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Molecular Dynamics Computations and Solid State Nuclear Magnetic Resonance of the Gramicidin Cation Channel
S.-W. Chiu, L.K. Nicholson, M.T. Brenneman, S. Subramaniam, Q. Teng, J.A. McCammon, T.A. Cross and E. Jakobsson
This paper reports on a coupled approach to determining the structure of the gramicidin A ion channel, utilizing solid state nuclear magnetic resonance (NMR) of isotopically labeled gramicidin channels aligned parallel to the magnetic field direction, and molecular dynamics (MD). MD computations using an idealized right-handed beta-helix as a starting point produce a refined molecular structure that is in excellent agreement with atomic resolution solid state NMR data. The data provided by NMR and MD are complementary to each other. When applied in a coordinated manner they provide a powerful approach to structure determination in molecular systems not readily amenable to x-ray diffraction.
Molecular Recognition, Encounter and Complex Formation in Solution
In "Theoretical Biochemistry and Molecular Biophysics, Vol. 2: Proteins," D.L. Beveridge and R. Lavery, Eds., Adenine Press, pp. 121-130 (1991)
Vector Optimization of AMBER 3.0 on the NEC SX2-400 Supercomputer
Michael J. Mitchell and J. Andrew McCammon
The AMBER 3.0 molecular mechanics and molecular dynamics programs have been ported to and vectorized on the NEC SX-2/400 supercomputer. A detailed discussion of the vector enhancement of the AMBER non-bonded pair list generation subroutine is presented. Automatic vectorization using the FORT77SX compiler yielded speed-up factors of 1.2 to 1.5 over unvectorized code. Recoding of key portions of the program, as described in this paper, yielded speed-up factors of 1.8-2.7. The perturbation molecular dynamics program, PERDYN, now runs up to 35 times faster on the SX-2/400 than the VAX optimized version of the same program runs on the VAX 8650.
Electrostatics and Diffusion of Molecules in Solution: Simulations with the University of Houston Brownian Dynamics Program
Malcolm E. Davis, Jeffry D. Madura, Brock A. Luty and J. Andrew McCammon
Brownian dynamics simulations are not new, but typically progrmas have been written for specific systems. In this paper, we describe a general-purpose Brownian dynamics program that has been developed at the University of Houston. The program can simulate the diffusion of flexible chains. The rates of diffusion-controlled reactions can be calculated for arbitrary reaction geometries. Electrostatic interactions among the diffusing species are modeled by the use of finite difference solutions of the linearized Poisson-Boltzmann equation. The program can also be used for electrostatic force and energy calculations. Provisions are made for coordinate and parameter manipulations. The basic structure of the program and its functionality are discussed and some example applications are cited.
Time-Correlation Analysis of Simulated Water Motion in Flexible and Rigid Gramicidin Channels
See-Wing Chiu, Eric Jakobsson, Shankar Subramaniam and J. Andrew McCammon
Molecular dynamics simulations have been done on a system consisting of the polypeptide membrane channel former gramicidin, plus water molecules in the channel and caps of waters at the two ends of the channel. In the absence of explicit simulation of the surrounding membrane, the helical form of the channel was maintained by artificial restraints on the peptide motion. The characteristic time constant of the artificial restraint was varied to assess the effect of the restraints on the channel structure and water motions. Time-correlation analysis was done on the motions of individual channel waters and on the motions of the center of mass of the channel waters. It is found that individual water molecules confined in the channel execute higher frequency motions than bulk water, for all degrees of channel peptide restraint. The center-of-mass motion of the chain of channel waters (which is the motion that is critical for transmembrane transport, due to the mandatory single filing of water in the channel) does not exhibit these higher frequency motions. The mobility of the water chain is dramatically reduced by holding the channel rigid. Thus permeation through the channel is not like flow through a rigid pipe; rather permeation is facilitated by peptide motion. For the looser restraints we used, the mobility of the water chain was not very much affected by the degree of restraint. Depending on which set of experiments is considered, the computed mobility of our water chain in the flexible channel is four to twenty times too high to account for the experimentally measured resistance of the gramicidin channel to water flow. From this result it appears likely that the peptide motions of an actual gramicidin channel embedded in a lipid membrane may be more restrained than in our flexible channel model, and that these restraints may be a significant modulator of channel permeability. For the completely rigid channel model the "trapping" of the water molecules in preferred positions throughout the molecular dynamics run precludes a reasonable assessment of mobility, but it seems to be quite low.
Free Energy Difference Calculations by Thermodynamic Integration: Difficulties in Obtaining a Precise Value
Michael J. Mitchell and J. Andrew McCammon
Free energy difference calculations have been performed by the "slow growth" method of thermodynamic integration of the AMBER 3.0 molecular dynamics program for the mutation of a conformationally restricted threonine dipeptide, N-acetyl threonyl-N-methylamide, to the corresponding alanyl dipeptide. By varying the total simulation length, it has been determined that precise free energy values are obtained only for simulations of greater than 100 ps total simulation time length. By varying the starting configurations for simulations of the same length, it has been determined that averaging the free energies obtained from shorter simulations may not give precise answers. Possible reasons for this behavior are discussed.
A Molecular Dynamics Study of Thermodynamic and Structural Aspects of the Hydration of Cavities in Proteins
Rebecca C. Wade, Michael H. Mazor, J. Andrew McCammon and Florante A. Quiocho
The structure and activity of a protein molecule are strongly influenced by the extent of hydration of its cavities. This is, in turn, related to the free energy change on transfer of a water molecule from bulk solvent into a cavity. Such free energy changes have been calculated for two cavities in a sulfate-binding protein. One of these cavities contains a crystallo graphically observed water molecule while the other does not. Thermodynamic integration and perturbation methods were used to calculate free energies of hydration for each of the cavities from molecular dynamics simulations of two separate events: the removal of a water molecule from pure water, and the introduction of a water molecule into each protein cavity. From the simulations for the pure water system, the excess chemical potential of water was computed to be -6.4 ± 0.4 kcal/mol, in accord with experiment and with other recent theoretical calculations. For the protein cavity containing an experimentally observed water molecule, the free energy change on hydrating it with one water molecule was calculated as -10.0 ± 1.3 kcal/mol, indicating the high probability that this cavity is occupied by a water molecule. By contrast, for the cavity in which no water molecules were experimentally observed, the free energy change on hydrating it with one water molecule was calculated as 0.2 ± 1.5 kcal/mol, indicating its low occupancy by water. The agreement of these results with experiment suggests that thermodynamic simulation methods may become useful for the prediction and analysis of internal hydration in proteins.
Theoretical Calculations of Relative Affinities of Binding
T.P. Straatsma and J.A. McCammon
The analysis and prediction of enzyme activity by means of computer simulation have become possible in recent years as a result of advances in theoretical and computational chemistry. The new computational tools allow the calculation of fundamental thermodynamic and kinetic quantities such as those displayed in Schemes I and II. Here, E, S, and P represent enzyme, substrate, and product, respectively, X represents a reaction intermediate, I represents a competitive inhibitor, Km is the Michaelis constant (commonly approximated by the equilibrium constant for dissociation of the enzyme-substrate complex), and KI is the equilibrium constant for the dissociation of inhibitor. Calculations of rate constants for initial binding, for example, k1 and k4, can be accomplished in some cases by simulations of the corresponding diffusional encounters. This is discussed elsewhere in this volume. The present chapter treats the calculation of thermodynamic quantities such as the equilibrium constants in Schemes I and II and, especially, the changes in such quantities associated with the chemical modification of ligands or enzymes. Such calculations are still rather limited in their ranges of reliability. The focus of this chapter is therefore on fundamental aspects of the methodology, and especially on the research that is being done to increase the reliability and scope of these methods. The general background for this work and the applications reported to date have been reviewed elsewhere.
Diffusion-Controlled Enzymatic Reactions
Malcolm E. Davis, Jeffry D. Madura, Jacqueline Sines, Brock A. Luty, Stuart A. Allison and J. Andrew McCammon
The rate of diffusional encounter between reactant molecules in solution sets the ultimate limit on the speed of enzymatic and other reactions. If the reactant molecules are such that subsequent events develop very rapidly when the reactants come into contact, the net rate of the reaction will be equal to the rate of diffusional encounter. The reaction is then said to be diffusion-controlled. Examples of such processes can be found among enzymatic and redox protein reactions, the binding of ligands to macromolecules and receptors, and the transport of ions or molecules by channels or other mechanisms. Because diffusion determines the maximum possible rate for such processes, the study of diffusional encounters will become increasingly important as protein engineering yields increasingly efficient systems.
Multiconfiguration Thermodynamic Integration
T.P. Straatsma and J.A. McCammon
A modified thermodynamic integration technique is presented to obtain free energy differences from molecular dynamics simulations. In this multiconfiguration thermodynamic integration technique, the commonly employed single configuration (slow growth) approximation is not made. It is shown, by analysis of the sources of error, how the multiconfiguration variant of thermodynamic integration allows for a soundly based assessment of the statistical error in the evaluated free energy difference. Since ensembles of configurations are generated for each integration step, a statistical error can be evaluated for each integration step. By generating ensembles of different lengths, the statistical error can be equally distributed over the integration. This eliminates the difficult problem in single configuration thermodynamic integrations of determining the best rate of change of the Hamiltonian, which is usually based on equally distributing the free energy change. At the same time, this procedure leads to a more efficient use of computer time by providing the possibility of added accuracy from separate calculations of the same Hamiltonian change. The technique is applied to a simple but illustrative model system consisting of a monatomic solute in aqueous solution. In a second example, a combination of multiconfiguration thermodynamic integration and thermodynamic perturbation is used to obtain the potentials of mean force for rotation of the sidechain dihedral angles for valine and threonine dipeptides with restrained backbones in aqueous solution.
Free Energy Evaluation from Molecular Dynamics Simulations Using Force Fields Including Electronic Polarization
T.P. Straatsma and J.A. McCammon
In a recent publication a method was described for the incorporation of electronic polarizability in molecular dynamics simulations using a noniterative procedure. For thermodynamic integrations, in which the polarizabilities are varied, simple equations can be derived for this noniterative method. In this article it will be shown how the method can be used for thermodynamic integrations and perturbation method calculations to evaluate free energy differences, in which polarizabilities as well as charges are varied.
Free Energy from Simulations
J. Andrew McCammon
Free energies derived from computer simulations can aid in the interpretation or prediction of experimental data on biomolecular structure, thermodynamics and kinetics. Progress made during the past year has improved the accuracy and speed of free energy calculations, and has provided new insights into molecular associations, protein folding and electron transfer.
Dielectric Boundary Smoothing in Finite Difference Solutions of the Poisson Equation: An Approach to Improve Accuracy and Convergence
Malcolm E. Davis and J. Andrew McCammon
Finite difference methods are becoming very popular for calculating electrostatic fields around molecules. Due to the large amount of computer memory required, grid spacings cannot be made extremely small in relation to the size of the van der Waals radii of the atoms. As a result, the calculations make a rather crude approximation to the molecular surface by defining grid line midpoints discontinuously as either interior or exterior. We present a method which "smoothes" the boundary, but more accurately models the potential from the analytic solution of the discontinuous dielectric problem and improves convergence in electrostatic energy calculations. In addition, a small improvement in convergence rate is observed.
Quantum Simulations of Conformation Reorganization in the Electron Transfer Reactions of Tuna Cytochrome c
Chong Zheng, J. Andrew McCammon and Peter G. Wolynes
Quantum simulation schemes based on the Feynman path integral molecular dynamics technique have been used to calculate the effective activation energy associated with nuclear reorganization in the self-exchange reaction of tuna cytochrome c. In addition, a quench technique is used to exhibit the instantons or most probable tunneling paths involved in the reorganization motion. At room temperature, the activation energy is calculated to be 8.8 kJ/mol, close to the estimate by Warshel et al., from purely classical considerations. The quantum contribution is small, 2.6 kJ/mol at room temperature. At lower temperature, the quantum tunneling becomes more significant and the free energy associated with the quantum correction factor begins to dominate, 4.2 kJ/mol at 150 K. The transient tunneling paths can deviate significantly from the transition direction, contrary to the picture one would expect for a purely harmonic system. Corrections to short time dynamics are discussed and shown to be small for tuna cytochrome c at room temperature, using an approximation based on the dispersed polaron method. In addition, the problem of conformational substates and their effect on the tunneling calculation is noted.
Molecular Dynamics Simulation of Superoxide Interacting with Superoxide Dismutase
Jian Shen and J. Andrew McCammon
Molecular dynamics simulations have been used to study the equilibrium distribution of a superoxide substrate molecule (O2-) in the channel to the active site of the enzyme Cu,Zn superoxide dismutase (SOD). The results are used to consider aspects of the kinetics of SOD.
Direct Dynamics Study of Intramolecular Proton Transfer in Hydrogenoxalate Anion
Thanh N. Truong and J. Andrew McCammon
We have carried out ab initio calculations for the intramolecular proton-transfer process in hydrogenoxalate anion using Møller-Plesset perturbation theory with a reasonably large basis set. We found that electron correlation is very important in predicting the barrier height as well as the equilibrium and transition-state structures. The classical barrier height calculated at the MP2/6-31++G** level is 3.1 kcal/mol. Including the zero-point energy correction reduces the barrier to only 0.4 kcal/mol for the proton transfer, and to 1.3 and 1.6 kcal/mol for the deuterium and tritium isotope substituted reactions, respectively. We also used these results with transition-state theory and an Eckart semiclassical tunneling method to calculate the rate constants and kinetic isotope effect for this reaction. We found that the tunneling contribution to the rate constant is smaller for the proton transfer than for other heavier isotopes. The calculated kinetic isotope effect is quite large and due mostly to the in-plane hydrogen stretch and bend vibrational modes.