Structure and dynamics of the homologous series of alanine peptides: A joint molecular dynamics/NMR study

Article abstract of DOI:10.1021/ja0660406

The φ,ψ backbone angle distribution of small homopolymeric model peptides is investigated by a joint molecular dynamics (MD) simulation and heteronuclear NMR study. Combining the accuracy of the measured scalar coupling constants and the atomistic detail of the all-atom MD simulations with explicit solvent, the thermal populations of the peptide conformational states are determined with an uncertainty of <5 %. Trialanine samples mainly (～90%) a poly-L-proline II helix-like structure, some (～10%) β extended structure, but no α_R helical conformations. No significant change in the distribution of conformers is observed with increasing chain length (Ala₃ to Ala₇). Trivaline samples all three major conformations significantly. Tryglycine samples the four corner regions of the Ramachandran space and exists in a slow conformational equilibrium between the cis and trans conformation of peptide bonds. The backbone angle distribution was also studied for the segment Ala₃ surrounded by either three or eight amino acids on both N- and C-termini from a sequence derived from the protein hen egg white lysozyme. While the conformational distribution of the central three alanine residues in the 9mer is similar to that for the small peptides Ala₃-Ala₇, major differences are found for the 19mer, which significantly (30-40%) samples α_R helical stuctures.

Full text of DOI:10.1021/ja0660406

Published on Web 01/17/2007
Structure and Dynamics of the Homologous Series of Alanine
Peptides: A Joint Molecular Dynamics/NMR Study
Ju¨rgen Graf,† Phuong H. Nguyen,‡ Gerhard Stock,*,‡ and Harald Schwalbe*,†
Contribution from the Institute of Organic Chemistry and Chemical Biology,
Center for Biomolecular Magnetic Resonance, and Institute of Physical and Theoretical
Chemistry, Johann Wolfgang Goethe-UniVersity Frankfurt, Max-Von-Laue Strasse 7,
D-60438 Frankfurt/Main, Germany
Received August 19, 2006; E-mail: stock@theochem.uni-frankfurt.de; schwalbe@nmr.uni-frankfurt.de
Abstract: The φ,ψ backbone angle distribution of small homopolymeric model peptides is investigated by
a joint molecular dynamics (MD) simulation and heteronuclear NMR study. Combining the accuracy of the
measured scalar coupling constants and the atomistic detail of the all-atom MD simulations with explicit
solvent, the thermal populations of the peptide conformational states are determined with an uncertainty of
<5 %. Trialanine samples mainly (∼90%) a poly-L-proline II helix-like structure, some (∼10%) â extended
structure, but no RR helical conformations. No significant change in the distribution of conformers is observed
with increasing chain length (Ala3 to Ala7). Trivaline samples all three major conformations significantly.
Tryglycine samples the four corner regions of the Ramachandran space and exists in a slow conformational
equilibrium between the cis and trans conformation of peptide bonds. The backbone angle distribution
was also studied for the segment Ala3 surrounded by either three or eight amino acids on both N- and
C-termini from a sequence derived from the protein hen egg white lysozyme. While the conformational
distribution of the central three alanine residues in the 9mer is similar to that for the small peptides Ala3-
Ala7, major differences are found for the 19mer, which significantly (30-40%) samples RR helical stuctures.
Introduction
Due to these difficulties, there is still some controversy about
the conformational sampling of alanine-based short peptides.
Employing two-dimensional (2D) infrared (IR) spectroscopy14
in combination with density functional theory (DFT) calcu-
lations and MD simulations, it was suggested that cationic
trialanine consists of two conformations at room-temperature,
mainly a poly-L-proline II helix-like structure (PPII) (g80%)
and some RR helix.15 Contrary to these findings, a 50:50 mixture
of PPII and an extended â-strand-like conformation was
postulated on the basis of Raman, FTIR, and circular dichroism
(CD) measurements.16,17 Tetraalanine as cation was reported
to adopt predominantly PPII conformations in water18 and
also as zwitterion in cesium pentadecafluorooctanoate/water.19
From CD and NMR spectra of the alanine-based peptide
The conformational properties of small, homopolymeric
polypeptides is a matter of ongoing interest.1,2 For example,
the sampling of φ,ψ space of the polypeptide chain is of
considerable interest for the understanding of protein folding.
In addition, it has been shown recently that homopolymeric
peptides can form fibrils if conditions are chosen properly.3
Homopolymeric polypeptides have also been used as catalysts
for organic reactions; the asymmetric epoxidation of R,â-
unsaturated ketones is catalyzed by homopolymeric polypeptides
such as polyalanine, but also polyisoleucine.4 However, it is
long known that investigation of the conformation of those
polypeptides is challenging. They are ensembles of rapidly
interconverting conformers, and a number of different ap-
proaches have been used to describe such conformational
sampling. Those methods include the use of φ,ψ distributions
derived from the database of protein structures and also
molecular dynamics (MD) descriptions.5-13
(7) Schwalbe, H.; Fiebig, K. M.; Buck, M.; Jones, J. A.; Grimshaw, S. B.;
Glaser, S. J.; Smith, L. J.; Dobson, C. M. Biochemistry 1997, 36, 8977-
8991.
(8) Mu, Y.; Kosov, D. S.; Stock, G. J. Phys. Chem. B 2003, 107, 5064-5073.
(9) Garcia, A. E.; Sanbonmatsu, K. Y. Proc. Natl. Acad. Sci. U.S.A. 2002, 99,
2782-2787.
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502-507.
† Institute of Organic Chemistry and Chemical Biology, Center for
Biomolecular Magnetic Resonance.
‡ Institute of Physical and Theoretical Chemistry.
(1) Shi, Z.; Woody, R. W.; Kallenbach, N. R. AdV. Protein Chem. 2002, 62,
163-240.
(12) Hu, H.; Elstner, M.; Hermans, J. Proteins 2003, 50, 451-463.
(13) Yoda, T.; Sugita, Y.; Okamoto, Y. Chem. Phys. Lett. 2004, 386, 460-
467.
(2) Shi, Z.; Chen, K.; Liu, Z.; Kallenbach, N. R. Chem. ReV. 2006, 106, 1877-
(14) Woutersen, S.; Hamm, P. J. Phys. Chem. B 2000, 104, 11316-11320.
(15) Woutersen, S.; Pfister, R.; Hamm, P.; Mu, Y.; Kosov, D. S.; Stock, G. J.
Chem. Phys. 2002, 117, 6833-6840.
1897.
(3) Fa¨ndrich, M; Dobson, C. M. EMBO J. 2002, 21, 5682-5690.
(4) Colonna, S.; Molinari, H.; Banfi, S.; Julia, S.; Masana, J.; Alvarez, A.
Tetrahedron 1983, 39, 1635-1641.
(16) Eker, F.; Cao, X.; Nafie, L.; Schweitzer-Stenner, R. J. Am. Chem. Soc.
2002, 124, 14330-14341.
(5) Smith, L. J.; Bolin, K. A.; Schwalbe, H.; MacArthur, M. W.; Thornton, J.
M.; Dobson, C. M. J. Mol. Biol. 1995, 255, 494-506.
(6) Fiebig, K. M.; Schwalbe, H.; Buck, M.; Smith, L. J.; Dobson, C. M. J.
Phys. Chem. 1996, 100, 2661-2666.
(17) Eker, F.; Griebenow, K.; Schweitzer-Stenner, R. J. Am. Chem. Soc. 2003,
125, 8178-8185.
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Am. Chem. Soc. 2004, 126, 2768-2776.
9
10.1021/ja0660406 CCC: $37.00 © 2007 American Chemical Society
J. AM. CHEM. SOC. 2007, 129, 1179-1189
1179

A R T I C L E S
Graf et al.
Ac-XXAAAAAAAOO-NH2 (short XAO, where X, A, and O
denote diaminobutyric acid, alanine, and ornithine, respectively)
it was proposed that PPII is the dominant conformation.20 This
view has been questioned by other experimental results for this
peptide which led to the conclusion that PPII is simply one of
several accessible conformational states.21,22 From a comparison
of Raman optical activity spectra of cationic Ala2 to Ala6 with
spectra of the peptide Ac-OOAAAAAAAOO-NH2 it was
concluded that the PPII propensity of alanine increases with the
number of residues.23 Trivaline, on the other hand, supposedly
adopts mostly an extended â-sheet conformation.16,17
Concerning the theoretical description of small peptides in
aqueous solution, numerous groups have performed quantum
mechanical ab initio calculations24,25 as well as classical MD
simulations using molecular mechanics force fields.8-13 While
most studies reported a similar distribution within the main
conformations RR, â, and PPII, the thermal populations of these
states differ considerably, depending on the employed theoretical
model.8,12,13 The latter finding is a consequence of the fact that
an accuracy ∆∆G of the relative free energy of ∼1-2 kcal/
mol already introduces an uncertainty exp(∆∆G/kBT) of a factor
of 10 to the population probability.
this, two peptides were synthesized comprising residues 6-14
and residues 1-19 of the full-length protein, respectively:
C(SMe)ELAAAMKR (short HEWL-9mer) and KVFGRC(SMe)-
ELAAAMKRHGLDN (short HEWL-19mer).
In our analysis, we find that trialanine samples mainly the
PPII conformation (∼90%) and the â-strand conformation
(∼10%), while R helical structures are not sampled at all. By
increasing the chain length from Ala3 to Ala7, no substantial
change in this distribution of conformers is observed. As
expected, the comparison of different trimeric peptides (Ala3,
Val3, and Gly3) reveals a significant variation of φ,ψ sampling
determined by the size of the side chain. The sequence context
of a given trimeric segment embedded within longer heteropoly-
meric peptides, however, modulates significantly the φ,ψ
sampling of the central trimeric segment. In addition, the length
of the polypeptide chain seems to be important, since significant
differences are observed between the short (HEWL-9mer) and
the long (HEWL-19mer) peptide derived from hen egg white
lysozyme.
Materials and Methods
Peptide Synthesis. Peptides were synthesized either manually, by
using standard Fmoc solid-phase peptide synthesis protocols,28 or by
using an Applied Biosystems 433A peptide synthesizer with standard
Fmoc chemistry. N-Fmoc-S-methyl-L-cysteine was synthesized as
published.29 2-Chlorotrityl chloride, H-Xaa-2-chlorotrityl resins, activat-
ing reagents and Fmoc amino acids were purchased from Novabiochem
and isotopically labeled products from Cambridge Isotope Laboratories
or Sigma-Aldrich. All other chemicals and solvents were of analytical
grade and if necessary dried with molecular sieves30 prior to use. The
products were purified on reversed-phase HPLC columns and freeze-
dried before preparation of samples. Peptide purifications were verified
by analytical HPLC and electrospray mass spectrometry analysis on a
Fisons Instruments VG Platform II to confirm molecular weight. The
synthesized peptides with their isotopic labeling pattern are listed in
Table S1 in the Supporting Information. All peptides investigated were
free of any N- or C-terminal modifications.
HPLC. Analytical reversed-phase HPLC was performed on a Merck
Hitachi system with a Eurospher-100 C18 column (5 µm, 4.6 mm ×
250 mm) using conditions of 1 mL/min flow rate and 2%/min linear
gradient of solvent B (0.1% trifluoroacetic acid in acetonitrile) in solvent
A (0.1% trifluoroacetic acid in water). Semi-preparative reversed-phase
HPLC was run on a Bruker LC21 system with a Kromasil-100 C18
column (5 µm, 20 mm × 250 mm) at a flow rate of 8 mL/min and a
2%/min linear gradient of solvent B in solvent A.
The φ,ψ backbone angle distribution can be probed experi-
mentally by NMR via spin-spin coupling constants which can
be related to specific torsion angles by Karplus relationships.26
3
For the backbone angle φ, four coupling constants J(HN,HR),
3J(HN,C′), 3J(HR,C′), 3J(HN,Câ) are readily accessible, while for
1
the backbone angle ψ, the three coupling constants J(N,CR),
3
2J(N,CR), and J(HN,CR) can be measured. The values of the
measured coupling constants reflect the ensemble character of
the conformational distribution, which has to be taken into
account in their analysis.27
In this report, we attempt to combine the accuracy of the
experimentally measured scalar coupling constants and the
atomistic detail of the calculated structures. We therefore adopt
the following strategy. Assuming that the force field gives a
reasonable description of the structure and its distribution of
the main conformations, we perform a global fit of their thermal
populations by minimizing the deviation between measured and
calculated NMR parameters. In this way, we have examined
the side-chain dependence of conformational sampling of the
tripeptides Ala3, Val3, and Gly3. In addition, we examined the
chain-length dependence of conformational sampling of Ala3
to Ala7. We were also interested in the comparison of the
homopolymeric segment Ala3 in the heteropolymeric sequence
context of the protein hen egg white lysozyme (HEWL). For
NMR Spectroscopy. The freeze-dried samples were dissolved in
water, pH 2, containing 10% D2O. The final concentrations of the NMR
samples were determined by the ERETIC method31 and varied between
0.9 and 88 mmol/L. The saturation concentrations of Ala6 and Ala7
were 8.8 and 0.9 mmol/L, respectively. For the XAO peptide, a
concentration dependence of the CD spectra was reported.22 We tested
the concentration dependence of the J-coupling constants on Ala3 for
(19) Pizzanelli, S.; Monti, S.; Forte, C. J. Phys. Chem. B 2005, 109, 21102-
21109.
(20) Shi, Z.; Olson, C. A.; Rose, G. D., Baldwin, R. L.; Kallenbach, N. R. Proc.
Natl. Acad. Sci. U.S.A. 2002, 99, 9190-9195.
3
(21) Zagrovic, B.; Lipfert, J.; Sorin, E. J.; Millett, I. S.; van Gunsteren, W. F.;
Doniach, S.; Pande, V. S. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 11698-
11703.
the J(HN,HR) coupling constant in the range from 0.2 to 88 mmol/L,
and these were found to be independent of the concentration. Thus,
we assume that this also holds true for the other peptides in this study.
The NMR data were acquired on a Bruker 400 MHz spectrometer
equipped with either a 5-mm 1H{13C/15N} z-axis gradient probe or a 5
(22) Makowska, J.; Rodziewicz-Motowidlo, S.; Baginska, K.; Vila, J. A.; Liwo,
A.; Chmurzynski, L.; Scheraga, H. A. Proc. Natl. Acad. Sci. U.S.A. 2006,
103, 1744-1749.
(23) McColl, I. H.; Blanch, E. W.; Hecht, L.; Kallenbach, N. R.; Barron, L. D.
J. Am. Chem. Soc. 2004, 126, 5076-5077.
1
mm H{BB} z-axis gradient probe, an 600 MHz instrument with a
(24) Beachy, M. D.; Chasman, D.; Murphy, R. B.; Halgren, T. A.; Friesner, R.
A. J. Am. Chem. Soc. 1997, 119, 5908-5920.
(25) Jalkanen, K. J.; Elstner, M.; Suhai, S. J. Mol. Struct. (THEOCHEM) 2004,
675, 61-77.
(28) Chan, W. C., White, P. D., Eds. Fmoc Solid Phase Peptide Synthesis; Oxford
University Press: Oxford, 2000.
(26) Karplus, M J. Chem. Phys. 1959, 30, 11-15.
(29) Hart, D. J.; Magomedov, N. A. J. Am. Chem. Soc. 2001, 123, 5892-5899.
(30) Merck KGaA, Drying Agents; http://uk.chemdat.info/mda/uk/broch/
index.html.
(27) Wirmer, J.; Schlo¨rb, C.; Schwalbe, H. Conformation and Dynamcis of
Nonnative States of Proteins studied by NMR Spectroscopy. In Protein
Folding Handbook. Part I; Buchner, J., Kiefhaber, T., Eds.; Wiley-VCH:
Weinheim, 2005; pp 737-808.
(31) Akoka, S.; Barantin, L.; Trierweiler, M. Anal. Chem. 1999, 71, 2554-
2557.
9
1180 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Structure−Dynamics of Homopolymeric Model Peptides
A R T I C L E S
5-mm 1H{13C/15N} z-axis gradient probe, a 700 MHz spectrometer
with a 5-mm 1H{13C/15N} z-axis gradient cryogenic probe, a 800 MHz
spectrometer with a 5-mm 1H{13C/15N} z-axis gradient cryogenic probe
and a 900 MHz spectrometer with a 5-mm 1H{13C/15N} z-axis gradient
cryogenic probe. The NMR data were processed with Bruker XWIN-
NMR 3.5 and TopSpin 1.3 programs and analyzed with either Bruker
programs or Felix2000 (Accelrys). An automated routine32 was used
for extracting the J-coupling constants from the E.COSY pattern in
Felix2000. The temperature was calibrated by methanol or glycol
thermometer33 for each spectrometer. 1H chemical shifts were referenced
to the methyl resonance of internal DSS (3-(trimethylsilyl)-1-propane-
sulfonic acid sodium salt). 13C and 15N chemical shifts were referenced
indirectly to the 1H standard using published34 conversion factors.
Spectral resonance assignment was done with a combination of standard
HSQC and HMBC experiments up to Ala5. For Ala6 and Ala7, a
semiconstant time version of the HNN35 experiment was applied. The
HEWL-peptides were assigned following the standard method36 utilizing
the program CARA.37 Chemical shift values are listed in the Supporting
Information. Chemical exchange was measured with phase-sensitive38
1H,1H NOESY experiments with excitation sculpting39 for water
suppression. The forward and reverse rate constants were obtained from
the experimental peak volumes by solving eq 26 in the review article
of Perrin and Dwyer40 using the program EXSYCalc (Mestrelab
Research). The given error is the standard deviation of the obtained
rate constants for different mixing times.
of the second kind on the coupling constant determination are very
small and can safely be neglected.
The temperature dependence of 3J(HN,HR) coupling constant of Ala3
were measured on AAA, AA#A, and AAA# (A# ) 15N isotopic labeled).
Coupling constants have been measured both from low to high
temperature and from high to low temperature to ensure proper thermal
equilibration of the NMR setup.
3J(HN,C’), 3J(HR,C’), 3J(C’,C’), 3J(HN,Câ), 3J(HN,CR), 1J(N,CR), and
2J(N,CR) were measured with soft HNCA-COSY,42 CO-coupled (H)-
NCAHA,43 (HN)CO(CO)NH,44,45 HNHB[CB] E.COSY,46 HNCO[CA]
E.COSY,47 and J-modulated 1H, 15N HSQC’s,48 respectively. The signal
overlap in the (HN)CO(CO)NH experiment was so severe that it was
only possible to measure the 3J(C′,C′) coupling constant in a few cases.
For the other experiments, the signal overlap of intra- and interresidual
correlations was avoided either by measuring at higher magnetic fields
or by the applied isotope-labeling schemes. The given statistical error
is obtained from at least two measurements. Examples for the excellent
quality of the experimental data and the summary of the used acquisition
and processing parameters are found in Figure 1 and in the Supporting
Information.
CD Spectroscopy. CD spectra were recorded on a Jasco J-810
spectropolarimeter equipped with a Jasco PTC-423S temperature control
unit using quartz cuvettes with 0.2-mm pathlengths. Data were collected
at 0.5-nm increments from 260 to 185 nm with a scanning speed of
100 nm/min. For the measurements the same solvents as for the NMR
measurements were used, and the peptide concentrations were the
following: c(Ala3) ) 1.6 mmol/L, c(Ala7) ) 0.9 mmol/L, c(Val3) )
2.6 mmol/L, c(HEWL-9mer) ) 0.6 mmol/L, and c(HEWL-19mer) )
0.1 mmol/L. Ten scans were averaged (HEWL-19mer 20 scans), and
the solvent baseline was subtracted, but no line smoothing was applied.
Molecular Dynamics Simulation. We used the GROMOS96 force
field 43a149 to model the peptides and the SPC water model50 to describe
the solvent. The peptides Alan were placed in cubic boxes containing
650, 807, 874, 1096, and 1243 water molecules for n ) 3, 4, 5, 6, and
7, respectively. The simulation boxes of the Gly3 and Val3 were similar
to that of Ala3. In all simulations, the GROMACS program suite51,52
was employed. The equations of motion were integrated by using a
leapfrog algorithm with a time step of 2 fs. Covalent bond lengths were
constrained via the SHAKE53 procedure with a relative geometric
tolerance of 10-4. We used the particle-mesh Ewald method to treat
the long-range electrostatics interactions.54 The nonbonded interaction
pair-lists were updated every 5 fs, using a cutoff of 1.2 nm. The systems
were minimized using the conjugate gradient method. Subsequently,
the solvated systems were equilibrated for 100 ps at constant pressure
(1 atm) and temperature (T ) 300 K), respectively, using the Berendsen
coupling procedure.55 Each system was then run for 100 ns, and the
data were collected every 0.2 ps.
3
1
It was found that the J(HN,HR) coupling constant measured in H
one-dimensional (1D) spectra depends on the exact NMR pulse
sequences which implement different water suppression schemes. For
gradient-based suppression methods such as excitation sculpting,
homonuclear scalar coupling evolves during the suppresion schemes
which leads to a significant larger coupling constant. Thus, the
1
3J(HN,HR) coupling constants were measured in 1D H spectra with
presaturation for water suppression. There, the time during which
homonuclear coupling can evolve is kept to a minimum and can be
safely corrected for by linear phase correction. Direct determination
of the 3J(HN,HR) coupling constants from the splitting of amide protons
underestimates the true coupling constant value whenever the doublet
components are not resolved to baseline. This seems to be the case for
the reported8 values of Ala3. However, deconvolution of the spectrum
by fitting a Lorentzian function to the peaks or apodization of the FID
with a Lorentz-to-Gauss transformation prior to Fourier transformation
recovers true J-coupling constants. In most cases, the average value
derived by both methods is given, except for residue A3, A5 of Ala5,
A11 of HEWL-9mer (same numbering as for HEWL-19mer for easy
comparison), and A9 to A11 of HEWL-19mer where we only applied
the apodization due to partial overlap of the signals. When applying
the deconvolution routine it did not matter if we used a prior Lorentzian
broadening factor for the window function between 0 and 1 Hz for
spectra processing. In the case of Gly3, the 3J(HN,HR) coupling constant
was measured on the HR protons because of line broadening of the
amides signals. Note also that for the peptides with low molecular
weight, systematic errors as reported by Harbison41 due to relaxation
The calculation of the J-coupling constants from the MD simulations
is based on Karplus relations of the type J(æ) ) A cos2(æ + θ) + B
(42) Weisemann, R.; Ru¨terjans, H.; Schwalbe, H.; Schleucher, J.; Bermel, W.;
Griesinger, C. J. Biomol. NMR 1994, 4, 231-240.
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(44) Hu, J.-S.; Bax, A. J. Am. Chem. Soc. 1996, 118, 8170-8171.
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(46) Lo¨hr, F.; Ru¨terjans, H. J. Biomol. NMR 1999, 13, 263-274.
(47) Hennig, M.; Bermel, W.; Schwalbe, H.; Griesinger, C. J. Am. Chem. Soc.
2000, 122, 6268-6277.
(32) Schwalbe, H.; Rexroth, A.; Eggenberger, U.; Geppert, T.; Griesinger, C.
J. Am. Chem. Soc. 1993, 115, 7878-7879.
(33) Braun, S.; Kalinowski, H.-O.; Berger, S. 150 and More Basic NMR
Experiments: A Practical Course, 2nd ed.; Wiley-VCH: Weinheim, 1998.
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D.; Wright, P. E.; Wu¨thrich, K. Pure Appl. Chem. 1998, 70, 117-142.
(35) Panchal, S. C.; Bhavesh, N. S.; Hosur, R. V. J. Biomol. NMR 2001, 20,
135-147.
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P.; Tironi, I. G. Biomolecular Simulation: The GROMOS96 Manual and
User Guide; Vdf Hochschulverlag at the ETH Zu¨rich: Zu¨rich, 1996.
(50) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J.
Intermolecular Forces; Reidel: Dordrecht, 1981; pp 331-342.
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Commun. 1995, 91, 43-56.
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23, 327-341.
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9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1181

A R T I C L E S
Graf et al.
Figure 1. Example of the experimental NMR data for Ala7. Each spectrum was recorded at 400 MHz and 300 K. Acquisition and processing parameters
are listed in the Supporting Information. If not otherwise stated, the measured J-coupling constant is indicated together with the statistical error obtained
1
from two measurements. Isotopical labeling pattern: A ) unlabeled; A* ) fully 13C,15N-labeled; A+
)
13C-C′ labeled. (a) H, 15N HSQC spectra of the
different isotopically labeled Ala7-peptides. On top, the proton 1D spectra with presaturation for water suppression of the unlabeled peptide. (b) Determination
of 1J(N,CR) and 2J(N,CR) coupling constants. Experimental peak volumes (black circles) of the J-modulated H, 15N HSQC spectra and fitting the equation
1
*
I ) A cos(π1Jτ) cos(π2Jτ) exp(-τ/T2 ) to them (gray line) for the peaks of A2. Four spectra with different mixing times were measured twice, and the largest
percentage deviation of the peak volumes was taken for the error bars of all peak volumes. The quality of the fit is R2 ) 0.9999. Fitting was performed using
the program SigmaPlot 9.0. The obtained J-coupling constants are indicated together with the error of the fit. (c) Determination of 3J(HN,CR) coupling
constant from a HNCO-E.COSY spectrum of A*A*A*A*A*A*A*. The contour plot shows a cross section through 1HN-13C′ signals taken at the 15N
resonance position of A2. (d) Determination of 3J(HN,Câ) coupling constant from a HNHB-E.COSY spectrum of A+A*A+A*A+A*A. The contour plot
shows a cross section through HN-1Hâ signals taken at the 15N resonance position of residue A2. (e) Determination of J(HN,C′) coupling constant from
1
3
HNCA-COSY spectrum of A+A*A+A*A+A*A. The contour plot shows a cross section through HN-13CR signals taken at the 15N resonance position of
1
3
residue A2. (f) Determination of J(HR,C′) coupling constant from (H)N(CA)HA spectrum of A+A*A+A*A+A*A.
cos(æ + θ) + C, where æ denotes either the φ or the ψ backbone
dihedral angle of the peptide, A, B, C represent the parametrization of
the relation, and θ signifies the phase shift for the specific J of interest.
For all J-coupling constants considered, Table S2 in the Supporting
Information lists the parameters of the Karplus relation adapted from
refs 47, 48, 56, 57, and Figure 2 shows the corresponding Karplus
curves J(æ) together with the typical conformational distributions (see
below) along the dihedral angles φ or ψ. The figure nicely shows, e.g.,
the calculated coupling constant in conformation s ) RR, â, and PPII,
respectively. The sum runs over all J-coupling constants available for
the fit. It is noted that each coupling constant J sk is obtained from its
corresponding Karplus relation (see Table S2) by averaging the coupling
J sk overall MD structures pertaining to conformation s.
Assuming that only the three main conformational states are
thermally populated, we have PR + Pâ + PPPII) 1 and ø2 in eq 1 can
be expressed in terms of only two variables, e.g.,
3
that the J(HN,HR) coupling constant represents an accurate probe of
R
PPII
â
PPII 2
ø2(PR,Pâ) )
[(J ekxp - JkPP ) - PR(Jk - Jk ) - Pâ(Jk - Jk )]
II
the peptide φ angle, since the Karplus curve varies considerably along
∑
2
the â and the PPII conformations. On the other hand, the J(N,CR) is
k
(2)
given as a function of the ψ angle and therefore allows clear discrim-
ination between helical RR from extended â and PPII conformations.
As explained in the Introduction, we will assume that the force field
gives a reasonable description of the structure of the main conformations
RR, â, and PPII, whereas the calculated thermal populations PR, Pâ, and
PPPII of these states may deviate considerably from their true value. To
determine the correct population probabilities, we therefore perform a
global fit of the populations by minimizing the deviation between
measured and calculated NMR parameters defined by
To determine the correct population probabilities Ps, this function
is minimized either analytically (requiring that 0 e Ps e 1) or
numerically by simply evaluating ø2(PR, Pâ) on a 2D grid. As a
representative example, Figure S1 in the Supporting Information shows
this function for the fourth residue of Ala7. The global minimum of ø2
at (PR ) 0, Pâ ) 0.15) is found to be relatively flat. Typically, we
therefore estimate the uncertainty of the populations to be e5 %. To
study the robustness of the fits, moreover, we have performed a number
of tests which study the behavior of ø2 when one or several coupling
constants were excluded from the fit or the Karplus curves were shifted
2
ø2(PR,Pâ,PPP ) )
[J ekxp - (PRJRk + PâJâk + PPP JkPP )]
(1)
II
∑
II
II
k
(56) Hu, J.-S.; Bax, A. J. Am. Chem. Soc. 1997, 119, 6360-6368.
(57) Ding, K.; Gronenborn, A. M. J. Am. Chem. Soc. 2004, 126, 6232-6233.
Here, Jekxprepresents the measured coupling constant and J sk denotes
9
1182 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Structure−Dynamics of Homopolymeric Model Peptides
A R T I C L E S
Results and Discussion
By NMR spectroscopy, a number of different structure-
dependent parameters can be measured, for example NOEs,
chemical shifts, residual dipolar and scalar coupling constants.
In highly flexible molecules like the homopolymeric peptides
studied here, the experimental NMR observables are an average
of the conformational distribution with specific averaging time
regime. NOEs are averaged by r-6 which biases toward shorter
distances in cases of conformational averaging. In addition,
strong signal overlap for NOEs is a serious problem in
homooligomers. Also, the time regime of internal and overall
rotational reorientation influences the NOE cross-peak intensi-
ties. Therefore, both chemical shifts and NOEs are rather
insensitive experimental restraints to derive information about
highly averaged structures. Hence, we have chosen to test the
conformational distribution by measuring scalar coupling con-
stants which in most cases report directly on a conformational
ensemble around a single torsion, e.g., the backbone angles
φ or ψ via Karplus parametrizations, which can be directly
related to predictions, derived from MD simulations.
The most precise and accurate way to measure vicinal
coupling constants is from analyzing the signal splitting in a
3
1D spectrum. This was possible for the J(HN,HR) coupling
constants for the peptides studied here. The 3J(HN,HR) coupling
constant is also the most sensitive reporter for the backbone
angle φ out of the six on φ-dependent coupling constants due
to the fact that refined Karplus parametrizations are available56,61
and the value of coupling constant varies by 8 Hz over the
Figure 2. Karplus curves (solid lines) of the measured J-coupling constants
(dashed lines) for residue A2 of Ala3, together with the conformational
distributions (gray shaded) obtained from the MD simulation.
2
interesting range of φ. For the angle ψ, the J(N,CR) coupling
constant is the most sensitive one, but its smaller variation of
about 3 Hz makes the possible error higher.
by an uncertainty of 0.5 Hz. As documented in the Supporting
Information, all tests yielded quite similar population probabilities.
Comparison of experimental J-coupling constants to calcu-
lated J-couplings from MD simulations reveals a remarkable
overall agreement (cf. Table 1, Table 3, and Tables S3 to S13)
considering the inherent error of each method. The average
deviation for each residue varies between 7 and 25%, with an
overall deviation of 14%. The largest deviations are observed
Besides the dependence on the Karplus relations, we furthermore
studied the reliability of our results with respect to the accuracy of the
force field and the convergence of the conformational sampling. Our
working assumption, that (apart from thermal weighting factors) the
force field gives a reasonable description of the structural distribution
within a conformational state, is based on a careful analysis of
comparisons of various force fields for polyalanines.8-10,12 For example,
by comparing the six popular MD force fields including AMBER94,58
CHARMM22,59 GROMOS96,49 and OPLS-AA60 for trialanine, Mu et
al.8 found that the mean values of the (φ, ψ)-distributions pertaining
to a specific conformational state differed at most by (20° between
the various force fields, while the width of the distributions were quite
similar. As shown in Table S14 and Figure S1 in the Supporting
Information, the fitted thermal populations are not very sensitive to a
25° shift of the conformational states, demonstrating that our results
are quite robust with respect to uncertainties of the force field. To test
if our results are converged with respect to the conformational sampling,
we have recalculated the (φ, ψ)-distributions using either the first or
the second half of the 100 ns trajectory. The resulting conformational
distributions are virtually the same, thus reflecting the fact that the
single-residue distributions P(φi,ψi) are highly averaged quantities. We
note in passing that the total conformational distribution P(φ1,ψ2, ...,
φn,ψn) of Alan is (by far) not converged in a 100 ns MD simulation,
but this information is not required in the present work.
3
1
2
3
for the J(HN,Câ), J(N,CR), J(N,CR), and J(HN,CR) coupling
constants, which is partly due to the smaller range of values
these coupling constants can adopt. Hence, the overall agreement
suggests that the force field gives a reasonable description of
the peptide structure and that the above-mentioned strategy
combining NMR and MD is justified.
Side-Chain Dependence of Tripeptide Conformational
Sampling. To obtain a first impression on the typical confor-
mational states sampled by MD simulations, Figure 3 displays
the Ramachandran probability distribution of the central dihedral
angles (φ,ψ) of the three tripeptides Ala3, Val3, and Gly3. For
Ala3 and Val3 peptides, there are essentially three populated
conformational states: the right-handed helix conformation RR
(-150° < φ < -25° and -150° < ψ < 0°), the â conformation
(-150° < φ < -90° and 80° < ψ < 160°), and the PPII (-90°
< φ < -25° and 80° < ψ < 160°) conformation, which are
located at (φ,ψ) ≈ (-80°, -50°), (-120°, 130°), (-60°, 140°),
respectively. In addition, there is a small population (e3%) of
the left-handed helix conformation RL located at (50°, 100°).
For each peptide, the population probability of each conformer
is listed in Table 1. The simulations using the GROMOS96 force
(58) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M., Jr.;
Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P.
A. J. Am. Chem. Soc. 1995, 117, 5179-5197.
(59) MacKerell, A. D., Jr.; et al. J. Phys. Chem. B 1998, 102, 3586-3616.
(60) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996,
118, 11225-11236.
(61) Vuister, G. W.; Bax, A. J. Am. Chem. Soc. 1993, 115, 7772-7777.
9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1183

A R T I C L E S
Graf et al.
Table 1. J-Coupling Constants for the Central Residue of the Tripeptides Ala3, Val3, and Gly3 as Obtained from Simulation (MD), Fitting
(Fit), and Experiment (Exp) Together with the Corresponding Populations Probability of the Conformations RR, â, and PPII
J-coupling constants/Hz
populations/%
peptide
3J(HN,HR)
3J(HN,C
′
)
3J(HR,C
′
)
3J(C
′
,C
′
)
3J(HN,Câ)
1J(N,CR)
2J(N,CR)
3J(HN,CR)
PMD
PFit
Ala3
RR
5.6 ( 2.5
9.4 ( 0.9
5.3 ( 1.7
7.0 ( 2.6
5.6
1.3 ( 1.0
0.8 ( 0.7
1.1 ( 0.8
1.1 ( 1.0
1.1
1.6 ( 0.6
2.6 ( 0.3
1.5 ( 0.4
2. ( 1.0
1.5
0.7 ( 0.4
1.5 ( 0.5
0.5 ( 0.1
0.9 ( 0.6
0.6
2.0 ( 0.7
0.6 ( 0.4
2.3 ( 0.2
1.5 ( 0.9
2.1
9.7 ( 0.2
10.9 ( 0.8
10.9 ( 0.8
10.8 ( 0.8
10.9
6.5 ( 0.5
8.4 ( 0.3
8.5 ( 0.3
8.3 ( 0.6
8.5
0.6 ( 0.1
0.8 ( 0.1
0.6 ( 0.1
0.7 ( 0.1
0.6
15
40
41
0
8
92
â
PPII
MD
Fit
Exp
RR
5.68
1.13
1.84
0.25
2.39
11.34
8.45
0.70
Val3
Gly3
7.1 ( 2.5
9.6 ( 0.7
5.4 ( 1.8
7.1 ( 2.5
7.9
7.94
5.8 ( 2.7
5.89
0.8 ( 0.8
0.6 ( 0.5
1.0 ( 0.9
0.9 ( 0.9
0.8
0.58
1.2 ( 1.1
1.10
2.0 ( 0.7
2.7 ( 0.2
1.5 ( 0.4
2.2 ( 1.1
2.2
2.42
3.3 ( 2.1
4.01
0.8 ( 0.4
1.3 ( 0.5
0.5 ( 0.1
0.8 ( 0.5
1.0
0.34
1.3 ( 0.8
0.26
1.7 ( 0.8
0.7 ( 0.4
2.2 ( 0.2
1.6 ( 0.8
1.3
1.38
-
-
9.6 ( 0.2
10.5 ( 0.8
10.5 ( 0.8
10.4 ( 0.8
10.3
10.80
10.4 ( 1.0
12.17
6.6 ( 0.5
8.3 ( 0.4
8.4 ( 0.3
8.1 ( 0.7
8.0
7.80
8.1 ( 0.6
9.05
0.7 ( 0.1
0.8 ( 0.1
0.6 ( 0.1
0.7 ( 0.1
0.7
0.77
0.8 ( 0.2
0.78
13
35
47
19
52
29
â
PPII
MD
Fit
Exp
MD
Exp
The amide proton signals in the 1D 1H spectrum of Gly3 show
significant line broadening. Exchange phenomena can be
measured with EXSY40 experiments related to the classical
1H,1H NOESY experiments but with longer mixing times. There
was no water-to-amide HN cross-peak detectable which rules
out significant contributions of water exchange to the entire line
width of 16 Hz observed for the HN of Gly3. At longer mixing
times chemical exchange cross-peaks of the amide proton
signals, with weak signals nearby, become visible (cf. Figure
S7). The ratio of the diagonal signals gives a population ratio
of 0.995 to 0.005 and 0.997 to 0.003 for HN2 and HN3
,
respectively. From the analysis of the experimental peak
volumes, using eq 26 in the review article of Perrin and Dwyer,40
one obtains the forward and reverse rate constants which are
0.005 ( 0.001 Hz and 0.842 ( 0.132 Hz for HN2 and 0.002 (
0.001 Hz and 0.818 ( 0.137 Hz for HN3. The resultant
equilibrium constants and free energy differences are Kcis/trans
) 0.006 ( 0.002, ∆G ) 3.1 ( 0.2 kcal/mol for HN2 and Kcis/trans
) 0.002 ( 0.002, ∆G ) 3.6 ( 0.4 kcal/mol for HN3. We
conclude that this chemical exchange process is a cis-trans
isomerization of the peptide amide bond. In the shorter time
scale sampled by the MD simulation this process is not vis-
ible. Such chemical exchange between cis and trans peptide
conformation was not detected for any other peptide under study
here.
Figure 3. Ramachandran probability distributions for the central residues
of Ala3, Val3, and Gly3 as obtained from the MD simulations.
field predict that both peptides exist mainly in the extended
conformations â and PPII (∼82%) and only little in the right-
handed helix conformation RR (∼15%). Also, the populations
of the â and PPII conformations are comparable with each other.
The Ramachandran plot of Gly3 is quite different since it exhibits
four populated regions with φ e -50° or φ g 50°, and ψ e
-50° or ψ g 50°. Note that these regions actually are connected
with each other due to the periodicity of the dihedral angles.
Overall, the agreement between the simulation and experiment
seems to be better for Val3 and Gly3 than for Ala3. Note that
for glycine residues, some of the Karplus parametrizations may
not be too accurate because of very restricted set of data used
for the parametrization.
Chain-Length Dependence of Alan Conformational Sam-
pling. The conformational distributions from MD of every
residue of the peptides Ala4, Ala5, Ala6, and Ala7 look quite
similar to their counterparts of the Ala3 peptide (data not shown),
although the population probability of the conformations are
different. Employing the Karplus relations described above, we
have calculated coupling constants directly from the MD
simulations for all polyalanines Alan (n ) 3-7). Each coupling
constant presented in Table 2 (denoted as MD) was averaged
over all values calculated from every snapshot of (i) the entire
trajectory and of (ii) each single conformational state RR, â,
and PPII.
From fitting the calculated to the experimental J-coupling
constants (see Materials and Methods) we find that trialanine
samples mainly the PPII conformation (∼90%). The â confor-
mation has a population probability of about 10%, whereas the
RR conformation is not sampled. This is in qualitative agreement
with the populations determined previously from a combination
of 2D IR spectroscopy and MD simulations,15 but does not
support the postulated 50:50 mixture of PPII and an extended
â-strand-like conformation.16,17 For trivaline with its branched
side chain the population shifts more toward â and RR
conformations (cf. Table 1). This is best reflected in the
J-coupling constants due to an increase in the 3J(HN,HR)
coupling constant and a decrease in the 2J(N,CR) coupling
constant. The literature for trivaline so far postulates that it
samples mostly the extended â-sheet conformation.16,17
Table 2 shows, as an example, the coupling constants
3J(HN,HR) and 2J(N,CR) which reflect the φ- and ψ-dependence
of a peptide conformation, respectively. Note that the widths
of the calculated coupling constants reported in the table account
for conformational fluctuations of the peptide. These values are
typically large for the 3J(HN,HR) coupling constant, because the
9
1184 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Structure−Dynamics of Homopolymeric Model Peptides
A R T I C L E S
Table 2. Selected J-Coupling Constants from Simulation (MD), Fitting (Fit), and Experiment (Exp) of the Alanine Peptides as well as the
Populations Obtained from Simulation and Fitting
Ala3
Ala4
Fit
Ala5
Fit
Ala6
Fit
Ala7
Fit
res.
MD
Fit
Exp
MD
Exp
MD
Exp
MD
Exp
MD
Exp
2
3J(HN,HR) 7.0 ( 2.6 5.6
2J(N,CR)
5.68 5.9 ( 2.6 5.5
8.45 7.9 ( 0.9 7.8
25,23,43 0,14,86
6.2 ( 2.6 5.9
5.62 5.9 ( 2.6 5.5
8.56 7.8 ( 1.0 7.8
31,20,40 0,14,86
5.89 6.0 ( 2.6 5.7
8.37 7.6 ( 1.0 7.5
34,20,40 0,16,84
6.4 ( 2.6 5.9
5.59 5.9 ( 2.6 5.5
8.55 8.0 ( 0.9 7.7
22,22,46 0,17,83
5.74 5.6 ( 2.6 5.6
8.40 7.4 ( 1.1 7.5
45,15,30 0,14,86
5.98 5.9 ( 2.5 5.7
8.27 7.3 ( 1.1 7.4
45,18,28 0,13,87
6.4 ( 2.7 6.0
5.60 5.5 ( 2.6 5.6
8.52 7.7 ( 1.0 7.6
40,17,35 0,17,83
5.67 5.4 ( 2.5 5.6
8.34 7.4 ( 1.0 7.6
44,15,29 0,16,84
5.80 5.5 ( 2.4 5.7
8.26 7.1 ( 1.0 7.3
57,12,21 0,15,85
6.02 5.9 ( 2.4 5.7
8.18 7.2 ( 1.1 7.4
52,16,22 0,14,86
6.2 ( 2.4 5.9
5.61
8.52
8.3 ( 0.6 8.5
PR,Pâ,PPP 15,40,41 0,8,92
II
3
4
5
6
3J(HN,HR)
5.66
8.29
2J(N,CR)
7.7 ( 1.0 8.3
PR,Pâ,PPP
25,23,40 0,19,81
II
3J(HN,HR)
5.77
8.22
2J(N,CR)
7.5 ( 1.1 7.5
PR,Pâ,PPP
33,23,33 0,17,83
II
3J(HN,HR)
5.92
8.24
2J(N,CR)
7.5 ( 1.1 7.4
PR,Pâ,PPP
34,25,31 0,18,82
II
3J(HN,HR)
6.04
8.18
2J(N,CR)
7.3 ( 1.1 8.1
PR,Pâ,PPP
43,21,25 0,17,83
II
corresponding Karplus relation is steep in the populated regions,
see Figure 2 (top left panel).
Let us first discuss the J(HN,HR) coupling constant as the
conformation with increasing chain length as published23,62
seems to be implausible.
3
Temperature Dependence of Ala3 Conformational Sam-
pling. To investigate the influence of the temperature on peptide
structure, we have measured seven J-coupling constants for Ala3
most sensitive reporter on the dihedral angle φ. Interestingly,
the experimental results show that the 3J(HN,HR) coupling
constants are very much the same (the variation of the results
is less than 0.5 Hz) for most peptides. A closer inspection,
however, reveals the trend that the value of 3J(HN,HR) increases
along a peptide chain going from the N-terminal to the
C-terminal end, which can be explained by a small change from
PPII toward more â conformations. The simulations also show
a similar behavior, except for the Ala3. The calculated values
of these constants for Ala3 are larger than their counterparts of
the other polyalanine peptides. This is due to the fact that the
â conformation of Ala3 is much more populated, and according
to the Karplus relation (Figure 1, top left panel), the 3J(HN,HR)
value is large for the â conformation.
3
at four temperatures. The results for J(HN,HR) increase with
temperature (from 5.33 Hz at 275 K to 6.29 Hz at 350 K for
residue A2), which is well represented by a linear fit, see Figure
3
4. While a linear increase of J(HN,HR) was also reported for
the XAO peptide,20 in Ac-GG(A)nGG-NH2 (n ) 1, 2, 3) peptides
3
the J(HN,HR) of the Ala residues were reported to exhibit a
transition curve behavior.63,64 As 3J(HN,HR) is significantly
higher in the â than in the PPII conformation, its increase with
temperature indicates that the â conformational state is more
populated, which agrees with the findings of refs 20, 63, and
64. The other three φ-dependent J-coupling constants, 3J(HR,C′),
3J(HN,Câ), and 3J(HN,C′) show a temperature behavior consistent
with that interpretation (cf. Table 4). On the other hand, both
The 2J(N,CR) is the most sensitive coupling constant for the
dihedral angle ψ and therefore may provide information on
the transition between the extended and helical states. How-
ever, its range of values for different conformations is not
1
2
ψ-dependent coupling constants J(N,CR) and J(N,CR) show
only a small decrease with increasing temperature, suggesting
that the population remains in the extended region and only a
minor R helical content is populated as the temperature
increases.
3
as large as that for the J(HN,HR) coupling constant (see the
Karplus curve in Figure 1, bottom right panel). Similar to the
2
3J(HN,HR), the experimental values of J(N,CR) for different
To support this interpretation by the MD simulations, we have
used the state-dependent J-coupling constants obtained for Ala3
at T0 ) 300 K (see Table 1) to calculate the thermal population
of the various conformational states via a global fit of the
calculated to the measured coupling constants J(T). (We note
that this assumes that the structural distribution within a
conformational state is similar for all considered temperatures.)
Table 4 shows that the resulting calculated J-coupling constants
are in excellent agreement with experiment and also confirms
the interpretation above. While the population of the â state
increases from 3 to 26% when the temperature is increased from
T ) 275-350 K, the R state is hardly (e1%) populated even
at T ) 350 K. From the thus obtained thermal populations for
the â and the PPII conformers, we may calculate the temperature-
peptide groups do not exhibit large variations. The values of
the simulated 2J(N,CR), however, are smaller than those obtained
from experiment, which suggests that the MD simulations
overestimate the helical conformations. The values of the
experimentally determined 2J(N,CR) decrease along peptide
chains from the N-terminal to the C-terminal end. This indicates
a trend toward a larger population of helical conformation along
the peptide chain. Interestingly, the experimental values of
2J(N,CR) (∼8.4 Hz) suggest that all polyalanine peptides under
study hardly exist in the helical conformations. The values are
around 6.5 Hz, otherwise, according to the Karplus relation.
Tables 3 and S3-S13 show in detail the simulated results
assuming resolved states of all the coupling constants of all
peptide groups for all polyalanine peptides, together with the
experimental data. Again, we note a good overall agreement
between theory and experiment. The values of the coupling
constants do not show significant deviation regardless of
different peptides or peptide groups. Therefore, the conforma-
tional sampling has to be very similar, and an increase of PPII
(62) Hagarman, A.; Measey, T.; Doddasomayajula, R. S.; Dragomir, I.; Eker,
F.; Griebenow, K.; Schweitzer-Stenner, R. J. Phys. Chem. B. 2006, 110,
6979-6986.
(63) Ding, L.; Chen, K.; Santini, P. A.; Shi, Z.; Kallenbach, N. R. J. Am. Chem.
Soc. 2003, 125, 8092-8093.
(64) Chen, K.; Liu, Z.; Kallenbach, N. R. Proc. Natl. Acad. Sci. U.S.A. 2004,
101, 15352-15357.
9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1185

A R T I C L E S
Graf et al.
Table 3. J-Coupling Constants for Residues A2 to A6 of Ala7; Shown Are Results from Simulation (MD), Fitting (Fit), and Experiment (Exp)
Together with the Populations of the Conformational States RR, â, and PPII, as Obtained from Simulation and Fitting
J-coupling constants/Hz
populations/%
res.
type (angle)
RR
â
PPII
MD
Fit
Exp
PR, Pâ, PPP
II
3J(HN,HR) (φ2)
3J(HN,C′) (φ2)
3J(HR,C′) (φ2)
3J(HN,Câ) (φ2)
1J(N,CR) (ψ2)
2J(N,CR) (ψ2)
3J(HN,CR) (φ2, ψ1)
3J(HN,HR) (φ3)
3J(HN,C′) (φ3)
3J(HR,C′) (φ3)
3J(HN,Câ) (φ3)
1J(N,CR) (ψ3)
2J(N,CR) (ψ3)
3J(HN,CR) (φ3, ψ2)
3J(HN,HR) (φ4)
3J(HN,C′) (φ4)
3J(HR,C′) (φ4)
3J(HN,Câ) (φ4)
1J(N,CR) (ψ4)
2J(N,CR) (ψ4)
3J(HN,CR) (φ4, ψ3)
3J(HN,HR) (φ5)
3J(HN,C′) (φ5)
3J(HR,C′) (φ5)
3J(HN,Câ) (φ5)
1J(N,CR) (ψ5)
2J(N,CR) (ψ5)
3J(HN,CR) (φ5, ψ3)
3J(HN,HR) (φ6)
3J(HN,C′) (φ6)
3J(HR,C′) (φ6)
3J(HN,Câ) (φ6)
1J(N,CR) (ψ6)
2J(N,CR) (ψ6)
3J(HN,CR) (φ6, ψ5)
4.7 ( 2.3
1.7 ( 1.2
1.5 ( 0.5
2.1 ( 0.6
9.7 ( 0.2
7.6 ( 1.0
0.6 ( 0.1
4.5 ( 2.1
1.7 ( 1.1
1.4 ( 0.5
2.2 ( 0.5
9.7 ( 0.2
7.3 ( 1.0
0.4 ( 0.2
4.7 ( 2.0
1.5 ( 1.0
1.4 ( 0.5
2.2 ( 0.5
9.7 ( 0.2
6.9 ( 0.9
0.3 ( 0.2
5.2 ( 2.1
1.3 ( 0.9
1.5 ( 0.5
2.2 ( 0.5
9.8 ( 0.2
7.0 ( 1.0
-
9.3 ( 1.0
0.8 ( 0.8
2.6 ( 0.3
0.6 ( 0.4
10.7 ( 0.9
7.6 ( 1.0
0.8 ( 0.1
9.4 ( 1.0
0.8 ( 0.8
2.6 ( 0.3
0.7 ( 0.4
10.6 ( 0.9
7.4 ( 1.1
0.6 ( 0.2
9.4 ( 1.0
0.8 ( 0.8
2.6 ( 0.3
0.7 ( 0.4
10.6 ( 0.9
7.0 ( 1.1
0.6 ( 0.2
9.4 ( 1.0
0.8 ( 0.8
2.6 ( 0.3
0.7 ( 0.4
10.5 ( 0.9
7.0 ( 1.0
-
4.8 ( 1.7
1.3 ( 0.9
1.4 ( 0.4
2.4 ( 0.2
11.0 ( 0.8
7.7 ( 1.0
0.6 ( 0.1
4.9 ( 1.7
1.3 ( 0.8
1.4 ( 0.4
2.3 ( 0.2
10.8 ( 0.8
7.6 ( 1.0
0.4 ( 0.2
5.0 ( 1.7
1.2 ( 0.9
1.4 ( 0.4
2. ( 0.2
10.7 ( 0.8
7.4 ( 1.1
0.4 ( 0.2
5. ( 1.7
1.2 ( 0.8
1.4 ( 0.4
2.3 ( 0.2
10.7 ( 0.8
7.4 ( 1.1
-
5. ( 2.6
1.5 ( 1.2
1.8 ( 1.2
1.8 ( 0.8
10.4 ( 0.9
7.7 ( 1.0
0.6 ( 0.1
5.4 ( 2.5
1.5 ( 1.2
1.9 ( 1.4
1.9 ( 0.7
10.2 ( 0.8
7.4 ( 1.0
0.5 ( 0.2
5.5 ( 2.4
1.5 ( 1.1
2.0 ( 1.5
1.9 ( 0.7
10.1 ( 0.7
7.1 ( 1.0
0.4 ( 0.3
5.9 ( 2.4
1.3 ( 1.0
2.0 ( 1.4
1.9 ( 0.8
10.1 ( 0.7
7.2 ( 1.1
0.4 ( 0.2
6.2 ( 2.4
1.3 ( 1.1
2. ( 1.6
5.6
1.2
1.6
2.0
10.9
7.6
0.6
5.6
1.2
1.6
2.0
10.8
7.6
0.5
5.7
1.1
1.6
2.0
10.7
7.3
0.5
5.7
1.1
1.6
2.0
10.6
7.4
-
5.61
1.15
1.89
2.31
11.37
8.52
0.71
5.66
1.20
1.85
2.20
11.27
8.29
0.66
5.77
1.20
1.80
2.23
11.22
8.22
0.56
5.92
1.19
1.56
2.23
11.29
8.24
-
40, 17, 35 (MD)
0, 17, 83 (Fit)
2
45, 15, 29 (MD)
0, 16, 84 (Fit)
3
4
5
6
57, 12, 21 (MD)
0, 15, 85 (Fit)
52, 16, 22 (MD)
0, 14, 86 (Fit)
5.5 ( 2.2
1.2 ( 0.9
1.5 ( 0.5
2. ( 0.6
9.8 ( 0.2
6.4 ( 0.4
-
9.3 ( 1.2
0.9 ( 0.9
2.6 ( 0.4
0.7 ( 0.4
10.4 ( 0.9
8.0 ( 0.9
-
5.3 ( 1.8
1.1 ( 0.9
1.5 ( 0.4
2.3 ( 0.2
10.6 ( 0.8
8.2 ( 0.7
-
5.9
1.1
1.6
2.0
10.6
8.1
-
6.04
1.10
1.67
2.21
11.29
8.18
-
43, 21, 25 (MD)
0, 17, 83 (Fit)
1.7 ( 0.8
10.1 ( 0.7
7.3 ( 1.1
0.4 ( 0.2
dependent free energy difference ∆G between the two conform-
300 K consists of ∆H ) 6 kcal/mol and -T∆S ) -4.5
kcal/mol. As expected, this finding indicates that the PPII state
is favored over the â state due to a lower enthalpy, although
the latter is stabilized by entropy.
ers as well as its enthalpic and entropic contributions. Using
the values of Pâ/PPP ) e-∆G/k T extracted from Table 4, we
B
II
obtain free energy differences ∆G ) 1.90, 1.45, 0.94, and 0.72
kcal/mol for T ) 275, 300, 325, and 350 K, respectively.
Assuming that the differences in enthalpy ∆H and entropy ∆S
are temperature-independent (an assumption that is difficult to
prove but commonly made for temperatures far from the
transition point), the free energy difference ∆G ) ∆H - T∆S
) 1.5 kcal/mol between the â and the PPII conformations at
Since only the â and the PPII conformation of Ala3 are
populated over the studied temperature range (i.e., Pâ + PPP
II
) 1), we may analyze the observed temperature dependence of
the J-coupling constants finding in terms of a two-state model.
Using Pâ/PPP ) e-∆G/k T, we find for the thermal population of
B
II
the â conformation Pâ ) 1/(e∆G/k T + 1). This yields the
B
temperature-dependent J-coupling constant
1
B
J(T) ) PâJâ + PPP JPP
)
(Jâ - JPP ) + JPP
II II
∆G/k T + 1
II
II
e
(3)
where Jâ and JPP are the (presumably temperature independent)
II
J-coupling constants pertaining to the â and the PPII conforma-
tions, respectively. Linearizing J(T) in the limit (T - T0)/T0 ,
1, we obtain
(T - T0)
J(T) ≈ J(T0) + (Jâ - JPP )K
(4)
II
T0
where
Figure 4. Temperature dependence of the 3J(HN,HR) coupling constants
of Ala3, showing the measured values for residue A2 (filled circles) and
A3 (open circles), fitted with linear regression (gray line) are plotted versus
temperature. Error bars are 0.05 Hz.
0
B
0
∆G0 ∆G′
0
e∆G /k T
K )
-
‚
2
(e∆G /k T + 1)
0
B 0
k T
kB
(
)
B
0
9
1186 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Structure−Dynamics of Homopolymeric Model Peptides
A R T I C L E S
Table 4. Temperature Dependence of the J-Coupling Constants for Residue A2 of Ala3
temperature/K
275
300
MD
325
350
J-coupling constants type (angle)
Exp
Fit
Exp
Fit
Exp
Fit
Exp
Fit
3J(HN,HR) (φ2)
3J(HN,C′) (φ2)
3J(HR,C′) (φ2)
3J(HN,Câ) (φ2)
1J(N,CR) (ψ2)
2J(N,CR) (ψ2)
3J(HN,CR) (φ2, ψ1)
5.33
1.08
1.84
2.28
11.43
8.45
0.73
5.4
1.1
1.5
2.2
10.9
8.5
5.68
1.13
1.84
2.39
11.34
8.45
0.70
7.0 ( 2.6
1.1 ( 1.0
2.1 ( 1.0
1.5 ( 0.9
10.8 ( 0.8
8.3 ( 0.6
0.7 ( 0.1
5.6
1.1
1.5
2.1
10.9
8.5
6.02
1.11
2.04
2.22
11.29
8.42
0.75
6.1
1.0
1.7
1.9
10.9
8.5
6.29
1.02
2.23
2.13
11.21
8.34
0.80
6.4
1.0
1.8
1.8
10.9
8.5
0.6
0.6
0.7
0.7
275 K
300 K
325 K
Fit
350 K
Fit
populations/%
Fit
MD
Fit
PR
Pâ
PPP
0
3
97
15
40
41
0
8
92
0
19
81
1
26
73
II
Table 5. J-Coupling Constants from Experiment (Exp) and Fitting (Fit) Together with the Populations Obtained from Fitting for the HEWL
Peptides
HEWL-9mer
J-coupling constants/Hz
HEWL-19mer
J-coupling constants/Hz
populations/%
populations/%
res.
J-coupling type (angle)
Exp
Fit
Pa, Pâ, PPP
Exp
Fit
Pa, Pâ, PPP
II
II
3J(HN,HR) (φ9)
3J(HN,C′) (φ9)
3J(HR,C′) (φ9)
3J(HN,Câ) (φ9)
1J(N,CR) (ψ9)
5.44
1.32
1.78
2.19
10.80
7.72
-
5.48
1.29
1.88
2.15
10.79
7.46
0.48
5.70
1.10
1.98
2.15
10.80
7.61
0.49
5.5
1.2
1.5
2.1
10.7
7.6
-
5.5
1.2
1.6
2.1
10.7
7.6
0.3
5.8
1.1
1.6
2.0
10.7
7.6
0.3
5.18
1.39
2.06
2.26
10.54
7.24
-
5.10
1.33
1.72
2.19
10.58
7.02
0.46
5.67
1.09
2.20
2.21
10.57
7.17
0.43
5.3
1.3
1.5
2.1
10.4
7.4
-
5.2
1.3
1.5
2.2
10.3
7.4
0.3
5.8
1.2
1.6
2.0
10.4
7.4
0.3
A9
0, 10, 90 (Fit)
5, 12, 83 (Fit)
0, 17, 83 (Fit)
34, 7, 59 (Fit)
40, 4, 56 (Fit)
27, 18, 55 (Fit)
2J(N,CR) (ψ9)
3J(HN,CR) (φ9, ψ8)
3J(HN,HR) (φ10)
3J(HN,C′) (φ10)
3J(HR,C′) (φ10)
3J(HN,Câ) (φ10)
1J(N,CR) (ψ10)
2J(N,CR) (ψ10)
3J(HN,CR) (φ10, ψ9)
3J(HN,HR) (φ11)
3J(HN,C′) (φ11)
3J(HR,C′) (φ11)
3J(HN,Câ) (φ11)
1J(N,CR) (ψ11)
2J(N,CR) (ψ11)
3J(HN,CR) (φ11, ψ10)
A10
A11
and
we decided to study the Ala3 sequence in two peptides derived
from the natural protein sequence. The shorter peptide, HEWL-
9mer, comprises the Ala3 sequence with three added amino
acids, and the longer peptide, HEWL-19mer, has added eight
amino acids at each side. The measured J-coupling constants
for the alanine residues show a clear shift toward RR helical
conformations already for HEWL-9mer, which becomes even
more pronounced for HEWL-19mer (cf. Table 5).
Since the MD simulation of longer peptides is cumbersome
(if converged conformational sampling is required), we em-
ployed the following simple procedure in order to estimate the
population of the conformational states from the measured
J-coupling constants. The method is based on the observation
that for all residues of peptides Ala4 to Ala7sexcept for the
terminal residuessthe calculated state-specific J-coupling con-
stants are quite similar, see Tables 3 and S3-S9. For example,
the 3J(HN,HR) coupling constant of Ala7 in the PPII state is 5.0
( 0.2 Hz, if one averages over the values of the five inner
residues. This finding suggests performing the fitting of the
∆G0 ) ∆G(T0)
∂∆G
∆G′ )
0
|
∂T T0
The approximation predicts a slope of J(T) of ∼0.011 Hz/K,
which is in good agreement with the experimental result of 0.013
Hz/K.
Comparison with the Ala3 Sequence in HEWL-Peptides.
Short homopolymeric peptides are often used as models for the
intrinsic properties of a segment of amino acids within longer
peptide sequences. We therefore were interested to compare the
studied alanine peptides with the natural Ala3 sequence in
lysozyme. The S-methylated full-length protein at pH 2 is well
studied and shows the features of an unfolded protein.65-67 Thus,
(65) Klein-Seetharaman, J.; Oikawa, M.; Grimshaw, S. B.; Wirmer, J.; Duchardt,
E.; Ueda, T.; Imoto, T.; Smith, L. J.; Dobson, C. M.; Schwalbe, H. Science
2002, 295, 1719-1722.
(66) Wirmer, J.; Schlo¨rb, C.; Klein-Seetharaman, J.; Hirano, R.; Ueda, T.; Imoto,
T.; Schwalbe, H. Angew. Chem., Int. Ed. 2004, 43, 5780-5785.
(67) Schlo¨rb, C.; Ackermann, K.; Richter, C.; Wirmer, J.; Schwalbe, H. J.
Biomol. NMR 2005, 33, 95-104.
9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1187

A R T I C L E S
Graf et al.
Table 6. Averaged J-Coupling Constants (in Hz) for Alanine Peptides
state
3J(HN,HR)
3J(HN,C
′
)
3J(HR,C
′
)
3J(HN,Câ)
1J(N,CR)
2J(N,CR)
3J(HN,CR)
R
5.2
9.4
5.0
1.4
0.8
1.2
1.5
2.6
1.4
2.0
0.7
2.3
9.7
10.6
10.8
7.4
7.6
7.7
0.5
0.7
0.5
â
PPII
1
Figure 6. Overlay of H, 15N HSQC spectra of the HEWL-9mer (green),
HEWL-19mer (red), and the full length S-methylated HEWL protein (black).
Shown is the spectral region around the Ala3 sequence. Each spectrum was
recorded at 700 MHz and at 293 K. Acquisition and processing parameters
and the full spectral region overlay is shown in the Supporting Information.
Figure 5. UV-CD spectra measured at 300 K of (a) Ala3, Ala7, and Val3;
(b) HEWL-9mer and HEWL-19mer.
at each side to resemble a full-length protein. Interestingly, the
same size was found for the persistence length70,71 in a random
coil model for the analysis of 15N relaxation rates of different
HEWL mutants.65
conformational populations (see Materials and Methods) on the
basis of state-averaged calculated J-coupling constants, which
are collected in Table 6. Proceeding this way, we find that the
conformational distribution of the central three alanine residues
in the 9mer is similar as for the small peptides Ala3-Ala7 (i.e.,
80-90% PPII). However, major differences are found for the
19mer, which significantly (30-40%) samples RR helical
structures (cf. Table 5).
Conclusions
We have studied the conformational distribution of short
alanine peptides in aqueous solution, employing a joint NMR/
MD strategy. For each peptide under consideration, we have
measured five φ-dependent and three ψ-dependent J-coupling
constants, respectively, and performed all-atom MD simulations
including explicit solvent. We have assumed that the MD force
field gives a reasonable description of the structure of the main
conformations R, â, and PPII, while the corresponding thermal
As an independent test, we consider the UV-CD spectra of
these peptides, which are given in Figure 5. The spectra of the
HEWL-9mer peptide show no significant difference when
compared to the spectra of Ala3 and Ala7 despite the value of
2
the ψ-dependent J(N,CR) coupling constant which is about 1
population probabilities PR, Pâ, and PPP are only predicted with
II
Hz lower than that for Ala3. In the spectra of HEWL-19mer
the shift toward more RR helical conformations is seen, and one
obtains a fractional R helicity of about 8% from the mean residue
molar ellipticity at 222 nm for the 19mer peptide.68 It is known
from the full-length S-methylated HEWL protein that the same
residues show a high induced helicity,66 and published69
3J(HN,HR) coupling constants for these residues are also almost
identical to the ones from the HEWL-19mer. In the overlay of
high degrees of uncertainty. In order to obtain accurate results
for the thermal populations, we therefore have performed a
global fit of PR, Pâ, and PPP by minimizing the deviation
II
between measured and calculated NMR parameters. Taking into
account the uncertainties of the parametrizations of the Karplus
relations and of the MD force field, we estimate an overall error
of about 5% for the population probabilities. This represents
an unprecedented accuracy, which may serve as a benchmark
for testing other experimental and computational approaches.
It has been found that the alanine peptides Alan (n ) 3-7)
exhibit virtually the same conformational distribution. They
mainly populate the PPII (∼90%) and the â (∼10%) conforma-
tions, while the RR helical conformation is not sampled at all.
This finding is in qualitative agreement with the results of
1
the H, 15N HSQC spectra of the two HEWL peptides and the
full-length S-methylated HEWL protein one sees that the
chemical shifts of the alanine residues of the HEWL-19mer are
identical with those from the full-length protein while the
chemical shifts for the HEWL-9mer are different (cf. Figure
6). This questions strongly the model character of short
homopolymeric peptides for longer peptide sequences. Instead,
it seems to be sufficient to have added about eight amino acids
(70) Pappu, R. V.; Srinivasan, R.; Rose, G. D. Proc. Natl. Acad. Sci. U.S.A.
2000, 97, 12565-12570.
(71) Mo¨glich, A.; Joder, K.; Kiefhaber, T. Proc. Natl. Acad. Sci. U.S.A. 2006,
103, 12394-12399.
(68) Rohl, C. A.; Baldwin, R. L. Biochemistry 1997, 36, 8435-8442.
(69) Grimshaw, S. B. Ph.D. Thesis, University of Oxford, 1999.
9
1188 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Structure−Dynamics of Homopolymeric Model Peptides
A R T I C L E S
Kallenbach and Hamm and their co-workers.1,2,14,15 The com-
parison of the tripeptides Ala3, Val3, and Gly3 reveals the
expected side-chain dependent variation of the (φ,ψ) sampling.
Considering the temperature dependence of the J-coupling
constants for the Ala3, experiment and theory reveals a linear
behavior of J(T) for T ) 275, ..., 350 K, which reflects the
increase of the â population at the expense of the PPII
population. The free energy difference ∆G ) 1.5 kcal/mol
between the two conformers at 300 K is caused by the enthalpic
contribution ∆H ≈ 6 kcal/mol and the entropic contribution
-T∆S ≈ -4.5 kcal/mol, indicating that the PPII state is favored
over the â state due to a lower enthalpy, although the latter is
stabilized by entropy.
Our MD results for short alanine peptides also facilitate the
estimation of the conformational distribution of larger alanine-
containing peptides. This is because for all residues of peptides
Ala4 to Ala7 the calculated state-specific J-coupling constants
are found to be quite similar. Hence, the thermal populations
of the conformational states of alanine residues can be obtained
on the basis of the averaged calculated J-coupling constants
collected in Table 6. Applied to a 9mer and a 19mer peptide of
HEWL protein, the approach reveals significant differences in
the conformational distribution of the Ala3 segment of these
peptides: Only the HEWL-19mer samples a significant amount
(30-40%) of RR helical conformation, while the HEWL-9mer
is predominately (80-90%) found in PPII conformation. This
finding seriously questions the model character of tripeptides
to predict the conformational distribution of longer peptide
sequences. Instead, it seems to be sufficient to have about eight
amino acids at each side to resemble a full-length protein in
agreement with earlier studies of persistence length in unfolded
proteins.
As explained in the Introduction, it is extremely difficult to
obtain accurate thermal population probabilities from a MD
force field calculation (even more so from ab initio calculations),
since a typical accuracy ∆∆G of the relative free energy of
∼1-2 kcal/mol already introduces an uncertainty exp(∆∆G/
kBT) of a factor of 10. Indeed, we have found that the
GROMOS96 force field clearly overestimates the population
of the RR helical state of the alanine peptides. In the worst case
of Ala7, the MD simulation predicts about 50% RR instead of
e5 %, corresponding to a deviation of the relative free energy
of about 1 kcal/mol. As shown in recent comparison studies of
various force field,8,12,13 this overestimation of RR helical
states is quite common and also occurs (often even more) for
other popular force field models including AMBER94,58
CHARMM22,59 OPLS-AA,60 as well as in QM/MM calcula-
tions.12 A notable exception is the model AMBER94/MOD put
forward by Garcia and co-workers.10 By modifying (actually
removing) the backbone dihedral angle terms of the AMBER94
force field, they obtained conformational distributions for
various alanine peptides which appear to be quite similar to
our NMR/MD results.
While it is obvious that modifications of the backbone
dihedral angle force field terms will change the resulting (φ,ψ)
probability distribution, it is still unclear whether these terms
are the only physical origin of the deviation between theory
and experiment. Using the GROMOS96 force field, for example,
we have obtained essentially the correct conformational distribu-
tion for Val3, althoughsby constructionsthe backbone dihedral
angle terms are identical for Val3 and Ala3. The joint NMR/
MD strategy proposed in this work is capable of providing
benchmark data for improving force fields that can well be
extended to other side chains.
Acknowledgment. We dedicate this work to Prof. Ju¨rgen
Bereiter-Hahn on the occasion of his 65th birthday. We are
grateful to Sarah Mensch for help with peptide synthesis and
purification. We thank Christian Richter for assistance with
NMR measurements and Christian Schlo¨rb for providing the
1H, 15N HSQC spectra of the full length S-methylated hen egg
white lysozyme. Financial support by the state of Hesse (Center
for Biomolecular Magnetic Resonance), the Deutsche For-
schungsgemeinschaft (SFB 579), the Center for Scientific
Computing of Frankfurt, and the EU-project UPMAN is
gratefully acknowledged.
Supporting Information Available: Complete ref 59; Table
S1 listing the synthesized peptides with their isotopic labeling
pattern; Table S2 with the Karplus parametrizations used in this
work; Tables S3-S13 with the J-coupling constants obtained
from NMR and MD together with populations from MD and
fitting; Table S14 and Figure S1 showing the results for the
test of the robustness of the fitting of the populations; Tables
S15-S49 with acquisition and processing parameters of the
NMR experiments; Tables S50-S63 with the assigned chemical
1
shifts of the peptides; Figures S2-S5 showing H,15N HSQC
1
and H 1D spectra of the studied peptides; Figure S6: the full
spectral region overlay of the 1H,15N HSQC spectra of
HEWL-9mer, HEWL-19mer, and the full length S-methylated
HEWL protein; Figure S7: the 1H,1H NOESY spectrum of Gly3.
This material is available free of charge via the Internet at
http://pubs.acs.org.
JA0660406
9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1189