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Electrophoretic Behavior of Complexes between Sodium Dextran Sulfate and Cationic Surfactants Yoshiko Moriyama and Kunio Takeda* Department of Applied Chemistry, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan
Kiyofumi Murakami Faculty of Education, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8513, Japan Received April 1, 2000. In Final Form: July 4, 2000 The interaction between sodium dextran sulfate (DxS) and alkyltrimethylammonium bromides was studied by means of potentiometric titration and electrophoretic light scattering methods in the phosphate buffer of pH 7.0 and ionic strength 0.014 at 25 °C. The bindings of dodecyltrimethylammonium ion and tetradecyltrimethylammonium ion to DxS occurred in two stages. In the first stage, the steep rise of the binding number is characteristic of a strong cooperative binding. The profile of hexadecyltrimethylammonium ion binding was similar to those of the others, as a whole. However, the concentration region, where the binding proceeded, became lower with an elongation of the hydrocarbon chain of the surfactant. The mobility of DxS was -3.7 × 10-4 cm2 s-1 V-1 in the absence of the surfactant. In the first binding stage, the negative mobility of DxS decreased with an increase in each surfactant concentration. It crossed zero mobility when the binding degree of the surfactant (moles of bound surfactant ion/mole of sulfate group of DxS) was 1. In the second stage where the binding degree exceeds 1 and approaches 2, a further binding of the surfactant ions appears to form micelle-like aggregates on DxS. The mobility of DxS became positive because of excessive positive charges introduced on the polymer. The mechanism of the complex formation is considered to consist of not only the binding process of the surfactant but also a change of shape of the complex itself.
Introduction The interactions between polyelectrolytes such as synthetic polymers, nucleic acids, and proteins, and charged surfactants have attracted much attention from the viewpoints of colloidal properties and biological activities of these systems.1-9 After the development of surfactant-ion-selective electrode methods, many investigators have obtained the binding isotherms and found that the binding of surfactants is highly cooperative for many systems.3-5,10-15 Furthermore, the cooperative binding theories16,17 based on the Zimm-Bragg theory18 for (1) Lindman, B.; Thalberg, K. In Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993. (2) Winnik, F. M.; Regismond, S. T. A. In Polymer-Surfactant Systems; Kwak, J. C. T., Ed. Surfactant Science Series 77; Marcel Dekker: New York, 1998. (3) Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1982, 86, 3866. (4) Santerre, J. P.; Hayakawa, K.; Kwak, J. C. T. Colloids Surf. 1985, 13, 35. (5) Hansson, P.; Almgren, M. J. Phys. Chem. 1995, 99, 16694. (6) Thalberg, K.; Lindman, B.; Karlstrom, G. J. Phys. Chem. 1991, 95, 3370. (7) Thalberg, K.; Lindman, B.; Bergfeldt, K. Langmuir 1991, 7, 2893. (8) Murakami, K. Bull. Chem. Soc. Jpn. 1998, 71, 2293. (9) Murakami, K. Langmuir 1999, 15, 4270. (10) Cutler, S. G.; Meares, P.; Hall, D. G. J. Electroanal. Chem. 1977, 85, 145. (11) Gilanyi, T.; Wolfram, E. Colloids Surf. 1981, 3, 181. (12) Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1983, 87, 506. (13) Hayakawa, K.; Santerre, J. P.; Kwak, J. C. T. Macromolecules 1983, 16, 1642. (14) Malovikova, A.; Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1984, 88, 1930. (15) Almgren, M.; Hansson, P.; Mukhtar, E.; van Stam, J. Langmuir 1992, 8, 2405. (16) Schwarz, G. Eur. J. Biochem. 1970, 12, 442. (17) Satake, I.; Yang, J. T. Biopolymers 1976, 15, 2263. (18) Zimm, B. H.; Bragg, J. K. J. Chem. Phys. 1959, 31, 526.
helix-coil transition have made it possible for us to obtain detailed information such as intrinsic binding constant, cooperativity parameters, and average cluster size of bound surfactants. Detailed examinations have been made also of the dependences of such a binding on temperature,4 addition of salt,3,12 alkyl chain length of surfactant,14 and charge density of polyions.19 These studies have clarified that a strong binding of surfactant ions with a polyelectrolyte is promoted by the electrostatic force between charged groups and the hydrophobic interaction between bound surfactants. Eight years ago, Shirahama et al. presented a very interesting feature of binding, i.e., bimodal binding, for a dodecylpyridinium bromide-sodium dextran sulfate (DxS, (C6H8O3(SO4Na)1-2)n) system, from the observation of two differently migrating species in the electrophoregrams obtained by the electrophoretic light scattering method.20 Although this method seems to provide detailed information on the state of such a complex, there is no electrophoretic light scattering study of similar cooperative binding systems except for theirs. In the present study, we have examined the complex formation between the polyelectrolyte, DxS, and cationic surfactants, alkyltrimethylammonium bromides, on the basis of electophoretic mobilities, measured by the electrophoretic light scattering method, and of the binding isotherms, determined by the potentiometric titration method. Charge changes of the polyelectrolyte due to the complex formation can be followed by measuring the electophoretic mobilities. With an increase in the degree of the cationic surfactant binding to the anionic polyelec(19) Hansson, P.; Almgren, M. J. Phys. Chem. 1996, 100, 9038. (20) Shirahama, K.; Kameyama, K.; Takagi, T. J. Phys. Chem. 1992, 96, 6817.
10.1021/la0005053 CCC: $19.00 © 2000 American Chemical Society Published on Web 08/30/2000
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trolyte, charges of the complexes would become less negative. The main purpose of the present study is to examine the mechanism of the mobility changes of the complexes with the progress of the binding. Experimental Section The sample of DxS (Mr 500 000) was purchased from Wako Pure Chemical Industries, Ltd. Dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB), and hexadecyltrimethylammonium bromide (HTAB) were purchased from Tokyo Kasei Co.21 In the present study, the phosphate buffer of rather low concentration (pH 7.0; ionic strength 0.014) was used in order to keep the critical micelle concentration (cmc) at a high concentration of each surfactant.21-25 In the buffer, the final concentrations of NaH2PO4 and Na2HPO4 were 3.33 and 3.56 mM, respectively.21-25 The final concentration of DxS was adjusted to 1 × 10-7 M under each experimental condition. Since the number of sulfate group of the present sample was evaluated to be about 2400 per DxS molecule by the colloidal titration method, the concentration of the group was about 2.4 × 10-4 M in all experiments. The binding isotherms of the surfactants to DxS were obtained by the potentiometric titration using a surfactant-ion-selective electrode26 at 25 °C. The surfactant-ion-selective membranes were composed of poly(vinyl chloride) (PVC), bis(2-ethylhexyl)phthalate, and carrier complexes. The carrier complexes used in these membranes were prepared by reacting each alkyltrimethylammonium bromide with sodium dodecyl sulfate, and by three recrystallizations from acetone solution. The potentiometric measurements were made using a digital multimeter (Advantest TR6846) connected with the electrochemical cell: Ag/AgCl, KCl | salt bridge | cationic surfactant (inner solution) | PVC membrane | sample solution | salt bridge | Ag/AgCl, KCl. In the cell, commercially available Ag/AgCl electrodes were used (TOA HS-205C). The slope of the plot of emf vs log surfactant concentration below the cmc in the buffer showed a good Nernstian slope, i.e., 59.4 mV/decade. The electrophoretic mobilities of the polyelectrolyte-surfactant complexes were measured at 25 °C with the electrophoretic light scattering photometer LEZA-600 of Otsuka Electronics Co.27 Figure 1 shows the optical system of the apparatus. The measurement was carried out at the scattering angle of 20° and 7.5° and the electric field of 36.6-36.8 V/cm.
Figure 1. Optical alignment in the electrophoretic light scattering photometer LEZA-600. A He-Ne laser of 10 mW is used as a light source (He-Ne). The laser light is conducted to a half-mirror (HM1) by a fixed mirror (M1). This half-mirror splits the beam into the reference beam and the sample beam. Another fixed mirror (M2) guides the sample beam to the electrophoresis cell (C) placed at the center of the goniometer. Frequency of the reference beam is modulated by the movable mirror (MD) attached to a modulator. A mirror and a halfmirror (M3 and HM2) rotate synchronously with the goniometer so that the reference beam always merges with the sample beam at all accessible angles between 5° and 22°. The scattered and reference beams are mixed on the photomultiplier cathode (PM) after passing through two pinholes (P) (this was added according to the indication by one of the reviewers). In a sister apparatus, the electrophoretic light scattering spectrophotometer ELS-800,28,29 a particle size distribution is also measurable by switching a mirror placed between HM1 and M2. In this case, the scattering angle may be set from 72° to 90°.
Results and Discussion The surface tensions of DTAB, TTAB, and HTAB solutions were measured in the absence and the presence of DxS (1 × 10-7 M) by a Du-Nou¨y ring tensiometer. In the absence of DxS, the cmc was determined to be 12.5 mM for DTAB, 2.1 mM for TTAB, and 0.33 mM for HTAB in the buffer by the surface tension method. In the presence of DxS, the surface tension of surfactant solution became constant at a critical concentration (cmcDxS) which was higher than the cmc value by about 0.5 mM in each case. The difference between the cmcDxS and the cmc of the pure surfactants might be due to the binding of the surfactant ions to DxS. If so, the maximum binding numbers can be estimated to be about 5000 mol/mol ()5 × 10-4 M/1 × 10-7 M) regardless of the hydrocarbon chain length of surfactant. On the other hand, the number of sulfate group of the present sample was evaluated to be about 2400 per (21) Takeda, K.; Shigeta, M.; Aoki, K. J. Colloid Interface Sci. 1987, 117, 120. (22) Takeda, K.; Miura, M.; Takagi, T. J. Colloid Interface Sci. 1981, 82, 38. (23) Takeda, K.; Sasa, K.; Kawamoto, K.; Wada, A.; Aoki, K. J. Colloid Interface Sci. 1988, 124, 284. (24) Takeda, K.; Wada, A.; Nishimura, T.; Ueki, T.; Aoki, K. J. Colloid Interface Sci. 1989, 133, 497. (25) Wada, A.; Takeda, K. J. Colloid Interface Sci. 1990, 138, 277. (26) Shirahama, K.; Nishiyama, Y.; Takisawa, N. J. Phys. Chem. 1987, 91, 5928. (27) Takeda, K.; Sasaoka, H.; Sasa, K.; Hirai, H.; Hachiya, K.; Moriyama, Y. J. Colloid Interface Sci. 1992, 154, 385.
Figure 2. Binding isotherms of the surfactants to DxS: (O) DTA+; (0) TTA+; (4) HTA+.
DxS molecule as stated in the Experimental Section. Then one sulfate group appears likely to bind two surfactant ions on an average. Figure 2 shows the binding isotherms of the surfactants to DxS measured by the potentiometric titration, in which the degree of binding (θ), defined as the amount of bound surfactant per sulfate group of DxS, is adopted in the ordinate. As seen in this figure, the binding of dodecyltrimethylammonium ion (DTA+) to DxS occurred in two stages. The value of θ for the DTA+ binding sharply increased up to 0.65 in a very narrow region of low surfactant concentration, and then gradually increased to unity (the first binding stage). The initial steep rise of θ in the narrow surfactant concentration region in this stage is characteristic of a strong cooperative binding. When the value of θ approached to unity, the solution became turbid. Thereafter, with a further increase in the surfactant concentration, θ sharply increased again (the second binding stage). The maximum value of θ was about 2. This indicates that two DTA+ ions are bound to one sulfate group of DxS, in agreement with the result of the surface tension measurement. Near the concentration at the end of the second binding stage, the solution became clear again. The profile of the binding of tetradecyltrimethylammonium ion (TTA+) to DxS resembled that of
Interaction between DxS and Cationic Surfactants
DTA+. In the case of HTAB, the binding measurement could be made only in the concentration region where θ gradually changed across the boundary between the two stages. This might be because the lowest and the highest sides of the concentration region are limited by the response of the electrode and the cmc of the surfactant, respectively. The profile of hexadecyltrimethylammonium ion (HTA+) binding might be anticipated to be similar to those of the others, as a whole. The cooperative nature comes from the hydrophobic interaction between the alkyl chains of bound surfactants. The chain length affects the surfactant concentration regions where the bindings occur: the longer the hydrocarbon chain of the surfactant is, the lower the concentration region shifts. We also notice from Figure 2 that the surfactant concentration region of the first binding stage becomes wider with an increase in the hydrocarbon chain length of the surfactant. A possibility of phase separation should be examined related to the phenomena that the complex solutions become insoluble and soluble when θ becomes 1 and 2, respectively. Lindman and Thalberg et al. have studied the solubility properties of the systems of anionic polyelectrolytes (sodium hyaluronate and sodium polyacrylate) and cationic surfactants (alkyltrimethylammonium bromides) at high concentrations of the polymer and the surfactants, typically, of the order of 10 wt %.1,6,7 On the basis of the observation of two clear and isotropic phases, they have interpreted the observed solubility behavior in terms of phase separation. They have found that the phase separation behavior is highly dependent on the concentrations of polymer and coexisting salt and also pointed out that the occurrence of the phase separation has not necessarily clear at their relatively low concentrations. Recently, on the other hand, one of the authors (K.M.) has studied the cooperative binding of dialkylaminophenylazobenzenesulfonates to a basic protein, lysozyme, by the equilibrium dialysis technique at a dilute protein concentration.8 In this system, a phase separation has not been observed, but the binding and precipitation behavior, which is quite similar to that in the present system, has been observed. That is, the cooperative binding occurs in two stages, in which the binding number of the first stage agrees to the number of cationic residues and that of the second stage is the same as the first one. The precipitates appear around the end of the first cooperative binding stage where the complexes become neutral due to the binding, and they are redissolved near the end of the second stage where the complexes are negatively charged by the binding of two dialkylaminophenylazobenzenesulfonate molecules per one cationic residue to form a bilayerlike structure around the protein. The precipitation and redissolution behavior appears likely to be common with the progress of the binding, when the concentrations of polymer and surfactant are low. If the phase separation takes place in the present systems, it might not be adequate to deal the data in terms of surfactant binding in the concentration region where the solutions become turbid. However, no evidence of the phase separation has been observed in the present system. The present polymer concentration (1 × 10-7 M), which corresponds to about 0.005 wt %, might be too low to cause such a phase separation. Rather, the present binding behavior must be a real binding. Then, the observed precipitates might be aggregates of the neutral complexes. This is supported by the agreement of the binding numbers determined from the surface tension measurement and from the potentiometric titration, and by the fact, as described below, that the observed positive mobilities in the second stage have reasonable values for such complexes.
Langmuir, Vol. 16, No. 20, 2000 7631 Table 1. Intrinsic Binding Constant (K), Cooperativity Parameter (u), and Average Cluster Size (m j ) in the First Stage of the Surfactant Binding to DxS surfactant
K/M-1
u
m ja
DTAB
174 85b 781 833b
48
11
147
39
TTAB
a The average cluster size was estimated at the final concentration of the first phase in the first binding stage. b These values were estimated from the binding isotherms at low concentrations, based on the Scatchard formulation.
Table 1 summarizes the intrinsic binding constants (K), the cooperativity parameters (u), and the average cluster size (m j ) estimated for DTA+ and TTA+ binding, obtained according to the procedure by Satake and Yang.17 As seen in Table 1, the values of K substantially agree with those estimated by using the Scatchard formulation30 from the binding isotherms at low concentrations where no cooperativity appears. The values of these parameters for TTAB are larger than those for DTAB. This fact suggests that the binding to an isolated site and the cooperativity between bound ligands for TTAB are stronger than those for DTAB. The values of the cooperativity parameters (48 for DTAB and 147 for TTAB) are comparable to the value (about 100) estimated for dodecylpyridinium bromide-DxS system by Shirahama et al.,20 where the two-stage binding has been observed. However, the values of K and u for DTAB in the present study (K ) 174 M-1 and u ) 48) are different from those (K ) ∼35 mol-1 kg and u ) ∼700), reported for the same system in similar experimental conditions,3,4 while the products of these parameters can be seen to be comparable to each other by taking account of the difference in the concentrations of coexisting salts. Hansson and Almgren have pointed out that the error in the estimations of K and u is large, while the product, Ku, can be obtained with good accuracy.5 This error is due to the difficulty of estimating u as 4 times the square of the slope of the binding isotherm at the half-saturation point. To avoid this uncertainty, the value of K was also estimated only from the data of low binding level, as mentioned above. The agreement between the K values obtained from the two kinds of estimations shows the self-consistency of the present result. Figure 3 shows a representative effect of the electroosmosis on the electrophoretic movement of DxS molecule. The electrophoretic mobility was evaluated from the value at the position of the stationary layer where the electroosmotic flow vanished. The DxS-surfactant solutions became turbid above 0.65 mM DTAB, 0.14 mM TTAB, and 0.08 mM HTAB. A further increase of surfactant concentration made the solution clear again in each case. Although the electrophoretic measurements of such turbid solutions were carried out for solutions obtained by the filtration using a membrane of 0.8 µm pore size, the observed mobilities did not differ from those before the filtrations. In other words, the electrophoretic mobilities of DxS-surfactant complexes in the turbid solutions were not affected by the present filtration. The electrophoretic mobility of DxS-DTA+ complex is shown as a function of the surfactant concentration in Figure 4. In the present phosphate buffer, the mobility of DxS was -3.7 × 10-4 cm2 s-1 V-1 in the absence of the (28) Kameyama, K.; Takagi, T. J. Colloid Interface Sci. 1990, 140, 517. (29) Oka, K.; Otani, W.; Kameyama, K.; Kidai, M.; Takagi, T. Appl. Theor. Electrophor. 1990, 1, 273. (30) Scatchard, G. Ann. N.Y. Acad. Sci. 1949, 51, 660.
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Figure 5. TTAB concentration dependence of the mobility of the DxS-TTA+ complex.
Figure 3. Electroosmotic plot of electrophoresis of DxS in the absence (A) and the presence (B) of 1.5 mM DTAB. The apparent mobility of DxS corresponds to the peak position of the mountain shape. The downward arrows indicate mobilities of very small amounts of impurities. The dimensions of the cell were 17 mm in length, 10 mm in width, and 2 mm in depth. The vertical axis corresponds to the depth of the cell. Two horizontal broken lines indicate the positions on the stationary layer where the electroosmotic flow vanishes.
Figure 4. DTAB concentration dependence of the mobility of the DxS-DTA+ complex.
surfactant. Upon the addition of DTAB, the negative mobility of the complex slightly increased below 0.29 mM, but, beyond this concentration, it sharply decreased with a further increase in the surfactant concentration. It crossed zero mobility at 1.4 mM DTAB and became positive beyond this concentration. Figure 5 shows the electrophoretic mobility of DxS-TTA+ complex as a function of the surfactant concentration. The negative mobility of the complex increased up to -4.2 × 10-4 cm2 s-1 V-1 at low TTAB concentrations below 0.24 mM but sharply decreased beyond this concentration. The negative mobility of DxS-HTA+ complex initially increased up to -4.7 × 10-4 cm2 s-1 V-1 below 0.22 mM but decreased with an
Figure 6. HTAB concentration dependence of the mobility of the DxS-HTA+ complex.
increase in the surfactant concentration, as shown in Figure 6. The mobilities of the DxS-TTA+ and the DxSHTA+ complexes crossed zero mobility at 0.4 and 0.27 mM, respectively. The complex mobilities become zero when the mixing ratio of surfactant/DxS reaches 14 000, 4000, and 2700 mol/mol in DTAB, TTAB, and HTAB, respectively: the shorter the hydrocarbon chain of the surfactant, the higher the surfactant concentration required to reach the zero mobility. In each case, the mobility crosses zero mobility, when θ ) 1, that is, when all the binding sites (sulfate groups) are occupied by the surfactant cations (trimethylammonium groups). The mobility of each complex finally reached a constant magnitude around 2.2 × 10-4 cm2 s-1 V-1 below the cmc of each surfactant as seen in Figures 4-6. In response to this, the bindings of DTA+, TTA+, and HTA+ to DxS are completed far below the cmc of each surfactant. In the interaction of DxS with the cationic surfactants, the negative potential of DxS seems to be first neutralized by the binding of the surfactants. A further binding of surfactant ions appears to form micelle-like aggregates on DxS, bringing excessive positive charges on the polymer. As a result, the mobilities of these complexes change from negative to positive sign. In order to examine the state of counterions on the positively charged complex at around θ ) 2 in the second binding stage, free Br- concentrations in DTAB and TTAB solutions were measured in the absence and the presence of DxS with a benchtop pH/ion meter (ORION 720A) connected to a bromide electrode (ORION 9436BN) and a reference electrode (ORION 9002). Figure 7 shows the changes of the free Br- concentrations in TTAB solutions as a function of the total surfactant concentration. In the absence and the presence
Interaction between DxS and Cationic Surfactants
Figure 7. Changes of the free Br- concentrations in TTAB solutions with (b) and without DxS (O) as a function of the total surfactant concentration.
of DxS, the free Br- concentrations began to deviate from a linear relationship beyond the cmc and the cmcDxS, respectively. Between the two systems, there is no appreciable difference in the linear relationships of free Br- concentration below the cmc and cmcDxS. This indicates that the Br- ions are attracted by the surface charge of TTAB micelle, but not by those of the complexes formed below the cmcDxS. Then, it can be concluded that the Brions are completely released from the complex surface. This is probably because the surface charge density of the complex at around θ ) 2 is smaller than that of pure micelle and then no polyelectrolyte effect has appeared. Comparison of the profiles of the mobility changes and the binding isotherms in more detail would give us an insight for more detailed mechanism of the complex formation. In the first binding stage, there are two phases in the mobility change, i.e., the first phase in which the value of the negative mobility slightly (DTAB) or considerably (TTAB and HTAB) increases with an increase in the corresponding surfactant concentration in the lower concentration regions, and the second phase in which the value of the negative mobility steeply decreases to reach zero mobility at θ ) 1 in the higher concentration region. The values of θ at the end of the first phase are 0.65 for DTAB, 0.89 for TTAB, and 0.91 for HTAB. This means that considerable binding is taking place in this phase. Then, it can be expected that the negative charge of the complex progressively decreases with an increase in each surfactant concentration. However, the negative mobility increases indeed (-3.7 × 10-4 cm2 s-1 V-1 (DTAB), -4.2 × 10-4 cm2 s-1 V-1 (TTAB), and -4.7 × 10-4 cm2 s-1 V-1 (HTAB)). This discrepancy may be solved by considering the shape of the complex, which is another factor to determine the electrophoretic mobility. In the absence of surfactant, DxS would be in an extended form due to the electrostatic repulsion between the negatively charged sulfate groups. This repulsion would become weak with the progress of the surfactant binding. Then the polymer can be expected to shrink; this causes the negative mobility to increase. This shrinkage would be accelerated by the hydrophobic interaction between the bound surfactants. Then, it is expected that as the length of the alkyl chain of the surfactant becomes long, this effect becomes strong to lead to some compact shape of the complex. This effect
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may be more important than the charge effect in the first phase of the mobility change. This consideration is consistent with the fact that the negative mobility increment of the complex in this phase becomes larger with an increase in the alkyl chain length of the surfactant. In addition, this consideration is in accordance with the suggestion by Thalberg et al. on the basis of the viscosity measurement that the surfactant binding makes the polymer conformation less extended prior to the phase separation as stated above.6,7 In the second phase of the mobility change, further shrinking does not occur and the charge effect may become predominant, resulting in the progressive decrease in the value of the negative mobility. In the second binding stage, the positive charge on the complex becomes large with an increase in the degree of the binding. In this process, the complex would somewhat elongate again due to the electrostatic repulsion between the introduced positive charges and the mobility of the complex is anticipated to reach the same absolute value at θ ) 2 as that of the negatively charged bare DxS. However, the absolute value of the positive mobility (2.2 × 10-4 cm2 s-1 V-1) at θ ) 2 is smaller than that of the negative mobility for the bare DxS (3.7 × 10-4 cm2 s-1 V-1). This suggests that the diameter of the positively charged complex is larger than that of the negatively charged bare DxS. In this context, the relation between the behavior of mobility change and the binding cooperativity should be discussed. Shirahama et al.20 measured electorophoretic mobilities of the complexes in the dodecylpyridinium bromide-DxS system. They found two kinds of migrating species (rapid and slow species) in the concentration region corresponding to the first binding stage of the present system. They interpreted the phenomenon as the appearance of bimodality, i.e., the rapidly migrating species with very little surfactants and the slowly migrating species with saturated with surfactants. However, the bimodality was not observed in the present study. Only one kind of complex species, which is probably loading ligands of an average number, has been detected in the first stage in the mobility measurement, although the cooperativity of the binding in the present systems is also strong. The difference between the present and their results may arise from the difference in the length of DxS and/or in the nature of ligands used. The present result seems to suggest that the cooperativity effect does not cover the whole molecule of DxS, but extends to some relatively short segments. This presumption is supported by the fact that the average numbers of surfactant ions (about 10-40), composing a cluster at the end of the first phase (Table 1), are smaller than the number of the binding site (2400) on the present DxS. If so at the middle degree of the binding, an alternate arrangement of the bare region and the fully bound region must be realized for one DxS molecule. This structure of DxS may be folded by the hydrophobic interaction between bound surfactants. Acknowledgment. The authors thank Mayo Nishio and Sanae Yamasaki of Okayama University of Science for their helpful assistance in the experiment. LA0005053
