged residues around the entrance to the
active-site gorge has only a small effect on the potential gradient
within the active-site gorge (Felder et al., 1997
), and that this small
change is strongly correlated with a concomitant small reduction in
catalytic efficiency (Shafferman et al., 1994
). The overall potential
difference along the axis of the active-site gorge is similar for AChE
of different species and is ~20% smaller for hBChE, as shown in Fig.
6. In this figure, it is interesting to
note that the slope of the potential gradient displays an inflection ~14 Å from the bottom of the gorge, in the neighborhood of D72, D82,
and D278. Antosiewicz et al. (1995b)
pointed out that the profile of
rate constant versus depth of penetration inside the gorge suggests a
"choke point" in the same region, beyond which the reactive species
becomes committed to a productive encounter. In DmAChE,
where the residue homologous to D72 is a tyrosine (Y109), the
inflection in gorge potential is less pronounced than for vertebrate
AChEs. Our hypothesis is that this smaller inflection is due to the
contribution of conserved negatively charged residues in
DmAChE (Felder et al., 1997
), homologous to D82 and D278,
which constitute the secondary components of the cationic surface trap. These considerations strengthen the case for a major role of D72, and
secondarily of D82 and D278, in the recognition of cationic substrates.

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FIGURE 6
Electrostatic potentials along the gorge axis for
ChEs. The potentials were calculated for TcAChE, mAChE,
hAChE, DmAChE, BfAChE, and hBChE.
|
|
Part II: quantitative treatment of the electrostatic forces
underlying ChE-ligand binding interactions
Contribution of electrostatic interactions to the binding of
transition-state analogs to ChEs
In the previous sections we showed that diffusion of cationic
species toward the active site of ChEs is enhanced both by a cationic
trap, which operates through local short-range electrostatic interactions, and by a steering effect that emerges from the global asymmetrical spatial distribution of charges in the ChE molecule. In
this section we analyze the contribution of a single positive charge to
the stabilization of the binding of transition-state analogs to ChEs,
with a treatment analogous to the one used in the previous sections.
Binding experiments have revealed a strong dependence upon ionic
strength of the Ki of TFK+, which is
not observed for TFK0 (Radic et al., 1997
). Mutation
studies have shown that stabilization of the binding of both
TFK+ and TFK0 is primarily due to short-range
interactions between W84 and the quaternary ammonium
(tert-butyl) moiety of TFK+ (TFK0)
(Radic et al., 1995
, 1997
), which take the form of cation-
interactions in the case of TFK+ and of short-range London
dispersion forces in the case of TFK0 (Nair et al., 1994
).
These studies show that binding of TFK+ to the W86A
(W84A) mutant of mAChE is ~1500-fold weaker than binding
to WT mAChE. In contrast, mutation of E199 or E443 (near the gorge
floor) results in only a ~10-fold decrease in binding strength, and
neutralization of the negative charge on D72 (at the top of the gorge)
in only a 20-fold decrease. Moreover, only the mutation of W84 affects
the binding strength of TFK0 to AChE (Radic et al., 1995
,
1997
; Hosea et al., 1996
). The primary role of W84 in the binding of
these transition-state analogs has been confirmed by the solution of
the 3D structure of the complex of TFK+ and
TcAChE (Harel et al., 1996
), and we can reasonably assume that the neutral analog, TFK0, would bind in an analogous fashion.
Consequently, we can consider the overall "charge effect," i.e.,
the added stabilization to the binding energy of cationic transition
state analogs for ChEs relative to their neutral isosteric counterparts, to be composed of two independent contributions, both
electrostatic:
| 1. |
A global term arising from long-range electrostatic
contributions that are screened at high salt concentrations.
|
| 2. |
A local term that can be identified with cation- and local,
short-range electrostatic interactions between the charged substrates and key binding residues, such as W84, in the active-site gorge.
|
The difference in binding between TFK+ and
TFK0 due to the positive charge, which we shall term

Gcharge, can be calculated from the
experimentally determined dissociation constants measured for WT
mAChE and can be defined as
|
(5)
|
With
GTFK+ =
RT ln Ki TFK+ and
GTFK0 =
RT ln
Ki TFK0 it follows that
|
(6)
|
If we assume 
Gcharge to be the sum of
all local interactions between the quaternary ammonium
(tert-butyl) moiety of TFK+ (TFK0)
and the aromatic side chains in the acyl binding pocket, and of global
electrostatic interactions due to the potential gradient within the
active-site gorge, we can express 
Gcharge
as
|
(7)
|
in which
|
(8)
|
and
|
(9)
|
If we consider the major contribution to the local term to be due
to interaction of TFK+ and TFK0 with W84, we
can isolate the contribution to the global term by considering the
change in Ki between WT AChE and the W84A. Although it is possible that the W84A mutation may produce structural rearrangements, these should affect binding of both TFK+
and TFK0 similarly, so that the only effect measured will
be that produced by the difference in charge of the two inhibitors.
In this case,
|
(10)
|
The value of the contribution to the local term can similarly be
isolated and assessed by examining the difference in binding energy
between TFK+ and TFK0 at very high salt
concentrations, where the steering effect should be completely
screened. In this case,
|
(11)
|
We can safely assume the value of
Ki TFK0 to be independent of salt
concentration because global electrostatic forces should have little
effect on TFK0 (Quinn et al., 1995
; Radic et al., 1997
).
If our assumptions are correct, the experimental data gathered for
these systems should yield values for 
GL
and 
GG which, when summed, should give
back the experimentally measured value for

Gcharge.
The validity of our assumption is shown in Table
5. Substituting in Eqs. 5, 10, and 11 the
appropriate experimental Ki values for
TFK+ and TFK0, tabulated in column 1 of Table
5, yields values for 
GL of ~3.4 kcal/mol
and for 
GG of 0.4 kcal/mol for
I = 0.145 mM and of 1.4 kcal/mol for I = 0.02 mM. Substitution of these values in Eq. 7 yields values for

Gcharge of 3.8 kcal/mol and 4.8 kcal/mol, at physiological and low salt concentrations, respectively, thus supporting our hypothesis.
Calculation of the potential inside the active-site gorge of AChE
from 
G
values for the activated complex of AChE
with TFK+ and TFK0
Having established that measurement of the difference in
Ki between TFK+ and TFK0
provides a powerful tool for calculating the contributions of electrostatic interactions, one can ask if the same tool can be employed to measure the electrostatic potential within the active site,
and if values so obtained will be in agreement with the ones calculated
by solving the PB equation for the system in question.
In a recent study (Stauffer and Karlin, 1994
), the electrostatic
potential of ACh binding sites in the nicotinic ACh receptor (nAChR)
was measured by analyzing the rate constants for the reactions of
charged and neutral methanethiosulfonates with binding-site cysteines
within the nAChR in terms of absolute rate theory and Debye-Huckel
theory, which, together, can be used to obtain rate constants as a
function of the electrostatic potential, the charges of the reactants,
and the ionic strength of the solution (Laidler, 1965
).
This treatment was applied to our system in an analogous fashion.
TFK+ and TFK0 bind to ChEs by forming a
hemiketal adduct with the active-site serine, S200. Reaction of either
TFK+ or TFK0 with AChE (Quinn et al., 1995
) can
be considered to take place according to the following scheme:
Formation of the hemiketal adduct can be considered
as proceeding through a short-lived activated complex,
EI
. Transition state theory provides the relationship
between rate constants and free energies of the enzyme, the inhibitor,
their complex, and the activated binding state (Glasstone et al.,
1941
):
|
(12.1)
|
|
(12.2)
|
where
is the vibrational frequency of the activated complex in
the degree of freedom leading to its decomposition, and
|
(13.1)
|
|
(13.2)
|
We can then apply the reasoning used in the previous section to
dete