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Biological systems in high magnetic field
43
Journal of Magnetism arid Magnetic Materials 90 & 91 (1990) 43-46 North-Holland
Invited paper
Biological systems in high magnetic field A. Yamagishi Research Center for Extreme Materials. Osaka University. Toyonaka, Osaka 560. Japan Diamagnetic orientation of biological systems have been investigated theoretically and experimentally. Fibrinogen, one of blood proteins, were polymerized in static high magnetic fields up to 8 T. Clotted gels composed of oriented fibrin fibers were obtained even in a field as low as 1 T. Red blood cells (RBC) show full orientation with their plane parallel to the applied field of 4 T . It is confirmed experimentally that the magnetic orientation of RBe is caused by diamagnetic anisotropy. Full orientation is also obtained with blood platelet in a field of 3 T.
1. Magnetic orientation of diamagnetic materials
The magnetic field effect on biological systems are widely expected and many experimental results have been reported in various fields such as physics, physiology, chemistry, morphology and so on. However, only a very small number of them seems to be clear and true. From a physical point of view, one of the clear effects is magnetic orientation of biological systems . In 1855 Faraday found diamagnetism with wood, ivory, beef, mutton, etc. [1]. However, it was the middle of the 20 century that the diamagnetic anisotropy of biological systems such as celIulosic materials were reported [2,3]. Since then variety of biological materials have been investigated in magnetic fields. Table 1 shows
the properties of typical biological systems. These materials have diamagnetic anisotropies except the sickle cell which has the paramagnetic anisotropy. As shown in the table, large biological systems composed of a number of small diagmagnetic molecules are easily oriented with low magnetic fields. This is physically understood as follows. Consider a rod like molecule with the anisotropic diamagnetic susceptibilities XII and X.!. along' the parallel and perpendicular directions to the molecule, respectively. The field induced energy U is given by [5,8].
(1) where t:.X = XII - X.!. and 8 is the angle between Hand
Table 1 Magnetic orientations of biological materials Sample
(M.W.] or size ( .... m)
tJ.X (emu/sample)
n.; (T)
peptide benzene fibrinogen DNA tobacco mosaic virus(TMV) purple membrane chlorella blood platelet red blood cell sickle cell polyethylene a) lecithin a) stearic acid a) fibrin fiber collagen fibril actin fibril retinal rod muscle fiber
[>40] [80] [3.4 X lOS) [4Xl0 6 ] [4XI0 7 ) 0.02" xO.3 0.5" X 0.005 3-10" 2"Xl 7.5"x2.5 5"x14 16x11 xO.l 36x18xO.l [(284)] I"Xl00
9XIO- JO 1 X 10- 28 2.5 X 10- 27 10- 24 1.5 X 10- 25
35 35 14 13
[(4.2 X 10 4 ) ] 7"x50 6X3X3 (mm)
1.2xI0- 18 10- 20 1.2xl0- 21 ax 10- 22 2.7xl0- 18 7xl0- 19 6.5xI0- 18 (5 X 10- 29 ) 2.5 X 10- 20 (10- 31) 2.4xlO- 8 1.2 X 10- 9
lIfT): maximum applied fields, H,: fields for full orientation,
0304-8853/9O/S03.50
«)
a
u, (T)
>14
2 3 8 8 0.5
1.7 1 3 4 < 0.3
0.5
< 0.5
8 13 13 1.4 0.3
1 1.9 <10 <1.4 <0.3
Ref. [4] (5) [6-8] [9] [10] [11] [12] this work thi s work [13] (14) [14] (2) [6-8) [15] [16] [17] 13]
single crystal, ( ): values for monomers or single molecules.
1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation
A . }''amagishi / Biological systems in high magnetic field
44
h
1.0
E v
....
ClI
ClI
E
~ 05 •
III Q.
.... ClI U
....
0
2
"
Magnetic Field
6
8
(T)
Fig. 1. Theoretically calculated order parameter (m) as a function of magnetic field intensity for various N, the number of aggregated molecules. liX is assumed to be 2.5 X 10- 27 emu/molecule, which is the value of fibrinogen molecule.
the molecular axis. The order parameter (111) = (3cos 20 - 1)/2 is written as
{(3cos10 -1) exp( - U/kT) sin 0 dO (111)
=
(2)
0
2[exp( - U/kT) sin 0 dO
o
where kT is the thermal energy. When N molecules aggregate with their diamagnetic principal axe s along the field direction, AX should be replaced by NAX so that large anisotropic diamagnetic energy is expected when N becomes large as biological systems shown in table 1. Fig. 1 shows the field dependence of the order parameter for various values of N, where AX = 2.5 X 10- 27 (emu/molecule) is assumed. Fig. 1 shows that high orientation is expected even in a low field as 1 T when 107 molecules are aggregated with their axes in one direction. It is important to measure the value of order parameter (111), that is, the degree of orientation, for qualitative and quantitative discussions of the phenomena. 2. Polymerization of fibrin in magnetic fields Fibrinogen, one of the plasma proteins, is known to polymerize into fibrin fiber and the magnetic-field effect on the polymerization has been reported [5-7]. A superconducting magnet with inner bore of 60 mm at room temperature is used for the exp eriment. Experimental set-up is shown elsewhere [8]. Polymerized gels are dehydrated and observed by a scanning electron microscope (SEM). Examples of SEM images arc shown
H Fig. 2. Electron microscopicphotograph of fibrin gels clotted with and without magnetic fields.
A. Yamagishi / Biological systems in high magnetic field
45 H= 8T
1.0
6
c
4
~1.1 c::
o
IV
2
a
c
III III
~
~Q5
E
III
c ~I.O
.....
0.5
1
Han
2
I,
Magnetic Field
6
8
Ssec
(T)
Fig. 3. Field dependence of degree of orientation of fibrin fibers.
in fig. 2. In a field of 8 T, fully oriented gels are obtained while gels polymerized without field are consisted of completely tangled fibers. As shown in fig. 2, even in a field as low as 1 T, partially oriented gels were obtained as expected from fig. 1. Fig. 3 shows a field dependence of the degree of orientation of polymerized fibers, which was obtained by analyzing polarization of light transmitted through samples. Field dependence of the degree of orientation may depend on the experimental conditions such as concentrations of fibrinogen and Ca + ion, pH, etc. In this experiment, 40% orientation is attained in a field of 1 T as seen in fig. 3. 3. Blood cells in magnetic fields Blood cells are freely movable and rotatable in the human body and their bilayer membrane are composed of a number of lipid molecules which have anisotropic diamagnetism. When a cell has anisotropic shape, magnetic anisotropy is expected as a whole cell. Here we show magnetic orientation of red blood cells (RBC) and blood platelet (BP). Red blood cell has the shape of biconcave disk with diameter of about 7.5 flm and thickness of about 2.5 urn. It contains hemoglobin which is diamagnetic in the oxygenated state (cells in an artery) and paramagnetic in the deoxygenated state (cells in a vein). Because of the oblate shape, the projected area of the cell changes depending on the tilting angle so that degree of orientation is monitored by observing optical transmission of the cell suspension. Red blood cells are suspended in an isotonic saline solution with the concentration of about 5000 cellymrrr' which is low enough to get a linear concentration dependence of light transmission. This concentration gives us enough signal to noise ratio and easy transformation of light transmission into the order
Time
Fig. 4. Time dependence of optical transmission of the red blood cell (RBC) suspension for various field strength. The concentration of RBC is 5000 cellsyrnnr', Samples were set into magnetic fields at the time of lion and taken out at the time of Ilo l l '
parameter (m). Experiment is carried out using the superconducting magnet and the same set-up as fibrin polymerization (8). An example of optical transmission measurements for various field strength is shown in fig. 4. When the sample is set in the magnetic fields (Hon ) ' transmission increases with field-dependent time constants. While the sample is taken out the fields (Ho rt ) ' transmission decreases with a time constant determined by viscosity of suspension, cell size and its shape. These characteristics are analyzed theoretically and well explained quantitatively with reasonable values of constants for viscosity, diamagnetic anisotropy and cell size. For the observation by optical microscope, jelly was added into suspension and the sample is coagulated in a field of 8 T.
el.O
...
°
E
s... 0.5 ro
R.B.C. Exp. {O axy • deoxy
...
Theory - (t."
""0
=8.2xI0"22 emu/cell )
o
o
2
4 Magnetic
Field
Fig. 5. Magnetic orientation of oxy- and deoxy-RBC which contains diamagnetic and paramagnetic hemoglobins, respectively.
A. Yamagishi / Biological systems in high magn etic field
46
Microphotographs show all cells were aligned with their disk plane parallel to the field direction. Fig. 5 shows the order parameter, calculated from optical transmission, as a function of magnetic field for two kinds of RBC's with oxy- and deoxy-hemoglobin. No significant differences are found between data for both RBC's and it means that magnetic orientation of RBC is caused only by diamagnetic susceptibility. Comparing these data with the theoretical curve, the diamagnetic anisotropy of RBC is determined as 8X = 8.2 X 10- 22 emu/cell. The origin of anisotropic diamagnetism 8X may come from protein and lipid molecules. However, the former is considered to be randomly directed in the cell so that its contribution seems 'fo be small. While lecithin, typical phospholipid molecule in membranes, has diamagnetic anisotropy of 8X = 7 X 10",,9 emu [18] and a number of them are aggregated to make a bilayer membrane with their long hydrocarbon chains normal to the membrane surface. For the calculation of 8X, we assume RBC to be a disk with a concentric hole and its outer diameter, thickness, hole diameter and its depth to be 7.5, 2.5, 2 and 211m, respectively. Calculated 8X of RBC is 1 X 10- 21 emu/cell. This is compared with the experimental value, 8X = 0.8 X 10- 21 emu/cell. They show good agreement in spite of rough estimation so that it may be concluded that 8X of RBC is mainly contributed by membrane lipid molecules. This is also in agreement with the optical microscopic observation because lipid molecules tend to orient normal to the field (14). A blood platelet normally has the shape of a disk with thickness of about 0.5 11m and diameter of about 2-3 11m. Fig. 6 shows the experiernental result of magnetic orientation of blood platelets. Comparing data with theoretical curve, 8X = 1.2 X 10- 21 emu/cell . is obtained. The value is larger than that of RBC even though it has smaller volume than RBe. 8X of a whole
" 1.0
E v
...G.o
G.o
Blood
E ... 05
t'll
~
Platelet
Exp.
.
0
Theory
...
(6Xo
QI
---21
::1.2xIO
ernu/cel l )
'0 L-
a
o
2
MagnE:'tic
4
6 Field
(T)
Fig. 6. Magnetic orientation of blood platelet.
8
blood platelet is calculated to be 0.2 X 10- 21 emu/cell by assuming a disk-shape with diameter of 2.5 11m and thickness of 0.5 Jim. The difference between measured and calculated 8X'S would come from protein filaments in the cell.
4. Conclusion It is stres sed here that aggregation of a number of diamagnetically anisotropic molecules with their axes in one direction is essential to attain high degree of diamagnetic orientation. Such aggregation is universally found in the biological systems like fibers, membranes and so on. Even in a low field as 1 T, magnetic orientation will take place as shown for the fibrin polymerization. By further investigations of various biological materials in high magnetic fields, the magnetic field effects on biology will be revealed more clearly.
I am very grateful to Profs. M. Date and T. Higashi for their enthusiasm and useful discussions and I thank T. Takeuchi for assistance. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture. References [1J M. Faraday, Exp. Res. Elect. (London) 3 (1855) 27. [2J K. Londsdale, Proc. Soc. London Ser. A 171 (1939) 541. [3J W. Arnold, R. Steele and H. Mueller. Proc. Natl. Acad. Sci. USA 44 (1958) 1. [4J L. Pauling. Proc. Natl. Acad . Sci. USA 76 (1979) 2293. [5J A. Yarnagishi , E. Nagao and M. Date, J. Phys. Soc. Jpn. 53 (1984) 928. [6J J. Torbct, Biochem. 25 (1986) 5309. [7J A. Yarnagishi, T. Takeuchi, M. Date and T. Higashi, Physica B 155 (1989) 433. [8J A. Yamagishi, T. Takeuchi, T. Higashi and M. Date, J. Phys. Soc. Jpn. 58 (1989) 2280. [9J G. Maret and G. Well. Biopolymers 22 (1983) 2727. [lOJ S. Fradcn, G. Maret, D.L.D. Caspar and R.B. Meyer, Phys. Rev. Lett. 63 (1989) 2068. [l1J D.-Ch . Neugebauer, A.E. B1aurock and D.L. Worcester. FEBS Lett. 78 (1977) 31. [12J N.E. Geacintov, F. Van Nostrand. J.F. Becker and J.B. Tinkel, Biochim. Biophys. Acta 267 (1972) 65. [13J P.e. Ribeiro, M.A. Davidovich , E. Wajnbcrg, G. Bemski and M. Kischinevsky, Biophys. J. 36 (1981) 443. [14J I. Sakurai, Y. Kawamura, A. lkegami and S. lwayanagi, Proc. Natl. Acad. Sci. USA 77 (1980) 7232. [15J J. Torbet and M.e. Ronziere, Biochem. J. 219 (1984) 1057. [16J J. Torbet and MJ. Dickens, FEBS Lett . 173 (1984) 403. [17J M. Chabre, Proc. Natl. Acad . Sci. USA 75 (1978) 5471. [18J e. Rosenblatt, P. Yager and P.E. Schoen. Biophys. J. 52 (1987) 295.
Journal of Magnetism arid Magnetic Materials 90 & 91 (1990) 43-46 North-Holland
Invited paper
Biological systems in high magnetic field A. Yamagishi Research Center for Extreme Materials. Osaka University. Toyonaka, Osaka 560. Japan Diamagnetic orientation of biological systems have been investigated theoretically and experimentally. Fibrinogen, one of blood proteins, were polymerized in static high magnetic fields up to 8 T. Clotted gels composed of oriented fibrin fibers were obtained even in a field as low as 1 T. Red blood cells (RBC) show full orientation with their plane parallel to the applied field of 4 T . It is confirmed experimentally that the magnetic orientation of RBe is caused by diamagnetic anisotropy. Full orientation is also obtained with blood platelet in a field of 3 T.
1. Magnetic orientation of diamagnetic materials
The magnetic field effect on biological systems are widely expected and many experimental results have been reported in various fields such as physics, physiology, chemistry, morphology and so on. However, only a very small number of them seems to be clear and true. From a physical point of view, one of the clear effects is magnetic orientation of biological systems . In 1855 Faraday found diamagnetism with wood, ivory, beef, mutton, etc. [1]. However, it was the middle of the 20 century that the diamagnetic anisotropy of biological systems such as celIulosic materials were reported [2,3]. Since then variety of biological materials have been investigated in magnetic fields. Table 1 shows
the properties of typical biological systems. These materials have diamagnetic anisotropies except the sickle cell which has the paramagnetic anisotropy. As shown in the table, large biological systems composed of a number of small diagmagnetic molecules are easily oriented with low magnetic fields. This is physically understood as follows. Consider a rod like molecule with the anisotropic diamagnetic susceptibilities XII and X.!. along' the parallel and perpendicular directions to the molecule, respectively. The field induced energy U is given by [5,8].
(1) where t:.X = XII - X.!. and 8 is the angle between Hand
Table 1 Magnetic orientations of biological materials Sample
(M.W.] or size ( .... m)
tJ.X (emu/sample)
n.; (T)
peptide benzene fibrinogen DNA tobacco mosaic virus(TMV) purple membrane chlorella blood platelet red blood cell sickle cell polyethylene a) lecithin a) stearic acid a) fibrin fiber collagen fibril actin fibril retinal rod muscle fiber
[>40] [80] [3.4 X lOS) [4Xl0 6 ] [4XI0 7 ) 0.02" xO.3 0.5" X 0.005 3-10" 2"Xl 7.5"x2.5 5"x14 16x11 xO.l 36x18xO.l [(284)] I"Xl00
9XIO- JO 1 X 10- 28 2.5 X 10- 27 10- 24 1.5 X 10- 25
35 35 14 13
[(4.2 X 10 4 ) ] 7"x50 6X3X3 (mm)
1.2xI0- 18 10- 20 1.2xl0- 21 ax 10- 22 2.7xl0- 18 7xl0- 19 6.5xI0- 18 (5 X 10- 29 ) 2.5 X 10- 20 (10- 31) 2.4xlO- 8 1.2 X 10- 9
lIfT): maximum applied fields, H,: fields for full orientation,
0304-8853/9O/S03.50
«)
a
u, (T)
>14
2 3 8 8 0.5
1.7 1 3 4 < 0.3
0.5
< 0.5
8 13 13 1.4 0.3
1 1.9 <10 <1.4 <0.3
Ref. [4] (5) [6-8] [9] [10] [11] [12] this work thi s work [13] (14) [14] (2) [6-8) [15] [16] [17] 13]
single crystal, ( ): values for monomers or single molecules.
1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation
A . }''amagishi / Biological systems in high magnetic field
44
h
1.0
E v
....
ClI
ClI
E
~ 05 •
III Q.
.... ClI U
....
0
2
"
Magnetic Field
6
8
(T)
Fig. 1. Theoretically calculated order parameter (m) as a function of magnetic field intensity for various N, the number of aggregated molecules. liX is assumed to be 2.5 X 10- 27 emu/molecule, which is the value of fibrinogen molecule.
the molecular axis. The order parameter (111) = (3cos 20 - 1)/2 is written as
{(3cos10 -1) exp( - U/kT) sin 0 dO (111)
=
(2)
0
2[exp( - U/kT) sin 0 dO
o
where kT is the thermal energy. When N molecules aggregate with their diamagnetic principal axe s along the field direction, AX should be replaced by NAX so that large anisotropic diamagnetic energy is expected when N becomes large as biological systems shown in table 1. Fig. 1 shows the field dependence of the order parameter for various values of N, where AX = 2.5 X 10- 27 (emu/molecule) is assumed. Fig. 1 shows that high orientation is expected even in a low field as 1 T when 107 molecules are aggregated with their axes in one direction. It is important to measure the value of order parameter (111), that is, the degree of orientation, for qualitative and quantitative discussions of the phenomena. 2. Polymerization of fibrin in magnetic fields Fibrinogen, one of the plasma proteins, is known to polymerize into fibrin fiber and the magnetic-field effect on the polymerization has been reported [5-7]. A superconducting magnet with inner bore of 60 mm at room temperature is used for the exp eriment. Experimental set-up is shown elsewhere [8]. Polymerized gels are dehydrated and observed by a scanning electron microscope (SEM). Examples of SEM images arc shown
H Fig. 2. Electron microscopicphotograph of fibrin gels clotted with and without magnetic fields.
A. Yamagishi / Biological systems in high magnetic field
45 H= 8T
1.0
6
c
4
~1.1 c::
o
IV
2
a
c
III III
~
~Q5
E
III
c ~I.O
.....
0.5
1
Han
2
I,
Magnetic Field
6
8
Ssec
(T)
Fig. 3. Field dependence of degree of orientation of fibrin fibers.
in fig. 2. In a field of 8 T, fully oriented gels are obtained while gels polymerized without field are consisted of completely tangled fibers. As shown in fig. 2, even in a field as low as 1 T, partially oriented gels were obtained as expected from fig. 1. Fig. 3 shows a field dependence of the degree of orientation of polymerized fibers, which was obtained by analyzing polarization of light transmitted through samples. Field dependence of the degree of orientation may depend on the experimental conditions such as concentrations of fibrinogen and Ca + ion, pH, etc. In this experiment, 40% orientation is attained in a field of 1 T as seen in fig. 3. 3. Blood cells in magnetic fields Blood cells are freely movable and rotatable in the human body and their bilayer membrane are composed of a number of lipid molecules which have anisotropic diamagnetism. When a cell has anisotropic shape, magnetic anisotropy is expected as a whole cell. Here we show magnetic orientation of red blood cells (RBC) and blood platelet (BP). Red blood cell has the shape of biconcave disk with diameter of about 7.5 flm and thickness of about 2.5 urn. It contains hemoglobin which is diamagnetic in the oxygenated state (cells in an artery) and paramagnetic in the deoxygenated state (cells in a vein). Because of the oblate shape, the projected area of the cell changes depending on the tilting angle so that degree of orientation is monitored by observing optical transmission of the cell suspension. Red blood cells are suspended in an isotonic saline solution with the concentration of about 5000 cellymrrr' which is low enough to get a linear concentration dependence of light transmission. This concentration gives us enough signal to noise ratio and easy transformation of light transmission into the order
Time
Fig. 4. Time dependence of optical transmission of the red blood cell (RBC) suspension for various field strength. The concentration of RBC is 5000 cellsyrnnr', Samples were set into magnetic fields at the time of lion and taken out at the time of Ilo l l '
parameter (m). Experiment is carried out using the superconducting magnet and the same set-up as fibrin polymerization (8). An example of optical transmission measurements for various field strength is shown in fig. 4. When the sample is set in the magnetic fields (Hon ) ' transmission increases with field-dependent time constants. While the sample is taken out the fields (Ho rt ) ' transmission decreases with a time constant determined by viscosity of suspension, cell size and its shape. These characteristics are analyzed theoretically and well explained quantitatively with reasonable values of constants for viscosity, diamagnetic anisotropy and cell size. For the observation by optical microscope, jelly was added into suspension and the sample is coagulated in a field of 8 T.
el.O
...
°
E
s... 0.5 ro
R.B.C. Exp. {O axy • deoxy
...
Theory - (t."
""0
=8.2xI0"22 emu/cell )
o
o
2
4 Magnetic
Field
Fig. 5. Magnetic orientation of oxy- and deoxy-RBC which contains diamagnetic and paramagnetic hemoglobins, respectively.
A. Yamagishi / Biological systems in high magn etic field
46
Microphotographs show all cells were aligned with their disk plane parallel to the field direction. Fig. 5 shows the order parameter, calculated from optical transmission, as a function of magnetic field for two kinds of RBC's with oxy- and deoxy-hemoglobin. No significant differences are found between data for both RBC's and it means that magnetic orientation of RBC is caused only by diamagnetic susceptibility. Comparing these data with the theoretical curve, the diamagnetic anisotropy of RBC is determined as 8X = 8.2 X 10- 22 emu/cell. The origin of anisotropic diamagnetism 8X may come from protein and lipid molecules. However, the former is considered to be randomly directed in the cell so that its contribution seems 'fo be small. While lecithin, typical phospholipid molecule in membranes, has diamagnetic anisotropy of 8X = 7 X 10",,9 emu [18] and a number of them are aggregated to make a bilayer membrane with their long hydrocarbon chains normal to the membrane surface. For the calculation of 8X, we assume RBC to be a disk with a concentric hole and its outer diameter, thickness, hole diameter and its depth to be 7.5, 2.5, 2 and 211m, respectively. Calculated 8X of RBC is 1 X 10- 21 emu/cell. This is compared with the experimental value, 8X = 0.8 X 10- 21 emu/cell. They show good agreement in spite of rough estimation so that it may be concluded that 8X of RBC is mainly contributed by membrane lipid molecules. This is also in agreement with the optical microscopic observation because lipid molecules tend to orient normal to the field (14). A blood platelet normally has the shape of a disk with thickness of about 0.5 11m and diameter of about 2-3 11m. Fig. 6 shows the experiernental result of magnetic orientation of blood platelets. Comparing data with theoretical curve, 8X = 1.2 X 10- 21 emu/cell . is obtained. The value is larger than that of RBC even though it has smaller volume than RBe. 8X of a whole
" 1.0
E v
...G.o
G.o
Blood
E ... 05
t'll
~
Platelet
Exp.
.
0
Theory
...
(6Xo
QI
---21
::1.2xIO
ernu/cel l )
'0 L-
a
o
2
MagnE:'tic
4
6 Field
(T)
Fig. 6. Magnetic orientation of blood platelet.
8
blood platelet is calculated to be 0.2 X 10- 21 emu/cell by assuming a disk-shape with diameter of 2.5 11m and thickness of 0.5 Jim. The difference between measured and calculated 8X'S would come from protein filaments in the cell.
4. Conclusion It is stres sed here that aggregation of a number of diamagnetically anisotropic molecules with their axes in one direction is essential to attain high degree of diamagnetic orientation. Such aggregation is universally found in the biological systems like fibers, membranes and so on. Even in a low field as 1 T, magnetic orientation will take place as shown for the fibrin polymerization. By further investigations of various biological materials in high magnetic fields, the magnetic field effects on biology will be revealed more clearly.
I am very grateful to Profs. M. Date and T. Higashi for their enthusiasm and useful discussions and I thank T. Takeuchi for assistance. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture. References [1J M. Faraday, Exp. Res. Elect. (London) 3 (1855) 27. [2J K. Londsdale, Proc. Soc. London Ser. A 171 (1939) 541. [3J W. Arnold, R. Steele and H. Mueller. Proc. Natl. Acad. Sci. USA 44 (1958) 1. [4J L. Pauling. Proc. Natl. Acad . Sci. USA 76 (1979) 2293. [5J A. Yarnagishi , E. Nagao and M. Date, J. Phys. Soc. Jpn. 53 (1984) 928. [6J J. Torbct, Biochem. 25 (1986) 5309. [7J A. Yarnagishi, T. Takeuchi, M. Date and T. Higashi, Physica B 155 (1989) 433. [8J A. Yamagishi, T. Takeuchi, T. Higashi and M. Date, J. Phys. Soc. Jpn. 58 (1989) 2280. [9J G. Maret and G. Well. Biopolymers 22 (1983) 2727. [lOJ S. Fradcn, G. Maret, D.L.D. Caspar and R.B. Meyer, Phys. Rev. Lett. 63 (1989) 2068. [l1J D.-Ch . Neugebauer, A.E. B1aurock and D.L. Worcester. FEBS Lett. 78 (1977) 31. [12J N.E. Geacintov, F. Van Nostrand. J.F. Becker and J.B. Tinkel, Biochim. Biophys. Acta 267 (1972) 65. [13J P.e. Ribeiro, M.A. Davidovich , E. Wajnbcrg, G. Bemski and M. Kischinevsky, Biophys. J. 36 (1981) 443. [14J I. Sakurai, Y. Kawamura, A. lkegami and S. lwayanagi, Proc. Natl. Acad. Sci. USA 77 (1980) 7232. [15J J. Torbet and M.e. Ronziere, Biochem. J. 219 (1984) 1057. [16J J. Torbet and MJ. Dickens, FEBS Lett . 173 (1984) 403. [17J M. Chabre, Proc. Natl. Acad . Sci. USA 75 (1978) 5471. [18J e. Rosenblatt, P. Yager and P.E. Schoen. Biophys. J. 52 (1987) 295.