J. Phys. Chem. 1996, 100, 2183-2188
2183
Oscillation of Membrane Potential in Chemically Modified Poly(r-amino acid) Membranes Akon Higuchi* and Mariko Hara Department of Industrial Chemistry, Faculty of Engineering, Seikei UniVersity, 3 Kichijoji Kita-machi, Musashino, Tokyo 180, Japan ReceiVed: June 12, 1995; In Final Form: September 21, 1995X
Chemically modified poly(γ-methyl-L-glutamate) membranes having several lengths of diamine segments generated oscillation of membrane potential under a concentration gradient of several salts, although nonmodified membranes showed constant potential. The oscillation of membrane potential is considered to be caused by the fluctuation of the fixed charge density originating from the thermal fluctuation of partially ionized amine segments in the modified membranes. The amplitude of the oscillation was greater in the modified membranes having longer diamine segments. It was also influenced by the salts used, and the highest amplitude of the oscillation was observed when LiCl was used as the salt. Fast Fourier transport analysis revealed that the oscillation of membrane potential is not chaotic but has specific frequencies. It might be possible to recognize a particular salt present in the solution from the information on the amplitude and the power spectrum of fast Fourier transport in the oscillation of membrane potential.
Introduction
SCHEME 1
Bio-oscillation is of vital importance in biophysics and physical chemistry. Pulsating and oscillatory phenomena are frequently observed in cells and living membranes.1-6 Receptor stimulation by several agonists7-9 or epidermal growth factor10 generates a pulsating release of calcium ion from intracellular stores.11 The fluctuations in intracellular calcium ion concentration cause periodic activation of ion channels,12,13 and spontaneous oscillation in membrane potential originating from the fluctuation of the calcium ion concentration has been generally observed.14-17 Stelling and Jacob13 recently reported the spontaneous oscillation of membrane potential in single pigmented epithelial cells which does not depend on an external agonist. Several kinds of artificial membranes18-26 which induce the oscillation of membrane potential have been developed as simple models of cells and living membranes, because it is rather difficult to investigate the physicochemical mechanism of excitation and oscillation in cells and living membranes. Most of the artificial membranes18-23 studied are bimolecular lipid or liquid membranes; there are only a few studies dealing with electrical oscillatory phenomena in artificial polymeric membranes.24-26 Shashoua24 observed spontaneous oscillations in a polyelectrolyte membrane formed by interfacial precipitation of poly(glutamic acid) and polylysine in an electric field. Huang and Spangler25 studied a poly(glutamic acid)-Ca2+ membrane in order to clarify the dynamic behavior of the electrical oscillation and proposed a model for the oscillation phenomena. Minoura et al.26 observed spontaneous oscillation of the electrical membrane potential in a triblock copolypeptide membrane separating KCl solutions of different concentrations. The oscillation of the membrane potential measured in the polymeric membranes provides reproducible data which are suitable for considering and investigating the physicochemical mechanism of excitation and oscillation in the artificial membranes. The present paper investigates the oscillation phenomena of membrane potential in chemically modified poly(γ-methyl-Lglutamate) membranes having several lengths of diamine segments. * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-2183$12.00/0
Experimental Section Materials. Poly(γ-methyl-L-glutamate), PMLG, was kindly supplied by Ajinomoto Co., Inc., and was purified by precipitation from 5 wt % dichloroethane in methanol. Other chemicals were of reagent grade and were used without further purification. Ultrapure water was used throughout the experiments. Chemical Modification of Membranes. PMLG membranes were prepared by casting 1 wt % PMLG solution onto flat Petri dishes and then drying at room temperature for 6 days. The PMLG membranes were subsequently dried under vacuum at room temperature for 24 h. The membranes having a thickness of 30-35 µm were selected to be used for the chemically modified reaction in this study. The reaction of aminolysis27 of the PMLG membranes (i.e., Scheme 1) was performed by dipping the membranes in ethylenediamine (EDA), 1,3-diaminopropane (DAP), 1,4-diaminobutane (DAB), and hexamethylenediamine (HMD) at 25 °C (in the cases of EDA and DAP reaction) or 50 °C (in the cases of DAB and HMD reaction) for 0-12 h. All of the modified membranes were rinsed with ethanol and subsequently dried and stored under vacuum at room temperature. Colorimetric Analysis of Ninhydrin Reaction. The modified membranes were immersed in 1.4 × 10-4 M ninhydrin solution for 5 min at 95 °C, subsequently washed with ultrapure water, and dried under vacuum at room temperature for 24 h. The absorbance of the membranes was measured with a UVvis spectrophotometer (Ubest V-550, JASCO Corp.). SEM and EPMA Measurements. SEM and EPMA measurements were performed with JEOL JSM 5200 (JEOL Co.) and EDX (JED-2100, JEOL Co.). Measurement of Membrane Potential. The membrane potential, ∆φ, was measured in cells that consisted of two © 1996 American Chemical Society
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Figure 1. Dependence of the substitution ratio of EDA (O), DAP (0), DAB (b) and HMD (9) segments on the reaction time in the aminolysis reaction of PMLG membranes.
chambers separated by the membranes.28-30 The concentrations of the aqueous salt solutions were 1 mM in one side of the chamber (side 1), C1, and 0.1 mM to 1 M in the other side of the chamber (side 0), C0. The revolution speed of magnetic spinbars in the cells was controlled (i.e., 230 rpm in this study) by magnetic stirrers. The potential was measured using a digital multimeter (Model 7561, Yokogawa Electronic Co.) with Ag/ AgCl electrodes (TOA HS-205C, TOA Electronics Ltd.), and the data were transferred to a 32-bit personal computer (PC9801BX, NEC Corp.).28-30 The pH in the cell was monitored with a pH meter (TOA HM-30S, TOA Electronics Ltd.) and was adjusted to pH 2-10 with the introduction of 0.01 M HCl or NaOH solution into the cells. The membrane potentials were measured when the pH in the cell reflected the desired pH based on a pH variation of (0.01 for 10 min. The solution in the cell was replaced with ultrapure water several times after each set of measurements. Each of the membranes is capable of withstanding more than 50 measurements over a 3 month period. Figures 4-9 show typical curves which were selected from at least five measurements performed under the same conditions. Results and Discussion Aminolysis Reaction of PMLG. The aminolysis reaction on PMLG membranes with EDA, DAP, DAB, and HMD is shown in Scheme 1. The degree of the substitution ratio in the aminolysis reaction was controlled by the dipping time of the membranes in the diamine solution. The degree of the substitution ratio was estimated from atomic analysis of the membranes, and the dependence of the degree of the substitution ratio on reaction time is shown in Figure 1. The degree of aminolysis was found to increase with increasing reaction time from the atomic analysis of the membranes. Colorimetric Analysis. It is known that the amount of free amine residue can be determined from colorimetric analysis using the ninhydrin reaction in the peptide solution.31 The ninhydrin reaction with the modified membranes was heterogeneously performed to estimate the amount of amine on the surface of the modified membranes qualitatively. The absorption spectra of the membranes reacted with the ninhydrin solution showed two peaks having λmax ) 420 and 570 nm. The relationship between the absorbance of the membranes at λ ) 570 nm, and the degree of substitution ratio was investigated and is shown in Figure 2. The absorbance of the membranes was found to increase with an increasing degree of substitution ratio in the aminolysis reaction. The ninhydrin reaction with the membranes in the reaction time of 5 min can be considered to occur on the surface of the membranes, because
Higuchi and Hara
Figure 2. Relationship between the absorbance of the modified membranes at λ ) 570 nm reacted with the ninhydrin solution and the degree of the substitution ratio of EDA (O), DAP (0), DAB (b), and HMD (9) segments.
the permeation of ninhydrin through the membranes is considered to be extremely low. If the aminolysis reaction in the membranes occurred heterogeneously (i.e., only near the surface) and the reacted layer with ninhydrin in the membranes increased with increasing reaction time of the aminolysis, the absorbance of the membranes after the ninhydrin reaction should show more or less a constant value and would give different values depending on the different diamines. However, Figures 1 and 2 show that the degree of aminolysis on the surface increases with increasing reaction time of the aminolysis. It is found that the degree of aminolysis was almost the same value for membranes reacted with four different diamines but having the same degree of aminolysis. EPMA Spectra. EPMA spectra for a cross-section of modified (HMD-PMLG-3) and nonmodified PMLG membranes were investigated and are shown in Figure 3. HMD-PMLG-X refers to the modified membranes reacted with HMD for X h. Both modified and nonmodified membranes were immersed in 0.1 M NaCl solution for 12 h and subsequently rinsed with pure water for 6 h before EPMA measurements. In Figure 3, the concentration of chloride is observed to be higher than the background and remains constant at any point inside the membranes in the HMD-PMLG-3 membrane, while no chloride is found in the cross-section of the nonmodified PMLG membranes. This indicates that the amine segments exist homogeneously inside the HMD-PMLG-3 membrane, although the chemical modification of the membrane was performed heterogeneously. It is suggested that the diamines permeate through the membrane swollen with the diamines in the aminolysis reaction of the membranes, and the aminolysis reaction, therefore, occurs homogeneously inside the membranes having a thickness of 3035 µm in this study. Oscillation of Membrane Potential. The time course of the membrane potential was investigated in PMLG membranes at C0 ) 0.1 M NaCl, C1 ) 1mM NaCl, pH ) 2-10 and 25 °C and is shown in Figure 4. Nonmodified PMLG membranes show a constant potential within (0.5 mV variation and can be considered to show no oscillation at pH ) 2-10. The membranes are also found not to show oscillation of the membrane potential at C0 ) 10-4 to 1 M and C1 ) 1 mM (which is not shown here). The time course of the membrane potential was investigated in the HMD-PMLG-6 membrane at C0 ) 0.1 M NaCl, C1 ) 1 mM NaCl, 25 °C, and pH ) 2-10 and is shown in Figure 5. The membrane potential is observed to generate spontaneous oscillation at pH ) 8 and 10, and the amplitude of oscillation
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Figure 3. EPMA (EDX) spectra for the cross section of a nonmodified PMLG membrane (a) and an HMD-PMLG-3 membrane (b). The bar indicates 10 µm.
is found to be greater at higher pH. The apparent ionization constant (pKa) of a side chain in lysine is known to be 10.53,32 and the pKa of ethylenediamine is reported to be 6.84 and 9.96.33 The pKa of the diamine segments in the modified membranes is estimated to be 9.5-10.5. Supposing that the pKa of the diamine segments in HMD-PMLG membranes is 10.0, the nonionized amine is calculated to be 10-6 % at pH ) 2, 10-4 % at pH ) 4, 10-2% at pH ) 6, 1% at pH ) 8, and 50% at pH ) 10. These results indicate that perfect dissociation of amine on the modified segments is not favorable for the oscillation of membrane potential, because the ionic repulsion and stretched conformation of the side segments in the membranes having completely ionized amine segments reduce the random and flexible movements of the ionized amine segments. Fluctuation
of partially ionized amine segments due to the thermal oscillation of the amine segments is considered to be the origin of oscillation. The membrane potential is generally expressed by the Teorell-Meyer-Sievers (TMS) theory:34-39
∆φ ) -
{[
]
C1[1 + 4y02]1/2 - R RT ln + zF C0[1 + 4y12]1/2 - R U ln
[
]}
[1 + 4y12]1/2 - RU
[1 + 4y02]1/2 - RU
(1)
where U ) [ξ+ - ξ-]/[ξ+ + ξ-], ξ+ and ξ- are the mobilities
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Higuchi and Hara
Figure 4. Time course of the membrane potential across a PMLG membrane between solutions of 1.0 mM NaCl and 0.1 M NaCl at pH ) 2-10 and 25 °C.
Figure 5. Time course of the membrane potential across an HMDPMLG-6 membrane between solutions of 1.0 mM NaCl and 0.1 M NaCl at pH ) 2-10 and 25 °C.
of the cation and the anion, y0 ) KC0/Cx, y1 ) KC1/Cx, Cx is the effective fixed charge concentration,34-39 K is the thermodynamic partition coefficient,34-39 R has a value of +1 or -1 when the membrane is positively or negatively charged (R ) +1 in this study), z is the valence of the ion (z ) 1 in this study), and R, T, and F have their conventional meanings. The only unknown parameters in eq 1 are Cx/K and U. Cx/K is known to have the predominant influence on the membrane potential.34 The fluctuation of the ionized amine in the membranes, therefore, contributes to the fluctuation and oscillation of the fixed charge density (i.e., Cx/K) and generates the oscillation of the membrane potential in the modified PMLG membranes under a constant gradient of salts. Most of the oscillations in membrane potential were measured at 25 °C in this study, but the oscillations in membrane potential at 2 and 38 °C were also measured to investigate the effect of temperature on the HMD-PMLG-6 membrane. The amplitudes of the oscillations at 2, 25, and 38 °C were observed to be approximately 3, 5, and 13 mV. The amplitude of the oscillation was found to increase with the increase in temperature in the cells. This evidence might also support the belief that the oscillation of membrane potential is caused by the thermal fluctuation and oscillation of ionized amine in the modified PMLG membranes. The time course of the membrane potential was investigated in several modified membranes (i.e., ethylenediaminated PMLG (EDA-PMLG), propanediaminated PMLG (DAP-PMLG), and butanediaminated PMLG (DAB-PMLG) membranes). Figure 6 shows the oscillation of membrane potential in various modified PMLG membranes of a substitution ratio ) 0.15 at C0 ) 0.1 M NaCl, C1 ) 1mM NaCl, pH ) 10, and 25 °C. The amplitude of oscillation was found to be greater in the modified
PMLG membranes having longer chains of diamine segments. The longer side segments such as HMD may contribute to higher fluctuation of ionized amine in the membranes. Power Spectra of the Oscillation in Membrane Potential. The oscillation of membrane potential in the excitable artificial membranes reported previously18-26 showed pulsating, rhythmic, and periodic oscillations. The oscillation of membrane potential in the modified PMLG membranes was analyzed using a fast Fourier transport method to investigate whether the oscillation of membrane potential is chaotic or has specific frequencies. The power spectrum of the oscillation of the membrane potential in HMD-PMLG-6 was analyzed by the Yule-Walker method40 and is shown in Figure 7. The fast Fourier transport analysis was performed on every 500 data points (i.e., every 50 s due to the sampling time ) 0.1 s) of the membrane potential in each experiment, and exactly the same tendencies were observed in the each power spectrum of the oscillation. Several specific peaks are observed in the power spectrum, and the oscillation of membrane potential found in HMD-PMLG-6 was found not to be chaotic but to have specific frequencies. Artificial oscillation of membrane potential was also synthesized to check whether the sum of some specific sign waves can describe the experimental oscillation. The artificial membrane potential at time t, ∆φ(t), is defined according to eq 2 in this study, where ∆φconst is the constant potential, Ai is the
∆φ(t) ) ∆φconst + ∑Ai sin(2πfit)
(2)
amplitude at i sign wave, and fi is the frequency at i sign wave. Figure 7a also shows the artificial oscillation of membrane potential synthesized from eq 2 having arbitrarily selected n, Ai, and fi (i.e., n ) 6, A1 ) 1.2, A2 ) 2.0, A3 ) 1.0, A4 ) 1.0,
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Figure 8. Time course of the membrane potential across an HMDPMLG-6 membrane between LiCl (a), NaCl (b), and CsCl (c) solutions at C0 ) 0.1 M, C1 ) 1 mM, pH ) 10, and 25 °C.
Figure 6. Time course of the membrane potential across EDA-PMLG (a), DAP-PMLG (b), DAB-PMLG (c), and HMD-PMLG (d) membranes between solutions of 1.0 mM NaCl and 0.1 M NaCl at pH ) 10 and 25 °C. The degree of the substitution ratio of the membranes was selected to be 0.15.
Figure 7. Time course of the membrane potential across an HMDPMLG-6 membrane (a) and its power spectra (b) obtained by experiment (s) and by simulation (--) using eq 2.
A5 ) 0.85, A6 ) 0.60, f1 ) 0.17 Hz, f2 ) 1.1 Hz, f3 ) 1.9 Hz, f4 ) 2.3 Hz, f5 ) 3.7 Hz, and f6 ) 5.4 Hz). The artificial oscillation of membrane potential was found to reproduce the experimental oscillation of membrane potential. Recognition of Salts. One might think that the amplitude or the components of specific frequencies in the oscillation of membrane potential analyzed by the fast Fourier transport
method vary when the various electrolytes were used in the measurements, and the recognition of ions would be qualitatively possible from the information of the amplitude and the components of specific frequencies. Several salts (i.e., LiCl, CsCl, KCl, NaNO3, Na2CO3, and Na2SO4) except for NaCl were also used in the measurements of oscillation of membrane potential in the HMD-PMLG-6 membrane. Figure 8 shows the oscillation of membrane potential measured using LiCl, NaCl and CsCl solutions at C0 ) 0.1 M, C1 ) 1 mM, pH ) 10, and 25 °C. The membrane potential measured using KCl solution (which is not shown here) showed exactly the same oscillation as that measured using CsCl at pH ) 10. The amplitudes of the oscillation of membrane potential measured using several salts were observed to increase in the following order at C0 ) 0.1 M, C1 ) 1 mM, pH ) 10, and 25 °C: CsCl ) KCl , Na2CO3 < NaNO3 ) NaCl ) Na2SO4 , LiCl. Not only the anion but also the cation in the salts was found to affect the amplitude of the oscillation of membrane potential. The amplitudes of oscillation in the membrane potential were observed to be higher when the ionic radius of the cation in the salts was less and the hydration radius of the cation in the salts was higher in this study (i.e., CsCl ) KCl < NaCl < LiCl). The power spectra of the oscillation in the membrane potential measured using Na2CO3, NaNO3, NaCl, and Na2SO4 in the HMD-PMLG-6 membrane are shown in Figure 9. Several specific peaks depending on the salt solutions are observed in the figure, although the amplitudes of the oscillation in the membrane potential are found to be nearly equal among the four salts. A strong peak at 1.5 Hz is specifically observed in the power spectrum of the oscillation measured using Na2SO4 solution. Several specific peaks every 0.35 Hz are observed in the power spectrum of the oscillation measured using NaNO3 solution. Patterns of frequencies appeared in the power spectra showed exactly the same tendencies in the power spectra that were measured on the different membranes prepared on the same conditions. No significant difference was found among the power spectra of LiCl, NaCl, KCl, and CsCl (which are not shown here), although the amplitudes of oscillation in
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Figure 9. Power spectra of the oscillation in membrane potential across an HMD-PMLG-6 membrane measured using NaNO3 (--), Na2CO3 (- ‚ -), NaCl (s), and Na2SO4 (‚‚‚) at C0 ) 0.1 M, C1 ) 1 mM, pH ) 10 and 25 °C.
the membrane potential depends on the salts having different cations. These results suggest that it may be possible to recognize a particular salt present in the solution from the information on the amplitude and the power spectrum of fast Fourier transport in the oscillation of membrane potential. Models of the Oscillation. Oscillation of the membrane potential in some artificial polymeric membranes was reported under a dc electric field24,25 or a constant gradient of salt solution.26 The oscillation of membrane potential showed periodic pulses and spikes and was unlike our oscillatory features such as those shown in Figures 5 and 6. Their models for the oscillation phenomena were based on a change in polymeric conformation induced by salt accumulation at the interfacial region in the membranes25 or by a periodic change in the conformation between the R-helix and the random coil structure of the poly(amino acid) chain.26 Their models cannot be applied to the oscillation of membrane potential in the modified PMLG membranes in this study, because there are no interfacial regions as proposed by Huang and Spangler.25 The oscillation of membrane potential in the modified PMLG membranes appears unlike their electrical patterns of periodic pulses and spikes but rather shows several specific peaks based on the fast Fourier transport analysis. It is, therefore, proposed that the oscillation in membrane potential is caused by the fluctuation of the fixed charge density originating from the thermal fluctuation of the partially ionized amine in the modified PMLG membranes under a constant gradient of salts. Acknowledgment. We are grateful to Dr. M. Iwatsuki and Dr. Y. Miyachi (Ajinomoto Co. Inc.) for the gift of PMLG solution. This research was partially supported by Special Investigation from Seikei University. References and Notes (1) Ritter, M.; Woll, E.; Waldegger, S.; Haussinger, D.; Lang, H. J.; Scholz, W.; Scholkens, B.; Lang, F. Pfluger Arch. 1993, 423, 221.
Higuchi and Hara (2) Lang, F.; Friedrich, F.; Kahn, E.; Woll, E.; Hammerer, M.; Waldegger, S.; Maly, K.; Grunicke, H. J. Biol. Chem. 1991, 266, 4938. (3) Janssen, L. J.; Daniel, E. E. J. Pharmacol. Exp. Ther. 1991, 259, 110. (4) Stelling, J. W.; Jacob, T. J. C. Am. J. Physiol. 1993, 265, C720. (5) Pickering, A. E.; Spanswick, D.; Logan, S. D. J. Physiol. 1994, 480, 109. (6) Bhattacharyya, M. L.; Sarker, S.; Seth, K. J. Electrocardiology 1994, 27, 105. (7) Devor, D. C.; Simasko, S. M.; Duffey, M. E. Am. J. Physiol. 1991, 260, C598. (8) Yada, T.; Okada, Y. J. Membr. Biol. 1984, 77, 33. (9) Lang, F.; Friedrich, F.; Kahn, E.; Woll, E.; Hammerer, M.; Wadeggor, S.; Maly, K.; Grunicke, H. J. Biol. Chem. 1991, 266, 4938. (10) Enomoto, K.-I.; Cossu, M. F.; Edwards, C.; Oka, T. Proc. Natl. Acad. U.S.A. 1986, 83, 4754. (11) Crawford, K. M.; E. L. Stuenkel, E. L.; Ernst, S. A. Am. J. Physiol. 1991, 261, C177. (12) Devor, D. C.; Simasko, S. M.; Duffey, M. E. Am. J. Physiol. 1990, 258, C318. (13) Stelling, J. W.; Jacob, T. J. C. Am. J. Physiol. 1993, 265, C720. (14) Gallin, E. K.; Wiederhold, M. L.; Lipsky, P. E.; Rosenthal, A. S. J. Cell Biol. 1975, 86, 653. (15) Ince, C.; Leijh, P. C. J.; Meijer, J.; Bavel, E. van; Ypey, D. L. J. Physiol. (London 1984, 352, 625. (16) Nelson, P. G.; Henkart, M. P. J. Exp. Biol. 1979, 81, 49. (17) Okada, Y.; Tsucjiya, W.; Yada, T. J. Physiol. (London) 1982, 327, 449. (18) Teorell, T. J. Gen. Physiol. 1959, 42, 831. (19) Monnier, A. M.; Monnier, A.; Goudean, H. G.; Rebuffel-Reynier, A. M. J. Cell Comp. Physiol. 1965, 66, 147. (20) Pant, H. C.; Rosenberg, B. Biochim. Biophys. Acta 1971, 225, 379. (21) Yoshikawa, K.; Matsubara, Y. J. Am. Chem. Soc. 1984, 106, 4423. (22) Yoshikawa, K.; Maeda, S.; Kawakami, H. Ferroelectrics 1988, 86, 281. (23) Yoshikawa, K.; Ogawa, N.; Shoji, M.; Nakata, S. Am. J. Phys. 1991, 59, 137. (24) Shashoua, V. E. Faraday Symp. Chem. Soc. 1974, 9, 174. (25) Huang, L. M.; Spangler, R. A. J. Membr. Biol. 1977, 36, 311. (26) Minoura, N.; Aiba, S.; Fujiwara, Y. J. Am. Chem. Soc. 1993, 115, 5902. (27) Kinoshita, T.; Takizawa, A.; Tsujita, Y.; Ishikawa, M. Kobunshi Ronbunshu 1986, 43, 827. (28) Higuchi, A.; Ando, Y.; Nakagawa, T. Polym. J. 1993, 25, 747. (29) Higuchi, A.; Hara, M.; Yun, K.-S.; Tak, T.-M. J. Appl. Polym. Sci. 1994, 51, 1735. (30) Higuchi, A.; Ogawa, S.; Nakagawa, T. J. Chem. Soc., Faraday Trans. 1991, 87, 695. (31) Kaiser, E.; Colescott, R. L.; Bossinger, C. D.; Cook, P. I. Anal. Biochem. 1970, 34, 595. (32) Armstrong, F. B. Biochemistry; Oxford University Press: Oxford, U.K., 1989; p 60. (33) Kagakubinran Kisohen (in Japanese), Maruzen: Tokyo, 1966; p 1054. (34) Higuchi, A.; Iijima, T. J. Appl. Polym. Sci. 1986, 31, 419. (35) Higuchi, A.; Nakagawa, T. J. Membr. Sci. 1987, 32, 267. (36) Higuchi, A.; Nakagawa, T. J. Chem. Soc., Faraday Trans. 1 1989, 85, 3609. (37) Kioshita, T.; Yamashita, T.; Iwata, T.; Takizawa, A.; Tsujita, Y. J. Macromol. Sci. Phys. 1983, B22, 1. (38) Teorell, T. Proc. Soc. Exp. Biol. Med. 1935, 33, 282. (39) Meyer, K. H.; Sievers, J. F. HelV. Chim. Acta 1936, 19, 649. (40) Shimizu, N.; Chiba, N. Treatments of Random Signals from a Personal Computer (in Japanese); Kyoritsu Shuppan: Tokyo, 1994; p 243.
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