Anti-Insulin Antibody Structure and Conformation. II. Molecular Dynamics With Explicit SolventJohn J. Tanner, Laura J. Nell and J. Andrew McCammonBiopolymers, Vol. 32, Issue 1, pp. 23-31 (1992) [PubMed 1617146]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 AntibodyLaura J. Nell, J. Andrew McCammon and Shankar SubramaniamBiopolymers, Vol. 32, Issue 1, pp. 11-21 (1992) [PubMed 1377513]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 DismutaseJacqueline J. Sines, J. Andrew McCammon and Stuart A. AllisonJournal of Computational Chemistry, Vol. 13, Issue 1, pp. 66-69 (1992)
We used Brownian dynamics simulations of substrate
O_{2}^{-} 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 DynamicsT.W. Clark, J.A. McCammon and L.R. ScottIn "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 MethodsThanh N. Truong, John J. Tanner, Piotr Ba&Journal of Chemical Physics, Vol. 96, Issue 3, pp. 2077-2084 (1992)
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 1Rebecca C. Wade and J. Andrew McCammonJournal of Molecular Biology, Vol. 225, Issue 3, pp. 679-696 (1992) [PubMed 1318383]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 IntegrationRebecca C. Wade and J. Andrew McCammonJournal of Molecular Biology, Vol. 225, Issue 3, pp. 697-712 (1992) [PubMed 1318384]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.
Computational AlchemyT.P. Straatsma and J.A. McCammonAnnual Review of Physical Chemistry, Vol. 43, No. 1, pp. 407-435 (1992)
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
L_{2} and L_{1} to receptor R is equal to the relative
free energy for interconversions of the ligands in and away from the
receptor binding site ΔG_{2} - ΔG_{1} =
ΔG_{4} - ΔG_{3}.
Ab Initio Studies and Quantum-Classical Molecular Dynamics Simulations for Proton Transfer Processes in Model Systems and in EnzymesPiotr Ba&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 SolutionThanh N. Truong, J. Andrew McCammon, Donald J. Kouri and David K. HoffmanJournal of Chemical Physics, Vol. 96, Issue 11, pp. 8136-8142 (1992)
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 http://dx.doi.org/10.1063/1.454028" target="_blank"
class="ref">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 EnergiesBrock Luty, Malcolm E. Davis and J. Andrew McCammonJournal of Computational Chemistry, Vol. 13, Issue 6, pp. 768-771 (1992)
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 10^{3} for small molecules.
Continuum Model Calculations of Solvation Free Energies: Accurate Evaluation of Electrostatic ContributionsV. Mohan, M.E. Davis, J.A. McCammon and B.M. PettittJournal of Physical Chemistry, Vol. 96, No. 15, pp. 6428-6431 (1992)
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.
Solving the Finite-Difference Non-Linear Poisson-Boltzmann EquationBrock A. Luty, Malcolm E. Davis and J. Andrew McCammonJournal of Computational Chemistry, Vol. 13, Issue 9, pp. 1114-1118 (1992)
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 InteractionMartin Zacharias, Brock A. Luty, Malcolm E. Davis and J. Andrew McCammonBiophysical Journal, Vol. 63, No. 5, pp. 1280-1285 (1992) [PubMed 1477279]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 SimulationsT.P. Straatsma, M. Zacharias and J.A. McCammonChemical Physics Letters, Vol. 196, Issues 3-4, pp. 297-302 (1992)
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.
Superperfect EnzymesJ. Andrew McCammonCurrent Biology, Vol. 2, Issue 11, pp. 585-586 (1992) [PubMed 15336030]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 TreatmentBrock A. Luty, J. Andrew McCammon and Huan-Xiang ZhouJournal of Chemical Physics, Vol. 97, Issue 8, pp. 5682-5686 (1992)
The algorithm of Northrup, Allison, and McCammon
http://dx.doi.org/10.1063/1.446900" target="_blank" class="ref">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.