Full text of DOI:10.1002/1097-458X(200012)38:12<1012::AID-MRC785>3.0.CO;2-O

MAGNETIC RESONANCE IN CHEMISTRY
Magn. Reson. Chem. 2000; 38: 1012–1018
Multiple-field carbon-13 and proton relaxation in sucrose in
viscous solution
∗
M. Effemey, J. Lang and J. Kowalewski
Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden
Received 22 June 2000; revised 28 August 2000; accepted 28 August 2000
ABSTRACT: Measurements of carbon-13 spin–lattice and spin–spin relaxation rates as well as nuclear Overhauser
enhancement (NOE) were combined with selected proton cross-relaxation measurements for sucrose in a viscous
cryosolvent, D2O–DMSO, at several magnetic fields and two temperatures. The results, which were outside the
extreme narrowing regime, were interpreted using the Lipari–Szabo formalism. All the carbon relaxation data and the
proton cross-relaxation rates give a consistent description, demonstrating that the two sugar residues display a similar
and highly limited internal mobility and that the hydroxymethyl groups are more mobile. Our combined carbon and
proton data do not give evidence for flexibility of the glycosidic linkage in sucrose. Copyright 2000 John Wiley &
Sons, Ltd.
1
KEYWORDS: NMR; 13C NMR; H NMR; relaxation; cross-relaxation; carbohydrates; internal motion
small sugars.20–23 The issue of the rigidity of its glycosidic
linkage has been controversial. The early carbon-13 relax-
ation work2,12,17 was in agreement with the concept of
limited mobility around the linkage, while the proton
cross-relaxation data of Poppe and Van Halbeek15 indi-
cated that the linkage was fairly flexible; their conclusions
were at least partly confirmed by molecular mechanics
studies.24 In this paper, we wish to contribute to this
debate. Our approach is characterized by two features:
we work with a dilute sucrose solution in a mixed solvent
(7 : 3 D2O–DMSO-d6), characterized by a higher viscos-
ity than water and a strongly reduced freezing point. In
this solution, it is easy to investigate sucrose outside the
extreme narrowing conditions, which allows a more accu-
rate determination of the dynamic properties.2 Moreover,
in analogy with the earlier study of another disaccharide,10
we combine the carbon and proton relaxation work in
order to elucidate the question of the internal mobility of
the molecule.
INTRODUCTION
Carbon-13 relaxation measurements are a widely used tool
for studies of reorientational dynamics in solution.1 In a
series of papers from our laboratory, we reported the use
of multiple-field carbon-13 relaxation experiments to eval-
uate the overall and local reorientational motion of CH
vectors in oligosaccharides.2–8 We have shown that, if the
experiments are carried out outside the extreme narrow-
ing conditions, it is possible to obtain a quantitative fit
of the data using the simple Lipari–Szabo model9 and
that parameters of the model allow at least a semiquanti-
tative evaluation of the extent of the internal mobility. In
a study of a disaccharide, ˛-D-Manp-(1 ! 3)-ˇ-D-Glcp-
OMe, we combined carbon-13 relaxation measurements
with studies of the field and temperature dependence of
proton cross-relaxation for intra- and inter-residue pro-
ton pairs.10 We found that the Lipari–Szabo parameters
obtained from the analysis of the carbon data could also
quantitatively explain the proton cross-relaxation rates,
with very reasonable proton–proton distances within a
single sugar ring and over the glycosidic linkage. Thus,
the combined carbon and proton relaxation data gave no
evidence of any significant flexibility of the glycosidic
linkage.
EXPERIMENTAL
A 14 mg amount of sucrose (Schuchardt) was dissolved
in D2O and treated with Chelex-100 in order to remove
paramagnetic impurities. It was then transferred into a
5 mm NMR tube and freeze-dried three times. Finally,
the sucrose sample was dissolved in a 7 : 3 molar ratio
mixture of D2O and DMSO-d6 to yield a 65 mM solution.
The sample was degassed by several freeze–pump–thaw
cycles before being sealed under vacuum.
The carbon-13 NMR and proton NMR experiments
were performed at 9.4 and 14.1 T using Varian Inova
spectrometers (for protons also at 11.75 and 18.8 T). All
the experiments were performed at 273 and 283 K, using
the Varian variable-temperature controllers. Before every
Sucrose is one of the most common disaccharides and
its reorientational dynamics in solution have been subject
to many NMR investigations,11–19 using both carbon-13
and proton relaxation measurements in aqueous solution.
The Lipari–Szabo (or similar) model has been used in
some of these papers12,13,15,17–19 and also in other work on
* Correspondence to: J. Kowalewski, Division of Physical Chemistry,
Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm,
Sweden.
Contract/grant sponsor: Swedish Natural Science Research Council.
Copyright 2000 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2000; 38: 1012–1018

1
MULTIPLE-FIELD 13C AND H RELAXATION IN VISCOUS SUCROSE SOLUTION
1013
we followed the recommendations of Stott et al.30 The
strengths and durations of the pulsed field gradients also
followed the recommendations of Stott et al.30 They rec-
ommend also the use of additional selective pulses at
the end of the mixing period, which we, however, did
not implement. The spectral width was typically around
5 ppm, the number of data points was 5–12K and the
number of transients was 32 or 64. The recycle delay of
about 20 s (eight times the longest proton T1) was used.
Twelve different mixing periods were used, ranging from
20 ms (shorter mixing periods are difficult to implement,
because of time required for gradient pulses) to 1 s. The
resulting spectra were phased, using the phase correction
for the longest mixing period. The intensities of the G2
and F1 signals were obtained after baseline correction
and integration. The cross-relaxation rates were derived
from the initial build-up of the intensities of the G2 and
F1 signals in the following way. The zero-mixing time
intensity of the inverted G1 signal, M1z.0/, was estimated
by fitting the G1 intensities to a single exponential. The
G2 and F1 intensities were normalized by division with
M1z.0/. Thus normalized intensities for the mixing times
up to 0.5 s (which is usually close to the maximum of
the build-up curve) were fitted to a second-degree poly-
nomial in the mixing time. The cross-relaxation rates were
identified with the coefficient of the linear term, i.e. were
obtained by taking the time derivative of the polynomial
at the zero mixing time.
All the experiments were repeated at least twice (but
usually many more times) and average values are reported.
The uncertainties of the cross-relaxation rates are esti-
mated to be better than 10% (this rather conservative error
estimate is much larger than the standard deviations of fits;
the error estimates are based on the sensitivity of the cross-
relaxation rate to the variation of the number of points in
the build-up data sets). The homonuclear NOEs from G1
to the other protons were much smaller. In some cases,
we estimated the NOE build-up from G1 to F4 using the
same procedure and were able to obtain semi-quantitative
results.
measurement, the temperature was carefully checked
using a methanol chemical shift thermometer.25 Deuterium
lock for field/frequency stabilization was used in all exper-
iments.
For carbon measurements, a modified 5 mm carbon-
13 probe head from Jeol was used on the 9.4 T instru-
ment, while a standard Varian 5 mm broadband probe-
head was used on the 14.1 T spectrometer. The carbon-
13 spin–lattice relaxation times .T1/ were measured
using the fast inversion–recovery (FIR) method26 with
10–12 different delays. The nuclear Overhauser enhance-
ments (NOE) were determined using the dynamic NOE
(DNOE) technique27 with one long (about 5 T1) and
one short (about 1 ms) delay. The NOE factor, 1 C Á,
is expressed as the intensity ratio of the enhanced sig-
nal (long delay in the DNOE experiment) to the unen-
hanced signal (short delay). Spin–spin relaxation times
.T2/ were measured at 9.4 T only, using a modification of
the Carr–Purcell–Meiboom–Gill experiments, designed
to suppress the cross-correlation effects.28,29 The carbon-
°
13 90 pulse duration was about 5–7 µs. The spectral
width was typically around 90 ppm, the number of data
points was 16–18K and the number of transients was
10 000–20 000. The recycle delay of about twice the
longest T1 was used in the FIR experiments, whereas it
was about 10T1 in the NOE experiments. The broadband
proton decoupling was carried out using the Waltz-16
scheme. The decoupler offset, power and modulation fre-
°
quency were carefully adjusted; the typical decoupler 90
pulse duration was about 100–150 µs. The line broadening
of 2–4 Hz was applied before evaluating line intensities.
The three-parameter exponential fitting routine provided
by the instrument manufacturer was used to evaluate the
spin–lattice and spin–spin relaxation times. The accu-
racy of the T1 data is estimated to be better than 5%,
the accuracy of the NOE factor is estimated to be better
than 0.1 units and the accuracy of the T2 measurements
is better than 10%. All the experiments were repeated at
least twice and average values are reported.
Measurements of proton cross-relaxation rates were car-
ried out using the DPFGSE method proposed by Stott
et al.30 Varian 5 mm double or triple resonance probes,
optimized for proton detection and equipped for pulsed
The analysis of the variable-field relaxation data was
carried out using program GENLSS33 running on an IBM
RISC 6000 workstation.
°
field gradient experiments, were used. The 90 hard
pulse duration was about 7 µs. The ISNOB selective
31
°
180 pulses during the excitation period were employed,
RESULTS AND DISCUSSION
with a duration of about 42 ms. The excitation sequence
results in one of the signals, in our case the G1 pro-
ton doublet (we adopt in this study the convention of
denoting protons with upper-case G (glucose) or F (fruc-
tose) with the IUPAC number of the carbon to which
the proton is bonded; the carbon atoms are denoted
with lower-case g or f), being inverted and all oth-
ers being saturated. The build-up of the signal inten-
sity for other protons during the mixing period is sup-
posed to occur through cross-relaxation, which requires
the self-relaxation of the saturated signals to be sup-
Assignments of the carbon and proton spectra are based
on the work of Bock and Lemieux.34 The relaxation rates
and the NOE factors for the methine carbons in sucrose
are collected in Table 1 (carbons 3g and 5g are excluded,
because the signals overlap). We can see that, at each tem-
perature and field, the relaxation data for all the methine
carbons are fairly uniform, in agreement with our earlier
study of sucrose. In most of our work on oligosaccha-
rides, we have used the concept of dynamic equivalence
of all CH carbons in a carbohydrate residue. The average
values for the glucose and fructose rings are also listed in
Table 1. Clearly, the two rings behave in a similar way.
In the following, we treat the two rings as dynamically
pressed. For this purpose, we inserted two composite
32
°
°
°
°
180 pulses [90 .X/240 .Y/90 .X/] during the mixing
period. In locating these pulses within the mixing period,
Copyright 2000 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2000; 38: 1012–1018

1014
M. EFFEMEY, J. LANG AND J. KOWALEWSKI
Table 1. Relaxation data for methine carbon-13 nuclei in sucrose
9.4 T
14.1 T
Carbon
Temperature (K)
Tꢀ1 1 .sꢀ1
/
Tꢀ2 1 .sꢀ1
/
1 C Á
Tꢀ1 1 .sꢀ1
/
1 C Á
g1
g2
g4
273
273
273
273
273
273
273
273
273
283
283
283
283
283
283
283
283
283
5.48
5.32
5.32
5.37
5.17
5.39
5.18
5.25
5.31
5.23
4.91
4.82
4.99
4.99
4.99
5.22
5.07
5.03
9.5
8.5
8.4
8.8
8.6
8.9
9.6
9.0
8.9
7.2
6.9
6.9
7.0
7.2
7.0
7.4
7.2
7.1
1.27
1.27
1.30
1.28
1.32
1.30
1.30
1.31
1.30
1.54
1.53
1.58
1.55
1.41
1.56
1.44
1.47
1.51
3.67
3.46
3.40
3.51
3.37
3.47
3.51
3.45
3.48
3.56
3.42
3.39
3.46
3.46
3.37
3.49
3.44
3.45
1.20
1.18
1.16
1.18
1.05
1.13
1.20
1.13
1.16
1.30
1.27
1.25
1.27
1.10
1.20
1.28
1.19
1.23
Average g
f3
f4
f5
Average f
Global average
g1
g2
g4
Average g
f3
f4
f5
Average f
Global average
Table 2. Relaxation data for hydroxymethyl carbon-13 nuclei in sucrose
9.4 T
14.1 T
Carbon
Temperature (K)
.nHT1/ꢀ1 (sꢀ1
/
.nHT2/ꢀ1 (sꢀ1
)
1 C Á
.nHT1/ꢀ1 (sꢀ1
)
1 C Á
g6
f1
f6
g6
f1
f6
273
273
273
283
283
283
4.63
4.56
4.37
4.23
4.41
3.95
6.9
7.7
6.8
5.6
5.3
4.81
1.35
1.34
1.45
1.62
1.63
1.77
3.09
3.14
2.93
3.01
3.05
2.65
1.32
1.23
1.39
1.36
1.32
1.52
equivalent and use the methine carbon relaxation data
averaged over the six carbons. The relaxation parameters
for the hydroxymethyl carbons are shown in Table 2. In
qualitative terms, we can note that the relaxation data in
both tables and at both temperatures are field dependent
and that the NOE factor 1 C Á is far below the maximum
possible value (2.99). These observations are consistent
with relatively slow reorientational dynamics, bringing
the relaxation out of the extreme narrowing regime.1–8
In addition, we can see that the relaxation rates for the
three hydroxymethyl carbons display significant differ-
ences among themselves and, corrected for the number
of directly bonded proton nH, with respect to the methine
carbons. This is indicative of the hydroxymethyl groups
undergoing additional internal motions.
The cross-relaxation rates between the proton G1, on
the one hand, and G2 and F1 (symbol F1 denotes the
two protons bound to the f1 carbon. The two protons
were found to have accidentally degenerate shifts by Bock
and Lemieux;34 our data at up to 800 MHz indicate an
almost degenerate AB pattern) on the other are shown in
Table 3. Also the proton cross-relaxation data are field
and temperature dependent. In order to interpret the data
set consisting of the relaxation data in Tables 1, 2 and
3, we adopt a procedure very similar to that used ear-
lier for ˛-D-Manp-(1 ! 3)-ˇ-D-Glcp-OMe.10 Briefly, we
assume that the carbon-13 relaxation is dominated by the
dipole–dipole interaction with the directly bonded protons
and that all other relaxation processes (including interfer-
ence between dipolar interactions) can be neglected. The
carbon-13 relaxation rates and the heteronuclear NOEs
can then be expressed in terms of the dipolar spectral
densities J(ω), taken at various combinations of carbon
and proton Larmor frequencies:
Table 3. Intra- and inter-residue proton cross-relaxation
data in sucrose
Cross-relaxation rate,
temperature
9.4 T
11.7 T
14.1 T
18.8 T
nH
Tꢀ1 1
Tꢀ2 1
D
D
D2[J.ωH ꢀ ωC/ C 3J.ωC/ C 6J.ωH C ωC/] .1/
D2[4J.0/ C J.ωH ꢀ ωC/ C 3J.ωC/ C 6J.ωH/
4
nH
ꢀG1G2 , 273 K
ꢀ0.318 ꢀ0.327 ꢀ0.366 ꢀ0.354
ꢀ0.338 ꢀ0.346 ꢀ0.407 ꢀ0.407
ꢀ0.173 ꢀ0.188 ꢀ0.214 ꢀ0.231
ꢀ0.142 ꢀ0.170 ꢀ0.209 ꢀ0.249
ꢀG1F1 , 273 K
ꢀG1G2 , 283 K
ꢀG1F1 , 283 K
8
C 6J.ωH C ωC/]
.2/
Copyright 2000 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2000; 38: 1012–1018

1
MULTIPLE-FIELD 13C AND H RELAXATION IN VISCOUS SUCROSE SOLUTION
1015
ꢀ
ꢁ
Equation (6) is identical with the formulation used in
the early work of McCain and Markley12 and from our
laboratory,2 with the order parameter having the same
meaning as the amplitude factor for the dipolar coupling
constant. The Lipari–Szabo analysis can be performed
in different ways. In the most common approach, one
assumes that there exists a single overall correlation time
and that every CH-bond axis is characterized by its own
order parameter and, possibly, a local correlation time
(the local correlation time cannot be determined if S2 is
about 0.8 or higher). We performed this type of global fit
for both temperatures for the full data set of Tables 1
and 2. For the methine carbons, the fitted S2 values
display very little variability (between 0.89 and 0.96 at
273 K and between 0.84 and 0.89 at 283 K). For these
carbons we therefore choose to report the averaged results,
making use of the assumption of dynamic equivalence
of different CH axes. The results of this analysis are
presented under entries a in Table 4. The fit is performed
using Eqns (1)–(3) combined with the truncated form of
the Lipari–Szabo spectral densities: the order parameter
at both temperatures is so high that it is not possible to
estimate ꢄe.
Entries b in Table 4 refer to the simultaneous fit of the
averaged ring carbon-13 relaxation data at two fields and
the intra-residue cross-relaxation rate ꢀG1G2 at four mag-
netic fields. The idea behind combining the two types of
data is that, under the assumptions of the Lipari–Szabo
model and of the dynamic equivalence of various intra-
residue axes, both types of data measure the same type of
dynamics. We can see in the table that including the pro-
ton data in the fit does not change the dynamic parameters
substantially and allows a reasonably accurate determina-
tion of the intra-residue proton–proton distance. The value
of rG1G2 thus obtained is indeed in excellent agreement
with the results of molecular modelling, 241 pm.36 The
value of the proton–proton distance estimated by this pro-
cedure is dependent on the assumed carbon–proton dis-
tance. If a slightly longer CH distance were assumed,37,38
the resulting order parameter and the proton–proton dis-
tance would have attained larger values. Another com-
ment that should be made in this context is that includ-
ing the proton–proton cross-relaxation rates in the global
Lipari–Szabo fit without assuming dynamic equivalence
would only allow an estimation of the order parameter
for the G1G2 axis if the G1G2 distance is assumed to be
ꢁH
6J.ωH C ωC/ ꢀ J.ωH ꢀ ωC/
Á D
.3/
ꢁC J.ωH ꢀ ωC/ C 3J.ωC/ C 6J.ωH C ωC/
The dipolar coupling constant, D D .ꢂ0/4ꢃ/ꢁCꢁHh¯rCꢀH3, is
related to the strength of the dipolar interaction between
the two spins and, consequently, is dependent on the
distance .rCH/ between these spins. A value of 109.8 pm
is used for rCH, corresponding to the dipolar coupling
constant of 22.82 kHz or 143.4 ð 103 rad sꢀ1, in analogy
with earlier work from this laboratory.3–8,10
The proton cross-relaxation rate can be expressed in a
similar way.10
ꢂ
ꢃ
2
1
4
ꢂ0
ꢀij D
h¯2ꢁH4 hriꢀj6i[6JŁ.2ωH/ ꢀ JŁ.0/]
.4/
4ꢃ
where the indices i and j denote protons, interacting
through dipolar interaction. The factor in front of the
square brackets is proportional to the square of the pro-
ton–proton dipole coupling constant and JŁ.ω/ is the
spectral density for the proton–proton dipolar interaction.
The frequency dependence of the spectral densities
in Eqns (1)–(3) is assumed to follow the ‘model-free’
description proposed by Lipari and Szabo.9 In this model,
two kinds of motions are assumed to modulate the interac-
tion causing relaxation: a rapid, local motion and a slower,
global motion. If the two motions are statistically indepen-
dent and if the global molecular reorientation is isotropic,
the reduced spectral density function can be written as
ꢄ
ꢅ
2
5
S2ꢄM
1 C ω2ꢄM2
.1 ꢀ S2/ꢄ
J.ω/ D
C
.5/
1 C ω2ꢄ2
where ꢄꢀ1 D ꢄM C ꢄeꢀ1, ꢄM is a correlation time for the
global motion, common to the whole molecule, ꢄe is the
correlation time for the fast local motion, and specific
for every individual axis in the molecule, and S is a
generalized order parameter for an axis in the molecule.
S reflects the spatial restriction of the local motion. The
spectral density JŁ.ω/ in Eqn (4) can be expressed in a
way analogous to Eqn (5), after replacing S by SŁ. SŁ
differs from S in that it includes also the averaging of
the radial part of the dipole–dipole interaction through
internal motions.35 If the order parameter is high and ꢄe
is short, then the second term in Eqn (5) contributes very
little and it may be useful to express the Lipari–Szabo
spectral densities in a truncated form:
ꢀ1
ꢀ
ꢁ
2
5
S2ꢄM
1 C ω2ꢄM2
J.ω/ D
.6/
Table 4. Results of the Lipari–Szabo analysis of the data for the ring carbons
and the intra-residue proton–proton cross-relaxation rates
Temperature
(K)
Type of
fita
rG1G2
(pm)
y
ꢄM (ns)
S2
(%)b
273
283
a
b
a
b
1.45 š 0.10
1.44 š 0.09
1.04 š 0.08
0.97 š 0.07
0.92 š 0.03
0.92 š 0.02
0.86 š 0.02
0.87 š 0.03
—
4.8
4.3
4.5
4.8
243 š 3
—
243 š 4
a a: Two-parameter fit of Eqns (1)–(3) and (6) to the averaged ring carbon-13 data at two fields.
b: Three-parameter simultaneous fit of Eqns (1)–(4) and (6) to the averaged ring carbon-13 data
at two fields and ꢀG1G2 at four fields.
b Standard deviation of the dependent variable.
Copyright 2000 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2000; 38: 1012–1018

1016
M. EFFEMEY, J. LANG AND J. KOWALEWSKI
known. We do not judge such a procedure to provide new
insights.
The proton cross-relaxation rates ꢀG1G2 , experimental
and calculated using the parameters in Table 4, entry b,
are displayed as functions of the magnetic field in Figs 1
(the 273 K data) and 2 (the 283 K data). The deviations
between calculations and experiments are sizable, but
never larger than the estimated 10% error bars.
The results of the Lipari–Szabo analysis of the carbon-
13 relaxation data for the hydroxymethyl groups are sum-
marized in Table 5. We used three types of fits. In the first
two types, we used the data for each hydromethyl carbon
Figure 2. Proton–proton cross-relaxation rates (in sꢀ1) for
sucrose at 283 K versus the magnetic field (in tesla). The
curves are calculated using the truncated Lipari–Szabo
model with the parameter sets b in Table 4 (ꢀG1G2, solid
line) and in Table 6 (ꢀG1F1, dashed line). The experimental
points are indicated by squares .ꢀG1G2/ and crosses .ꢀG1F1/.
individually, using the truncated form of the spectral den-
sity, Eqn (6), and the full form, Eqn (5). The calculations
based on the truncated spectral densities (entries a in
Table 5) yield the order parameters squared slightly below
0.8, i.e. indicate that the motion of the hydroxymethyl CH
vectors is less restricted than for the CH vectors in the
tertiary ring CH groups. The lower values of the order
parameter also mean that it can be meaningful to attempt
three-parameter fits (entries b in Table 5). In five (out
of six) cases, the three-parameter fit providing estimates
of ꢄM, S2 and ꢄe turned out to be possible. In addition,
we report the order parameters and the correlation times
Figure 1. Proton–proton cross-relaxation rates (in sꢀ1) for
sucrose at 273 K versus the magnetic field (in tesla). The
curves were calculated using the truncated Lipari–Szabo
model with the parameter sets b in Table 4 (ꢀG1G2, solid
line) and in Table 6 (ꢀG1F1, dashed line). The experimental
points are indicated by squares (ꢀG1G2) and crosses .ꢀG1F1/.
Table 5. Results of the Lipari–Szabo analysis of the data for hydroxymethyl carbons
Temperature
(K)
Type of
fita
y
Carbon
ꢄM (ns)
S2
ꢄe (ns)
(%)b
273
g6
g6
g6
f1
f1
f1
f6
f6
f6
g6
g6
g6
f1
f1
f1
f6
f6
f6
a
b
c
a
b
c
a
b
c
a
b
c
a
b
c
a
b
c
1.19 š 0.07
1.26 š 0.08
1.43 š 0.04
1.37 š 0.11
1.38 š 0.15
1.43 š 0.04
1.15 š 0.14
1.35 š 0.07
1.43 š 0.04
0.81 š 0.05
0.83 š 0.10
0.98 š 0.04
0.79 š 0.04
—
0.78 š 0.02
0.76 š 0.02
0.74 š 0.03
0.80 š 0.02
0.80 š 0.04
0.79 š 0.03
0.75 š 0.03
0.69 š 0.02
0.69 š 0.03
0.75 š 0.02
0.74 š 0.05
0.69 š 0.04
0.75 š 0.02
—
—
3.6
3.2
5.4c
5.2
6.3
5.4c
7.1
2.8
5.4c
3.2
3.8
6.5c
3.0
0.021 š 0.015
0.036 š 0.019
—
0.006 š 0.031
0.010 š 0.023
—
0.048 š 0.011
0.053 š 0.018
—
0.007 š 0.027
0.031 š 0.022
—
283
d
—
—
0.98 š 0.04
0.64 š 0.05
0.79 š 0.16
—
0.69 š 0.04
0.71 š 0.03
0.62 š 0.07
—
0.025 š 0.021
6.5c
5.0
5.5
—
0.038 š 0.027
—
d
—
a a: Two-parameter fit of Eqns (1)–(3) and (6) to the hydroxymethyl carbon-13 data at two fields. b: Three-parameter fit
of Eqns (1)–(3) and (5) to the hydroxymethyl carbon-13 data at two fields. c: Global fit of all the data in Tables 1 and
2 at a single temperature.
b Standard deviation of the dependent variable.
c Refers to a simultaneous fit of 13 parameters to 45 data points.
d Unphysical results, ꢄe < 0.
Copyright 2000 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2000; 38: 1012–1018

1
MULTIPLE-FIELD 13C AND H RELAXATION IN VISCOUS SUCROSE SOLUTION
1017
resulting from the global Lipari–Szabo fit of all the data
in Tables 1 and 2. The data at each temperature were
analysed independently, assuming a single overall rotation
correlation time, and the results are presented in Table 5
as entries c. For five of the six cases, it was also possible
to estimate ꢄe in this way, while the fit for f6 at 283 K
resulted in an unphysical, negative value for this parame-
ter. The fits of type b and c are in reasonable agreement
with each other, in terms of both the resulting ꢄM values
and the order parameters, which is gratifying. The local
correlation times range between 6 and about 50 ps, with
very large uncertainties, but including them improves the
determination of the overall correlation time. This is in
agreement with our earlier experience.3–8 The differences
between the three hydroxymethyl groups are fairly small;
in agreement with the findings of McCain and Markley13
and of Girlich and Lu¨demann,17 the f6 group seems to
have the highest mobility and the least restricted motion
(the lowest S2). A definite conclusion from Tables 4 and 5
is that the hydroxymethyl groups in sucrose display addi-
tional mobility, compared with the sugar rings. This is
also in agreement with our earlier experience.3–8
The inter-residue cross-relaxation rate, ꢀG1F1 , measures
the interaction between the proton G1, bonded to a ring
carbon, and the protons F1 in a hydroxymethyl group.
From the carbon data, we can see that the CH vectors
of the hydroxymethyl group f1 have a certain degree
of additional internal mobility, which can presumably
be associated with the rotation around the f1 –f2 bond.
There is no a priori reason to assume that this rotational
motion has the same effect on the order parameter of
the CH axis as on the order parameter of the G1F1
proton–proton axis. On the other hand, we wish to treat
the inter-residue cross-relaxation rate in a similar fashion
as the intra-residue rate and without introducing additional
parameters. Thus, we choose to report a simultaneous fit of
the carbon data for the f1 carbon and the cross-relaxation
rate ꢀG1F1 , neglecting the local correlation time, using the
fixed CH bond length (109.8 pm), and optimizing three
variable parameters: ꢄM and S2, common for both vectors,
and the G1F1 proton–proton distance. The results of the
fits are collected in Table 6. Under entry a, we repeat the
values from Table 5 (entry a there also). Under entry b,
we report the results based on the carbon-13 relaxation
parameters and the proton cross-relaxation rates at four
fields. We can see that the introduction of the proton
cross-relaxation rates ꢀG1F1 has a very small effect on
the global correlation time and the order parameter, in
analogy with the entries b in Table 4. Moreover, the three-
parameter fits under b in Table 6 are of similar quality to
the analogous fits in Table 4, in spite of the fact that the
assumption of a single common order parameter is less
well grounded in the case involving the hydroxymethyl
group. The values of the proton–proton distance obtained
at the two temperatures are in reasonable agreement with
each other and are shorter than the intra-ring G1G2
distance. The distance is in reasonable agreement with
molecular modelling36 (in the MD simulation, two G1F1
distances are reported, corresponding to the two protons,
pro-R and pro-S, in the CH2 group;36 averaging the hrꢀ6i
values for the two protons and taking the result to the
power of ꢀ1/6 yields an effective distance of 243 pm).
The experimental and calculated (dashed lines, obtained
using the parameters of Table 6, entries b) cross-relaxation
rates ꢀG1F1 are plotted against the magnetic field in Figs 1
and 2. The calculated inter-residue cross-relaxation rates
are also within the error bars of the experiments. There is
one comment to be made concerning Figs 1 and 2. We can
see that the field dependences of the two rates are similar
at 273 K, whereas the differences are larger at 283 K. The
important point is, however, that the differences between
the two rates at the two temperatures can be accounted for
using a model which takes into consideration the internal
motion of the hydroxymethyl group but does not require
including any additional mobility around the glycosidic
linkage.
The conclusion we reach concerning the internal mobil-
ity around the glycosidic linkage in sucrose is in con-
flict with other work on the same compound in aqueous
solution.15,24 In order to validate our conclusion, we also
used the DPFGSE data at 273 K to estimate another inter-
glycosidic cross-relaxation rate, ꢀG1F4 . The rate is only
about one tenth of ꢀG1G2 , so the estimation can be at
best semiquantitative. The ꢀG1F4 value increases slightly
in absolute value (not shown) between 9.4 and 18.8 T, in
analogy with ꢀG1G2 . Its magnitude and the field depen-
dence can be reproduced using the parameters ꢄM and S2
in Table 4 and the distance rG1F4 of about 360 pm, to be
compared with about 400 pm from simulations.36 Hence,
this semiquantitive result does not indicate any motion
over the glycosidic linkage and confirms the principal con-
clusion. A possible explanation of the disagreement with
Table 6. Results of the Lipari–Szabo analysis of the data for the hydroxymethyl
carbon f1 and the inter-residue proton–proton cross-relaxation rates
Temperature
(K)
Type of
fita
rG1F1
(pm)
y
ꢄM (ns)
S2
(%)b
273
283
a
b
a
b
1.37 š 0.11
1.33 š 0.11
0.79 š 0.04
0.70 š 0.04
0.80 š 0.02
0.80 š 0.03
0.75 š 0.02
0.78 š 0.03
—
5.2
5.8
3.0
5.9
231 š 4
—
222 š 3
a a: Two-parameter fit of Eqns (1)–(3) and (6) to the hydroxymethyl carbon-13 data at two fields
(the same as in Table 5). b: Three-parameter simultaneous fit of Eqns (1)–(4) and (6) to the carbon-
13 data for hydroxymethyl f1 at two fields and ꢀG1F1 at four fields.
b Standard deviation of the dependent variable.
Copyright 2000 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2000; 38: 1012–1018

1018
M. EFFEMEY, J. LANG AND J. KOWALEWSKI
4. Kowalewski J, Widmalm G. J. Phys. Chem. 1994; 98: 28.
5. Ma¨ler L, Lang J, Widmalm G, Kowalewski J. Magn. Reson. Chem.
1995; 33: 541.
some of the earlier work may perhaps be related to our
use of a mixed solvent.
6. Ma¨ler L, Widmalm G, Kowalewski J. J. Biomol. NMR 1996; 7: 1.
7. Kjellberg A, Rundlo¨f T, Kowalewski J, Widmalm G. J. Phys. Chem.
B 1998; 102: 1013.
8. Kowalewski J, Ma¨ler L, Widmalm G. J. Mol. Liq. 1998; 78: 255.
9. Lipari G, Szabo A. J. Am. Chem. Soc. 1982; 104: 4546.
10. Ma¨ler L, Widmalm G, Kowalewski J. J. Phys. Chem. 1996; 100:
17103.
11. McCain DC. Carbohydr. Res. 1986; 152: 73.
12. McCain DC, Markley JL. J. Am. Chem. Soc. 1986; 108: 4259.
13. McCain DC, Markley JL. J. Magn. Reson. 1987; 73: 244.
14. Herve´ Du Penhoat C, Imberty A, Roques N, Michon V, Mentech J,
Descotes G, Perez S. J. Am. Chem. Soc. 1991; 113: 3720.
15. Poppe L, Van Halbeek H. J. Am. Chem. Soc. 1992; 114: 1092.
16. Arulmozhi V, Rao AS. Phys. Chem. Liq. 1993; 26: 201.
17. Girlich D, Lu¨demann HD. Z. Naturforsch., Teil C 1993; 48: 407.
18. Engelsen B, Herve´ Du Penhoat C, Perez S. J. Phys. Chem. 1995;
99: 13334.
CONCLUSIONS
The combined carbon-13 and proton relaxation study for
sucrose in a viscous cryosolvent, D2O–DMSO, gives
a new example of the wealth of dynamic information
available from multiple-field relaxation measurements for
small molecules outside the extreme narrowing regime.
In particular, we have demonstrated that the two sugar
residues display a similar and highly limited internal
mobility and that the hydroxymethyl groups are more
mobile. In this sense, the sucrose molecule certainly does
not behave in solution as a rigid object. Most interesting is
our finding concerning the controversial issue of flexibility
of the glycosidic linkage in sucrose: our combined carbon
and proton data do not give evidence for such motions. In
fact, our combined data set can be accounted for using a
model which takes into consideration the internal motion
of the hydroxymethyl group but does not require the
inclusion of any additional mobility around the glycosidic
linkage.
19. Casset F, Imberty A, Herve´ Du Penhoat C, Koca J, Perez S. J. Mol.
Struct. (Theochem) 1997; 395: 211.
20. Van Halbeek H. In Encyclopedia of Nuclear Magnetic Reso-
nance, Grant DM, Harris RK (eds). Wiley: Chichester, 1996;
1107.
21. Hajduk PJ, Horita DA, Lerner LE. J. Am. Chem. Soc. 1993; 115:
9196.
22. Batta G, Ko¨ve´r KE, Gervay J, Hornya´k M, Roberts GM. J. Am.
Chem. Soc. 1997; 119: 1336.
23. So¨derman P, Widmalm G. Magn. Reson. Chem. 1999; 37: 586.
24. Engelsen SB, Pe´rez S. J. Mol. Graphics Model. 1997; 15: 122.
25. Ammann C, Meier P, Merbach AE. J. Magn. Reson. 1982; 46: 319.
26. Canet D, Levy GC, Peat IR. J. Magn. Reson. 1975; 18: 199.
27. Kowalewski J, Ericsson A, Vestin R. J. Magn. Reson. 1978; 31:
165.
Acknowledgements
28. Palmer AG, Skelton NJ, Chazin WJ, Wright PE, Rance M. Mol.
Phys. 1992; 75: 699.
This work was supported by the Swedish Natural Science Research
Council. We are indebted to the Swedish NMR Centre at Gothenburg
University for generous grants of spectrometer time and to Ms Charlotta
Damberg for skilful assistance with experiments. Valuable discussions
with Dr Lena Ma¨ler, Dr Alexandra Kjellberg, Dr Gyula Batta and
Professor Go¨ran Widmalm are gratefully acknowledged.
29. Kay LE, Nicholson LK, Delaglio F, Bax A, Torchia DA. J. Magn.
Reson. 1992; 97: 359.
30. Stott K, Keeler J, Van QN, Shaka AJ. J. Magn. Reson. 1997; 125:
302.
31. Kupce E, Boyd J, Campbell ID. J. Magn. Reson. B 1995; 106:
300.
32. Levitt MH, Freeman R. J. Magn. Reson. 1979; 33: 473.
33. DeTar DF. Computer Programs for Chemistry, vol. IV. Academic
Press: New York, 1972.
34. Bock K, Lemieux R. Carbohydr. Res. 1982; 100: 63.
35. Bru¨schweiler R, Roux B, Blackledge M, Griesinger C, Karplus M,
Ernst RR. J. Am. Chem. Soc. 1992; 114: 2289.
36. Bagley S, Odelius M, Laaksonen A, Widmalm G. Acta Chem.
Scand. 1994; 48: 792.
37. Nakai T, Ashida J, Terao T. Mol. Phys. 1989; 67: 839.
38. Ottiger M, Bax A. J. Am. Chem. Soc. 1998; 120: 12334.
REFERENCES
1. Canet D. Nuclear Magnetic Resonance: Concepts and Methods.
Wiley: Chichester, 1996.
2. Kovacs H, Bagley S, Kowalewski J. J. Magn. Reson. 1989; 85: 530.
3. Bagley S, Kovacs H, Kowalewski J, Widmalm G. Magn. Reson.
Chem. 1992; 30: 733.
Copyright 2000 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2000; 38: 1012–1018