carbon-13 relaxation study of motional properties of lacto-n-neotetraose in solution

MAGNETIC RESONANCE IN CHEMISTRY, VOL. 30, 733-739 (1992)

Carbon-13 Relaxation Study of Motional Properties of Lacto=N=neotetraose in Solution

Stephen Bagley Division of Physical Chemistry, Arrhenius Laboratory, University of Stockholm, S-106 91 Stockholm, Sweden

Helena Kovacs Centre for Structural Biochemistry, Karolinska Institute, NOVUM, S-141 57 Huddinge, Sweden

Jozef Kowalewski* Division of Physical Chemistry, Arrhenius Laboratory, University of Stockholm, S-106 91 Stockholm, Sweden

Goran Widmalm Department of Organic Chemistry, Arrhenius Laboratory, University of Stockholm, S-106 91 Stockholm, Sweden

Carbon-13 spin-lattice relaxation times and NOE factors are reported for a tetrasaccharide, lacto-N-neotetraose, in solution as a function of temperature and magnetic field. The data that are outside the extreme narrowing regime are analysed using the 'model-free' approach of Lipari and Szabo. The global reorientation is assumed to be isotropic. The experimental data for the inner rings can be fitted very well using a simplified version of the equations, neglecting the local motion term in the spectral densities. The complete expression for the spectral densities is required for the outer rings, and three different fitting procedures are compared.

KEY WORDS Carbon-13 relaxation Molecular dynamics Model-free approach Variable field Variable temperature

INTRODUCTION

A few years ago we reported measurements of I3C spin- lattice relaxation times and nuclear Overhauser enhancement factors at several magnetic fields and temperatures for two disaccharides.' By using a cryogenic solvent (a 7 : 3 molar mixture of D 2 0 and DMSO-d,), we were able to obtain data outside the regime of extreme narrowing and found that the results could be interpreted using a very simple motional model. In this paper we report similar measurements for lacto-N-neotetraose in the same solvent mixture. Lacto-N-neotetraose (LNnT) (see Scheme 1) is a tetrasaccharide of ellipsoidal shape, where a more complex motional behaviour can be expected.

In the previous disaccharide work' we followed the approach of McCain and M a r k l e ~ , ~ . ~ and formulated the spectral densities occurring in the expressions for the spin-lattice relaxation rate and the NOE factor in terms of isotropic rotational motion of a rigid body. The fact that the disaccharide molecules are not com- pletely rigid rotors4 was taken into consideration by

* Author to whom correspondence should be addressed.

scaling the dipole-dipole interaction strength (the dipolar coupling constant, DCC) by an amplitude factor. In this study the tetrasaccharide molecule is found to display more diversified internal dynamics, and we need a more sophisticated model for spectral densities. Two closely related models are commonly used5v6 to describe the reorientational dynamics in complex, non-rigid molecular systems in isotropic liquids : the 'model-free' approach of Lipari and Szabo7z8 and the 'two-step model' of Wennerstrom and co-w~rkers.~-" Both models invoke the concept of a rapid, local motion (that averages out a part of the rele- vant interaction) and a slower, global motion (that modulates the remainder of the interaction). Assuming that the two motions are statistically independent and that the global motion is isotropic, Lipari and Szabo7 derived the following expression for the spectral density function:

f (w) = - ) (1) 5 ( 1 + szzM W 2 t M 2 + ( l - 1 + W 2 T 2 s2)7

where 2 - l = 7;' + z,', z, is a correlation time for the fast local motion, tM is a correlation time for the slower global motion and S is a generalized order parameter, a measure of the spatial restriction of the local motion. The spectral density of the two-step model contains a

CH20H Ho-oJ--Lo*J NHAc OH

HO C"' C" C ' C

Scheme 1

0749- 158 1/92/080733-07 $08.50 0 1992 by John Wiley & Sons, Ltd.

Received 20 January Accepted 6 M a y

1992 1992

134 S. BAGLEY, H. KOVACS, J. KOWALEWSKI AND G. WIDMALM

slow motion term similar to the first term in Eqn (1) and a fast motion term analogous to the second term in Eqn (1) with z, rather than z. The physical assumptions of the two-step model are somewhat different:" the two motions must be time-scale separated and the local director for the fast motion has to be a threefold or higher symmetry axis; on the other hand, the require- ment that the global motion has to be isotropic is not necessary. The interpretation of the S parameter in the two models also differs slightly.

If the assumption of the isotropic motion is moti- vated and if the first term in Eqn (1) dominates over the second (high S 2 , not too large zM), we can truncate Eqn (1) and obtain

which is identical in the two models. Equation (2) is identical with the expression for the spectral density for the isotropic rotational small-step diffusion with interaction strength scaled by an amplitude factor, if the latter is identified with S2.

EXPERIMENTAL

LNnT was obtained from BioCarb and chromato- graphed on a Bio-Gel P-2 column prior to use. A 0.10 M solution, prepared in a solvent mixture of 0.70 mole fraction of D,O and 0.30 mole fraction DMSO-d,, was placed in a 5 mm NMR tube and sealed after degassing by the freeze-pump-thaw procedure. The 13C Tl experiments were performed at four magnetic fields using the following spectrometers: Bruker MSL 200 (4.7 T), Jeol GSX 270 (6.3 T), Jeol GX 400 (9.4 T) and Varian Unity 500 (1 1.8 T). The fast inversion-recovery pulse sequencet3 was used, in combination with three- parameter non-linear fitting of line intensit ie~. '~ The accuracy of the relaxation rates is estimated to be of the order of 5%, except for the reducing residue where the signal-to-noise ratio was lower than for the other rings. The NOE measurements were performed at 6.3 and 9.4 T using the same spectrometers and the dynamic NOE te~hnique. '~ The accuracy is of the order of 10-20%. Standard pulsed broadband decoupling techniques were used in all experiments, with the decoupler power attenuated in order to avoid sample heating. Deuterium lock was used for the field/frequency stabilization. The spectral window covered about 90 ppm and the number of data points was 16-32K. All the reported values are averages of at least two measurements.

Standard variable-temperature equipment provided by the manufacturers was used on all instruments. The temperature calibration on the 4.7-9.4 T instruments was carried out using the proton shift thermometer,16 while the I3C shift t he rm~mete r '~ was used at the highest field. The temperature was estimated to be accu- rate to within i 2 "C.

The least-squares fitting of the model parameters (see below) was carried out using the GENLSS program," running on a Convex C220 computer. Sums of squares of relative (rather than absolute) errors were minimized,

which allowed treatment of the relaxation rates and NOE factors in a balanced way.

RESULTS AND DISCUSSION

The CASPER program" was used to simulate and assign the 13C spectrum of LNnT in the r*- and /3- configurations. The labelling of the four rings in LNnT starts from the reducing end, without a prime (C), followed by prime (C'), double prime (C") and triple prime (C"'). The spectra of rings C', C" and C"' are identical in the two forms, within the measuring accuracy, and the relaxation data are weighted averages. According to the 13C spectra for the reducing residue, the population of the /3-form is about 1.5 times larger than that of the a-form. The relaxation data for the carbons in this ring refer to the b-configuration only. The chemical exchange between the two forms can, in principle, have an influence on the spin-lattice relaxation rates,20 but in this case it is probably too slow to give a measurable effect.

Two sets of relaxation times for the ring carbons in LNnT, obtained at about 350 K at a magnetic field of 6.3 and 9.4 T, are given in Table 1 (the complete data table consisting of 15 TI and 6 NOE data sets corresponding to different combinations of temperature and magnetic field can be obtained on request). Several interesting observations can be made using these repre- sentative data sets without any attempt to quantify the data according to any particular dynamic model. The relaxation rates are field dependent. This observation indicates that the motion of LNnT is outside the extreme narrowing regime even at this elevated temperature. The relaxation rates for the carbons in the two inner rings ( C and C ) are fairly uniform, except for C'-4, which relaxes faster than the other nuclei (the devi-

Table l. Carbon-I3 T , values for well resolved signals of LNnT at two magnetic fields

Carbon T, (ma)"

c-p-1 324 c-p-2 320 C'-1 280 c - 2 290 C'-3 280 C'-4 248 C"-1 277 C"-2 260 C"-3 286 C"-5 286 c"'-1 C"-2 345 c"'-3 c"-4 272 C"'-5 358

T ,

328 31 4 229

21 7 21 5 229 223 238

300 287 300 21 7 333

a T , measured at 351 K and at 9.4 T. T, measured at 350 K and at 6.3 T.

CARBON-13 RELAXATION I N LACTO-N-NEOTETRAOSE 735

ating behaviour of this particular carbon is only observed at elevated temperatures). The similarity of relaxation rates for different nuclei in a molecule is usually considered to be an indication of isotropic m o t i ~ n . ’ * ~ ’ ~ This argument should be treated, in the present case, with some caution. In fact, all the inner- ring carbons except C’-4 have axial CH bonds which are almost parallel to each other, and therefore have similar orientations with respect to any molecule-fixed frame, e.g. to the principal axis system of a possibly anisotropic diffusion tensor. The carbon with the deviating relaxation rate, C‘-4, has, indeed, an equatorial CH bond with a deviating orientation in the molecular frame. The relaxation rates of the carbons in the outer ring C”’ are lower than those for the inner rings and fairly uniform, while C”’-4 with an equatorial CH bond again deviates from the remainder of the data. C-fi-1 and C-fi-2 behave in a similar way.

We now turn to the description of the fittings of the I3C relaxation data for LNnT to the models corresponding to Eqns (1) and (2). For carbons relaxed by the dipole-dipole relaxation with a single directly bonded proton, the spin-lattice relaxation rate, T ; ’, and the NOE factor, q are related to the spectral densities of Eqns (1) and (2) by21,22

T;’ = $(DCC)*

- + 3J(WC) + 6J(WH + OC)] ( 3 )

where the dipolar coupling constant, DCC, is equal to (p,/4n)yc yH hr,, ~ ’. Here, rcH is the directly bonded carbon-proton distance, a quantity that we set at 109.9 pm. The spectral densities of Eqns (1) and (2) are temperature dependent. In order to accommodate the variable-temperature data into a single fitting scheme, we assume that the correlation times follow an Arrhenius-type relationship:

where c is either M or e, zf” is the correlation time at 298 K and EaC is an Arrhenius activation energy. Equa- tion (5) is, in spite of its approximate character and limited physical significance, often used as a tool for describing the temperature dependence of rotational correlaton times. 1*5 ,6 The generalized order parameter is, on the other hand, assumed to be independent of temperature. The rationale behind this assumption is that S is not a rate parameter. The same assumption was made by Gillies et in their study of semi-rigid hydrocarbons, while temperature-dependent generalized order parameters were employed in studies of more flex- ible systems.24 Thus, if we combine Eqns (3) and (4) for the observable quantities with Eqns (2) and (5) for the frequency and temperature dependencies, the data for each individual carbon atom, or a group of atoms, will be described by three parameters: S , zi9’ and EaM. If we choose to use Eqn (1) instead of Eqn (2), we obtain two additional parameters, T,”~ and Eae.

In view of the observations above, which indicate the possibility of anisotropy in the global motion, one

might ask whether this should somehow be included in the fitting procedure. We decided not to do so, for the following reasons. A modification of the Lipari and Szabo equation [Eqn (l)] allowing the global motion to be anisotropic has been presented (without de r i~a t ion )~ but, as the authors pointed out themselves, it is only approximately valid. Wennerstrom and co- workers’ modelg-’ can accommodate the anisotropic global motion, but it seems uncertain whether LNnT indeed fulfils the assumptions of this model as it was originally developed for a different type of system. Finally, we recognize the fact that our data have a limited accuracy and are taken over a relatively narrow range of magnetic fields and temperatures. Hence, it was our judgement that we should limit ourselves to working with the very simple models given by Eqns (1 ) and (2). For the same reason, we chose not to work with data for individual carbons but rather with averages over rings, possibly excluding deviating signals.

We begin the discussion by analysing the two inner rings. We choose to work with the truncated expression for the spectral densities, Eqn (2), rather than with Eqn (1). The fitted parameters obtained including and excluding C’-4, are summarized in Table 2. The two sets of parameters are very similar to each other. Among the results in Table 2 we note the high value of the generalized order parameter, similar to the values reported for sugar rings in nuclei and for some ”N-H bonds in the protein staphylococcal n~clease.~’ The resulting calculated relaxation rates and NOE factors are compared with the experimental values in Fig. 1. The agreement is satisfactory, showing that neglecting the local motion term in the spectral densities (using the truncated expression) is probably appropriate.

An alternative (but equivalent) method for the analysis of the inner-ring carbon relaxation data would be analogous to the approach applied previously to disa~charides.‘-~ There, the generalized order parameter was set to unity and the effect of local motions was included in the dipolar coupling constant. After taking the average of all the C’ and C” carbons, this fitting method yields DCC = 128.0 i 0.7 kHz (this DCC corre- sponds to a carbon-proton distance of 114 pm), EaM = 23.1 k 0.8 kJ moI-’ and 7i9’ = 1.5 f 0.5 ns. These values can be compared with the results for sucrose in the same solvent mixture: DCC = 131.2 & 0.8 kHz, ExM = 35.4 1.1 kJ mol-’ and ti9’ = 0.8 f 0.4 ns. Clearly, the DCCs are similar and the difference in the zM is reasonable in view of the difference of the molecular size ; the difference in the activation energy should

Table 2. Results from the least squares fits of the inner-ring

Fitb r g 8 (ns) EaM (kJ mol-’) s2 AYc

a 1.48 f 0.05 23.1 i0.8 0.79 f 0.01 4.2 23.3 i 0.8 0.79 f 0.01 4.0 b 1.46 f 0.05

carbon data in LNnT”

a The error bounds are one standard deviation.

included in the averages. (a) C’-4 data included in the averages. (b) C’-4 data not

Standard deviation (%) of the dependent variable.

736 S. BAGLEY, H. KOVACS, J. KOWALEWSKI AND G. WIDMALM

A

10.0 X

0.0 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

1000/Temp(K)

I3

0 . 0 ~ , ~ , ~ ~ ~ 1 ~ ~ ~ 1 ~ , ~ ~ ~ 1 ~ 1 ~ ~ ~ 1 ~ 1 ~ 1 ~ 1 ~

2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

1000/Temp(K)

Figure 1. Field and temperature dependence of (A) the spin-lattice relaxation rates and (6) NOE factors as calculated using the parameters of the first row in Table 2 and Eqns (2), (3), (4) and ( 5 ) . The experimental data for the inner-ring (C' and C") carbons are also indicated (x) 4.7 T; (0) 6.3 T; (0) 9.4 T ; (X) 11.8 T.

not be disturbing because this quantity has limited physical significance.

We turn next to the outer rings. As can be seen in Table 1, the relaxation rates here are lower. If it can be assumed that the global motion correlation times, z M , are the same (as should be the case within the model), one would therefore expect smaller generalized order parameters for the C"' and C-B rings. Smaller order parameters lead in turn to an increased importance of the local motion terms in the spectral densities. For the outer rings we therefore choose not to neglect these terms and to work with Eqns (3), (4), (5) and (1) rather than Eqn (2). The data fitting is carried out in several ways. First, we assume that the global motion correlation time parameters, 7k9' and EaM, obtained from the inner ring data (Table 2, first row) can be used. This reduces the number of parameters to be simultaneously

fitted to three for each ring, S 2 , 7f98 and Eae. The results of this fitting procedure are given in Table 3. Generally, it can be seen that the internal motion parameters ,a9' and E,' are poorly determined, with standard deviations of 25-50%. The origin of these large uncertainties can probably be traced to the fact that the second term in Eqn (1) gives only a minor contribution (at most 5% for the C"' ring and at most 18% for the C-p ring) to the total spectral densities. The experimental data are therefore only weakly dependent on the values of these parameters. The generalized order parameter for the outer rings is substantially smaller than for the inner rings, which is easy to rationalize in terms of lesser motional restrictions at the ends of a semi-rigid rod. It is of interest that the local motion correlation times are roughly an order of magnitude shorter than the corresponding 'sM, i.e. that the time

CARBON-I3 RELAXATION IN LACTO-N-NEOTETRAOSE 737

j 1.75-

1.5-

1.25-

q 1.0-

0.75-

0.5-

scales of the two motions are not very well separated. The effect of excluding a single deviating carbon in the C"' ring (C"'-4) here has a larger effect than for the inner rings-the differences between rows a and b in Table 3 are larger than those between the similar rows in Table 2. The quality of the fit (as measured by the standard deviation of the dependent variable) is independent, however, of whether the C"'-4 data are included in the ring-average or not. We also note that the quality of the fit for the C - j ring (row c in Table 3) is much worse than for the C ring. This observation may, perhaps, be explained by poorer statistics and signal-to-noise ratio for the C-p ring, where we used data for only two carbon atoms. The experimental and calculated data (using parameters corresponding to row a in Table 3) for the C"' ring are compared graphically in Fig. 2. The agreement between the experimental results and the

Table 3. Results from the least-squares fits of the outer-ring

Fitb I:,, (PSI Eae (kJ mol-') S' Av'

a 60 * 20 2 8 1 1 5 0.65 * 0.02 6.9 b 120*20 2 0 * 6 0.57 0.02 6.9 C 150*50 37 * 15 0.54 * 0.04 14

a The global motion correlation time parameters, T',"" and EaM, are taken from the 1st row of Table 2. The error bounds are one standard deviation.

(a) C"' ring. C"'-4 data included in the averages. (b) C"' ring, C"'-4 data not included in the averages. (c) C-fi.

Standard deviation (Yo) of the dependent variable.

carbon data in LNnT'

model seems, by and large, reasonable, although not as fully satisfactory as for the inner rings.

Next, we also performed fits of the outer ring data using five parameters, S 2 , T?', EaM, 22'' and Eae. The

A

I

,' 1 x 0 1

x ------- - _ - z.- __

0.0 2.5 2.6 2.7 2.0 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

1000/Temp(K)

B

2.03

0.2'i- 0.0 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

1000/Temp(K)

Figure 2. Field and temperature dependence of (A) the spin-lattice relaxation rates and 6) NOE factors as calculated using Eqns (1). (3), (4) and (5) and the following parameters: S2 = 0.65, T:'" = 1.48 ns, EaM = 23.1 kJ mol-', 7:'' = 6 0 ps, E," = 28 kJ mol-' (compare Tables 2 and 3). The experimental average data for the C"' ring are also indicated (X ) 4.7 T; ( 0 ) 6.3 T; (0) 9.4 T; (X) 11.87.

738 S . BAGLEY, H. KOVACS, J. KOWALEWSKI AND G. WIDMALM

Table 4. Results from the least-squares fits of the outer-ring carbon data in LNnT"

Fitb r','" (ns) EeM (kJ mol-') r298 (ps) E,' (kJ mol-') 52 w a 2 . 2 i 0 4 26 * 2 200 f 60 2 3 f 4 0.51 f0.05 5.2 b 2.2f0.5 26 f 2 260 f 60 21 f 3 0.42 f 0.06 6.9 c 2.5 f 0 . 9 23*4 300 f 70 28 f 5 0.35 fO.06 1 1


in the averages. (c) C-/? ring. (a) C"' ring, C"'-4 data included in the averages. ( b ) C"' ring, C"'-4 data not included

Standard deviation ("A) of the dependent variable.

results of these fits are given in Table 4. It can be seen that all the parameters are afflicted with sizable errors. The origin of the uncertainties is to be sought in the correlation of parameters. Another general comment that can be made concerning Table 4 is that the simul- taneous fit of all parameters makes the contributions from the global and local motion terms in Eqn (1) more comparable to each other than the three-parameter fits of Table 3. The differences between the two ways of

1 A

m_j

1

2.51

averaging the data for the C"' ring (rows a and b) in Table 4 seem to be well within the error bounds of each other and, in fact, the difference between the C"' and the C-p rings is also no longer obvious. The experimental and calculated data for the C" ring are compared graphically in Fig. 3. Neither these graphs, nor the standard deviations of the dependent variable in Table 4, show any substantial improvement with respect to the results in Table 3 and Fig. 2. We therefore believe that a

, . . . . . . ,'

" Y 0 1 -

-

0.0 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

1000/Temp(K)

2.07 B

1.75-

1.5-

1.25-

T l 1.0-

0.75-

0.0 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

1000/Ternp(K)

Figure 3. Field and temperature dependence of (A) the spin-lattice relaxation rates and (6) NOE factors as calculated using Eqns (1). (3). (4) and (5) and the following parameters: S2 = 0.51, 7;'' = 2.2 ns, faM = 26 kJ mol-', 7:'* = 200 ps, E,' = 23 kJ mol-' (compare Table 4). The experimental average data for the C ring are also indicated. ( x) 4.7 T; (0 ) 6.3 T; (0) 9.4 T; (X) 11.8 T.

CARBON-13 RELAXATION IN LACTO-N-NEOTETRAOSE 739

Table 5. Results from the least-squares fits of the carbon data for rings C’, C and C“‘ in LNnT”

Fitb .:’a (ns) EaM (kJ mol-’) 7Zs8 (ps) E,* (kJ mol-’) S2(C”’) S’(mner) AYc

a 1.49 f 0.04 23.2 f 0.6 6 0 f 2 0 27 f11 0.65 f 0.02 0.79 i 0.01 5.1 b 1.47 f0.04 23.3f0.6 120f20 21 f 5 0.57 f 0.02 0.79 + 0.01 5.1


the averages. (a) All carbons in C‘. C“ and C”’ rings included in the averages. (b) C’-4 and C - 4 data not included in

Standard deviation (%) of the dependent variable.

cautious conclusion from the comparisons of the two methods of fitting the data might be that the simpler approach in Table 3 is preferable and probably provides more physical insight.

Finally, we also used two combined data sets for the inner rings and the C”’ ring. One of these sets contained the ring averages for the C’, and C” and C”’ rings, including all proton-bearing carbons, while the other excluded C’-4 and C”’-4. Using these data sets we performed least-squares fits, simultaneously optimizing six parameters : the two global motion parameters, the generalized order parameter for the inner rings and the three local motion parameters for the C”’ residue. This approach is similar to the method of Dellwo and Wand,” except that we carried out all calculations with ring averages rather than individual carbons. The results of this approach are summarized in Table 5. The changes with respect to Tables 2 (for the inner rings) and 3 (for the C”’ ring) are very small, which again indicates that the simple approach of Table 3 is reasonable.

CONCLUSION

We find that the model-free method of Lipari and Szabo7*’ provides a reasonable approach to the analysis

of the 13C relaxation data in a tetrasaccharide. The local motions of the inner rings are restricted (high generalized order parameter). This fact, in combination with the not too long global reorientational correlation times, allows for the description of the spectral densities in terms of the truncated expression [Eqn (2) ] , neglecting the local motion term. The local motion of the outer rings is less restricted and the full expressions for spectral densities are required, The fits of the data for the outer rings are poorer than for the inner rings.

All the data analysis was carried out under the assumption of isotropic global reorientation. We find the results not to disprove this assumption, but further work will be needed to settle the issue of the global anisotropy effects.

Acknowledgements

This work was supported by the Swedish Natural Science Research Council and Procordias Forskningsstiftelse. A grant from the Knut and Alice Wallenberg Foundation that made the purchase of the MSL 200 spectrometer possible i s gratefully acknowledged.

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carbon-13 relaxation study of motional properties of lacto-n-neotetraose in solution

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