Determination of molecular torsion angles using nuclear singlet relaxation

Article abstract of DOI:10.1021/ja1012917

The exponential relaxation time constant, TS , of a nuclear singlet state is influenced by the proximity of neighboring NMR-active nuclei. For methylene groups in particular this dependence is much stronger than the case for other NMR relaxation constants, including the conventional relaxation time constant, T1 , of the longitudinal magnetization. This sensitivity provides a new route for determining torsional angles plus other molecular structural details in the isotropic solution phase.

Full text of DOI:10.1021/ja1012917

Published on Web 05/27/2010
Determination of Molecular Torsion Angles Using Nuclear Singlet Relaxation
Michael C. D. Tayler, Sabrina Marie, A. Ganesan, and Malcolm H. Levitt*
School of Chemistry, UniVersity of Southampton, SO17 1BJ, Southampton, U.K.
Received February 12, 2010; E-mail: mhl@soton.ac.uk
Nuclear magnetic resonance (NMR) is used routinely to inves-
tigate molecular conformations in solution. Bond torsion angles may
be estimated from vicinal scalar coupling constants, while the
nuclear Overhauser effect (NOE) provides information on inter-
nuclear distances.1 However, in some cases, these standard methods
are unavailable, ambiguous, or insufficiently accurate. In this
communication, we demonstrate that the relaxation of nuclear
singlet states2-4 can provide complementary information. In
favorable cases, a comparison of the singlet relaxation time constant
Figure 1. (a) Molecular graph of the 2× protected Phe isotopologues
highlighting the diastereotopic Cꢀ protons where singlet states are prepared.
(b) The characteristic antiphase NMR signal derived from the long-lived
state is shown decaying with exponential time constant TS ) 51 ( 2 s for
d6-Phe (half-doublets shown, proton Larmor frequency )400 MHz).
TS with the ordinary spin-lattice constant T1 provides useful
qualitative information on the molecular conformation without
resorting to detailed models of the NMR relaxation.
The singlet state of a spin-1/2 pair is denoted as follows:
each additional spin to the center of the spin pair.8 Magnetic nuclei
at long-range therefore have a negligible effect, even if they are
present in large numbers. The comparison of TS and T1 may hence
be used to set strong geometric restraints on the immediate
molecular environment of the CH2 group.
To test this concept we prepared a series of three deuterated
phenylalanine isotopologues. Substitutions were made (i) alone at
CR (referred as d1-Phe), (ii) on only the proton sites of the phenyl
ring (d5), and (iii) both of these environments (d6-Phe) (Figure 1a).
Methyl and N-phthalimido groups, which were not deuterated, were
added to block solvent-induced relaxation at the carboxyl and amino
groups respectively. At a proton frequency of 400 MHz, the nuclear
singlet populations were excited on the pair at Cꢀ using the method
described by Sarkar et al.5 The singlets were locked under resonant
continuous-wave RF irradiation, and the relaxation rates were
measured (for details, see the SI). NMR signals not passing through
the singlet states were suppressed by isotropic signal filtration using
a tetrahedral phase cycle.11
For d6-Phe the singlet relaxation time was TS ) 51 ( 2 s,
approximately 37 times longer than the conventional spin-lattice
relaxation time of T1 ) 1.38 ( 0.05 s (Figure 1b). In d1-Phe, which
differs only by protonation of the ring, the decay time was reduced
to TS ) 8.0 ( 0.1 s or only 6.8 times longer than T1 ) 1.17 (
0.04 s. This change is attributable to the spin interactions between
the two ꢀ-protons and the phenyl protons, in particular, the two
ortho protons of the ring; the data confirm that the T1 of the
ꢀ-protons is dominated by the large dipolar interaction between
them and, conversely, that the singlet state in d1-Phe is relaxed by
the DD couplings to the neighboring ortho protons of the ring. The
long singlet lifetime for the d6 compound indicates that chemical
shift anisotropy has only a small contribution to the relaxation of
the methylene singlet state and that the contributions of the
protonated blocking groups are also negligible.
|S0〉 ) 2-1/2(|Rꢀ〉 - |ꢀR〉)
(1)
where the symbols R and ꢀ indicate quantum states with an angular
momentum ( p/2 along the applied magnetic field. Such states
can be observed for inequivalent spin-1/2 pairs by a variety of
methods.3-7 Their lifetimes may exceed the ordinary relaxation
time constant T1 by over an order of magnitude, depending on
factors such as the spatial proximity of neighboring magnetic
nuclei8,9 and the relative orientations of chemical shift anisotropy
tensors.10
The proton spin pair of an inequivalent CH2 group is a
particularly favorable case for the quantitative study of singlet
relaxation. The conventional T1 relaxation is dominated by a single
mechanism, namely, the modulation of the internuclear magnetic
dipole-dipole coupling by molecular tumbling in solution. In
consequence T1 provides an effective internal calibration of the
rotational correlation time. The relaxation time ratio TS/T1 may
depend, within plausible assumptions and to a good approximation,
only on molecular geometry and the spin-spin coupling strengths
and be insensitive to the rotational behavior of the molecules.
For the case where the CH2 protons have no significant
J-couplings to neighboring protons, the relaxation time ratio TS/T1
is only dependent on geometry, to a good approximation. As
detailed in the Supporting Information (SI), the following form
describes the predicted ratio TS/T1 in the absence of scalar spin
couplings to neighboring nuclei, which is valid for small molecules
in the extreme-narrowing regime:
TS
T1
3b212
=
(2)
∑
2(b21j + b22j - 2b1jb2jP2(cos θ1j2))
j>2
In this expression indices 1 and 2 indicate the members of the
proton pair and j those nuclei in their vicinity; bjk ) spγ2µ0 /4πrjk
The T1 value of 1.38 ( 0.05 s corresponds to a rotational
correlation time of τc ≈ 24 ps, which verifies that the molecular
rotation is within the extreme narrowing limit.
Since the ꢀ-protons do not have significant J-couplings with the
ring protons, eq 2 can be used to analyze the dependence of the
singlet relaxation rate constant upon the torsional angle, ꢁꢀγ, around
3
indicates the dipolar coupling factor, which is inversely proportional
to the third power of the internuclear distance rjk, P2(x) ) 1/2(3x2
-1) is a Legendre polynomial, and θ1j2 is the angle between the
two vectors joining spins 1 and 2 with spin j. Above r1j ≈ 2 Å, the
ratio decays with the inverse eighth power of the distance from
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C O M M U N I C A T I O N S
Figure 2. Theoretical ratio TS/T1 for d1-Phe plotted as a function of the
ring torsion angle ꢁꢀγ in the limit of static molecular geometry (solid line)
and in the presence of rapid two-site jumps (dashed line). The horizontal
band indicates the experimental ratio of relaxation time constants and its
confidence limits.
the Cꢀ/Cγ bond. Coordinates of the two ortho protons are con-
structed as a function of ꢁꢀγ by using standard bond lengths and
bond angles, and the derived dipole-dipole couplings and angles
θ are then used with eq 2 to predict the ratio TS(ꢁꢀγ)/T1. In our
convention the angle ꢁꢀγ ) 0 indicates the midpoint of the vector
joining the two ꢀ-protons is in the plane of the phenyl ring. The
theoretical estimate of TS/T1 against the phenyl torsion angle is
plotted in Figure 2 (solid curve). The values show a variation in
the theoretical TS/T1 ratio between ∼14 near ꢁꢀγ ) 0° and ∼6 in
the vicinity of |ꢁꢀγ| ) 90°. The experimental ratio for d1-Phe is
TS/T1 ) 6.8 ( 0.2 indicating an angle between |ꢁꢀγ| ) 45° and
135°. This orientation is consistent with the crystal structure of
L-phenylalanine.12
Figure 3. (a) Theoretical ratio TS/T1 for d5-Phe plotted as a function of
the ring torsion angle ꢁRꢀ. The horizontal band indicates the experimental
ratio of relaxation time constants and its confidence limits. (b) Karplus curves
for the vicinal 3JRꢀ-couplings,16 emphasizing the complementary nature of
the torsion angle dependence, compared to TS/T1.
curves. In this particular demonstration the value of TS/T1 merely
confirms the torsional angle estimate from the vicinal J-couplings.
We must stress, however, that an analysis using a single or
dominant conformation will not be appropriate in all cases. In
systems that are less rigid, where steric factors are not so strong,
especially acyclic aliphatics, one must address the possibility of
rotamer interconversion. If the conformational exchange is much
slower than τc, the rate constants 1/T1 and 1/TS are given by an
average over their values in the relevant conformations, weighted
by the equilibrium populations.
In summary, CH2 singlet relaxation is highly sensitive to the
local magnetic environment of the proton pair and depends in a
predictable way on local geometric parameters, such as torsional
angles. Singlet relaxation may therefore provide geometrical
information that is hard to otherwise obtain and, in general, provides
complementary information that is useful for verifying geometric
models or for resolving ambiguities. We also anticipate that singlet
relaxation is less sensitive to effects such as spin diffusion that
readily confound cross-relaxation measurements. We expect numer-
ous applications to molecular conformational studies in solution.
Aromatic rings of amino acid side chains, such as those of
phenylalanine and tyrosine, execute sporadic 180° rotations.13,14
Ring flips that are fast compared to the rotational correlation time
would have a strong effect on the CH2 singlet relaxation as a
consequence of geometrical averaging of dipolar couplings between
the ꢀ- and ring ortho-protons. Figure 2 (dashed curve) shows the
predicted ꢁ-dependence of TS/T1 for the case of these rapid jumps
between conformations with torsions ꢁꢀγ and ꢁꢀγ+180°. This
“rapid-flip” model predicts much longer singlet relaxation times,
with TS/T1 varying between 13 and ∼26. That the experimental
value of TS/T1 ) 6.8 is inconsistent with this jump model for all
values of ꢁꢀγ proves that 180° ring flips are infrequent on the
molecular rotational time scale of ∼24 ps.
In the d5-Phe isotopologue, the CꢀH2 singlet relaxation is caused
predominantly by dipole-dipole interactions with the R proton.
We observed TS ) 16 ( 0.2 s and T1 ) 1.33 ( 0.04 s to give the
ratio TS/T1 ) 12.0 ( 0.5. In this case, however, eq 2 cannot be
used to determine the dependence of TS on the torsion angle ꢁRꢀ,
for the singlet relaxation is strongly influenced by the vicinal 3JRꢀ-
couplings, which are themselves dependent on ꢁRꢀ. In such an
instance the conformational dependence of TS/T1 on ꢁRꢀ is made
by Liouvillian eigenvalue analysis15 using Karplus relationships
Acknowledgment. This work is supported by EPSRC-UK. The
authors thank O. G. Johannessen for experimental help and G. Pileio
for discussions.
Supporting Information Available: Derivation of eq 2, full details
of experiments and simulations. This material is available free of charge
via the Internet at http://pubs.acs.org.
3
to treat the torsion angle dependence of JRꢀ (see Supporting
Information). The predicted TS/T1 curve is shown in Figure 3a, with
a minimum in TS/T1 at the eclipsed syn conformations (|ꢁRꢀ| ) 60°)
and a maximum in the vicinity of the anti configuration (|ꢁRꢀ| )
140°-180°). The experimental ratio of the relaxation times supports
an angle |ꢁRꢀ| ≈ 100° which approximately agrees with the value
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