Bioconjugate Chem. 2003, 14, 1185−1190
1185
Growth of Large Polymer-Actin Complexes Akira Kakugo,† Kazuhiro Shikinaka,† Kanae Matsumoto,† Jian Ping Gong,*,†,‡ and Yoshihito Osada† Graduate School of Science Hokkaido University, and Presto, JST, Sapporo 060-0810, Japan. Received May 6, 2003; Revised Manuscript Received August 28, 2003
Polymer-actin complexes as large as 10-50 µm with filamentous, branched, stranded, and ring shapes are obtained when fluorescent phalloidin-labeled F-actin is mixed with some synthetic polymers carrying positive charges such as poly-L-lysine, x,y-ionene bromide polymers. All growth of these complexes occurs cooperatively at some certain critical polymer concentrations, regardless of the chemical structure of the polymer, while the morphology of the complexes is substantially influenced by the chemical structure of the polymer. Poly-Lys-actin complex grows preferentially along the filament axis even above the critical concentration. 3,3-ionene-actin complexes show completely homogeneous filaments below the critical concentration but forms bundles at a higher concentration. Occasionally, ring shape complexes can be observed in the 6,6-ionene-actin complex.
INTRODUCTION
Recently, we have constructed an adenosine triphosphate (ATP)-fueled soft gel machine constructed from chemically cross-linked actin gel and myosin gel (1). Actins and myosins are major components of muscle proteins and play an important role in dynamic motion of creatures that is caused by the molecular deformation using the chemical energy released by hydrolysis of ATP. We have found that chemically cross-linked giant actin gel filaments, several tens of times the length of native actin filaments, move along a chemically cross-linked myosin fibrous gel with a velocity as high as that of native actins, by coupling to ATP hydrolysis. This result indicates that muscle proteins can be tailored into desired shape and size without sacrificing their bioactivities. The above-described giant actin gel filaments were obtained by forming complexes with poly-L-Lysine (p-Lys) by subsequent chemical cross-linking (1). However, the selforganized growth process of actin-p-Lys complexes has not been clarified yet. In this paper we systematically study the complex formation between actins and various kinds of polycations, such as p-Lys and x,y-ionene bromide polymers (x ) 3 or 6; y ) 3, 4, 6, 10, or 12). x,y-ionene polymers are cationic polymers having positive charges on their chain backbone with periodical alkyl spacers x and y (Chart 1). Native actins (G-actin), which are globular proteins of 5 nm in diameter, form thin filaments with a diameter about 9 nm in living muscle. In physiological ionic solution (F-buffer), G-actins extracted from muscles undergo self-assembly reaction polymerization transferring to a single-stranded filament with a pitch of 5.9 nm which resembles the actin filaments within sarcomere (2). This actin filament polymerized from G-actin in physiological ionic solution is called F-actin. The F-actins of several nanometers in length can be conveniently observed under a fluorescence microscope by binding fluorescent phalloidin to the F-actins. Since the isoelectric point of actins is pH 4.7, F-actins in F-buffer of pH 7.2 are negatively * To whom correspondence should be addressed. E-mail:
[email protected]. † Graduate School of Science. ‡ Presto, JST.
Chart 1. Molecular Structure of x,y-ionene Bromide Polymers
charged. Therefore, they were assumed to form complexes with cationic polymers through electrostatic interaction. When synthetic polymers carrying positive charges are mixed with fluorescent phalloidin-labeled F-actin, polymer-actin complexes grew with time. The complex growth kinetics and thermodynamics are investigated and compared with the morphological features of the complexes by using fluorescent optical images and transmission electron microscope (TEM) images. EXPERIMENTAL PROCEDURES
Sample Preparations. x,y-ionene (x ) 3 or 6; y ) 3, 4, 6, 10, or 12) bromide polymers (x,y-ionene), which have the chemical structures as shown in Chart 1, were synthesized by the method reported previously (3). The intrinsic viscosities of 6,6- and 6,12-ionene polymers in 0.4 M LiBr aqueous solution at 25 °C were 0.19 and 0.22 dL/g, respectively. The viscosity value of the 6,6-ionene polymer corresponds to a weight-average molecular weight of 1.9 × 104. Poly-L-lysine hydrochloride (p-Lys) and poly-D-glutamic acid sodium salt (p-Glu) were purchased from Peptide Institute Inc. Deoxyribonucleic acid sodium salt (DNA) was purchased from Sigma Chemical Co. Poly(ethylene glycol) (PEG) was purchased from Aldrich Chemical Co., Inc. G-actins (0.1 mg/mL) were obtained from scallops by the method of Spudich et al. (4). Fluorescently labeled F-actins were obtained by stoichiometrically mixing G-actins and rhodamine-phalloidin (Molecular Probes No. 4171) in F-buffer (5 mM HEPES (pH 7.2), 0.2 mM ATP, 0.2 mM CaCl2, 100 mM KCl, 2 mM MgCl2) for 24 h at 4 °C. Phalloidin bonds to G-actin stoichiometrically and stabilizes the F-actin against depolymerization at a decreased critical concentration of actin. Measurement. The rhodamine-phalloidin-labeled Factin (later denotes as F-actin) solution was diluted to 0.001 mg/mL with F-buffer and mixed with various kinds
10.1021/bc0340722 CCC: $25.00 © 2003 American Chemical Society Published on Web 10/31/2003
1186 Bioconjugate Chem., Vol. 14, No. 6, 2003
Kakugo et al.
Figure 1. Fluorescence microscope images of polymer-actin complexes formed by mixing F-actin and various cationic polymers at room temperature. (a) p-Lys, (b) 3,3-ionene, (c) 6,6-ionene, (d) 6,12-ionene, (e) F-actin only. The molar ratio of ammonium cation of polymer to monomeric actin was kept constant at 30:1 for x,y-ionene polymers and 100:1 for p-Lys, which corresponding-to-weight ratios of [3,3-ionene]/[actin] ) 0.41 g/g, [6,6-ionene]/[actin] ) 0.61 g/g, [6,12-ionene]/[actin] ) 0.81 g/g, [p-Lys]/[actin] ) 0.35 g/g. Actin concentration was 0.001 mg/mL.
of polymers with a prescribed weight ratio of [polymer]/ [F-actin] at room temperature. A cover glass was placed on a slide glass equipped with two spacers 1.1-1.4 mm high at both sides to form a flow-cell. Solution of F-actin and polymer mixture about 30 µm was introduced into the flow-cell by a micropipet at a prescribed time after mixing. The flow-cell was then placed on the stage of a fluorescence microscope (Olympus BX 50) and observed under a ×60 objective. F-actins and its complexes with polymers absorbed on the slide glass surface can be clearly visualized under a microscope. The fluorescence images were recorded by a CCD-camera (Olympus CD300T-RC), and images of filament length were analyzed by using a computer-analyzing program (MetaMorph, Nippon ROPER). The length of filaments, measured from the contour length of long axis, was the average over 50 samples. Transmission electron microscopy (TEM) was performed by using a JEOL (JEM-1200EX) at 120 kV acceleration voltage. A drop of F-actin-polymer mixture of about 10 µL was put on carbon-coated 200-mesh grids that were rendered hydrophilically by glow discharge in a reduced pressure. After waiting for 180 s for adsorption, the grids were stained by one drop of phosphotungstic acid (pH 7.2). The length or width of filament was the average over 20 samples. RESULTS AND DISCUSSION
Figure 1a-d shows some examples of fluorescence microscope images of polymer-actin complexes obtained by mixing F-actins with p-Lys (Figure 1a) and x,y-ionene polymers (Figure 1b-d) for 120 min. One can see that large filamentous, stranded and branched complexes of 20-30 µm in size are formed in the presence of p-Lys and 3,3-, 6,6-, 6,12- ionene polymers and their morphological nature, both of size and shape, are strongly in contrast to that of native F-actin (Figure 1e). Figure 2a shows time courses of the average length of the complexes in the presence of various kinds of polymers. Polymers have been mixed with following weight ratios keeping the actin concentration constant at 0.001 mg/mL as well as the molar ratio of ammonium cation of polymer to actin monomer of F-action as 100:1 for p-Lys and 30:1 for ionene polymers: [p-Lys]/[actin] ) 0.35 g/g, [3,3ionene]/[actin] ) 0.41 g/g, [6,4-ionene]/[actin] ) 0.54 g/g, [6,6-ionene]/[actin] ) 0.61 g/g, [6,10-ionene]/[actin] ) 0.74 g/g, [6,12-ionene]/[actin] ) 0.81 g/g. The number-average length of fluorescence image of F-actins is 2.14 µm with a standard deviation of 0.11 µm (average over 784 samples) in the F-buffer. However, polymer-actin complexes grow with time and reach as large as 5-20 µm within one or 2 h, which is about 2-10 times larger than that of native F-actin. The growth profiles depend on the chemical structure of the
Figure 2. (a) Time courses of polymer-actin complexes growth. (b): 3,3-ionene-actin complexes, (2): 6,4-ionene-actin complexes, (9): 6,6-ionene-actin complexes, (O): 6,10-ionene-actin complexes, (4): 6,12-ionene-actin complexes, (0): p-Lys-actin complexes, ([): p-Glu-actin complexes, (×): [DNA-actin complexes, (+): PEG-actin complexes. (b) Average length of polymer-actin complexes observed from fluorescence microscope images (white columns) and from transmission electron microscopy (TEM) images (shade columns) at 210-300 min. The molar ratio of ammonium cation to monomeric actin was 30:1 for x,yionene polymers and 100:1 for p-Lys. The corresponding weight ratios were as follows: [3,3-ionene]/[actin] ) 0.41 g/g, [6,4ionene]/[actin] ) 0.54 g/g, [6,6-ionene]/[actin] ) 0.61 g/g, [6,10ionene]/[actin] ) 0.74 g/g, [6,12-ionene]/[actin] ) 0.81 g/g, [p-Lys]/[actin] ) 0.35 g/g, [p-Glu]/[actin] ) 0.36 g/g, [DNA]/ [actin] ) 0.77 g/g, [PEG]/[actin] ) 0.10 g/g. Actin concentration: 0.001 mg/mL.
Growth of Polymer−Actin Complexes
polycations. P-Lys shows a relatively slow growth profile but gives out a large complex. On the other hand, 3,3ionene polymer gives the smallest complexes. These results indicate that hydrophobicity and charge density of the ionene polymers are important in complex formation. The average lengths of actin-polymer complexes are shown in Figure 2b. To confirm that this kind of actin growth is due to the complex formation via electrostatic interaction between the negatively charged actins and positively charged polymers, we further studied the actin growth in the mixture solution of actins and negatively charged polymers such as p-Glu, DNA, and neutral polymer, such as PEG at a molar ratio of monomeric units of polymer to F-actin of 100:1, which correspondingto-weight ratios of [p-Glu]/[actin] ) 0.36 g/g, [DNA]/ [actin] ) 0.77 g/g, [PEG][actin] ) 0.10 g/g. As shown in Figure 2a, the F-actins do not grow into large filaments with time in the presence of these anionic or neutral polymers. Therefore, the formation of polymer-actin complexes should be attributed to the electrostatic interaction between actins and cationic polymers. As shown in Figure 2a, although 3,3-ionene has a similar high charge density as that of p-Lys that has charged moiety on its side chain, it shows a much less ability of complex growth. This indicates that although the complex formation is initiated by the electrostatic interaction, the flexibility of the charged moiety is important. The complicated x,y value dependence of the complex growth observed in x,y-ionene polymers might be associated with the complementary effect between the charge density and the flexibility of the charged moiety. Both 3,3-ionene and 6,10-ionene form short complexes because the former has a high charge density but with a less flexibility, while the latter has a high flexibility but with a low charge density. 6,6-Ionene gives longest complex due to its proper charge density and flexibility. Here, we could not find a clear role related to the hydrophobicity of the x,yionene polymers. The decrease in the filament length after 100min of complex formation observed for 6,4- and 6,12-ionene complexes seems to be due to the aggregation of the complex. Since the formation of polymer-actin complexes is an equilibrium reaction, the morphological features of the product should depend not only on time and polymer structure, but also on concentrations of actins and polymers. Figure 3a shows the effect of actin concentration on the equilibrium size of the polymer-actin complexes when mixed with p-Lys of a constant concentration (3.5 × 10-4 mg/mL). When the actin concentration exceeds 0.001 mg/mL, the actin complexes increase the length steeply with the increase in the concentration and then saturate to a length around 15-20 µm. Figure 3b shows the effect of p-Lys concentration on the relative length β of polymer-actin complexes in the equilibrium at a constant actin concentration (0.001 mg/mL). Here β is defined as a ratio of average length to maximum length of actin-polymer complex. No actin growth is observed at all when the mixing ratio of p-Lys to actin is lower than 0.14 g/g, indicating that the polymer-actin complex does not form at such a low concentration. However, the length of polymer-actin complexes abruptly increases when the mixing ratio of p-Lys to F-actin exceeds 0.21 g/g. Thus, there exists a critical p-Lys concentration to form complex, indicating that the complex formation is cooperative. The similar cooperative behavior was also observed in the complex formation with ionene polymers, and the critical mixing ratios of 3,3-, 6,4-, 6,6-, 6,10-, and 6,12-ionene to F-actin were about 0.81, 0.054, 0.12, 0.024, and 0.022 g/g at a constant
Bioconjugate Chem., Vol. 14, No. 6, 2003 1187
Figure 3. Average length of polymer-actin complexes as a function of F-actin concentration (a) and dependence of β on the mixing ratio of polymer to actin (b). Here β is defined as the ratio of average length to maximum length of actin-polymer complex. (b): p-Lys; (O): 3,3-ionene; (9): 6,4-ionene; (0): 6,6ionene. Data in part a were obtained at [p-Lys]) 3.5 × 10-4 mg/mL at 60 min and in part b at an actin concentration of 0.001 mg/mL at 90 min.
F-actin concentration (0.001 mg/mL), respectively (Figure 3b). These results explain why we observed a shortest complex length of 3,3-ionene in Figure 2a performed at [3,3-ionene]/[actin] ) 0.41 g/g, which was less than the critical value of 0.81 g/g. Now, we can conclude that interaction between polymers and actins behave cooperatively, and polymer-actin complexes are formed only when both F-actin concentration and the mixing ratio exceed the critical values. From Figure 3b we can obtain the binding constant (K) as well as the other thermodynamic parameters of the actin-polymer interaction by the following equation (5-7). K ) K0u ) 1/(Cs)0.5, where K0 is the binding constant of the cationic polymer bound to an isolated binding site on the actin filament (initiation process), (Cs)0.5 is the cationic polymer concentration at β ) 0.5 (β is defined as a ratio of average length to maximum length of actin-polymer complex), and u is the cooperative parameter which tells the extra interaction energy between the binding sites (propagation process). The value of u can be calculated from the slope of the growth profile at the half-length point. (dβ/d ln Cs)0.5 ) xu/4. K0 and u as well as the total binding energy (∆Ftotal ) -RT ln K) and cooperative energy change (∆Fcoop. ) -RT ln
1188 Bioconjugate Chem., Vol. 14, No. 6, 2003
Kakugo et al.
Table 1. Thermodynamic Interaction Parameters of Complex Formation between F-Actin and Various Cationic Polymers polymer
K [106]u
u
K0 [105]
∆Ftotal [kJ mol-1]
∆Fcoop. [kJ mol-1]
p-Lys 3,36,46,66,106,12-
3.7 0.3 2.9 2.4 1.1 1.6
31 32 4.4 20 7.0 2.2
1.2 0.1 6.6 1.2 1.5 7.1
-37 -31 -37 -36 -34 -35
-8.5 -8.6 -3.7 -7.4 -4.8 -1.9
u) were calculated, and the results are summarized in Table 1. One can see a large value of the cooperative parameter (u) and therefore a large cooperative energy (∆Fcoop.) change for p-Lys and 3,3-ionene, and the smallest value of cooperative parameter is observed for 6,12ionene, which is 1 order of magnitude smaller than the u value of the other polymers. On the contrary, 6,12ionene shows the highest binding constant of the initiation process (K0). The growth of polymer-actin complexes in size is accompanied by a substantial decrease in the number of actin filament. Figure 4 shows a logarithmic plot of the number (N) as a function of the length (L) of polymeractin complexes at various actin concentrations at a constant mixing ratio of [p-Lys]/[actin] ) 0.35 g/g. As shown in the figure, the number of complexes (N) decreases with increase in the length (L), and they follow a power law as N ∝ L-R. The exponent R that is the fractal dimension (8) should characterize the growth process of the complexes. If R is 1, the complexes grow one-dimensionally, i.e., the actins aggregate along the axis of filament. If R > 1, lateral growth occurs simultaneously with the longitudinal growth. When the fractal dimension R is plotted against the concentration of actin, we obtain Figure 4 (insert) which shows an abrupt increase in R at an actin concentration of 0.0033 mg/mL. When the concentration of actin is lower than this concentration, R is ca. 1.4, but abruptly increases to 2.2 when it exceeds this concentration. In other words, at low concentration the complexes grow preferentially along the filament axis extending their length, but above the critical concentration, they begin to grow in lateral direction as well. As shown in Figure 2 that among x,y-ionenes, 6,6ionenes form the longest polymer-actin complexes which is followed by 6,12-, 6,4-, 6,10-, and 3,3-ionene. Therefore, we further investigate the fractal dimension of the complexes with x,y-ionenes. It is found that R values were 2.1, 2.9, 2.2, 3.5, and 2.3, for 3,3-, 6,4-, 6,6-, 6,10-, and 6,12-ionenes, respectively, at a constant actin concentration (0.001 mg/mL) and molar ratio of ammonium cation to actin monomer unit (30:1). These results indicate that 6,4-, 6,10-, and 6,12-ionenes grow in a three-dimensional direction, and 3,3-, 6,6-ionene promotes a preferential growth along the filament direction with a less vague growth in the lateral direction. Since the complex length of 3,3-ionene is much shorter than that of 6,6-ionene, we can expect that much thinner filaments were formed in 3,3-ionene than that in 6,6-ionene. As the lateral structures of the polymer-actin complexes are too small to be clearly observed by fluorescent optical microscope, we further studied polymer-actin complexes by TEM, using the negative staining technique. Figure 5 shows the TEM images of the actin complexes prepared at a molar ratio of ammonium cation of polymer to monomeric actin as 100:1 for p-Lys and 30:1 for ionene polymers at a constant F-actin concentration
Figure 4. Logarithmic plot of number of p-Lys-actin complexes (N) as a function of length (L) for different F-actin concentration after 90 min. N and L follow a power law N ∝ L-R where the exponent R depends on actin concentration as shown in the inserted figure. Actin concentration: (closed circle): 0.001 mg/mL, (closed square): 0.002 mg/mL, (open circle): 0.0033 mg/mL, (open square): 0.0066 mg/mL, (closed triangle): 0.01 mg/mL. The molar ratio of ammonium cation to monomeric actin was 100:1.
0.001 mg/mL. As shown in Figure 5a, actin forms a relatively homogeneous and thin filament in the presence of p-Lys, which agrees well with the small fractal dimension at a F-actin concentration 0.001 mg/mL in Figure 4 (insert). We also found that actin is able to form an extremely homogeneous nanoscale wire (nanowire) with 3,3-ionene (Figure 5b), and this is also in agreement with the prediction from the fractal dimension value. Filamentous complexes are observed in the presence of 6,6-ionene, (Figure 5c). Occasionally, a ring-shaped complex (nano-ring) is observed in a 6,6-ionene-actin complex (Figure 5d). The average width of the p-Lys-actin complex is 21.0 nm with a standard deviation of 2.6 nm. Compared with the native F-actins that have an average width of 12.1 nm with a standard deviation of 1.2 nm, p-Lys-actin complexes are only slightly thicker than that of the native F-actin with almost the same width scattering. 3,3-ionene complexes also showed a very thin and homogeneous wirelike morphology showing an average width of 16.1 nm with a standard deviation of 1.7 nm. However, from Figure 3b, we know that at a molar ratio of ammonium cation to actin monomer as 30:1, the 3,3-ionene polymer concentration is still below the critical concentration. Since the complex morphology is strongly dependent on the polymer concentration, we further investigated the 3,3-ionene-actin complex at a molar ratio of ammonium cation to actin monomer of 300:1 ([3,3-ionene]/[actin] ) 4.1 g/g), which is above the critical concentration of complex formation. As shown in Figure 5e, bundles of thin filaments are formed when the 3,3-ionene polymer exceeds the critical concentration. Similar morphology are observed for other x,y-ionene polymers above their critical concentration. Actin-6,4-, 6,6-, 6,10-, and 6,12ionene complexes have an average width of 79.0 nm, 59.3, 38.7, and 66.1 nm with a standard deviation of 60, 29, 21, and 27 nm, respectively (Figure 6a). The large scattering in the width of actin-6,4-, 6,6-, 6,10-, and 6,12-ionene complexes quantitatively indicates the randomness of the morphology of the complexes.
Growth of Polymer−Actin Complexes
Bioconjugate Chem., Vol. 14, No. 6, 2003 1189
Figure 5. Transmission electron microscopy (TEM) images of polymer-actin complexes formed by mixing F-actin and various polymers at room temperature for 240 min. (a) p-Lys, (b) 3,3-ionene, (c) 6,6-ionene, (d) 6,6-ionene, (e) 3,3-ionene, (f) F-actin only. Mixing molar ratios are the same as fluorescence microscope observation (Figure 1), except for part e which is carried out at 300:1 ([3,3-ionene]/[actin] ) 4.1 g/g). Actin concentration: 0.001 mg/mL.
The average length of the complexes as observed by TEM showed a similar dependence on the polymers, but the absolute values of the length are about 2 times shorter than that obtained from fluorescent observations (Figure 2b). This discrepancy is due to the breakage of the long filament during the sample drying process for TEM measurements. The axial ratio of polymer-actin complexes, which is the ratio of the average length from fluorescence image (Figure 2b) to the average width from TEM images, was estimated (Figure 6b). We find that the axial ratios are 653, 245, 104, 340, 179, and 196 for p-Lys, 3,3-, 6,4-, 6,6-, 6,10-, and 6,12-ionene, respectively. This tendency in the axis ratio values well coincides with that of the growth fractal dimension R as estimated from the fluorescent images of the complex during growth process. For example, P-Lys showed a smallest fractal dimension (Figure 4) which agrees well with the highest axial ratio. Furthermore, 3,3-, and 6,6-ionene showed a relatively smaller fractal dimension, and this is in agreement with a relatively high axial ratio of the complex as shown in Figure 6b. As a conclusion, p-Lys keeps the axial growth even above the critical concentration of cooperative growth, forming long and thin filaments, while x,y-ionene polymers change their growth mode from axial to lateral at the critical concentration and their average width at the concentration which gives half-length point is dominated by the cooperative energy (Fcoop.) between actin and ionene polymers. Thus, designed micro-order polymeractin complexes could be obtained by changing the structure of cationic polymer and other conditions. The motility of these actin-ionene complexes will be explored in future studies. Figure 6. Average width of polymer-actin complexes obtained at 240 min by TEM images (a), and axial ratios of polymeractin complexes evaluated by dividing the average length of complex obtained from fluorescence image by the average width obtained from TEM images (b). Error bar means standard deviation.
ACKNOWLEDGMENT
This research is financially supported by PRESTO, JST, and the Ministry of Education, Science, Sports, and Culture, Japan (Grand-in-Aid of Creative Scientific Research).
1190 Bioconjugate Chem., Vol. 14, No. 6, 2003 LITERATURE CITED (1) Kakugo, A., Sugimoto, S., Gong, J. P., and Osada, Y. (2002) Gel machines constructed from chemically cross-linked actins and myosins. Adv. Mater. 14, 1124-1126. (2) Oosawa, F., Asakura, S., Hotta, K., Imai, N., and Ooi. T. (1959) G-F transformation of actin as a fibrous condensation. J. Polymer. Sci. 37, 323-336. (3) Chen, L., Yu, S. Y., Kagami, Y., Gong, J. P., and Osada, Y. (1998) Surfactant binding of polycations carrying charges on the chain backbone: Cooperativity, stoichiometry and crystallinity. Macromolecules 31, 787-794. (4) Spudich, J. A., and Watt, S. (1971) The regulation of rabbit skeletal muscle contraction. I. Biochemical studies of the interaction of the tropomyosin-troponin complex with actin and the proteolytic fragments of myosin. J. Biol. Chem. 246, 4866-4871.
Kakugo et al. (5) Hayakawa, K., Santerre, J. P., and Kwak, J. C. (1983) Study of surfactant-polyelectrolyte interactions. Binding of dodecyland tetradecyltrimethylammonium bromide by some carboxylic polyelectrolytes. Macromolecules 16, 1642-1645. (6) Gong, J. P., Mizutani, T., and Osada, Y. (1996) A comparative study on the cooperative binding of surfactants with solubilized polymers and networks. Polym. Adv. Techol. 7, 797-804. (7) Satake, I., and Yang, J. T. (1976) Interaction of sodiumdecyl sulfate with poly (L-ornithine) and poly (L-lysine) in aqueous solution. Biopolymers 15, 2263-2275. (8) Gong, J. P., Kagami, Y., Yamada, K., and Osada, Y. (1990) Fractal pattern formation of metal containing polymeric thin films prepared by plasma reaction. Bull. Chem. Soc. Jpn. 63, 1578-1583.
BC0340722
