Molecular Dynamics Computations and Solid State Nuclear Magnetic Resonance of the Gramicidin Cation ChannelS.-W. Chiu, L.K. Nicholson, M.T. Brenneman, S. Subramaniam, Q. Teng, J.A. McCammon, T.A. Cross and E. JakobssonBiophysical Journal, Vol. 60, No. 4, pp. 974-978 (1991) [PubMed 1720680]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 SolutionJ.A. McCammonIn "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 SupercomputerMichael J. Mitchell and J. Andrew McCammonComputers & Chemistry, Vol. 15, Issue 1, pp. 79-85 (1991)
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 ProgramMalcolm E. Davis, Jeffry D. Madura, Brock A. Luty and J. Andrew McCammonComputer Physics Communications, Vol. 62, Issues 2-3, pp. 187-197 (1991)
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 ChannelsSee-Wing Chiu, Eric Jakobsson, Shankar Subramaniam and J. Andrew McCammonBiophysical Journal, Vol. 60, No. 1, pp. 273-285 (1991) [PubMed 1715766]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 ValueMichael J. Mitchell and J. Andrew McCammonJournal of Computational Chemistry, Vol. 12, Issue 2, pp. 271-275 (1991)
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 ProteinsRebecca C. Wade, Michael H. Mazor, J. Andrew McCammon and Florante A. QuiochoBiopolymers, Vol. 31, Issue 8, pp. 919-931 (1991) [PubMed 1782354]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 BindingT.P. Straatsma and J.A. McCammonMethods in Enzymology, Vol. 202, Ch. 23, pp. 497-511 (1991) [PubMed 1784186]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,
K
_{m} is the Michaelis constant (commonly approximated by the
equilibrium constant for dissociation of the enzyme-substrate complex),
and K
_{I} is the equilibrium constant for the dissociation of
inhibitor. Calculations of rate constants for initial binding, for
example, k
_{1} and k
_{4}, 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 ReactionsMalcolm E. Davis, Jeffry D. Madura, Jacqueline Sines, Brock A. Luty, Stuart A. Allison and J. Andrew McCammonMethods in Enzymology, Vol. 202, Ch. 22, pp. 473-497 (1991) [PubMed 1784185]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 IntegrationT.P. Straatsma and J.A. McCammonJournal of Chemical Physics, Vol. 95, Issue 2, pp. 1175-1188 (1991)
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 PolarizationT.P. Straatsma and J.A. McCammonChemical Physics Letters, Vol. 177, Issues 4-5, pp. 433-440 (1991)
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 SimulationsJ. Andrew McCammonCurrent Opinion in Structural Biology, Vol. 1, Issue 2, pp. 196-200 (1991)
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 ConvergenceMalcolm E. Davis and J. Andrew McCammonJournal of Computational Chemistry, Vol. 12, Issue 7, pp. 909-912 (1991)
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 cChong Zheng, J. Andrew McCammon and Peter G. WolynesChemical Physics, Vol. 158, Issues 2-3, pp. 261-270 (1991)
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 DismutaseJian Shen and J. Andrew McCammonChemical Physics, Vol. 158, Issues 2-3, pp. 191-198 (1991)
Molecular dynamics simulations have been used to study the equilibrium
distribution of a superoxide substrate molecule
(O_{2}^{-}) 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 AnionThanh N. Truong and J. Andrew McCammonJournal of the American Chemical Society, Vol. 113, No. 20, pp. 7504-7508 (1991)
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.