J. Phys. Chem. 1995, 99, 43 1-435
431
Comparison of Water Relaxation Time in Serum Albumin Solution Using Nuclear Magnetic Resonance and Time Domain Reflectometry Minoru Fukuzaki,"??Nobuhiro Miura, Naoki Shinyashiki, Daisaku Kurita, Sumie Shioya, Munetaka Haida, and Satoru Mashimo Department of Communication Engineering, Tokai University Junior College, Tokyo Campus, Takanawa 2-3-23, Minatoku, Tokyo 108, Japan, Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-12, Japan, and Department of Intemal Medicine, Tokai University School of Medicine, Isehara, Kanagawa 259-11, Japan Received: March 30, 1994; In Final Form: September 26, 1994@
We measured the nuclear magnetic resonance (NMR) relaxation times TI and T2 of water in an albumin solution and compared them with values calculated using dielectric relaxation parameters obtained by time domain reflectometry (TDR)and translational diffusion coefficients obtained by NMR. The calculated NMR relaxation times reproduced well the observed values. In a globular protein, three kinds of rotational relaxation parameters are observed by TDR method; these can be assigned to the protein, the bound water, and the free water rotations. The observed NMR relaxation time constitutes, however, a single component, indicating that the extreme narrowing condition is met and free,bound, and next-to-bound water molecules are exchanging rapidly on the NMR time scale. The NMR relaxation times TI and T2 are, however, not equal to one another for the same albumin solution. Since low-frequency fluctuating field inhomogeneity affects T2, our results suggest that the long correlation time associated with the overall rotation of albumin is a main fraction in the transversal water relaxation mechanism.
Introduction
Measurements of the motional state of biological water have been pursued using various methods such as X-ray diffraction,' dielectric relaxation? and NMR relaxati~n.~These methods provide useful information for elucidating the molecular motion of water and estimating the amount of bound water. The interpretation of experimental results depends heavily on the method by which the data were obtained. These may be obtained from samples as different as crystals and aqueous solutions andor derived with instrumental procedures with different frequency resolution on the experimental time scale. We compared previouslp results obtained by time domain reflectometry (TDR) and nuclear magnetic resonance (NMR) measurements for DNA solutions and showed that the NMR relaxation times can be interpreted using the TDR relaxation time and the fast exchange model. Useful information is thus obtained by interpreting results obtained by different experimental methods. The amount of water bound to proteins in aqueous solutions has been estimated by NMR and calorimetric methods to be about 0.3 g of H2O/g of p r ~ t e i n .In ~ recent studies using X-ray diffraction' or TDR,2the estimates were considerably lower than those obtained with NMR. This discrepancy can be explained by the difference in the experimental time scales of the various methods used. TDR has a time resolution of the order of a few picoseconds. On the other hand, the NMR experiment has a time resolution of a few milliseconds. In the present study, we calculated NMR relaxation times of albumin solutions using TDR relaxation parameters and transitional diffusion coefficient obtained by the NMR and compared them with observed NMR
* Author to whom correspondence should be addressed. Tokai University Junior College. @
Abstract published in Advance ACS Abstracts, November 1, 1994.
0022-365419512099-0431$09.00/0
relaxation times. This comparison yields a deeper understanding of the relationship between TDR and NMR results. Experimental Section
Human serum albumin (Fraction V, fatty acid free; Lot:21) was purchased from Miles. The albumin was deionized by gel filtration (Sephadex G-25 prepackaged column PD-10; Pharmacia) and was dissolved in distilled water (Walkersville; Lot: 1M1721). The albumin concentration was adjusted to 5, 10, 15, and 20 wt %. We used 'H 90 MHz, FT-NMR, EX-90 (JEOL) for measuring the water proton relaxation time TIand T2, and their translational diffusion coefficient D . The Can-Purcell-Meiboom-Gill (CPMG) pulse sequence (90°-(zcp-1800-z,p-)n) was used to measure the water proton transverse relaxation time, T2; the inversion recovery (IR)pulse sequence (180°-2-90") was used to measure the longitudinal relaxation time, TI.The TI and T2 values were calculated from the following equations5).
I.
91
M ( z ) = M, 1 - 2 exp - -
(
M(t) = Mo[- t - Ly2GDtc:t] T2 3 where MOis the magnetization intensity at thermal equilibrium, z the recovery time of IR sequence (the times z range from 50 to 3000 ms), t the echo time of the CPMG sequence which satisfies the relationship t = 2nzcp,zcpthe interpulse delay time of the CPMG sequence, n the number of 180" pulses, y the gyromagnetic ratio, G the magnetic field gradient due to the inhomogeneous field, and D the translational diffusion coefficient. The second term of eq 2 is negligible when the time 0 1995 American Chemical Society
432 J. Phys. Chem., Vol. 99, No. 1, 1995
Fukuzaki et al. 5x1O3
q -0,
n
,
loo
o
500
1000
t
, , I 1500
(msec) 5x10' 0
5
10
15
20
Albumin concentration ( % )
Figure 2. NMR relaxation times TI(0)and T2 (A)as a function of albumin concentration.
NE
2.1
v
Figure 1. Water proton magnetization decay curve of CPMG pulse sequence as a function of the echo times i ( t = 2nz,) (a) and recovery curve of IR pulse sequence as a function of the recovery time 5 (b) for 5 wt % albumin solution at 25 "C.
zcp is considerably shorter than the echo time t. We used tcp value of 250 or 500 ps, and the echo times t ranging from 10 to 2000 ms, for T2 measurement. The field gradient spin echo method6 was used to measure the translational diffusion coefficient D, which was calculated using following equation
2.0 L
._5
E
1.9
0
8
1.8
C
1.7
:*
a
r:0
1.6
0
5
10
15
20
Albumin concentration ( OO/ )
Figure 3. Translational diffusion coefficient D versus albumin concentration.
where M(2z)* and M(22) are the spin echo intensities at echo time t = 22 in the presence and absence of the field gradient pulse, y is the gyromagnetic ratio, g the magnetic field gradient (g = 83 Gkm), 6 the field gradient pulse duration, A = 200 ms the diffusion time (i.e., the time interval between two gradient pulses), and D the translational diffusion coefficient. In the absence of the field gradient (g = 0), the pulse sequence is the same as the Hahn spin echo sequence. The TDR method was used to measure the dielectric relaxation spectrum of the albumin solution. The detailed procedure associated with this method was reported previ0usly.7-~ The Fourier transformed (FT) spectrum of the reflected signal (induced by a step pulse) shows relaxation peaks due to molecular rotational motions occurring in the frequency domain of 106-1010Hz. The complex permittivity ( E * ) obtained from this analysis is given by the following equationZ E*
A%
=
(1
+ iwrd)ua
+
[1
A% AEf + (iwrdbp]ab+ 1 + (iot$ + E , (4)
where 2d is the dielectric relaxation time, A6 is the relaxation intensity, w is the angular frequency, and E- denotes the highfrequency limit of the dielectric constant. The subscripts a, b, and f denote parameters associated with the rotational reorientation of albumin, bound water, and free water, respectively. The
relaxation parameters in eq 4 were obtained using the leastsquares method to best fit the experimental data. The sample temperature was maintained at 25 f.0.2 "C in the both NMR and TDR measurements.
Results Figure 1 shows the water proton transverse magnetization decay curve (a) and recovery curve (b) for 5 wt % albumin solution at 25 "C. Except for the distilled water, the curves decay as a monoexponential functions, and the relaxation time T2 is shorter than T I , Figure 2 shows the relaxation times TI and TZ as a function of the albumin concentration. The translational diffusion coefficient D is plotted versus the albumin concentration in Figure 3. Figure 4 shows the dielectric dispersion and absorption curves for a 15 wt % albumin solution. The dielectric relaxation times r d associated with the rotational reorientation of free water, bound water, and albumin are plotted versus the albumin concentration in Figure 5. The values of the dielectric parameters, 2d and AE,are summarized in Table 1.
Discussion According to the BPP theory,1° the NMR relaxation of proton pertaining to a rigid molecule tumbling in solution is dominated by the magnetic dipole-dipole interaction of protons, and the
J. Phys. Chem., Vol. 99, No. 1, 1995 433
Water Relaxation Time in Serum Albumin A
40
t -m .-s
CI
m
0
K
I
.-
-9
0
-7
5
10
15
20
Albumin concentration ( % )
Log f(Hz) Figure 4. Dielectric dispersion and absorption curves for a 15 wt % albumin solution at 25 "C. -12
,
I
-10
-9 -8 -7 -6
L 5
0
10
15
20
Albumin concentration ( % )
Figure 5. Dielectric relaxation times td associated with the rotation of free water t d r (e),bound water Zd, (A)and albumin Zda (m). TABLE 1: Dielectric Relaxation Parameters of Aqueous Solution of Albumin Obtained by the TDR Method %
log (Tdr S
0
5 10 15 20
-6.727 -6.657 -6.556 -6.266
A6
-
log (Tdb),
log ( T d , S -11.06 1.56 -11.05 2.60 -11.06 5.35 -11.05 8.61 -11.05
AEb
S
-
18.9 30.05 30.37 32.72
-
-8.706 -8.750 -8.724 -8.600
AO 73.0 69.68 65.28 60.21 54.00
relaxation rates are given by the following equations:
-_
where B is
B=
+
2y4h2Z(Z 1 )
802r6
(7)
o is the Larmor frequency, zc the rotational correlation time of an allegedly rigid molecule, I the spin number, h the Plank constant, y the gyromagnetic ratio of a proton, and r the distance between dipole-coupled protons. In the BPP theory, the molecule is assumed as rigid and its motion is random rotational motion. Also, the time correlation function between dipole-
Figure 6. Calculated rotational effective correlation time 3"t,", obtained from the measured N M R relaxation times TI (0)and TZ(A), and the dipole-dipole interaction parameters.
coupled protons is assumed to decay as a single exponential. Thus, zc in eqs 5 and 6 is associated with unique relaxation times TI and T2. If the solution contains several species of protons in fast exchange, an "empirical" correlation time "z'; can be calculated based on eqs 5 and 6. We thus calculated "z," from observed values of TI and T2, as shown in our previous study! In genera, for isotropic rotational motion, the NMR correlation time z, is related to the dielectric relaxation time d1as 32, = zd. The 3"2," values are plotted in Figure 6 . The plots lie between the dielectric relaxation times zd of free and bound water, in accord with the assumption of fast exchange occurring between free and bound water. The monoexponential magnetization decay curve indicates that, indeed, the exchange between the free and the bound water is fast, and the extreme narrowing condition is satisfied. However, the TI and Tz values for the same albumin solution are different, with TI > T2. Hence, except for the distilled water, two different "z," values are calculated from TI and T2. Furthermore, the observed correlation time "7'; depends on the albumin concentration (Figure 6 ) . These observations can be reconciled as outlined below. Odajima12 and Sasaki et al.13 found that for water adsorbed on cellulose, TI > T2 under the extreme narrowing condition. They explained their results by the prevalence of a heterogeneous water proton environment. Our results also indicate that TI > T2 under the extreme narrowing condition. To explain our results quantitatively, we interpret the empirical NMR relaxation time obtained for the albumin solutions in terms of the experimentally measured dielectric relaxation times zd, and the 'H translational diffusion coefficient D. The amount of bound water was determined by dielectric experiments to be 150 water molecules per albumin molecule, i.e. 0.039 g of H20/g of albumin.2 These water molecules are considered to be rigidly bound to the albumin molecules. Since the albumin overall rotation is relatively slow, the NMR relaxation rates of bound water protons will be large. The N M R correlation time of bound water, z,(bound), is calculated from the albumin overall rotation, zda, obtained by the TDR method, as z,(bound) = q j 3 . Furthermore, the amount of "unfrozen" water was calculated in a previous NMR study3 to be 0.3 g of HzO/g of albumin. This water fraction is assumed to exchange rapidly with the bound water during NMR signal observation time. We denote it as ex-bound water. As indicated above, the rotational motion of bound water is slow, and therefore the associated NMR relaxation rates are large. The reorientational correlation time of bound water, zb, obtained from the TDR measurements is used to derive the NMR rotational correlation time of ex-bound
434 J. Phys. Chem., Vol. 99, No. 1, 1995
Fukuzaki et al. TABLE 4: NMR Relaxation Time TI and TZCalculated as Weighted Averages of Bound and Free Water Fractions albumin (%) 0 5 10 15 20 1391 895 633 458 TI (ms) 3676 529 264 152 66 TZ(ms) 3676
TABLE 2: NMR Relaxation Time T I and Tz of Bound Water Calculated As Explained in the Text protein overall rotation bound water rotation %
TI, ms
Tz,ms
5
1660 1950 2460 4800
1.79 1.52 1.21 0.62
10 15 20
TI,ms 30.5 31.9 31.0 28.2
T2, ms
24.3 26.3 25.1 20.3
1
TABLE 3: NMR Relaxation Times of Free Water, Tu and Tzf, Calculated from the Rotational and the Translational Motions, As Explained in the Text albumin % rotational motion, s translational motion, s T1f = Tzf,s 0 4.78 15.9 3.68 5 4.67 14.7 3.54 10 4.78 13.5 3.53 15 4.67 12.8 3.42 20 4.67 11.9 3.35
water as z,(ex-bound) = zdb/3. The NMR relaxation times, TI and T2, associated with these bound water states, Tl(bound), Tz(bound), Tl(ex-bound) and T’(ex-bound), were calculated using eqs 5 and 6 and are shown in Table 2. Both translational and rotational diffusion of the free water molecule contribute to the free water NMR relaxation time. The contribution of the translation diffusion to TI of free water, Tldtrans), is given by following equationI4
where y is the gyromagnetic ratio of the proton, h the Plank constant, N the proton concentration ( N = 6.75 x loz2 for water), r the distance between dipole-coupled protons, r = 1.75 x cm,14 and D the translational diffusion coefficient. The free water NMR relaxation time component associated with the rotational motion, Tldrot), is calculated using eqs 4 and 5 with Zc(fiee) = rd43 and r = 1.51 x lo-’ cm.” Under extreme narrowing conditions T2 = TI for the free water and the relaxation rate l/T,(free) is the sum of the translational and rotational components; that is,
--1
-
TI(free)
1
T ,Jtrans)
1 +-TlJrot)
(9)
T,(free) = Tl(free)
(10)
NMR relaxation times of free water calculated from TDR data and the translational diffusion coefficient D are summarized in Table 3. According to the fast exchange model, water molecules interconvert rapidly on the NMR timescale between the bound, ex-bound and free water states. The overall relaxation rate UT, is therefore obtained as the weighted average of the various contributions;
-1_T,
Bbound
T,(bound)
+
Bex-bound
Tl(ex-bound)
+
- Bbound - Bex-bound T, (free) (11)
where Bbound and Bex-bound denote the rigidly bound (as obtained from dielectric measurements) and exchangeably bound water fractions, as described above. Thus, Tl(bound), Tl(ex-bound), and TI(free) denote the NMR relaxation times of each site. The sum of the overall bound water fraction, Bbound Bex-bound, is the amount of the bound water fraction obtained from NMR measurement, Le., 0.3 g of HzO/g of a l b ~ m i n .T2 ~ values are
+
.-cE
9:
f 0
5
10
15
Albumin concentration (
20 OO /
)
Figure 7. NMR relaxation time, TI (0)and TZ(A) calculated from the diffusion coefficient D and the dielectric relaxation times td. The dashed line indicates the calculated N M R relaxation time as a funcion of albumin concentration for td,, q,,td, and D values at a 5 wt % albumin concentration. TI (0)and T2 (A)denote the observed NMR relaxation.
obtained in a similar way. These results are summarized in Table 4 and are illustrated in Figure 7. It can be seen that the calculated TI and T2 values reproduce reasonably well the observed values. In the region of albumin concentration exceeding 15 wt %, we find that the calculated T2 value is shorter than the observed value. This is due to the decrease in the rate of albumin overall rotational reorientation due to aggregation. Since the effect of aggregation on the TDR values zd,, rdb, and t d f is lowest at 5% albumin, we used these TDR values to calculate of the NMR relaxation times as a funcion of albumin concentration. Using the dielectric relaxation parameters and translational diffusion coefficient, we calculated the NMR relaxation times as a function of albumin concentrations. Based on the rationale outlined above, TI > T2 in view of the functional form of eqs 5 and 6 for extreme narrowing. It can be seen that lowfrequency fluctuating field inhomogeneity is more effective in enhancing T2 relaxation. Therefore the long rotational correlation time associated with the overall rotation of albumin dominates the water NMR relaxation time T2 implying that T I > T2. The TDR method can discem between bound and free water. On the other hand, the NMR time scale is too long to separate them and the observed relaxation times are weighted average of these water states. Hence, the amount of “unfrozen” water obtained from N M R measurements includes water exchangeable with the rigidly bound water (such as the Bex-bound fraction), and is therefore larger than that determined by TDR measurement, which reflects solely water bound rigidly to the albumin surface. References and Notes (1) Edsall, J. T.; McKenzie, H. A. Adv. Biophs. 1983, 16, 53. (2) Miura, N.; Asaka, N.; Shinyashiki, N; Mashimo, S . Biopolymer, in press. ( 3 ) Kuntz, I. D.; Kauzman, W. Adv. Protein Chem. 1974, 28, 239. (4) Fukuzaki, M.; Umehara, T.; Kurita, D.; Shioya, S . ; Haida, M.; Mashimo, S. J. Phys. Chem. 1992,96,10087.
Water Relaxation Time in Serum Albumin (5) Farrar,T. C.; Becker, E. D. Pulse and Fourier Transform NMR; Academic Press: New York, 1971; Chapters 2 and 4. (6) Stejskal, E. 0.;Tarrer, T. E. J. Chem. Phys. 1965, 42, 288. (7) Mashimo, S.; Umehara, T.; Ota,T.; Kuwabara, S. Shinyashiki,N.; Yagihara, S.J. Mol. Liq. 1987, 36, 135. (8) Shinyashiki, N.; Asaka, N.; Mashimo, S.; Yagihara, S.; Sasaki, N. Biopolymer 1990,29, 1185. (9) Mashimo, S.; Miura, N.; Shinyashiki,N.; Ota,T. Macromolecules 1993, 26, 6859.
J. Phys. Chem., Vol. 99, No. 1, 1995 435 (10) Bloembergen, N.; b e l l , E. M.; Pound, R. V. Phys. Rev. 1948, 73, 679. (11) Hem, H. G. Water, Feliks F., Ed.; PlenumPress: New York, 1973; Vol. 3, Chapter 7. (12) Odajima, A. J. Phys. SOC.Jpn. 1959, 14, 308. (13) Sasaki, M.; Kawai, T.; &ai, A.; Hayashi, T.; Odajima, A. J. Phys. SOC.Jpn. 1960, 15, 1652. (14) Carrington, A.; McLachlan, A. D. Introduction to magnetic resonance; Chapman and Hall: London, 1967, Chapter 11.
