Internal motion in carbohydrates as probed by n.m.r. spectroscopy

Internal motion in carbohydrates as probed by n.m.r, spectroscopy I. Braccini, V. Michon and C. Herv6 dn Penhoat* Laboratoire de Chimie de l'Ecole Normale Supbrieure, 24 rue Lhomond, 75230 Paris, France

A. Imberty LSO-CNRS, Facultk des Sciences et Techniques, 2 rue de la Houssinibre, 44072 Nantes cedex 03, France

and S. P6rez Ingbnierie Molkculaire, INRA, BP527, 44026 Nantes, France

(Received 7 August 1992; revised 23 Septembfr 1992) In the present study a combination o f proton and carbon relaxation rates have been measured for several oligosaccharides at different temperatures. Correlation times, which have been calculated from both sets o f data, have been compared in an attempt to establish the relative rate o f internal motion. All the data suggest that these motions are not slow with respect to the overall tumbling. Keywords: Oligosaccharides;relaxation rates; internal motion; conformation

Introduction

Experimental

In recent years, conformational analysis by n.m.r. spectroscopy and molecular modelling has become the method of choice for studying the solution behaviour of oligosaccharides. Work in this field has been summarized recently by Carver 1. The conformational flexibility of carbohydrates has been amply demonstrated by molecular modelling. Although pyranose rings are rigid to a first approximation, evidence for considerable flexibility about both glycosidic linkages and bonds to exocyclic groups has been given. In the case of internal motion slower than molecular tumbling, this flexibility is accounted for by averaging the inverse sixth power of the internuclear distances over all microstates of conformational mapping according to a Boltzmann distribution. However, if the internal motions are fast with respect to overall rotation, interproton distances obtained from the dynamics trajectory are averaged according to the inverse third power. This averaging assumes that the overall and internal motions are not correlated which is reasonable when the rates are separated by several orders of magnitude. The intermediate case in which internal motions occur on a timescale comparable to that of the overall tumbling requires that the full dipolar interaction (both angular and distance) be evaluated from the dynamics trajectory. Both the technique used to average the internuclear distances obtained with molecular mechanics and the spectral density functions appropriate for calculation of cross-relaxation rates from internuclear distances require knowledge of these rates of motion. Only a few estimations of these rates based on experimental data have reported z-4. This paper presents an experimental probe of rates of motion for various oligosaccharides at different temperatures.

The formulae for the oligosaccharides used in this study are given in Figure 1. The ~H and 13C chemical shifts of sucrose 5 (1), methyl-d 3 ~-galactopyranuronosyl-~galactopyranuronoside dimethyl-d 6 diester 6 (2), sucralose 7 (3), 1-kestose 8 (4), 1-nystose 9 (5) and ethyl ]~-galactopyranosyl-j%glucopyranoside1° (6) or closely related compounds have been reported. The assignments for the pentasaccharide, 7, were obtained by comparison with those of 4 and 5. All the samples were prepared in D 2 0 (99.96%) as previously described 5. The non-selective T~ measurements were made with the inversion-recovery sequence (180°-z-90°-FID). In the case of the selective T~ experiments the 180 ° pulse which was obtained with the Dante sequence 11 was 20 ms. In order to evaluate the accuracy of the selective Ta measurements spectra were also recorded for the galacturonic acid dimer 2 at 296 K. The corresponding rates are analogous to the ones obtained at this temperature from a phase-sensitive NOESY experiment 6 (diagonal elements of the corresponding relaxation matrix), + 5% (five data points). Although variations in temperature were expected to be a major source of error, the mean deviation between two measurements was less than 8% (12 data points). It should be noted that the ~H chemical shifts of all of the compounds varied strongly with the temperature ( > 5 H z / K ) . Only measurements with chemical shift variations of less than 1 Hz were used for the correlation time calculations.

*To whom correspondenceshould be addressed. 0141-8130/93/010052-04 © 1993 Butterworth-HeinemannLimited 52

Int. J. Biol. Macromol., 1993, Vol. 15, February

Results and discussion Relative rates of overall and internal motions can be probed by n.m.r, spectroscopy. The longitudinal relaxation time of carbon, T1, can be expressed as a function of the spectral densities, J,,(o), as follows T1-1 =

K[Jo(cO ) + 3Jl(co) + 6Jz(co)]

Internal motion in carbohydrates: L Braccini et al. 277

K

CH20H 2.9X" I "o. 4.2 H O ~-~''~t'~ __~",l"r CH2OH

.o~.'

3?-° o-~ OH

283

K

4.3

HO

C!CHOH

l c°2C~o 3 . 2 ~

C~('~ °.

2.9~9

3

4.8

..r__.~3.0 CH.C' O"

.o--~ -o.~, ~

HO-'~.2 HO OCO~

o~

CH2OHoOH 0" 4 ~ 8

CHaOH H O H ~

I

4.4 k" j O

OH

I

2C H;eOH

CH2 0

5

•7 ~ O . ~ o

CH20H0

4

OH

O

~

I

OH

2°

H~OH C H2OH

. o - ~ - ~ "3~

4

°- ,,r~>" ~..o. OH

287

2.4

HtcH,~.O~ o

HO~

2.8

K 7CHzOH LJZ._~,.~o,,

C.H20~O

~

g

HO'\-HO

3.5

\ ----CHOH 2.U z 0

"OH3.1

6

296

1

K

CH~O.o

T--'~.3 CH,OH

OH

294

K

o~CHzOH l

OH

CHz 0

CHzOHo0

o ~ C H 7

I

5

CHI 0 0~ C H ~ O H

CH20H^ _V~'-'

I

"

I

o,

ell2 O

O ~ CHzOH ..- ~o

OH

•

o~CHa OH

zOH

o.

H~OH

I

OH

~ OH

OH

c HzOH N o

CHaOH

Figure 1 Formulae and correlation times (zH x 10- lo s) from 400 MHz 1H longitudinal relaxation rates for the oligosaccharides (1-7) under study and in the case of isotropic motion, the spectral density for a rigid molecule can be expressed as a function of a single correlation time

J(~o) = (A2(0))~R/(1 + ~o2rR2) where zR is the overall tumbling and (A2(0)) is the initial amplitude factor which by definition is set to 1. For carbohydrates, an approximate value of zR, is generally obtained from the average 13C T1 of the methine carbons 12: 1 lhZTc27H 2 T1

{

Tc

10 r c 6 _ H

3Zc

1 + (o n -- 0)c)2'17c 2 + 1 + (Dc2Zc 2

t-

-6~c-

;

1 -~- (O) H Jr- (DC)2%'C2~

where Yc and yn are the carbon and proton magnetogyric ratios respectively, h is Planck's constant divided by 21-1, and zc denotes the rotational correlation time from carbon relaxation data. The value of the carbon-proton internuclear distance, rc_n, used in this work is 1.11/~13. Correlation times vary strongly with this distance but the relative error associated with this parameter is undoubtedly minor for a given family of oligosaccharides (i.e. 1, 4, 5 and 7). The values of the carbon rotational correlation times, Zc, are collected in the Table 1. As expected, the correlation times increase regularly with decreasing temperature and with increasing molecular weight. Various spectral density functions which take into account fast internal motion have been proposed 14-16.

Int. J. Biol. Macromol., 1993, Vol. 15, February

53

Internal motion in carbohydrates: L Braccini et al. Table 1 Rotational correlation times a, Zc, calculated from the average 100 MHz 13C T1 values (mean deviation of the T1 values, %) measured at various temperatures for oligosaccharides 1-7 Temperature (K) Compound

277

1 6 2 3 4 5 7

2.8 (4)

283

2.4 2.2 3.0 4.5

(3) (8) (4) (6)

287

294

1.7 (5) 1.5 (5)

1.2 (3)

296

1.2 (3) 0.88 (5) 2.3 (7) 2.7 (8)

1.9 (11)

alO- a0 s

In the model-free approach of Lipari and Szabo 14 the spectral density is considered to be a sum of two terms. J(co ) = S2zR/( I "k- coZrR2) q- (l -- S2)re where S is a 'generalized order parameter' (its square represents the proportion of C - H vector rotational averaging that is accomplished by tumbling) and % is an effective correlation time for internal motion. It should be noted that the presence of infinitely fast internal motions (vibrations or torsional oscillations) can be approximated in the above expression of T~-~ as a reduction of the amplitude factor, ( A 2 ( 0 ) ) , in front of the term for the spectral densities 2. This treatment of internal fluctuations is equivalent to neglecting the second term in Lipari and Szabo's expression as has been previously shown to be appropriate for sucrose 3. Thus, the theoretical values, rc, are expected to be exact in the case of slow motion and too small in the case of very rapid internal motion 17. In the intermediate case, the equation which expresses T11 as a function of a single correlation time is not appropriate. In 1H n.m.r., correlation times for a specific dipolar interaction can be determined from the ratio of transverse to longitudinal cross-relaxation rates is. These rates are established from n.O.e, build-up curves using the initial-slope approximation. It is difficult to obtain accurate data as the method relies on difference spectra acquired with very short mixing times and therefore a low signal-to-noise ratio. Moreover, in the case of disaccharides, previous work 5'6 has shown that the fit between cross-relaxation rates obtained from N O E S Y experiments and those obtained from n.O.e, build-up curves is not satisfactory. Correlation times for individual spins can be obtained from the ratio of the selective to non-selective T1 values. Due to their different dependence on the spectral density terms, the ratio of these relaxation rates depends only on z n as followsl9: T1s Tins

24co2rn a + 15rH 10r n + 23co2rn 3 + 4co4zn 5

In the regime of 0.1 > c o r n > 10 the ratio of the non-selective to selective relaxation rates changes from 1.5 to 0.01. In the case of disaccharides it is necessary to, conduct these 7"1 experiments at low temperature (0 < 290 K ) in order to be in the dispersion range of field-dependent relaxation parameters.

54

Int. J. Biol. Macromol., 1993, Vol. 15, February

The correlation times for individual protons, zH, are indicated on the formulae in Figure 1. As with the Zc parameters, the zn times also decrease regularly with increasing temperature and increase with increasing molecular weight, at least until a degree of polymerization ( D P ) of 4. However, the zn values of the anomeric protons of the glucose residue ( H - l g ) of 5 and 7 at room temperature, 0.36 and 0.35 ns respectively, are very similar while the zc values differ, 0.23 and 0.27 ns respectively. It is known 2° that for the glucose oligomers of the Pullulan series 13C relaxation parameters approach a characteristic asymptotic limit at about D P = 12. At this point, it was suggested that control of dipolar relaxation shifts from overall motion, which depends on the molecular weight, to segmental motion, which does not. As the zn values are the result of a ratio of spectral densities the initial amplitude factor cancels out. Thus, in the presence of very fast internal motion the rn value should be greater than the Zc one at least in the simplest case of protons whose short internuclear distances (those efficient for relaxation) do not fluctuate with internal motions. It can be seen that the rn values are effectively larger than the corresponding rc ones suggesting that internal motions are not slow with respect to the overall tumbling. Generally speaking, the difference is greater for the protons of the flexible fructofuranose rings than for those of the more rigid pyranose residues. In a recent study2 i of an aromatic dipeptide, where internal rotation about the carbonyl carbon-Cot bond is known 22 to be slow compared with molecular tumbling, these rH and r c values are very similar (mean deviation of __+12%, seven data points). Kovacs et al. z have reported the temperature dependence of both the overall motion and the methyl group rotation of methyl 3-O-c~D-rhamnopyranosyl-~Dglucopyranoside in the dispersion range of fielddependent relaxation parameters. The correlation times in a mixture of water and D M S O are 0.49 and 0.06 ns at 303 K. At 273 K, these values diverge notably, 2.31 and 0.11 ns respectively, for the overall and methyl group rotation. It is likely that the temperature dependence of overall tumbling, torsional motion about the glycosidic linkage and hydroxymethyl group rotation are very different. Moreover, the fact that a similar r H value for H - l g of 1 at 277 K (0.37 ns), 4 at 283 K (0.37 ns), 5 at 294 K (0.35 ns), and 7 at 296 K (0.36 ns) for a limited range of Zc values, 0.19-0.30 ns, may indicate that the torsional motion about the glycosidic linkage is correlated with the overall motion. In conclusion, it would appear that the rates of overall and internal motion for the oligosaccharides under study may well be occurring on similar timescales. The method used to measure the individual correlation times assumes a priori that the distance and orientation contributions to the autocorrelation function are independent, an assumption that is probably not valid. Thus, the values which have been established can only be analysed in a qualitative way. Physical models which reproduce the dynamic behaviour of oligosaccharides will be required for quantitative analysis of such relaxation data.

Acknowledgements I.B. acknowledges support from the French Ministry of Research and Technology. We thank the Pierre and Marie

Internal motion in carbohydrates." I. Braccini et al. University (Paris VI) and the C N R S ( U R A 1110) for financial help.

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