This journal is c The Royal Society of Chemistry 2011 Chem. Commun., 2011, 47, 9209–92119209
Citethis: Chem. Commun.,2011,47,9209–9211
A convenient method for the measurements of transverse relaxation rates
in homonuclear scalar coupled spin systemsw
Caroline Barre ` re, Pierre Thureau,* Andre ´ The ´ vand and Ste ´ phane Viel
Received 24th May 2011, Accepted 23rd June 2011
A new solution-state NMR method is proposed to determine
apparent transverse NMR relaxation rates in both weakly and
strongly scalar coupled two-spin systems.
Nuclear Magnetic Resonance currently represents one of
the most powerful techniques to provide molecular dynamic
information with atomic resolution.1In this context, Nuclear
Magnetic Resonance experiments based on spin echoes2are of
great relevance because they allow homogeneous transverse
relaxation rates (R2),3translational diffusion coefficients,4
and chemical exchange rate constants5,6to be determined.
However, echo modulations arising from homonuclear scalar
couplings seriously complicate the corresponding NMR data
analysis, especially for R2measurements in organic materials
with a high density of
acquisition and processing strategies have been proposed to obtain
broadband decoupled spectra under specific circumstances,7–12
echo modulations observed in R2measurements are usually
suppressed using a multiple refocusing Carr–Purcell–Meiboom–
Gill (CPMG) pulse sequence.13,14However, the so-obtained
refocusing is hardly complete and residual oscillations prevent
accurate R2data to be achieved.
More recently, Bodenhausen and coworkers have proposed
an alternative NMR experiment based on the CPMG pulse
sequence, which uses moderately strong radiofrequency (RF)
pulses. This methodology was shown to quench the echo
modulations for scalar coupled two-spin systems, hereby
allowing the R2determination of some of the backbone and
side-chain protons (i.e. mainly those appearing as doublets) in
peptides.15–17However, in this case, the experimental parameters,
such as the carrier irradiation frequency and the CPMG
pulse repetition time (t), need to be optimized for each sample
under study and, most importantly, for each NMR resonance
of interest. This significantly increases the required number
of NMR experiments and hence the total acquisition time.
13C-labelled nuclei. While
Moreover, the impact of strong coupling was not clearly
assessed. Here, we present a broadband method that allows
transverse relaxation rates of individual spins to be measured
in the presence of homonuclear scalar couplings. In this
communication, we focused on the case of two-spin systems.
The methodology for echo modulation suppression proposed
here is based on a linear combination of multiple-quantum
filtered experiments.18The related NMR pulse sequence is
depicted in Fig. 1. In this sequence, the initial 901 RF pulse is
followed by two spin-echo blocks that are placed on each side
of two strong 901 RF pulses. Each spin-echo block consists of
two successive variable evolution delays (t/4) separated by
a strong 1801 RF pulse. Multiplex phase cycling19is used to
filter the experimental NMR signals through either zero-
quantum or double-quantum coherences at the junction of
the two 901 pulses. The transverse relaxation rate is estimated
by repeating the pulse sequence in Fig. 1 for several values of
the total delay t.
In practice, the cancellation of echo modulations can only
be effective if the transverse relaxation rates are identical for
the zero quantum-filtered experiments (ZQF) and the double
quantum-filtered experiments (DQF). This aspect was explored
with accurate numerical simulations using the software
Mathematica assisted by the mPackages routines.20The
numerical simulations tracked the spin dynamics through the
pulse sequence displayed in Fig. 1, including the effect of
transverse relaxation. The effect of transverse relaxation was
modelled using the approximation of the fluctuating random
The results showed that the ZQF and DQF signals obtained
in this case are characterized by the same transverse relaxation
rate. Thus, for a scalar coupled two-spin system, with J being
the associated scalar coupling constant, the intensity of the
transverse relaxation rates (R2). Combination of the ZQF and DQF
signal amplitudes as a function of t allows R2values to be estimated.
The phase cycling is reported in the ESI.w
Multiple quantum-filtered pulse sequence used to measure the
Laboratoire Chimie Provence, Spectrome´tries Applique´es a ` la Chimie
Structurale, UMR 6264, Universite´s Aix-Marseille I, II et III-CNRS,
13397 Marseille, France. E-mail: firstname.lastname@example.org;
Fax: +33 491 282 897; Tel: +33 491 288 578
w Electronic supplementary information (ESI) available: Experimental
parameters, details of the phase cycling, impact of diffusion, ZQ + DQ
curve for a strongly coupled spin system and uracil CPMG and Spin-
Echo curves. See DOI: 10.1039/c1cc13042k
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9210 Chem. Commun., 2011, 47, 9209–9211 This journal is c The Royal Society of Chemistry 2011
ZQF and DQF signals obtained using the pulse sequence
shown in Fig. 1 can be written as:
sZQFðtÞ ¼ cos2pJt
exp½?t ? R2?ð1Þ
sDQFðtÞ ¼ sin2pJt
exp½?t ? R2?ð2Þ
Therefore, the modulations due to the scalar coupling can be
suppressed by summing the amplitude of the ZQF and
DQF signals (eqn (1) and (2), respectively). In other words,
the amplitude of the resulting signal (hereafter referred to as
the ZQF + DQF signal for simplicity) only depends on the
transverse relaxation rate R2. Typically, additional signal
attenuation due to molecular translational diffusion in the
presence of background gradients should be accounted for
method. However, on modern well shimmed magnets, these
gradients are extremely small and the corresponding diffusion
attenuation can be safely neglected.w
It should be noted that eqn (1) and (2) are valid under
the weak coupling conditions, i.e. when the chemical shift
difference of the two coupled spins is much larger than the
scalar coupling constant J. Under the strong coupling condi-
tions, i.e. when the chemical shift difference of the two coupled
spins is close to J, we observed that the ZQF + DQF signal is
still modulated by the scalar coupling. However, the modulation
is significantly reduced and is periodically refocused over
prolonged time periods. Therefore, even in the case of strongly
coupled spins, unmodulated echo decays can still be obtained
by selecting the t sampling time adequately. In this case,
however, the method may lose its broadband character because
different sampling times may need to be used according to the
chemical shifts and J coupling constant of the spin system under
investigation. Experimental ZQF + DQF signal amplitudes for
a strongly coupled spin system are available in the ESI.w
Fig. 2 shows the experimental ZQF + DQF signal amplitudes
obtained with the pulse sequence shown in Fig. 1 for a uracil
sample (proton H1) dissolved in a DMSO-d6/D2O mixture. The
H1and H2protons of uracil form a weakly coupled two-spin
(AX) system with a scalar coupling constant of 8 Hz.z For
comparison purposes, Fig. 2 also shows the experimental
signal amplitudes obtained using the CPMG pulse sequence
(with CPMG pulse repetition times t of 1 ms and 2 ms).y In all
cases, no optimization of the carrier irradiation frequency
was performed. We clearly see in Fig. 2 that, contrary to the
CPMG experiments, the sum of the ZQF and DQF signal
amplitudes is practically free of scalar coupling modulations.
Moreover, in the case of the CPMG pulse sequence, the
experimental value of the pulse repetition time t strongly alters
the modulations of the echo curve.
Fig. 3 shows the full experimental ZQF + DQF signal
amplitudes obtained for both the H1and H2protons of uracil,
with an evolution delay t ranging from 4 ms to 10 s. Both
curves were obtained in a single experiment with the same
acquisition parameters. The related transverse relaxation rate
was determined simply by fitting the data with a
mono-exponential function. The so-achieved R(ZQF+DQF)
for H1and H2are compared in Table 1 with the transverse
relaxation rates obtained with a classical Hahn echo experiment.
In this case, the echo decay was adjusted with a mono-
exponential function multiplied by a cosine wave, leading to
relaxation rate values that were used as references (R(ref)
similarly to the work described in ref. 16. Transverse relaxation
rates obtained by CPMG with a pulse repetition time of 1 ms
) are also displayed in Table 1. As can be seen, the
accuracy of the apparent R2values obtained by the ZQF + DQF
method isvery muchimproved with respectto therelaxation rates
obtained by CPMG.
In summary, we have shown that multiple-quantum filtra-
tion can suppress the scalar coupling modulations observed in
the spin-echoes based R2measurements of homonuclear two-
spin systems. In the weak coupling regime, the methodology is
broadband and gives more accurate results than the conven-
tional CPMG method without requiring any experimental
optimization. In the strong coupling regime, echo modulations
can still be quenched but the sampling time t needs to be
optimized. Overall, while its potential for analyzing more
complex three-spin systems is still to be assessed (currently
underway), we believe that the proposed methodology will
already prove useful for the dynamic investigation of a large
range of chemical and biological molecules.
a function of t of the1H signal amplitude of a uracil sample (proton H1)
dissolved in a DMSO-d6/D2O mixture and obtained with: (K) the sum
of the ZQF and DQF experiments; (’) CPMG with t = 1 ms.
(E) CPMG with t = 2 ms.y In all three cases, the 1801 RF-pulse
duration was 18 ms.
(a) Molecular structure of uracil. (b) Experimental evolution as
a function of t for a uracil sample dissolved in a DMSO-d6/D2O
mixture; (a) proton H1(b) proton H2. The solid curve represents the
best fit to the mono-exponential decay.
Experimental1H ZQF + DQF signal amplitudes obtained as
uracil measured by Hahn echo (used as reference), ZQF + DQF
method and CPMG (t = 1 ms)
Transverse relaxation rates of the H1and H2protons of
0.45 ? 0.03
0.44 ? 0.02
0.45 ? 0.02
0.46 ? 0.02
0.37 ? 0.02
0.36 ? 0.02
This journal is c The Royal Society of Chemistry 2011 Chem. Commun., 2011, 47, 9209–9211 9211 Download full-text
Notes and references
z The possible weak coupling with the labile N–H proton can be safely
neglected as a first approximation.
y In the CPMG experiments, the total evolution delay t shown in
Fig. 2 and 3 is given by t ? n, where t is the CPMG pulse repetition
time (i.e. the time between two consecutive 1801 RF-pulses) and n is
the number of CPMG cycles.
1 V. I. Bakhmutov, Practical NMR Relaxation for Chemists,
John Wiley & Sons, Chischester, 2004.
2 E. L. Hahn, Phys. Rev., 1950, 80, 580–594.
3 R. L. Vold, J. S. Waugh, M. P. Klein and D. E. Phelps, J. Chem.
Phys., 1968, 48, 3831–3832.
4 P. Stilbs, Prog. Nucl. Magn. Reson. Spectrosc., 1987, 19, 1–47.
5 A. D. Bain, Prog. Nucl. Magn. Reson. Spectrosc., 2003, 43, 63–103.
6 V. Y. Orekhov, D. M. Korzhnev and L. E. Kay, J. Am. Chem.
Soc., 2004, 126, 1886–1891.
7 J. Garbow, D. Weitekamp and A. Pines, Chem. Phys. Lett., 1982,
8 L. Mahi, J. Duplan and B. Fenet, Chem. Phys. Lett., 1993, 211,
9 V. A. Mandelshtam, Q. N. Van and A. J. Shaka, J. Am. Chem.
Soc., 1998, 120, 12161–12162.
10 A. J. Pell and J. Keeler, J. Magn. Reson., 2007, 189, 293–299.
11 M. Nilsson and G. A. Morris, Chem. Commun., 2007, 933–935.
12 A. Botana, J. A. Aguilar, M. Nilsson and G. A. Morris, J. Magn.
Reson., 2011, 208, 270–278.
13 H. Y. Carr and E. M. Purcell, Phys. Rev., 1954, 94, 630–638.
14 S. Meiboom and D. Gill, Rev. Sci. Instrum., 1958, 29, 688–691.
15 J. Dittmer and G. Bodenhausen, J. Am. Chem. Soc., 2004, 126,
16 B. Baishya, T. F. Segawa and G. Bodenhausen, J. Am. Chem. Soc.,
2009, 131, 17538–17539.
17 T. F. Segawa, B. Baishya and G. Bodenhausen, ChemPhysChem,
2010, 11, 3343–3354.
18 P. Thureau, A. C. Sauerwein, M. Concistre and M. H. Levitt,
Phys. Chem. Chem. Phys., 2011, 13, 93–96.
19 G. Bodenhausen, H. Kogler and R. R. Ernst, J. Magn. Reson.,
1984, 58, 370–388.
20 M. H. Levitt, Experimental Nuclear Magnetic Resonance Conference,
Asilomar CA, 2011.
21 A. Abragam, The principles of Nuclear Magnetism, Oxford
University Press, London/New York, 1961.