Acetylcholinesterase: Role of the enzyme's charge distribution in steering charged ligands toward the active site

The electrostatic steering of charged ligands toward the active site of Torpedo californica acetylcholinesterase is investigated by Brownian dynamics simulations of wild type enzyme and several mutated forms, in which some normally charged residues are neutralized. The simulations reveal that the total ligand influx through a surface of 42 Å radius centered in the enzyme monomer and separated from the protein surface by I-14 Å is not significantly influenced by electrostatic interactions. Electrostatic effects are visible for encounters with a surface of 32 Å radius, which is partially hidden inside the protein, but mostly within the solvent. A clear accumulation of encounter events for that sphere is observed in the area directly above the entrance to the active site gorge. In this area, the encounter events are increased by 40% compared to the case of a neutral ligand. However, the differences among the encounter rates for the various mutants considered here are not pronounced, all rate constants being within ±10% of the average value. The enzyme charge distribution becomes more important as the charged ligand moves toward the bottom of the gorge, where the active site is located. We show that neither the enzyme's total charge, nor its dipole moment, fully account for the electrostatic steering of ligand to the active site. Higher moments of the enzyme's charge distribution are also important. However, for a series of mutations for which the direction of the enzyme dipole moment is constant within a few degrees, one observes a gradual decrease in the diffusional encounter rate constant with the number of neutralized residues. On the other hand, for other mutants that change the direction of the dipole moment from that of the wild type, the calculated encounter rate constants can be very close to that of the wild type. The present work yields two new insights to the kinetics of acetylcholinesterase. First, evolution appears to have built a redundant electrostatic steering capability into this important enzyme through the overall distribution of its thousands of partially charged atoms. And second, roughly half of the rate enhancement due to electrostatics arises from steering of the substrate outside the enzyme; the other half of the rate enhancement arises from improved trapping of the substrate after it has entered the gorge. The computational results reproduce qualitatively, and help to rationalize, many surprising experimental results obtained recently for human acetylcholinesterase. © 1996 John Wiley & Sons, Inc.     

Species dependence of enzyme-substrate encounter rates for triose phosphate isomerases

Triose phosphate isomerase (TIM) is a diffusion-controlled enzyme whose rate is limited by the diffusional encounter of the negatively charged substrate glyceraldehyde 3-phosphate (GAP) with the homodimeric enzyme's active sites. Translational and orientational steering of GAP toward the active sites by the electrostatic field of chicken muscle TIM has been observed in previous Brownian dynamics (BD) simulations. Here we report simulations of the association of GAP with TIMs from four species with net charges at pH 7 varying from -12e to +12e. Computed second-order rate constants are in good agreement with experimental data. The BD simulations and computation of average Boltzmann factors of substrate–protein interaction energies show that the protein electrostatic potential enhances the rates for all the enzymes. There is much less variation in the computed rates than might be expected on the basis of the net charges. Comparison of the electrostatic potentials by means of similarity indices shows that this is due to conservation of the local electrostatic potentials around the active sites which are the primary determinants of electrostatic steering of the substrate. Proteins 31:406–416, 1998. © 1998 Wiley-Liss, Inc.     

Tetrameric mouse acetylcholinesterase: continuum diffusion rate calculations by solving the steady-state Smoluchowski equation using finite element methods

The tetramer is the most important form for acetylcholinesterase in physiological conditions, i.e., in the neuromuscular junction and the nervous system. It is important to study the diffusion of acetylcholine to the active sites of the tetrameric enzyme to understand the overall signal transduction process in these cellular components. Crystallographic studies revealed two different forms of tetramers, suggesting a flexible tetramer model for acetylcholinesterase. Using a recently developed finite element solver for the steady-state Smoluchowski equation, we have calculated the reaction rate for three mouse acetylcholinesterase tetramers using these two crystal structures and an intermediate structure as templates. Our results show that the reaction rates differ for different individual active sites in the compact tetramer crystal structure, and the rates are similar for different individual active sites in the other crystal structure and the intermediate structure. In the limit of zero salt, the reaction rates per active site for the tetramers are the same as that for the monomer, whereas at higher ionic strength, the rates per active site for the tetramers are approximately 67%-75% of the rate for the monomer. By analyzing the effect of electrostatic forces on ACh diffusion, we find that electrostatic forces play an even more important role for the tetramers than for the monomer. This study also shows that the finite element solver is well suited for solving the diffusion problem within complicated geometries.     

The association between a negatively charged ligand and the electronegative binding pocket of its receptor.

Many examples exist of charged amino acids that play a role in attracting or holding a charged ligand toward or inside an oppositely charged binding pocket of the protein. For example, the enzymes superoxide dismutase, triose-phosphate isomerase, and acetylcholinesterase can steer ligands toward their oppositely charged binding pockets or gorges. Interestingly, in our Brownian dynamics simulations of a phosphate-binding protein, we discovered that negatively charged phosphate (HPO(2-)(4)) could make its way into the negatively charged binding pocket. In fact, the phosphate-binding protein exhibits counterintuitive kinetics of association. That is, one would expect that the rate of association would increase on increases to the ionic strength since the interaction between the ligand, with a charge of -2, and the electronegative binding pocket would be repulsive and greater screening should reduce this repulsion and increase the rate of association. However, the opposite is seen-i.e., the rate of association decreases on increases in the ionic strength. We used Brownian dynamics techniques to compute the diffusion limited association rate constants between the negatively charged phosphate ligand and several open forms of PBP (wild-type and several mutants based on an x-ray structure of open-form PBP, mutant T141D). With the appropriate choices of reaction criteria and molecular parameters, the ligand was able to diffuse into the binding pocket. A number of residues influence binding of the ligand within the pocket via hydrogen bonds or salt bridges. Arg135 partially neutralizes the charges on the HPO(2-)(4) ligand in the binding pocket, allowing it to enter. It is also found that the positive electrostatic patches above and below the binding entrance of PBP contribute the major attractive forces that direct the ligand toward the surface of the protein near the binding site.     

Role of the electrostatic loop charged residues in Cu,Zn superoxide dismutase.

We have expressed and characterized a mutant of Xenopus laevis Cu,Zn superoxide dismutase in which four highly conserved charged residues belonging to the electrostatic loop have been replaced by neutral side chains: Lys120 --> Leu, Asp130 --> Gln, Glu131 --> Gln, and Lys134 --> Thr. At low ionic strength, the mutant enzyme is one of the fastest superoxide dismutases ever assayed (k = 6.7 x 10(9) M(-1) s(-1), at pH 7 and mu = 0.02 M). Brownian dynamics simulations give rise to identical enzyme-substrate association rates for both wild-type and mutant enzymes, ruling out the possibility that enhancement of the activity is due to pure electrostatic factors. Comparative analysis of the experimental catalytic rate of the quadruple and single mutants reveals the nonadditivity of the mutation effects, indicating that the hyperefficiency of the mutant is due to a decrease of the energy barrier and/or to an alternative pathway for the diffusion of superoxide within the active site channel. At physiological ionic strength the catalytic rate of the mutant at neutral pH is similar to that of the wild-type enzyme as it is to the catalytic rate pH dependence. Moreover, mutation effects are additive. These results show that, at physiological salt conditions, electrostatic loop charged residues do not influence the diffusion pathway of the substrate and, if concomitantly neutralized, are not essential for high catalytic efficiency of the enzyme, pointing out the role of the metal cluster and of the invariant Arg141 in determining the local electrostatic forces facilitating the diffusion of the substrate towards the active site.     

Electrostatic facilitation of the reaction catalyzed by the manganese-containing and the iron-containing superoxide dismutases

Both the iron-containing and the manganese-containing superoxide dismutases from Escherichia coli show diminished activity with increasing ionic strength, indicative of electrostatic facilitation of the catalyzed reaction. Since both enzymes bear a net negative charge at the assay pH, as does the substrate, this suggests a cationic locale in the active site region. Acetylation of the enzymes inverted their response to increasing ionic strength. It thus appears that lysine residues provide the observed electrostatic facilitation. A specific inhibition by large monovalent anions was observed with the iron-containing superoxide dismutase and was taken to indicate the presence of a cationic group, within a hydrophobic crevice, at the active site.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.     

Enzymatic Activity versus Structural Dynamics: The Case of Acetylcholinesterase Tetramer

The function of many proteins, such as enzymes, is modulated by structural fluctuations. This is especially the case in gated diffusion-controlled reactions (where the rates of the initial diffusional encounter and of structural fluctuations determine the overall rate of the reaction) and in oligomeric proteins (where function often requires a coordinated movement of individual subunits). A classic example of a diffusion-controlled biological reaction catalyzed by an oligomeric enzyme is the hydrolysis of synaptic acetylcholine (ACh) by tetrameric acetylcholinesterase (AChEt). Despite decades of efforts, the extent to which enzymatic efficiency of AChEt (or any other enzyme) is modulated by flexibility is not fully determined. This article attempts to determine the correlation between the dynamics of AChEt and the rate of reaction between AChEt and ACh. We employed equilibrium and nonequilibrium electro-diffusion models to compute rate coefficients for an ensemble of structures generated by molecular dynamics simulation. We found that, for the static initial model, the average reaction rate per active site is ∼22-30% slower in the tetramer than in the monomer. However, this effect of tetramerization is modulated by the intersubunit motions in the tetramer such that a complex interplay of steric and electrostatic effects either guides or blocks the substrate into or from each of the four active sites. As a result, the rate per active site calculated for some of the tetramer structures is only ∼15% smaller than the rate in the monomer. We conclude that structural dynamics minimizes the adverse effect of tetramerization, allowing the enzyme to maintain similar enzymatic efficiency in different oligomerization states.     

A modular treatment of molecular traffic through the active site of cholinesterase

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 approximately 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.     

Exploration of swapping enzymatic function between two proteins: A simulation study of chorismate mutase and isochorismate pyruvate lyase

The enzyme chorismate mutase EcCM from Escherichia coli catalyzes one of the few pericyclic reactions in biology, the transformation of chorismate to prephenate. The isochorismate pyruvate lyase PchB from Pseudomonas aeroginosa catalyzes another pericyclic reaction, the isochorismate to salicylate transformation. Interestingly, PchB possesses weak chorismate mutase activity as well thus being able to catalyze two distinct pericyclic reactions in a single active site. EcCM and PchB possess very similar folds, despite their low sequence identity. Using molecular dynamics simulations of four combinations of the two enzymes (EcCM and PchB) with the two substrates (chorismate and isochorismate) we show that the electrostatic field due to EcCM at atoms of chorismate favors the chorismate to prephenate transition and that, analogously, the electrostatic field due to PchB at atoms of isochorismate favors the isochorismate to salicylate transition. The largest differences between EcCM and PchB in electrostatic field strengths at atoms of the substrates are found to be due to residue side chains at distances between 0.6 and 0.8 nm from particular substrate atoms. Both enzymes tend to bring their non‐native substrate in the same conformation as their native substrate. EcCM and to a lower extent PchB fail in influencing the forces on and conformations of the substrate such as to favor the other chemical reaction (isochorismate pyruvate lyase activity for EcCM and chorismate mutase activity for PchB). These observations might explain the difficulty of engineering isochorismate pyruvate lyase activity in EcCM by solely mutating active site residues.     

Substrate inhibition of acetylcholinesterase: residues affecting signal transduction from the surface to the catalytic center.

Amino acids located within and around the 'active site gorge' of human acetylcholinesterase (AChE) were substituted. Replacement of W86 yielded inactive enzyme molecules, consistent with its proposed involvement in binding of the choline moiety in the active center. A decrease in affinity to propidium and a concomitant loss of substrate inhibition was observed in D74G, D74N, D74K and W286A mutants, supporting the idea that the site for substrate inhibition and the peripheral anionic site overlap. Mutations of amino acids neighboring the active center (E202, Y337 and F338) resulted in a decrease in the catalytic and the apparent bimolecular rate constants. A decrease in affinity to edrophonium was observed in D74, E202, Y337 and to a lesser extent in F338 and Y341 mutants. E202, Y337 and Y341 mutants were not inhibited efficiently by high substrate concentrations. We propose that binding of acetylcholine, on the surface of AChE, may trigger sequence of conformational changes extending from the peripheral anionic site through W286 to D74, at the entrance of the 'gorge', and down to the catalytic center (through Y341 to F338 and Y337). These changes, especially in Y337, could block the entrance/exit of the catalytic center and reduce the catalytic efficiency of AChE.     

Effects of quaternary ligands on the inhibition of acetylcholinesterase by arsenite.

Arsenite inhibits acetylcholinesterase in a second-order reaction. The rate and equilibrium constants depend upon pH and have values on the order of 10(2) M-1 min-1 and 10(5) M (dissociation), respectively. Some quaternary ammonium ligands completely block the arsenite inhibition of the enzyme, others decrease the rate of the reaction and some, notably pyridine-2 aldoxime methiodide, greatly accelerate the rate of the reaction, up to 220-fold. Accelerators may bind at a separate enzyme site distinct form the anionic site involved in substrate binding. Although the kinetic data are consistent with a covalent reaction between arsenite and acetylcholinesterase, chemical evidence excludes the involvement of sulfhydryl groups which are usually implicated in arsenite inhibition.     

The role of arginine 143 in the electrostatics and mechanism of Cu,Zn superoxide dismutase: Computational and experimental evaluation by mutational analysis

Cu, Zn superoxide dismutase protects cells from oxidative damage by removing superoxide radicals in one of the fastest enzyme reactions known. The redox reaction at the active-site Cu ion is rate-limited by diffusion and enhanced by electrostatic guidance. To quantitatively define the electrostatic and mechanistic contributions of sequence-invariant Arg-143 in human Cu, Zn superoxide dismutase, single-site mutants at this position were investigated experimentally and computationally. Rate constants for several Arg-143 mutants were determined at different pH and ionic strength conditions using pulse radiolytic methods and compared to results from Brownian dynamics simulations. At physiological pH, substitution of Arg-143 by Lys caused a 2-fold drop in rate, neutral substitutions (Ile, Ala) reduced the rate about 10-fold, while charge-reversing substitutions (Asp, Glu) caused a 100-fold decrease. Position 143 mutants showed pH dependencies not seen in other mutants. At low pH, the acidic residue mutations exhibited pro-tonation/deprotonation effects. At high pH, all enzymes showed typical decreases in rate except the Lys mutant in which the rate dropped off at an unusually low pH. Increasing ionic strength at acidic pH decreased the rates of the wild-type enzyme and Lys mutant, while the rate of the Glu mutant was unaffected. Increasing ionic strength at higher pH (>10) increased the rates of the Lys and Glu mutants while the rate of the wild-type enzyme was unaffected. Reaction simulations with Brownian dynamics incorporating electrostatic effects tested computational predictability of ionic strength dependencies of the wild-type enzyme and the Lys, Ile, and Glu mutants. The calculated and experimental ionic strength profiles gave similar slopes in all but the Glu mutant, indicating that the electrostatic attraction of the substrate is accurately modeled. Differences between the calculated and experimental rates for the Glu and Lys mutants reflect the mechanistic contribution of Arg-143. Results from this joint analysis establish that, aside from the Cu ligands, Arg-143 is the single most important residue in Cu, Zn superoxide dismutase both electrostatically and mechanistically, and provide an explanation for the evolutionary selection of arginine at position 143. © 1994 Wiley-Liss, Inc.     

Fruitful and Futile Encounters along the Association Reaction between Proteins

The association reaction between pairs of proteins proceeds through an encounter complex that develops into the final complex. Here, we combined Brownian dynamics simulations with experimental studies to analyze the structures of the encounter complexes along the association reaction between TEM1-β-lactamase and its inhibitor, β-lactamase-inhibitor protein. The encounter complex can be considered as an ensemble of short-lived low free-energy states that are stabilized primarily by electrostatic forces and desolvation. For the wild-type, the simulation showed two main encounter regions located outside the physical binding site. One of these regions was located near the experimentally determined transition state. To validate whether these encounters are fruitful or futile, we examined three groups of mutations that altered the encounter. The first group consisted of mutations that increased the experimental rate of association through electrostatic optimization. This resulted in an increase in the size of the encounter region located near the experimentally determined transition state, as well as a decrease in the energy of this region and an increase in the number of successful trajectories (i.e., encounters that develop into complex). A second group of mutations was specifically designed to either increase or decrease the size and energy of the second encounter complex, but either way it did not affect k_on. A third group of mutations consisted of residues that increased k_on without significantly affecting the encounter complexes. These results indicate that the size and energy of the encounter regions are only two of several parameters that lead to fruitful association, and that electrostatic optimization is a major driving force in fast association.     

Mechanism of reactant and product dissociation from the anthrax edema factor: a locally enhanced sampling and steered molecular dynamics study

The anthrax edema factor is a toxin overproducing damaging levels of cyclic adenosine monophosphate (cAMP) and pyrophosphate (PPi) from ATP. Here, mechanisms of dissociation of ATP and products (cAMP, PPi) from the active site are studied using locally enhanced sampling (LES) and steered molecular dynamics simulations. Various substrate conformations and ionic binding modes found in crystallographic structures are considered. LES simulations show that PPi and cAMP dissociate through different solvent accessible channels, while ATP dissociation requires significant active site exposure to solvent. The ionic content of the active site directly affects the dissociation of ATP and products. Only one ion dissociates along with ATP in the two-Mg(2+) binding site, suggesting that the other ion binds EF prior to ATP association. Dissociation of reaction products cAMP and PPi is impaired by direct electrostatic interactions between products and Mg(2+) ions. This provides an explanation for the inhibitory effect of high Mg(2+) concentrations on EF enzymatic activity. Breaking of electrostatic interactions is dependent on a competitive binding of water molecules to the ions, and thus on the solvent accessibility of the active site. Consequently, product dissociation seems to be a two-step process. First, ligands are progressively solvated while preserving the most important electrostatic interactions, in a process that is dependent on the flexibility of the active site. Second, breakage of the electrostatic bonds follows, and ligands diffuse into solvent. In agreement with this mechanism, product protonation facilitates dissociation.     

Theory of the kinetics of reactions catalyzed by enzymes attached to membranes

A theoretical treatment has been worked out for the kinetics of solid-supported enzyme systems, with diffusive and electrostatic effects taken into account. A utilization factor, defined as the ratio of the actual reaction rate to the rate of substrate consumption in the outer solution, is defined, and equations to evaluate the utilization factor are given for five kinetic conditions: (a) Michaelis-Menten behavior, (b) substrate inhibition, (c) product inhibition (competitive), (d) product inhibition (noncompetitive), and (e) product inhibition (anticompetitive). When the solid-supported enzymes obey a Michaelis-Menten relationship, an equation for the apparent Michaelis constant is given and a criterion for insignificant diffusion effects is shown. A substrate-inhibited enzyme reaction may display multiple steady-state behavior, and a criterion for uniqueness is presented. In the case of product-inhibited enzyme reactions, the utilization factor is always less than that which corresponds to a Michaelis-Menten relationship. Equations to evaluate the apparent Michaelis and inhibition constants are given.     

Kinetic parameters of enzymatic reactions in states of maximal activity; an evolutionary approach

A theoretical investigation is presented which allows the calculation of states of maximal reaction rates for single enzymes and for unbranched enzymatic chains. As an extension to previous papers (Heinrich & Holzhütter, 1985, Biomed. biochim. Acta 44, 959-969; Heinrich et al., 1987, Bull. math. Biol. 49, 539-595) a detailed enzymatic mechanism was taken into consideration. Conclusions are drawn for the optimal values of the microscopic rate constants as well as of the maximal activities and Michaelis constants. Ten solutions are found which depend on the equilibrium constant as well as on the concentrations of substrates and products. It is shown that for high equilibrium constants one of the solutions applies to a very large range of the concentrations of the outer reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. In contrast to previous assumptions (Albery & Knowles, 1976b, Biochemistry 15, 5631-5640; Burbaum et al., 1989, Biochemistry 28, 9293-9305) states of maximal reaction rate are not always characterized by the highest possible values of the second-order rate constants which are related to the diffusion of the substrate and the product to the active site of the enzyme. Predictions are made concerning the ratios of maximal activities in optimal states as well as for the adaptation of the Michaelis constants to the concentrations of the outer reactants. Using metabolic control analysis it is shown that the solutions obtained for single enzymes may also be applied in multi-enzyme systems.