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Anti-Insulin Antibody Structure and Conformation. II. Molecular Dynamics With Explicit Solvent
John J. Tanner, Laura J. Nell and J. Andrew McCammon
Molecular dynamics at 300 K was used as a conformation searching tool to analyze a knowledge-based structure prediction of an anti-insulin antibody. Solvation effects were modeled by packing water molecules around the antigen binding loops. Some loops underwent backbone and side-chain conformational changes during the 95-ps equilibration, and most of these new, lower potential energy conformations were stable during the subsequent 200-ps simulation. Alterations to the model include changes in the intraloop, main-chain hydrogen bonding network of loop H3, and adjustments of Tyr and Lys side chains of H3 induced by hydrogen bonding to water molecules. The structures observed during molecular dynamics support the conclusion of the previous paper that hydrogen bonding will play the dominant role in antibody-insulin recognition. Determination of the structure of the antibody by x-ray crystallography is currently being pursued to provide an experimental test of these results. The simulation appears to improve the model, but longer simulations at higher temperatures should be performed.
Anti-Insulin Antibody Structure and Conformation. I. Molecular Modeling and Mechanics of an Insulin Antibody
Laura J. Nell, J. Andrew McCammon and Shankar Subramaniam
A knowledge-based three-dimensional model of an anti-insulin antibody, 125, was constructed using the structures of conserved residues found in other known crystallographic immunoglobulins. Molecular modeling and mechanics were done with the 125 amino acid sequences using QUANTA and CHARMm on a Silicon Graphics 4D70GT workstation. A minimal model was made by scaffolding using crystallography coordinates of the antibody HyHEL-5, because it had the highest amino acid sequence homology with 125 (84% light chain, 65% heavy chain). The three hypervariable loop turns that are longer in 125 than in HyHEL-5 (L1, L3, and H3) were modeled separately and incorporated into the HyHEL-5 structure; then other amino acid substitutions were made and torsions optimized. The 125 model maintains all the structural attributes of an antibody and the structures conserved in known antibodies. Although there are many polar amino acids (especially serines) in this site, the overall van der Waals surface shape is determined by positions of aromatic side chains. Based on this model, it is suggested that hydrogen bonding may be key in the interaction between the human insulin A chain loop antigenic epitope and 125.
Kinetic Effects of Multiple Charge Modifications in Enzyme-Substrate Reactions: Brownian Dynamics Simulations of Cu, Zn Superoxide Dismutase
Jacqueline J. Sines, J. Andrew McCammon and Stuart A. Allison
We used Brownian dynamics simulations of substrate O2- encounters with the enzyme bovine erythrocyte Cu, Zn superoxide dismutase (SOD) to study the effects of multiple charge modifications in the enzyme on the kinetics of its diffusion-controlled reaction. When the charges of two or three residues were changed, the calculated rate consant relative to that for the unmodified enzyme was usually found to be the product of relative rate constants for the enzymes with the corresponding single-site changes. This "multiplicativity" rule may be useful in the design of enzymes that operate with diffusion-controlled kinetics. Residues that deviate from the general rule are found in the active site channel of SOD, and the origin of these deviations is considered.
Parallel Molecular Dynamics
T.W. Clark, J.A. McCammon and L.R. Scott
In "Proc. Fifth SIAM Conf. on Parallel Proc. for Sci. Comp.," J. Dongarra, et al., Eds., SIAM, Philadelphia, pp. 338-344 (1992, refereed)
A Comparative Study of Time Dependent Quantum Mechanical Wavepacket Evolution Methods
Thanh N. Truong, John J. Tanner, Piotr Bała, J. Andrew McCammon, Donald J. Kouri, Bogdan Lesyng and David K. Hoffman
We present a detailed comparison of the efficiency and accuracy of the second- and third-order split operator methods, a time dependent modified Cayley method, and the Chebychev polynomial expansion method for solving the time dependent Schrodinger equation in the one-dimensional double well potential energy function. We also examine the efficiency and accuracy of the split operator and modified Cayley methods for the imaginary time propagation.
Binding of an Antiviral Agent to a Sensitive and a Resistant Human Rhinovirus. Computer Simulation Studies with Sampling of Amino Acid Side-chain Conformations. I. Mapping the Rotamers of Residue 188 of Viral Protein 1
Rebecca C. Wade and J. Andrew McCammon
The mutation of valine 188 to leucine in the viral protein 1 of human rhinovirus 14 renders the virus resistant to certain antiviral compounds. Thermodynamic-cycle perturbation theory provides a means of calculating the difference in the binding free energies of an antiviral compound to the wild-type virus and to the mutant virus. In calculating the relevant free-energy differences in molecular dynamics simulations, it is important to sample the multiple rotational isomers of residue 188 correctly. In general, these rotamers will not be fully sampled during a single molecular dynamics simulation. However, the contributions of all the rotamers to the free-energy differences associated with mutation of residue 188 may be considered explicitly once they have been identified and their relative free energies determined.
Binding of an Antiviral Agent to a Sensitive and a Resistant Human Rhinovirus. Computer Simulation Studies with Sampling of Amino Acid Side-chain Conformations. II. Calculation of Free Energy Differences by Thermodynamic Integration
Rebecca C. Wade and J. Andrew McCammon
Thermodynamic-cycle perturbation theory and molecular dynamics simulations were used to calculate the difference in the free energy of binding of the antiviral compound WIN53338 to the wild-type human rhinovirus 14 and to a drug-resistant mutant of the virus in which valine 188 of the viral protein 1 is mutated to leucine. Because of the difficulty of achieving adequate sampling of all of the rotational isomers of amino acid side-chains in molecular dynamics simulations, an explicit treatment of the effects of the existence of multiple rotational isomers of residue 188 on the calculated free energies was used. The rotamers of residue 188 were first mapped by steric and energetic techniques as described in the accompanying article. Thermodynamic integration was then carried out during simulations of the virus, both with and without the antiviral compound bound, by mutating residue 188 while restraining its side-chain to one conformation. The contributions of the other rotamers of residue 188 to the free-energy changes for this mutation were then added to those calculated by thermodynamic integration as correction factors. Binding of WIN53338 to the wild-type virus was calculated to be favored over binding to the mutant virus by 1.7(±3.0) kcal/mol. This is consistent with experimental data which, if differences in activity are assumed to be due to differences in binding, indicate that the binding affinity of WIN53338 for the wild-type virus is at least 0.15 to 1.7 kcal/mol greater than for the mutant virus. Thermodynamic integration was also performed in the conventional manner without restraints and was found to give less accurate results.
T.P. Straatsma and J.A. McCammon
Understanding the differences in behavior of different chemical systems isa central goal of chemistry. Investigators would like, for example, to predict and explain the relative affinity of different ligands for a given receptor, the relative electrode potentials of different substances, and the relative rates of reaction of different sets of reactants. This review appraises the thermodynamic cycle free energy methods, which have recently become a popular tool for calculating and analyzing such differences. These methods were originally introduced in connection with the ligand binding problem (1, 2). As Figure 1 and Equation 1 indicate, the relative free energy of binding ligands L2 and L1 to receptor R is equal to the relative free energy for interconversions of the ligands in and away from the receptor binding site ΔG2 - ΔG1 = ΔG4 - ΔG3.
Ab Initio Studies and Quantum-Classical Molecular Dynamics Simulations for Proton Transfer Processes in Model Systems and in Enzymes
Piotr Bała, Bogdan Lesyng, Thanh N. Truong and J.A. McCammon
In "Molecular Aspects of Biotechnology: Computational Models and Theories," J. Bertran, Ed., NATO, pp. 299-326 (1992)
A Combined Quantum-Classical Dynamics Method for Calculating Thermal Rate Constants of Chemical Reactions in Solution
Thanh N. Truong, J. Andrew McCammon, Donald J. Kouri and David K. Hoffman
We present a combined quantum-classical-stochastic dynamics method based on the flux-flux correlation function for calculating the thermal rate constants of chemical reactions in solution or in biological systems. The present method is an extension of an earlier method by Metiu and co-workers [J. Chem. Phys. 88, 2478 (1988)] to include stochastic dynamics. The method is tested by applying it to a simple model of hydrogen atom transfer reaction in solution. We also examine the behavior of the flux-flux correlation function and the rate constants as functions of viscosity.
Electrostatic Energy Calculations by a Finite-Difference Method: Rapid Calculation of Charge-Solvent Interaction Energies
Brock Luty, Malcolm E. Davis and J. Andrew McCammon
Finite-difference Poisson-Boltzmann (FDPB) methods allow a fast and accurate calculations of the reaction field (charge-solvent) energies for molecular systems. Unfortunately, the energy in the FDPB calculations includes the self-energies and the finite-difference approximation to the Coulombic energies as well as the reaction field energy. A second finite-difference calculation, in a uniform dielectric, is therefore necesssary to eliminate these contributions. In this article we describe a rapid and accurate method to calculate the self energy and finite-difference Coulombic energies in a uniform dielectric thus eliminating the need for a second finite-difference calculation. The computational savings for this method range from a factor of 4 for a typical protein to a factor of 103 for small molecules.
Continuum Model Calculations of Solvation Free Energies: Accurate Evaluation of Electrostatic Contributions
V. Mohan, M.E. Davis, J.A. McCammon and B.M. Pettitt
The electrostatic contributions to free energies of solvation of several small molecules have been calculated, treating the solvent as a statistical continuum. The computational method is based on solving the linearized Poisson-Boltzmann equation for the electrostatic potentials using the finite-difference scheme. A careful study of convergence indicates the importance of a fine grid spacing, as well as the short comings of rotational averaging. The computed free energies of solvation are in excellent agreement with the experimental results as well as the free energy perturbation calculations. The free energies of hydration of the natural nucleic acid bases are calculated and shown to be somewhat sensitive to charge model.
Computation Unravels Mysteries of Molecular Biophysics
James M. Briggs and J. Andrew McCammon
Solving the Finite-Difference Non-Linear Poisson-Boltzmann Equation
Brock A. Luty, Malcolm E. Davis and J. Andrew McCammon
The Poisson-Boltzmann equation can be used to calculate the electrostatic potential field of a molecule surrounded by a solvent containing mobile ions. The Poisson-Boltzmann equation is a non-linear partial differential equation. Finite-difference methods of solving this equation have been restricted to the linearized form of the equation or a finite number of non-linear terms. Here we introduce a method based on a variational formulation of the electrostatic potential and standard multi-dimensional maximization methods that can be used to solve the full non-linear equation.
Poisson-Boltzmann Analysis of the Lambda Repressor-Operator Interaction
Martin Zacharias, Brock A. Luty, Malcolm E. Davis and J. Andrew McCammon
A theoretical study of the ion atmosphere contribution to the binding free energy of the lambda repressor-operator complex is presented. The finite-difference form of the Poisson-Boltzmann equation was solved to calculate the electrostatic interaction energy of the amino-terminal domain of the lambda repressor with a 9 or 45 base pair oligonucleotide. Calculations were performed at various distances between repressor and operator as well as at different salt concentrations to determine ion atmosphere contributions to the total electrostatic interaction. Details in the distribution of charges on DNA and protein atoms had a strong influence on the calculated total interaction energies. In contrast, the calculated salt contributions are relatively insensitive to changes in the details of the charge distribution. The results indicate that the ion atmosphere contribution favors association at all protein-DNA distances studied. The theoretical number of ions released upon repressor-operator binding appears to be in reasonable agreement with experimental data.
Holonomic Constraint Contributions to Energy Differences from Thermodynamic Integration Molecular Dynamics Simulations
T.P. Straatsma, M. Zacharias and J.A. McCammon
A method is presented for the evaluation of holonomic constraint contributions to free energy differences obtained from molecular dynamics simulations. The method is used with the thermodynamic integration technique in which analytical derivatives of the Hamiltonian are evaluated. The free energy contributions are shown to be easily derived from the constraint forces that can be evaluated from the SHAKE coordinate corrections. The problem of poor statistical accuracy associated with the creation or annihilation of atoms can be treated using a sprouting/desprouting technique, in which it is essential to be able to evaluate constraint contributions to free energy differences. This is illustrated for the mutation of ethanol to ethane in aqueous solution and in vacuo. For this system, experimental free energies of hydration are compared with the calculated values using different sprouting/desprouting protocols.
J. Andrew McCammon
In 1976, Albery and Knowles introduced the useful concept of kinetic perfection in enzymes. By one criterion, an enzyme is said to have evolved to perfection if it catalyses the conversion of substrate to product as rapidly as the former diffuses to the active site of the enzyme under physiological conditions. The question naturally arises as to whether one can redesign an enzyme to surpass this evolutionary limit. Theoretical studies have suggested that this might be possible, for example by modifying residues at the surface of an enzyme to create an electrostatic field that improves the steering of charged substrate molecules to the active site. Getzoff and colleagues have now proven in the laboratory that an enzyme can be redesigned successfully along these lines. This work raises interesting fundamental and practical questions concerning the activity of enzymes.
Diffusive Reaction Rates from Brownian Dynamics Simulations: Replacing the Outer Cutoff Surface by an Analytical Treatment
Brock A. Luty, J. Andrew McCammon and Huan-Xiang Zhou
The algorithm of Northrup, Allison, and McCammon [J. Chem. Phys. 80, 1517 (1984)] for calculating diffusive reaction rates using Brownian dynamics simulations is reexamined. A new method is described in which a time-consuming portion of the algorithm is replaced by an analytical solution. When applied to two illustrative model systems, the new method is found to reduce the computational work by a factor of 2 or more.