1 ; r ~

E L S E V I E R Journal of Molecul~Liquids 75 (1998) 45-59

journal of MOLECU LA R LIQUIDS

NMR OXYGEN-17 STUDIES OF THE STATE OF WATER IN A SATURATED SUCROSE SOLUTION

Brian P.Hiils, Hui-ru Tang and Peter S.Belton

Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7UA, UK

Abdul Khaliq and Robin K. Harris

Dept. of Chemistry, University of Durham, South Rd., Durham DH1 3LE

Received I September; accepted 28 January 1997

ABSTRACT

The frequency dependence of the water oxygen-17 transverse and longitudinal relaxation times is used to investigate the dynamic state of water in a saturated sucrose solution at 298K. Assuming that the observed frequency dependence originates from the slow modulation of the residual quadrupole coupling of the water-sucrose interaction, an anisotropic rotation model is used to extract water rotational correlation times and the order parameter characterizing the water-sucrose dynamic complex. Although the theory succeeds in providing a quantitative fit to the longitudinal data there is an unexpected anomalous dephasing enhancement in the transverse relaxation, and the paper concludes with a discussion of the possible origins of this enhancement and of alternative models for the dynamic state of the water. © 1998 Elsevier Science B.V. INTRODUCTION

NMR oxygen-17 water relaxation measurements are an extremely rich source of information about the dynamic state of water in aqueous solutions and gels. The application to dilute protein solutions was first reported in the seminal work of Halle et. ai. (1). In these early works, the oxygen-17 relaxation data were interpreted using a model based on the fast exchange of water between the bulk phase and water hydrating the protein surface. The surface was assumed to cause anisotropy in the reorientational motion of the associated water such that the majority of the quadrupolar interaction is averaged by fast, near-isotropic rotation characterized by a short correlation time, xf. The residual quadrupolar interaction is only averaged by slower motions, characterized by a longer correlation time, x,. The degree of anisotropy induced in the surface hydration water is characterized by an order parameter, S. This model provided a quantitative fit to the frequency-dependent transverse and longitudinal oxygen-17 relaxation data in dilute protein solutions (1) and in a variety of colloidal systems (2).

The success of this relaxation model in dilute protein solutions stimulated its application to carbohydrate solutions. The concentration of a simple sugar solution spans a huge range (e.g. up to 73 % w/w in a saturated sucrose solution at 298K) and it is straightforward to prepare glassy states at even higher concentrations (12). The question therefore arises as to the nature of the water dynamics in these concentrated carbohydrate solutions and glasses. Our earlier studies of this question focused on the water deuterium (3) and oxygen-17 (4) relaxation over the lower concentration range. In the dilute solutions it was observed that the longitudinal and transverse oxygen-17 relaxation rates were equal within experimental error, justifying the

O167-7322/98/$19.00 © 1998 Elsevier Science B.V. All rights reservec] Pll S0167-7322(97) 00019-6

46

assumption of extreme motional narrowing in the fast and slow relaxation terms characterized by the correlation times, zr and x, respectively. The effect of increasing sugar concentration on the dynamic state of the water was modelled by assuming that the rotational correlation time, ~5, characterizing the averaging of the residual quadrupolar interaction of the water hydrogen bonded to the sugar hydroxyl groups, increased with increasing solution viscosity according to the Stokes-Einstein relationship. The fast correlation time, xr, was assumed to be concentration independent. Although this theory succeeded in providing a quantitative fit to the concentration dependence of the relaxation data up to concentrations approaching saturation, the theoretical analysis indicated that in a saturated glucose solution the assumption of extreme motional narrowing may begin to break down. If the oxygen- 17 relaxation in very concentrated carbohydrate solutions is not in the extreme motional-narrowing regime, then the rela~xation rates should become frequency dependent, so that the longitudinal and transverse relaxation rates will no longer be equal. In this case a detailed study of the frequency dependence of both the longitudinal and transverse oxygen-17 relaxation rates should provide a rich source of information about the dynamic state of water in these water-poor, high-sugar environments and give a more rigorous test of the theoretical model.

In this paper we therefore focus on the measurement and interpretation of the frequency dependence of oxygen-17 longitudinal and transverse relaxation in a saturated sucrose solution at 298K. The data are analyzed by removing the assumption of extreme motional narrowing in the earlier theoretical model, and the frequency dependence of the relaxation rates is used to determine the rotational correlation times and order parameters characterizing the water in the saturated solution. To our surprise this apparently straightforward protocol presents an inconsistency in the data analysis which is traced to an anomalous enhancement in the transverse relaxation. The origin of this anomalous transverse relaxation enhancement is discussed in the last part of the paper, together with a discussion of alternative relaxation mechanisms stimulated by more recent oxygen-17 dispersion studies on protein solutions (10,11).

EXPERIMENTAL

Sample preparation Sucrose solutions were prepared by addition of a calculated amount of sucrose to 1 g. of 21.8% oxygen-17 enriched water. To avoid proton exchange contributions to the oxygen-17 transverse relaxation the pH of the water was in all cases lowered to less than 3 by addition of a few microlitres of 1 molar HC1 before addition of the sucrose. For all solutions the pH was measured before and after addition of sucrose and this confirmed that sucrose had very little effect on the pH, even in the saturated solution. The alternative strategy of using proton decoupling to remove the proton exchange broadening was not available on all five spectrometers and so, for consistency, was not used. Preparation of the saturated solution (73% w/w at 298K) required heating to 70°C for ca. one hour to dissolve the sucrose. All solutions were then degassed and sealed in NMR sample tubes.

NMR measurements Oxygen-17 relaxation rates were then measured at 298K on each of the sealed sucrose samples using the following five spectrometers: A Bruker MSL-100 (13.557 MHz), Bruker AC-250 (33.909 MHz), Bruker MSL-300 (40.671 MHz), Bruker AMX-500 (67.789 Ml-Iz) and a Varian VXR-600 (81.330 MHz). The oxygen-17 resonance frequencies are shown in brackets.

47

Transverse relaxation times were determined from the Free Induction Decay foUowing a 90 o pu|se; Longitudinal relaxation times were determined by the inversion-recovery pulse sequence. Each relaxation time determination was repeated 3 times and the average value calculated.

In view of the subsequent discussion it is important to verify that the longitudinal and transverse relaxation data are single exponential within experimental error. Figures 1 and 2 show representative examples of the raw inversion-recovery and on-resonance Free Induction Decays (FID), together with the single-exponential fits. The scatter in the FID signal is due to noise in the baseline, and only the first part of the curve, corresponding to log-linear decay

I I I I I I I I I

1 2

/ Figure 1. Typical oxygen-17 inversion recovery data 3 for a saturated sucrose solution together with the

fit to a single exponential function. The sucrose concentration was 73%, pH 2.6, the spectrometer frequency 40.671 MHz and the temperature 298K.

Log [Signal}

3.75

2.50 °*" ~** "

1.25 L

0.5 Time (msec)

Figure 2. The oxygen-17 Free Induction Decay together with the single exponential fit for the same solution as figure I.

°I • •

• ... ~... °ll •

• ii~ o o ooO •

• • • ° I

II • •• • e ° ,°

, i I

10

I I d

48

Rehlxation r n I:e/s- i

35000

3000O

25000

20000

15000

tO000

5000

0

IZI I(1( Itl 557) II 1~.2(I:1.557) ~' R2(33 909) A RI(,V) 671) • 1t2(67 789) h, RI(8 L330) 0 R2(81.330)

[ ]

0 g

i

,= , m~ wl illl P i l 10 20 30 .10 50 60 70 80

% W/W S;LICI'OSe

Figure 3. The dependence of the oxygen-17 longitudinal and transverse relaxation rates on sucrose concentration at 298K at the indicated spectrometer frequencies.

over approximately two orders of magnitude, was used in deriving the transverse relaxation time. As a number of authors have pointed out (5), the observation of single exponential decay with a quadrupolar nucleus such as oxygen-17 (I=5/2) does not preclude the possibility that there are actually two (or more) exponential terms in the decay. For the moment we ignore this complication and proceed on the assumption that the decay is genuinely single exponential.

A GENERALIZED THEORY OF WATER OXYGEN-17 RELAXATION IN VERY CONCENTRATED SUGAR SOLUTIONS

Figure 3 shows the concentration dependence of the experimental oxygen-17 transverse and longitudinal relaxation rates in sucrose solutions measured at five spectrometer frequencies. In all cases the relaxation is apparently single exponential within experimental error, even in the saturated solution, so we assume fast exchange of water between all sites in the system. At sugar concentrations below saturation the longitudinal and transverse relaxation times are equal within experimental error and independent of spectrometer frequency so that, for these concentrations, the assumption of extreme motional narrowing used in the previous analysis of these systems (3,4) is fully justified. However it can be seen in figure 3 that this is not the case in the saturated solution where the longitudinal and transverse relaxation rates become unequal and frequency dependent. In the rest of the paper we therefore focus exclusively on the saturated solution and attempt to analyze the data by simply removing the assumption of extreme motional narrowing in the term containing the long correlation time, %.

in this case the relaxation equations become (4)

R I = Pb~(R,b,, ~ + R,b~ t') + (1 - Pbw)Rw R~_ = Pb~(R~.b~ ~ + R2b,J) + (1 - Pbw)R~

where

Rtbw S = KS2X2Xs{0.2/(1 + ~S2~s 2) + 0.8/(1 + 4m2z~:)}

R2bw S = KS2Z2Xs{0.3 + 0.5/(1 + m2"Cs 2) + 0.2/(1 + 4t~2zs2)}

and it is normally assumed that

Rib,J = R2bw r = Kz2zt(1 + fl"/3 - S")

-but see the discussion below.

49

[ll [2]

[3]

[4]

[5]

Here R~ refers to relaxation rate of bulk water (169s"), assumed to be in extreme motional narrowing, ~¢ is the quadrupole coupling constant, which is taken to be 6.67 MHz for oxygen- 17 in water, rl is the asymmetry parameter taken to be 0.93 (6), S is the order parameter and K is a constant :

K = 3n-'(2I +3)/1012(2I-1) [6]

The meaning of these various terms has been fully described in previous publications (3,4). The subscript "bw" refers to "bound water" so that Pbw is the fraction of "bound water" in the system. The label "bound" is merely one of convenience and does not, of course, imply anything about the lifetime of the water-sucrose interaction. Rather it refers to all water whose reorientational correlation times are lengthened by interaction with sucrose molecules. The subscripts and superscripts "P' and "s" refer to the fast, nearly isotropic, reorientational motion of the bound water and the slower motions averaging the residual quadrupolar interaction respectively.

The advantage of relaxation measurements at a variety of spectrometer frequencies is now apparent in equations [3] and [4] because fitting the frequency dependence permits an unambiguous extraction of the slow correlation time, % To this we now turn.

The direct calculation of z,

Provided it is assumed that the fast reorientational motion, characterized by Tf. remains in the extreme motional narrowing regime the term Rtb,, r is frequency independent. Moreover, for the bulk water phase, Rtw = R2,,, which implies that, i f two particular frequencies (co 1 and 0h) are chosen, then for a general frequency o~, the ratio, A, defined as,

A = [R,(w 0 - R,(w2)]/[R,(w,) - R,(m)] [7]

is dependent only on the slow relaxation terms in ~,~' , such that

50

A

7 - a)

6 -

5 b)

4

3

2

I I I l I I II [ 0 10-I0 10-9 lO-S 10-7

% (sec)

a) 33.909 I b) 40.671 c) 67.789

Figure 4. Plot of the theoretical ratio, A, against the correlation time, L, for three intermediate spectrometer frequencies for a saturated sucrose solution at 298K. The estimated values of xs are indicated.

, , i i , , J ~ l

10-6

A = [R,bwS(w,) - R,bwS(~2)]/[R,bw'(W0 - R,b~S(~)] [8]

Taking this ratio eliminates the unknown order parameter, S 2, as well as Rlbw f, so that the correlation time, x s, is the only unknown parameter in A. The highest sensitivity is achieved when w I and w 2 are the lowest and highest frequencies (13.557 and 81.33 MHz respectively). Figure 4 shows the calculated dependence of A on xs for three values of the intermediate frequency, w, together with the values of L, corresponding to the experimental values of A. The results are listed in Table I.

Table 1 Parameter values derived by the direct calculation method

w(MHz) A xs(ns ) PbwS 2 S(Pbw = 1) 33.909 1.6 7:0.1 4.9 0.12 0.34 40.671 1.3 7:0.1 4.9 0.10 0.32 67.789 1.1 7:0.1 2.8 0.11 0.32

Because of the smaller amplitude of the dispersion for a spectrometer frequency of 67.789 MHz, the value of 2.8 ns for x s in table 1 is less reliable than the other two values. We therefore deduce that L is 4.9 nanoseconds, which is of the same order of magnitude as values derived less directly in previous work (4).

51

Calculation of the order parameter. S

Having obtained the correlation time, zs, it is possible to estimate the order parameter, S. To do this we use equations [I] and [2] and note that because we assume that the fast reorientational component is in extreme motional narrowing it follows that R,bw f = R,b~ r so that

R z - R 1 = Pbw(R2b,,, S - Rib,J ) [9]

Substituting the values for the relaxation rates, K and z, the product PbwS 2 can be calculated and is listed in table 1. To obtain the order parameter an independent value for the fraction of hydration water, Pb,,, is needed. In previous work (4) it was reasoned that there should be no free, bulk water in the saturated solution so that Pb~ is simply unity. The resulting values of the order parameter are listed in table 1 and are found to be of the order of 0.32. Such a high value for the order parameter is quite unusual in a macroscopically disordered system and reflects strong directional interaction between the water and sucrose molecules. As we shall demonstrate in a later section, some caution needs to be placed on the value of the order parameter derived from equation [9] because of an anomalous contribution to the transverse relaxation rate. In the next section we therefore present an alternative method of data analysis which does not make any use of the transverse relaxation data. This gives a somewhat smaller value for the order parameter.

An alternative method of data analysis

This uses direct, iterative fitting of the frequency dependence of the longitudinal relaxation rate of the saturated solution. According to equations [1] and [3], the longitudinal relaxation rate, assuming Pbw=l and that Rt f= R2 r is given as

Rt(0 ) - RI(w ) = KS2z2"Cs{1 - 0.2/(1 + m2Zs ~) - 0.8/(1 + 4m~z2)} [10]

This shows that iterative fitting of the experimental longitudinal relaxation data can provide values of the order parameter, S and the correlation time, x,. The continuous line in figure 5 shows the best fit to the experimental longitudinal relaxation data and gives a value for T S of 4.8ns and an order parameter, S, of 0.26. The value of the correlation time, x,, is in good agreement with that based on direct calculation in table 1. However the order parameter is significantly smaller. As we shall see, this discrepancy is a result of an anomalous contribution in the transverse relaxation rate, so the iterative fitting procedure, based solely on longitudinal relaxation data, probably gives more reliable values than the method using Rz- RI . It also has the advantage of using all the longitudinal data instead of values at selected intermediate frequencies as in equation [8].

Calculation of RbJ and "r!

Knowing the order parameter and z s from either the direct calculation or iterative fitting procedures, it is now possible to return to equations [1] to [4] and derive values for R I J and R,_J (hence zf.via equation [5], but without requiring R~bw f equals R.,b, j ). In this way the assumption of extreme motional narrowing in P%w r can be checked. Table 2 lists the values obtained using both the direct calculation and the iterative fitting methods.

52

Table 2. The fast, bound water contributions

Direct method m(MHz) Rlb,,,r(S "l) T r (ps) R.,b,,,.,t'(S a ) zf (ps)

13.557 33.909 5918±590 103 7005±700 122 40.671 6025±600 105 5854±585 102 67.789 6991±700 122 4250±425 74 81.330

Iterative fitting method

w(MTqz) R J ( s ~) "~r (ps) R~_bwf(s "~ ) "~f (ps)

13.557 7799±780 136 18698±1870 325 33.909 7651±765 133 11226±11230 195 40.671 7348±735 128 9676±970 168 67.789 7554±755 131 7222±720 126 81.330 7173±720 125 5412±540 94

The results in table 2 are surprising because they show that Rtbw f does not equal R2bw r and that the latter is frequency dependent. This appears to contradict the assumption of extreme motional narrowing (i.e. that nrrf<<l) in the fast, bound water contribution. However, taking the highest frequency • equal to 81.33 MI-/z and the longest z r equal to 325 ps the product mxf is only 0.17 which appears to justify the assumption of extreme motional narrowing. Moreover it can be seen that the values derived solely from the longitudinal relaxation data by the iterative fitting method give consistent frequency independent values for R~b,, f and % (see columns 2 and 3, iterative firing method). This suggests that the fast bound water contribution is indeed in extreme motional narrowing but that there is some additional, anomalous contribution to the transverse relaxation contribution creating an apparent frequency dependence in Rzbw f and zf whenever they are derived using transverse relaxation data. In the next section we attempt to isolate this anomalous transverse relaxation contribution by direct comparison of the frequency dependence of the longitudinal and transverse relaxation rates. However, one should note the inbuilt assumption that there is no anomalous behaviour for R t.

The frequency dependence of the longitudinal and transverse relaxation rates

Figure 5 shows the experimental frequency dependence of both the longitudinal and transverse relaxation rates for a saturated sucrose solution at 298K and at pH 2.6. For comparison, the theoretical curve used in the iterative fitting of the longitudinal data is included, together with the corresponding theoretical curve for the transverse relaxation rates calculated using the same parameter values.

RI,R2/s-J

35000

30000

250O0

20000

15000:

10000

5000

0 6.5

I_~_ Rl(exp R2(exp) Rl(the) R2(the

53

Figure 5. Iterative fitting of the longitudinal relaxation rates as a function of frequency for a saturated sucrose solution at 298K based on equation [10]. The dashed line shows

• the corresponding theoretical prediction for the transverse relaxation rates.

. •

I I I I I 7 7.5 8 3.5 9

Log (<o/rad s -z)

A number of points are noteworthy about figure 5. First the longitudinal relaxation rates appear to behave as expected and can be fitted within experimental error by the theory. However the transverse relaxation is anomalous for two reasons. First the difference between the experimental transverse and longitudinal relaxation rates is observed to decrease with increasing frequency, which is opposite to the theoretical prediction and to the frequency dependence predicted by conventional spectral densities (7). Secondly, the transverse relaxation rate appears to be increasingly enhanced at low frequencies. It is also interesting to observe that the experimental data in figure 5 can be fitted by adding an extra term, AR(m), in the transverse relaxation rate such that,

AR(w) = Cx/(1 + w2x 2) [11]

where the parameters have the values C = 1.72.10 t2 and x = 9 ns. Although equation [11] has the standard form of a spectral density its use in the present context is purely empirical and it is not at all clear why this additional term is needed. However the curve in figure 6 shows that equation [11] succeeds in providing an improved fit to the data. In the next section we speculate about possible origins for this anomalous behaviour of the transverse relaxation.

POSSIBLE ORIGINS OF THE ENHANCED TRANSVERSE RELAXATION

One possible explanation of this anomalous transverse relaxation behaviour is that it is an effect of slow proton exchange, which only becomes significant in the saturated solution in the absence of proton decoupling. Figure 7 shows the experimental dependence of the longitudinal and transverse relaxation rates on pH for an unsaturated 52% sucrose solution at 298K and at a spectrometer frequency of 33.909 MHz in the absence of proton decoupling.

54

Relaxation rate/s-I

,l.O0E +0,1

3.50E+0,t

3.00E+04

2.50E+04

2.00E+04

1.50E+04

1.00E+04

5.00E+03

0.00E+00

I .~_ I~.l data p~i,~t R2 data plaint RI theor~tical R2 theoretical

[ I I I I I 6.5 7 7.5 8 8.5 9

Log (~)/rad s-t)

Figure 6. The theoretical fit to the frequency dependence of the longitudinal and transverse oxygen-17 relaxation rates for a saturated sucrose solution at 298K. The transverse relaxation calculation includes the anomalous contribution described by equation [11].

The observed enhancement in the transverse relaxation rate is caused, in this case, by the slow modulation of the oxygen-17-proton spin-spin coupling by proton exchange and has been discussed in the classic work of Meiboom (8). It should be noted that the mechanism involves dephasing of the transverse magnetization by proton exchange modulation of the proton- oxygen-17 spin-spin coupling. It therefore causes an enhancement only of the transverse relaxation and not the longitudinal relaxation. The effect is removed by increasing the proton exchange rate by working at pH values less than 3. For this reason all the measurements reported in this paper were undertaken at pH values of less than or equal to 2.6 in the absence of proton decoupling. The effectiveness of this low pH strategy was checked at the beginning of the experimentation by direct comparison of the widths at half height measured on the 53% sucrose solution at 298K at 33.909 MHz by lowering the pH in the absence of proton decoupling (width at half height = 320 -T- 30 Hz) with the values obtained at neutral pH with gated decoupling (296 • 20 Hz). Within experimental error these values were equal, justifying the use of the simple pH protocol.

Unforttmately a similar comparison was not undertaken at higher sucrose concentrations because there was no reason to suspect the existence of an anomaly in the transverse relaxation. However, further consideration suggests that the proton exchange rate at any fixed pH will decrease as the sucrose concentration increases upto saturation and examination of figure 7 shows that it would only take a small decrease in the exchange rate at pH 2.7 to move into the regime where the transverse relaxation rate is enhanced. Indeed the decrease in proton exchange rate with increasing sugar concentration in glucose solutions has already

55

RI,R2/s 4

1300

1200

Ii00

i000

900

800

700

o

©

©

o

o

0

0

~ • • • O ° • • • •

600 i l i , r l i 0 2 4 6 8 I0 12 14

pH

Figure 7. The experimental dependence of the water oxygen-17 relaxation rates on pH for a 52% sucrose solution at a spectrometer frequency of 33.909 MHz. at 298K.

been reported using deuterium NMR (3). A substantial reduction in the proton exchange rate in a saturated sucrose solution, even at pH's less than 3 would not therefore be surprising, especially if it is remembered that the above model assumes the absence of any bulk water phase. A subsequent experiment was therefore undertaken to check this possibility. The longitudinal and transverse relaxation rates for a saturated sucrose solution were measured at a single frequency (40.671MHz) at pH 2.9 with and without proton decoupling. If proton exchange broadening is occurring proton decoupling should result in an increase in the transverse relaxation time while leaving the longitudinal relaxation times unaffected. The results, which are shown in table 3, confirm the existence of the proton exchange broadening mechanism even at pH 2.9. An attempt to lower the pH further by addition of more concentrated acid resulted in a "yellowing" of the sample, presumably by hydrolysis and condensation reactions of the sugar.

Table 3 The effect of proton deeoupling on the relaxation times at 40.67MHz.

T, (.104s) T~ (.104s) pH 2.9 No decoupling 1.51 (~0.01) 1.15 (~0.01)

IH decoupling 1.45 (T0.01) 1.31 (~0.01)

56

Unfortunately, proton exchange gives a frequency-independent contribution to the transverse relaxation rate and cannot therefore provide the complete explanation for the relaxation data which shows enhanced transverse relaxation at lower frequencies. The enhanced transverse relaxation rate, AR,_, for a saturated sucrose solution can be calculated using the expression of Meiboom (8). 8w which is the frequency splitting induced in the oxygen-17 resonance by proton spin-spin coupling (which is independent of spectrometer frequency) is about 73 Hz for the oxygen-17-proton interaction and R,. is of the order of 10 a s "~ so it is safe to assume that 8,~ << R,. so that (8)

&R: = 0.5kbR, "/(R,+kb) [12]

where k b is the reciprocal lifetime of the proton on a water oxygen-17 nucleus. If we further assume that k b << R: equation [13] reduces to AR2(w) = 0.5kbR,.(w). A very rough estimate of kb can be made from the data in figure 5. Taking the experimental R,. at a frequency of 13.557 MHz (ca. 3. I 0 * s "~) and the theoretical R2 (in the absence of exchange dephasing) from the dotted line in figure 5 (ca. 2.25.104 s~), we find that k b needs to be about 0.7 s "~ in order to account for the observed enhanced dephasing at this frequency. This is a plausible exchange rate for the saturated solution bearing in mind that there is no "bulk" water phase. Nevertheless, this explanation of the origin of the enhanced transverse relaxation does not account for the observed increase of the enhanced dephasing rate, AR2, at lower frequencies seen in figure 5 and modelled in figure 6 with equation [1 I]. It appears therefore that, besides the proton-exchange dephasing enhancement, there must be some other, as yet unidentified, frequency-dependent dephasing contribution.

Multiple quantum coherences set up during the initial 900 pulse is another possible explanation of the transverse relaxation anomaly. The transverse relaxation times are not long compared to the 900 pulse length and the instrument deadtimes, so multiple-quantum artefacts could exist. This could, perhaps be investigated using other pulse sequences, including the quadrupolar echo sequence, but this remains a future challenge.

DISCUSSION

Our results show the importance of undertaking oxygen-17 relaxation measurements at a variety of different spectrometer frequencies on both transverse and longitudinal relaxation when testing any model of the dynamic state of water in solution. By exploiting this frequency dependence we have shown how it is possible to extract separate values for the correlation times and the order parameter and test the assumption of motional narrowing in the near-isotropic component of the water reorientational motion.

Although our theoretical analysis goes a long way towards providing a quantitative explanation of the oxygen-17 relaxation data in sucrose solutions it is clear that other explanations based on different relaxation mechanisms and different models for the water dynamics cannot be excluded. In our model the observed frequency dependence arises solely from the slow averaging of the residual quadrupolar interaction of the water whose motion is anisotropic and retarded by their proximity to sugar molecules. One possible mechanism for this retardation is hydrogen-bonding to sugar hydroxyl groups but in a saturated solution simple steric crowding effects may be important as well. The motional anisotropy is consistent with earlier work on protein solutions (1).

57

In more recent work on the frequency dependence of water oxygen-17 relaxation in dilute protein solutions (10 , l l ) an alternative explanation of the frequency dispersion has been presented. In this latest model the frequency-dependent term corresponding to equations [3] and [4] has been assigned, not to the slow averaging of residual quadrupolar interactions in surface-perturbed water but rather to a much smaller number of more tightly bound water molecules within the protein molecules. These internal water molecules have residence times of the order of 10 "s to 10 .6 seconds, which is longer than the rotational correlation time of the protein. Accordingly, the frequency dependence arises from rotational modulation of the quadrupolar interaction of these internal water molecules by reorientation of the whole protein molecule (I0). In the case of a saturated sucrose solution there is no longer a clear distinction between "internal" water and "surface" water. Nevertheless it raises the question as to the nature of the modulation characterized by the slow correlation time, "¢s, and whether this could correspond to the modulation of long-lived hydration water by rotation of the sucrose molecules. Some estimate can be made for the rotational correlation time of the sucrose molecule in the saturated solution. ~3C relaxation and NOE studies on a 70% wlw/ sucrose solution give a rotational correlation time for the sucrose molecule of about 4.4 nsec. (14). Assuming this scales with the solution shear viscosity this gives an estimated sucrose rotational correlation time of ca. 10 nsec. in the 73% saturated solution (r I for a 70% sucrose solution is 321,6 centipoise at 25°C and 738.9 centipoise for the 73% w/w solution (15)). This is to be compared with the value of 5 nsec estimated for the slow correlation time of water ('~s) for the 73% solution derived in the present paper. It can be seen that the two correlation times are of the same order of magnitude and suggests that the averaging of the residual quadrupole coupling of the water is correlated in some way with the rotational motion of the sucrose molecule. There is also an upper limit to the water-sucrose interaction time because this has to be shorter than the experimental longitudinal relaxation time. Otherwise the modulation would no longer provide a relaxation mechanism. The shortest T~ is 0.06 ms (at a spectrometer frequency of 13.557 MHz) which implies that the upper limit on the modulation or interaction time is 10 "a seconds. Correlated motions between water and sucrose motions have been suggested by recent molecular dynamic simulations of a hydrated sucrose molecule during a 1.3 ns time period (13) which show that there is one particularly persistent hydration site (a water bridging conformation).

The whole concept of a relaxation model based on the fast exchange dynamics of the water between the free and hydrated (or "bound") states may also need to be reevaluated at a more fundamental level in these concentrated, low water carbohydrate systems. The model provides a quantitative explanation of the concentration behaviour in the more dilute regime where it is reasonable to assume there is still a bulk water phase (4). However, in the saturated solution there is no bulk water phase so Pb,, is unity and the equations reduce to a "one-phase" model. As we have shown, it is still possible to account quantitatively for the longitudinal relaxation data using this "one-phase" model with anisotropic motion of the water. But even taking into account proton-exchange dephasing, there still appears to be an unexplained anomaly in the transverse relaxation behaviour. In this situation it may be necessary to re- consider the theoretical analysis by defining new dynamic states of water in the saturated solution and introducing a multi-state exchange model. For example we could define a dynamic state of water in the saturated solution where it reorients nearly isotropically in the spaces between sugar molecules (but with a rotational correlation time considerably less than that of bulk water) and define other dynamic states of water where more specific interactions with sugar molecules further retard the rotational motion and induce rotational anisotropy.

58

If the "exchange" between these various dynamic states of water is no longer sufficient to ensure extreme motional narrowing then the exchange itself could provide another relaxation pathway.

This "multistate" picture of the water dynamics in a saturated sugar solution is reminiscent of the state of water in sugar glasses. Our earlier work on proton and deuterium NMR studies of water dynamics in the glassy state of glucose solutions (12) showed the existence of highly mobile water whose dynamic state had apparently become substantially decoupled from that of the rigid matrix of sugar molecules in the glass. It is not therefore unreasonable to postulate the existence of a more mobile dynamic state of water in the saturated solution. The theoretical and experimental implications of this alternative picture of the water dynamics remain subjects for future investigation. Since the submission of this paper, an alternative theory of water oxygen-17 relaxation in dilute sugar solutions has been developed (Leyte, J.C., personal communication). This argues that the lifetime of water at hydration sites on the sugar in dilute solution is short compared to x~ so that the exchange lifetime needs to be incorporated into the formalism by solving the rotational diffusion equation for water molecules with exchange terms between the hydration and free states. Although this theory provides an alternative explanation of the dilute regime it breaks down in the saturated solution. Nevertheless it may provide an alternative starting point for the development of a more general theory of relaxation in concentrated sugar solutions.

The origin of the anomalous enhancement of the transverse relaxation rate at low frequencies remains to be more fully investigated. A more extensive study of the frequency dependence in a saturated sucrose solution over a wider frequency range using a field-cycling spectrometer under conditions of proton decoupling would be especially valuable in this regard, and remains high on the list for further investigation.

ACKNOWLEDGEMENTS

The authors wish to thank the Biological and Biotechnology Research Council for supporting this work and for awarding Abdul Khaliq a CASE studentship to undertake this work as part of a Ph.D. at the University of Durham. We are grateful to the former Science & Engineering Research Council for access to the high-field NMR (Varian VXR-600) service at the University of Edinburgh and to Dr.J.Parkinson for his expert assistance with the experiments using this spectrometer. We thank Prof. B.Halle for helpful suggestions during the revision stage of the manuscript.

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