A 240-Fold Electrostatic Rate-Enhancement for Acetylcholinesterase−Substrate Binding Can Be Predicted by the Potential within the Active Site

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.

Rate Constants and Mechanisms of Protein-Ligand Binding

Whereas protein-ligand binding affinities have long-established prominence, binding rate constants and binding mechanisms have gained increasing attention in recent years. Both new computational methods and new experimental techniques have been developed to characterize the latter properties. It is now realized that binding mechanisms, like binding rate constants, can and should be quantitatively determined. In this review, we summarize studies and synthesize ideas on several topics in the hope of providing a coherent picture of and physical insight into binding kinetics. The topics include microscopic formulation of the kinetic problem and its reduction to simple rate equations; computation of binding rate constants; quantitative determination of binding mechanisms; and elucidation of physical factors that control binding rate constants and mechanisms.

BDflex: a method for efficient treatment of molecular flexibility in calculating protein-ligand binding rate constants from brownian dynamics simulations

A method developed by Northrup et al. [J. Chem. Phys. 80, 1517 (1984)] for calculating protein-ligand binding rate constants (k(a)) from brownian dynamics (BD) simulations has been widely used for rigid molecules. Application to flexible molecules is limited by the formidable computational cost to treat conformational fluctuations during the long BD simulations necessary for k(a) calculation. Here, we propose a new method called BDflex for k(a) calculation that circumvents this problem. The basic idea is to separate the whole space into an outer region and an inner region, and formulate k(a) as the product of k(E) and η(d), which are obtained by separately solving exterior and interior problems. k(E) is the diffusion-controlled rate constant for the ligand in the outer region to reach the dividing surface between the outer and inner regions; in this exterior problem conformational fluctuations can be neglected. η(d) is the probability that the ligand, starting from the dividing surface, will react at the binding site rather than escape to infinity. The crucial step in reducing the determination of η(d) to a problem confined to the inner region is a radiation boundary condition imposed on the dividing surface; the reactivity on this boundary is proportional to k(E). By confining the ligand to the inner region and imposing the radiation boundary condition, we avoid multiple-crossing of the dividing surface before reaction at the binding site and hence dramatically cut down the total simulation time, making the treatment of conformational fluctuations affordable. BDflex is expected to have wide applications in problems where conformational fluctuations of the molecules are crucial for productive ligand binding, such as in cases where transient widening of a bottleneck allows the ligand to access the binding pocket, or the binding site is properly formed only after ligand entrance induces the closure of a lid.

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.

Theory and simulation of diffusion-influenced, stochastically gated ligand binding to buried sites

We consider the diffusion-influenced rate coefficient of ligand binding to a site located in a deep pocket on a protein; the binding pocket is flexible and can reorganize in response to ligand entrance. We extend to this flexible protein-ligand system a formalism developed previously [A. M. Berezhkovskii, A, Szabo, and H.-X. Zhou, J. Chem. Phys. 135, 075103 (2011)] for breaking the ligand-binding problem into an exterior problem and an interior problem. Conformational fluctuations of a bottleneck or a lid and the binding site are modeled as stochastic gating. We present analytical and Brownian dynamics simulation results for the case of a cylindrical pocket containing a binding site at the bottom. Induced switch, whereby the conformation of the protein adapts to the incoming ligand, leads to considerable rate enhancement.

Rate theories for biologists

Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.

Electrostatic rate enhancement and transient complex of protein-protein association

The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to approximately 10(5)-10(6) M(-1) s(-1). Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys J 1997;73:2441-2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by $k_{\bf D}$ = $k_{D}0\ {exp} ( - \langle U_{el} \rangle;{\star}/k_{B} T),$ where k(D) and k(D0) are the rates in the presence and absence of electrostatic interactions, respectively, U(el) is the average electrostatic interaction energy in a "transient-complex" ensemble, and k(B)T is the thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with the experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007;15:215-224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations.

Prediction of salt and mutational effects on the association rate of U1A protein and U1 small nuclear RNA stem/loop II

We have developed a computational approach for predicting protein-protein association rates (Alsallaq and Zhou, Structure 2007, 15, 215). Here we expand the range of applicability of this approach to protein-RNA binding and report the first results for protein-RNA binding rates predicted from atomistic modeling. The system studied is the U1A protein and stem/loop II of the U1 small nuclear RNA. Experimentally it was observed that the binding rate is significantly reduced by increasing salt concentration while the dissociation changes little with salt concentration, and charges distant from the binding site make marginal contribution to the binding rate. These observations are rationalized. Moreover, predicted effects of salt and charge mutations are found to be in quantitative agreement with experimental results.

Synthesis, enzymatic activity, and X-ray crystallography of an unusual class of amino acids

The synthesis of two novel amino acids, nitrogen analogues of the naturally occurring glycosidase inhibitor, salacinol, containing a carboxylate inner salt are described, along with the crystal structure of one of these analogues in the active site of Drosophila melanogaster Golgi mannosidase II (dGMII). Salacinol, a naturally occurring sulfonium ion, is one of the active principals in the aqueous extracts of Salacia reticulata that are traditionally used in Sri Lanka and India for the treatment of diabetes. The synthetic strategy relies on the nucleophilic attack of 2,3,5-tri-O-benzyl-1,4-dideoxy-1,4-imino l- or d-arabinitol at the least hindered carbon of 5,6-anhydro-2,3-di-O-benzyl-l-ascorbic acid to yield coupled adducts. Deprotection, stereoselective catalytic reduction, and hydrolysis of the coupled products give the target compounds. The compound derived from d-arabinitol inhibits dGMII, one of the critical enzymes in the glycoprotein processing pathway, with an IC(50) of 0.3mM. Inhibition of GMII has been identified as a target for control of metastatic cancer. An X-ray crystal structure of the complex of this compound with dGMII provides insight into the requirements for an effective inhibitor. The same compound inhibits recombinant human maltase glucoamylase, one of the key intestinal enzymes involved in the breakdown of glucose oligosaccharides in the small intestine, with a K(i) value of 21microM.

Diffusion-Controlled Reactions: Hydrodynamic Interaction between Charged, Uniformly Reactive Spherical Reactants

In this work, different models of hydrodynamic interaction (HI) are examined in the diffusion-controlled reaction between uniformly reactive charged spherical particles. In addition to Oseen "stick" and "slip" models of HI, one is considered that accounts for the disturbance of fluid flow by the ions around one reactive partner as they interact with a neighboring reactive species. This interaction is closely related to the "electrophoretic effect" in electrokinetics and can be described by a fairly simple electrophoretic, or E-tensor. These models are applied to the electron-transfer quenching reaction of Ru(bpy)3(2+) and methyl viologen (MV2+) over a wide range of NaCl concentrations (Chiorboli, C. et al., J. Phys. Chem. 1988, 92, 156). The back reaction is also considered. From a comparison of the salt dependence of the model and experimental rates, it is concluded that the "E-tensor" model works best and ignoring HI altogether works worst. The Oseen "stick" and "slip" models fall between these.

Chance and design—Proton transfer in water, channels and bioenergetic proteins

Proton transfer and transport in water, gramicidin and some selected channels and bioenergetic proteins are reviewed. An attempt is made to draw some conclusions about how Nature designs long distance, proton transport functionality. The prevalence of water rather than amino acid hydrogen bonded chains is noted, and the possible benefits of waters as the major component are discussed qualitatively.

Small weak acids reactivate proton transfer in reaction centers from Rhodobacter sphaeroides mutated at AspL210 and AspM17

In reaction centers of Rhodobacter sphaeroides, site-directed mutagenesis has implicated several acidic residues in the delivery of protons to the secondary quinone (Q(B)) during reduction to quinol. In a double mutant (Asp(L210) --> Asn + Asp(M17) --> Asn) that is severely impaired in proton transfer capability over a wide pH range, proton transfer was "rescued" by added weak acids. For low pK(a) acids the total concentration of salt required near neutral pH was high. The ionic strength effect of added salts stimulated the rate of proton-coupled electron transfer at pH < 7, but decreased it at pH > 7.5, indicating an effective isoelectric point between these limits. In this region, a substantial rate enhancement by weak acids was clearly evident. A Brønsted plot of activity versus pK(a) of the rescuing acids was linear, with a slope of -1, and extrapolated to a diffusion-limited rate at pK(a)(app) approximately 1. However, the maximum rate at saturating concentrations of acid did not correlate with pK(a), indicating that the acid and anion species compete for binding, both with weak affinity. This model predicts that pK(a)(app) corresponds to a true pK(a) = 4-5, similar to that for a carboxylic acid or Q(B)(-), itself. Only rather small, neutral acids were active, indicating a need to access a small internal volume, suggested to be a proton channel to the Q(B) domain. However, the on-rates were near the diffusion limit. The implications for intraprotein proton transfer pathway design are discussed.

A hypothesis concerning diffusion-limited protein-ligand interactions

A simple assumption allows the prediction of the numerical value for a 'universal' limiting kinetic rate for wholly diffusion-limited reactions between small neutral molecules and macromolecules. This prediction is compared with appropriate experimental data for binding of ligands to myoglobin and to enzymes. It is shown that in the absence of electrostatic effects, this limit is approached but not exceeded. The model also makes very specific predictions concerning the viscosity and temperature dependence of such reactions.

Properties of water molecules in the active site gorge of acetylcholinesterase from computer simulation

A 10-ns trajectory from a molecular dynamics simulation is used to examine the structure and dynamics of water in the active site gorge of acetylcholinesterase to determine what influence water may have on its function. While the confining nature of the deep active site gorge slows down and structures water significantly compared to bulk water, water in the gorge is found to display a number of properties that may aid ligand entry and binding. These properties include fluctuations in the population of gorge waters, moderate disorder and mobility of water in the middle and entrance to the gorge, reduced water hydrogen-bonding ability, and transient cavities in the gorge.

Kinetics of diffusion-assisted reactions in microheterogeneous systems

This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.

Comparison of salt effects on the reactions of acetylcholinesterase with cationic and anionic inhibitors

The influence of inorganic salts on the inhibition of acetylcholinesterase by charged organophosphorous inhibitors has been studied. It has been shown that the salt effect on the reaction of acetylcholinesterase with anionic bis(p-nitrophenyl) phosphate is determined by the influence of added salts on the activity coefficient of the inhibitor. In contrast to the salt effects on the reaction of acetylcholinesterase with cationic compounds, it does not include contribution from the enzyme charges. The smaller salt effect in the case of anionic inhibitor can be explained assuming that the anionic inhibitor does not form a non-covalent complex with the enzyme before the phosphorylation step of the reaction. Comparison of salt effects on the substrate turnover showed that in the case of cholinesterases from natural sources they are larger than in the case of enzymes expressed in recombinant cell clones. The enhanced salt effects may result from post-translational modification of the enzyme.

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.

Electrostatic steering of substrate to acetylcholinesterase: analysis of field fluctuations

Based on previous molecular dynamics simulation results for acetylcholinesterase dimer, we calculate and analyse the electrostatic field fluctuations around the enzyme. The results show that dynamic features of the electrostatic field favor attraction of the positively-charged substrate. An Internet link to an animation of the results is also provided.

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.

On the protein-protein diffusional encounter complex

When two proteins diffuse together to form a bound complex, an intermediate is formed at the end-point of diffusional association which is called the encounter complex. Its characteristics are important in determining association rates, yet its structure cannot be directly observed experimentally. Here, we address the problem of how to construct the ensemble of three-dimensional structures which constitute the protein-protein diffusional encounter complex using available experimental data describing the dependence of protein association rates on mutation and on solvent ionic strength and viscosity. The magnitude of the association rates is fitted well using a variety of definitions of encounter complexes in which the two proteins are located at up to about 17 A root-mean-squared distance from their relative arrangement in the bound complex. Analysis of the ionic strength dependence of bimolecular association rates shows that this is determined to a greater extent by the (protein charge) - (salt ion) separation distance than by the protein-protein charge separation distance. Consequently, ionic strength dependence of association rates provides little information about the geometry of the encounter complex. On the other hand, experimental data on electrostatic rate enhancement, mutation and viscosity dependence suggest a model of the encounter complex in which the two proteins form a subset of the contacts present in the bound complex and are significantly desolvated.

Theoretical and experimental investigations of electrostatic effects on acetylcholinesterase catalysis and inhibition

The role of electrostatics in the function of acetylcholinesterase (AChE) has been investigated by both theoretical and experimental approaches. Second-order rate constants (kE = k(cat)/Km) for acetylthiocholine (ATCh) turnover have been measured as a function of ionic strength of the reaction medium for wild-type and mutant AChEs. Also, binding and dissociation rate constants have been measured as a function of ionic strength for the respective charged and neutral transition state analog inhibitors m-(N,N,N-trimethylammonio)trifluoroacetophenone (TMTFA) and m-(t-butyl)trifluoroacetophenone (TBTFA). Linear free-energy correlations between catalytic rate constants and inhibition constants indicate that kE for ATCh turnover is rate limited by terminal binding events. Comparison of binding rate constants for TMTFA and TBTFA attests to the sizable electrostatic discrimination of AChE. Free energy profiles for cationic ligand release from the active sites of wild-type and mutant AChEs have been calculated via a model that utilizes the structure of T. californica AChE, a spherical ligand, and energy terms that account for electrostatic and van der Waals interactions and chemical potential. These calculations indicate that EA and EI complexes are not bound with respect to electrostatic interactions, which obviates the need for a 'back door' for cationic ligand release. Moreover, the computed energy barriers for ligand release give linear free-energy correlations with log(kE) for substrate turnover, which supports the general correctness of the computational model.

Future directions for combining molecular and continuum models in protein simulations

In order to perform useful computer simulations on protein molecules, models that combine atomistic and continuum approaches will be necessary. The use of continuum models will reduce the number of system variables and allow studies of longer time scales. On the other hand, one will still need to retain atomic detail in certain parts of the protein molecule, such as an enzyme active site. Most of the important advances to date have been continuum models of the surrounding solvent, but simplified descriptions of the protein itself also are being developed. Finally, in order to study these several different levels of complexity simultaneously in a single simulation, it will be necessary to use modern software engineering techniques.

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.

Electrostatic steering and ionic tethering in enzyme-ligand binding: insights from simulations

To bind at an enzyme's active site, a ligand must diffuse or be transported to the enzyme's surface, and, if the binding site is buried, the ligand must diffuse through the protein to reach it. Although the driving force for ligand binding is often ascribed to the hydrophobic effect, electrostatic interactions also influence the binding process of both charged and nonpolar ligands. First, electrostatic steering of charged substrates into enzyme active sites is discussed. This is of particular relevance for diffusion-influenced enzymes. By comparing the results of Brownian dynamics simulations and electrostatic potential similarity analysis for triose-phosphate isomerases, superoxide dismutases, and beta-lactamases from different species, we identify the conserved features responsible for the electrostatic substrate-steering fields. The conserved potentials are localized at the active sites and are the primary determinants of the bimolecular association rates. Then we focus on a more subtle effect, which we will refer to as "ionic tethering." We explore, by means of molecular and Brownian dynamics simulations and electrostatic continuum calculations, how salt links can act as tethers between structural elements of an enzyme that undergo conformational change upon substrate binding, and thereby regulate or modulate substrate binding. This is illustrated for the lipase and cytochrome P450 enzymes. Ionic tethering can provide a control mechanism for substrate binding that is sensitive to the electrostatic properties of the enzyme's surroundings even when the substrate is nonpolar.

Electrostatic enhancement of diffusion-controlled protein-protein association: comparison of theory and experiment on barnase and barstar

The electrostatic enhancement of the association rate of barnase and barstar is calculated using a transition-state theory like expression and atomic-detail modeling of the protein molecules. This expression predicts that the rate enhancement is simply the average Boltzmann factor in the region of configurational space where association occurs instantaneously in the diffusion-controlled limit. Based on experimental evidence, this "transition state" is defined by configurations in which, relative to the stereospecifically bound complex, the two proteins are shifted apart by approximately 8 A (so a layer of water can be accommodated in the interface) and the two binding surfaces are rotated away by 0 degrees to 3 degrees. The values of the average Boltzmann factor, calculated by solving the Poisson-Boltzmann equation, for the wild-type complex and 16 complexes with single mutations are found to correlate well with experimental results for the electrostatic rate enhancement. The predicted rate enhancement is found to be somewhat insensitive to the precise definition of the transition state, due to the long-range nature of electrostatic interactions. The experimental ionic strength dependence of the rate enhancement is also reasonably reproduced.

Correlation between rate of enzyme-substrate diffusional encounter and average Boltzmann factor around active site

The utility of the average Boltzmann factor around the active site of an enzyme as the predictor of the electrostatic enhancement of the substrate binding rate is tested on a set of data on wild-type acetylcholinesterase and 18 charge mutants recently obtained by Brownian dynamics simulations. A good correlation between the average Boltzmann factors and the substrate binding rate constants is found. The effects of single charge mutations on both the Boltzmann factor and the substrate binding rate constant are modest, i.e., < 5 fold increase or decrease. This is consistent with the experimental results of Shafferman et al. but does not support their suggestion that the overall rate of the catalytic reaction is not limited by the diffusional encounter of acetylcholinesterase and its substrate.

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.

Design of fast enzymes by optimizing interaction potential in active site

The diffusional encounter between substrate and enzyme, and hence catalytic efficiency, can be enhanced by mutating charged residues on the surface of the enzyme. In this paper we present a simple method for screening such mutations. This is based on our earlier result that electrostatic enhancement of the enzyme-substrate binding rate constant can be accounted for just by the interaction potential within the active site. Assuming that catalytic and structural integrity is maintained, the catalytic efficiency can be optimized by surface charge mutations which lead to stronger interaction potential within the active site. Application of the screening method on superoxide dismutase shows that only charge mutations close to the active site will have practical effect on the catalytic efficiency. This rationalizes a large number of findings obtained in previous simulation and experimental studies.