Prediction of pKas of Titratable Residues in Proteins Using a Poisson-Boltzmann Model of the Solute-Solvent SystemJ. Antosiewicz, E. B&In "Computational Molecular Dynamics: Challenges, Methods, Ideas," P. Deuflhard, J. Hermans, B. Leimkuhler, A.E. Mark, S. Reich, R.D. Skeel, Eds., Springer, Berlin, pp. 176-196 (1999)
This article provides an overview of an algorithm used for the
prediction of ionization constants of titratable residues in proteins.
The algorithm is based on an assumption that the difference in
protonation behavior of a given group in an isolated state in solution,
for which the ionization constant is assumed to be known, and the
protonation behavior in the protein environment is purely electrostatic
in origin. Calculations of the relevant electrostatic free energies are
based on the Poisson-Boltzmann (PB) model of the protein-solvent system
and the finite-difference solution to the corresponding PB equation. The
resultant multiple site titration problem is treated by one of two
methods. The first is a Hybrid approach, based on collecting ionizable
groups into clusters. The second method is a Monte Carlo approach based
on the Metropolis algorithm for extracting a sufficient number of
low-energy ionization states out of all possible states, to obtain a
correct estimation of thermodynamic properties of the system. As
examples of applications, we present the overall accuracy of predicted
ionization constants for about 50 groups in 4 proteins, changes in the
average charge of bovine pancreatic trypsin inhibitor at pH 7 along a
molecular dynamics trajectory, and finally, we discuss some preliminary
results obtained for protein kinases and protein phosphatases.
What Do We Need to Know about Proteins and Nucleic Acids?K.A. Dill, J. Deisenhofer, G.R. Fleming, H. Frauenfelder, K. Gerwert, J.A. McCammon and H. MichelIn "Simplicity and Complexity in Proteins and Nucleic Acids," H. Frauenfelder, J. Deisenhofer, P.G. Wolynes, Eds., Berlin: Dahlem University Press, pp. 81-106 (1999)
What do we need to know about the structures of proteins and nucleic
acids? What do we need to know about their mechanisms of action? What
methodological advances in theory/simulation/experiment will lead to
progress in our understanding of structure, dynamics, and function? We
explore these issues here.
Conformational Transitions of Proteins from Atomistic SimulationsV. Helms and J.A. McCammonIn "Computational Molecular Dynamics: Challenges, Methods, Ideas," P. Deuflhard, J. Hermans, B. Leimkuhler, A.E. Mark, S. Reich, R.D. Skeel, Eds., Springer, Berlin, pp. 66-77 (1999)
The function of many important proteins comes from their dynamic
properties, and their ability to undergo conformational transitions.
These may be small loop movements that allow access to the protein's
active site, or large movements such as those of motor proteins that are
implicated with muscular extension. Yet, in spite of the increasing
number of three-dimensional crystal structures of proteins in different
conformations, not much is known about the driving forces of these
transitions. As an initial step towards exploring the conformational and
energetic landscape of protein kinases by computational methods,
intramolecular energies and hydration free energies were calculated for
different conformations of the catalytic domain of cAMP-dependent
protein kinase (cAPK) with a continuum (Poisson) model for the
electrostatics. In this paper, we will put the previous results into
context and discuss possible extensions into the dynamic regime.
Ewald Artifacts in Computer Simulations of Ionic Solvation and Ion-Ion Interaction: A Continuum Electrostatics StudyPhilippe H. Hünenberger and J. Andrew McCammonJournal of Chemical Physics, Vol. 110, pp. 1856-1872 (1999)
The use of Ewald and related methods to handle electrostatic
interactions in explicit solvent simulations of solutions imposes an
artificial periodicity on systems which are inherently non-periodic. The
consequences of this approximation should be assessed, since they may
crucially affect the reliability of those computer simulations. In the
present study, we propose a general method based on continuum
electrostatics to investigate the nature and magnitude of
periodicity-induced artifacts. As a first example, this scheme is
applied to the solvation free energy of a spherical ion. It is found
that artificial periodicity reduces the magnitude of the ionic solvation
free energy, because the solvent in the periodic copies of the central
unit cell is perturbed by the periodic copies of the ion, thus less
available to solvate the central ion. In the limit of zero ionic radius
and infinite solvent permittivity, this undersolvation can be corrected
by adding the Wigner self-energy term to the solvation free energy. For
ions of a finite size or a solvent of finite permittivity, a further
correction is needed. An analytical expression for this correction is
derived using continuum electrostatics. As a second example, the effect
of artificial periodicity on the potential of mean force for the
interaction between two spherical ions is investigated. It is found that
artificial periodicity results in an attractive force between ions of
like charges, and a repulsive force between ions of opposite charges.
The analysis of these two simple test cases reveals that two
individually large terms, the periodicity-induced perturbations of the
Coulomb and solvation contributions, often cancel each other
significantly, resulting in an overall small perturbation. Three factors
may prevent this cancellation to occur and enhance the magnitude of
periodicity-induced artifacts: (i) a solvent of low dielectric
permittivity, (ii) a solute cavity of non-negligible size compared to
the unit cell size, and (iii) a solute bearing a large overall charge.
Calculation of the pKa Values for the Ligands and Side Chains of Escherichia coli D-Alanine:D-Alanine LigaseHeather A. Carlson, James M. Briggs and J. Andrew McCammonJournal of Medicinal Chemistry, Vol. 42, pp. 109-117 (1999) [PubMed 9888837]Poisson-Boltzmann electrostatics methods have been used to calculate the
pKa shifts for the ligands and titratable side chains of
D-alanine:D-alanine ligase of the ddlb gene of
E. coli (DdlB).
The focus of this study is to determine the ionization state of the
second D-alanine (D-ala2) in the active site of DdlB. The pKa of the
amine is shifted over five pKa units more alkaline in the protein,
clearly implying that D-ala2 is bound to DdlB in its zwitterionic state
and not in the free-base form as had been previously suggested.
Comparisons are made to the depsipeptide ligase from the
vancomycin-resistance cascade, VanA. It is suggested that VanA has
different enzymatic properties due to a change in binding specificity
rather than altered catalytic behavior and that the specificity of
binding D-lactate over D-ala2 may arise from the difference in
ionization characteristics of the ligands.
Phosphorylation Stabilizes the N-Termini of α-HelicesJason L. Smart and J. Andrew McCammonBiopolymers, Vol. 49, Issue 3, pp. 225-233 (1999) [PubMed 9990840]The role of phosphorylation in stabilizing the N-termini of
α-helices is examined using computer simulations of model
peptides. The models comprise either a phosphorylated or
unphosphorylated serine at the helix N-terminus, followed by nine
alanines. Monte Carlo/Stochastic Dynamics simulations were performed on
the model helices. The simulations revealed a distinct stabilization of
the helical conformation at the N-terminus after phosphorylation. The
stabilization was attributable to favorable electrostatic interactions
between the phosphate and the helix backbone. However, direct helix
capping by the phosphorylated sidechain was not observed. The results of
the calculations are consistent with experimental evidence on the
stabilization of helices by phosphates and other anions.
Determinants of Ligand Binding to cAMP-Dependent Protein KinasePhilippe H. Hünenberger, Volkhard Helms, Narendra Narayana, Susan S. Taylor and J. Andrew McCammonBiochemistry, Vol. 38, No. 8, pp. 2358-2366 (1999) [PubMed 10029529]Protein kinases are essential for the regulation of cellular growth and
metabolism. Since their dysfunction leads to debilitating diseases, they
represent key targets for pharmaceutical research. The rational design
of kinase inhibitors requires an understanding of the determinants of
ligand binding to these proteins. In the present study, a theoretical
model based on continuum electrostatics and a surface-area dependent
non-polar term is used to calculate binding affinities of balanol
derivatives, H-series inhibitors and ATP analogs towards the catalytic
subunit of cAMP-dependent protein kinase (cAPK or protein kinase A). The
calculations reproduce most of the experimental trends, and provide
insight into the driving forces responsible for binding. Non-polar
interactions are found to govern protein-ligand affinity. Hydrogen bonds
represent a negligible contribution, because hydrogen bond formation in
the complex requires the desolvation of the interacting partners.
However, the binding affinity is decreased if hydrogen-bonding groups of
the ligand remain unsatisfied in the complex. The disposition of
hydrogen-bonding groups in the ligand is therefore crucial for binding
specificity. These observations should be valuable guides in the design
of potent and specific kinase inhibitors.
Molecular Dynamics Simulations of the Hyperthermophilic Protein Sac7d from Sulfolobus acidocaldarius: Contribution of Salt Bridges to ThermostabilityPaul I.W. de Bakker, Philippe H. Hünenberger and J. Andrew McCammonJournal of Molecular Biology, Vol. 285, pp. 1811-1830 (1999) [PubMed 9917414]Hyperthermophilic proteins often possess an increased number of surface
salt bridges compared to their mesophilic homologues. Yet, salt bridges
are generally thought to be of minor importance in protein stability at
room temperature. In an effort to understand why this may no longer be
true at elevated temperatures, we performed molecular dynamics
simulations of the hyperthermophilic protein Sac7d at 300 K, 360 K, and
550 K. The three trajectories are stable on the nanosecond timescale, as
evidenced by the analysis of several time-resolved properties. The
simulations at 300 K and (to a lesser extent) 360 K are also compatible
with NOE-derived distances. Raising the temperature from 300 K to 360 K
results in a less favorable protein-solvent interaction energy, and a
more favorable intraprotein interaction energy. Both effects are almost
exclusively electrostatic in nature and dominated by contributions due
to charged side chains. The reduced solvation is due to a loss of
spatial and orientational structure of water around charged side chains,
which is a consequence of the increased thermal motion in the solvent.
The favorable change in the intraprotein Coulombic interaction energy is
essentially due to the tightening of salt bridges. Assuming that charged
side chains are on average more distant from one another in the unfolded
state than in the folded state, it follows that salt bridges may
contribute to protein stability at elevated temperatures because (i) the
solvation free energy of charged side chains is more adversely affected
in the unfolded state than in the folded state by an increase in
temperature, and (ii) due to the tightening of salt bridges, unfolding
implies a larger unfavorable increase in the intraprotein Coulombic
energy at higher temperature. Possible causes for the unexpected
stability of the protein at 550 K are also discussed.
Dynamic and Rotational Analysis of Cryptophane Host-Guest Systems: Challenges of Describing Molecular RecognitionPaul D. Kirchhoff, Jean-Pierre Dutasta, André Collet and J. Andrew McCammonJournal of the American Chemical Society, Vol. 121, No. 2, pp. 381-390 (1999)
Cryptophanes are aromatic hosts which bind a variety of guests. Here, we
describe three 25 ns molecular dynamics simulations of a particular
cryptophane in water. Simulations have been conducted on the uncomplexed
cryptophane, the cryptophane-tetramethylammonium ion (TMA+) complex, and
the cryptophane-neopentane (NEO) complex. TMA+ and NEO are both
tetrahedral molecules and are nearly isomorphic. In the current study,
we examine how the presence of these guests influences motions of the
host. Also examined are the preferred orientations and the motions of
the guests relative to the cryptophane. This study demonstrates some of
the many challenges of describing molecular recognition.
Mouse Acetylcholinesterase Unliganded and in Complex with Huperzine A: A Comparison of Molecular Dynamics SimulationsSylvia Tara, T.P. Straatsma and J. Andrew McCammonBiopolymers, Vol. 50, Issue 1, pp. 35-43 (1999) [PubMed 10341665]A 1 ns molecular dynamics simulation of unliganded mouse
acetylcholinesterase (AChE) is compared to a previous simulation of
mouse AChE complexed with Huperzine A (HupA). Several common features
are observed. In both simulations, the active site gorge fluctuates in
size during the 1 ns trajectory, and is completely pinched off several
times. Many of the residues in the gorge that formed hydrogen bonds with
HupA in the simulation of the complex, now form hydrogen bonds with
other protein residues and water molecules in the gorge. The opening of
a "backdoor" entrance to the active site that was found in the
simulation of the complex is also observed in the unliganded simulation.
Differences between the two simulations include overall lower structural
RMS deviations for residues in the gorge in the unliganded simulation, a
smaller diameter of the gorge in the absence of HupA, and the
disappearance of a side channel that was frequently present in the
liganded simulation. The differences between the two simulations can be
attributed, in part, to the interaction of AChE with HupA.
OOMPAA - Object-Oriented Model for Probing Assemblages of AtomsGary A. Huber and J. Andrew McCammonJournal of Computational Physics, Vol. 151, Issue 1, pp. 264-282 (1999)
OOMPAA is a library of C++ classes that can be used to generate
molecular simulation software. The core of OOMPAA includes scripts for
generating user-defined atom classes, as well as classes that represent
groups of atoms, like bonds, aromatic rings, lists of atoms, etc. It has
easy and efficient parameter lists and facilities for allowing one to
treat attributes of lists of atoms (like positions) as large vectors.
OOMPAA is designed to grow; additions include energy minimizers,
integrators, facilities for dealing with protein molecules, and
interfaces to established electrostatic equation solvers. It is designed
with efficiency in mind; with a good optimizing C++ compiler, simulation
speed can approach that of Fortran, while retaining the elegance of
expression afforded by object-oriented programming.
Association and Dissociation Kinetics of Bobwhite Quail Lysozyme with Monoclonal Antibody HyHEL-5K. Asish Xavier, Shawn M. McDonald, J. Andrew McCammon and Richard C. WillsonProtein Engineering, Vol. 12, No. 1, pp. 79-83 (1999) [PubMed 10065714]The anti-hen egg lysozyme monoclonal antibody HyHEL-5 and its complexes
with various species-variant and mutant lysozymes have been the subject
of considerable experimental and theoretical investigation. The affinity
of HyHEL-5 for bobwhite quail lysozyme (BWQL) is over 1000-fold lower
than its affinity for the original antigen, hen egg lysozyme (HEL). This
difference is believed to arise almost entirely from the replacement in
BWQL of the structural and energetic epitope residue Arg68 by lysine. In
this study, the association and dissociation kinetics of BWQL with
HyHEL-5 were investigated under a variety of conditions and compared
with previous results for HEL. HyHEL-5-BWQL association follows a
bimolecular mechanism and the dissociation of the antibody-antigen
complex is a first-order process. Changes in ionic strength (from 27 to
500 mM) and pH (from 6.0 to 10.0) produced about a 2-fold change in the
association and dissociation rates. The effect of viscosity modifiers on
the association reaction was also studied. The large difference in the
HEL and BWQL affinities for HyHEL-5 is essentially due to differences in
the dissociation rate constant.
Situs: A Package for Docking Crystal Structures into Low-Resolution Maps from Electron MicroscopyWilly Wriggers, Ronald A. Milligan and J. Andrew McCammonJournal of Structural Biology, Vol. 125, Issues 2-3, pp. 185-195 (1999) [PubMed 10222274]Three-dimensional image reconstructions of large-scale protein
aggregates are routinely determined by electron microscopy (EM). We
combine low-resolution EM data with high-resolution structures of
proteins determined by X-ray crystallography. A set of visualization and
analysis procedures, termed the Situs package, has been developed to
provide an efficient and robust method for the localization of protein
subunits in low-resolution data. Topology-representing neural networks
are employed to vector-quantize and to correlate features within the
structural data sets. Microtubules decorated with kinesin-related ncd
motors are used as model aggregates to demonstrate the utility of this
package of routines. The precision of the docking has allowed for the
extraction of unique conformations of the macromolecules and is limited
only by the reliability of the underlying structural data.
Non-Boltzmann Rate Distributions in Stochastically Gated ReactionsNathan A. Baker and J. Andrew McCammonJournal of Physical Chemistry B, Vol. 103, No. 4, pp. 615-617 (1999)
Recently, a new mechanism for reaction selectivity, arising from
conformational gating of the reactions, has been reported in the
acetylcholinesterase system. Fluctuations in the enzyme are thought to
greatly slow the access of molecules larger than the normal substrate to
the active site region. By assuming the gate fluctuations occur as a
Brownian process in a harmonic well, it is possible to approximate the
reaction rates for various limiting cases of substrate size. However, it
is not possible to simplify the rates into a ratio which is equivalent
to the Boltzmann distribution of states for the gate fluctuations.
Internal Dynamics of Green Fluorescent ProteinVolkhard Helms, T.P. Straatsma and J. Andrew McCammonJournal of Physical Chemistry B, Vol. 103, No. 16, pp. 3263-3269 (1999)
A 1 ns molecular dynamics simulation was performed to study the dynamic
behavior of wild type green fluorescent protein from Aequorea
victoria. We find the protein to be remarkably rigid, both overall,
because the cylindrical beta-barrel provides a stable framework, but
also on an atomic level in the immediate surrounding of the chromophore.
Here, a tight H-bond network is formed mainly involving six internal
water molecules. The perfect barrel is interrupted only between
beta-strands 7 and 8 where contact is made via side chain interactions,
and we investigated the dynamic behavior of this region in detail. After
ca. 320 ps of simulation, an Arginine residue, initially sticking out
into solution, folded over the cleft to form a H-bond with a backbone
oxygen atom on the opposite strand. This contact appears important for
stabilization of the overall protein architecture.
Effect of Artificial Periodicity in Simulations of Biomolecules under Ewald Boundary Conditions: A Continuum Electrostatics StudyP.H. Hünenberger and J.A. McCammonBiophysical Chemistry, Vol. 78, Issues 1-2, pp. 69-88 (1999) [PubMed 10343384]Ewald and related methods are nowadays routinely used in
explicit-solvent simulations of biomolecules, although they impose an
artificial periodicity in systems which are inherently non-periodic. The
consequences of this approximation should be assessed, since it may
crucially affect the reliability of computer simulations under Ewald
boundary conditions. In the present study we use a method based on
continuum electrostatics to investigate the nature and magnitude of
possible periodicity-induced artifacts on the potentials of mean force
for conformational equilibria in biomolecules. Three model systems and
pathways are considered: polyalanine oligopeptides (unfolding), a DNA
tetranucleotide (separation of the strands), and the protein Sac7d
(conformations from a molecular dynamics simulation). Artificial
periodicity may significantly affect these conformational equilibria, in
each case stabilizing the most compact conformation of the biomolecule.
Three factors enhance periodicity-induced artifacts:
(i) a
solvent of low dielectric permittivity,
(ii) a solute size which
is non-negligible compared to the size of the unit cell, and
(iii) a non-neutral solute. Neither the neutrality of the solute
nor the absence of charge pairs at distances exceeding half the edge of
the unit cell do guarantee the absence of artifacts.
Molecular Dynamics Studies on the HIV-1 Integrase Catalytic DomainRoberto D. Lins, James M. Briggs, T.P. Straatsma, Heather A. Carlson, Jason Greenwald, Senyon Choe and J. Andrew McCammonBiophysical Journal, Vol. 76, No. 6, pp. 2999-3011 (1999) [PubMed 10354426]The HIV-1 integrase, which is essential for viral replication, catalyzes
the insertion of viral DNA into the host chromosome thereby recruiting
host cell machinery into making viral proteins. It represents the third
main HIV enzyme target for inhibitor design, the first two being the
reverse transcriptase and the protease. Two 1 ns molecular dynamics
simulations have been carried out on completely hydrated models of the
HIV-1 integrase catalytic domain, one with no metal ions and another
with one magnesium ion in the catalytic site. The simulations predict
that the region of the active site that is missing in the published
crystal structures has more secondary structure than previously thought.
The flexibility of this region has been discussed with respect to the
mechanistic function of the enzyme. The results of these simulations
will be used as part of inhibitor design projects directed against the
catalytic domain of the enzyme.
Polarization Around an Ion in a Dielectric Continuum with Truncated Electrostatic InteractionsNathan A. Baker, Philippe H. Hünenberger and J. Andrew McCammonJournal of Chemical Physics, Vol. 110, Issue 22, pp. 10679-10692 (1999)
In order to reduce the computational effort and to allow for the use of
periodic boundary conditions, electrostatic interactions in explicit
solvent simulations of molecular systems do not obey Coulomb's law.
Instead, a number of "effective potentials" have been proposed,
including truncated Coulomb, shifted, switched, reaction-field
corrected, or Ewald potentials. The present study compares the
performance of these schemes in the context of ionic solvation. To this
purpose, a generalized form of the Born continuum model for ion
solvation is developed, where ion-solvent and solvent-solvent
interactions are determined by these effective potentials instead of
Coulomb's law. An integral equation is formulated for calculating the
polarization around a spherical ion from which the solvation free energy
can be extracted. Comparison of the polarizations and free energies
calculated for specific effective potentials and the exact Born result
permits an assessment of the accuracy of these different schemes.
Additionally, the present formalism can be used to develop corrections
to the ionic solvation free energies calculated by molecular simulations
implementing such effective potentials. Finally, an arbitrary effective
potential is optimized to reproduce the Born polarization.
Shedding Light on the Dark and Weakly Fluorescent States of Green Fluorescent ProteinsWolfgang Weber, Volkhard Helms, J. Andrew McCammon and Peter W. LanghoffProceedings of the National Academy of Sciences of the USA, Vol. 96, No. 11, pp. 6177-6182 (1999) [PubMed 10339561]Recent experiments on various similar green fluorescent protein (GFP)
mutants at the single-molecule level and in solution provide evidence of
previously unknown short- and long-lived "dark" states and of related
excited-state decay channels. Here, we present quantum chemical
calculations on
cis-trans photoisomerization paths of neutral,
anionic, and zwitterionic GFP chromophores in their ground and first
single excited states which explain the observed behaviors from a common
perspective. The results suggest that favorable radiationless decay
channels can exist for the different protonation states along these
isomerizations, which apparently proceed via conical intersections.
These channels are suggested to rationalize the observed dramatic
reduction of fluorescence in solution. The observed single-molecule fast
blinking is attributed to conversions between the fluorescent anionic
and the dark zwitterionic forms while slow switching is attributed to
conversions between the anionic and the neutral forms. The predicted
nonadiabatic crossings are seen to rationalize the origins of a variety
of experimental observations on a common basis, and may have broad
implications for photobiophysical mechanisms in GFP.
Molecular Dynamics of Mouse Acetylcholinesterase Complexed with Huperzine ASylvia Tara, Volkhard Helms, T.P. Straatsma and J. Andrew McCammonBiopolymers, Vol. 50, Issue 4, pp. 347-359 (1999) [PubMed 10423544]Two molecular dynamics simulations were performed for a modeled complex
of mouse acetylcholinesterase (AChE) liganded with Huperzine A (HupA).
Analysis of these simulations shows that HupA shifts in the active site
towards Tyr 337 and Phe 338 and that several residues in the active site
area reach out to make hydrogen bonds with the inhibitor. Rapid
fluctuations of the gorge width are observed, ranging from widths that
allow substrate access to the active site, to pinched structures that do
not allow access of molecules as small as water. Additional openings or
channels to the active site are found. One opening is formed in the side
wall of the active site gorge by residues Val 73, Asp 74, Thr 83, Glu
84, and Asn 87. Another opening is formed at the base of the gorge by
residues Trp 86, Val 132, Glu 202, Gly 448, and Ile 451. Both of these
openings have been observed separately in the
T. californica form
of the enzyme. These channels could allow transport of waters and ions
to and from the bulk solution.
Dynamical Properties of Fasciculin-2Nathan A. Baker, Volkhard Helms and J. Andrew McCammonProteins: Structure, Function, and Genetics, Vol. 36, Issue 4, pp. 447-453 (1999) [PubMed 10450086]Fasciculin-2 (FAS2) is a potent protein inhibitor of the hydrolytic
enzyme acetylcholinesterase. A 2 ns isobaric-isothermal ensemble
molecular dynamics simulation of this toxin was performed to examine the
dynamic structural properties which may play a role in this inhibition.
Conformational fluctuations of the FAS2 protein were examined by a
variety of techniques to identify flexible residues and determine their
characteristic motion. The tips of the toxin "finger" loops and the turn
connecting loops I and II were found to fluctuate, while the rest of the
protein remained fairly rigid throughout the simulation. Finally, the
structural fluctuations were compared to NMR data of fluctuations on a
similar timescale in a related three-finger toxin. The molecular
dynamics results were in good qualitative agreement with the
experimental measurements.
Molecular Dynamics of Cryptophane and its Complexes with Tetramethylammonium and Neopentane Using a Continuum Solvent ModelMichael J. Potter, Paul D. Kirchhoff, Heather A. Carlson and J. Andrew McCammonJournal of Computational Chemistry, Vol. 20, Issue 9, pp. 956-970 (1999)
Time-scales currently obtainable in explicit-solvent molecular dynamics
simulations are inadequate for the study of many biologically important
processes. This has led to increased interest in the use of continuum
solvent models. In order for such models to be used effectively, it is
important that their behavior relative to explicit simulation be clearly
understood. Accordingly, 5 ns stochastic dynamics simulations of a
derivative of cryptophane-E alone, and complexed with
tetramethylammonium and neopentane were carried out. Solvation
electrostatics were accounted for via solutions to the Poisson equation.
Non-electrostatic aspects of solvation were incorporated using a
surface-area-dependent energy term. Comparison of the trajectories to
those from previously reported 25 ns explicit-solvent simulations shows
that use of a continuum solvent model results in enhanced sampling. Use
of the continuum solvent model also results in a considerable increase
in computational efficiency. The continuum solvent model is found to
predict qualitative structural characteristics which are similar to
those observed in explicit solvent. However, some differences are
significant, and optimization of the continuum parameterization will be
required for this method to become an efficient alternative to
explicit-solvent simulation.
Poisson-Boltzmann Model Studies of Molecular Electrostatic Properties of the cAMP-Dependent Protein KinaseEl&European Biophysics Journal, Vol. 28, No. 6, pp. 457-467 (1999) [PubMed 10460339]Protonation equilibria of residues important in the catalytic mechanism
of a protein kinase were analyzed on the basis of the Poisson-Boltzmann
electrostatic model along with a cluster-based treatment of the multiple
titration state problem. Calculations were based upon crystallographic
structures of the mammalian cAMP dependent protein kinase (PKA), one
representing the so called closed form of the enzyme and the other
representing an open conformation. It was predicted that at pH 7 the
preferred form of the phosphate group at the catalytically essential
threonine 197 (P-Thr197) in the closed form is dianionic, whereas in the
open form a monoanionic ionization state is preferred. This dianionic
state of P-Thr197, in the closed form, is stabilized by interactions
with ionizable residues His87, Arg165 and Lys189. Our calculations
predict that the hydroxyl of the Ser residue in the peptide substrate is
very difficult to ionize, both in the closed and open structures of the
complex. Also, the supposed catalytic base, Asp166, does not seem to
have a pKa appropriate to remove the hydroxyl group proton of the
peptide substrate. However, when Ser of the peptide substrate is forced
to remain ionized, the predicted pKa of Asp166 increases strongly which
suggests that the Asp residue is a likely candidate to attract the
proton if the Ser residue becomes deprotonated, possibly during some
structural change preceding formation of the transition state. Finally,
in accord with suggestions made on the basis of the pH-dependence of
kinase kinetics, our calculations predict that Glu230 ahnd His87 are the
residues responsible for the molecular pKas of 6.2 and 8.5, observed in
the experiment.
Computer Simulation of Protein-Protein Association Kinetics: Acetylcholinesterase-FasciculinAdrian H. Elcock, Razif R. Gabdoulline, Rebecca C. Wade and J. Andrew McCammonJournal of Molecular Biology, Vol. 291, Issue 1, pp. 149-162 (1999) [PubMed 10438612]Computer simulations were performed to investigate the role of
electrostatic interactions in promoting fast association of
acetylcholinesterase with its peptidic inhibitor, the neurotoxin
fasciculin. The encounter of the two macromolecules was simulated with
the technique of Brownian dynamics (BD), using atomically detailed
structures, and association rate constants were calculated for the wild
type and a number of mutant proteins. In a first set of simulations, the
ordering of the experimental rate constants for the mutant proteins was
correctly reproduced, although the absolute values of the rate constants
were overestimated by a factor of around 30. Rigorous calculations of
the full electrostatic interaction energy between the two proteins
indicate that this overestimation of association rates results at least
in part from approximations made in the description of interaction
energetics in the BD simulations. In particular, the initial BD
simulations neglect the unfavourable electrostatic desolvation effects
resulting from the exclusion of high dielectric solvent that accompanies
the approach of two low dielectric proteins. This electrostatic
desolvation component is so large that the overall contribution of
electrostatics to the binding energy of the complex is unlikely to be
strongly favourable. Nevertheless, electrostatic interactions are still
responsible for increased association rates because even if they are
unfavourable in the fully-formed complex, they are still favourable at
intermediate protein-protein separation distances. It therefore appears
possible for electrostatic interactions to promote the kinetics of
binding even if they do not make a strongly favourable contribution to
the thermodynamics of binding. When an approximate description fo these
electrostatic desolvation effects is included in a second set of BD
simulations, the relative ordering of the mutant proteins is again
correctly reproduced, but now association rate constants that are much
closer in magnitude to the experimental values are obtained. Inclusion
of electrostatic desolvation effects also improves reproduction of the
experimental ionic strength dependence of the wild type associate rate.
Method for Including the Dynamic Fluctuations of a Protein in Computer-Aided Drug DesignHeather A. Carlson, Kevin M. Masukawa and J. Andrew McCammonJournal of Physical Chemistry A, Vol. 103, No. 49, pp. 10213-10219 (1999)
We have recently presented a new pharmacophore design method that allows
for the incorporation of the inherent flexibility of a target active
site. The flexibility of the enzymatic system is described by collecting
many conformations of the uncomplexed protein; this ensemble of
conformational states can come from a molecular dynamics (MD)
simulation, multiple crystal structures, or many NMR structures. Binding
sites that complement the active site are determined through
multiple-copy calculations. These calculations are conducted for each
protein conformation, providing a large collection of potential binding
sites. The Cartesian coordinates from each protein conformation are
overlaid through RMS fitting of essential catalytic residues, and the
pharmacophore model is described by binding regions that are conserved
over many protein conformations. Previously, we developed a "dynamic"
pharmacophore model for HIV-1 integrase using 11 conformations of the
protein from an MD simulation; the MUSIC procedure was used to calculate
binding positions for methanol molecules in each configuration of the
active site. Here we present "static" pharmacophore models developed
with a single conformation of the protein from two new crystal
structures (standard protocol for multiple-copy methods). The static
models do not perform as well as the previous dynamic model in fitting
known inhibitors of HIV-1 integrase. To test the applicability of the
dynamic pharmacophore method and the assumption that any reliable source
of protein conformations is applicable, we have now developed a second
dynamic pharmacophore model based on the two crystal structures also
used for the development of the static models. Though the dynamic model
based on the two crystal structures does not fit as many known
inhibitors as the previous dynamic model, it is a significant
improvement over the static models. Even better performance is expected
with the addition of more crystal structures if they become available.
However, it is notable that using only two structures leads to great
improvement in the models.
Annealing Accounts for the Length of Actin Filaments Formed by Spontaneous PolymerizationDavid Sept, Jingyuan Xu, Thomas D. Pollard and J. Andrew McCammonBiophysical Journal, Vol. 77, No. 6, pp. 2911-2919 (1999) [PubMed 10585915]We measured the lengths of actin filaments formed by spontaneous
polymerization of highly purified actin monomers by fluorescence
microscopy after labeling with rhodamine-phalloidin. The length
distributions are exponential with a mean of about 7 um (2600 subunits),
independent of the initial concentration of actin monomer. The
polymerizaiton of actin is modeled using a nucleation-elongation
reaction scheme. With the addition of filament annealing and fragmenting
we can reproduce the observed average length over a wide range of actin
concentrations. The effect of capping protein, CapZ, on the mean length
is also modeled.
Technique for Developing a Pharmacophore Model that Accommodates Inherent Protein Flexibility: An Application to HIV-1 IntegraseKevin M. Masukawa, Heather A. Carlson and J. Andrew McCammonIn "Pharmacophore Perception, Development, and Use in Drug Design," O.F. Güner, Ed., International University Line, La Jolla, CA, pp. 409-427 (1999)
We present a new method for the development of pharmacophore models that
account for the inherent flexibility of a target active site. The
flexibility of the enzymatic system is described by collecting many
conformations of the uncomplexed protein from a molecular dynamics (MD)
simulation. The binding sites for functional groups that complement the
active site are determined through a series of multi-unit search for
interacting conformers (MUSIC) simulations. MUSIC simulations are
conducted for each saved conformation of the protein, providing a large
ocllection of potential binding sites. The binding sites from each
protein conformation are overlaid, and the pharmacophore model is
described by the conserved binding regions for the probe molecules. The
"dynamic" pharmacophore model presented in this study is the first
reported receptor-based pharmacophore model for HIV-1 integrase. Using
standard protocol for multiple-copy simulations, "static" pharmacophore
models were developed with the crystal structure that was used to
initialize the MD studies and two additional crystal structures that
became available after the completion of the MD study. The pharmacophore
models were compared to known inhibitors of the integrase. The dynamic
model compares much more favorably with the set of known inhibitors than
do the static models, implying that new compounds determined with the
dynamic model have a greater potential for inhibition than those
identified with the static models.
Computer Simulations of Actin Polymerization Can Explain the Barbed-Pointed End AsymmetryDavid Sept, Adrian H. Elcock and J. Andrew McCammonJournal of Molecular Biology, Vol. 294, Issue 5, pp. 1181-1189 (1999) [PubMed 10600376]Computer simulations of actin polymerization were performed to
investigate the role of electrostatic interactions in determining
polymerization rates. Atomically-detailed models of actin monomers and
filaments were used in conjunction with a Brownian dynamics method. The
simulations were able to reproduce the measured barbed end association
rates over a range of ionic strengths and predicted a slower growing
pointed end, in agreement with experiment. Similar simulations
neglecting electrostatic interactions indicate that configurational and
entropic factors may actually favor polymerization at the pointed end,
but electrostatics interactions remove this trend. This result would
indicate that polymerization at the pointed end is not only limited by
diffusion, but faces electrostatic forces that oppose binding. The
binding of the Actin Depolymerizing Factor (ADF) and G-actin complex to
the end of a filament was also simulated. In this case, electrostatic
steering effects lead to an increase in the simulated association rate.
Together, the results indicate that simulations provide a realistic
description of both polymerization and the binding of more complex
structures to actin filaments.