Article
pubs.acs.org/JACS
Molecular Dynamics of β‑Hairpin Models of Epigenetic Recognition
Motifs
Xiange Zheng,† Chuanjie Wu,† Jay W. Ponder,† and Garland R. Marshall*,‡
†
Departments of Chemistry and of Biochemistry and ‡Molecular Biophysics, Washington University, St. Louis, Missouri 63105,
United States
* Supporting Information
ABSTRACT: The conformations and stabilities of the β hairpin
model peptides of Waters (Riemen, A. J.; Waters, M. L. Biochemistry
2009, 48, 1525; Hughes, R. M.; Benshoff, M. L.; Waters, M. L.
Chemistry 2007, 13, 5753) have been experimentally characterized as a
function of lysine ε methylation. These models were developed to
explore molecular recognition of known epigenetic recognition motifs.
This system offered an opportunity to computationally examine the
role of cation−π interactions, desolvation of the ε methylated
ammonium groups, and aromatic/aromatic interactions on the
observed differences in NMR spectra. AMOEBA, a second generation
force field (Ponder, J. W.; Wu, C.; Ren, P.; Pande, V. S.; Chodera, J.
D.; Schnieders, M. J.; Haque, I.; Mobley, D. L.; Lambrecht, D. S.;
DiStasio, R. A., Jr.; Head Gordon, M.; Clark, G. N.; Johnson, M. E.;
Head Gordon, T. J. Phys. Chem. B 2010, 114, 2549), was chosen as it includes both multipole electrostatics and polarizability
thought to be essential to accurately characterize such interactions. Independent parametrization of ε methylated amines was
required from which aqueous solvation free energies were estimated and shown to agree with literature values. Molecular
dynamics simulations (100 ns) using the derived parameters with model peptides, such as Ac R W V W V N G Orn K(Me)n I
L Q NH2, where n = 0, 1, 2, or 3, were conducted in explicit solvent. Distances between the centers of the indole rings of the
two tryptophan residues, 2 and 4, and the ε methylated ammonium group on Lys 9 as well as the distance between the N and
C termini were monitored to estimate the strength and orientation of the cation−π and aromatic/aromatic interactions. In
agreement with the experimental data, the stability of the β hairpin increased significantly with lysine ε methylation. The ability
of MD simulations to reproduce the observed NOEs for the four peptides was further estimated for the monopole based force
fields, AMBER, CHARMM, and OPLSAA. AMOEBA correctly predicted over 80% of the observed NOEs for all 4 peptides,
while the three monopole force fields were 40−50% predictive in only 2 cases and approximately 10% in the other 10 examples.
Preliminary analysis suggests that the decreased cost of desolvation of the substituted ammonium group significantly
compensated for the reduced cation−π interaction resulting from the increased separation due to steric bulk of the ε methylated
amines.
■
INTRODUCTION
Cation−π interactions play a vital role in biomolecular
recognition. Interactions between basic and aromatic side
chains have been shown to contribute to folding in natural and
de novo designed proteins as well as small structured
peptides.1−6 Interactions between small molecules and proteins
are also mediated by cation−π interactions.7−10 Perhaps, the
best studied system in which a small molecule, acetylcholine, is
selectively hydrolyzed by the enzyme acetylcholinesterase,
depends on diffusion of the charged tetramethylammonium
group of choline down a long tunnel of aromatic residues to the
active site.11,12 In one well studied example of the role of
cation−π interactions in protein/protein recognition,13 the
photoactivated rhodopsin bound conformation of an undeca
peptide was shown to be folded with an almost ideal cation−π
interaction.14 The ε nitrogen of lysine was ideally located above
the phenyl ring of the phenylalanine and also salt bridged with
© 2012 American Chemical Society
the C terminal carboxyl group. As such, this provided a unique
experimental system to probe the relative contributions of the
cation−π and salt bridge interactions to the conformational
stability.15,16 This receptor bound conformation has recently
been independently confirmed by DEER spectroscopy.17
Molecular Recognition in Epigenetics. Some protein−
protein interactions that control gene expression are recognized
by a cation−π interaction between trimethyllysine (KMe3,
where methylation is on the ε amino group) and an aromatic
pocket.4,18−20 Incorporation of methylated lysine residues at
specific locations of the histone tails facilitates recruitment of
chromatin remodeling proteins regulating chromatin conden
sation and gene expression.18 Proteins involved in chromatin
remodeling, including chromodomains, PHD domains, and
Received: July 18, 2012
Published: August 30, 2012
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Figure 1. Diagnostic NOEs observed by Rieman and Waters21 in the series of four peptides differing by the degree of lysine 9 ε N methylation. (a)
Lys; (b) Lys(Me); (c) Lys(Me2); (d) Lys(Me3). Red arrows indicate NOEs between Lys(Me)n and Trp2; green arrows indicate NOEs between
Lys(Me)n and Trp4; cyan arrows indicate NOEs between Lys(Me)n and Leu11.
Tudor domains, recognize and bind the histone ε trimethylated
lysine with an aromatic cage made up of three or four aromatic
rings,19,20 for example, KMe3 of histone 3A bound to the
aromatic pocket containing two tyrosines and a tryptophan of
the HP1 chromodomain (PDB code: 1KNE, Figure 2a). The
stabilizing forces between the ε methylated lysine and its
aromatic binding pocket are driven by cation−π and van der
Waals interaction (Figure 1).4,19,20 Model peptides to
investigate interactions of methylated lysines were developed
by Rieman and Waters based on known biological systems of
epigenetic recognition.21 In each case of the four model β
hairpin peptides of this study, two of the aromatic residues
reside within a β sheet, forming a cleft for the modified lysine
side chains (Figure 2).
Gas-phase Models of Cation−π Interactions. A
prototypical example of a cation−π system is a single
monatomic ion interacting with a benzene molecule in the
gas phase.5 For example, a classic study from Kebarle’s group
determined an experimental standard state interaction enthalpy
(ΔH) of −18.3 kcal/mol for the K+ benzene system22 via
molecular beam mass spectrometry methods. Amicangelo and
Armentrout23 used threshold collision induced dissociation
(TCID) experiments to obtain ΔH = −17.5 kcal/mol for K+
benzene. Quantum mechanical estimation of this cation−π
interaction energy (ΔE) exhibits only a relatively weak
dependence on basis set and level of theory. Amunugama
and Rodgers24 reported ΔE = −18.5 kcal/mol at MP2/6
311+G(2d,2p), while Feller, et al.25 obtained ΔE = −20.6 kcal/
Figure 2. (a) Structure of the aromatic binding pocket of the HP1
chromodomain bound to a histone peptide containing trimethyllysine
(KMe3, green); β sheet structure is shown in blue (PDB 1KNE). (b)
Structure of the aromatic binding pocket of the BPTF PHD domain
bound to a histone peptide containing KMe3 (green); β sheet
structure is shown in blue (PDB 2FUU). (c) NMR structure of the β
hairpin peptide WKMe3 indicating the cation−π interaction between
Trp and KMe3 (green); β sheet structure is shown in blue (3). From
Rieman and Waters.21
mol and ΔH = −20.1 kcal/mol at CCSD(T)/CBS. Standard
fixed charge force field models, such as CHARMM, Amber and
OPLS AA, use ion parameters fit to reproduce liquid phase ion
hydration and benzene parameters reasonable for liquid
benzene. Due to the neglect of polarization, these parameters
underestimate the strength of the K+ benzene interaction.
Simple energy minimization yields interaction energies of −9.3
kcal/mol (OPLS AA), −11.1 kcal/mol (CHARMM22) and
−12.6 kcal/mol (Amber ff 99). The AMOEBA force field yields
an interaction energy of −20.6 kcal/mol and a corresponding
ΔH of −19.4 kcal/mol. In AMOEBA, roughly half of the
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Tyr. Only the Arg/Phe combination proved more stable than
the control, Lys/Glu, and the authors suggested that hydro
phobic packing of Arg side chain methylenes rather than a
cation−π interaction was responsible. Other studies by Andrew
et al.37 of interactions between Val/Ile and Lys/Arg in the i and
i + 4 positions found helix stabilizations between −0.14 and
−0.32 kcal/mol. In addition, the nonpolar/polar pairs Ile Lys,
Ile Arg, and Val Lys occur in protein helices more often than
expected. Phe Lys, Lys Phe, Phe Arg, Arg Phe, and Tyr Lys
were all stabilizing by −0.10 to −0.18 kcal/mol when placed i, i
+ 4 on the surface of a helix in aqueous solution. The similarity
in the experimental values for helix stabilization between
nonaromatic hydrophobic side chains such as Val and Ile and
aromatic side chains with Arg and Lys suggest that much of the
stabilization energy measured for aromatic residues with Lys/
Arg may simply arise from hydrophobic forces rather than
cation−π stabilization alone. Tatko and Waters, however,
compared2 the interaction of norleucine (Nle) and Lys with
Phe, Trp, or Cha (R cyclohexylalanine) in the diagonal
positions of a designed β hairpin and found that interaction
energies between Lys and Phe or Trp were between −0.2 and
−0.4 kcal/mol. The interaction energies between Nle and Phe
or Trp were slightly less favorable (−0.1 to −0.2 kcal/mol).
The NMR and thermal denaturation studies showed that the
Lys side chain interacts in a specific manner with Phe or Trp
through the polarized Cε, and Nle does not interact in a
specific manner with either aromatic side chain. These results
indicate that Lys and Nle interact in fundamentally different
ways with aromatic residues, arguing that observed cation−π
interactions were not predominately hydrophobic in nature.
The debate about the strength of cation−π interactions and
their role in protein/peptide folding is ongoing and multi
faceted; while there is little doubt about the importance of the
cation−π interaction among noncovalent forces, considerable
controversy still exists in the literature regarding the relative
strengths of such interactions. The large differences in
energetics predicted by calculations and the question of the
relative strengths of cation−π versus salt bridge interactions
prompted a detailed computational analysis of the best
characterized experimental system of β hairpins developed by
the Waters group,21,38−40 one of the most robust for
experimentally probing the strength of cation−π interactions.
In particular, the papers of Rieman and Waters describing the
syntheses and physical chemical characterization of two differ
ent sequences of dodecameric peptides that form β hairpins
differing only in the degree of lysine ε methylation21,38 (Figure
1) and another by Hughes et al. describing the impact of
shortening the lysine side chain by one or two methylenes for a
similar series of ε N methylated peptides41 provided excellent
biophysical characterizations. This characterization of peptide
conformations afforded an excellent opportunity for molecular
dynamics simulations in explicit solvent to examine in detail the
fundamental basis of differences in stability with direct
comparison to precise experimental characterization. One
might speculate that the enhanced lipophilicity of the
methylated ammonium groups would be counter balanced by
a decrease in the cation−π interaction due to delocalization of
the charge and steric repulsion of the N methyls by the indole
rings. In order to computationally characterize these peptides, a
second generation force field AMOEBA was chosen as it
includes multipole electrostatics and polarizability.42 Limita
tions of monopole electrostatics in reproducing the geometries
of aromatic interactions are well known.43 The AMOEBA force
overall attraction arises from polarization terms. Experimental
results for the similar sized NH4+ ion provide a NH4+ benzene
enthalpy of −19.3 kcal/mol,26 while AMOEBA dynamics
simulation gives ΔH = −19.0 kcal/mol for this system.
Strength of Cation−π Interactions. The role of cation−π
interactions in molecular recognition has been a topic of some
controversy. In particular, the relative strength of cation−π
interactions compared with salt bridges has produced
significant disagreement between theoretical and experimental
estimates.15 Theoretical studies by Gallivan and Dougherty27
suggested that a cation−π interaction in solvent with a protein
like dielectric (ethyl acetate, ε ≈ 5.99) contribute maximally
−6.2 kcal/mol to the free energy (ΔG) of the system. By their
calculations, the cation−π interaction was relatively insensitive
to dielectric since the calculated value in water (ε ≈ 78) was
only reduced to −5.5 kcal/mol. The value for the salt bridge,
however, was −19.7 kcal/mol in ethyl acetate and reduced to
−2.2 kcal/mol in water in agreement with Coulomb’s law.
Additional gas phase calculations by Mo et al.28 estimated the
intermolecular interaction energy at between −6 and −12 kcal/
mol for a series of nonbonded complexes of N substituted
piperidines and substituted monocyclic aromatics and sug
gested that the interaction had significant polarization and
charge transfer components. The procedure used in both cases,
however, compared a charged state for the cation−π interaction
with a neutral state for the salt bridge.15
On the other hand, Hunter et al.29,30 estimated the energy of
a pyridinium cation−π interaction in chloroform (ε ≈ 4−5) at
only −2.5 ± 0.4 kJ/mol or −0.6 ± 0.1 kcal/mol by a chemical
double mutant cycle, in agreement with experimental studies on
the modeled system. Bartoli and Roelens31 showed both
experimentally and computationally that the counteranion has a
dramatic effect on the strength of the interaction in a cation−π
interaction in a model lipophilic cyclophane system with a
series of tetramethylammonium (TMA) and acetylcholine salts
in CDCl3. The charge dispersion on the anion was a major
factor in determining the influence of the anion on the strength
of the cation−π interaction. An anion with a diffuse negative
charge such as picrate yielded a ΔG of approximately −2 kcal/
mol for the cation−π interaction in chloroform, but an anion
with a more concentrated charge such as acetate limited the ΔG
of the interaction to approximately −0.6 kcal/mol in CDCl3.
Experimental Estimates of the Interaction Strength of
Cation−π Interactions. The most thorough experimental
estimates of cation−π strengths have come from model peptide
studies. Such studies often focus on helix or β hairpin32 model
peptides whose relative stabilities as a function of amino acid
sequence can be quantitated. Fernandez Recio et al.33 studied
the interaction between tryptophan and histidine pairs in either
the i and i + 3 or i and i +4 positions in an α helix. Helix
stabilization was only seen with Trp/His+ in the i/i + 4
orientation and estimated at −1 kcal/mol. Tsou et al.34
estimated the extent of α helix stabilization by the interaction
between a protonated amine (lysine, ornithine, and diamino
butyric acid) and the phenyl ring of phenylalanine in water as
−0.4 kcal/mol, seen only in the Phe Orn case. Similar studies
using a designed β hairpin to orient the interacting residues
measured interaction energies between Phe or Trp and Lys or
Arg in diagonal positions on the β hairpin at between −0.20
and −0.48 kcal/mol.35 It has been suggested that observed
cation−π interactions are more hydrophobic in nature than
electrostatic. Slutsky and Marsh36 used a model coil−coil
peptide to estimate the interaction between Arg and Phe/Trp/
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nonpolarizable force fields, including the CHARMM22 Proteins,51
AMBER,49 and OPLS AA.52 Each system was solvated with a 12 Å
water box using the TIP3P water model53 and neutralized with an
ionic strength of 40 mM NaCl. The parameters and settings used in all
simulations with these force fields were as follows: (1) the isothermal
isobaric ensemble (NPT) at 1 atm pressure, using the Nosé Hoover
Langevin piston54 with a decay period of 200 fs (damping time scale of
100 fs for heating and equilibration phases and 500 fs for production
phase); (2) a bond interactions calculation frequency of 2 fs, short
range electrostatics and van der Waals interactions frequency of 2 fs,
with 10.0 Å as cutoff and 8.5 Å as smooth switching; (3) long range
computing frequency of 4 fs, with PME grid points at least 1 Å in all
directions, and (4) rigidBonds applied to constrain all bonds between
hydrogens and heavy atoms. Minimization, heating and equilibration
were performed prior to the MD run in order to eliminate steric
clashes, minimize water−protein interactions, and stabilize the
solvated systems. A time step of 1 fs was used in minimization while
2 fs in heating and equilibration. Other parameters utilized in these
steps include: (1) minimization of the system for 6 ps with backbone
atoms fixed followed by another 6 ps with the constraints removed;
(2) heating the system from 0 to 300 K in 75 K intervals, each for 16
ps; with restraints applied on C alpha atoms; (3) equilibrating the
system for 80 ps with C alpha atoms restrained followed by another
600 ps with all restraints removed. The MD simulations were then
resumed as production runs for 100 ns.
Force-field Preparation and Parametrization of Nonstandard
Residues. Parameterization methodology of the methylated lysine
residues for the AMOEBA force field is described in detail below. In
simulations using the NAMD package, three types of force field were
used: AMBER, CHARMM, and OPLSAA. In the CHARMM force
field, the parameters of nonstandard residues were transferred from
similar atom types of the lysine residue in the same force field. With
the AMBER force field, the two input files required by NAMDthe
topology/parameter file (.prmtop) and initial coordinate file
(.inpcrd)as well as the parameters of nonstandard residues, were
prepared using the xleap module and the leaprc.ff10 force field of
AMBER 11.55 The CHARMM format OPLS AA force field of
standard residues was obtained from Mackerell’s charmm tarball
(http://mackerell.umaryland.edu/CHARMM ff params.html) that
was included in the c35b2 and c36a2 release of the CHARMM
program and derived from the Jorgensen’s original OPLS force field.52
The OPLS AA parameters for nonstandard residues were imple
mented manually: their RESP charges were derived from QM
calculations performed for the AMOEBA parameters, and valence
and vdW parameters transferred to similar atom types of the regular
lysine residue in the CHARMM force field.
Analyses of MD Simulations. The primary source for
experimental validation was the NMR experimental NOE studies
monitoring the stability of the β hairpin structure with the cation−π
and aromatic/aromatic interactions between the two indole rings
(Trp 2 and Trp 4) and the ε methylated ammonium groups of Lys 9
that were essential. For this reason, the distances between the α
carbons of the C and N terminal residues of the peptide were
monitored as well as distances between the protonated nitrogen of
Lys(Me)n, where n = 0 to 3 and the centers of mass of the two indole
rings of Trp 2 and Trp 4. In addition, the MD simulations were
evaluated with regards to their ability to predict the diagnostics NOEs
for the four model peptides reported by Rieman and Waters21 (Figure
1).
field has been validated by numerous studies comparing
calculated structures with high resolution experimental data.42
In particular, the relative solvation free energies of protonated
ammonium, methyl ammonium, dimethyl ammonium and
trimethyl ammonium were calculated with AMOEBA42 after
parametrization in this study and shown to agree with
experimental estimates as well as those calculated by Kelley
et al. using the SM6 continuum solvation model.3
■
METHODS
Parameterization of Methylammonium Series. Most of the ε
methylated lysine parameters were transferred from the existing
AMOEBA force field for proteins and small organic molecules. The
−N−CH3 group related torsion and vdW parameters did not exist in
current parameters and were developed with methylammonium ion
model compounds. The vdW parameters of −NH atoms in the ε
methylated lysine were adjusted to reproduce the methylammonium
ion−water dimer hydrogen bond structure optimized at MP2 level
with the 6 311++G(d,p) basis set using Gaussian 09, Revision A.02.44
The HCNC torsion in ε methyl lysine and CCNC torsion parameters
in ε mono , di , trimethyl lysine residues were fit to the ab initio
potential energy surfaces obtained with MP2/6 31G* calculations.
The potential surfaces were reproduced by restrained optimization
while fixing the specific torsions examined. Torsional parameter fitting
was carried out with TINKER TORSFIT program.45
The electrostatic parameters for the ε methylated lysine dipeptides
(lysine capped with N methylamide and acetyl groups) were derived
with Stone’s distributed multipole analysis program GDMA46 and
TINKER POLEDIT.45 DMA was set to the original setting for
calculating multipoles with the fully analytical integrals (set parameter
SWITCH in GDMA 2.x to 0). The wave functions were from MP2/6
311G(d,p) calculations. The AMOEBA electrostatic potentials around
the methylated lysines were validated with the TINKER POTENTIAL
program.45 Potential grids were 1.0 Å distant from the vdW shell of
each atom. There were 5 layers of grids spherically and uniformly
distributed around the molecule with a spacing of 0.35 Å between the
layers on which comparative electrostatic potentials were calculated
(for a more detailed description of current AMOEBA parametrization,
see Ren et al.47).
Molecular Dynamics Simulations. All MD simulations were
preformed at the Washington University High Performance Comput
ing Facility. The group of Prof. Pengyu Ren of the Department of
Biomedical Engineering at the University of Texas assisted Mr.
Malcolm Tobias and Dr. Xiange Zheng in installing their version
(PMEMD) of AMOEBA42 on the IBM supercomputer cluster. The β
hairpin systems were solvated with water, and neutralized with Na+
and Cl− counterions. The fully solvated systems contained between
7460 and 7661 atoms depending on the degree of methylation. The
MD simulations were undertaken with periodic boundary conditions
using both the NAMD version 2.6b148 and PMEMD49 simulation
package. Particle mesh Ewald (PME)50 was used to account for long
range electrostatics interactions.
PMEMD is the parallel version of AMBER49 module Sander; a
customized version of PMEMD from Prof. Pengyu Ren’s group at the
University of Texas, which incorporated the multipole, polarizable
force field AMOEBA,42 was utilized in this work. Each system was
prepared in the following steps before the production MD run: (1)
minimization to 0.1 D with a restraint of 500.0 kcal/mol/Å2 applied to
the protein; (2) minimization to 0.01 D with a restraint of 100.0 kcal/
mol/Å2 applied to the protein; (3) minimization to 0.01 D with
restraint removed; (4) heating from 0 to 300 K for 50 ps and
equilibration for 25 ps with protein restrained by 2.0 kcal/mol/Å2; (5)
equilibration for 200 ps with restraint removed. Subsequently, The
MD simulations were performed for 100 ns with a 1 fs time step, and
trajectories were saved every 20 ps. A nonbonded cutoff of 12 Å was
applied in the PMEMD simulations.
MD Simulations using NAMD. To determine the utility of
multipole electrostatics and polarization, simulations were also
performed with the NAMD program using several monopole,
■
RESULTS AND DISCUSSION
MD simulations of the ε methylated lysine series of β hairpin
models of Waters21,41 have been conducted with multiple force
fields in explicit solvent. The use of AMOEBA was essential
since it includes both multipole electrostatic and polarizability
that were crucial in reproducing the physics of electrostatic in
the cation−π and aromatic/aromatic interactions. One possible
limitation in this study was the length of the MD simulations
achieved to adequately sample conformational transitions.
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Because of the enhanced complexity of energetic interactions
with the AMOEBA multipole potentials compared with those
using simpler monopole electrostatics, AMOEBA requires
significantly longer computational times for the same
simulation.
AMOEBA Force-Field Parameterization. The first prior
ity was AMOEBA parametrization of the ε methylated amines
of lysine. We used mono through tetramethylammonium ions
to model the ε methylated lysines for parametrizing necessary
vdW and valence parameters. The vdW parametrization results
for the N and the polar H atoms in methylammonium are
shown in Table 1. The model compound here was
methylammonium ion. It interacted with water at the N−H
side. The hydrogen bond energy is for the dimer with N−H
O hydrogen bond (Figure 3).
Table 1. Methylammonium Ion Water Dimer Results after
Adjusting N and HN vdW Parameters
QM (MP2/6-311++G** opt., MP2/aug-ccpVTZ single point with BSSE)
N(MeAm+)
O(water)
C(MeAm+)
O(water)
Intermolecular
Energy
2.75 Å
2.78 Å
3.50 Å
3.53 Å
18.30 kcal/mol (after BSSE)
18.92 kcal/mol (before BSSE)
Figure 4. Torsional parameters for methylated ammoniums. Lines =
QM potential energy plots. Symbols = AMOEBA energies for the
corresponding conformations. C−N−CH torsion in dimethylammo
nium, rmsd = 0.07 kcal/mol; (blue line, triangle): CCNC torsion in
dimethylammonium, rmsd = 0.13 kcal/mol; (green line, star): CCNC
torsion in trimethylammonium, rmsd = 0.39 kcal/mol; (red line,
square): CCNC in tetramethylammonium, rmsd = 0.40 kcal/mol
(pink line, circle).
AMOEBA
18.74
kcal/mol
Table 2. Calculated Hydration Free Energy (kcal/mol) of
Methylated Ammoniums Using AMOEBA Parameters
Versus Experimental Values58
Kelley et al.58
AMOEBA
absolute
NH4+
CH3NH3+
(CH3)2NH2+
(CH3)3NH+
(CH3)4N+
Figure 3. Methylammonium ion water dimer.
AMOEBA gave excellent agreement with the QM results for
both structure and energetics. The necessary torsional fitting
shown in Figure 4. Lys(Me) was represented by a
dimethylammonium ion, Lys(Me2) was represented by the
trimethylammonium ion, and Lys(Me3) was represented by the
tetramethylammonium ion.
On the basis of Figure 4, the AMOEBA torsional potentials
agreed with the QM results. C−N−C−H torsion in
dimethylammonium, rmsd = 0.07 kcal/mol; (blue line,
triangle): CCNC torsion in dimethylammonium, rmsd = 0.13
kcal/mol; (green line, star): CCNC torsion in trimethylammo
nium, rmsd = 0.39 kcal/mol; (red line, (pink line, circle)
square): CCNC in tetramethylammonium, rmsd = 0.40 kcal/
mol. All the RMSDs were 0.4 kcal/mol or less. This ensured
reliable dynamic torsional sampling during the MD simulations.
AMOEBA has recently been used to study the solvation of
chloride ion56 and Zn(II).57 AMOEBA parameters for the
substituted ammonium ions were first used to predict their
solvation free energies. Fortunately, experimental solvation free
energies for these compounds had been carefully collected by
the Truhlar group58 for the series with the exception of
tetramethylammonium. They also did the implicit SCRF
solvation calculation for these compounds with their SM6
model. These data provided an independent method to validate
(Table 2) the AMOEBA parameters derived from quantum
mechanics and distributed multipole analysis.59
a
73.429
64.325
56.394
49.336
43.215
relative
absolute*a
relative
0.0
9.1
17.0
24.1
30.2
180.7
189.5
197.3
204.8
N/A
0.0
8.8
17.4
24.1
Absolute* = scaled relative to the solvation of a proton.
As mentioned in the Methods Section, the electrostatic
parameters were derived directly from the QM calculated wave
functions of the ε methylated lysine dipeptides. The potential
validation results are shown in Table 3. They show an excellent
reproduction of the potentials around the molecules with the
newly parametrized AMOEBA force field.
Parameterization of ε-Methylated Lysines for Monopole Force Fields. A comparison of the ability of AMOEBA
with three monopole force fields (AMBER, CHARMM and
OPLS) utilizing monopole electrostatics without polarizability
to predict the observed NOEs for the four peptides required
Table 3. Electrostatic Potential Validation Results for ε
Methylated Lysines
average potential
(kcal/mol/grid)
Lys(Me)
Lys(Me2)
Lys(Me3)
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number of potential
grids
QM
AMOEBA
rms
(kcal/mol)
22808
23617
24278
51.76
51.07
50.40
51.82
51.11
50.48
0.48
0.72
0.55
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Figure 5. Distance distributions for 100 ns MD simulations in explicit solvent of four model β hairpin peptides with four different force fields. (a)
Data from MD simulation with OPLSaa force field. (b) Data from MD simulation with AMBER force field. (c) Data from MD simulation with
CHARMM force field. (d) Data from MD simulation with AMOEBA force field. W2K9 = distance between indole of Trp 2 and ε amine of Lys 9;
W2K9 = distance between indole of Trp 4 and ε amine of Lys 9; W2W4 = distance between indoles of Trp 2 and Trp 4; NTCT = distance between
carbon alphas of N and C terminal amino acids. Ordinate = relative percentage (%), Axis = Distance between residues (Å).
similar care in parametrization of the ε methylated lysines for
the monopole force fields. The CHARMM, AMBER, and
OPLS parameter charges were obtained from RESP fitting to
B3LYP/cc pVTZ potential. Torsions were validated with MP2/
6 31G* potential surface (the same as for AMOEBA). The
parameters and methodology used in their derivation for
AMBER, CHARMM and OPLSAA parameters are available for
further examination (see Supporting Information).
In order to determine whether the lengths of the MD
simulations were sufficient for adequate conformational
sampling, two 100 ns MD simulations from different starting
NMR conformations were run for both AMOEBA and
CHARMM for all four peptide hairpins. Examination of the
distribution of distances cover by the two simulations gave
confidence that 100 ns MD simulations gave adequate coverage
of conformational space (data not shown). Comparison of
distance distribution plots for all MD simulations were
consistent with adequate sampling. In addition, visual
inspection of MD runs showed significant exploration of
conformational space.
Other conformational parameters, such as N to C terminal
carbon alpha distances, indoles to ε ammonium distance as well
as location of turn residues, strand register, and interstrand
hydrogen bonding (data not shown), were also monitored. The
distance distributions determined for the four hairpin models
were quite distinct in the AMOEBA simulations (Figure 5d)
15975
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Journal of the American Chemical Society
Article
Figure 6. (a) Diagnostic NOEs predicted by MD simulations for the Lys 9 peptide. Blue lines = correctly predicted NOEs; red lines = experimental
NOEs that were not predicted. (b) Diagnostic NOEs predicted by MD simulations for the Lys(Me) containing peptide. Blue lines = correctly
predicted NOEs; red lines = experimental NOEs that were not predicted. (c) Diagnostic NOEs predicted by MD simulations on the hairpin peptide
containing Lys(Me2). Blue lines = correctly predicted NOEs; red lines = experimental NOEs that were not predicted. (d) Diagnostic NOEs
predicted by MD simulations for the Lys(Me3) containing peptide. Blue lines = correctly predicted NOEs; red lines = experimental NOEs that were
not predicted.
and different from the other monopole force fields (Figure 5a−
c), but consistent with the different patterns of NOEs
determined experimentally by Rieman and Waters21 (Figure
1). In contrast, the distance distributions seen with the
monopole force fields were dramatically different, especially
as Lys 9 was methylated (Figure 5b−d). In particular, the
proximity of the Lys ε amino group to the indole rings,
especially the W2/K9 distance, was preserved across the series
of methylated hairpins in the AMOEBA simulations. Increased
methylation did destabilize the hairpin to some extent as
estimated by changes in the distributions of N−C distances
(Figure 5d); the decreased cost of desolvation of the ε
methylated Lys 9 ammonium group would appear to
significantly compensate hairpin stability for the reduced
cation−π interaction resulting from the increased distance
due to the steric bulk of the ε methylated amines.
One significant issue was the dramatic difference in distance
distributions seen between the MD results for each of the
three monopole force fields. This would seem to indicate that
the balance between specific intermolecular interactions has
been parametrized differently for AMBER, CHARMM and
OPLS to attempt to overcome limitations in the monopole
approximation. These differences may help to explain the
observations that the different monopole force fields favor
different secondary structures.
Comparison with NMR Data. The question remaining was
validation of the MD results with the experimental measure
ments. We analyzed differences in the MD simulations of the
four peptides to determine if the NOE patterns observed by
Rieman and Waters21 (Figure 1) were consistent with the
conformational ensembles observed by MD. The NOE patterns
observed between the indole rings and the ε amine of the lysine
side chains (Figure 1) seemed most diagnostic of differences in
peptide dynamics and the resulting conformational ensembles
as a function of lysine ε methylation. One must realize,
however, that the NOE patterns result from ensemble averages,
and do not represent any unique conformer(s).
15976
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Journal of the American Chemical Society
Article
Long MD simulations (100 ns) in water were performed for
each hairpin model with the four force fields. From the MD
simulations, the predicted NOEs were estimated by weighting
interatomic proton positions by 1/r6 in accord with previous
approaches.60,61 The predictability of the observed NOEs by
each of the four force fields for each of the four hairpin peptides
is shown in Figure 6a−d. It is apparent that AMOEBA
generates a conformational ensemble during the MD
simulations that, to a first approximation, resembles that
observed experimentally regardless of the amount of lysine ε
methylation (Figure 7). The monopole force fields do not,
peptides will be resynthesized, and additional NMR experi
ments will be performed to provide further relaxation data for
validation.
■
ASSOCIATED CONTENT
* Supporting Information
ε Methylated lysine parameters for the AMOEBA, OPLS AA
and Amber force fields in TINKER format. Figure S1. This
material is available free of charge via the Internet at http://
pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
garlandm@gmail.com
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
X.Z. and G.R.M. acknowledge support by contract HDTRA1
08 C 0015 from the Department of Defense. C.W. and J.W.P.
acknowledge support from NSF (CHE 0535675) and NIH
(R01 GM6955302). Discussions with Prof. Marcey L. Waters
of the Department of Chemistry at the University of North
Carolina, whose lab developed the model hairpin peptide
system and measured the experimental NOEs, were extremely
helpful.
Figure 7. Summary of the percentage of experimentally observed
NOEs for the four model β hairpin peptides predicted by 100 ns MD
simulation in explicit solvent by the four force fields compared.
■
presumably due to their inability to reproduce the complex
electrostatics of aromatic interactions. What is even more
perplexing is the lack of convergence of the different monopole
force fields in their predictions (Figure 6a−d, Figure 7,
Supplemental Figure 1a−d, Supporting Information). This
again suggests that the parameters developed for each
monopole force field may have chosen different weightings of
intermolecular forces. Supplemental Figure 1a−d shows the
overlap between NOEs predicted by the four different force
fields (including NOEs predicted and not observed) and the
experimentally measured NOEs for the four model hairpin
peptides. Again, the variance in prediction by the three
monopole force fields is consistent with fundamental differ
ences in parameter weights between them.
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■
CONCLUSIONS
The agreement between predicted and observed NOEs for
these four β hairpin model peptides, where the dynamics of
systems with aromatic/aromatic and cation−π interactions are
crucial, requires both an accurate force field as well as adequate
conformational sampling. The inability of the three force fields
using monopole electrostatics in common use raises serious
questions regarding any conclusions from molecular simu
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modeling studies of one recognition motif of epigenetics, ε
methylated lysines, can be studied with second generation force
f ields that consider multipole electrostatics and polarizability.
While the agreement between the NOEs predicted by the MD
simulations with AMOEBA are impressive and demonstrate the
necessity for more complex electrostatics in dealing with
aromatic/aromatic and cation−π interactions, the lack of
complete agreement raises a question. Is this an indication of
a need for further improvement in the parametrization of
AMOEBA, or simply minor experimental error in the NMR
experiments. In order to address this question, the four
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Journal of the American Chemical Society
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■
NOTE ADDED AFTER ASAP PUBLICATION
The Supporting Information file published September 17, 2012,
was incomplete. The complete file was posted September 26,
2012.
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S1
Supplementary:
ε -­Methylated Lysine Parameters in the Force-­Field Format for TINKER for
OPLS-­AA, AMBER Force Fields
a
a
a
Xiange Zheng , Chuanjie Wu , Jay W. Ponder , and Garland R. Marshall
a
b
b
Departments of Chemistry and of Biochemistry and Molecular Biophysics , Washington
University in St. Louis, MO 63105
Since ε-­‐methylated lysine parameters were missing in both AMOEBA and fixed
charges force fields OPLS-­‐AA, AMBER and CHARMM, force field parameterization or
proper parameter adaption was necessary before the simulations. The
parameterization for AMOEBA and the basis for CHARMM were described in the full
text. The parameterization for the missing parameters for ε-­‐methylated lysines in
OPLS-­‐AA and AMBER force fields follows:
1. Model Compounds
The three model compounds for parameterization are shown in Figure S1.
(a)
(b)
(c)
Figure S1. The ε-­methylated lysine dipeptides were used as model compounds for force
field paramerization. (a)(b)(c): ε-­mono-­, di-­, tri-­methylated lysine dipeptides.
2. Parameterization
We derived charges for OPLS-­‐AA and AMBER with RESP fitting for the ESP from
B3LYP/cc-­‐pVTZ as suggested by AMBER for MP2/6-­‐31g* optimized ε-­‐methylated
dipeptide compounds.
The stretch, bend, improper torsion and torsion parameters, vdW parameters were
transferred from atom types with similar chemical environment.
To validate the quality of the parameters adapted, we tested the potential surface of
torsion CCNC for the terminal methyl group. See Figure S2. The QM torsional energy
profile was from MP2/6-­‐31g* calculations. The torsional potential-­‐energy error for
S2
AMEBAR99 force field is 0.296 kcal/mol and the error for OPLS-­‐AA is 0.346
kcal/mol. They both show good transferability.
7
6
5
4
3
2
1
0
-­‐200
-­‐100
QM RE
0
100
AMBER RE
200
OPLS RE
Figure S2. The CCNC torsional potential-­energy profile comparison between MP2/6-­
31g*, AMBER99 force field and OPLS-­AA force field.
3. List of parameters
3.1. AMOEBA parameters for ε-­methylated lysines
(The following parameters work with amoebabio09.prm in TINKER 5.x or 6.x. The
atoms types here are only for the ε-­carbon, and atoms in ε-­methylated ammonium
groups. The other atoms in ε-­methylated lysine residues use atom-­type definitions for
the standard lysine residue in amoebabio09.prm)
#############################
##
##
## Atom Type Definitions ##
##
##
#############################
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
8
9
80
81
2
6
8
9
80
81
2
6
8
9
80
36
6
C1
H1
N
HN
C5
H5
C1
H1
N
HN
CM
HM
C1
H1
N
CM
HM
"MeLysine CE "
"MeLysine HE "
"MeLysine NZ "
"MeLysine HN "
"MeLysine CMe "
"MeLysine HMe "
"DiMeLysine CE "
"DiMeLysine HE "
"DiMeLysine NZ "
"DiMeLysine HN "
"DiMeLysine CMe"
"DiMeLysine HMe"
"TriMeLysine CE"
"TriMeLysine HE"
"TriMeLysine NZ"
"TriMeLysine CMe"
"TriMeLysine HMe"
################################
##
##
6
1
7
1
6
1
6
1
7
1
6
1
6
1
7
6
1
12.011
1.008
14.007
1.008
12.011
1.008
12.011
1.008
14.007
1.008
12.011
1.008
12.011
1.008
14.007
12.011
1.008
4
1
4
1
4
1
4
1
4
1
4
1
4
1
4
4
1
S3
## Van der Waals Parameters ##
##
##
################################
vdw
vdw
80
81
3.710
2.480
0.1050
0.0180
0.91
################################
##
##
## Bond Stretching Parameters ##
##
##
################################
bond
bond
bond
bond
2
8
36
80
80
80
80
81
381.3000
381.3000
381.3000
461.9000
1.5000
1.5150
1.5000
1.0150
################################
##
##
## Angle Bending Parameters ##
##
##
################################
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
6
8
9
6
2
2
2
2
8
8
8
36
36
81
2
8
8
36
80
80
80
80
80
80
80
80
80
80
80
80
80
80
2
8
81
81
8
36
81
36
81
81
59.0000
56.1000
59.0000
59.0000
65.0000
65.0000
43.2000
43.2000
65.0000
65.0000
43.2000
65.0000
43.2000
43.5000
108.500
109.500
108.500
108.500
110.520
114.520
109.500
109.500
110.520
114.520
107.500
110.520
109.500
105.500
################################
##
##
##
Stretch-Bend Parameters ##
##
##
################################
strbnd
strbnd
strbnd
strbnd
strbnd
strbnd
strbnd
strbnd
strbnd
strbnd
strbnd
strbnd
6
8
9
6
2
2
2
8
8
8
36
36
2
8
8
36
80
80
80
80
80
80
80
80
80
80
80
80
2
8
81
8
36
81
36
81
11.50
18.70
11.50
11.50
7.20
7.20
4.30
7.20
7.20
4.30
7.20
4.30
11.50
18.70
11.50
11.50
7.20
7.20
4.30
7.20
7.20
4.30
7.20
4.30
################################
##
##
##
Torsional Parameters
##
##
##
################################
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
6
6
6
8
9
8
8
8
8
9
9
9
9
6
6
6
2
2
2
8
8
8
8
8
8
8
8
8
8
36
36
36
80
80
80
8
8
80
80
80
80
80
80
80
80
80
80
80
2
8
81
80
80
2
8
36
81
2
8
36
81
8
36
81
1.765
0.000
0.000
0.000
0.000
1.394
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.252
0.000
-0.081
0.064
0.000
-0.233
-0.071
-0.071
0.000
0.000
0.000
0.000
-0.081
0.000
-0.071
-0.081
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1.030
0.000
0.370
0.605
0.374
1.308
0.886
0.886
-0.110
0.000
0.000
0.000
0.370
0.000
0.886
0.370
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
S4
#################################
##
##
## Atomic Multipole Parameters ##
##
##
#################################
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
multipole
163
163
163
400
401
402
403
404
405
406
407
408
409
410
411
400
406
412
402
400
400
402
402
404
408
406
406
408
408
410
161
161
161
163
402
404
400
405
402
163
408
410
406
411
408
-0.12718
0.12429
-0.01732
0.00000
-0.22732
-0.13698
0.11614
-0.00286
0.00000
-0.26264
-0.13773
0.11394
0.00198
0.00000
-0.24821
-0.03296
0.16603
-0.14932
0.00000
-0.13181
0.09334
-0.03664
-0.01377
0.00000
-0.02067
0.08833
0.13572
0.08279
0.00000
0.00389
0.18929
0.00673
0.00995
0.00000
0.01246
-0.02889
0.01865
-0.48932
0.00000
0.02644
0.09913
-0.02160
0.00472
0.00000
-0.01360
-0.08539
0.20162
-0.12691
0.00000
-0.13207
0.09377
-0.03374
-0.01110
0.00000
-0.01287
0.13019
0.14890
-0.04827
0.00000
-0.03040
0.20579
-0.00271
-0.00119
0.00000
0.00771
-0.06384
-0.01250
-0.46972
0.00000
-0.02857
0.09808
-0.02106
0.00592
0.00000
-0.00847
0.00000
0.29741
-0.57867
0.00000
0.59599
0.00000
0.29539
-0.58416
0.00000
0.58702
0.00000
0.30241
-0.55616
0.00000
0.55418
0.00000
0.21049
-0.73914
0.00000
0.88846
0.00000
-0.12153
0.01040
0.00000
0.00337
0.00000
0.16039
-0.30871
0.00000
0.22592
0.00000
-0.15689
0.00329
0.00000
-0.01324
0.00000
0.33839
-0.47604
0.00000
0.96536
0.00000
-0.15222
-0.00189
0.00000
-0.00283
0.00000
0.16753
-0.74314
0.00000
0.87005
0.00000
-0.11432
0.00380
0.00000
0.00730
0.00000
0.20881
-0.18819
0.00000
0.23646
0.00000
-0.12435
0.00826
0.00000
-0.00707
0.00000
0.33598
-0.50244
0.00000
0.97216
0.00000
-0.14714
-0.00913
0.00000
0.00321
S5
multipole
412
multipole
414
413
multipole
412
414
multipole
414
412
415
multipole
163
415
414
416
416
415
414
-0.15288
0.22193
-0.06542
0.00000
-0.13044
0.09491
-0.03254
-0.01078
0.00000
-0.01619
0.35898
0.02438
-0.15295
0.00000
0.06086
-0.12449
-0.00357
-0.46714
0.00000
-0.00656
0.09747
-0.02004
0.00175
0.00000
-0.00970
0.00000
0.11448
-0.85089
0.00000
0.91631
0.00000
-0.10870
0.00198
0.00000
0.00880
0.00000
0.13860
-0.00706
0.00000
0.16001
0.00000
0.28967
-0.47766
0.00000
0.94480
0.00000
-0.14251
-0.00632
0.00000
0.00457
######################################
##
##
## Dipole Polarizability Parameters ##
##
##
######################################
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
polarize
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
1.334
0.496
1.073
0.496
1.334
0.496
1.334
0.496
1.073
0.496
1.334
0.496
1.334
0.496
1.073
1.334
0.496
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
0.390
402
400
400
402
402
404
408
406
406
408
408
410
413
412
412
414
415
401
404
403
405
407
410
409
411
414
415
416
3.2. OPLS AA parameters in the force-­field format of TINKER:
(The following parameters are compatible with oplsaa.prm in TINKER 5.0 or 6.0)
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
35
13
3
13
4
36
13
36
13
36
13
36
13
36
43
44
13
36
35
13
N
CT
C
H
O
H1
CT
HC
CT
HC
CT
HC
CT
HP
N3
H
CT
HC
N
CT
"MetLysine N"
"MetLysine CA"
"MetLysine C"
"MetLysine HN"
"MetLysine O"
"MetLysine HA"
"MetLysine CB"
"MetLysine HB"
"MetLysine CG"
"MetLysine HG"
"MetLysine CD"
"MetLysine HD"
"MetLysine CE"
"MetLysine HE"
"MetLysine NZ"
"MetLysine HZ"
"MetLysine CH"
"MetLysine HC"
"DiMetLysine N"
"DiMetLysine CA"
7
6
6
1
8
1
6
1
6
1
6
1
6
1
7
1
6
1
7
6
14.010
12.010
12.010
1.008
16.000
1.008
12.010
1.008
12.010
1.008
12.010
1.008
12.010
1.008
14.010
1.008
12.010
1.008
14.010
12.010
3
4
3
1
1
1
4
1
4
1
4
1
4
1
4
1
4
1
3
4
S6
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
charge
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
3
34
4
36
13
36
13
36
13
36
13
36
43
44
13
36
35
13
3
34
4
36
13
36
13
36
13
36
13
36
43
13
36
C
H
O
H1
CT
HC
CT
HC
CT
HC
CT
HP
N3
H
CT
HC
N
CT
C
H
O
H1
CT
HC
CT
HC
CT
HC
CT
HP
N3
CT
HC
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
"DiMetLysine C"
"DiMetLysine HN"
"DiMetLysine O"
"DiMetLysine HA"
"DiMetLysine CB"
"DiMetLysine HB"
"DiMetLysine CG"
"DiMetLysine HG"
"DiMetLysine CD"
"DiMetLysine HD"
"DiMetLysine CE"
"DiMetLysine HE"
"DiMetLysine NZ"
"DiMetLysine HZ"
"DiMetLysine CH"
"DiMetLysine HC"
"TriMetLysine N"
"TriMetLysine CA"
"TriMetLysine C"
"TriMetLysine HN"
"TriMetLysine O"
"TriMetLysine HA"
"TriMetLysine CB"
"TriMetLysine HB"
"TriMetLysine CG"
"TriMetLysine HG"
"TriMetLysine CD"
"TriMetLysine HD"
"TriMetLysine CE"
"TriMetLysine HE"
"TriMetLysine NZ"
"TriMetLysine CH"
"TriMetLysine HC"
3.2500
3.5000
3.7500
0.0000
2.9600
2.5000
3.5000
2.5000
3.5000
2.5000
3.5000
2.5000
3.5000
2.5000
3.2500
0.0000
3.5000
2.5000
3.2500
3.5000
3.7500
0.0000
2.9600
2.5000
3.5000
2.5000
3.5000
2.5000
3.5000
2.5000
3.5000
2.5000
3.2500
3.5000
2.5000
1050 -0.5447
0.1700
0.0660
0.1050
0.0000
0.2100
0.0300
0.0660
0.0300
0.0660
0.0300
0.0660
0.0300
0.0660
0.0300
0.1700
0.0000
0.0660
0.0300
0.1700
0.0660
0.1050
0.0000
0.2100
0.0300
0.0660
0.0300
0.0660
0.0300
0.0660
0.0300
0.0660
0.0300
0.1700
0.0660
0.0300
6
1
8
1
6
1
6
1
6
1
6
1
7
1
6
1
7
6
6
1
8
1
6
1
6
1
6
1
6
1
7
6
1
12.010
1.008
16.000
1.008
12.010
1.008
12.010
1.008
12.010
1.008
12.010
1.008
14.010
1.008
12.010
1.008
14.010
12.010
12.010
1.008
16.000
1.008
12.010
1.008
12.010
1.008
12.010
1.008
12.010
1.008
14.010
12.010
1.008
3
1
1
1
4
1
4
1
4
1
4
1
4
1
4
1
3
4
3
1
1
1
4
1
4
1
4
1
4
1
4
4
1
S7
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
-0.2249
0.7395
0.3194
-0.5321
0.1446
0.0329
0.0528
0.1470
-0.0298
0.0203
0.0057
-0.0156
0.0839
-0.0543
0.2644
-0.2484
0.1541
-0.5902
-0.1229
0.6970
0.3287
-0.5282
0.1264
0.0555
0.0369
0.0709
-0.0236
0.2525
-0.0224
-0.3419
0.1810
-0.0773
0.3619
-0.4568
0.2229
-0.6084
-0.0817
0.6839
0.3311
-0.5271
0.1161
0.0413
0.0455
0.0124
-0.0089
0.2666
-0.0241
-0.2370
0.1360
0.0959
-0.3850
0.1961
3.3. AMEBER parameters in the force-­field format of TINKER:
(The following parameters are compatible with amber99.prm in TINKER 5.0 or 6.0)
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
650
651
652
653
654
655
656
657
658
659
660
661
14
1
2
29
24
35
1
34
1
34
1
34
N
CT
C
H
O
H1
CT
HC
CT
HC
CT
HC
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
"MetLysine
N"
CA"
C"
HN"
O"
HA"
CB"
HB"
CG"
HG"
CD"
HD"
7
6
6
1
8
1
6
1
6
1
6
1
14.010
12.010
12.010
1.008
16.000
1.008
12.010
1.008
12.010
1.008
12.010
1.008
3
4
3
1
1
1
4
1
4
1
4
1
S8
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
1
38
20
29
1
38
14
1
2
29
24
35
1
34
1
34
1
34
1
38
20
29
1
38
14
1
2
29
24
35
1
34
1
34
1
34
1
38
20
1
38
CT
HP
N3
H
CT
HC
N
CT
C
H
O
H1
CT
HC
CT
HC
CT
HC
CT
HP
N3
H
CT
HC
N
CT
C
H
O
H1
CT
HC
CT
HC
CT
HC
CT
HP
N3
CT
HC
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
"MetLysine CE"
"MetLysine HE"
"MetLysine NZ"
"MetLysine HZ"
"MetLysine CH"
"MetLysine HC"
"DiMetLysine N"
"DiMetLysine CA"
"DiMetLysine C"
"DiMetLysine HN"
"DiMetLysine O"
"DiMetLysine HA"
"DiMetLysine CB"
"DiMetLysine HB"
"DiMetLysine CG"
"DiMetLysine HG"
"DiMetLysine CD"
"DiMetLysine HD"
"DiMetLysine CE"
"DiMetLysine HE"
"DiMetLysine NZ"
"DiMetLysine HZ"
"DiMetLysine CH"
"DiMetLysine HC"
"TriMetLysine N"
"TriMetLysine CA"
"TriMetLysine C"
"TriMetLysine HN"
"TriMetLysine O"
"TriMetLysine HA"
"TriMetLysine CB"
"TriMetLysine HB"
"TriMetLysine CG"
"TriMetLysine HG"
"TriMetLysine CD"
"TriMetLysine HD"
"TriMetLysine CE"
"TriMetLysine HE"
"TriMetLysine NZ"
"TriMetLysine CH"
"TriMetLysine HC"
-0.5447
-0.2249
0.7395
0.3194
-0.5321
0.1446
0.0329
0.0528
0.1470
-0.0298
0.0203
0.0057
-0.0156
0.0839
-0.0543
0.2644
-0.2484
0.1541
-0.5902
-0.1229
0.6970
0.3287
-0.5282
0.1264
0.0555
0.0369
0.0709
-0.0236
0.2525
6
1
7
1
6
1
7
6
6
1
8
1
6
1
6
1
6
1
6
1
7
1
6
1
7
6
6
1
8
1
6
1
6
1
6
1
6
1
7
6
1
12.010
1.008
14.010
1.008
12.010
1.008
14.010
12.010
12.010
1.008
16.000
1.008
12.010
1.008
12.010
1.008
12.010
1.008
12.010
1.008
14.010
1.008
12.010
1.008
14.010
12.010
12.010
1.008
16.000
1.008
12.010
1.008
12.010
1.008
12.010
1.008
12.010
1.008
14.010
12.010
1.008
4
1
4
1
4
1
3
4
3
1
1
1
4
1
4
1
4
1
4
1
4
1
4
1
3
4
3
1
1
1
4
1
4
1
4
1
4
1
4
4
1
S9
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
charge
679
680
681
682
683
684
685
686
687
689
690
691
692
693
694
695
696
697
698
699
700
700
701
702
703
-0.0224
-0.3419
0.1810
-0.0773
0.3619
-0.4568
0.2229
-0.6084
-0.0817
0.6839
0.3311
-0.5271
0.1161
0.0413
0.0455
0.0124
-0.0089
0.2666
-0.0241
-0.2370
0.1360
0.1360
0.0959
-0.3850
0.1961
Supplemental Figure 1. Comparison of Experimental (dark blue) NOEs with predicted
NOEs from 100 nsec MD simulations in explicit solvent.
Suppl. Fig. 1a = data for Lys-9 hairpin model.
Supplemental Figure 1b. Data for Lys(Me)-9 hairpin model.
Supplemental Figure 1c. Data for Lys(Me2)-9 hairpin model.
Supplemental Figure 1d. Data for Lys(Me3)-9 hairpin model.