6337
J. Phys. Chem. 1987, 91, 6337-6338
Dielectric Relaxation Time and Structure of Bound Water in Biological Materials Satoru Mashimo,* Shinichi Kuwabara, Department of Physics, Tokai University, Hiratsuka-shi, Kanagawa 259- 12, Japan
Shin Yagihara, Department of Communications Engineering, Tokai University Junior College, Tokyo Campus, Takanawa, Minato-ku, Tokyo 108, Japan
and Keniti Higasi Science and Engineering Research Laboratory, Waseda University, Okubo, Shinjuku- ku, Tokyo 160, Japan (Received: August 17, 1987)
The dielectric behavior of living tissues and a number of biological materials was examined by new equipment of the time domain reflectometry method in a wide frequency range of 107-1010Hz. We found two peaks of Debye absorption around 100 MHz and 20 GHz for all the materials. The low-frequency absorption is probably due to bound water while the high-frequency absorption to free water. From the observed relaxation times of bound water a hypothesis is ventured on the structure of bound water and its relaxation mechanism.
Introduction The state of knowledge of dielectric relaxation of bound water in biologically important materials is not yet satisfactory.' For a good understanding one would require reliable data quickly obtainable over a wide range of frequencies. The time domain reflectometry method (TDR) introduced in the 1970s was considered extremely useful for this purpose but soon found disappointing because TDR often provided us with inaccurate data. However, in 1980 Cole and his co-workers2 at Brown University succeeded in eliminating most of the weaknesses of TDR, and rapid development of TDR techniques f~llowed.~" In this Letter we report the results of dielectric measurements on a number of living tissues and moist biomaterials by the use of new TDR equipment at Tokai University in a wide frequency range. For all the materials studied we confirmed the existence of two peaks of Debye absorption around 20 GHz and 100 MHz at 20 O C . The former is due to free water and the latter possibly to bound water of the system.'-1° The peak height of an absorption is related to the number of water molecules concerned, and from the relaxation time of the bound water one can form a conjecture on the structure of bound water. Experimental Section The rapid development of the time domain reflectometry method (TDR) in the 1980s has been remarkable. We can now measure dielectric properties of both solid and liquid samples over a wide and high frequency range, 107-10'0 Hz, with high speed (within 1 min) and high accuracy (within a few percent error).*" The details of the equipment used in this work are described in a previous paper? Recently, an improvement of the sample cells has been introduced; an extremely thin and small cell with "zero" (1) Hasted, J. B. Aqueous Dielectrics; Chapman and Hall: London, 1973; pp 198, 205, 235. (2) Cole, R. H.; Mashimo, S.; Winsor IV, P. J . Phys. Chem. 1980,84,786. (3) Winsor IV, P.; Cole, R . H. J . Phys. Chem. 1982, 86, 2486. (4) Imamatsu, K.; Nozaki, R.; Yagihara, S.; Mashimo, S.; Hashimoto, H. J . Chem. Phys. 1986, 84, 6511. (5) Berberian, J. G.; Cole, R. H. J . Chem. Phys. 1986, 84, 6921. (6) Nakamura, H.; Mashimo, S . ; Wada, A. Jpn. J . Appl. Phys. 1982, 21, 467. (7) Takashima, S.; Casaleggio, A,; Giuliano, F.; Morando, M.; Arrigo, P.; Ridella, S . Biophys. J . 1986, 49, 1003. (8) Harvey, S.; Hoekstra, P. J . Phys. Chem. 1972, 76, 2987. (9) Blicharska, B.; Florkowski, 2.;Hennel, J. W.; Held, G . ;Noack, F. Biochim. Biophys. Acta 1970, 207, 38 1. (10) Koenig, S. H.; Schillinger, W. E. J . Biol. Chem. 1969, 244, 3283.
0022-3654/87/2091-6337$01,50/0
TABLE I: Dielectric Relaxation Parameters of Free and Bound Water in Biomaterials at 20 O C lowhighfrequency frequency process process sample Aq T ~ ns , Ach Q,ps living materials 17.9 1.18 15.0 7.1 human skin (36 "C) 1.67 53.5 38.6 10.0 carp (muscle) 11.2 8.88 1.62 65.7 radish 5.44 2.00 9.72 18.6 dogwood 13.2 6.05 1.37 51.7 apple 1.23 69.5 12.0 13.3 tomato 1.36 67.5 13.2 29.8 potato 16.1 1.67 64.6 9.8 egg albumin other materials 31.6 0.98 55.2 12.0 tuna fish (muscle) 34.4 1.34 52.7 14.5 beef (muscle) 32.6 1.39 53.4 13.5 pork (muscle) 31.9 1.21 57.6 13.8 chicken (muscle) 1.12 24.2 11.7 23.5 natural cheese 31.2 1.96 59.8 11.2 boiled egg albumen 20.9 14.8 1.33 48.4 boiled green pea 8.3 human red cell ghost (25 OC, 1.04 1.85 72.3
c,
3.97 4.11 3.93 3.17 4.15 4.12 3.95 3.22 3.24 3.34 3.73 3.34 3.97 4.30 3.24 4.41
0.192 wt %)
homogenized milk biopolymers in aqueous solution DNA (0.5 wt %, from salmon testes, 0.1 SSC buffer) DNA (0.5 wt %, from E . coli, 0.1 SSC buffer) lysozyme (6.01 wt %)
6.26
2.02
70.3
11.5
4.46
2.86
1.38
74.6
9.8
4.76
3.11
1.30
73.1
7.9
4.66
2.46
1.22
73.3
10.0
4.14
length and a very small diameter is connected to the flexible coaxial line. Soft contact of the cell with the surface of the sample gave us sufficiently exact data; further, when the living materials were measured, a small piece of skin was cut off previously and the cell was put just on the bare spot-this was not done in the case of human skin. The dielectric relaxation of biomaterials was measured in this way in vivo, too, for the first time. A step voltage pulse with about 40-ps rise time and 200-mV height, generated by a tunnel diode, passes through a flexible coaxial line (Junko-sha, DGM224, 50 R, dc, 26.5 GHz) to the sample surface on which the applied pulse reflects and returns backwards. The form of the reflected pulse is examined by a sampling scope (Iwatsu, SAS-601B, dc, 12.4 GHz) and digitized by a signal analyzer (Iwatsu, SM2100A, 12 bit, 4096 word^).^ 0 1987 American Chemical Society
6338 The Journal of Physical Chemistry, Vol. 91, No. 25, 1987 ’
0
°
Letters
7
IY’
Y
i
O-H...O-H-.O-H
p
H
_ _ _ _0-H I
(b)
Figure 2. Hydrogen-bond linkage: (a) alcohol, (b) bound water.
l o g f(Hz)
Figure 1. Dielectric dispersions and absorptions of living biomaterials and DNA in 0.1 SSC buffer ( 5 mg/cm3): M, carp; A, human skin; 0, radish; 0 , DNA in 0.1 SSC. Solid, dotted, and broken curves are calculated from eq 3 by using relaxation parameters listed in Table I.
The complex permittivity is given by4 e*
t*
= t’ - jt” of the unknown sample
1 + (cfS)/LMrs)%lP
=
+ liw(rd)tsl/(cfs)P
f, f,
(1)
and p=-
rs - rx
rs + rx where r, is the Fourier transform of the reflected pulse from the standard sample Rs(t),r, is that from the unknown sample R,(t), yd is the effective length of cylindrical cell, el is the known permittivity of the standard sample such as pure water or acetone, j is the imaginary unit, w is the angular frequency, and c is the speed of propagation. The function f is given by
f = z cot
z
(2)
and z =
(Wd/C)d/*
where d is the length of the cell. In this work we used a cell with 2.5-mm diameter and geometrically zero length, and the function f is inferred to take a value nearly equal to the unity.
Results and Discussion In this work we measured living materials such as human skin (arm), muscle of living fish (carp), and radish and found two absorption peaks around 100 M H z and 20 G H z in all of them. Figure 1 shows the dependence of permittivities, e’, and losses, e”, upon logarithms of the frequencies. These two peaks were observed not only in living materials but also in other biomolecules in aqueous solutions and in moist biomaterials. An example of DNA (Escherichia coli in 0.1 SSC buffer) is shown in Figure 1 . Contribution of dc conductivity to the absorption was eliminated from the total absorption in Figure 1. The observed dispersion and absorption curves can be explained as the sum of two Debye relaxations, that is t*
=
em
At1 ++1 1
Ath
~
+jOT1
+jW7h
(3)
where Atl and Ath are the relaxation strengths for the low- and high-frequency processes, respectively, 7 , and 7h are the corresponding relaxation times, respectively, and t, is the high-frequency limiting permittivity. The high-frequency process with the relaxation times of 7.1 ps (human skin) to 18.6 ps (dogwood) is due to free water, while the low-frequency process with the
relaxation times of 0.98 ns (tuna fish) to 2.02 ns (homogenized milk) is possibly” due to bound We report that these two relaxation processes are found in all other biomaterials we examined in this work. All the specimens from human skin to lysozyme solution listed in Table I have two relaxation times of 1.46 f 0.30 ns and 11.7 f 2.6 ps, respectively. Table I records the values of dielectric parameters At,, Ath, T ~ , i-h, and em obtained in this experiment. The high-frequency parameters Ath and Th are somewhat inaccurate because measurements were not possible at frequencies greater than 10 GHz. However, the observed values 7h = 1 1.7 f 2.6 ps for free water compare favorably with the literature values of pure water at 20 OC, viz., 9.56,14 10.1,i5and 12.6 ps.I6 The low-frequency relaxation time for bound water q = 1.46 f 0.30 ns is 125 times larger than 711 and is close to those of straight-chain heptanols in the liquid at 20 OC, viz., 1.38, 1.42, 1.18, and 1.18 ns for heptan- 1-,-2-, -3-, and -4-ols, respectively.” The principal relaxation of alcohol is explained as a cooperative process of [O-H--O] hydrogen bonds in the long-chain alcohol multimer.” (SeeFigure 2a.) Suppose that one of the two 0-H bonds in bound water makes a similar contribution while the remaining 0-H bond is engaged in binding the water molecule to the surface of the protein or biomaterial (Figure 2b). If this hypothesis be correct, the presence of the protein surface in the neighborhood would make T~larger than Th because the relaxation time of primary alcohol becomes larger with increasing chain length; its magnitude depends on the alkyl chain length.i8 For example, heptan-1-01 has a large value of 1.42 ns while methanol and ethanol have values of 73 and 138 ps, respectively.16 Some water molecules having their two 0-H bonds strongly bound to the protein surface would show different behavior from the above. However, their contribution may not be significant because the number of these molecules is not large?9 The dielectric strength At is a rough measure of the water content multiplied by square of its dipole moment.*O If the polarity is not much changed on absorption, the ratio Atl/Ath will be equal to the ratio of water contents, bound to free. And when both water contents are known, we can estimate the dipole moment of bound water from this ratio. (1 1) The dielectric relaxation in this frequency region is assumed to be due to bound water here, but one may point out that some portions of the protein molecules have a sufficient freedom to rotate partially. The latter contributions are ignored in this work due to the following reasons: (1) if they exist, variations in 7, would be much larger than observed, and (2) the observed low-frequency absorptions of 20 biomaterials are of the pure Debye type-this excludes the existence of two or more polar species. (12) Schwan, H. P.; Li, K . Ann. N.Y. Acad. Sci. 1965, 125, 344. (13) (a) Grant, E. H. Ann. N.Y. Acad. Sci. 1965, 125, 148. (b) Grant, E. H. J . Mol. Biol. 1966, 19, 133. (14) Collie, C. H.; Hasted, J. B.; Ritson, D. M. Proc. Phys. SOC.,London 1948, 60, 145. (15) Saxton, J. A. Proc. R . SOC.London 1952, A213, 473. (16) Hill, N. E.; Vaughan, W.; Price, A. H.; Davies, M. Dielectric Propertief and Molecular Behauiour; van Nostrand Reinhold: London, 1969; p 352. (17) Middtlhcek, J.; Bottcher, C. J. F. Molecular Relaxation Processes; The Chemical Society: London, 1966; p 69. (18) Garg, S. K.;Smyth, C. P. J . Phys. Chem. 1965, 69, 1294. (19) Kuntz, I. D.;Kauzmann, W. Adu. Protein Chem. 1974, 28, 239. (20) Reference 13; p 289. Equation 5.5, a relation for dilute solution, is used approximately here.
