Determination of Molecular Self-Diffusion Coefficient Using Multiple

The pulsed-field gradient (G) and background gradient (G0) are expressed using filled rectangles. ... If the condition g02τ3 ≪ g2δ2Δ is not fulfi...
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Anal. Chem. 2001, 73, 3528-3534

Determination of Molecular Self-Diffusion Coefficient Using Multiple Spin-Echo NMR Spectroscopy with Removal of Convection and Background Gradient Artifacts Xu Zhang, Cong-Gang Li, Chao-Hui Ye, and Mai-Li Liu*

Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China

A new approach is presented for the measurement of the self-diffusion coefficients of molecules in solution. It has been applied to metabolites in biofluids such as seminal and blood plasma at physiological temperature. The method is based on the double-gradient-spin-echo pulse sequence in which CPMG and bipolar gradient pulses have been implemented. The double-gradient spin-echo is shown to be useful in reducing the thermal convection that can cause over-estimation of the diffusion coefficients. The multiple spin-echoes in association with the CPMG approach is also insensitive to background gradient artifacts. In addition, the CPMG sequence enables longer diffusion periods (up to seconds) to be used without phase distortion; therefore, the proposed method is suitable for determining the diffusion coefficients of small metabolites in biofluids, where the resonances of large molecules, such as proteins, are suppressed during the spin-echo period as a result of their fast relaxation. Building on the pioneering experiment of Stejksal and Tanner in 1965,1 noninvasive measurement of self-diffusion coefficients using pulsed-field-gradient (PFG) nuclear magnetic resonance spectroscopy (NMR), has enjoyed widespread applications.2-6 In the original PFG spin-echo NMR experiment (Figure 1a, PFGSE), the signal attenuation can be described using eq 1.1

ln[A(g)/A(0)] ) -γ2D[2g02τ3/3 + g‚g0δ(3τ2/2 - δ2/6) + g2δ2(∆ - δ/3)] - 2τ/T2 (1) Here A(g) and A(0) are the signal intensities in the presence and absence of the PFG, γ is the gyromagnetic ratio of the spin, g and δ are the strength and duration of the rectangularly shaped * To whom correspondence should be addressed. Tel: 86-27-8786-9305. Fax: 86-27-87885291. E-mail: [email protected]. (1) Stejskal, E. O.; Tanner J. E. J. Chem. Phys. 1965, 42, 288-292. (2) Tanner, J. E. J. Phys. Chem. 1970, 52, 2523-2526. (3) Johnson, C. S., Jr. Prog. NMR Spectrosc. 1999, 34, 203-256. (4) Gounarides, J. S.; Chen, A. D.; Shapiro, M. J. J. Chromatogr. 1999, B725, 79-90. (5) Chen, A. D.; Shapiro, M. J. Anal. Chem. 1999, 71, 669A-675A. (6) Liu, M.; Nicholson, J. K.; Parkinson, J. A.; Lindon, J. C. Anal. Chem. 1997, 69, 1504-1509.

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Figure 1. (a) Conventional gradient spin-echo (SE) pulse sequence for diffusion coefficient measurement. (b) Multiple spin-echo pulse sequence (MSE) achieved by implementation of both CPMG and bipolar gradient pulses into SE. (c) Double MSE sequence (DMSE) for thermal convection compensation. The thin and wide bar symbols represent 90° and 180° pulses, respectively. The pulsed-field gradient (G) and background gradient (G0) are expressed using filled rectangles. A 2.5-ms trim pulse (Tr) before data acquisition is used to remove any dispersive components from the detected signals.

PFG, g0 is the strength of the background magnetic field gradient, ∆ is the time between the starting point of the two gradient pulses, D is the diffusion coefficient of the molecule, 2τ is the total spinecho time, and T2 is the transverse relaxation time. 10.1021/ac0101104 CCC: $20.00

© 2001 American Chemical Society Published on Web 07/03/2001

When g02τ3 , g2δ2∆, eq 1 simplifies to

ln[A(g)/A(0)] ) -γ2Dg2δ2(∆ - δ/3) - 2τ/T2

(2)

This is known as the Stejksal and Tanner equation for measuring diffusion coefficients. The derivation of D is straightforward from the signal attenuation as a function of the gradient strength. If the condition g02τ3 , g2δ2∆ is not fulfilled, the effect of the background gradient, which mainly comes from the cross-term (g‚g0) of eq 1, must be considered. The background gradient is caused by inhomogeneity of the static magnetic field and the sample. The field inhomogeneity can be efficiently eliminated by the spin-echo technique.7-9 This approach has been widely used for transverse relaxation-time measurements. The other negative contribution to the accuracy of the measurement is thermal convection, especially when the experiment is carried out at higher temperature. To get reliable diffusion coefficients of metabolites in biological fluids, it is necessary to measure the diffusion coefficient at physiological temperature.5,6 Most NMR spectrometers use a stream of temperature-regulated gas (nitrogen or air) to control the sample temperature. The gas is commonly fed into the NMR probe from the bottom of the probe. When the temperature of the gas is above room temperature, a temperature gradient results along the sample tube. If the thermal gradient is large enough, convective flow can occur along the NMR tube. In addition, switching of the gradient pulses, with their consequential heating effects, can cause time-dependent temperature gradients. This problem of convection was analyzed by Carr and Purcell in early NMR studies of the spin-echo and diffusion.10 If the convection current is present, the amplitude of the even-numbered echo is larger than that of the odd-numbered one in a multiple gradient spin-echo experiment.10 This is because the effect of the thermal convection during the odd-numbered echo is compensated during the even-numbered one.10,11 Therefore, the simplest method to reduce the convection effect is to measure the evennumbered echoes. This principle has been implemented in the stimulated spin-echo (PFG-STE) method and its variations by simply doubling the pulse sequence.12,13 It should be pointed out that the diffusion gradients in the PFGSTE sequence and its variations, such as the longitudinal eddy current delay (LED) method,14 have the function of coherence selection. This is similar to that in PFG-enhanced NMR spectroscopy.15 It is known that the coherence-selecting gradient results in a reduction of sensitivity by a factor of 2. For the same reason, doubling of the STE and LED pulse sequences can cause a sensitivity loss by another factor of 2, or 4 in total. This 4× sensitivity reduction is equivalent to a transverse relaxation (7) Karlicek, R. F., Jr.; Lowe, I. J. J. Magn. Reson. 1980, 37, 75-91. (8) Cotts, R. M.; Hoch, M. J. R.; Sun, T.; Markert, J. T. J. Magn. Reson. 1989, 83, 252-266. (9) Sørland, G. H.; Aksnes, D.; Gjerdåker, L. J. Magn. Reson. 1999, 137, 397401. (10) Carr, H. Y.; Purcell E. M. Phys. Rev. 1954, 94, 630-638. (11) Loening, N. M.; Keeler, J. J. Magn. Reson. 1999, 139, 334-341. (12) Jerschow A.; Mu ¨ ller N. J. Magn. Reson. 1997, 125, 372-375. (13) Jerschow A.; Mu ¨ ller N. J. Magn. Reson. 1998, 132, 13-18. (14) Gibbs S. J.; Johnson, C. S., Jr. J. Magn. Reson. 1991, 93, 395-402. (15) Ruiz-Cabello. J.; Vuister, G. W.; Moonen, C. T. W.; Van Gelderen, P.; Cohn. J. S.; Van Zijl, P. C. M. J. Magn. Reson. 1992, 100, 282-302.

attenuation during a period of 1.4 T2. For the spins of metabolic molecules in a biofluid, T2 is generally in the range of a few hundred milliseconds to seconds; therefore, a double PFG-SEbased thermal-compensated method, with diffusion time less than T2, is expected to be more sensitive than that with coherence transfer. The Carr-Purcell-Meiboom-Gill (CPMG)16 spin-echo pulse sequence has been used extensively for T2 measurement with a spin-lock time as long as seconds with minimum phase distortion. It is known that the CPMG sequence can remove static field inhomogeneity (background gradient) and compensate for artifacts associated with imperfect 180° refocusing pulses.17 These advantages make the CPMG sequence ideal for diffusion coefficient measurement in the presence of a strong background gradient. In this article, the CPMG and double-gradient spin-echo approaches are implemented into the PFG-SE sequence for diffusion coefficient measurements at physiological temperature. The new method is independent of both background and convection gradients. THEORY OF THE PULSE SEQUENCE, INCLUDING REMOVAL OF BACKGROUND AND THERMAL GRADIENTS Figure 1a shows the original PFG-SE pulse sequence. There is no coherence-transfer stage between the two gradient pulses, and therefore, there is no additional sensitivity loss associated with the PFGs apart from the diffusion and relaxation attenuations, as defined in eq 1. In the new sequence, the gradient pulse in Figure 1a is replaced by the bipolar-gradient pulses, as shown in Figure 1b. In addition, a 180° pulse train, instead of a single 180° pulse, is used to achieve a CPMG effect (multiple spin-echoes, MSE), and this allows a long diffusion time to be used. A trim pulse (try) before data acquisition removes any remaining dispersive component from the detected signals. The scheme is repeated twice, resulting in the double PFG spin-echoes (DMSE), as shown in Figure 1c. The 180° pulse in the center of the sequence ensures that all of the gradient pulses are bipolar types in nature. The signal attenuation for the new pulse sequences (Figure 1b,c) is of the form

ln[A(g)/A(0)] ) -kγ2D{g2δ2 (∆ - τ/2 - δ/12) + 4g02(τ3 + 2nτ′3)/3} - k(∆ + 2τ)/T2 (3) Here, k ) 1 and 2 for the pulse sequences MSE and DMSE, respectively, and n is the number of spin-echoes in a CPMG train. When τ ) τ′and ∆ ) 2(2n + 1)τ, eq 3 becomes

{

ln[A(g)/A(0)] ) -kγ2D g2δ2 (∆ - τ/2 - δ/12) +

}

(n + 1) - k(∆ + 2τ)/T2 (4) g02∆3 6(2n + 1)3 It can be seen from eqs 3 and 4 that the cross-term containing the background gradient has been eliminated. If n . 1, the (16) Meiboom S.; Gill D. Rev. Sci. Instrum. 1958, 29, 688-691. (17) Gullion, T.; Baker, D. B.; Corradi, M. S. J. Magn. Reson. 1990, 89, 479480.

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contribution from the background gradient is reduced by a factor of n2. The new sequences retain the attenuation as a result of transverse relaxation, and the phase distortion caused by the spin-spin coupling remains at a minimum because the CPMG sequence is used. The remaining antiphase component is further removed by the trim pulse before data acquisition. The diffusion coefficient can be derived in a straightforward manner by varying the gradient strength, g, and keeping all of the time intervals constant. In the presence of convection flow, it is assumed that the spins are moving in the z-direction with velocity v. The position of the spins can be written as z0 + vt, where z0 is the initial position at the start of the gradient pulse. For the generality, the total phase acquired by a coherence of order p at position z(t) during the gradient pulse is given by

∫

ti+δ

ti

)

∫

γpG(t)z(t)dt )

ti+δ

ti

γpG(t) z0 dt +

∫

∫

ti+δ

γpG(t)[z0 + vt]dt

ti

ti+δ

γpG(t) vt dt ) φ0i + φvi

ti

(5)

The total phase change has been separated into the usual spatial-dependent phase, φ0i ) γpgδ, and the velocity-dependent phase, φvi ) 1/2γpgv(2tiδ + δ2), where ti is the time at the start of ith rectangular gradient pulse. For the MSE pulse sequence (Figure 1b) and the first spin-echo (SE1) of the DMSE pulse sequences (Figure 1c) with identical gradient strength and duration, the total velocity-dependent phase is given by 4

φvSE1 )

∑φ

vi

i)1

) 1/2γgv(t1δ + δ2/4) + 1/2γgv(t2δ + δ2/4) - 1/2γgv(t3δ + δ2/4) - 1/2γgv(t4δ + δ2/4) ) γgv∆δ

(6)

Using the same principle, it is possible to obtain the velocitydependent phase of the second part (SE2) of the DMSE sequence as 8

φvSE2 )

∑φ

vi

) -γgv∆δ

(7)

i)5

Therefore, the phase acquired during the first spin-echo (SE1) is compensated during the second spin-echo (SE2). 8

φv )

∑φ

vi

) φvSE1 + φvSE2

i)1

) γgv∆δ - γgv∆δ ) 0

(8)

The MSE and DMSE pulse sequences have an additional advantage of spectral editing (known as T2-weighting).8 When a long diffusion time (∆) is used, the broad peaks from large molecules, such as lipoproteins, can be efficiently suppressed 3530

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because of their short T2. This is useful for measuring the diffusion coefficients of small metabolites in complex biofluid mixtures. On the other hand, when the macromolecules are of interest, a short diffusion time and large initial gradient strength should be applied to cause the resonances of the fast-diffusing small molecules to be eliminated.8 EXPERIMENTAL SECTION The MSE and DMSE pulse sequences were tested using a solution of H2O at temperatures ranging from 298.2 to 323.2 K. The DMSE sequence was also used to measure the diffusion coefficients of the metabolites in both human seminal and blood plasma from healthy volunteers. The seminal plasma was allowed to liquefy for 45 min at 30 °C, and 10% (v/v) of D2O was added to the samples for the spectrometer magnetic field lock. All of the experiments were carried out on a Bruker ARX500 NMR spectrometer operating at 500.13 MHz for 1H observation with a 5-mm broadband probe. The NMR machine was equipped with an actively shielded gradient unit having a maximum gradient strength output of 49 G/cm. The temperature was controlled by a Bruker B-VT 2000 regulator with an airflow rate of 0.5 L/min. The experimental temperatures were 298.2, 300.2, 308.3, 310.2, 318.2, and 323.2 K set within a variation of (0.1 K. The sample was allowed to equilibrate in the probe for about 1 h after each temperature change. The delay τ was set to 1.2 ms, which ensured a 0.1-ms delay before and after the 1.0-ms gradient pulse (δ/2). An identical total spin-echo time of 200 ms was used for all of the experiments. The same parameters were also used for the BPLED18 experiment. Sine-shaped gradient pulses having a duration of 1 ms at the base were used. Either 16 gradient strengths ranging linearly from 4.9 to 19.6 G/cm or 32 gradient strengths ranging linearly from 4.9 to 34.3G/cm were used for the samples of H2O and the plasmas, respectively. Typically, 32 and 64 transients were acquired into 2 k and 16 k complex data points covering a spectral width of 1000 and 8000 Hz for the H2O and the plasma samples, respectively. The data sets were zero-filled by a factor of 2 before Fourier transformation. The peak areas and the corresponding experimental parameters were used to determine the diffusion coefficients according to the eq 3. RESULTS AND DISCUSSION Figure 2 showed the diffusion coefficients of water measured using the MSE and DMSE pulse sequences together with that measured using the BP-LED sequence18 over the temperature range of 298.2 to 323.2 K. The literature values of diffusion coefficient of water were also plotted in the figure.19 To make a reasonable comparison, the diffusion coefficient of water was corrected to 2.23 × 10-9 m2/s at 298.2 K for all of the methods. It can be seen from Figure 2 that when the temperature is over 305 K, the differences between the measured diffusion coefficients become significant. The BP-LED method gives rise to a value of about 7 times that of the expected value19 at 323.2 K. This is not surprising, because the BP-LED method is sensitive to the thermal gradient.12 The results are improved when the MSE method is used, but in particular, the diffusion coefficients obtained using (18) Wu, D. H.; Chen, A. D.; Johnson, C. S., Jr. J. Magn. Reson. 1995, A115, 260-264. (19) Bruker Almanac, 1998, p 69.

Figure 2. Diffusion coefficients of water that were measured using the BP-LED (9), MSE (b), and DMSE (2) methods over the temperature range of 298.2-323.2 K. Literature values of the diffusion coefficients are showed (1).

Figure 3. 500 MHz 1H NMR spectrum of human seminal plasma obtained using pulse-sequence DMSE with a spin-echo time of 200 ms and a gradient strength of 4.9 G/cm. The major resonances of the metabolites are labeled.

the DMSE sequence are very close to the expected diffusion coefficients of water.19 This reveals, as expected, that the proposed DMSE method is insensitive to the thermal gradient; however, the gradient induced convection and the nonlinear thermal flow may contribute to the errors. These artifacts cannot be compensated for by the pulse sequences. Figure 3 shows a typical 1H NMR spectrum of seminal plasma obtained using the DMSE pulse sequence with a gradient strength of 4.9 G/cm, where in addition, the water resonance had been suppressed. The improved line shapes and baseline, as well as the high efficiency of solvent signal-suppression, are demonstrated in Figure 3. These are essential for the accurate measurement of

the diffusion coefficient in the plasmas samples. The resonance assignments were confirmed by comparing the chemical shifts and line shapes with the literature20 and by conventional COSY experiments (data not shown). The DMSE method was used to measure the diffusion coefficients of the metabolites in a seminal plasma sample at 298.2 and 310.2 K, respectively. Thirty-one peaks at 298.2 K and 32 peaks at 310.2 K from 16 compounds were identified from the 1D spectra. Areas of the peaks were determined by carefully choosing the integral regions in order to avoid peak overlaps. Those areas were (20) Nicholson, J. K.; Foxall, P. D.; Spraul, M.; Farrant, R. D.; Lindon, J. C. Anal. Chem. 1995, 34, 793-811.

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Table 1. Duplicate Diffusion Coefficientsa of the Metabolites in Seminal Plasma, Measured Using the DMSE Pulse Sequence metabolite

assignment

alanine aspartate aspartate aspartate choline choline citrate citrate citrate citrate glutamate glutamate glutamine glycine histidine histidine isolucine isolucine isolucine lactate leucine leucine phenylalanine phenylalanine phenylalanine serine serine threonine tyrocine tyrocine valine valine valine

CH3 β-CH2 β-CH2 β-CH2 O-CH2 N-CH2 CH2 CH2 CH2 CH2 γ-CH2 β-CH2 γ-CH2 CH2 C2-H C4-H CH2 CH3 CH3 CH CH3 CH3 aromatic H aromatic H aromatic H CH2 CH2 O-CH aromatic H aromatic H CH3 CH3 CH3

a

chemical exp 1 exp 2 exp 1 exp 2 shift, δ 298.2 K 298.2 K 310.2 K 310.2 K 1.48 2.83 2.80 2.65 4.07 3.52 2.70 2.67 2.55 2.52 2.35 2.13 2.40 3.56 7.79 7.06 1.26 1.02 0.94 4.12 0.96 0.94 7.42 7.38 7.33 3.97 3.84 4.25 7.20 6.90 1.05 1.04 0.98

7.4 7.4 7.4

7.5 7.5 7.1

7.9 7.6 5.4 4.8 4.7 5.0 6.7 6.3 6.8 8.3 5.2 6.2 6.1 6.6 5.8 7.8 6.3

8.0 7.7 5.4 4.9 4.6 5.0 6.7 6.2 6.8 8.6 5.5 6.2 6.6 6.4 6.0 8.2 6.3

6.3 5.6 6.0 7.5 7.7 8.3 5.9 5.8 7.0 6.9 6.6

6.3 6.0 6.2 7.7 7.8 7.5 5.7 5.9 6.8 6.8 6.4

9.8 11.4 10.8 11.6 11.3 12.1 7.5 6.8 6.8 7.0 9.1 8.9 10.2 12.9 8.3 8.2

9.6 11.2 11.2 12.5 11.2 11.9 7.7 6.8 6.9 7.0 8.5 8.8 10.1 13.5 8.9 7.4

8.9 7.9 10.5 9.1 8.8 8.9 8.5 8.7 10.8 10.8 9.9 7.9 8.1 10.3 10.0 9.7

9.9 8.6 10.3 9.4 9.6 9.5 8.3 8.7 10.9 10.9 9.7 8.0 8.3 10.8 10.6 9.9

D (×1010 m2/S), exp 1, 2.

used to derive the diffusion coefficient according to eq 3. The results are listed in Table 1. It can be seen from Table 1 that the mean diffusion coefficients of the metabolites fall in a range of 5.0 × 10-10 to 8.5 × 10-10 m2 s-1 at 298.2 K and 7.1 × 10-10 to 13.2 × 10-10 m2 s-1 at 310.2K, respectively. The mean value was obtained by averaging two measurements from at least one peak of a compound. The mean standard deviations were 3.5% (298.2 K) and 3.7% (310.2 K), respectively. If the ratio of diffusion coefficients of individual compounds at the two temperatures (298.2 K and 310.2 K) is calculated, one gets a average ratio (increment) of 1.42 ( 0.09, which is in agreement with the ratio (1.46) of water calculated from the literature data19 in Figure 2. This reveals that the DMSE pulse sequence is reliable for determining the diffusion coefficients of biological metabolites under physiological conditions. The ratio of the diffusion coefficients reflects the temperature dependence of the mobility of the metabolite in the plasma. If a molecule is bound to a macromolecule, the measured diffusion coefficient is the weighted average of the free and the bound forms, and its value is expected to be smaller than that of the free form. When the temperature is increased, the dissociation constant is generally increased, and the fraction of the free form is increased. Therefore, the diffusion coefficient of a small molecule in a binding equilibrium with a macromolecule is expected to have a larger temperature dependence than a molecule that does not bind. The similar value of the ratios can be understood as the compounds are moving independently and that there is unlikely to be any intermolecular interaction in seminal plasma. This is different with blood plasma, in which the binding of the metabolites to lipopro3532 Analytical Chemistry, Vol. 73, No. 15, August 1, 2001

Figure 4. Plot of the diffusion coefficients of the metabolites in seminal plasma as a function of molecular weight at 298.2 and 310.2 K. The line symbols show the result of linear fitting together with (95% confidence limits.

teins have been observed.6 The small variations in the diffusion coefficients’ increments of the metabolites when the temperature is increased may be caused by the differences in the molecular structures. The different signal-to-noise ratios resulting from the differences in concentrations certainly contribute to experimental errors. The values of the measured diffusion coefficients were generally related to the molecular weight and, hence, approximate molecular size, as shown in Figure 4. The linear fit and the (95% confident limits are also showed in the figure. Glycine is the smallest molecule (molecular weight, 75.05) and, thus, has the largest diffusion coefficient of 8.5 × 10-10 m2 s-1 and 13.2 × 10-10 m2 s-1 at 298.2 and 310.2 K, respectively, among the compounds listed in Table 1. Conversely, citrate is the slowest diffusing molecule [5.0 × 10-10 m2 s-1 (298.2 K) and 7.1 × 10-10 m2 s-1 (310.2 K)], because it is the largest one in the table. Although the correlation between the observed diffusion coefficients and the molecular weight showed a large dispersion, the results in Figure 4 indicate that there are no significant intermolecular interactions among the metabolites. However, the interaction of the metabolites with solvent water cannot be excluded. The efficiency of the spectral editing by T2-weighting when using the DMSE sequence is demonstrated in Figure 5. Figure 5a shows a conventional 1D 1H NMR spectrum of blood plasma in which the water signal has been suppressed, but the resonances of the metabolites are obscured by the broad peaks of proteins. Two-dimensional experiments are required to measure the diffusion coefficients of the components under these circumstances.6,21 The spectrum in Figure 5b was obtained using the DMSE pulse sequence with a spin-echo time of 200 ms and a gradient strength of 4.9 G/cm. The broad resonances of the proteins have been attenuated as a result of their fast relaxation. The remaining sharp peaks are from the small molecules and the flexible moieties of proteins. Those peaks were assigned by comparing the chemical shifts and the line shapes with those in the literature.6,21 When the gradient strength was increased to 34.3 G/cm, the signals from small metabolites had been further attenuated, and the only (21) Liu, M. L.; Nicholson, J. K.; Lindon, J. C. Anal. Chem. 1996, 68, 33703376.

Figure 5. (a) 500 MHz 1H NMR spectrum of blood plasma with water suppression shows the resonances of the small molecules being blocked by the broad peaks of proteins. (b) Spectrum that was obtained using the DMSE method with a spin-echo time of 200 ms and a gradient strength of 4.9 G/cm. The sharp peaks are resolved and can be used to measure the diffusion coefficients. (c) At high gradient strength, the remaining peaks are from the flexible moieties of the proteins, and their diffusion properties can also be studied.

remaining peaks were from the slowly diffused moieties of the proteins (Figure 5c). The diffusion coefficients of the metabolites and the proteins can be measured in the lower and higher gradient strength ranges, respectively, and the results are listed in Table 2. The diffusion coefficients of alanine, creatine, glucose, and valine obtained in this work are significantly smaller than the values measured previously using a two-dimensional method.6 The viscosity of blood plasma taken from different people may vary, and its effect on the determined diffusion coefficients should be the same for all compounds in the solution. As had been proposed,6 the thermal convection may be the source of overestimation of the diffusion coefficients in the previous work. The diffusion coefficient of lactate derived in this work is 8.8 × 10-10 m2 s-1, which in contrast to the other components, is ∼7% higher than that measured previously.6 It has been postulated that ∼30% of the lactate in blood plasma is bound to human serum albumin (HSA), with the free and bound lactate NMR signals in slow exchange on the chemical shifts time scale.23 In the case of chemical exchange, the determined diffusion coefficient is the weighted average of the two forms weighted by their mole fractions.24 The 200-ms spin-echo time in the DMSE sequence is expected to reduce the contribution of the HSA-bound lactate to the diffusion coefficient because of the short T2 of the bound form. Thus, the increased diffusion coefficient of lactate is evidence of the binding of lactate to HSA. The diffusion coefficient of human serum albumin (HSA) obtained in the present work is 0.69 × 10-10 m2 s-1. This is in (22) Chen, A.; Wu, D.; Johnson, C. S., Jr. J. Phys. Chem. 1995, 99, 828-834. (23) Gaigalas, A. K.; Hubbard, J. B.; McCurrley, M.; Woo, S. J. Phys. Chem. 1992, 96, 2355-2359. (24) Liu, M. L.; Toms, H. C.; Hawkes, G. E.; Nicholson, J. K.; Lindon, J. C. J. Biomol. NMR, 1999, 13, 25-50.

Table 2. Diffusion Coefficients of the Metabolites in Blood Plasma Measured Using the DMSE Sequence at 310.2 K

metabolites

chemical shift, δ

D (×1010m2s-1) DMSE ref 6

alanine creatine

1.47 3.04

9.36 7.92

12.8 12.4

R-glucose R-glucose R-glucose R-glucose mean

5.23 4.50 3.84 3.43

6.95 7.18 7.26 7.04 7.11 ( 0.14

7.8

β-glucose β-glucose β-glucose mean

3.89 3.74 3.27

6.55 7.25 6.89 6.90 ( 0.34

7.6

lactate lactate mean

1.33 4.11

8.87 8.88 8.87 ( 0.01

8.2

valine valine mean

1.04 0.99

8.75 8.49 8.60 ( 0.18

12.9

lipoproteins (dCH) lipoproteins (CH2)n lipoproteins CH3 mean

5.29 1.27 0.86

0.28 0.18 0.23 0.23 ( 0.05

1.2

glycoproteins (N-acetyl) lysyl residues of HSA

2.05 3.22

0.46 0.69

2.1

reasonable agreement with the value of 0.54 × 10-10 m2 s-1, as measured by Chen et al.,22 but it is only one-third of that derived using the two-dimensional method.6 Although the diffusion coefficient of albumin varies considerably according to the solution conditions (concentration, buffer salts, pH, temperature),23 the effect of thermal convection at physiological temperature may Analytical Chemistry, Vol. 73, No. 15, August 1, 2001

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contribute significantly to the difference. The other possible source of the errors is self-aggregation of albumin. Such a molecular complex is expected to have a smaller diffusion coefficient and a shorter transverse-relaxation time than that of the monomer. The long spin-echo time in the present method results in a large attenuation on the signal of the complex and, therefore, gives rise to the diffusion coefficient that is closer to the value of the monomer. The smaller average diffusion coefficients of glycoproteins (0.46 × 10-10 m2 s-1), as compared to HSA, may reflect the difference in the molecular size and shape of the proteins. The method, therefore, provides a potential alternative way for the distinguishing of proteins. Finally, the diffusion coefficient determined for lipoproteins in blood plasma was based on the NMR resonances ar δ 5.29 (olefinic protons), δ 1.27 (alkyl CH2 protons) and δ 0.86 (methyl protons), all from the fatty acyl chains of lipoproteins. The measured diffusion coefficient, therefore, represents an average value over all types of lipoprotein. CONCLUSION The results presented here demonstrate that the DMSE technique is an effective approach for thermal convection com-

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pensation. The method is also insensitive to the background gradients. Adding a CPMG component to the DMSE sequence enables both a long diffusion time to be used and suppression of the broad NMR peaks with a short T2. This spectral editing feature makes the method suitable to the study of the mobility of both small molecules and macromolecules in complex systems. The method can be used to measure the diffusion coefficients and to probe the molecular interactions in biological fluids. ACKNOWLEDGMENT This work was supported by grants from the National Natural Science Foundation of China (nos. 29875034 and 29925515) and the Multidisciplinary Research Program of the Chinese Academy of Sciences. The authors thank Professor John Lindon, Imperial College, London University, for assistance in preparation of the manuscript.

Received for review January 24, 2001. Accepted May 16, 2001. AC0101104