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A Molecular Mechanics/Grid Method for Evaluation of Ligand-Receptor Interactions
Brock A. Luty, Zelda R. Wasserman, Pieter F.W. Stouten, C. Nicholas Hodge, Martin Zacharias and J. Andrew McCammon
We present a computational method for prediction of the conformation of a ligand when bound to a macromolecular receptor. The method is intended for use in systems in which the approximate location of the binding site is known and no large-scale rearrangements of the receptor are expected upon formation of the complex. The ligand is initially placed in the vicinity of the binding site and the atomic motions of the ligand and binding site are explicitly simulated, with solvent represented by an implicit solvation model and using a grid representation for the bulk of the receptor protein. These two approximations make the method computationally efficient and yet maintain accuracy close to that of an all-atom calculation. For the benzamidine/trypsin system, we ran 100 independent simulations, in many of which the ligand settled into the low-energy conformation observed in the crystal structure of the complex. The energy of these conformations was lower than and well-separated from that of others sampled. Extensions of this method are also discussed.
Conservative and Nonconservative Mutations in Proteins: Anomalous Mutations in a Transport Receptor Analyzed by Free Energy and Quantum Chemical Calculations
William R. Cannon, James M. Briggs, Jian Shen, J. Andrew McCammon and Florante A. Quiocho
Experimental studies on a bacterial sulfate receptor have indicated anomalous relative binding affinities for the mutations Ser(130) -> Cys, Ser(130) -> Gly, and Ser(130) -> Ala. The loss of affinity for sulfate in the former mutation was previously attributed to a greater steric effect on the part of the Cys side chain relative to the Ser side chain, whereas the relatively small loss of binding affinity for the latter two mutations was attributed to the loss of a single hydrogen bond. In this report we present quantum chemical and statistical thermodynamic studies of these mutations. Qualitative results from these studies indicate that for the Ser(130) -> Cys mutation the large decrease in binding affinity is in part caused by steric effects, but also significantly by the differential work required to polarize the Cys thiol group relative to the Ser hydroxyl group. The Gly mutant cobinds a water molecule in the same location as the Ser side chain resulting in a relatively small decrease in binding affinity. Results for the Ala mutant are in disagreement with experimental results but are likely to be limited by insufficient sampling of configuration space due to physical constraints applied during the simulation.
Binding of Cations and Protons in the Active Site of Acetylcholinesterase
Stanislaw T. Wlodek, Jan Antosiewicz, J. Andrew McCammon and Michael K. Gilson
The active site of acetylcholinesterase contains a number of ionizable residues. The pKas of the catalytic histidine, His 440, is believed to be 6.3, based upon enzyme kinetic studies. However, the pKas of the other residues have not been measured. Here, we describe aclculations of the pKa of the ionizable groups in this enzyme. Interestingly, the initial calculations predict a pKa of 9.3 for His 440. The deviation of 3 pKa units from the measured pKa is traceable to the influence of Glu 199 and Glu 443 upon His 440. We argue that the deviation does not represent a failure of the computational method. Rather it points to the need for an adjustment in the model of the protein. The adjustment we suggest involves a monovalent cation bound in the active site, near Glu 199 and His 440. Including such a cation in the calculations brings the computed pKa of His 440 into agreement with the measured value. Futhermore, the idea that a bound cation substantially reduces the pKa of His 440 leads to satisfying explantions of a number of otherwise puzzling experimental data.
Acetylcholinesterase: Diffusional Encounter Rate Constants for Dumbbell Models of Ligand
Jan Antosiewicz, Michael K. Gilson, Irwin H. Lee and J. Andrew McCammon
For some enzymes, virtually every substrate molecule that encountersthe entrance to the active site proceeds to reaction, at lowsubstrate concentrations. Such diffusion-limited enzymes displayhigh apparent bimolecular rate constants ((kcat/KM)), whichdepend strongly upon solvent viscosity. Some experimental studiesprovide evidence that acetylcholinesterase falls into this category.Interestingly, the asymmetric charge distribution of acetylcholinesterase,apparent from the crystallographic structure, suggests thatits electrostatic field accelerates the encounter of its cationicsubstrate, acetylcholine, with the entrance to the active site.Here we report simulations of the diffusion of substrate inthe electrostatic field of acetylcholinesterase. We find thatthe field indeed guides the substrate to the mouth of the activesite. The computed encounter rate constants depend upon theparticular relative geometries of substrate and enzyme thatare considered to represent successful encounters. With loosereaction criteria, the computed rates exceed those measuredexperimentally, but the rate constants vary appropriately withionic strength. Although more restrictive reaction criterialower the computed rates, they also lead to unrealistic variationof the rate constants with ionic strength. That these simulationsdo not agree well with experiment suggests that the simple diffusionmodel is incomplete. Structural fluctuations in the enzyme orevents after the encounter may well contribute to rate limitation.
Parallelization of Poisson-Boltzmann and Brownian Dynamics Calculations
A. Ilin, B. Bagheri, L.R. Scott, J.M. Briggs and J.A. McCammon
American Chemical Society Symposium Series, No. 592, pp. 170-185 (1995)
Quantum-Classical Molecular Dynamics and Its Computer Implementation
P. Bała, P. Grochowski, B. Lesyng and J.A. McCammon
Quantum-classical and quantum-stochastic molecular dynamics (QCMD/QSMD) models are formulated and applied for quantum proton transfer processes. The protein dynamics are described by the time-dependent Schroedinger equation and the motion of classical atoms by the Newtonian or Langevin equations of motion. Instantaneous positions of the classical atoms determine the potential energy surface for the proton dynamics. In turn, the proton wavefunction influences the classical atoms through nonstationary Hellmann-Feynman forces (Bala et al., 1994c). The QCMD/QSMD algorithm is described and numerical results for a proton-bound ammonia-ammonia dimer and an enzyme, phospholipase A2, are presented. In the case of the enzyme molecule a valence-bond orbital method is used to compute the potential energy function for the proton transfer. The methods are found to be promising tools in studies of molecular and enzymatic reactions in which quantum-dynamical effects cannot be neglected.
Secondary Structure Prediction of the H5-Pore of Potassium Channels
K.V. Soman, J.A. McCammon and A.M. Brown
The 'H5' segment located between the putative fifth and sixth transmembrane helices is the most highly conserved region in voltage-gated potassium channels and it is believed to constitute a major part of the ion conduction path (pore). Here we present a two-step procedure, comprising secondary structure prediction and hydrophobic moment profiling, to predict the structure of this important region. Combined results from the application of the procedure to the H5 region of four voltage-gated and five other K+ channel sequences lead to the prediction of a β-strand-turn-(3-strand) structure for H5. The reasons for the application of these soluble protein methods to parts of membrane proteins are: (i) that pore-lining residues are accessible to water and (ii) that a large enough database of high-resolution membrane protein structures does not yet exist. The results are compared with experimental results, in particular spectroscopic studies of two peptides based on the H5 sequence of SHAKER potassium channel. The procedure developed here maybe applicable to water accessible regions of other membrane proteins.
Molecular Dynamics Simulation with a Continuum Electrostatic Model of the Solvent
Michael K. Gilson, J. Andrew McCammon and Jeffry D. Madura
The accuracy and simplicity of the Poisson-Boltzmann electrostatics model has led to the suggestion that it might offer an efficient solvent model for use in molecular mechanics calculations on biomolecules. We report a successful merger of the Poisson-Boltzmann and molecular dynamics approaches, with illustrative calculations on the small solutes dichloroethane and alanine dipeptide. The algorithm is implemented within the program UHBD. Computational efficiency is achieved by the use of rather coarse finite difference grids to solve the Poisson-Boltzmann equation. Nonetheless, the conformational distributions generated by the new method agree well with reference distributions obtained as Boltzmann distributions from energies computed with fine finite difference grids. The conformational distributions also agree well with the results of experimental measurements and conformational analyses using more detailed solvent models. We project that when multigrid methods are used to solve the finite difference problem and the algorithm is implemented on a vector supercomputer, the computation of solvent electrostatic forces for a protein of modest size will add only about 0.1 s computer time per simulation step relative to a vacuum calculation.
Simulation of Charge-Mutant Acetylcholinesterases
Jan Antosiewicz, J. Andrew McCammon, Stanislaw T. Wlodek and Michael K. Gilson
A recent experimental study of human acetylcholinesterase has shown that the mutation of surface acidic residues has little effect on the rate constant for hydrolysis of acetylthiocholine. It was concluded, on this basis, that the reaction is not diffusion controlled and that electrostatic steering plays only a minor role in determining the rate. Here we examine this issue through Brownian dynamics simulations on Torpedo californica acetylcholinesterase in which the surface acidic residues homologous with those mutated in the human enzyme are artificially neutralized. The computed effects of the mutations on the rate constants reproduce quite well the modest effects of the mutations upon the measured encounter rates. Nonetheless, the electrostatic field of the enzyme is found to increase the rate constants by about an order of magnitude in both the wild type and the mutants. We therefore conclude that the mutation experiments do not disprove that electrostatic steering substantially affects the catalytic rate of acetylcholinesterase.
Free Energy Simulations of the HyHEL-10/HEL Antibody-Antigen Complex
R. Pomés, R.C. Willson and J.A. McCammon
Free energy simulations are reported for the N31L-D mutation, both in the HyHEL-10-HEL antibody-lysozyme complex and in the unliganded antibody, using the thermo-dynamic-cycle perturbation method. The present study suggests that the mutation would change the free energy of binding of the complex by -5.6 kcal/mol (unrestrained free energy simulations), by -0.5 kcal/mol (free energy simulations with a restrained backbone) and by 1.8 kcal/mol (Poisson-Boltzmann calculations, which also use a restrained geometry model). A detailed structural analysis helps in estimating the contributions from various residues and regions of the system. Enhanced recognition of HEL by the mutant HyHEL-10 would arise from the combination of thermodynamically more favorable conformational changes of the CDR loops upon association and subsequent charge pairing with Lys96 in the antigen.
Electrostatics and Diffusion of Molecules in Solution: Simulations with the University of Houston Brownian Dynamics Program
Jeffry D. Madura, James M. Briggs, Rebecca C. Wade, Malcolm E. Davis, Brock A. Luty, Andrew Ilin, Jan Antosiewicz, Michael K. Gilson, Babak Bagheri, L. Ridgway Scott and J. Andrew McCammon
This paper is a follow-up to the initial communication (Comput. Phys. Commun. 62 (1991) 187-197) on the Brownian Dynamics/Electrostatics program UHBD developed at the University of Houston. The program is now capable of computing pKas of ionizable groups in proteins, performing Brownian dynamics simulations with a flexible substrate and target, and molecular mechanics/dynamics calculations using a continuum solvent. These new capabilities and other features are discussed along with selected applications which illustrate the capabilities of the current version of UHBD.
Computer Modeling of Acetylcholinesterase and Acetylcholinesterase-Ligand Complexes
S.T. Wlodek, J. Antosiewicz, M.K. Gilson, J.A. McCammon, T.W. Clark and L.R. Scott
Determination of the pKa Values of Titratable Groups of an Antigen-Antibody Complex: HyHEL5-HEL
Shawn M. McDonald, Richard C. Willson and J. Andrew McCammon
The titration behavior of the ionizable residues of the HyHEL-5-hen egg lysozyme complex and its individual components has been studied using continuum electrostatic calculations. Several residues of HyHEL-5 had pKa values shifted away from model values for isolated residues by more than three pH units. Shifts away from the model values were smaller for the residues of hen egg lysozyme. A moderate variation in the pKa values of the titratable groups was observed upon increase of the ionic strength from 0 to 100 mM, amounting to 1-2 pH units in most cases. Under physiological conditions, the net charge of HyHEL-5 was opposite that for hen egg lysozyme. Several residues, including those involved in the Arg-Glu salt bridges that have been proposed to be important in antibody-antigen binding, had pKa values that were changed significantly upon binding. The main titration event upon antibody-antigen binding appears to be loss of a proton from residue GluH50 of the Fv molecule. The limitations of our calculation methods and the role they might play in the design of antibodies for use in assays, sensors and separations are discussed
Electrostatic and Hydrodynamic Orientational Steering Effects in Enzyme-Substrate Association
J. Antosiewicz and J.A. McCammon
Diffusional encounters between a dumbbell model of a cleft enzyme and a dumbbell model of an elongated ligand are simulated by Brownian dynamics. The simulations take into account electrostatic and hydrodynamic interactions between the molecules. It is shown that the primary effect of inclusion of hydrodynamic interactions into the simulation is an overall decrease in the rate constant. Hydrodynamic orientational effects are of modest size for the systems considered here. They are manifested when changes in the rate constants for diffusional encounters favored by hydrodynamic interactions are compared with those favored by electrostatic interactions as functions of the overall strength of electrostatic interactions. The electrostatic interactions modify the hydrodynamic torques by modifying the drift velocity of the substrate toward the enzyme. We conclude that simulations referring only to electrostatic interactions between an enzyme and its ligand may yield rate constants that are somewhat (e.g., 20%) too high, but provide realistic descriptions of the orientational steering effects in the enzyme-ligand encounters.
I/O Limitations in Parallel Molecular Dynamics
Terry W. Clark, L. Ridgway Scott, Stanislaw Wlodek and J. Andrew McCammon
We discuss data production rates and their impact on the performance of scientific applications using parallel computers. On one hand, too high rates of data production can be overwhelming, exceeding logistical capacities for transfer, storage and analysis. On the other hand, the rate limiting step in a computationally-based study should be the human-guided analysis, not the calculation. We present performance data for a biomolecular simulation of the enzyme, acetylcholinesterase, which uses the parallel molecular dynamics program EulerGROMOS. The actual production rates are compared against a typical time frame for results analysis where we show that the rate limiting step is the simulation, and that to overcome this will require improved output rates.
Sequence Dependent Hydration of DNA: Theoretical Results
Adrian H. Elcock and J. Andrew McCammon
Hydration effects are crucial to the static and dynamic behabior of DNA and its interactions with other molecules. DNA hydration has been studied by a variety of experimental methods: X-ray crystallography, NMR spectroscopy, voumetric, and densitometric techniques have all been employed. Despited such studies, however, there is little experimental data regarding specifically the thermodynamics of hydration, largely because of the difficulties in spearating out effects due soley to hydration from those due to other causes. Drug-DNA binding equilibria, for example, are governed by energetics of the drug-DNA interaction itself, conformational changes in the drug and/or the DNA, and effects due to changes in the ionic atmosphere, in addition to those resulting soley from changes in hydration. In this paper we use a theoretical method to focus entirely on this latter aspect and report on the sequence dependence of solvation free energies calculated for DNA oligonucleotides.
Quantum Mechanical Simulation Methods for Studying Biological Systems
P. Bała, P. Grochowski, B. Lesyng and J.A. McCammon
Les Houches Physics Schools Series, Springer Verlag, Berlin, pp. 119-156 (1995)