The Low Dielectric Interior of Proteins is Sufficient to Cause Major Structural Changes in DNA on AssociationAdrian H. Elcock and J. Andrew McCammonJournal of the American Chemical Society, Vol. 118, No. 15, pp. 3787-3788 (1996)
Structural changes in DNA resulting from protein association were
studied by computer simulation. A model protein defined simply as a
region of low dielectric was found to cause a dramatic opening of the
minor groove upon close approach to the DNA. Since in these simulations
no direct forces acted between the protein and the DNA, the structural
changes observed can result only from changes in the solvent and ionic
environment of the DNA. From these results it seems likely that a
significant driving force for DNA structural changes accompanying
complex formation may be provided by the replacement of regions of high
dielectric solvent by the low dielectric protein.
Structural Fluctuations of a Cryptophane Host: A Molecular Dynamics SimulationP.D. Kirchhoff, M.B. Bass, B.A. Hanks, J.M. Briggs, Andre Collet and J.A. McCammonJournal of the American Chemical Society, Vol. 118, No. 13, pp. 3237-3246 (1996)
Cryptophanes are aromatic hosts which bind a variety of guests. Here, we
describe a 20 nanosecond molecular dynamics simulation of a particular
cryptophane in water. This cryptophane features three pores which open
onto a cavity where the guests bind. The molecular dynamics simulation
in combination with a surfacing algorithm provides information on the
frequency with which these pores open wide enough to admit guest
molecules of any given size. We discuss these fluctuations and their
possible consequences for binding kinetics.
Surface Titration: A Continuum Electrostatics ModelJason L. Smart and J. Andrew McCammonJournal of the American Chemical Society, Vol. 118, No. 9, pp. 2283-2284 (1996)
This communication presents a computational study of a highly simplified
model of a titrating docosyl amine monolayer at an air/water interface.
The specific goal of the study is to reproduce experimentally measured
pKa shifts associated with the formation of the monolayer. The
calculations also demonstrate the strong dependence of the pKa shift on
distance of the amine groups from the interface and the weak dependence
of the pKa shift on the size and type of hydrophobic tailgroup. By
comparing computation with experiment, an estimate of the
amine-interface separation can be made. The dependence of the pKa shift
on the ionic strength is calculated at this separation.
Time-Dependent Rate Coefficients from Brownian Dynamics SimulationsMichael J. Potter, Brock Luty, Huan-Xiang Zhou and J. Andrew McCammonJournal of Physical Chemistry, Vol. 100, No. 12, pp. 5149-5154 (1996)
The kinetics of diffusion-influenced reaction is described by a
time-dependent rate coefficient k(t). In this paper, we implement an
algorithm for calculating k(t), introduced by one of us, in the UHBD
software package. In the implementation, the electrostatic force exerted
on a diffusing substrate by an enzyme is obtained from a
finite-difference solution of the Poisson equation. The rate coefficient
is obtained by starting the substrate in the active site and monitoring
its survival probability using Brownian dynamics simulations. The
technique is applied to the binding of superoxide to Cu/Zn superoxide
dismutase. The long-time limit of k(t) is found to be in agreement with
both the experimental value and that calculated using an algorithm
designed specifically for finding k(t=infinity).
Free Energy Simulations: Correcting for Electrostatic Cutoffs by Use of the Poisson EquationHaluk Resat and J. Andrew McCammonJournal of Chemical Physics, Vol. 104, No. 19, pp. 7645-7651 (1996)
The use of electrostatic cutoffs in calculations of free energy changes
by molecular dynamics or Monte Carlo simulation is known to introduce
errors, which can be quite large when the net charge of the system is
changed. The Born equation has often been used to correct for such
errors, but this and other analytical methods cannot be used for many
systems with complicated structures. Here, we show that numerical
methods for solving the Poisson equation, which have been extensively
developed recently for studies of solvation thermodynamics, provide a
more generally applicable alternative to the traditional Born-type
corrections.
The Determinants of pKas in ProteinsJan Antosiewicz, J. Andrew McCammon and Michael K. GilsonBiochemistry, Vol. 35, No. 24, pp. 7819-7833 (1996) [PubMed 8672483]The formulation of realistic and predictive models for protonation
equilibria in proteins represents a fundamental challenge in physical
chemistry. A number of laboratories have used detailed solutions of the
linearized Poisson- Boltzmann (PB) equation for proteins in solution to
estimate the energetics of ionization processes. Although certain
components of the PB model, such as the ionic strength and the dielctric
constant of the solvent, are fixed by the experimental conditions to be
simulated, other components of the model are less certain. These
components include the atomic charges and radii used in the
electrostatics calculations; the conformation or conformational
distribution of the protein; and the dielectric constant of the protein.
The present study makes use of the substantial body of structural and
pKa data for the proteins hen egg white lysozyme (HEWL), bovine
pancreatic ribonuclease A (RNAse A), bovine pancreatic trypsin inhibitor
(PTI), and turkey ovomucoid third domain (OMTKY3), to examine the
influence of the dielectric constant of the protein, of atomic
parameters, and of protein conformation, upon the accuracy of the
calculations. This part of the paper is based upon cumulative
comparisons of computed pKas with measurements, and aims to establish
models that are increasingly accurate and thus, it is presumed,
increasingly realistic. However, closer examination of some of these
systems, and of the experimental data themselves, is also of
considerable interest. Accordingly, an additional study of the influence
of bound phosphate upon the pKas of histidine side chains in RNAse A is
provided, and the basis for the pKa shifts or carboxylic acids in OMTKY3
is analyzed. In addition, observations resulting from a cumulative
analysis of 63 measured and calculated pKas are presented.
Quantum-Classical Molecular Dynamics Simulations of Proton Transfer Processes in Molecular Complexes and in EnzymesP. Ba&Journal of Physical Chemistry, Vol. 100, No. 7, pp. 2535-2545 (1996)
A quantum-classical molecular dynamics model (QCMD) designed for
simulations of proton or electron transfer processes in molecular
systems is described and applied to several model problems. The primary
goal of this work is the elucidation of enzymatic reactions. For
example, using the QCMD model, the dynamics of key protons in an
enzyme's active site might be described by the time-dependent
Schroedinger equation while the dynamics of the remaining atoms are
described using MD. The coupling between the quantum proton(s) and the
classical atoms is accomplished via extended Hellman-Feynman forces as
well as the time dependence of the potential energy function in the
Schroedinger equation. The potential energy function is either
parameterized prior to the simulations or can be computed using a
parameterized valence bond (VB) method (QCMD/VB model). The QCMD method
was used to simulate proton transfer in a proton bound ammonia-ammonia
dimer as well as to simulate dissociation of a Xe-HI complex in its
electronic excited state. The simulation results are compared with data
obtained using a quantum-classical time-dependent self-consistent field
method (Q/C TDSCF) and with results of fully quantum-dynamical
simulations. Finally QCMD/VB simulations of a hydrolytic process
catalyzed by phospholipase A(2), including quantum-dynamical
dissociation of a water molecule in the active site, are reported. To
the best of our knowledge, these are the first simulations that
explicitly use the time-dependent Schroedinger equation to describe
enzyme catalytic activity.
Orientational Steering in Enzyme-Substrate Association: Ionic Strength Dependence of Hydrodynamic Torque EffectsJan Antosiewicz, James M. Briggs and J. Andrew McCammonEuropean Biophysics Journal, Vol. 24, No. 3, pp. 137-141 (1996) [PubMed 8852560]The effect of hydrodynamic torques on the association rate constants for
enzyme-ligand complexation is investigated by Brownian dynamics
simulations. Our hydrodynamic models of the enzyme and ligand are
composed of spherical elements with friction forces acting at their
centers. A quantitative measure of hydrodynamic torque orientational
effects is introduced by choosing, as a reference system, an
enzyme-ligand model with the same average hydrodynamic interactions but
without orientational dependence. Our simple models show a 15% increase
in the rate constant caused by hydrodynamic torques at physiological
ionic strength. For more realistic hydrodynamic models, which are not
computationally feasible at present, this effect is probably higher. The
most important finding of this work is that hydrodynamic complementarity
in shape (i.e. like the fitting together of pieces of a puzzle) is most
effective for interactions between molecules at physiological ionic
strength.
Comparison of Continuum and Explicit Models of Solvation: Potentials of Mean Force for Alanine DipeptideTami J. Marrone, Michael K. Gilson and J. Andrew McCammonJournal of Physical Chemistry, Vol. 100, No. 5, pp. 1439-1441 (1996)
We compute the potential of mean force (PMF) around the phi and psi
torsions of alanine dipeptide with a Poisson-Boltzmann (PB) method and
compare these results to simulations in explicit water. The PB methods,
which includes an apolar solvation term, qualitatively reproduces the
PMF profiles generated in the explicit solvent simulation at a markedly
lower computational cost. These results motivate more extensive testing
of continuum methods for the study of conformational and binding
equilibria in solution.
Binding of Tacrine and 6-Chlorotacrine by AcetylcholinesteraseS.T. Wlodek, J. Antosiewicz, J.A. McCammon, T.P. Straatsma, M.K. Gilson, J.M. Briggs, C. Humblet and J.L. SussmanBiopolymers, Vol. 38, Issue 1, pp. 109-117 (1996) [PubMed 8679940]Multiconfiguration thermodynamic integration was used to determine the
relative binding strength of tacrine and 6-chlorotacrine by Torpedo
californica acetylcholinesterase. 6-Chlorotacrine appears to be bound
stronger by 0.7+/-0.4 kcal/mol than unsubstituted tacrine when the
active site triad residue His-440 is deprotonated. This result is in
excellent agreement with experimental inhibition data on electric eel
acetylcholinesterase. Electrostatic Poisson-Boltzmann calculations
confirm that order of binding strength, resulting in ΔG of binding
of -2.9 and -3.3 kcal/mol for tacrine and chlorotacrine, respectively,
and suggest inhibitor binding does not occur when His-440 is charged.
Our results suggest that electron density redistribution upon tacrine
chlorination is mainly responsible for the increased attraction
potential between protonated inhibitor molecule and adjacent aromatic
groups of Phe-330 and Trp-84.
Use of the Grand Canonical Ensemble in Potential of Mean Force CalculationsH. Resat, M. Mezei and J.A. McCammonJournal of Physical Chemistry, Vol. 100, No. 4, pp. 1426-1433 (1996)
Understanding and predicting the thermodynamics of association reactions
at the microscopic level requires that it be possible to sample
respresentative configurations of the reactants and solvent as a
function of the reaction pathways. Because of geometric effects, certain
methodological improvements in molecular simulation techniques are
necessary before the reaction thermodynamics of complicated systems such
as biopolymers with interlocking shapes can be investigated. Here, we
propose the use of the grand canonical ensemble in molecular simulations
when the traditional canonical ensemble based methods cannot
appropriately account for the confined space effects. The success of the
grand canonical ensemble molecular simulations in studying the
association reaction profile is shown by testing it on simpler systems.
Implications for future work and various possible application areas of
the grand canonical ensemble simulations are discussed.
Study of Global Motions in Proteins by Weighted Masses Molecular Dynamics: Adenylate Kinase as a Test CaseSamir Elamrani, Michael B. Berry, George N. Phillips, Jr. and J. Andrew McCammonProteins, Vol. 25, Issue 1, pp. 79-88 (1996) [PubMed 8727320]The weighted masses molecular dynamics (WMMD) technique is applied to
the protein adenylate kinase. A novel set of restraints has been
developed to allow the use of this technique with proteins. The WMMD
simulation is successful in predicting the flexibility of the two mobile
domains of the protein. The end product of the simulation is similar to
the known open and AMP bound forms of the enzyme. The biological
relevance of the restraints used and potential methods of improving the
technique are discussed.
Theoretical Study of Inhibition of Adenosine Deaminase by 8R-Coformycin and 8R-DeoxycoformycinTami J. Marrone, T.P. Straatsma, James M. Briggs, David K. Wilson, Florante A. Quiocho and J. Andrew McCammonJournal of Medicinal Chemistry, Vol. 39, No. 1, pp. 277-284 (1996) [PubMed 8568817]Molecular dynamics and free energy simulations were performed to examine
the binding of (8
R)-deoxycoformycin and (8
R)-coformycin to
adenosine deaminase. The two inhibitors differ only at the 2' position
of the sugar ring; the sugar moiety of conformycin is ribose, while it
is deoxyribose for deoxycoformycin. The 100 ps molecular dynamics
trajectories reveal that Asp 19 and His 17 interact strongly with the 5'
hydroxyl group of the sugar moiety of both inhibitors and appear to play
an important role in binding the sugar. The 2' and 3' groups of the
sugars are near the protein-water interface and can be stabilized by
either protein residues or water. The flexibility of the residues at the
opening of the active site helps to explain the modest difference in
binding of the two inhibitors and how substrates/inhibitors can enter an
otherwise inaccessible binding site.
Density Functional Based Parametrization of a Valence Bond Method and its Applications in Quantum-Classical Molecular Dynamics Simulations of Enzymatic ReactionsP. Grochowski, B. Lesyng, P. Ba&International Journal of Quantum Chemistry, Vol. 60, Issue 6, pp. 1143-1164 (1996)
An approximate valence bond (AVB) method was parametrized at a
microscopic level for proton transfer and hydroxyanion nucleophilic
reactions in enzyme catalytic processes. The method was applied to
describe hydrolytic activity of phospholipase A2. The AVB
parametrization is based on density functional and conventional ab
initio calculations calibrated with respect to experimental data in the
gas phase. The method was used as a fast generator of the potential
energy function in a quantum-classical molecular dynamics (QCMD)
simulations describing atomic motions as well as propagation of the
proton wave function in the enzyme active site. The protein environment
surrounding the active site and solvent effects are included in the
model via electrostatic interactions perturbing the original AVB
Hamiltonian.
Electrostatic Channeling in the Bifunctional Enzyme Dihydrofolate Reductase-Thymidylate SynthaseAdrian H. Elcock, Michael J. Potter, David A. Matthews, Daniel R. Knighton and J. Andrew McCammonJournal of Molecular Biology, Vol. 262, Issue 3, pp. 370-374 (1996) [PubMed 8845002]The bifunctional enzyme dihydrofolate reductase-thymidylate synthase
(DHFR-TS) carries out two distinct reactions, with the dihydrofolate
produced by the TS-catalysed reaction acting as the substrate for the
DHFR-catalysed reaction. Brownian dynamics simulation techniques were
used to investigate the possible role of electrostatics in determining
efficient channeling of the substrate, by explicitly simulating
substrate diffusion between the two active sites. With a substrate
charge of -2, almost all (>95%) substrate molecules leaving the TS
active site reached the DHFR active site at zero ionic strength. Under
the same conditions, but in the absence of electrostatic effects,
successful channeling was reduced to only around 6%: electrostatic
effects therefore appear essential to explain the efficient channeling
observed experimentally. The importance of substrate charge, the
relative contributions of specific basic residues in the protein, the
role played by the second monomer of the dimer in channeling and the
effects of changing ionic strength were all investigated. Simulations
performed for substrate transfer in the opposite direction suggest that
channeling in DHFR-TS is not strongly directional and that the role of
electrostatics is perhaps more one of restricting diffusion of the
substrate than one of actively guiding it from the TS to the DHFR active
site. The results demonstrate that electrostatic channeling can be a
highly efficient means of transferring charged substrates between active
sites in solvent-exposed environments.
Computational Science: New Horizons and Relevance to Pharmaceutical DesignJames M. Briggs, Tami J. Marrone and J. Andrew McCammonTrends in Cardiovascular Medicine, Vol. 6, Issue 6, pp. 198-204 (1996) [PubMed 21232297]Computer methods are used extensively in the design and refinement of
drug leads. A short summary is given for several computational methods
followed by a description of how some of these methods have been applied
to design drugs targeted to the renin-angiotensin system and to
cholinergic synapses. These methods include quantitative structure
activity relationship (QSAR) methods, comparative molecular field
analyses (CoMFA), 3D database searching, de novo design of ligands,
docking, and computational alchemy (free energy perturbation, FEP,
thermodynamic integration, MCTI). Most of these methods can be used
whether or not detailed structural information about the binding site is
available, although without an X-ray structure, the analyses are more
qualitative. All of these methods are used extensively in the commercial
design of pharmaceuticals. The main problem with most of these mthods is
in the scoring (ranking) of interactions or matches. Advances in this
area and others (methods development and increase in capabilities of
computers) will increase the predictive power of these mthods and help
to speed the time to market of new pharmaceuticals.
A Speed Limit for Protein Folding (Commentary)J. Andrew McCammonProceedings of the National Academy of Sciences of the USA, Vol. 93, Issue 21, pp. 11426-11427 (1996) [PubMed 8876151]Recent observations of fast steps in protein folding address the
question: What is the shortest time that would be required for folding?
The paper by Hagen et al. in the current issue of the Proceedings
provides strong experimental support for a speed limit that is governed
by diffusion. Diffusion is known to limit the rates of many of the
activities of proteins, including enzymatic activity, electron transfer,
and binding to other macromolecules. The new evidence suggests that
folding can be added to this list.
Evidence for Electrostatic Channeling in a Fusion Protein of Malate Dehydrogenase and Citrate SynthaseAdrian H. Elcock and J. Andrew McCammonBiochemistry, Vol. 35, No. 39, pp. 12652-12658 (1996) [PubMed 8841108]Brownian dynamics simulations were performed to investigate a possible
role for electrostatic channeling in transferring substrate between two
of the enzymes of the citric acid cycle. The diffusion of oxaloacetate
from one of the active sites of malate dehydrogenase (MDH) to the active
sites of citrate synthase (CS) was simulated in the presence and absence
of electrostatic forces using a modeled structure for a MDH-CS fusion
protein. In the absence of electrostatic forces, fewer than 1% of
substrate molecules leaving the MDH active site are transferred to CS.
When electrostatic forces are present at zero ionic stength however,
around 45% of substrate molecules are successfully channeled. As
expected for an electrostatic mechanism of transfer, increasing the
ionic strength in the simulations reduces the calculated transfer
efficiency. Even at 150mM however, the inclusion of electrostatic forces
results in an increase in transfer efficiency of more than one order of
magnitude. The simulations therefore provide evidence for the
involvement of electrostatic channeling in guiding substrate transfer
between two of the enzymes of the citric acid cycle. Similar effects may
opeate between other members of the citric acid metabolon.
Acetylcholinesterase: Role of the Enzyme's Charge Distribution in Steering Charged Ligands Toward the Active SiteJan Antosiewicz, Stanislaw T. Wlodek and J. Andrew McCammonBiopolymers, Vol. 39, Issue 1, pp. 85-94 (1996) [PubMed 8924629]The electrostatic steering of charged ligands toward the active site of
Torpedo californica acetylcholinesterase is investigated by Brownian
dynamics simulations of wild type enzyme and several mutated forms, in
which some normally charged residues are neutralized. The simulations
reveal that the total ligand influx through a surface of 42A radius
centered in the enzyme monomer and separated from the protein surface by
1-14A is not significantly influenced by electrostatic interactions.
Electrostatic effects are visible for encounters with a surface of 32A
radius, which is partially hidden inside the protein, but mostly within
the solvent. A clear accumulation of encounter events for that sphere is
observed in the area directly above the entrance to the active site
gorge. In this area, the encounter events are increased by 40% compared
to the case of a netural ligand, However, the differences among the
encounter rates for the various mutants considered here are not
pronouned, all rate constants being within plus or minus 10% of the
average value. The enzyme charge distribution becomes more important as
the charged ligand moves toward the bottom of the gorge, where the
active site is located. We show that neither the enzyme's total charge,
nor its dipole moment, fully account for the electrostatic steering of
ligand to the active site. Higher moments of the enzyme's charge
distribution are also important. However, for a series of mutations for
which the direction of the enzyme dipole moment is constant within a few
degrees, one observes a gradual decrease in the diffusional encounter
rate constant with the number of neutralized residues. On the other
hand, for other mutants that change the direction of the dipole moment
from that of the wild type, the calculated encounter rate constants can
be very close to that of the wild type. The present work yields two new
insights to the kinetics of acetylcholinesterase. First, evolution
appears to have built a redundant electrostatic steering capability into
this important enzyme through the overall distribution of its thousands
of partially charged atoms. And second, roughly half of the rate
enhancement due to electrostatics arises from steering of the substrate
outside the enzyme; the other half of the rate enhancement arises from
improved trapping of the substrate after it had entered the gorge. The
computational results reproduce qualitatively, and help to rationalize,
many surprising experimental results obtained recently for human
acetylcholinesterase.
Computing the Ionization States of Proteins with a Detailed Charge ModelJan Antosiewicz, James M. Briggs, Adrian H. Elcock, Michael K. Gilson and J. Andrew McCammonJournal of Computational Chemistry, Vol. 17, Issue 14, pp. 1633-1644 (1996)
A convenient computational approach for the calculation of the
pKas of ionizable groups in a protein is described.
The method uses detailed models of the charges in both the neutral and
ionized form of each ionizable group. A full derivation of the
theoretical framework is presented, as are details of its implementation
in the UHBD program. Application to four proteins whose crystal
structures are known shows that the detailed charge model improves
agreement with experimentally determined pKas when a
low protein dielectric constant is assumed, relative to the results with
a simpler single-site ionization model. It is also found that use of the
detailed charge model increases the sensitivity of the computed
pKas to the details of proton placement.
A 240-Fold Electrostatic Rate-Enhancement for Acetylcholinesterase - Substrate Binding can be Predicted by the Potential within the Active SiteHuan-Xiang Zhou, James M. Briggs and J. Andrew McCammonJournal of the American Chemical Society, Vol. 118, No. 51, pp. 13069-13070 (1996)
An approximate relation that allows easy prediction of the enhancement
of enzyme-substrate binding rates by an interaction potential was
derived recently by one of us (http://dx.doi.org/10.1063/1.472530"
target="_blank" class="ref">Zhou, J. Chem. Phys., 1996, 105, 7235). This
is given by the average of the Boltzmann factor over the region in which
the substrate can effectively bind to the enzyme. We test this relation
on the enzyme Torpedo californica acetylcholinesterase. The interaction
potential was found by solving the Poisson-Boltzmann equation and
treating the substrate as a test charge. At an ionic strength of 150 mM,
the electrostatic rate-enhancement as calculated by Brownian dynamics
simulation is enormous (~240 fold), yet it can be predicted by the
average Boltzmann factor (~1000) to within a factor of 4. The simulated
binding rate constants are in reasonable agreement with experimental
results.