A complete set of NMR chemical shifts and spin-spin coupling constants for L-Alanyl-L-alanine zwitterion and analysis of its conformational behavior.

Abstract

With the aid of labeling with stable isotopes ((15)N and (13)C) a complete set of chemical shifts and indirect spin-spin coupling constants was obtained for the zwitterionic form of L-alanyl-L-alanine in aqueous solution. Different sensitivities of the NMR parameters to the molecular geometry were discussed on the basis of comparison with ab initio (DFT) calculated values. An adiabatic two-dimensional vibrational wave function was constructed and used for determination of the main chain torsion angle dispersions and conformational averaging of the NMR shifts and coupling constants. The quantum description of the conformational dynamics based on the density functional theory and a polarizable continuum solvent model agrees reasonably with classical molecular dynamics simulations using explicit solvent. The results consistently evidence the presence of a single form in the aqueous solution with equilibrium main chain torsion angle values (psi = 147 degrees, varphi = -153 degrees), close to that one found previously in an X-ray study. Under normal temperature the torsion angles can vary by about 10 degrees around their equilibrium values, which leads, however, to minor corrections of the NMR parameters only. The main chain heavy atom chemical shifts and spin-spin coupling constants involving the alpha-carbon and hydrogen atoms appear to be most useful for the peptide structural predictions.

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A Complete Set of NMR Chemical Shifts and Spin-Spin
Coupling Constants for L-Alanyl-L-alanine Zwitterion and
Analysis of Its Conformational Behavior
Petr Bour ˇ,* Milos ˇ Bude ˇs ˇı ´nsky ´,* Vladimı ´r S ˇpirko,* Josef Kapita ´n,
Jaroslav S ˇebestı ´k, and Vladimı ´r Sychrovsky ´*
Contribution from the Institute of Organic Chemistry and Biochemistry, Academy of Sciences of
the Czech Republic, FlemingoVo na ´m. 2, 16610, Praha 6, Czech Republic
Received August 16, 2005; E-mail: bour@uochb.cas.cz; budesinsky@uochb.cas.cz; spirko@uochb.cas.cz; sychrovsky@uochb.cas.cz
Abstract: With the aid of labeling with stable isotopes (15N and13C) a complete set of chemical shifts and
indirect spin-spin coupling constants was obtained for the zwitterionic form of L-alanyl-L-alanine in aqueous
solution. Different sensitivities of the NMR parameters to the molecular geometry were discussed on the
basis of comparison with ab initio (DFT) calculated values. An adiabatic two-dimensional vibrational wave
function was constructed and used for determination of the main chain torsion angle dispersions and
conformational averaging of the NMR shifts and coupling constants. The quantum description of the
conformational dynamics based on the density functional theory and a polarizable continuum solvent model
agrees reasonably with classical molecular dynamics simulations using explicit solvent. The results
consistently evidence the presence of a single form in the aqueous solution with equilibrium main chain
torsion angle values (ψ ) 147°, ? ) -153°), close to that one found previously in an X-ray study. Under
normal temperature the torsion angles can vary by about 10° around their equilibrium values, which leads,
however, to minor corrections of the NMR parameters only. The main chain heavy atom chemical shifts
and spin-spin coupling constants involving the R-carbon and hydrogen atoms appear to be most useful
for the peptide structural predictions.
Introduction
Small molecules which model fundamental parts and proper-
ties of peptides and proteins become increasingly popular
because they can be well manipulated and their accurate
theoretical analysis is still feasible. For example, unique
knowledge of structure, flexibility, and solute-solvent interac-
tions was obtained recently for N-methylacetamide,1,2alanine,3,4
diglycin,5,6alanine diamide,7and other peptide building blocks.8-13
The L-alanyl-L-alanine (LALA) molecule itself, one of the
simplest chiral peptides, appears particularly challenging because
of its strong interaction with the solvent. As a matter of fact,
the neutral zwitterionic form cannot exist in a vacuum, as was
confirmed by theoretical14and experimental15studies. Similar
attention was devoted also to other charged forms of L-alanyl-
L-alanine.16Despite numerous investigations of LALA,14,15,17-20
no definite conclusion concerning LALA conformation and
dynamics in solution was deduced because of the limited
accuracy of the simulation techniques. Although previous studies
suggested rather semirigid conformation,14,18the usual approach
may not have been adequate for description of the torsional
motions opposed by soft potentials. Knowledge of such torsional
flexibility can enlighten peptide biological activity21and has
additional implications important for a correct determination
of the peptide structures from the NMR data. Thus we find it
worthwhile to analyze the conformational dependence of the
chemical shifts and spin-spin coupling constants of LALA in
the framework of a two-dimensional (2D) torsional model. Using
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Published on Web 11/11/2005
10.1021/ja0552343 CCC: $30.25 © 2005 American Chemical Society
J. AM. CHEM. SOC. 2005, 127, 17079-17089 9 17079

Page 2

the 2D property surfaces for the shifts and indirect coupling
constants, the torsion angle ?, ψ values can be determined by
comparing with experimental values.
Though the NMR spectroscopy is routinely used to probe
molecular structure,22-28interpretation of the spectra based on
the first principles became feasible only lately by efficient
implementations of the coupled-perturbed techniques generally
available software. Especially the density functional theory
(DFT) methods thus have significantly reduced computer cost
for the calculation of the chemical shifts and indirect NMR
spin-spin coupling constants for systems of biochemical
interest.29-34Reliable calculation of the NMR parameters is
feasible for systems such as nucleic acid bases,35,36porphyrins,37
or fullerenes.38Traditionally, the relation between the spin-
spin coupling constants and molecular structures is described
by empirical Karplus-type relations.39-44It is, however, prob-
lematic to apply these equations for compounds chemically
different from those ones used for their calibration.45,46In such
a situation it is more suitable to use ab initio analysis which
provides more reliable estimates of the sensitivity of various
types of the constants on the molecular conformation.
The resolution of molecular structure on the basis of
comparison of calculated NMR parameters with experiment is
not straightforward and may be affected by a number of factors
including accuracy of the calculation,29the effect of solvent and
averaging of molecular motion (as shown, for example, in refs
37 and 46-48). In the case of longer peptides and proteins the
number of the spin-spin coupling constants becomes very large
and not all of them can be used for reliable structural analysis.
Thus constants suitable for the measurement can be selected
conveniently by means of the ab initio calculations.
In LALA, as in most peptides, conformational dynamics is
governed mostly by the main chain torsions which can be
assumed to be adiabatically separable from the remaining
molecular movements. In other words changes of the LALA
molecular shape can be described using a two-dimensional
torsional Schro ¨dinger equation and the sought structural char-
acteristics can be obtained by averaging over corresponding
wave functions. Note also that the previous molecular dynamics
(MD) studies indicate that the usual vibrational averaging based
on the harmonic approximation is problematic for simple
peptides exhibiting large-amplitude vibrations.49An alternative
approach can be based, for example, on conventional or quantum
molecular-dynamics simulations. To complete our study, the
theoretical chemical shift and spin-spin coupling constants are
thus compared to experimental data, and the conformational
dependence of the NMR parameters on the main chain angles
is analyzed and possible generalization for peptide structural
analyses is suggested. We suppose that internal rotational
motions of the CH3, NH3+, and CO2-groups do not change
the peptide secondary structure and that NMR parameters of
rotating atoms can be replaced by an average value due to their
fast movements.50
Experiment
Synthesis of Isotopically Labeled Dipeptide. A series of isotopi-
cally labeled dipeptides H-Ala-Ala-OH was prepared from isotopically
labeled alanine compounds (L-Alanine (15N, 98%) and L-Alanine (13C,
98%;15N, 98%) purchased from Stable Isotopes, Inc. Conventional
peptide synthesis in solution was employed with maximization of the
reaction efficiencies. In the first step, the benzyloxycarbonyl (Z)
protection group was introducted by treatment with N-benzyloxycar-
bonyloxysuccinimide.51Then the protected alanine was converted to
its active ester with DCC and N-hydroxysuccinimide.52After aminolysis
of the prepared active ester with unprotected labeled alanine, the
zwitterionic dipeptide was obtained by hydrogenolysis on Pd-black53
and purified by HPLC.
NMR Experiments. The NMR spectra of nonlabeled L-Ala-L-Ala,
15N labeled l-Ala(15N)-L-Ala(15N), and fully15N- and13C-labeled L-Ala-
(13C,15N)-L-Ala(13C,15N) were measured with FT NMR spectrometers
Varian UNITY-500 and Bruker AVANCE-500 (1H at 500 MHz,13C
at 125.7 MHz,15N at 50.7 MHz,17O at 67.8 MHz) in D2O and/or in
the mixture H2O/D2O (9:1). All spectra were measured at room
temperature except for the17O NMR spectrum which was recorded at
80°C. Chemical shifts were referenced to either internal (DSS for1H
and13C; H2O for17O) or external (nitromethane in the capillary for
15N) standards. The nonlabeled compound was used to determine1H,
13C, and17O chemical shifts and J(H,H) and J(C,H) couplings. The
structural assignment of the hydrogen and carbon chemical shifts was
achieved using homonuclear two-dimensional 2D-1H pulse field gradient
correlation spectroscopy (1H-PFG-COSY) and heteronuclear 2D-1H
pulse field gradient heteronuclear single-quantum coherence (13C-PFG-
HSQC) and 2D-1H pulse field gradient heteronuclear multibond
correlation (13C-PFG-HMBC) experiments in D2O. The solvent mixture
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A R T I C L E S
Bour ˇ et al.
17080 J. AM. CHEM. SOC.9VOL. 127, NO. 48, 2005

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H2O/D2O (9:1) was used to observe the signals of NH and NH3+
protons. Only the couplings of amide NH could be observed in this
mixture because of the high exchange rate of amine NH3+protons with
water. The J(H,H) values were determined from 1D-1H NMR spectrum
and J(C,H) couplings from a nondecoupled 1D-13C NMR spectrum. A
series of selective1H-decoupled13C NMR spectra was used to assign
individual J(C,H) couplings. The17O chemical shifts were obtained at
80 °C (to narrow very broad17O lines) and assigned tentatively to
NHCO and COOH according to the signal intensities and known relative
shift values of these groups. The labeled15N and15N,13C L-Ala-L-Ala
samples were used mainly for obtaining J(N,H), J(N,C), and J(C,C)
coupling constants using 1D-1H and
INADEQUATE (Incredible Natural Abundance Double Quantum
Transfer Experiment) and 2D-1H,15N-PFG-HMBC spectra.
13C NMR spectra, 1D-13C-
Calculations
Geometries. A two-dimensional potential energy surface (PES) of
LALA was obtained by scanning the main chain torsion angles ?, ψ
defined in Figure 1. The scan was performed at the BPW9154,55/6-
311++G** level in conjunction with the PCM56and COSMO57,58
continuum water models as implemented in the Gaussian program
package.59The COSMO surface (as well as those obtained by control
computations utilizing the Becke3LYP functional and/or a smaller basis,
6-31G**) was found quite similar to PCM and is not analyzed further.
First, the angles ?, ψ were scanned with a step of 60°, and then other
geometries in vicinities of the minima were added to the total of about
80 points. Finally, an analytical surface was obtained by a fitting with
polynomials. The scans were started with the trans-conformation of
the amide group (ω ) 180°) because no experimental data indicate
the presence of the cis-conformer. But the angle ω was not constrained,
and all coordinates except ? and ψ were fully optimized at each point.
To check the influence of explicit hydrogen bonding not included in
the PCM model, explicit water molecules were added to LALA in a
vacuum (the geometry is displayed in Figure 2) and in combination
with the PCM model for outer hydration shells. Probable positions of
the solvent molecules were selected using the Tinker60molecular
dynamics (MD) program package from an MD simulation of LALA
in a water box.
NMR Parameters. Chemical shifts and the indirect spin-spin
coupling constants were calculated analytically by Gaussian using the
GIAO method61-63with the Becke3LYP64functional, as this approach
was found suitable for analogous computations previously.31,32All four
important contributions, diamagnetic spin-orbit, paramagnetic spin-
orbit, Fermi contact, and spin dipolar, were included, and an extended
set of atomic orbitals was used: the (9s,5p,1d/5s,1p) [6s,4p,1d/3s,1p]
bases for carbon and nitrogen, the (5s,1p) [3s,1p] basis for hydrogen
(referred to as IGLO II), and in some cases also a larger set (11s,7p,2d/
6s,2p) [7s,6p,2d/4s,2p] (IGLO III), all of them proposed for computation
of magnetic properties previously.65The same PCM solvent correction
was used as in the case of the geometry surfaces. The property surfaces,
dependencies of the chemical shifts and coupling constants on the
conformation, were obtained analogously as was the energy by a scan
over the angles ? and ψ.
Molecular Dynamics. Alternatively to the ab initio PES mapping,
we performed a molecular dynamic (MD) simulation of the LALA
molecule in a box containing 502 water molecules using the AMBER
program package.66The Amber94,67Amber99,68and Amber0369peptide
force fields of AMBER and the Charmm2770field of Tinker60,71were
applied with the periodic boundary conditions, constant pressure of 1
atm, a temperature of 300 K, a weak-coupling algorithm,72a nonbonded
cutoff of 8 Å, and the TIP3P water model.73A time step of 1 fs was
used for integration of the Newton equations, and the trajectory
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A. J. Am. Chem. Soc. 1995, 117, 5179-5197.
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Figure 1. Calculated (BPW91/PCM/6-311++G**) lowest-energy geom-
etry of LALA (conformer A) and the atom numbering used for the
description of chemical shifts and the coupling constants. Hydrogen and
oxygen numbers correspond to the connected heavy atoms.
Figure 2. Geometry of the LALA zwitterion solvated with 9 water
molecules of the first hydration sphere. Hydrogen bonds are marked by the
dashed green lines.
L-Alanyl-L-alanine Zwitterion and Conformational Behavior
A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 127, NO. 48, 2005 17081

Page 4

coordinates and free-energies were recorded every 1 ps within a total
simulation time of 20 ns and analyzed by a software written by us.
Vibrational Dynamics. The quantum and quantum dynamical effects
of the torsional motions involving the angles (?, ψ) were studied using
an approximate Hamiltonian,
where Pγ ) - ip∂/∂γ (γ ) ?,ψ), V(?,ψ) is the potential energy
function, and GR? are matrix elements of the generalized vibrational
kinematic matrix.74The eigenvalue problem HΨ ) EΨ was solved
variationally in basis set functions expressed as products of the
eigenfunctions of the corresponding uncoupled one-dimensional Schro ¨-
dinger equations. The one-dimensional functions were determined
numerically using the Numerov-Cooley integration procedure.75Aver-
age values of the NMR parameters for each state i were calculated as
the expectation values
where g(?,ψ) are theoretically evaluated surfaces of the studied
properties (shifts, couplings). For selected localized excited vibrational
states their lifetimes were estimated from simplified one-dimensional
modeling described below.
Results and Discussion
Potential Energy Surface. Despite the strong interaction with
the solvent and the presence of the rotating single covalent
bonds, only one conformation (A) viable under normal condi-
tions was found by the BPW91/6-311++G**/PCM method. The
other three local minima (B-D) on the adiabatic two-
dimensional potential energy surface (Figure 3, Table 1) cannot
be significantly populated at room temperature. The equilibrium
torsion angles (?,ψ) ) (-153°, 147°) pertaining to the studied
conformers are collected in Table 1. The prevalence of
conformer A is in agreement with the X-ray data (Table 1)76
and also with previous Raman optical activity14and other ab
initio studies.15Note, that explicit hydrogen bonding not
included in our PCM model may lead to a certain stabilization
of different forms of the molecule.18We thus realize that our
results can be affected by this simplification.
Interestingly, similar MD equilibrium structures as those for
LALA were obtained also for a similar but neutral diamide (Ac-
Ala-NMe).77,78Thus, we can speculate that the influence of the
charged ends on the zwitterion conformation is significantly
reduced by water. Various MD force fields, however, provide
different average conformations (cf. Table 1) only vaguely
related to the conformer A obtained ab initio. The Amber family
force fields (Amber94, Amber99 and Amber03) lead to two
variously populated conformers with the same ψ (∼ 145°) but
different ? (-150° and -65°) angles, while only one minimum
on the free energy surface was obtained by the Charmm27 force
field with average angles (ψ ) 175°, ? ) -90°). Supposedly,
these results are inferior to the Becke3LYP/6-311++G**/PCM
ab initio prediction, because the MD force field was developed
rather for longer peptides and proteins.
It is nevertheless remarkable that the probability conformer
distribution obtained from molecular dynamics reasonably
agrees with the quantum picture, as can be seen in Figure 4
where the probabilities obtained by the two approaches are
compared. Although explicit hydrogen bonds and coupling with
water motion somewhat stabilize rare conformers, the MD free-
energy landscape (for the Amber99 force field) clearly leads to
one prevalent conformation close to the conformer A obtained
by ab initio computation. It should be stressed that the
comparison is only qualitative because we are using only a
simplified two-dimensional quantum model. Nevertheless, the
torsion angle dispersions estimated for the lowest-vibrational
states appear to be representative, at least as a lower limit of
the dispersion. Apparently, the lowest-energy conformer (A) is
well-stabilized by the potential well; however its flexibility is
rather profound as the (?, ψ) angles can almost freely vary
within about (10°. This behavior must be clearly taken into
account when physical properties of the molecule are considered.
In other words, the term “conformation” cannot be related to a
classically rigid structure for LALA. We suppose that longer
(73) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D. J. Chem. Phys. 1983,
79, 926-935.
(74) C ˇejchan, A.; S ˇpirko, V. J. Mol. Spectrosc. 2003, 217 (1), 142-145.
(75) Ixaru, L. Numerical Methods for Differential Equations and Applications;
Reidel: Dordrecht, 1984.
(76) Fletterick, R. J.; Tsai, C.; Hughes, R. E. J. Phys. Chem. 1971, 75 (7), 918-
922.
(77) Gnanakaran, S.; Garcia, A. E. J. Phys. Chem. B 2003, 107, 12555-12557.
(78) Hu, H.; Elstner, M.; Hermans, J. Proteins: Struct., Funct., Genet. 2003,
50, 451-463.
Figure 3. Dependence of relative conformer energy of the LALA zwitterion
in water on the main chain torsion angles as calculated at the Becke3LYP/
6-311++G**/PCM level. The minima A-D, dots (b) on the surface and
crosses (+) at the ?,ψ plane projection, correspond to those in Table 1.
H )1
2∑
R,?
GR?(?,ψ)PRP?+ V(?,ψ)(1)
〈gi〉 ) 〈Ψi(?,ψ)|g(?,ψ)|Ψi(?,ψ)〉
(2)
Table 1. Geometries and Relative Conformer Energies of LALA
Obtained by Various Techniques
conformer
?
(deg)
ψ
(deg)
E
(kcal/mol)
This Work
BPW91/
6-311++G**/PCM
A
B
C
D
MD simulation
(A)
(A)
(A)
-153147
150
-50
-45
0.0
3.7
5.2
9.3
67
-150
64
Amber9968
Amber9467, Amber0369
Charmm2770
-150
-65
-90
145
145
175
Other Works
A
A
A
E
X-ray76
B3LYP/6-31G*/Onsager15
BPW91/6-311G**/COSMO14-162
B3LYP/6-31G*/Onsager,
cluster with 14 H2Os18
-113
-170
165
172
179
-65 -164
A R T I C L E S
Bour ˇ et al.
17082 J. AM. CHEM. SOC.9VOL. 127, NO. 48, 2005

Page 5

peptides behave similarly, which can obviously contribute to
the universality of their biological function. For LALA, the first
two excited vibrational functions (d, e in Figure 4) which are
nearly degenerate (with energies of 104 and 120 cm-1) in the
system reminds us of a two-dimensional harmonic oscillator79
and suggests significant coupling of the rotations involving the
two angles.
Lifetime of the Conformer B. From the four minima on
the total potential energy function only two (A, B) are deep
enough to support profoundly localized states. To estimate
quantitatively the stability of the states trapped in the energeti-
cally higher potential energy well, we found it suitable to rely
on the stabilization procedure (80and references therein). The
actual calculations were performed by repeatedly diagonalizing
the following one-dimensional Hamiltonians
(V1(?) ) V(?); V2(?) ) V(?) and 0 for ? e ?eand ? > ?e,
(79) Papous ˇek, D.; Aliev, M. R. Molecular Vibrational/Rotational Spectra;
Academia: Prague, 1982.
Figure 4. Probability conformer distribution as a function of the torsion angles (?, ψ) obtained by molecular dynamics simulation (a) and as a sum of
probabilities of the first three quantum states obtained for the ab inito surface (b). The wave functions of the quantum states are plotted below (c, d, e,
amplitudes are normalized to angles in radians).
Figure 5. One-dimensional section of the potential energy surface from Figure 3 (solid line) and the eigenfunctions of the lowest (V ) 0) and localized (V
) 11, 13, 16) states of the ?-torsional motion.
H )1
2G??(?)P?
2+ Vi(?)(i ) 1,2)(3)
L-Alanyl-L-alanine Zwitterion and Conformational Behavior
A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 127, NO. 48, 2005 17083