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Biophys J, November 1999, p. 2430-2450, Vol. 77, No. 5

A Modular Treatment of Molecular Traffic Through the Active Site of Cholinesterase

Simone A. Botti,*# Clifford E. Felder,* Shneior Lifson,§ Joel L. Sussman,* and Israel Silman#

Departments of  *Structural Biology,  #Neurobiology, and  §Chemical Physics Weizmann Institute of Science, Rehovot 76100, Israel

    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS: ELECTROSTATIC...
RESULTS AND DISCUSSION
CONCLUSIONS
REFERENCES

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
TOP
ABSTRACT
INTRODUCTION
METHODS: ELECTROSTATIC...
RESULTS AND DISCUSSION
CONCLUSIONS
REFERENCES

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 pi  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 Omega  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 alpha -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
TOP
ABSTRACT
INTRODUCTION
METHODS: ELECTROSTATIC...
RESULTS AND DISCUSSION
CONCLUSIONS
REFERENCES

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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TABLE 1   List of mAChE mutants employed in this study



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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
TOP
ABSTRACT
INTRODUCTION
METHODS: ELECTROSTATIC...
RESULTS AND DISCUSSION
CONCLUSIONS
REFERENCES

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, theta . The bottom of this duct is delimited by a spherical cap of radius rho , 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
k(ϑ, s)=4&pgr;DR <FR><NU>1</NU><DE>2</DE></FR>[1−<UP>cos</UP> ϑ]<FENCE><FENCE><FR><NU>1−s</NU><DE>s</DE></FR></FENCE>+&eegr;(<UP>cos</UP> ϑ)</FENCE><SUP><UP>−</UP>1</SUP> (1)
where s is given by rho /R, D is the diffusion coefficient of the ligand, and the function eta (cos theta ) is given by the following expression:
&eegr;(x)=<FR><NU>1</NU><DE>2</DE></FR><FENCE>(1−x)+<LIM><OP>∑</OP><LL><UP>l=1</UP></LL><UL><UP>∞</UP></UL></LIM><FR><NU>P<SUB><UP>l−1</UP></SUB>(x)−P<SUB><UP>l+1</UP></SUB>(x)</NU><DE>l+1</DE></FR></FENCE> (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 rho  can be estimated by subtracting the transit region of the gorge (as defined in Methods) from the value of R, and the value of theta  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 theta  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, rho , theta , 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% (rho /R = s = 0.38) of the way down a conical duct of aperture theta  = 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:
k(ϑ)=4&pgr;DR<FR><NU>1</NU><DE>2</DE></FR> [1−<UP>cos</UP> ϑ]/&eegr;(<UP>cos</UP> ϑ) (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 theta  = 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.


                              
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TABLE 3   Experimental kinetic constants for cationic substrates at high and low salt concentrations


                              
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TABLE 4   Experimental kinetic constants for neutral substrates at high and low salt concentrations

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 eta 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):
k<SUB><UP>on</UP></SUB>=4&pgr;NDR<SUB><UP>eff</UP></SUB>/1000 (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-pi 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-pi 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-pi 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 alpha -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-pi 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-pi 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 Delta Delta Gcharge, can be calculated from the experimentally determined dissociation constants measured for WT mAChE and can be defined as
&Dgr;&Dgr;G<SUB><UP>charge</UP></SUB>=&Dgr;G<SUB><UP>TFK<SUP>+</SUP></UP></SUB>−&Dgr;G<SUB><UP>TFK<SUP>0</SUP></UP></SUB> (5)
With Delta GTFK+ = -RT ln Ki TFK+ and Delta GTFK0 = -RT ln  Ki TFK0 it follows that
&Dgr;&Dgr;G<SUB><UP>charge</UP></SUB>=RT <UP>ln</UP> (K<SUB><UP>i TFK<SUP>0</SUP></UP></SUB>/K<SUB><UP>i TFK<SUP>+</SUP></UP></SUB>) (6)
If we assume Delta Delta 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 Delta Delta Gcharge as
&Dgr;&Dgr;G<SUB><UP>charge</UP></SUB>=&Dgr;&Dgr;G<SUB><UP>L</UP></SUB>+&Dgr;&Dgr;G<SUB><UP>G</UP></SUB> (7)
in which
&Dgr;&Dgr;G<SUB><UP>L</UP></SUB>=&Dgr;G<SUB><UP>L TFK<SUP>+</SUP></UP></SUB>−&Dgr;G<SUB><UP>L TFK<SUP>0</SUP></UP></SUB> (8)
and
&Dgr;&Dgr;G<SUB><UP>G</UP></SUB>=&Dgr;G<SUB><UP>G TFK<SUP>+</SUP></UP></SUB>−&Dgr;G<SUB><UP>G TFK<SUP>0</SUP></UP></SUB> (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,
&Dgr;&Dgr;G<SUB><UP>G</UP></SUB>=&Dgr;G<SUB><UP>W84A TFK<SUP>+</SUP></UP></SUB>−&Dgr;G<SUB><UP>W84A TFK<SUP>0</SUP></UP></SUB>=RT<UP>ln</UP>(K<SUB><UP>i W84A TFK<SUP>0</SUP></UP></SUB>/K<SUB><UP>i W84A TFK<SUP>+</SUP></UP></SUB>) (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,
&Dgr;&Dgr;G<SUB><UP>L</UP></SUB>=&Dgr;G<SUB><UP>high TFK<SUP>+</SUP></UP></SUB>−&Dgr;G<SUB><UP>high TFK<SUP>0</SUP></UP></SUB>=RT<UP>ln</UP>(K<SUB><UP>i high TFK<SUP>+</SUP></UP></SUB>/K<SUB><UP>i high TFK<SUP>0</SUP></UP></SUB>) (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 Delta Delta GL and Delta Delta GG which, when summed, should give back the experimentally measured value for Delta Delta 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 Delta Delta GL of ~3.4 kcal/mol and for Delta Delta 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 Delta Delta Gcharge of 3.8 kcal/mol and 4.8 kcal/mol, at physiological and low salt concentrations, respectively, thus supporting our hypothesis.


                              
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TABLE 5   Experimental values of Ki for TFK+ and TFK0 employed in the calculation of Delta Delta Gcharge, Delta Delta GL, and Delta Delta Gg

Calculation of the potential inside the active-site gorge of AChE from Delta Delta GDagger 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:
<UP>E</UP>+<UP>I</UP> <LIM><OP><ARROW>⇌</ARROW></OP><LL>k<SUB><SUB><UP>off</UP></SUB></SUB></LL><UL><SUB>k<SUB><UP>on</UP></SUB></SUB></UL></LIM> <UP>EI</UP>
Formation of the hemiketal adduct can be considered as proceeding through a short-lived activated complex, EIDagger . 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):
k<SUB><UP>on TFK</UP></SUB>=&ngr; <UP>exp</UP>(−&Dgr;G<SUP>‡</SUP><SUB><UP>on</UP></SUB>/RT) (12.1)

k<SUB><UP>off TFK</UP></SUB>=&ngr; <UP>exp</UP>(−&Dgr;G<SUP>‡</SUP><SUB><UP>off</UP></SUB>/RT) (12.2)
where nu  is the vibrational frequency of the activated complex in the degree of freedom leading to its decomposition, and
&Dgr;G<SUP><UP>‡</UP></SUP><SUB><UP>on</UP></SUB>=G<SUP><UP>0</UP></SUP><SUB><UP>EI<SUP>‡</SUP></UP></SUB>−G<SUP>0</SUP><SUB><UP>E</UP></SUB>+G<SUP>0</SUP><SUB><UP>I</UP></SUB> (13.1)

&Dgr;G<SUP><UP>‡</UP></SUP><SUB><UP>off</UP></SUB>=G<SUP><UP>0</UP></SUP><SUB><UP>EI<SUP>‡</SUP></UP></SUB>−G<SUP>0</SUP><SUB><UP>EI</UP></SUB> (13.2)
We can then apply the reasoning used in the previous section to dete