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Absolute Configuration of Bromochlorofluoromethane from Molecular Dynamics Simulation of its Enantioselective Complexation by Cryptophane-C
J. Costante-Crassous, T.J. Marrone, J.M. Briggs, J.A. McCammon and A. Collet
Earlier NMR experiments have shown that the inclusion of bromochlorofluoromethane (CHFClBr) 1 within the cavity of (-)-cryptophane-C 2 in chloroform solution is enantioselective and that (-)-1 is more strongly bound than (+)-1 with a free energy difference (delta delta G) of 1.1 kJ/mol. In order to gain information on the relative configuration of the diastereomeric complexes and hence on the absolute configuration of 1, we have tried to reproduce these experiments by computational methods, and we have calculated the free energy difference for the binding of (R) and (S)-1 to (-)-2. For this purpose, the OPLS parameters for CHFClBr were optimized by Monte Carlo (MC) simulations of the pure liquid. Then molecular dynamics (MD) simulations were performed on the host-guest system in a solvent box of chloroform using multiconfiguration thermodynamic integration (MCTI) and free energy perturbation (FEP) methods to calculate the free energy difference between the diastereomeric complexes. The [(R)-1@(-)-2] complex was thus calculated to be more stable than the [(S)-1@(-)-2] one by 0-2.6 kJ/mol, which is of the same order of magnitude as the experimental result. Since the [(-)-1@(-)-2] complex is more stable than the [(+)-1@(-)-2] one, and since the absolute configuration of 2 is known, it was concluded that the absolute configuration of CHFClBr must be (R)-(-) (or (S)-(+)); this conclusion is in agreement with a recent independent assignment based on Raman Optical Activity studies.
Simulation of Electrostatic and Hydrodynamic Properties of Serratia Endonuclease
Jan Antosiewicz, Mitchell D. Miller, Kurt L. Krause and J. Andrew McCammon
We analyze the electrostatic and hydrodynamic properties of a nuclease from the pathogenic Gram-negative bacterium Serratia marcescens using finite-difference Poisson-Boltzmann methods for electrostatic calculations and a bead-model approach for diffusion coefficient calculations.
Electrostatic properties are analyzed for the enzyme in monomeric and dimeric forms and also in the context of DNA binding by the nuclease. Our preliminary results show that binding of a dsDNA dodecamer by nuclease, causes an overall shift in the charge of the protein by approximately three units of elementary charge per monomer resulting in a positively charged protein at physiologic pH. In these calculations, the free enzyme was found to have a negative (-1e) charge per monomer at pH7. The most dramatic shift in pKa involves His 89 whose pKa increases by three pH units upon DNA binding. This shift leads to a protonated residue at pH7, in contrast to the unprotonated form in the free enzyme. DNA binding also leads to a decrease in the energetic distances between the most stable protonation states of the enzyme. Dimerization has no significant effect on the electrostatic properties of each of the monomers for both free enzyme and that bound to DNA.
Results of hydrodynamic calculations are consistent with the dimeric form of the enzyme in solution. The computed translational diffusion coefficient for the dimer model of the enzyme is in very good agreement with measurements from light scattering experiments. Preliminary electro-optical calculations indicate that the dimer should possess a large dipole moment (approximately 600 Debye units) as well as substantial optical anisotropy (limiting reduced linear electric dichroism of about 0.3). Therefore, this system may serve as a good model for investigation of electric and hydrodynamic properties by relaxation electro-optical experiments.
Structure-Based Drug Design: Computational Advances
T.J. Marrone, J.M. Briggs and J.A. McCammon
Structure-based computational methods continue to show progress in the discovery and refinement of therapeutic agents. Several such methods and their applications are described. These include molecular modeling, docking, fragment methods, 3D database techniques, and free energy perturbation. Related issues that are discussed include the use of simplified energy functions and the determination of the positions of tightly-bound waters. Strengths and weaknesses of the various methods are described.
Application of Poisson-Boltzmann Solvation Forces to Macromolecular Simulations
A.H. Elcock, M.J. Potter and J.A. McCammon
One of the most difficult problems encountered in the dynamical simulation of large macromolecular systems is how to deal adequately with the huge number of atomic interactions involved. For aqueous phase simulations the computational burden associated with solvent water molecules can easily outstrip that associated with the macromolecule, even though the behavior of the solvent itself may not be of much interest. Not surprisingly therefore considerable interest has been focused on the use of methods in which explicit solvent water molecules are replaced by an implicit dielectric continuum representation. Perhaps the most generally accepted continuum-based approach centers on the use of the Poisson-Boltzmann (PB) equation of classical electrostatics, a method which owes its success to the fact that many solvation-related phenomena (with the notable exception of the hydrophobic effect) appear to be essentially electrostatic in nature. Until very recently, use of the PB approach has largely been restricted to calculations involving static representations of molecular structure, but the recent development of methods to obtain solvation forces from the PB equation means that it can now in principle also be used in dynamics simulations. Applications of the former type have been comprehensively reviewed in the literature and are not discussed further in this article; instead, we restrict our attention here to the potential use of PB electrostatics in dynamical simulations of macromolecules.
Enzyme-Inhibitor Association Thermodynamics: Explicit and Continuum Solvent Studies
Haluk Resat, Tami J. Marrone and J. Andrew McCammon
Studying the thermodynamics of biochemical association reactions at the microscopic level requires efficient sampling of the configurations of the reactants and solvent as a function of the reaction pathways. In most cases, the associating ligand and receptor have complementary interlocking shapes. Upon association, loosely connected or disconnected solvent cavities at and around the binding site are formed. Disconnected solvent regions lead to severe statistical sampling problems when simulations are performed with explicit solvent. It was recently proposed that, when such limitations are encountered, they might be overcome by use of the grand canonical ensemble [Resat et al., J. Phys. Chem. 100, 1426 (1996)]. Here, we investigate one such case and report the association free energy profile (potential of mean force) between trypsin and benzamidine along a chosen reaction coordinate as calculated using the grand canonical Monte Carlo method. The free energy profile is also calculated for a continuum solvent model using the Poisson equation, and the results are compared to the explicit water simulations. The comparison shows that the continuum solvent approach is surprisingly successful in reproducing the explicit solvent simulation results. The Monte Carlo results are analyzed in detail with respect to solvation structure. In the binding site channel, there are waters bridging the carbonyl oxygen groups of Asp189 with the NH(2) groups of benzamidine which are displaced upon inhibitor binding. A similar solvent-bridging configuration has been seen in the crystal structure of trypsin complexed with bovine pancreatic trypsin inhibitor. The predicted locations of other internal waters are in very good agreement with the positions found in the crystal structures which supports the accuracy of the simulations.
Electrostatic effects in homeodomain-DNA interactions
F. Fogolari, A.H. Elcock, G. Esposito, P. Viglino, J.M. Briggs and J.A. McCammon
Electrostatics plays an important role in protein-DNA association. The Poisson-Boltzmann equation is a powerful tool to study these effects. It allows free energies of association to be calculated and allows detailed analyses of the electrostatic dependence of thermodynamic quantities to be made.
We report here an investigation on the role of electrostatics in homeodomain-DNA interaction. Compared to the proteins considered in previous investigations of protein-DNA systems, the homeodomain is a highly charged small protein and forms extensive ion pairs upon binding DNA. It is not obvious, therefore, whether the previous results extend to this class of molecules. We investigated the salt dependence of the binding constant for specific association and for different models of non-specific association. Our results indicate that counterion release accounts for a significant fraction of the salt dependence of the free energy.
Thermodynamic data for some specific homeodomain mutants can be explained by favorable electrostatic interactions in the major groove of DNA.
Prediction of Titration Properties of Structures of a Protein Derived from Molecular Dynamics Trajectories
S.T. Wlodek, J. Antosiewicz and J.A. McCammon
This paper explores the dependence of the molecular dynamics (MD) trajectory of a protein molecule upon the titration state assigned to the molecule. Four 100 ps molecular dynamics trajectories of bovine pancreatic trypsin inhibitor (BPTI) were generated, starting from two different structures, each of which was held in two different charge states. The two starting structures were the X-ray crystal structure and one of the solution structures determined by NMR, and the charge states differed only in the ionization state of N terminus.
Although it is evident that the MD simulations were too short to fully sample the equilibrium distribution of structures in each case, standard Poisson-Boltzmann titration state analysis of the resulting configurations shows general agreement between the overall titration behavior of the protein and the charge state assumed during MD simulation: at pH 7, the total net charge of the protein resulting from the titration analysis is consistently lower for the protein with the N terminus assumed to be neutral than for the protein with the N terminus assumed to be charged.
For most of the ionizable residues, the differences in the calculated pKa's among the four trajectories are statistically negligible, and remain in good agreement with the data obtained by crystal structure titration and by experiment. The exceptions include the N terminus which directly responds to the change of its imposed charges, the C terminus which in the NMR structure strongly interacts with the former, and a few other residues, (Arg1, Glu7, Tyr35 and Arg42) whose pKa's reflect the initial structure and the limited trajectory lengths.
This study illustrates the importance of the careful assignment of protonation states at the start of MD simulations, and points to the need for simulation methods that allow for the variation of the protonation state in the calculation of equilibrium properties.
The Statistical-Thermodynamic Basis for Computation of Binding Affinities: A Critical Review
M.K. Gilson, J.A. Given, B.L. Bush and J.A. McCammon
The noncovalent association of molecules is of central importance in biology and pharmacology. It underlies the action of hormones, the control of DNA transcription, the recognition of antigens by the immune system, the catalysis of chemical reactions by enzymes, and the actions of many drugs. Therefore, methods of predicting the affinity of such noncovalent association would be of great practical value. For example, predictive computational models for the noncovalent association of biomolecules and their ligands would be useful in structure-based drug design and in the redesign of enzymes. As recently reviewed, many groups have invested ingenuity and effort into the development of such models. However, although the physical chemistry of these association processes is rooted in statistical themodynamics, few models are explicitly derived from these underlying principles. This has led to a certain amount of confusion in the field, as discussed below. The present paper therefore presents a statistical-thermodynamic derivation of the standard free energy of binding, and uses this to review the underpinnings of methods for computing noncovalent binding affinities.
Rational Design of HIV Protease Inhibitors
C.N. Hodge, T.P. Straatsma, J.A. McCammon and A. Wlodawer
Replication of the human immunodeficiency virus (HIV) requires the action of a virally encoded protease to produce components of progeny virions within infected cells. Therefore much effort has been devoted to developing specific inhibitors of protease in the hope that these may prove valuable in the management of HIV infections. Fortunately, the structures of protease and many of its inhibitor complexes have been determined by X-ray crystallography. This chapter describes how such structural data are being used in computer modeling and computer simulation studies to speed the discovery of clinically useful protease inhibitors. The first section outlines the crystallographic results that have been obtained for protease-inhibitor complexes. Subsequent sections describe how computer modeling has helped in the discovery of a promising new class of protease inhibitors, and how free energy simulations can help in deciding which inhibitors within a given class will have the highest affinity for protease.
Weighted-Ensemble Simulated Annealing: Faster Optimization on Hierarchical Energy Surfaces
G.A. Huber and J.A. McCammon
A new method, Weighted-Ensemble Annealing, is proposed for finding the global minima of complicated functions, such as those found in biological problems. This method performs simulated annealing using multiple system copies; it automatically adjusts the distribution of copies and the allocation of computer resources as the cooling proceeds. This readjustment procedure is designed to take advantage of the hierarchical structure of the energy landscape of biomolecules and other systems. This method is applied to a fractal-like function with energy barriers of many sizes and a large entropy barrier. It is shown that using an optimnal number of system copies results in a success rate for finding the global minimum which is an order of magnitude higher that the success rate from traditional single-copy annealing, using the same total number of function evaluations.
Conformational Sampling with Poisson-Boltzmann Forces and a Stochastic Dynamics/Monte Carlo Method: Application to Alanine Dipeptide
J.L. Smart, T.J. Marrone and J.A. McCammon
We apply a combination of stochastic dynamics and Monte Carlo methods (MC/SD) to the alanine dipeptide, with solvation forces derived from a Poisson- Boltzmann model supplemented with apolar terms. Our purpose is to study the effects of the model parameters, such as the friction constant and the size of the electrostatic finite difference grid, on the rate of conformational sampling and on the accuracy of the resulting free energy map. For dialanine, a converged Ramachandran map is produced in significantly less time than what is required by stochastic dynamics or Monte Carlo alone. MC/SD is also shown to be faster, per timestep, than explicit methods.
Modeling the Electrophoresis of Lysozyme II. Inclusion of Ion Relaxation
S.A. Allison, M. Potter and J.A. McCammon
In this work, boundary element methods are used to model the electrophoretic mobility of lysozyme over the pH range 2-6. The model treats the protein as a rigid body of arbitrary shape and charge distribution derived from the crystal structure. Extending earlier studies, the present work treats the equilibrium electrostatic potential at the level of the full Poisson-Boltzmann (PB) equation and accounts for ion relaxation. This is achieved by solving simultaneously the Poisson, ion transport, and Navier-Stokes equations by an iterative boundary element procedure. Treating the equilibrium electrostatics at the level of the full rather than the linear PB equation, but leaving relaxation out, does improve agreement between experimental and simulated mobilities. Including ion relaxation improves it even more. The effects of nonlinear electrostatics and ion relaxation are greatest at low pH where the net charge on lysozyme is greatest. In the absence of relaxation, a linear dependence of mobility and average polyion surface potential is observed.
Colloquium on Signaling and Molecular Structure in Pharmacology
P. Taylor, E.M. Ross, P.C. Sternweis, R. Neubig and J.A. McCammon
The first international meeting of major biological research societies within a supercomputer center is described. The meeting occurred in March 1997 at the San Diego Supercomputer Center. The resources of the center allowed the audience to view biomolecular structure and dynamics in three dimensions as the speakers delivered their lectures.
Structural Fluctuations of a Cryptophane-Tetramethylammonium Host-Guest System: A Molecular Dynamics Simulation
P.D. Kirchhoff, J.-P. Dutasta, A. Collet and J.A. McCammon
Cryptophanes are aromatic hosts which bind a variety of guests. Here, we describe a 25 nanosecond molecular dynamics simulation of a particular cryptophane host-guest complex in water. The cryptophane used in this study was used previously in a 20 nanosecond molecular dynamics simulation to describe the fluctuations of the uncomplexed host. This cryptophane features three pores which open onto a cavity where the guests bind. In the current study, tetramethylammonium ion (TMA+) has been placed within the cryptophane cavity to form the host-guest complex. The molecular dynamics simulation in combination with a surfacing algorithm provides information on the frequency with which the cryptophane pores open wide enough to admit or release guest molecules of any given size. We discuss these fluctuations and their possible consequences for binding kinetics, making comparisons between the cryptophane and the cryptophane-TMA+ complex.
Electrostatic Influence on the Kinetics of Ligand Binding to Acetylcholinesterase: Distinctions Between Active Center Ligands and Fasciculin
Zoran Radić, Paul D. Kirchhoff, Daniel M. Quinn, J. Andrew McCammon and Palmer Taylor
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 (Glu84, Glu91, Asp280, Asp283, Glu292 and Asp372), and three residues within the active center gorge (Asp74 at the rim, Glu202 and Glu450 at the base). The peripheral site ligand, fasciculin2 (FAS2), a peptide of 6.5 kD 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-trimethylammonio trifluoroacetophenone (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.
Molecular Properties of Amphotericin B Membrane Channel - A Molecular Dynamics Simulation
M. Baginski, H. Resat and J.A. McCammon
Amphotericin B is a powerful, but also toxic, anti-fungal antibiotic used to treat systemic infections. It forms ionic membrane channels in fungal cells. These antibiotic-sterol channels are responsible for the leakage of ions which causes cell destruction. The detailed molecular properties and structure of amphotericin B channels are still unknown. In the present study, two molecular dynamic simulations of a particular model AmB-cholesterol channel were performed. The water and phospholipid environment were included in our simulations, and the results obtained were compared with available experimental data. It was found that it is mainly the hydrogen bonding interactions which keep the channel stable in its open form. Our study also revealed the important role of the intermolecular interactions between the hydroxyl, amino and carboxyl groups of the channel forming molecules. Particularly, some hydroxyl groups stand out as new "hot spots" potentially useful for chemotherapeutic investigations. Our results also help to understand why certain antibiotic derivatives, with a blocked amino group, are less active. We also present a hypothesis for the role of membrane lipids and cholesterol in the channel.
Molecular Dynamics of Acetylcholinesterase Dimer Complexed with Tacrine
S.T. Wlodek, T.W. Clark, L.R. Scott and J.A. McCammon
We have studied the dynamic properties of acetylcholinesterase dimer from Torpedo californica liganded with tacrine (AChE-THA) in solution using molecular dynamics. The simulation reveals fluctuations in the width of the primary channel to the active site that are large enough to admit substrates. Alternative entries to the active site through the side walls of the gorge have been detected in a number of structures. This suggests that transport of solvent molecules participating in catalysis can occur across the porous wall, contributing to the efficiency of the enzyme.
Kinase Conformations: A Computational Study of the Effect of Ligand Binding
Volkhard Helms and J. Andrew McCammon
Protein function is often controlled by ligand-induced conformational transitions. Yet, in spite of the increasing number of three-dimensional crystal structures of proteins in different conformations, not much is known about the driving forces of these transitions. As an initial step towards exploring the conformational and energetic landscape of protein kinases by computational methods, intramolecular energies and hydration free energies were calculated for different conformations of the catalytic domain of cAMP-dependent protein kinase (cAPK) with a continuum (Poisson) model for the electrostatics. Three protein kinase crystal structures for ternary complexes of cAPK with the peptide inhibitor PKI(5-24) and ATP or AMP-PNP were modelled into idealized intermediate and open conformations. Concordant with experimental observation, we find that the binding of PKI(5-24) is more effective in stabilizing the closed and intermediate forms of cAPK than ATP. PKI(5-24) seems to drive the final closure of the active site cleft from intermediate to closed state since ATP does not distinguish between these two states. Binding of PKI(5-24) and ATP is energetically additive.
A Continuum Solvation Model for Studying Protein Hydration Thermodynamics at High Temperatures
A.H. Elcock and J.A. McCammon
A macroscopic solvation model which combines a solvent-accessible surface area term to describe hydration of non-polar groups with a continuum electrostatics term to describe the hydration of polar groups has previously been shown to provide an excellent description of amino acid hydration free energies at 25 degrees centigrade (Sitkoff et al. 1994, J. Phys. Chem. vol. 98. pp. 1978-1988). We describe here the extension of this method and its accompanying parameter set (known as PARSE) to handle temperatures in the range from 5 degrees to 100 degrees centigrade. For the neutral amino acids, hydration free energies were taken from the literature; for the charged amino acids Asp, Glu, and Lys, hydration free energies were obtained by combining results for the neutral analogues with information on the pKa value at the required temperature. An important result of this analysis is that the hydration free energies of the charged residues are much more strongly affected by increasing temperature than their neutral analogues. In extending the PARSE method to reproduce hydration free energies over a range of temperatures, a number of alternative models were investigated: best results were obtained when separate surface area dependent terms were used to represent the hydration of aliphatic and aromatic regions and when the continuum electrostatics term was made strongly temperature dependent. The temperature dependence of the electrostatic component stems partly from changes in the dielectric constant of water, but appears to be rather better described when the atomic radii are also made temperature dependent, increasing in size as the temperature rises. This requirement for temperature dependent radii gains important support from previous studies using the Born model to descibe the entropies of hydration of simple ions. The extension of the PARSE method described here permits its use in investigating the effects of hydration on protein stability over a wide range of biologically-relevant temperatures.
pH Dependence of Antibody/Lysozyme Complexation
C.J. Gibas, S. Subramaniam, J.A. McCammon, B.C. Braden and R.J. Poljak
Association between proteins often depends on the pH and ionic strength conditions of the medium in which it takes place. This is especially true in complexation involving titratable residues at the complex interface. Continuum electrostatics methods were used to calculate the pH-dependent energetics of association of hen-egg lysozyme with two closely related monoclonal antibodies raised against it and the association of these antibodies against an avian species variant. A detailed analysis of the energetic contributions reveals that even though the hallmark of association in the two complexes is the presence of conserved charged-residue interactions, the environment of these interactions significantly influences the titration behavior and concomitantly the energetics. The contributing factors include, minor structural rearrangements, buried interfacial area, dielectric environment of the key titratable residues and the geometry of the residue dispositions. Modeled structures of several mutant complexes were also studied so as to further delineate the contribution of individual factors to the titration behavior.
Electrostatic Channeling of Substrates Between Enzyme Active Sites: Comparison of Simulation and Experiment
A.H. Elcock, G.A. Huber and J.A. McCammon
Recent simulation work has indicated that channeling of charged substrates between the active sites of bifunctional enzymes or bienzyme complexes can be significantly enhanced by favorable interactions with the electrostatic field of the enzymes. The results of such simulations are expressed in terms of transfer efficiencies, which describe the probability that substrate leaving the active site of the first enzyme will reach the active site of the second enzyme before escaping out into bulk solution. The experimental indicators of channeling on the other hand, are factors such as a decrease in the transient (lag) time for appearance of the final product of the coupled enzyme reaction, or a decreased susceptibility of the overall reaction rate to the presence of competing enzymes or competitive inhibitors. The work reported here aims to establish a connection between the transfer efficiencies obtained from simulation, with the above-mentioned experimental observables. We accomplish this by extending previously reported analytical approaches to combine the simulated transfer efficiency with the Michaelis-Menten kinetic parameters Km and Vmax of the enzymes involved; expressions are derived to allow both transient times and steady state rates to be calculated. We then apply these results to the two systems which have been studied both theoretically and experimentally. In the first case, that of the bifunctional enzyme dihydrofolate reductase-thymidylate synthase (DHFR-TS), the experimentally observed decrease in transient times is found to be consistent with a transfer efficiency of greater than or equal to 80%. In the second case, that of a citrate synthase-malate dehydrogenase (CS-MDH) fusion protein, a transfer efficiency of 73% is consistent with the experimental transient time measurements. Separate and independent analysis of the effects of adding the competing enzyme aspartate aminotransferase (AAT) gives a transfer efficiency of 69%, in excellent agreement with the transient time results. The transfer efficiencies thus obtained from experimental results are in both cases in reasonable agreement with those obtained from simulation. One important discrepancy between simulation and experiment is however found in the reported effects of adding a competitive inhibitor in the DHFR-TS system: qualitatively different results are expected from the theoretical analysis. A possible reason for this apparent contradiction is discussed.
Parallel Version of the Combined Quantum Classical Molecular Dynamics Code for Complex Molecular and Biomolecular Systems
P. Bała, T. Clark, P. Grochowski, B. Lesyng and J.A. McCammon
In "Recent Advances in Parallel Virtual Machine and Message Passing Interface," M. Bubak, J. Dongarra, J. Wasniewski, Eds., (Lecture Notes in Computer Science 1332), Springer-Verlag Berlin-Heidelberg, pp. 409-416 (1997)
A Quantum-Classical Molecular Dynamics model (QCMD) and its parallel version are presented. PFortran and MPI were used in the parallelization process. The code was tested on Cray T3D and Cray T3E computers. The execution time scales almost linearly with the number of processors, which ensures the high efficiency of the presented method.
Quantum Classical Molecular Dynamics Simulation of Phospholipid Hydrolysis
P. Bała, P. Grochowski, B. Lesyng and J.A. McCammon
Recent advances in the use of quantum dynamical simulations for the study of enzymatic catalytis are described.