Acetylcholinesterase: diffusional encounter rate constants for dumbbell models of ligand

Rapid Regulation of Glutamate Transport: Where Do We Go from Here?

Glutamate is the predominant excitatory neurotransmitter in the mammalian central nervous system (CNS). A family of five Na⁺-dependent transporters maintain low levels of extracellular glutamate and shape excitatory signaling. Shortly after the research group of the person being honored in this special issue (Dr. Baruch Kanner) cloned one of these transporters, his group and several others showed that their activity can be acutely (within minutes to hours) regulated. Since this time, several different signals and post-translational modifications have been implicated in the regulation of these transporters. In this review, we will provide a brief introduction to the distribution and function of this family of glutamate transporters. This will be followed by a discussion of the signals that rapidly control the activity and/or localization of these transporters, including protein kinase C, ubiquitination, glutamate transporter substrates, nitrosylation, and palmitoylation. We also include the results of our attempts to define the role of palmitoylation in the regulation of GLT-1 in crude synaptosomes. In some cases, the mechanisms have been fairly well-defined, but in others, the mechanisms are not understood. In several cases, contradictory phenomena have been observed by more than one group; we describe these studies with the goal of identifying the opportunities for advancing the field. Abnormal glutamatergic signaling has been implicated in a wide variety of psychiatric and neurologic disorders. Although recent studies have begun to link regulation of glutamate transporters to the pathogenesis of these disorders, it will be difficult to determine how regulation influences signaling or pathophysiology of glutamate without a better understanding of the mechanisms involved.

Forebrain Cholinergic Signaling: Wired and Phasic, Not Tonic, and Causing Behavior

Conceptualizations of cholinergic signaling as primarily spatially diffuse and slow-acting are based largely on measures of extracellular brain ACh levels that require several minutes to generate a single data point. In addition, most such studies inhibited the highly potent catalytic enzyme for ACh, AChE, to facilitate measurement of ACh. Absent such inhibition, AChE limits the presence of ambient ACh and thus renders it unlikely that ACh influences target regions via slow changes in extracellular ACh concentrations. We describe an alternative view by which forebrain signaling in cortex driving cognition is largely phasic (milliseconds to perhaps seconds), and unlikely to be volume-transmitted. This alternative is supported by new evidence from real-time amperometric recordings of cholinergic signaling indicating a specific function of rapid, phasic, transient cholinergic signaling in attentional contexts. Previous neurochemical evidence may be reinterpreted in terms of integrated phasic cholinergic activity that mediates specific behavioral and cognitive operations; this reinterpretation fits well with recent computational models. Optogenetic studies support a causal relationship between cholinergic transients and behavior. This occurs in part via transient-evoked muscarinic receptor-mediated high-frequency oscillations in cortical regions. Such oscillations outlast cholinergic transients and thus link transient ACh signaling with more sustained postsynaptic activity patterns to support relatively persistent attentional biases. Reconceptualizing cholinergic function as spatially specific, phasic, and modulating specific cognitive operations is theoretically powerful and may lead to pharmacologic treatments more effective than those based on traditional views.Dual Perspectives Companion Paper: Diverse Spatiotemporal Scales of Cholinergic Signaling in the Neocortex, by Anita A. Disney and Michael J. Higley.

Computational Studies on Acetylcholinesterases

Functions of biomolecules, in particular enzymes, are usually modulated by structural fluctuations. This is especially the case in a gated diffusion-controlled reaction catalyzed by an enzyme such as acetylcholinesterase. The catalytic triad of acetylcholinesterase is located at the bottom of a long and narrow gorge, but it catalyzes the extremely rapid hydrolysis of the neurotransmitter, acetylcholine, with a reaction rate close to the diffusion-controlled limit. Computational modeling and simulation have produced considerable advances in exploring the dynamical and conformational properties of biomolecules, not only aiding in interpreting the experimental data, but also providing insights into the internal motions of the biomolecule at the atomic level. Given the remarkably high catalytic efficiency and the importance of acetylcholinesterase in drug development, great efforts have been made to understand the dynamics associated with its functions by use of various computational methods. Here, we present a comprehensive overview of recent computational studies on acetylcholinesterase, expanding our views of the enzyme from a microstate of a single structure to conformational ensembles, strengthening our understanding of the integration of structure, dynamics and function associated with the enzyme, and promoting the structure-based and/or mechanism-based design of new inhibitors for it.

Recent advances in acetylcholinesterase Inhibitors and Reactivators: an update on the patent literature (2012-2015)

INTRODUCTION

Acetylcholinesterase (AChE) is the major enzyme that hydrolyzes acetylcholine, a key neurotransmitter for synaptic transmission, into acetic acid and choline. Mild inhibition of AChE has been shown to have therapeutic relevance in Alzheimer's disease (AD), myasthenia gravis, and glaucoma among others. In contrast, strong inhibition of AChE can lead to cholinergic poisoning. To combat this, AChE reactivators have to be developed to remove the offending AChE inhibitor, restoring acetylcholine levels to normal. Areas covered: This article covers recent advances in the development of acetylcholinesterase modulators, including both inhibitors of acetylcholinesterase for the efforts in development of new chemical entities for treatment of AD, as well as re-activators for resurrection of organophosphate bound acetylcholinesterase. Expert opinion: Over the past three years, research efforts have continued to identify novel small molecules as AChE inhibitors for both CNS and peripheral diseases. The more recent patent activity has focused on three AChE ligand design areas: derivatives of known AChE ligands, natural product based scaffolds and multifunctional ligands, all of which have produced some unique chemical matter with AChE inhibition activities in the mid picomolar to low micromolar ranges. New AChE inhibitors with polypharmacology or dual inhibitory activity have also emerged as highlighted by new AChE inhibitors with dual activity at L-type calcium channels, GSK-3, BACE1 and H3, although most only show low micromolar activity, thus further research is warranted. New small molecule reactivators of organophosphate-inhibited AChE have also been disclosed, which focused on the design of neutral ligands with improved pharmaceutical properties and blood-brain barrier (BBB) penetration. Gratifyingly, some research in this area is moving away from the traditional quaternary pyridinium oximes AChE reactivators, while still employing the necessary reactivation group (oximes). However, selectivity over inhibition of native AChE enzyme, effectiveness of reactivation, broad-spectrum reactivation against multiple organophosphates and reactivation of aged-enzyme continue to be hurdles for this area of research.

Hybrid finite element and Brownian dynamics method for charged particles

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Internal Diffusion-Controlled Enzyme Reaction: The Acetylcholinesterase Kinetics

Acetylcholinesterase is an enzyme with a very high turnover rate; it quenches the neurotransmitter, acetylcholine, at the synapse. We have investigated the kinetics of the enzyme reaction by calculating the diffusion rate of the substrate molecule along an active site channel inside the enzyme from atomic-level molecular dynamics simulations. In contrast to the previous works, we have found that the internal substrate diffusion is the determinant of the acetylcholinesterase kinetics in the low substrate concentration limit. Our estimate of the overall bimolecular reaction rate constant for the enzyme is in good agreement with the experimental data. In addition, the present calculation provides a reasonable explanation for the effects of the ionic strength of solution and the mutation of surface residues of the enzyme. The study suggests that internal diffusion of the substrate could be a key factor in understanding the kinetics of enzymes of similar characteristics.

Macrodipoles. Unusual electric properties of biological macromolecules

The wide range of different effects induced by electric fields in biological macromolecules is clearly due to the unusual quality and quantity of their electric parameters. A general concept for a quantitative description of the polarizability of macromolecules remains to be established. In the case of DNA, experimental data indicate the existence of an effective polarization length N(p); at chain lengths N < N(p) the polarizability increases with N(2), whereas saturation is approached at N > or = N(p). The polarization length decreases with increasing ionic strength in close analogy to the Debye length, but is approximately 10 times larger than the Debye length. The dynamics of DNA polarization at high field strengths has been observed in the ns time range and is consistent with biased field induced ion dissociation. In the range of chain lengths from approximately 400 to approximately 850 base pairs DNA molecules exhibit permanent dipole moments, which are in a preferentially perpendicular direction to the end-to-end-vector, leading to a positive electric dichroism. These results are consistent with a "frozen" ensemble of bent DNA configurations and provide evidence for the existence of slow, non-elastic bending transitions. The electric parameters of proteins are usually dominated by a permanent anisotropy of the charge distribution, corresponding to permanent dipole moments of the order of several hundred Debye up to about 1500 Debye. Relatively small dipole moments of protein monomers add up to millions of Debye, when these proteins are in a vectorial organization in membrane patches, as found for bacteriorhodopsin and Na (+)K (+)-ATPase . In these cases the dipole vector may support vectorial ion transport. It is remarkable that the dipole moments of proteins usually show a relatively small dependence on the salt concentration; a rational for these observations is provided by a dipole potential at the plane of shear for rotational diffusion, which is defined in close analogy to the zeta-potential for translational diffusion. Symmetry breaking leading to huge electric dipole moments may be expected for mixed lipid vesicles: according to model calculations the phase separation of lipid components with and without net charges may lead to very high dipole moments; the expectation has been verified experimentally for vesicles containing DMPA and DMPC. The state of these systems should be extremely sensitive to electric fields. In summary, there is an unusual wide variation of electric parameters associated with biological macromolecules and with biomolecular assemblies, which is the basis for the complexity of different phenomena induced by electric fields in biological systems.

Stopped-flow studies of guanine binding by calf spleen purine nucleoside phosphorylase

The binding of guanine to calf spleen purine nucleoside phosphorylase at 20 degrees C, in 20 mM Hepes-NaOH buffer, pH 7.0, at several ionic strength between 5 and 150 mM was investigated using a stopped-flow spectrofluorimeter. The kinetic transients registered after mixing a protein solution with ligand solutions of different concentrations were simultaneously fitted by several association reaction models using nonlinear least-squares procedure based on numerical integration of the chemical kinetic equations appropriate for given model. It is concluded that binding of a guanine molecule by each of the binding sites is a two-step process and that symmetrical trimeric calf spleen purine nucleoside phosphorylase represents a system of (identical) interacting binding sites. The interaction is visible through relations between the rate constants and non-additivity of changes in "molar" fluorescence for different forms of PNP-guanine complexes. It is also probable that electrostatic effects in guanine binding are weak, which indicates that it is the neutral form of the ligand which is bound and dissociated by PNP molecule.

Finite element solution of the steady-state Smoluchowski equation for rate constant calculations

This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.

Robust biased Brownian dynamics for rate constant calculation

A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics-i.e., biased Brownian dynamics with weight control-to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a bias force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the bias force and the target weight are constructed from the solution of the reaction probability problem. In reality, an approximate reaction probability has to be used to construct the bias force and the target weight. Thus, the performance of the algorithm depends on the quality of the approximation. Given here is a method to calculate a good approximation, which is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The numerically approximated reaction probability is shown by computer experiments to give a factor-of-two speedup over the use of a purely heuristic approximation. Also, the fully developed method is compared to unbiased Brownian dynamics. The tests for human superoxide dismutase, Escherichia coli superoxide dismutase, and antisweetener antibody NC6.8, show speedups of 17, 35, and 39, respectively. The test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3341 for another set of configurations.

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.

Kinetic model of ethopropazine interaction with horse serum butyrylcholinesterase and its docking into the active site

The action of a potent tricyclic cholinesterase inhibitor ethopropazine on the hydrolysis of acetylthiocholine and butyrylthiocholine by purified horse serum butyrylcholinesterase (EC 3.1.1.8) was investigated at 25 and 37 degrees C. The enzyme activities were measured on a stopped-flow apparatus and the analysis of experimental data was done by applying a six-parameter model for substrate hydrolysis. The model, which was introduced to explain the kinetics of Drosophila melanogaster acetylcholinesterase [Stojan et al. (1998) FEBS Lett. 440, 85-88], is defined with two dissociation constants and four rate constants and can describe both cooperative phenomena, apparent activation at low substrate concentrations and substrate inhibition by excess of substrate. For the analysis of the data in the presence of ethopropazine at two temperatures, we have enlarged the reaction scheme to allow primarily its competition with the substrate at the peripheral site, but the competition at the acylation site was not excluded. The proposed reaction scheme revealed, upon analysis, competitive effects of ethopropazine at both sites; at 25 degrees C, three enzyme-inhibitor dissociation constants could be evaluated; at 37 degrees C, only two constants could be evaluated. Although the model considers both cooperative phenomena, it appears that decreased enzyme sensitivity at higher temperature, predominantly for the ligands at the peripheral binding site, makes the determination of some expected enzyme substrate and/or inhibitor complexes technically impossible. The same reason might also account for one of the paradoxes in cholinesterases: activities at 25 degrees C at low substrate concentrations are higher than at 37 degrees C. Positioning of ethopropazine in the active-site gorge by molecular dynamics simulations shows that A328, W82, D70, and Y332 amino acid residues stabilize binding of the inhibitor.

Multiple advantages of capillary zone electrophoresis for exploring protein conformational stability

This review summarizes the work of our laboratory to explore the use of capillary zone electrophoretic (CZE) methods for the investigation of protein conformational stability. Early CZE works on protein denaturation as well as fundamental and theoretical considerations are discussed. Instrumental aspects of the CE-based approach including general and particular CE requirements are documented. Several aspects dealing with estimation of stability of enzymes (cholinesterases and organophosphate-hydrolyzing enzymes) interacting with organophosphates profusely illustrate the multiple advantages of CZE. The discrimination of parameters controlling the "good compromise" stability/plasticity for allowing functional efficiency of these enzymes is exemplified. Thermal stability, susceptibility to high electric field, alteration of stability by bound ligands and the role of associated cations in metalloenzymes have been successfully investigated.

Slow detection reaction can mimic initial inhibition of an enzymic reaction

An analysis of sigmoid-shaped progress curves in the reaction between Electric Eel acetylcholinesterase (acetylcholine acetylhydrolase, EC 3.1.1.7, AChE) and its substrate acetylthiocholine in low concentrations at pH 7 is presented. In order to be able to explain an initial apparent inhibition of the enzyme-substrate reaction, the rate of detection reaction had to be taken into account. The theoretical curves obtained by the fitting of differential equations for the reaction mechanism to the data of six progress curves simultaneously, exactly reproduce the course of the experimental curves. The measurements performed with various concentrations of detection reagent confirm the proposed cause of sigmoidity.

Dual effect of high electric field in capillary electrophoresis study of the conformational stability of Bungarus fasciatus acetylcholinesterase

The effect of high electric field in capillary zone electrophoresis (CZE) was evaluated for the study of the thermally induced unfolding of Bungarus fasciatus acetylcholinesterase. This monomer enzyme is characterised by two interdependent uncommon structural features, the asymmetrical distribution of charged residues and a relatively low thermal denaturation temperature. Both traits were presumed to interfere in the thermal unfolding of this enzyme as investigated by CZE. This paper analyses the effect of high electric field on the behaviour of the enzyme native state. It is shown that increasing the applied field causes denaturation-like transition of the enzyme at a current power which does not induce excessive Joule heating in the capillary. The susceptibility to electric field of proteins like cholinesterases, with charge distribution anisotropy, large permanent dipole moment and notable molecular flexibility associated with moderate thermal stability, was subsequently discussed.

Sequence and mechanical implications of titin's PEVK region

A widely used titin monoclonal antibody (9D10) was epitope mapped to the PEVK region in the I-band portion of titin. Sequence analysis of the titin PEVK region revealed a large number of 28 amino acid modules (termed "PPAK" repeats) alternating with glutamic acid rich segments. Species differences in cardiac rest tension could not be ascribed to differences in the PEVK length of the N2B titin isoform. The low rest tension generated by dog cardiac muscle also does not appear to be explained by the N2 and PEVK segment lengths in the N2A titin isoform.

Bimolecular reaction simulation using Weighted Ensemble Brownian dynamics and the University of Houston Brownian Dynamics program

We discuss here the implementation of the Weighted Ensemble Brownian (WEB) dynamics algorithm of Huber and Kim in the University of Houston Brownian Dynamics (UHBD) suite of programs and its application to bimolecular association problems. WEB dynamics is a biased Brownian dynamics (BD) algorithm that is more efficient than the standard Northrup-Allison-McCammon (NAM) method in cases where reaction events are infrequent because of intervening free energy barriers. Test cases reported here include the Smoluchowski rate for association of spheres, the association of the enzyme copper-zinc superoxide dismutase with superoxide anion, and the binding of the superpotent sweetener N-(p-cyanophenyl)-N'-(diphenylmethyl)-guanidinium acetic acid to a monoclonal antibody fragment, NC6.8. Our results show that the WEB dynamics algorithm is a superior simulation method for enzyme-substrate reaction encounters with large free energy barriers.

Pathways of ligand clearance in acetylcholinesterase by multiple copy sampling

The clearance of seven different ligands from the deeply buried active-site of Torpedo californica acetylcholinesterase is investigated by combining multiple copy sampling molecular dynamics simulations, with the analysis of protein-ligand interactions, protein motion and the electrostatic potential sampled by the ligand copies along their journey outwards. The considered ligands are the cations ammonium, methylammonium, and tetramethylammonium, the hydrophobic methane and neopentane, and the anionic product acetate and its neutral form, acetic acid. We find that the pathways explored by the different ligands vary with ligand size and chemical properties. Very small ligands, such as ammonium and methane, exit through several routes. One involves the main exit through the mouth of the enzyme gorge, another is through the so-called back door near Trp84, and a third uses a side door at a direction of approximately 45 degrees to the main exit. The larger polar ligands, methylammonium and acetic acid, leave through the main exit, but the bulkiest, tetramethylammonium and neopentane, as well as the smaller acetate ion, remain trapped in the enzyme gorge during the time of the simulations. The pattern of protein-ligand contacts during the diffusion process is highly non-random and differs for different ligands. A majority is made with aromatic side-chains, but classical H-bonds are also formed. In the case of acetate, but not acetic acid, the anionic and neutral form, respectively, of one of the reaction products, specific electrostatic interactions with protein groups, seem to slow ligand motion and interfere with protein flexibility; protonation of the acetate ion is therefore suggested to facilitate clearance. The Poisson-Boltzmann formalism is used to compute the electrostatic potential of the thermally fluctuating acetylcholinesterase protein at positions actually visited by the diffusing ligand copies. Ligands of different charge and size are shown to sample somewhat different electrostatic potentials during their migration, because they explore different microscopic routes. The potential along the clearance route of a cation such as methylammonium displays two clear minima at the active and peripheral anionic site. We find moreover that the electrostatic energy barrier that the cation needs to overcome when moving between these two sites is small in both directions, being of the order of the ligand kinetic energy. The peripheral site thus appears to play a role in trapping inbound cationic ligands as well as in cation clearance, and hence in product release.

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.

Effect of tetramethylammonium, choline and edrophonium on insect acetylcholinesterase: test of a kinetic model

Cholinesterases display a non-Michaelian behaviour with respect to substrate concentration. With the insect enzyme, there is an activation at low substrate concentrations and an inhibition at high concentrations. Previous studies allow us to propose a kinetic model involving a secondary non-productive binding site for the substrate. Unexpectedly, this secondary site has a very high affinity for the substrate when the enzyme is free. On the contrary, when the catalytic site of the enzyme is occupied a strong decrease of this affinity was observed. Moreover, a substrate molecule bound to the peripheral site results in a global decrease of the acylation and/or the deacylation step. Kinetic studies with three reversible inhibitors, tetramethylammonium, edrophonium and choline supported the kinetic model and enable its further refinement.

Inhibition of Drosophila acetylcholinesterase by 7-(methylethoxyphosphinyloxy)1-methyl-quinolinium iodide

The kinetic behaviour of Drosophila melanogaster acetylcholinesterase toward its substrate shows, in comparison with classic Michaelis-Menten kinetics, an apparent homotropic cooperative double activation-inhibition pattern. In order to construct an appropriate kinetic model and obtain further information on the mechanism of the catalytic action of this enzyme, the hydrolysis of acetylthiocholine in the absence and presence of different concentrations of synthetic quaternary methylphosphonate, 7-(methylethoxyphosphinyloxy)1-methyl-quinolinium iodide (MEPQ), was followed on a stopped-flow apparatus. The reaction at low substrate concentrations was followed until the change of the absorbance became negligible and at high concentrations only initial parts were recorded. A simultaneous analysis of the progress curves using numerical integration showed that the powerful organophosphonate inhibitor binds and compete with the substrate for the same binding sites. The results are also in accordance with the hypothesis that virtually every substrate or quasi-substrate molecule that enters into the gorge of active site is hydrolysed.

Effect of transport and competition on ligand binding

We present a model to describe the physics of chemoreception in processes determined by competitive ligand binding. Our model describes the competition between various populations, such as ligands vs. blockers and receptors vs. decoys, in protein activation when diffusion is rate-determining. Full spatio-temporal solutions can be obtained numerically. The model structure is kept simple enough as to permit its easy generalization to describe a large subset of the manifold of possible situations occurring in nature. The power and simplicity of the proposed method are exhibited through the solution of several examples which are discussed in detail.

A putative kinetic model for substrate metabolisation by Drosophila acetylcholinesterase

Insect acetylcholinesterase, an enzyme whose catalytic site is located at the bottom of a gorge, can metabolise its substrate in a wide range of concentrations (from 1 microM to 200 mM) since it is activated at low substrate concentrations. It also presents inhibition at high substrate concentrations. Among the various rival kinetic models tested to analyse the kinetic behaviour of the enzyme, the simplest able to explain all the experimental data suggests that there are two sites for substrate molecules on the protein. Binding on the catalytic site located at the bottom of the gorge seems to be irreversible, suggesting that each molecule of substrate which enters the active site gorge is metabolised. Reversible binding at the peripheral site of the free enzyme has high affinity (2 microM), suggesting that this binding increases the probability of the substrate entering the active site gorge. Peripheral site occupation decreases the entrance rate constant of the second substrate molecule to the catalytic site and strongly affects the catalytic activity of the enzyme. On the other hand, catalytic site occupation lowers the affinity of the peripheral site for the substrate (34 mM). These effects between the two sites result both in apparent activation at low substrate concentration and in general inhibition at high substrate concentration.

Conformation gating as a mechanism for enzyme specificity

Acetylcholinesterase, with an active site located at the bottom of a narrow and deep gorge, provides a striking example of enzymes with buried active sites. Recent molecular dynamics simulations showed that reorientation of five aromatic rings leads to rapid opening and closing of the gate to the active site. In the present study the molecular dynamics trajectory is used to quantitatively analyze the effect of the gate on the substrate binding rate constant. For a 2. 4-A probe modeling acetylcholine, the gate is open only 2.4% of the time, but the quantitative analysis reveals that the substrate binding rate is slowed by merely a factor of 2. We rationalize this result by noting that the substrate, by virtue of Brownian motion, will make repeated attempts to enter the gate each time it is near the gate. If the gate is rapidly switching between the open and closed states, one of these attempts will coincide with an open state, and then the substrate succeeds in entering the gate. However, there is a limit on the extent to which rapid gating dynamics can compensate for the small equilibrium probability of the open state. Thus the gate is effective in reducing the binding rate for a ligand 0.4 A bulkier by three orders of magnitude. This relationship suggests a mechanism for achieving enzyme specificity without sacrificing efficiency.

Brownian dynamics simulation of protein-protein diffusional encounter

Protein association events are ubiquitous in biological systems. Some protein associations and subsequent responses are diffusion controlled in vivo. Hence, it is important to be able to compute bimolecular diffusional association rates for proteins. The Brownian dynamics simulation methodology may be used to simulate protein-protein encounter, compute association rates, and examine their dependence on protein mutation and the nature of the physical environment (e.g., as a function of ionic strength or viscosity). Here, the theory for Brownian dynamics simulations is described, and important methodological aspects, particularly pertaining to the correct modeling of electrostatic forces and definition of encounter complex formation, are highlighted. To illustrate application of the method, simulations of the diffusional encounter of the extracellular ribonuclease, barnase, and its intracellular inhibitor, barstar, are described. This shows how experimental rates for a series of mutants and the dependence of rates on ionic strength can be reproduced well by Brownian dynamics simulations. Potential future uses of the Brownian dynamics method for investigating protein-protein association are discussed.

External and internal electrostatic potentials of cholinesterase models

The electrostatic potentials for the three-dimensional structures of cholinesterases from various species were calculated, using the Delphi algorithm, on the basis of the Poisson-Boltzmann equation. We used structures for Torpedo californica and mouse acetylcholinesterase, and built homology models of the human, Bungarus fasciatus, and Drosophila melanogaster acetylcholinesterases and human butyrylcholinesterase. All these structures reveal a negative external surface potential, in the area around the entrance to the active-site gorge, that becomes more negative as the rim of the gorge is approached. Moreover, in all cases, the potential becomes increasingly more negative along the central axis running down the gorge, and is largest at the base of the gorge, near the active site. Ten key acidic residues conserved in the sequence alignments of AChE from various species, both in the surface area near the entrance of the active-site gorge and at its base, appear to be primarily responsible for these potentials. The potentials are highly correlated among the structures examined, down to sequence identities as low as 35%. This indicates that they are a conserved property of the cholinesterase family, could serve to attract the positively charged substrate into and down the gorge to the active site, and may play other roles important for cholinesterase function.

Electrostatic influence on the kinetics of ligand binding to acetylcholinesterase. Distinctions between active center ligands and fasciculin

To explore the role that surface and active center charges play in electrostatic attraction of ligands to the active center gorge of acetylcholinesterase (AChE), and the influence of charge on the reactive orientation of the ligand, we have studied the kinetics of association of cationic and neutral ligands with the active center and peripheral site of AChE. Electrostatic influences were reduced by sequential mutations of six surface anionic residues outside of the active center gorge (Glu-84, Glu-91, Asp-280, Asp-283, Glu-292, and Asp-372) and three residues within the active center gorge (Asp-74 at the rim and Glu-202 and Glu-450 at the base). The peripheral site ligand, fasciculin 2 (FAS2), a peptide of 6.5 kDa with a net charge of +4, shows a marked enhancement of rate of association with reduction in ionic strength, and this ionic strength dependence can be markedly reduced by progressive neutralization of surface and active center gorge anionic residues. By contrast, neutralization of surface residues only has a modest influence on the rate of cationic m-trimethylammoniotrifluoroacetophenone (TFK+) association with the active serine, whereas neutralization of residues in the active center gorge has a marked influence on the rate but with little change in the ionic strength dependence. Brownian dynamics calculations for approach of a small cationic ligand to the entrance of the gorge show the influence of individual charges to be in quantitative accord with that found for the surface residues. Anionic residues in the gorge may help to orient the ligand for reaction or to trap the ligand. Bound FAS2 on AChE not only reduces the rate of TFK+ reaction with the active center but inverts the ionic strength dependence for the cationic TFK+ association with AChE. Hence it appears that TFK+ must traverse an electrostatic barrier at the gorge entry imparted by the bound FAS2 with its net charge of +4.

Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel

The synthetic channel [acetyl-(LeuSerSerLeuLeuSerLeu)3-CONH2]6 (pore diameter approximately 8 A, length approximately 30 A) is a bundle of six alpha-helices with blocked termini. This simple channel has complex properties, which are difficult to explain, even qualitatively, by traditional theories: its single-channel currents rectify in symmetrical solutions and its selectivity (defined by reversal potential) is a sensitive function of bathing solution. These complex properties can be fit quantitatively if the channel has fixed charge at its ends, forming a kind of macrodipole, bracketing a central charged region, and the shielding of the fixed charges is described by the Poisson-Nernst-Planck (PNP) equations. PNP fits current voltage relations measured in 15 solutions with an r.m.s. error of 3.6% using four adjustable parameters: the diffusion coefficients in the channel's pore DK = 2.1 x 10(-6) and DCl = 2.6 x 10(-7) cm2/s; and the fixed charge at the ends of the channel of +/- 0.12e (with unequal densities 0.71 M = 0.021e/A on the N-side and -1.9 M = -0.058e/A on the C-side). The fixed charge in the central region is 0.31e (with density P2 = 0.47 M = 0.014e/A). In contrast to traditional theories, PNP computes the electric field in the open channel from all of the charges in the system, by a rapid and accurate numerical procedure. In essence, PNP is a theory of the shielding of fixed (i.e., permanent) charge of the channel by mobile charge and by the ionic atmosphere in and near the channel's pore. The theory fits a wide range of data because the ionic contents and potential profile in the channel change significantly with experimental conditions, as they must, if the channel simultaneously satisfies the Poisson and Nernst-Planck equations and boundary conditions. Qualitatively speaking, the theory shows that small changes in the ionic atmosphere of the channel (i.e., shielding) make big changes in the potential profile and even bigger changes in flux, because potential is a sensitive function of charge and shielding, and flux is an exponential function of potential.

Role of ionic interactions in cholinesterase catalysis

Acetylcholinesterase (AChE, EC 3.1.1.7) is an enzyme terminating the transmission of nerve impulse in synapses by rapid and selective hydrolysis of the neurotransmitter acetylcholine. Recent years have added a considerable amount of structural knowledge about this protein as well as opened new perspectives to the study of the molecular mechanism of cholinesterase catalysis. In this paper the current state of understanding the molecular recognition by cholinesterases is critically surveyed with particular emphasis on the role of electrostatic interactions.

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 A radius centered in the enzyme monomer and separated from the protein surface by 1-14 A is not significantly influenced by electrostatic interactions. Electrostatic effects are visible for encounters with a surface of 32 A 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.

Electrooptical measurements demonstrate a large permanent dipole moment associated with acetylcholinesterase

Acetylcholinesterase (AChE) from krait (Bungarus fasciatus) venom is a soluble, nonamphiphilic monomer of 72 kDa. This snake venom AChE has been analyzed by measurements of the stationary and the transient electric dichroism at different field strengths. The stationary values of the dichroism are consistent with the orientation function for permanent dipoles and are not consistent with the orientation function for induced dipoles. The permanent dipole moment obtained by least-squares fits for a buffer containing 5 mM MES is 1000 D, after correction for the internal directing field, assuming a spherical shape of the protein. The dipole moment decreases with increasing buffer concentration to 880 D at 10 mM MES and 770 D at 20 mM MES. The dichroism decay time constant is 90 ns (+/- 10%) which is clearly larger than the value expected from the size/shape of the protein and indicates contributions from sugar residues attached to the protein. The dichroism rise times observed at low field strengths are larger than the decay times and, thus, support the assignment of a permanent dipole moment, although it has not been possible to approach the limit where the energy of the dipole in the electric field is sufficiently low compared to kT. The experimental value of the permanent dipole moment is similar to that calculated for a model structure of Bungarus fasciatus AChE, which has been constructed from its amino and acid sequence, in analogy to the crystal structure of AChE from Torpedo californica.

Weighted-ensemble Brownian dynamics simulations for protein association reactions

A new method, weighted-ensemble Brownian dynamics, is proposed for the simulation of protein-association reactions and other events whose frequencies of outcomes are constricted by free energy barriers. The method features a weighted ensemble of trajectories in configuration space with energy levels dictating the proper correspondence between "particles" and probability. Instead of waiting a very long time for an unlikely event to occur, the probability packets are split, and small packets of probability are allowed to diffuse almost immediately into regions of configuration space that are less likely to be sampled. The method has been applied to the Northrup and Erickson (1992) model of docking-type diffusion-limited reactions and yields reaction rate constants in agreement with those obtained by direct Brownian simulation, but at a fraction of the CPU time (10(-4) to 10(-3), depending on the model). Because the method is essentially a variant of standard Brownian dynamics algorithms, it is anticipated that weighted-ensemble Brownian dynamics, in conjunction with biophysical force models, can be applied to a large class of association reactions of interest to the biophysics community.

Electrostatic and hydrodynamic orientational steering effects in enzyme-substrate association

Diffusional encounters between a dumbbell model of a cleft enzyme and a dumbbell model of an elongated ligand are simulated by Brownian dynamics. The simulations take into account electrostatic and hydrodynamic interactions between the molecules. It is shown that the primary effect of inclusion of hydrodynamic interactions into the simulation is an overall decrease in the rate constant. Hydrodynamic orientational effects are of modest size for the systems considered here. They are manifested when changes in the rate constants for diffusional encounters favored by hydrodynamic interactions are compared with those favored by electrostatic interactions as functions of the overall strength of electrostatic interactions. The electrostatic interactions modify the hydrodynamic torques by modifying the drift velocity of the substrate toward the enzyme. We conclude that simulations referring only to electrostatic interactions between an enzyme and its ligand may yield rate constants that are somewhat (e.g., 20%) too high, but provide realistic descriptions of the orientational steering effects in the enzyme-ligand encounters.