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.

Computer simulations of actin polymerization can explain the barbed-pointed end asymmetry

Computer simulations of actin polymerization were performed to investigate the role of electrostatic interactions in determining polymerization rates. Atomically detailed models of actin monomers and filaments were used in conjunction with a Brownian dynamics method. The simulations were able to reproduce the measured barbed end association rates over a range of ionic strengths and predicted a slower growing pointed end, in agreement with experiment. Similar simulations neglecting electrostatic interactions indicate that configurational and entropic factors may actually favor polymerization at the pointed end, but electrostatic interactions remove this trend. This result would indicate that polymerization at the pointed end is not only limited by diffusion, but faces electrostatic forces that oppose binding. The binding of the actin depolymerizing factor (ADF) and G-actin complex to the end of a filament was also simulated. In this case, electrostatic steering effects lead to an increase in the simulated association rate. Together, the results indicate that simulations provide a realistic description of both polymerization and the binding of more complex structures to actin filaments.

Annealing accounts for the length of actin filaments formed by spontaneous polymerization

We measured the lengths of actin filaments formed by spontaneous polymerization of highly purified actin monomers by fluorescence microscopy after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of approximately 7 microm (2600 subunits). This length is independent of the initial concentration of actin monomer, an observation inconsistent with a simple nucleation-elongation mechanism. However, with the addition of physically reasonable rates of filament annealing and fragmenting, a nucleation-elongation mechanism can reproduce the observed average length of filaments in two types of experiments: 1) filaments formed from a wide range of highly purified actin monomer concentrations, and 2) filaments formed from 24 microM actin over a range of CapZ concentrations.

Molecular dynamics of mouse acetylcholinesterase complexed with huperzine A

Two molecular dynamics simulations were performed for a modeled complex of mouse acetylcholinesterase liganded with huperzine A (HupA). Analysis of these simulations shows that HupA shifts in the active site toward Tyr 337 and Phe 338, and that several residues in the active site area reach out to make hydrogen bonds with the inhibitor. Rapid fluctuations of the gorge width are observed, ranging from widths that allow substrate access to the active site, to pinched structures that do not allow access of molecules as small as water. Additional openings or channels to the active site are found. One opening is formed in the side wall of the active site gorge by residues Val 73, Asp 74, Thr 83, Glu 84, and Asn 87. Another opening is formed at the base of the gorge by residues Trp 86, Val 132, Glu 202, Gly 448, and Ile 451. Both of these openings have been observed separately in the Torpedo californica form of the enzyme. These channels could allow transport of waters and ions to and from the bulk solution.

Dynamical properties of fasciculin-2

Fasciculin-2 (FAS2) is a potent protein inhibitor of the hydrolytic enzyme acetylcholinesterase. A 2-ns isobaric-isothermal ensemble molecular dynamics simulation of this toxin was performed to examine the dynamic structural properties which may play a role in this inhibition. Conformational fluctuations of the FAS2 protein were examined by a variety of techniques to identify flexible residues and determine their characteristic motion. The tips of the toxin "finger" loops and the turn connecting loops I and II were found to fluctuate, while the rest of the protein remained fairly rigid throughout the simulation. Finally, the structural fluctuations were compared to NMR data of fluctuations on a similar timescale in a related three-finger toxin. The molecular dynamics results were in good qualitative agreement with the experimental measurements. Proteins 1999;36:447-453.

Poisson-Boltzmann model studies of molecular electrostatic properties of the cAMP-dependent protein kinase

Protonation equilibria of residues important in the catalytic mechanism of a protein kinase were analyzed on the basis of the Poisson-Boltzmann electrostatic model along with a cluster-based treatment of the multiple titration state problem. Calculations were based upon crystallographic structures of the mammalian cAMP-dependent protein kinase, one representing the so called closed form of the enzyme and the other representing an open conformation. It was predicted that at pH 7 the preferred form of the phosphate group at the catalytically essential threonine 197 (P-Thr197) in the closed form is dianionic, whereas in the open form a monoanionic ionization state is preferred. This dianionic state of P-Thr197, in the closed form, is stabilized by interactions with ionizable residues His87, Arg165, and Lys189. Our calculations predict that the hydroxyl of the Ser residue in the peptide substrate is very difficult to ionize, both in the closed and open structures of the complex. Also, the supposed catalytic base, Asp166, does not seem to have a pK(a) appropriate to remove the hydroxyl group proton of the peptide substrate. However, when Ser of the peptide substrate is forced to remain ionized, the predicted pK(a) of Asp166 increases strongly, which suggests that the Asp residue is a likely candidate to attract the proton if the Ser residue becomes deprotonated, possibly during some structural change preceding formation of the transition state. Finally, in accord with suggestions made on the basis of the pH-dependence of kinase kinetics, our calculations predict that Glu230 and His87 are the residues responsible for the molecular pK(a) values of 6.2 and 8.5, observed in the experiment.

Computer simulation of protein-protein association kinetics: acetylcholinesterase-fasciculin

Computer simulations were performed to investigate the role of electrostatic interactions in promoting fast association of acetylcholinesterase with its peptidic inhibitor, the neurotoxin fasciculin. The encounter of the two macromolecules was simulated with the technique of Brownian dynamics (BD), using atomically detailed structures, and association rate constants were calculated for the wild-type and a number of mutant proteins. In a first set of simulations, the ordering of the experimental rate constants for the mutant proteins was correctly reproduced, although the absolute values of the rate constants were overestimated by a factor of around 30. Rigorous calculations of the full electrostatic interaction energy between the two proteins indicate that this overestimation of association rates results at least in part from approximations made in the description of interaction energetics in the BD simulations. In particular, the initial BD simulations neglect the unfavourable electrostatic desolvation effects that result from the exclusion of high dielectric solvent that accompanies the approach of the two low dielectric proteins. This electrostatic desolvation component is so large that the overall contribution of electrostatics to the binding energy of the complex is unlikely to be strongly favourable. Nevertheless, electrostatic interactions are still responsible for increased association rates, because even if they are unfavourable in the fully formed complex, they are still favourable at intermediate protein-protein separation distances. It therefore appears possible for electrostatic interactions to promote the kinetics of binding even if they do not make a strongly favourable contribution to the thermodynamics of binding. When an approximate description of these electrostatic desolvation effects is included in a second set of BD simulations, the relative ordering of the mutant proteins is again correctly reproduced, but now association rate constants that are much closer in magnitude to the experimental values are obtained. Inclusion of electrostatic desolvation effects also improves reproduction of the experimental ionic strength dependence of the wild-type association rate.

Mouse acetylcholinesterase unliganded and in complex with huperzine A: a comparison of molecular dynamics simulations

A 1 ns molecular dynamics simulation of unliganded mouse acetylcholinesterase (AChE) is compared to a previous simulation of mouse AChE complexed with huperzine A (HupA). Several common features are observed. In both simulations, the active site gorge fluctuates in size during the 1 ns trajectory and is completely pinched off several times. Many of the residues in the gorge that formed hydrogen bonds with HupA in the simulation of the complex now form hydrogen bonds with other protein residues and water molecules in the gorge. The opening of a "backdoor" entrance to the active site that was found in the simulation of the complex is also observed in the unliganded simulation. Differences between the two simulations include overall lower structural rms deviations for residues in the gorge in the unliganded simulation, a smaller diameter of the gorge in the absence of HupA, and the disappearance of a side channel that was frequently present in the liganded simulation. The differences between the two simulations can be attributed, in part, to the interaction of AChE with HupA.

Molecular dynamics studies on the HIV-1 integrase catalytic domain

The HIV-1 integrase, which is essential for viral replication, catalyzes the insertion of viral DNA into the host chromosome, thereby recruiting host cell machinery into making viral proteins. It represents the third main HIV enzyme target for inhibitor design, the first two being the reverse transcriptase and the protease. Two 1-ns molecular dynamics simulations have been carried out on completely hydrated models of the HIV-1 integrase catalytic domain, one with no metal ions and another with one magnesium ion in the catalytic site. The simulations predict that the region of the active site that is missing in the published crystal structures has (at the time of this work) more secondary structure than previously thought. The flexibility of this region has been discussed with respect to the mechanistic function of the enzyme. The results of these simulations will be used as part of inhibitor design projects directed against the catalytic domain of the enzyme.

Shedding light on the dark and weakly fluorescent states of green fluorescent proteins

Recent experiments on various similar green fluorescent protein (GFP) mutants at the single-molecule level and in solution provide evidence of previously unknown short- and long-lived "dark" states and of related excited-state decay channels. Here, we present quantum chemical calculations on cis-trans photoisomerization paths of neutral, anionic, and zwitterionic GFP chromophores in their ground and first singlet excited states that explain the observed behaviors from a common perspective. The results suggest that favorable radiationless decay channels can exist for the different protonation states along these isomerizations, which apparently proceed via conical intersections. These channels are suggested to rationalize the observed dramatic reduction of fluorescence in solution. The observed single-molecule fast blinking is attributed to conversions between the fluorescent anionic and the dark zwitterionic forms whereas slow switching is attributed to conversions between the anionic and the neutral forms. The predicted nonadiabatic crossings are seen to rationalize the origins of a variety of experimental observations on a common basis and may have broad implications for photobiophysical mechanisms in GFP.

Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: a continuum electrostatics study

Ewald and related methods are nowadays routinely used in explicit-solvent simulations of biomolecules, although they impose an artificial periodicity in systems which are inherently non-periodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of computer simulations under Ewald boundary conditions. In the present study we use a method based on continuum electrostatics to investigate the nature and magnitude of possible periodicity-induced artifacts on the potentials of mean force for conformational equilibria in biomolecules. Three model systems and pathways are considered: polyalanine oligopeptides (unfolding), a DNA tetranucleotide (separation of the strands), and the protein Sac7d (conformations from a molecular dynamics simulation). Artificial periodicity may significantly affect these conformational equilibria, in each case stabilizing the most compact conformation of the biomolecule. Three factors enhance periodicity-induced artifacts: (i) a solvent of low dielectric permittivity; (ii) a solute size which is non-negligible compared to the size of the unit cell; and (iii) a non-neutral solute. Neither the neutrality of the solute nor the absence of charge pairs at distances exceeding half the edge of the unit cell do guarantee the absence of artifacts.

Situs: A package for docking crystal structures into low-resolution maps from electron microscopy

Three-dimensional image reconstructions of large-scale protein aggregates are routinely determined by electron microscopy (EM). We combine low-resolution EM data with high-resolution structures of proteins determined by x-ray crystallography. A set of visualization and analysis procedures, termed the Situs package, has been developed to provide an efficient and robust method for the localization of protein subunits in low-resolution data. Topology-representing neural networks are employed to vector-quantize and to correlate features within the structural data sets. Microtubules decorated with kinesin-related ncd motors are used as model aggregates to demonstrate the utility of this package of routines. The precision of the docking has allowed for the extraction of unique conformations of the macromolecules and is limited only by the reliability of the underlying structural data.

Phosphorylation stabilizes the N-termini of alpha-helices

The role of phosphorylation in stabilizing the N-termini of alpha-helices is examined using computer simulations of model peptides. The models comprise either a phosphorylated or unphosphorylated serine at the helix N-terminus, followed by nine alanines. Monte Carlo/stochastic Dynamics simulations were performed on the model helices. The simulations revealed a distinct stabilization of the helical conformation at the N-terminus after phosphorylation. The stabilization was attributable to favorable electrostatic interactions between the phosphate and the helix backbone. However, direct helix capping by the phosphorylated sidechain was not observed. The results of the calculations are consistent with experimental evidence on the stabilization of helices by phosphates and other anions.

Determinants of ligand binding to cAMP-dependent protein kinase

Protein kinases are essential for the regulation of cellular growth and metabolism. Since their dysfunction leads to debilitating diseases, they represent key targets for pharmaceutical research. The rational design of kinase inhibitors requires an understanding of the determinants of ligand binding to these proteins. In the present study, a theoretical model based on continuum electrostatics and a surface-area-dependent nonpolar term is used to calculate binding affinities of balanol derivatives, H-series inhibitors, and ATP analogues toward the catalytic subunit of cAMP-dependent protein kinase (cAPK or protein kinase A). The calculations reproduce most of the experimental trends and provide insight into the driving forces responsible for binding. Nonpolar interactions are found to govern protein-ligand affinity. Hydrogen bonds represent a negligible contribution, because hydrogen bond formation in the complex requires the desolvation of the interacting partners. However, the binding affinity is decreased if hydrogen-bonding groups of the ligand remain unsatisfied in the complex. The disposition of hydrogen-bonding groups in the ligand is therefore crucial for binding specificity. These observations should be valuable guides in the design of potent and specific kinase inhibitors.

Molecular dynamics simulations of the hyperthermophilic protein sac7d from Sulfolobus acidocaldarius: contribution of salt bridges to thermostability

Hyperthermophilic proteins often possess an increased number of surface salt bridges compared with their mesophilic homologues. However, salt bridges are generally thought to be of minor importance in protein stability at room temperature. In an effort to understand why this may no longer be true at elevated temperatures, we performed molecular dynamics simulations of the hyperthermophilic protein Sac7d at 300 K, 360 K, and 550 K. The three trajectories are stable on the nanosecond timescale, as evidenced by the analysis of several time-resolved properties. The simulations at 300 K and (to a lesser extent) 360 K are also compatible with nuclear Overhauser effect-derived distances. Raising the temperature from 300 K to 360 K results in a less favourable protein-solvent interaction energy, and a more favourable intraprotein interaction energy. Both effects are almost exclusively electrostatic in nature and dominated by contributions due to charged side-chains. The reduced solvation is due to a loss of spatial and orientational structure of water around charged side-chains, which is a consequence of the increased thermal motion in the solvent. The favourable change in the intraprotein Coulombic interaction energy is essentially due to the tightening of salt bridges. Assuming that charged side-chains are on average more distant from one another in the unfolded state than in the folded state, it follows that salt bridges may contribute to protein stability at elevated temperatures because (i) the solvation free energy of charged side-chains is more adversely affected in the unfolded state than in the folded state by an increase in temperature, and (ii) due to the tightening of salt bridges, unfolding implies a larger unfavourable increase in the intraprotein Coulombic energy at higher temperature. Possible causes for the unexpected stability of the protein at 550 K are also discussed.

Calculation of the pKa values for the ligands and side chains of Escherichia coli D-alanine:D-alanine ligase

Poisson-Boltzmann electrostatics methods have been used to calculate the pKa shifts for the ligands and titratable side chains of D-alanine:D-alanine ligase of the ddlb gene of Escherichia coli (DdlB). The focus of this study is to determine the ionization state of the second D-alanine (D-Ala2) in the active site of DdlB. The pKa of the amine is shifted over 5 pKa units more alkaline in the protein, clearly implying that D-Ala2 is bound to DdlB in its zwitterionic state and not in the free-base form as had been previously suggested. Comparisons are made to the depsipeptide ligase from the vancomycin-resistance cascade, VanA. It is suggested that VanA has different enzymatic properties due to a change in binding specificity rather than altered catalytic behavior and that the specificity of binding D-lactate over D-Ala2 may arise from the difference in ionization characteristics of the ligands.

Association and dissociation kinetics of bobwhite quail lysozyme with monoclonal antibody HyHEL-5

The anti-hen egg lysozyme monoclonal antibody HyHEL-5 and its complexes with various species-variant and mutant lysozymes have been the subject of considerable experimental and theoretical investigation. The affinity of HyHEL-5 for bobwhite quail lysozyme (BWQL) is over 1000-fold lower than its affinity for the original antigen, hen egg lysozyme (HEL). This difference is believed to arise almost entirely from the replacement in BWQL of the structural and energetic epitope residue Arg68 by lysine. In this study, the association and dissociation kinetics of BWQL with HyHEL-5 were investigated under a variety of conditions and compared with previous results for HEL. HyHEL-5-BWQL association follows a bimolecular mechanism and the dissociation of the antibody-antigen complex is a first-order process. Changes in ionic strength (from 27 to 500 mM) and pH (from 6.0 to 10.0) produced about a 2-fold change in the association and dissociation rates. The effect of viscosity modifiers on the association reaction was also studied. The large difference in the HEL and BWQL affinities for HyHEL-5 is essentially due to differences in the dissociation rate constant.

Self-organizing neural networks bridge the biomolecular resolution gap

Topology-representing neural networks are employed to generate pseudo-atomic structures of large-scale protein assemblies by combining high-resolution data with volumetric data at lower resolution. As an application example, actin monomers and structural subdomains are located in a three-dimensional (3D) image reconstruction from electron micrographs. To test the reliability of the method, the resolution of the atomic model of an actin polymer is lowered to a level typically encountered in electron microscopic reconstructions. The atomic model is restored with a precision nine times the nominal resolution of the corresponding low-resolution density. The presented self-organizing computing method may be used as an information-processing tool for the synthesis of structural data from a variety of biophysical sources.

Rapid binding of a cationic active site inhibitor to wild type and mutant mouse acetylcholinesterase: Brownian dynamics simulation including diffusion in the active site gorge

It is known that anionic surface residues play a role in the long-range electrostatic attraction between acetylcholinesterase and cationic ligands. In our current investigation, we show that anionic residues also play an important role in the behavior of the ligand within the active site gorge of acetylcholinesterase. Negatively charged residues near the gorge opening not only attract positively charged ligands from solution to the enzyme, but can also restrict the motion of the ligand once it is inside of the gorge. We use Brownian dynamics techniques to calculate the rate constant kon, for wild type and mutant acetylcholinesterase with a positively charged ligand. These calculations are performed by allowing the ligand to diffuse within the active site gorge. This is an extension of previously reported work in which a ligand was allowed to diffuse only to the enzyme surface. By setting the reaction criteria for the ligand closer to the active site, better agreement with experimental data is obtained. Although a number of residues influence the movement of the ligand within the gorge, Asp74 is shown to play a particularly important role in this function. Asp74 traps the ligand within the gorge, and in this way helps to ensure a reaction.

Brownian and essential dynamics studies of the HIV-1 integrase catalytic domain

The three-dimensional structure of the active site region of the enzyme HIV-1 integrase is not unambiguously known. This region includes a flexible peptide loop that cannot be well resolved in crystallographic determinations. Here we present two different computational approaches with different levels of resolution and on different time-scales to understand this flexibility and to analyze the dynamics of this part of the protein. We have used molecular dynamics simulations with an atomic model to simulate the region in a realistic and reliable way for 1 ns. It is found that parts of the loop wind up after 300 ps to extend an existing helix. This indicates that the helix is longer than in the earlier crystal structures that were used as basis for this study. Very recent crystal data confirms this finding, underlining the predictive value of accurate MD simulations. Essential dynamics analysis of the MD trajectory yields an anharmonic motion of this loop. We have supplemented the MD data with a much lower resolution Brownian dynamics simulation of 600 ns length. It provides ideas about the slow-motion dynamics of the loop. It is found that the loop explores a conformational space much larger than in the MD trajectory, leading to a "gating"-like motion with respect to the active site.

Analysis of synaptic transmission in the neuromuscular junction using a continuum finite element model

There is a steadily growing body of experimental data describing the diffusion of acetylcholine in the neuromuscular junction and the subsequent miniature endplate currents produced at the postsynaptic membrane. To gain further insights into the structural features governing synaptic transmission, we have performed calculations using a simplified finite element model of the neuromuscular junction. The diffusing acetylcholine molecules are modeled as a continuum, whose spatial and temporal distribution is governed by the force-free diffusion equation. The finite element method was adopted because of its flexibility in modeling irregular geometries and complex boundary conditions. The resulting simulations are shown to be in accord with experiment and other simulations.

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 contributions to the stability of halophilic proteins

Examination of the first crystal structures of proteins from a halophilic organism suggests that an abundance of acidic residues distributed over the protein surface is a key determinant of adaptation to high-salt conditions. Although one extant theory suggests that acidic residues are favored because of their superior water-binding capacity, it is clear that extensive repulsive electrostatic interactions will also be present in such proteins at physiological pH. To investigate the magnitude and importance of such electrostatic interactions, we conducted a theoretical analysis of their contributions to the salt and pH-dependence of stability of two halophilic proteins. Our approach centers on use of the Poisson-Boltzmann equation of classical electrostatics, applied at an atomic level of detail to crystal structures of the proteins. We first show that in using the method, it is important to account for the fact that the dielectric constant of water decreases at high salt concentrations, in order to reproduce experimental changes in pKa values of small acids and bases. We then conduct a comparison of salt and pH effects on the stability of 2Fe-2S ferredoxins from the halophile Haloarcula marismortui and the non-halophile anabaena. In both proteins, substantial upward shifts in pKa accompany protein folding, though shifts are considerably larger, on average, in the halophile. Upward shifts for basic residues occur because of favorable salt-bridge interactions, whilst upward shifts for acidic residues result from unfavorable electrostatic interactions with other acidic groups. Our calculations suggest that at pH 7 the stability of the halophilic protein is decreased by 18.2 kcal/mol on lowering the salt concentration from 5 M to 100 mM, a result that is in line with the fact that halophilic proteins generally unfold at low salt concentrations. For comparison, the non-halophilic ferredoxin is calculated to be destabilized by only 5.1 kcal/mol over the same range. Analysis of the pH stability curve suggests that lowering the pH should increase the intrinsic stability of the halophilic protein at low salt concentrations, although in practice this is not observed because of aggregation effects. We report the results of a similar analysis carried out on the tetrameric malate dehydrogenase from H. marismortui. In this case, we investigated the salt and pH dependence of the various monomer-monomer interactions present in the tetramer. All monomer-monomer interactions are found to make substantial contributions to the salt-dependence of stability of the tetramer. Excellent agreement is obtained between our calculated results for the stability of the tetramer and experimental results. In particular, the finding that at 4 M NaCl, the tetramer is stable only between pH 4.8 and 10 is accurately reproduced. Taken together, our results suggest that repulsive electrostatic interactions between acidic residues are a major factor in the destabilization of halophilic proteins in low-salt conditions, and that these interactions remain destabilizing even at high salt concentrations. As a consequence, the role of acidic residues in halophilic proteins may be more to prevent aggregation than to make a positive contribution to intrinsic protein stability.

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.