- Email: [email protected]
[10] Nuclear magnetic resonance study of water interactions with proteins, biomolecules, membranes, and tissues
[10]
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[10] N u c l e a r M a g n e t i c R e s o n a n c e S t u d y o f W a t e r Interactions with Proteins, Biomolecules, Membranes, and Tissues
By B. M. FUNG Nuclear magnetic resonance (NMR) is a powerful tool in studying the structure and dynamics of chemical and biochemical systems. Some basic aspects of the application of NMR to the study of biomolecules have been reviewed in recent volumes of this series.l Water is the major component of most biological systems. When the proton N M R of a biological sample is studied, the water signal usually dominates the spectrum. The domination of the water signal is advantageous to N M R measurement of water in biological systems. When it is desirable to observe signals due to organic molecules in the system, either D20 is used to replace H20 or the technique of water suppression is applied. The use of special pulse sequences to suppress the water signal in proton N M R in aqueous solutions has been discussed I and a study on whole tissues has been reported recently. 2 In this chapter, we will only be concerned with the NMR study of water in biological systems. In addition to proton (nuclear spin ! = ½), three other nuclei in water avail themselves to NMR experiments. These are deuterium (I = 1), tritium (I = ½), and oxygen-17 (I = )). Tritium NMR of water offers no particular advantage over proton NMR and has rarely been investigated. Deuterium and oxygen-17 have nuclear quadrupole moments and their NMR characteristics are different from those of proton. Because of the low natural abundance and small magnetic moments of deuterium and oxygen-17, enriched water is usually used in the NMR studies of these two isotopes. The general aspects of proton, deuterium, and oxygen-17 NMR of water have been reviewed. 3 There are several parameters of general interest to NMR. These are chemical shifts, intensities, coupling constants, and relaxation times. In most biological systems, the chemical shift of water changes very little with experimental conditions and is not a very informative parameter. A. G. Redfield, this series, Vol. 49, p. 253, p, 359; B. D. Sykes, and W. E. Hull, this series, Vol. 49, p. 270; B. D. Sykes and J. J. Grimaldi, this series, Vol. 49, p. 295; A. S. Mildvan and R. K. Gupta, this series, Vol. 49, p. 322; R. K. Gupta and A. S. Mildvan, this series, Vol. 54, p. 151. 2 C. Artis, M. Bfirfiny, W. M. Westler, and J. L. Markley, J. Magn. Reson. 57, 519 (1984). 3 j. A. Glasel, in "Water, A Comprehensive Treatise" (F. Franks, ed.), Vol. 1, p. 215. Plenum, New York, 1972.
METHODS IN ENZYMOLOGY, VOL. 127
Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.
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The NMR intensity of liquid water can be used to determine the amount of nonfreezable water, 4 but its application is rather limited. In macroscopically ordered systems such as collagen 5 and oriented DNA, 6 the NMR spectra of water show splitting patterns due to nonzero dipolar or quadrupolar coupling. However, there are not many systems that exhibit this behavior. The most widely investigated parameters of water in biological systems are relaxation times, including longitudinal or spin-lattice relaxation time (T1), transverse or spin-spin relaxation time (T2), and spinlattice relaxation time in the rotating frame (Tip). Relaxation times are determined by the rotational and translational correlation times (~-) of a molecule and are useful parameters in the study of molecular motions, molecular dynamics, and molecular interactions. T~ and Tz are given by the following equations 7 and Tip is discussed in detail by Jones. 8 1/T1 = 2K[J(£0) + 4J(2£0)]
(1)
1/T2 = K[3J(0) + 5J(£0) + 2J(2£0)]
(2)
and
where K is a proportionation constant and J(£0) is the spectral density. For isotropic motions with dipolar interaction between two like spins with nuclear spin L for rotation: K = "y4h21(I + 1 ) / 5 r 6
(3)
J(£0) = 1/(1 + £02r 2)
(4)
K = 2 N 7r'y4h2](l + 1)/5RD
(5)
and for translation:
J(£0)
2 fo [(sin u/u) - cos/,/]2 ll 4 + ~o2-~ du
-~
(6)
where 7 is the gyromagnetic ratio, r is the intramolecular distance between two spins, N is the number of spins per unit volume, R is the intermolecular distance between two spins, and D is the diffusion coefficient. The contribution of rotational motion to I/T~ and 1/I"2 is familiar to many investigators, but the contribution of translational relaxation is of4 W. Derbyshire, in "Water, A Comprehensive Treatise" (F. Franks, ed.), Vol. 7, p. 339. Plenum, New York, 1982. 5 C. Migchelsen and H. J. C. Berendsen, J. Chem. Phys. 59, 296 (1973). 6 C. Migchelsen, H. J. C. Berendsen, and A. Rupprecht, J. Mol. Biol. 37, 235 (1968). 7 A. Abragam, "Principles of Nuclear Magnetism." Oxford Univ. Press, London, 1961. 8 G. P. Jones, Phys. Rev. 148, 332 (1966).
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N M R STUDY OF WATER INTERACTIONS
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ten neglected. This does not cause serious problems when deuterium and oxygen-17 relaxation are concerned, but it m a y bring considerable errors to the calculation of p r o t o n relaxation times. The results of Eqs. (1)-(6) are plotted in Fig. 1. A p p r o p r i a t e constants for bulk water at 298°K have b e e n used in Eqs. (3) and (6) for this calculation. It is obvious that the relaxation rates strongly depend on the correlation times. Since interactions b e t w e e n w a t e r and m a c r o m o l e c u l e s change the motional behavior of the w a t e r molecules, relaxation m e a s u r e m e n t s offer important information on the state o f w a t e r in biological systems. H o w e v e r , it must be noted that motions of w a t e r molecules hydrated to macromolecules are not isotropic, and Eqs. (4) and (6) cannot be applied quantitatively. This point will be further discussed below.
10 6
,o,I-
/
10 2
Tm~ o
10°
I,--:
1 0_2
C
10-4
Wor=0.62
10-6 D 10- 8 10-12
10-10
10-8
T,
10-6
10- 4
10-2
sec
FIG. 1. Calculated dipolar relaxation rates with isotropic motions. A, Rotational 1/T2; the dashed line indicates that I/T2 would not further increase in a solid. B, Rotational 1/T~. C, Translational I/T2. D, Translational 1/T~. It is to be noted that the translational and rotational correlation times (r) of a molecule need not be the same.
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Proteins and Biomolecules In an aqueous solution, water molecules hydrated to macromolecules are in rapid exchange with water molecules in the bulk. The relaxation rate is a weighted average of the two fractions of water: 1 x 1-x 7//=~+--~if
'
i = 1,2, lp
(7)
where x is the mole fraction of bound (b) water, and I - x is the fraction of free (f) water, x is usually very small. However, because of slow motions of the macromolecule, T,1, can be reduced from Tif by several orders of magnitude and the overall change in the observed T/can be significant. This change would be very large if the macromolecule contains a bound paramagnetic ion such as Mn 2+ which would lead to enhanced paramagnetic relaxation. In actuality, water molecules hydrated to a macromolecule may have different correlation times and T;b of all the bound water molecules need not be the same. Thus, Eq. (7) is only a simplification. In an N M R study of water in a biological system, the most comprehensive work should include temperature and frequency dependence of the relaxation times of proton, deuterium, and oxygen-17 in the same system. Conventional NMR spectrometers can be used to measure proton T1 and T2 from about 4 to 600 MHz and deuterium and oxygen-17 T1 and T2 from about 4 to 80 MHz. The low-frequency limit is determined by the signal sensitivity and the high-frequency limit is determined by the magnetic field strength available. Tip depends on the Larmor frequency as well as the spin-locking frequency, which is usually in the kHz range. In bulk water, T1 = Tz = Tip for all nuclei, and they are independent of frequency. On the other hand, the three kinds of relaxation times of water in biological systems are usually not the same and often vary considerably with frequency. The results of T1 and/'2 obtained in the high-frequency range cannot be readily extrapolated to frequencies lower than 1 MHz. In order to measure proton and deuterium T1 at low frequencies down to the kHz range, a technique based upon the rapid switching of magnetic field9 can be used, and its principle is briefly described in the following. To create a reasonable difference in the populations of different nuclear spin states for effective NMR measurement, a sample is first " s o a k e d " in a high magnetic field of the order of 1 tesla (T) so that a Boltzmann equilibrium is established. Then, the magnetic field is suddenly reduced to a value of 10-4-10 -1 T. While the spin system tries to 9 F. Noack, in " N M R - - B a s i c Principles and Progress" (P. Diehl, E. Fluck, and R. Kosfeld, eds.), Vol. 3, p. 84. Springer-Verlag, Berlin, 1971.
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N M R STUDY OF WATER INTERACTIONS
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9 0 ° 180° echo
'o
Preparation
Relaxation
Detection
Time FIG. 2. A schematic drawing of the measurement of T~ at low frequencies by rapid switching of magnetic field. See Noack 9 and Bryant et al.~° for detailed description.
reach a new Boltzmann equilibrium at this magnetic field, it undergoes spin-lattice relaxation at the corresponding Larmor frequency to = 2~ru, for which u can be as low as l0 kHz. After the sample has stayed in the low magnetic field for a short time t and before a new equilibrium is established, the field is rapidly switched back to a higher value and the residual magnetization is measured. The magnitude of the detecting field is about 1 T again, but need not be the same as that of the soaking field (Fig. 2). 10By measuring the amplitude of the residual magnetization as a function of t, T~ at the low Larmor frequency can be obtained. This method can be used to study T1 of proton and deuterium, but not T~ of oxygen-17 because the latter is too short and is comparable to the time constant of switching the magnetic field. Application of the field switching technique to measure the frequency dependence of TI over a wide frequency range (relaxation dispersion) is fruitful in studying the nature and motional properties of many chemical and biological systems. 9 In particular, Koenig and co-workers have made extensive studies of relaxation dispersion of water in a number of protein solutions. H In earlier works, it was suggested that the T~ dispersion of water was determined by the rotational correlation time of the macromolecules because 1/1Tib in Eq. (1) dominates the relaxation rate. 12 This is certainly true for deuterium and oxygen-17 because their relaxation rates l0 R. G. Bryant, R. D. Brown III, and S. H. Koenig, Biophys. Chem. 16, 133 (1982). i1 C. F. Brewer, R. D. Brown, and S. H. Koenig, J. Biomol. Struct. Dyn. 1, 961 (1983). 12 S. H. Koenig and W. E. Schillinger, J. Biol. Chem. 244, 3283 (1969).
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WATER, IONS, AND BIOMOLECULES
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are mainly determined by nuclear quadrupole interaction, which depends only on rotational motions. For proton relaxation, the major contribution is the dipolar interaction, which can be intramolecular as well as intermolecular in nature and depends on both rotational and translational motions. It was later recognized that the major relaxation mechanism for water protons in macromolecular systems including protein solutions and biological tissues is the cross-relaxation between protons in water and protons in macromolecules.13-~5 Thus, when it is carefully measured, the longitudinal magnetization decay of protons is not strictly a single exponential function of time. The apparent Tj and T2 are determined by the translational diffusion of water molecules to and fro and along the surfaces of the macromolecules as well as their rotational motions. This is a complex problem and a detailed mathematical model has yet to be formulated. However, even without quantitative treatment of the complete relaxation mechanism, T~ relaxation dispersion still offers the most detailed information on water-protein interaction.
Membranes
A basic characteristic of biological membranes is their permeability to water and ions. The transport of water through cell membranes and the diffusion of water inside the cell can be investigated by NMR along with other methods such as isotope diffusion. The membrane permeability for water diffusion, P, is related to the mean lifetime of water inside the cells, ti, by e = ( V / A ) (I/t0
(8)
where V is the inner cell volume and A is the cell surface area. The lifetime ti can be obtained by NMR using several methods. The most commonly used method is to add MnCI2 into the extracellular space and study Tz of the system. 16Mn2+ is a very effective paramagnetic relaxation ion and causes T2 of water to decrease. Since Mn 2÷ is impermeable to most membranes, the decrease in T2 is limited to that of extracellular water only. T2 of intracellular water is not affected, and the transverse magnetization decay of water in the presence of Mn 2÷ is composed of the sum of two exponentials with time constants Z2a (fast) and T2b (slow), 13 S. H. Koenig, R. G. Bryant, K. Hallinga, and G. S. Jacob, Biochemistry 17, 4348 (1978). 14 H. T. Edzes and E. T. Samulski, Nature (London) 265, 521 (1977); J. Magn. Reson. 31, 207 (1978). 15 B. M. Fung, Biophys. J. 18, 235 (1977). 16 T. Conlon and R. Outhred, Biochim. Biophys. Acta 288, 354 (1972); 511, 418 (1978).
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N M R STUDY OF WATER INTERACTIONS
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respectively. The apparent exchange time, /a, is then obtained from 1 ta
-
1
1
T2b
T2i
(9)
where Tzi is the decay time in isolated cells, t, approaches ti in the limits of low-packed cell volume and high Mn z+ concentration. A concern over the effect of Mn 2+ on the chemical shift of water led to the use of proton TI to determine the exchange rate of water. 17 However, this requires the determination of the longitudinal magnetization over a range of up to 2 × 10 -3, which is usually not accurate in the lower range. A reliable method of measuring the rate constant for water exchange by NMR without the addition of Mn 2+ is to study T1 of oxygen-17 with enriched water. TM T1 of oxygen-17 in cell suspensions is the superposition of two components, and one needs only to measure the longitudinal magnetization within a factor of 10. The method of data analysis is similar to that of T2 measurement, and the results are in good agreement with those using other methods. The rate of water exchange through cell membranes can also be measured by applying pulse field gradients to the sample during the NMR experiment. 19 This will be discussed later. Many investigations have been made on erythrocyte membranes. It has been found that chemicals which modify the membranes affect the permeability of water through the membranes. ~3,16,J7 The permeability decreases in human subjects with certain diseases such as Gaucher's disease and obstructive jaundice.Z° A summary of the results of water permeability for various membranes is given in the table) 1 The self-diffusion coefficient of water inside a cell can also be obtained by NMR. The method is to impose a steady or pulsed magnetic field gradient on the sample inside a homogeneous magnetic field and to observe the change in the amplitude of the spin echo compared to that in the absence of the field gradient. In careful experimental work, the time interval between the field gradient pulses is varied and the results are extrapolated to zero interval. 2z In cases where there is an appreciable amount of extracellular water, such as that in whole blood, an analysis of the amplitude of the spin echo as a function of the time interval between the field gradient pulses can yield the rate of exchange of water through the memo7M. E. Fabry and M. Eisenstadt, Biophys. J. 15, 1101 (1975). is M. Shporer and M. M. Civan, Biochim. Biophys. Acta 385, 81 (1975). 19 j. Andrasko, Biochirn. Biophys. Acta 428, 304 (1976). 2o Gh. Benga, O. Popescu, R. P. Holmes, and V. I. Pop, Bull. Magn. Reson. 5, 265 (1983). 21 H. Degani and M. Avron, Biochim. Biophys. Acta 690, 174 (1982). 22 j. E. Tanner, Biophys. J. 28, 107 (1979).
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WATER PERMEABILITY COEFFICIENT AND ACTIVATION ENERGIES IN VARIOUS CELLS"
System Dunaliella bardawil Dunaliella salina Halobacterium halobium
Human erythrocytes Bovine erythrocytes Dog erythrocytes Chlorella oulgaris Elechea leaf cells Valnia etricularis Nitella translucens
Phosphatidylcholine vesicles
Permeability at 25 °
Energy of activation
(10 -3 c m / s e c )
(kcal/mol)
Method b
1.8 1.5 1.0 2.4-3.2 --2.1 3.0 (20 °) 1.2 -2.9
3.7 3.7 9 5.3-8.7 4.0 3.7 ---8.5 10.5
NMR NMR NMR N M R , ID NMR ID NMR NMR HC HC NMR
a From Degani and Avron 2~ with permission. b ID, isotope diffusion; HC, hydraulic conductivity.
branes. ~9 The result compares favorably with those obtained by other methods. Tissues Since the first report by Bratton et al. on proton T~ and/'2 of water in frog muscle, 23 there have been numerous studies on the relaxation times of water in biological tissues. Many authors have observed that proton T~ and T2 of water are different in different tissues, and they are dependent on the physiological state of the tissue. For example, TI of water protons in skeletal muscle is longer than that in many internal organs. For the same kind of tissue, the neoplastic state and tissue with tumor usually have longer T1 than normal adult tissue. 24 These and many other interesting observations prompted many attempts to interpret the results qualitatively and quantitatively by theories in magnetic relaxation so that better understanding in the significance of the experimental data can be achieved. The most prominent characteristic of the magnetic relaxation of water in tissue is that T~ values of proton, deuteron, and oxygen-17 are all considerably shorter than the corresponding values in bulk water. Furthermore, the TI values are strongly dependent on frequency. ~5,25 Many 23 C. B. Bratton, 24 R. D a m a d i a n , 25 S. H. Koenig, Radiol. 19, 76
A. L. Hopkins, and J. W. Weinberg, N a t u r e (London) 147, 139 (1965). Science 171, 1151 (1971). R. D. B r o w n , III, D. A d a m s , D. Emerson, and C. G. Harrison, Invest. (1984).
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N M R STUDY OF WATER INTERACTIONS
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investigators now agree that these observations can be explained by Eq. (7). The longitudinal relaxation rate of water bound to macromolecules, T~b, is shorter than T~f and is strongly frequency dependent. Tlf is essentially the same as T1 of bulk water and is independent of frequency. The increase in the observed T~ of tumor tissues is due to an increase of the percentage of water content and a corresponding decrease in the fraction of bound water rather than a substantial change in T~b. A different point of view is that a major fraction or all of the cell water is more organized than water in a dilute electrolyte solution, causing the relaxation times of cell water to be shorter than those in bulk water. 24,a6 This interpretation has yet to be substantiated by quantitative treatments of the frequency-dependent proton T~ data and of the differences between Tj and T2 of proton, deuterium, and oxygen-17, as discussed below. Since deuterium and oxygen-17 have nuclear quadrupole moments, their relaxation times are mainly determined by intramolecular interactions. Intermolecular dipole-dipole interaction does not contribute significantly to either T~ or T2 and the translational motions need not be considered. The rotational motions of the bound water molecules, however, are not necessarily isotopic, as described by the spectral density in Eq. (4). When the surface orientation of the bound water molecules is taken into account, the calculated T~ values of deuterium agree reasonably well with experimental data over a frequency range from 103 to 10 7 H z . 27 The case of proton T~ is quite different. Cross-relaxation due to intermolecular dipole-dipole interaction between water and the immobile macromolecules must now be considered. ~3-~5The importance of the contribution of intermolecular interaction to T~ of protons is clearly demonstrated by comparing the ratio of r = T1 (liquid water)/Tj (muscle water) for different nuclei. At a constant frequency of 9.21 MHz, r is essentially the same for deuterium and oxygen-17 over the temperature range of 0 40 °, but r for proton is larger by a factor of 2-2.5.27 The difference is more pronounced at low frequencies. A recent calculation treats the intermolecular dipole-dipole interaction by the formula of isotropic translational motion (Eq. 6) and successfully accounts for proton T~ above 2 MHz. 28 However, when the calculation is extended to lower frequencies (Fig. 3), the result does not agree with experimental data. Obviously, the highly anisotropic nature of the translational motions of the bound water molecules must be considered and a new theory must be developed. Another characteristic of magnetic relaxation of water in biological 26 C. F. Hazlewood, in "Cell-Associated Water" (W. Drost-Hansen, ed.), p. 165. Academic Press, New York, 1979. 27 B. M. Fung and T. W. McGaughy, Biophys. J. 28, 293 (1979). 28 j. M. Escanye, D. Canet, and J. Robert, Biochim. Biophys. Acta 721, 305 (1982), 762, 445 (1983); J. Magn. Reson. 58, 118 (1984).
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30
O
O
7
O
20
O
c
O
10
B
A
I
I
I
I
L
I
5.0 x 10- 3 -112
I
I
I
1.0 x 10 - 2
sec-1/2
FIG. 3. Dispersion of proton spin-lattice relaxation rate of water in muscle. The experimental data are from Ref. 15 and the solid lines are calculated. A, Rotational contribution calculated by multiplying the appropriate proportionation constant to the deuterium data given in Ref. 15. B, Isotropic translational contribution calculated from Eqs. (1), (5), and (6) with ~" = 5 x 10-8 sec, as suggested in Escanye et al. 28 C, Sum of A and B. The deviation of curve C from experimental data at low frequencies indicates the anisotropic nature of the translational motion of bound water molecules.
tissues is that the transverse magnetizations of proton and deuterium do not exhibit exponential decay as a function of time. An earlier interpretation is that the T2 curve is a superposition of two terms, those due to intracellular water and extracellular water, respectively. 29-31 This interpretation has been disputed based upon the following evidences32: (1) When the proton and deuteron curves are analyzed in terms of the sums of two exponentials, the weighting factors are different for the two nuclei. If the two-compartment interpretation were correct, this would mean that the proton data correspond to 5-10% extracellular water and the deuteron data correspond to 30-40% extracellular water, which are clearly incom29 p. S. Belton, R. R. Jackson, and K. J. Packer, Biochim. Biophys. Acta 286, 16 (1972). 30 C. F. Hazlewood, D. C. Chang, B. L. Nichols, and D. E. Woessner, Biophys. J. 14, 583 (1974). 31 K. F. Foster, J. A. Resing, and A. N. Garroway, Science 194, 324 (1976). 32 B. M. Fung and P. S. Puon, Biophys. J. 33, 27 (1981).
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N M R STUDY OF WATER INTERACTIONS
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patible results. (2) The T2 nonexponentiality increases with postmortem rigor. (3) When muscle is glycerinated to disrupt the cell membranes, the nonexponential behavior of T2 persists, and it increases with decreasing pH. (4) The nonexponentiality changes with the orientation of the muscle fiber with respect to the magnetic field and is smallest at 0 = 55 °. (5) The lifetime of the water molecules can be calculated from the rate of diffusion of water through cell membranes; the value is far shorter than that predicted by the two-exponential theory. In short, the nonexponential behavior of T2 cannot be attributed to slow exchange between intracellular water and extracellular water. A different explanation which is consistent with all these observations has been given. 32 T2 of both proton and deuterium are affected by the hydrogen exchange between water and the amino groups in the immobilized proteins. The latter has nonzero dipolar (for proton) or quadrupolar (for deuteron) splitting. The result of hydrogen exchange with intermediate rates would indeed render the transverse magnetization decay to be nonexponential. It is interesting to note that the ratios of T2(apparent)/Tl (apparent) are essentially the same for proton and deuterium in muscle from 0 to 40°C, but that for oxygen-17 is larger by a factor of 4-5. Since the relaxation of oxygen-17 is not appreciably affected by hydrogen exchange, it shows normal /'2 which can be predicted from the TI value at the same frequency. 32 On the other hand, T2(apparent)/T6apparent) for proton and deuterium are much smaller because T2 values of these two nuclei are affected by hydrogen exchange between water and proteins. An important application of the study of magnetic relaxation in tissues is magnetic resonance imaging (MRI). This technique is based upon the detection of in vivo NMR signals, often in the presence of magnetic field gradients. Proton is the most common nucleus studied, but P-31 is also of interest. Since water in different tissues has different relaxation times, careful programming of radiofrequency and field gradient pulses plus sophisticated data processing can produce clear images of various parts of the body. Abnormalities in tissues and organs can be detected at an early stage and MRI may be very useful in clinical diagnosis. The reader is referred to specialized monographs on this subject. 33-35
33 L. Kaufman, L. E. Crooks, and A. R. Margulis (eds.), "Nuclear Magnetic Resonance Imaging in Medicine." Igaku-Shoin, New York, 1981. 34 p. Mansfield and P. G. Morris, Adv. Magn. Reson. (Suppl. 2), 1 (1982). 35 A. Margulis, C. Higgins, L. Kaufman, and L. E. Crooks (eds.), "Clinical Magnetic Resonance Imaging." Univ. of California Press, San Francisco, 1983.
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[10] N u c l e a r M a g n e t i c R e s o n a n c e S t u d y o f W a t e r Interactions with Proteins, Biomolecules, Membranes, and Tissues
By B. M. FUNG Nuclear magnetic resonance (NMR) is a powerful tool in studying the structure and dynamics of chemical and biochemical systems. Some basic aspects of the application of NMR to the study of biomolecules have been reviewed in recent volumes of this series.l Water is the major component of most biological systems. When the proton N M R of a biological sample is studied, the water signal usually dominates the spectrum. The domination of the water signal is advantageous to N M R measurement of water in biological systems. When it is desirable to observe signals due to organic molecules in the system, either D20 is used to replace H20 or the technique of water suppression is applied. The use of special pulse sequences to suppress the water signal in proton N M R in aqueous solutions has been discussed I and a study on whole tissues has been reported recently. 2 In this chapter, we will only be concerned with the NMR study of water in biological systems. In addition to proton (nuclear spin ! = ½), three other nuclei in water avail themselves to NMR experiments. These are deuterium (I = 1), tritium (I = ½), and oxygen-17 (I = )). Tritium NMR of water offers no particular advantage over proton NMR and has rarely been investigated. Deuterium and oxygen-17 have nuclear quadrupole moments and their NMR characteristics are different from those of proton. Because of the low natural abundance and small magnetic moments of deuterium and oxygen-17, enriched water is usually used in the NMR studies of these two isotopes. The general aspects of proton, deuterium, and oxygen-17 NMR of water have been reviewed. 3 There are several parameters of general interest to NMR. These are chemical shifts, intensities, coupling constants, and relaxation times. In most biological systems, the chemical shift of water changes very little with experimental conditions and is not a very informative parameter. A. G. Redfield, this series, Vol. 49, p. 253, p, 359; B. D. Sykes, and W. E. Hull, this series, Vol. 49, p. 270; B. D. Sykes and J. J. Grimaldi, this series, Vol. 49, p. 295; A. S. Mildvan and R. K. Gupta, this series, Vol. 49, p. 322; R. K. Gupta and A. S. Mildvan, this series, Vol. 54, p. 151. 2 C. Artis, M. Bfirfiny, W. M. Westler, and J. L. Markley, J. Magn. Reson. 57, 519 (1984). 3 j. A. Glasel, in "Water, A Comprehensive Treatise" (F. Franks, ed.), Vol. 1, p. 215. Plenum, New York, 1972.
METHODS IN ENZYMOLOGY, VOL. 127
Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.
152
WATER, IONS, AND BIOMOLECULES
[10]
The NMR intensity of liquid water can be used to determine the amount of nonfreezable water, 4 but its application is rather limited. In macroscopically ordered systems such as collagen 5 and oriented DNA, 6 the NMR spectra of water show splitting patterns due to nonzero dipolar or quadrupolar coupling. However, there are not many systems that exhibit this behavior. The most widely investigated parameters of water in biological systems are relaxation times, including longitudinal or spin-lattice relaxation time (T1), transverse or spin-spin relaxation time (T2), and spinlattice relaxation time in the rotating frame (Tip). Relaxation times are determined by the rotational and translational correlation times (~-) of a molecule and are useful parameters in the study of molecular motions, molecular dynamics, and molecular interactions. T~ and Tz are given by the following equations 7 and Tip is discussed in detail by Jones. 8 1/T1 = 2K[J(£0) + 4J(2£0)]
(1)
1/T2 = K[3J(0) + 5J(£0) + 2J(2£0)]
(2)
and
where K is a proportionation constant and J(£0) is the spectral density. For isotropic motions with dipolar interaction between two like spins with nuclear spin L for rotation: K = "y4h21(I + 1 ) / 5 r 6
(3)
J(£0) = 1/(1 + £02r 2)
(4)
K = 2 N 7r'y4h2](l + 1)/5RD
(5)
and for translation:
J(£0)
2 fo [(sin u/u) - cos/,/]2 ll 4 + ~o2-~ du
-~
(6)
where 7 is the gyromagnetic ratio, r is the intramolecular distance between two spins, N is the number of spins per unit volume, R is the intermolecular distance between two spins, and D is the diffusion coefficient. The contribution of rotational motion to I/T~ and 1/I"2 is familiar to many investigators, but the contribution of translational relaxation is of4 W. Derbyshire, in "Water, A Comprehensive Treatise" (F. Franks, ed.), Vol. 7, p. 339. Plenum, New York, 1982. 5 C. Migchelsen and H. J. C. Berendsen, J. Chem. Phys. 59, 296 (1973). 6 C. Migchelsen, H. J. C. Berendsen, and A. Rupprecht, J. Mol. Biol. 37, 235 (1968). 7 A. Abragam, "Principles of Nuclear Magnetism." Oxford Univ. Press, London, 1961. 8 G. P. Jones, Phys. Rev. 148, 332 (1966).
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N M R STUDY OF WATER INTERACTIONS
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ten neglected. This does not cause serious problems when deuterium and oxygen-17 relaxation are concerned, but it m a y bring considerable errors to the calculation of p r o t o n relaxation times. The results of Eqs. (1)-(6) are plotted in Fig. 1. A p p r o p r i a t e constants for bulk water at 298°K have b e e n used in Eqs. (3) and (6) for this calculation. It is obvious that the relaxation rates strongly depend on the correlation times. Since interactions b e t w e e n w a t e r and m a c r o m o l e c u l e s change the motional behavior of the w a t e r molecules, relaxation m e a s u r e m e n t s offer important information on the state o f w a t e r in biological systems. H o w e v e r , it must be noted that motions of w a t e r molecules hydrated to macromolecules are not isotropic, and Eqs. (4) and (6) cannot be applied quantitatively. This point will be further discussed below.
10 6
,o,I-
/
10 2
Tm~ o
10°
I,--:
1 0_2
C
10-4
Wor=0.62
10-6 D 10- 8 10-12
10-10
10-8
T,
10-6
10- 4
10-2
sec
FIG. 1. Calculated dipolar relaxation rates with isotropic motions. A, Rotational 1/T2; the dashed line indicates that I/T2 would not further increase in a solid. B, Rotational 1/T~. C, Translational I/T2. D, Translational 1/T~. It is to be noted that the translational and rotational correlation times (r) of a molecule need not be the same.
154
WATER, IONS, AND BIOMOLECULES
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Proteins and Biomolecules In an aqueous solution, water molecules hydrated to macromolecules are in rapid exchange with water molecules in the bulk. The relaxation rate is a weighted average of the two fractions of water: 1 x 1-x 7//=~+--~if
'
i = 1,2, lp
(7)
where x is the mole fraction of bound (b) water, and I - x is the fraction of free (f) water, x is usually very small. However, because of slow motions of the macromolecule, T,1, can be reduced from Tif by several orders of magnitude and the overall change in the observed T/can be significant. This change would be very large if the macromolecule contains a bound paramagnetic ion such as Mn 2+ which would lead to enhanced paramagnetic relaxation. In actuality, water molecules hydrated to a macromolecule may have different correlation times and T;b of all the bound water molecules need not be the same. Thus, Eq. (7) is only a simplification. In an N M R study of water in a biological system, the most comprehensive work should include temperature and frequency dependence of the relaxation times of proton, deuterium, and oxygen-17 in the same system. Conventional NMR spectrometers can be used to measure proton T1 and T2 from about 4 to 600 MHz and deuterium and oxygen-17 T1 and T2 from about 4 to 80 MHz. The low-frequency limit is determined by the signal sensitivity and the high-frequency limit is determined by the magnetic field strength available. Tip depends on the Larmor frequency as well as the spin-locking frequency, which is usually in the kHz range. In bulk water, T1 = Tz = Tip for all nuclei, and they are independent of frequency. On the other hand, the three kinds of relaxation times of water in biological systems are usually not the same and often vary considerably with frequency. The results of T1 and/'2 obtained in the high-frequency range cannot be readily extrapolated to frequencies lower than 1 MHz. In order to measure proton and deuterium T1 at low frequencies down to the kHz range, a technique based upon the rapid switching of magnetic field9 can be used, and its principle is briefly described in the following. To create a reasonable difference in the populations of different nuclear spin states for effective NMR measurement, a sample is first " s o a k e d " in a high magnetic field of the order of 1 tesla (T) so that a Boltzmann equilibrium is established. Then, the magnetic field is suddenly reduced to a value of 10-4-10 -1 T. While the spin system tries to 9 F. Noack, in " N M R - - B a s i c Principles and Progress" (P. Diehl, E. Fluck, and R. Kosfeld, eds.), Vol. 3, p. 84. Springer-Verlag, Berlin, 1971.
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N M R STUDY OF WATER INTERACTIONS
155
9 0 ° 180° echo
'o
Preparation
Relaxation
Detection
Time FIG. 2. A schematic drawing of the measurement of T~ at low frequencies by rapid switching of magnetic field. See Noack 9 and Bryant et al.~° for detailed description.
reach a new Boltzmann equilibrium at this magnetic field, it undergoes spin-lattice relaxation at the corresponding Larmor frequency to = 2~ru, for which u can be as low as l0 kHz. After the sample has stayed in the low magnetic field for a short time t and before a new equilibrium is established, the field is rapidly switched back to a higher value and the residual magnetization is measured. The magnitude of the detecting field is about 1 T again, but need not be the same as that of the soaking field (Fig. 2). 10By measuring the amplitude of the residual magnetization as a function of t, T~ at the low Larmor frequency can be obtained. This method can be used to study T1 of proton and deuterium, but not T~ of oxygen-17 because the latter is too short and is comparable to the time constant of switching the magnetic field. Application of the field switching technique to measure the frequency dependence of TI over a wide frequency range (relaxation dispersion) is fruitful in studying the nature and motional properties of many chemical and biological systems. 9 In particular, Koenig and co-workers have made extensive studies of relaxation dispersion of water in a number of protein solutions. H In earlier works, it was suggested that the T~ dispersion of water was determined by the rotational correlation time of the macromolecules because 1/1Tib in Eq. (1) dominates the relaxation rate. 12 This is certainly true for deuterium and oxygen-17 because their relaxation rates l0 R. G. Bryant, R. D. Brown III, and S. H. Koenig, Biophys. Chem. 16, 133 (1982). i1 C. F. Brewer, R. D. Brown, and S. H. Koenig, J. Biomol. Struct. Dyn. 1, 961 (1983). 12 S. H. Koenig and W. E. Schillinger, J. Biol. Chem. 244, 3283 (1969).
156
WATER, IONS, AND BIOMOLECULES
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are mainly determined by nuclear quadrupole interaction, which depends only on rotational motions. For proton relaxation, the major contribution is the dipolar interaction, which can be intramolecular as well as intermolecular in nature and depends on both rotational and translational motions. It was later recognized that the major relaxation mechanism for water protons in macromolecular systems including protein solutions and biological tissues is the cross-relaxation between protons in water and protons in macromolecules.13-~5 Thus, when it is carefully measured, the longitudinal magnetization decay of protons is not strictly a single exponential function of time. The apparent Tj and T2 are determined by the translational diffusion of water molecules to and fro and along the surfaces of the macromolecules as well as their rotational motions. This is a complex problem and a detailed mathematical model has yet to be formulated. However, even without quantitative treatment of the complete relaxation mechanism, T~ relaxation dispersion still offers the most detailed information on water-protein interaction.
Membranes
A basic characteristic of biological membranes is their permeability to water and ions. The transport of water through cell membranes and the diffusion of water inside the cell can be investigated by NMR along with other methods such as isotope diffusion. The membrane permeability for water diffusion, P, is related to the mean lifetime of water inside the cells, ti, by e = ( V / A ) (I/t0
(8)
where V is the inner cell volume and A is the cell surface area. The lifetime ti can be obtained by NMR using several methods. The most commonly used method is to add MnCI2 into the extracellular space and study Tz of the system. 16Mn2+ is a very effective paramagnetic relaxation ion and causes T2 of water to decrease. Since Mn 2÷ is impermeable to most membranes, the decrease in T2 is limited to that of extracellular water only. T2 of intracellular water is not affected, and the transverse magnetization decay of water in the presence of Mn 2÷ is composed of the sum of two exponentials with time constants Z2a (fast) and T2b (slow), 13 S. H. Koenig, R. G. Bryant, K. Hallinga, and G. S. Jacob, Biochemistry 17, 4348 (1978). 14 H. T. Edzes and E. T. Samulski, Nature (London) 265, 521 (1977); J. Magn. Reson. 31, 207 (1978). 15 B. M. Fung, Biophys. J. 18, 235 (1977). 16 T. Conlon and R. Outhred, Biochim. Biophys. Acta 288, 354 (1972); 511, 418 (1978).
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N M R STUDY OF WATER INTERACTIONS
157
respectively. The apparent exchange time, /a, is then obtained from 1 ta
-
1
1
T2b
T2i
(9)
where Tzi is the decay time in isolated cells, t, approaches ti in the limits of low-packed cell volume and high Mn z+ concentration. A concern over the effect of Mn 2+ on the chemical shift of water led to the use of proton TI to determine the exchange rate of water. 17 However, this requires the determination of the longitudinal magnetization over a range of up to 2 × 10 -3, which is usually not accurate in the lower range. A reliable method of measuring the rate constant for water exchange by NMR without the addition of Mn 2+ is to study T1 of oxygen-17 with enriched water. TM T1 of oxygen-17 in cell suspensions is the superposition of two components, and one needs only to measure the longitudinal magnetization within a factor of 10. The method of data analysis is similar to that of T2 measurement, and the results are in good agreement with those using other methods. The rate of water exchange through cell membranes can also be measured by applying pulse field gradients to the sample during the NMR experiment. 19 This will be discussed later. Many investigations have been made on erythrocyte membranes. It has been found that chemicals which modify the membranes affect the permeability of water through the membranes. ~3,16,J7 The permeability decreases in human subjects with certain diseases such as Gaucher's disease and obstructive jaundice.Z° A summary of the results of water permeability for various membranes is given in the table) 1 The self-diffusion coefficient of water inside a cell can also be obtained by NMR. The method is to impose a steady or pulsed magnetic field gradient on the sample inside a homogeneous magnetic field and to observe the change in the amplitude of the spin echo compared to that in the absence of the field gradient. In careful experimental work, the time interval between the field gradient pulses is varied and the results are extrapolated to zero interval. 2z In cases where there is an appreciable amount of extracellular water, such as that in whole blood, an analysis of the amplitude of the spin echo as a function of the time interval between the field gradient pulses can yield the rate of exchange of water through the memo7M. E. Fabry and M. Eisenstadt, Biophys. J. 15, 1101 (1975). is M. Shporer and M. M. Civan, Biochim. Biophys. Acta 385, 81 (1975). 19 j. Andrasko, Biochirn. Biophys. Acta 428, 304 (1976). 2o Gh. Benga, O. Popescu, R. P. Holmes, and V. I. Pop, Bull. Magn. Reson. 5, 265 (1983). 21 H. Degani and M. Avron, Biochim. Biophys. Acta 690, 174 (1982). 22 j. E. Tanner, Biophys. J. 28, 107 (1979).
158
WATER, IONS, AND BIOMOLECULES
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WATER PERMEABILITY COEFFICIENT AND ACTIVATION ENERGIES IN VARIOUS CELLS"
System Dunaliella bardawil Dunaliella salina Halobacterium halobium
Human erythrocytes Bovine erythrocytes Dog erythrocytes Chlorella oulgaris Elechea leaf cells Valnia etricularis Nitella translucens
Phosphatidylcholine vesicles
Permeability at 25 °
Energy of activation
(10 -3 c m / s e c )
(kcal/mol)
Method b
1.8 1.5 1.0 2.4-3.2 --2.1 3.0 (20 °) 1.2 -2.9
3.7 3.7 9 5.3-8.7 4.0 3.7 ---8.5 10.5
NMR NMR NMR N M R , ID NMR ID NMR NMR HC HC NMR
a From Degani and Avron 2~ with permission. b ID, isotope diffusion; HC, hydraulic conductivity.
branes. ~9 The result compares favorably with those obtained by other methods. Tissues Since the first report by Bratton et al. on proton T~ and/'2 of water in frog muscle, 23 there have been numerous studies on the relaxation times of water in biological tissues. Many authors have observed that proton T~ and T2 of water are different in different tissues, and they are dependent on the physiological state of the tissue. For example, TI of water protons in skeletal muscle is longer than that in many internal organs. For the same kind of tissue, the neoplastic state and tissue with tumor usually have longer T1 than normal adult tissue. 24 These and many other interesting observations prompted many attempts to interpret the results qualitatively and quantitatively by theories in magnetic relaxation so that better understanding in the significance of the experimental data can be achieved. The most prominent characteristic of the magnetic relaxation of water in tissue is that T~ values of proton, deuteron, and oxygen-17 are all considerably shorter than the corresponding values in bulk water. Furthermore, the TI values are strongly dependent on frequency. ~5,25 Many 23 C. B. Bratton, 24 R. D a m a d i a n , 25 S. H. Koenig, Radiol. 19, 76
A. L. Hopkins, and J. W. Weinberg, N a t u r e (London) 147, 139 (1965). Science 171, 1151 (1971). R. D. B r o w n , III, D. A d a m s , D. Emerson, and C. G. Harrison, Invest. (1984).
[10]
N M R STUDY OF WATER INTERACTIONS
159
investigators now agree that these observations can be explained by Eq. (7). The longitudinal relaxation rate of water bound to macromolecules, T~b, is shorter than T~f and is strongly frequency dependent. Tlf is essentially the same as T1 of bulk water and is independent of frequency. The increase in the observed T~ of tumor tissues is due to an increase of the percentage of water content and a corresponding decrease in the fraction of bound water rather than a substantial change in T~b. A different point of view is that a major fraction or all of the cell water is more organized than water in a dilute electrolyte solution, causing the relaxation times of cell water to be shorter than those in bulk water. 24,a6 This interpretation has yet to be substantiated by quantitative treatments of the frequency-dependent proton T~ data and of the differences between Tj and T2 of proton, deuterium, and oxygen-17, as discussed below. Since deuterium and oxygen-17 have nuclear quadrupole moments, their relaxation times are mainly determined by intramolecular interactions. Intermolecular dipole-dipole interaction does not contribute significantly to either T~ or T2 and the translational motions need not be considered. The rotational motions of the bound water molecules, however, are not necessarily isotopic, as described by the spectral density in Eq. (4). When the surface orientation of the bound water molecules is taken into account, the calculated T~ values of deuterium agree reasonably well with experimental data over a frequency range from 103 to 10 7 H z . 27 The case of proton T~ is quite different. Cross-relaxation due to intermolecular dipole-dipole interaction between water and the immobile macromolecules must now be considered. ~3-~5The importance of the contribution of intermolecular interaction to T~ of protons is clearly demonstrated by comparing the ratio of r = T1 (liquid water)/Tj (muscle water) for different nuclei. At a constant frequency of 9.21 MHz, r is essentially the same for deuterium and oxygen-17 over the temperature range of 0 40 °, but r for proton is larger by a factor of 2-2.5.27 The difference is more pronounced at low frequencies. A recent calculation treats the intermolecular dipole-dipole interaction by the formula of isotropic translational motion (Eq. 6) and successfully accounts for proton T~ above 2 MHz. 28 However, when the calculation is extended to lower frequencies (Fig. 3), the result does not agree with experimental data. Obviously, the highly anisotropic nature of the translational motions of the bound water molecules must be considered and a new theory must be developed. Another characteristic of magnetic relaxation of water in biological 26 C. F. Hazlewood, in "Cell-Associated Water" (W. Drost-Hansen, ed.), p. 165. Academic Press, New York, 1979. 27 B. M. Fung and T. W. McGaughy, Biophys. J. 28, 293 (1979). 28 j. M. Escanye, D. Canet, and J. Robert, Biochim. Biophys. Acta 721, 305 (1982), 762, 445 (1983); J. Magn. Reson. 58, 118 (1984).
160
WATER, IONS, AND BIOMOLECULES
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30
O
O
7
O
20
O
c
O
10
B
A
I
I
I
I
L
I
5.0 x 10- 3 -112
I
I
I
1.0 x 10 - 2
sec-1/2
FIG. 3. Dispersion of proton spin-lattice relaxation rate of water in muscle. The experimental data are from Ref. 15 and the solid lines are calculated. A, Rotational contribution calculated by multiplying the appropriate proportionation constant to the deuterium data given in Ref. 15. B, Isotropic translational contribution calculated from Eqs. (1), (5), and (6) with ~" = 5 x 10-8 sec, as suggested in Escanye et al. 28 C, Sum of A and B. The deviation of curve C from experimental data at low frequencies indicates the anisotropic nature of the translational motion of bound water molecules.
tissues is that the transverse magnetizations of proton and deuterium do not exhibit exponential decay as a function of time. An earlier interpretation is that the T2 curve is a superposition of two terms, those due to intracellular water and extracellular water, respectively. 29-31 This interpretation has been disputed based upon the following evidences32: (1) When the proton and deuteron curves are analyzed in terms of the sums of two exponentials, the weighting factors are different for the two nuclei. If the two-compartment interpretation were correct, this would mean that the proton data correspond to 5-10% extracellular water and the deuteron data correspond to 30-40% extracellular water, which are clearly incom29 p. S. Belton, R. R. Jackson, and K. J. Packer, Biochim. Biophys. Acta 286, 16 (1972). 30 C. F. Hazlewood, D. C. Chang, B. L. Nichols, and D. E. Woessner, Biophys. J. 14, 583 (1974). 31 K. F. Foster, J. A. Resing, and A. N. Garroway, Science 194, 324 (1976). 32 B. M. Fung and P. S. Puon, Biophys. J. 33, 27 (1981).
[10]
N M R STUDY OF WATER INTERACTIONS
161
patible results. (2) The T2 nonexponentiality increases with postmortem rigor. (3) When muscle is glycerinated to disrupt the cell membranes, the nonexponential behavior of T2 persists, and it increases with decreasing pH. (4) The nonexponentiality changes with the orientation of the muscle fiber with respect to the magnetic field and is smallest at 0 = 55 °. (5) The lifetime of the water molecules can be calculated from the rate of diffusion of water through cell membranes; the value is far shorter than that predicted by the two-exponential theory. In short, the nonexponential behavior of T2 cannot be attributed to slow exchange between intracellular water and extracellular water. A different explanation which is consistent with all these observations has been given. 32 T2 of both proton and deuterium are affected by the hydrogen exchange between water and the amino groups in the immobilized proteins. The latter has nonzero dipolar (for proton) or quadrupolar (for deuteron) splitting. The result of hydrogen exchange with intermediate rates would indeed render the transverse magnetization decay to be nonexponential. It is interesting to note that the ratios of T2(apparent)/Tl (apparent) are essentially the same for proton and deuterium in muscle from 0 to 40°C, but that for oxygen-17 is larger by a factor of 4-5. Since the relaxation of oxygen-17 is not appreciably affected by hydrogen exchange, it shows normal /'2 which can be predicted from the TI value at the same frequency. 32 On the other hand, T2(apparent)/T6apparent) for proton and deuterium are much smaller because T2 values of these two nuclei are affected by hydrogen exchange between water and proteins. An important application of the study of magnetic relaxation in tissues is magnetic resonance imaging (MRI). This technique is based upon the detection of in vivo NMR signals, often in the presence of magnetic field gradients. Proton is the most common nucleus studied, but P-31 is also of interest. Since water in different tissues has different relaxation times, careful programming of radiofrequency and field gradient pulses plus sophisticated data processing can produce clear images of various parts of the body. Abnormalities in tissues and organs can be detected at an early stage and MRI may be very useful in clinical diagnosis. The reader is referred to specialized monographs on this subject. 33-35
33 L. Kaufman, L. E. Crooks, and A. R. Margulis (eds.), "Nuclear Magnetic Resonance Imaging in Medicine." Igaku-Shoin, New York, 1981. 34 p. Mansfield and P. G. Morris, Adv. Magn. Reson. (Suppl. 2), 1 (1982). 35 A. Margulis, C. Higgins, L. Kaufman, and L. E. Crooks (eds.), "Clinical Magnetic Resonance Imaging." Univ. of California Press, San Francisco, 1983.