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Langmuir 1999, 15, 4208-4212
Novel Polyion Complex Micelles Entrapping Enzyme Molecules in the Core. 2. Characterization of the Micelles Prepared at Nonstoichiometric Mixing Ratios† Atsushi Harada and Kazunori Kataoka* Department of Materials Science, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Received August 24, 1998. In Final Form: January 21, 1999 Physicochemical properties of polyion complex (PIC) micelles formed from chicken egg white lysozyme and poly(ethylene glycol)-poly(aspartic acid) block copolymer at nonstoichiometric mixing ratios were investigated using dynamic and static light scattering as well as laser-Doppler electrophoresis measurements. The formation of spherical PIC micelles with core-shell architecture was suggested by dynamic light scattering and laser-Doppler electrophoresis measurements despite a change in mixing ratio. Estimation of the critical association concentration (cac) using Debye plots of static light scattering (SLS) confirmed that the cac values converted to the concentration of the charged segments were independent of the mixing ratio. Further, the association number of lysozyme and PEG-P(Asp), the core size, and the corona thickness were calculated by using the apparent weight average molecular weight determined from Zimm plots of SLS and the density of lysozyme and P(Asp). It was indicated that the association number of PEG-P(Asp) and the corona thickness increased with an increase in the mixing ratio. However, the association number of lysozyme and the core size kept constant and were determined to be ca. 50 molecules and ca. 7 nm, respectively. That is, the density of lysozyme in the core was also independent of the mixing ratio. Such PIC micelles entrapping enzymes in the core are expected to be available as functional materials including a carrier system in drug delivery and a nanoreactor for enzymes.
Introduction Supramolecular assembly has recently received considerable attention from various fields of polymer science.1,2 This includes polymeric micelles formed from block copolymers in selective solvents. Many studies on polymeric micelles have been reported by several research groups.3-13 Polymeric micelles were studied not only from the viewpoint of fundamental interests but also from applied fields. Their characteristics, which are relevant size with several tens of nanometers and the core-shell structure, lend for many application including drug delivery systems,14-19 separation technology,20,21 optoelectronic devices,22 and surface modification.23,24 * To whom correspondence should be addressed. Tel: +81-33812-2111 (ext. 7138). Fax: +81-3-3815-8363. E-mail: kataoka@ bmw.mm.t.u-tokyo.ac.jp. † Presented at Polyelectrolytes ’98, Inuyama, Japan, May 31June 3, 1998. (1) Whitesides, G. M.; Mathias, J. P.; Seto, C. T. Science 1991, 254, 1312. (2) Fre´chet, J. M. Science 1994, 263, 1710. (3) Tuzar, Z.; Kratochvı´l, P. Adv. Colloid Interface Sci. 1976, 6, 201. (4) Zhou, Z.; Chu, B. J. Colloid Interface Sci. 1988, 126, 171. (5) Zhao, C.-L.; Winnik, M. A.; Riess, G.; Croucher, M. D. Langmuir 1990, 6, 514. (6) Cao, T.; Munk, P.; Ramireddy, C.; Tuzar, Z.; Webber, S. E. Macromolecules 1991, 24, 6300. (7) Qin, A.; Tian, M.; Ramireddy, C.; Webber, S. E.; Munk, P.; Tuzar, Z. Macromolecules 1994, 27, 120. (8) Prochazka, K.; Martin, T. J.; Munk, P.; Webber, S. E. Macromolecules 1996, 29, 6518. (9) Zhang, L.; Eisenberg, A. Science 1995, 268, 1728. (10) Astafieva, I.; Khougaz, K.; Eisenberg, A. Macromolecules 1995, 28, 7127. (11) Moffitt, M.; Khougaz, K.; Eisenberg, A. Acc. Chem. Res. 1996, 29, 95. (12) Kwon, G.; Naito, M.; Yokoyama, M.; Okano, T.; Sakurai, Y.; Kataoka, K. Langmuir 1993, 9, 945. (13) Cammas, S.; Kataoka, K. Macromol. Chem. Phys. 1995, 196, 1899. (14) Yokoyama, M.; Miyauchi, M.; Yamada, N.; Okano, T.; Sakurai, Y.; Kataoka, K.; Inoue, S. Cancer Res. 1990, 11, 269.
Recently, we have reported a new concept for the formation of polymeric micelles in aqueous medium. This involves the spontaneous formation of a macromolecular assembly, “polyion complex (PIC) micelle”, driven through electrostatic interaction in aqueous medium from a pair of oppositely charged block copolymers with poly(ethylene glycol) segments.25,26 The PIC micelles are totally water soluble under electrically neutralized mixing ratios and narrowly distributed. The PIC micelles were formed not only from a pair of oppositely charged block copolymers but also from mixtures of an oppositely charged pair of block copolymers with the other kind of polyelectrolytes including poly(amino acid), oligo DNA, and enzyme and vinyl polymers.27-32 In our previous paper, we have (15) Kataoka, K. J. Macromol. Sci., Pure Appl. Chem. 1994, A31, 1759. (16) Kataoka, K.; Kwon, G. S.; Yokoyama, M.; Okano, T.; Sakurai, Y. J. Controlled Release 1993, 24, 119. (17) Kwon, G. S.; Suwa, S.; Yokoyama, M.; Okano, T.; Sakurai, Y.; Kataoka, K. J. Controlled Release 1994, 29, 17. (18) Kabanov, A. V.; Cheknonin, V. P.; Alakhov, V. Y.; Betrakova, E. V.; Lebedev, A. S.; Mellik-Nubarov, N. S.; Arzhakov, S. A.; Lerashov, A. S.; Morozov, G. V.; Severin, E. S.; Kabanov, V. A. FEBS Lett. 1989, 258, 343. (19) Zhang, X.; Jackson, J. K.; Burt, H. M. Int. J. Pharm. 1996, 132, 195. (20) Nagarajan, R.; Barry, M.; Ruckenstein, E. Langmuir 1986, 2, 210. (21) Hurter, P. N.; Hatton, T. A. Langmuir 1992, 8, 1291. (22) Spartz, J. P.; Sheiko, S.; Mo¨ller, M. Macromolecules 1996, 29, 3220. (23) Webber, S. E. J. Phys. Chem. B 1998, 102, 2618. (24) Emoto, K.; Nagasaki, Y.; Kataoka, K. Langmuir, submitted for publication. (25) Harada, A.; Kataoka, K. Macromolecules 1995, 28, 5294. (26) Harada, A.; Kataoka, K. Science 1999, 283, 65. (27) Kataoka, K.; Togawa, H.; Harada, A.; Yasugi, K.; Matsumoto, T.; Katayose, S. Macromolecules 1996, 29, 8556. (28) Harada, A.; Kataoka, K. J. Macromol. Sci., Pure Appl. Chem. 1997, A34, 2119. (29) Harada, A.; Kataoka, K. Macromolecules 1998, 31, 288. (30) Katayose, S.; Kataoka, K. Bioconjugate Chem. 1997, 8, 702.
10.1021/la981087t CCC: $18.00 © 1999 American Chemical Society Published on Web 04/06/1999
Micelles Entrapping Enzyme Molecules
reported the stoichiometry of the formation of PIC micelles from chicken egg white lysozyme as model enzyme and poly(ethylene glycol)-poly(R,β-aspartic acid) block copolymer (PEG-P(Asp)).29 The stoichiometric mixing ratio was an equal molar ratio of the number of aspartic acid residues in PEG-P(Asp) compared to that of arginine and lysine residues in lysozyme. PIC micelles prepared at a stoichiometric mixing ratio had a spherical shape and nanoscopic diameter with extremely narrow distribution. Also, when PIC micelles were prepared at the mixing ratio including excess lysozyme, the formation of PIC micelles occurred in a cooperative manner; i.e., there was coexistence of free lysozyme and PIC micelles formed at a stoichiometric mixing ratio. On the other hand, the formation of PIC micelles was in a noncooperative manner under excess PEG-P(Asp). However, the formed PIC micelles kept an extremely narrow distribution in a wide range of mixing ratios, suggesting the formation of a macromolecular assembly with a highly regular structure. Here, we focus in more detail on PIC micelles prepared at nonstoichiometric mixing ratios. It was expected that they form a regular structure. The detailed physicochemical properties of PIC micelles were estimated by dynamic and static light scattering as well as laser-Doppler electrophoresis measurements. It might be important to clarify the physicochemical properties from a fundamental viewpoint involving the formation of polyion complexes from enzymes and synthetic polyelectrolytes or the formation of polymeric micelles in aqueous medium. In addition, it was expected to be useful in the design of novel functional materials including carrier systems in drug delivery and nanometric-scale reactors for enzymes. Experimental Section Materials. R-Methoxy-ω-aminopoly(ethylene glycol) (Mw ) 12 000 g/mol) was a kind gift from Nippon Oil & Fats Co., Ltd., Tokyo, Japan. β-Benzyl-L-aspartate N-carboxyanhydride (BLANCA) was synthesized from β-benzyl-L-aspartate by the FuchsFarthing method using triphosgene.33,34 Chicken egg white lysozyme was purchased from Sigma, St. Louis, MO, and used without further purification. Synthesis of Poly(ethylene glycol)-Poly(r,β-aspartic acid) Block Copolymer.25,29,33,34 Poly(ethylene glycol)-poly(R,β-aspartic acid) block copolymer [PEG-P(Asp)] was obtained by the procedure previously reported.25,29,33,34 Briefly, PEGP(Asp) was synthesized by alkali hydrolysis of benzyl groups at the side chain of poly(ethylene glycol)-poly(β-benzyl-L-aspartate) block copolymer (PEG-PBLA), which was synthesized by the ring-opening polymerization of BLA-NCA initiated by the terminal primary amino group of R-methoxy-ω-aminopoly(ethylene glycol) (Mw ) 12 000 g/mol) under argon atmosphere in dimethylformamide (DMF). From the 1H NMR spectrum (400 MHz, EX400, JEOL, Tokyo, Japan) in D2O, the polymerization degree of aspartic acid unit was determined to be 15. Preparation of Polyion Complex Micelles. Given amounts of lysozyme and PEG-P(Asp) were dissolved in sodium phosphate buffer (10 mM, pH 7.4; Na2HPO4‚12H2O, 2.865 g/L; NaH2PO4‚ 2H2O, 0.312 g/L). These solutions were mixed at various mixing ratio after filtration through a 0.1 µm filter to remove dust. The number of aspartic acid residues in PEG-P(Asp) against the total number of lysine and arginine residues in lysozyme (r ) [Asp in PEG-P(Asp)]/[Lys and Arg in lysozyme]) was used as a major parameter in this study. (31) Kabanov, A. V.; Bronich, T. K.; Kabanov, V. A.; Yu, K.; Eisenberg, A. Macromolecules 1996, 29, 6797. (32) Bronich, T. K.; Kabanov, A. V.; Kabanov, V. A.; Yu, K.; Eisenberg, A. Macromolecules 1997, 30, 3519. (33) Yokoyama, M.; Inoue, S.; Kataoka, K; Yui, N; Sakurai, Y. Macromol. Chem. Rapid Commun. 1987, 8, 431. (34) Yokoyama, M.; Inoue, S.; Kataoka, K.; Yui, N.; Okano, T.; Sakurai, Y. Makromol. Chem. 1989, 190, 2041.
Langmuir, Vol. 15, No. 12, 1999 4209 Light Scattering Measurements.29 The light scattering measurements were carried out using a DLS-700 instrument (Otsuka Electronics Co., Ltd., Osaka, Japan). Vertically polarized light of 488 nm wavelength from Ar ion laser (15 mW) was used as an incident beam. All measurements were carried out at 25.0 ( 0.2 °C. In dynamic light scattering measurements, the autocorrelation function, g(τ), was analyzed using the cumulant method35 in which
g(τ) ) exp[-Γ h τ + (µ2/2)τ2 - (µ3/3!)τ3 + ...] yielding an average characteristic line width Γ h . The z-averaged diffusion coefficient was obtained from Γ h on the basis of the following equations:
Γ h ) Dq2 q ) (4πn/λ) sin(θ/2) Here q is the magnitude of the scattering vector, n is the refractive index of solvent, and θ is the detection angle. The hydrodynamic radius, Rh, can then be calculated using the Stokes-Einstein equation:
Rh ) kBT/(6πηD) Here kB is the Boltzmann constant, T is the absolute temperature, and η is the viscosity of solvent. In static light scattering measurements, the light scattered by a dilute polymer solution may be expressed by the following equation:
KC/∆R(θ) ) (1/Mw,app)(1 + q2Rg2/3) + 2A2C Here C is the concentration of polymer, ∆R(θ) is the difference between the Rayleigh ratio of the solution and that of the solvent, Mw,app is the apparent weight average molecular weight, Rg2 is the mean-square radius of gyration, A2 is the second virial coefficient, and K ) (4π2n2(dn/dc)2)/(NAλ4) (NA is Avogadro’s number). The known Rayleigh ratio of benzene was used as a calibration standard. The increments of refractive index, dn/dc, of the solutions were measured using a DRM-1020 double-beam differential refractometer (Otsuka Electronics Co., Ltd., Osaka, Japan). For the system investigated here, it was already confirmed that the experimental dn/dc values agreed well with the calculated dn/dc values.29 Laser-Doppler Electrophoresis Measurements.29 LaserDoppler electrophoresis measurements were carried out using a LEZA-600 (Otsuka Electronics Co., Ltd., Osaka, Japan) at 25.0 ( 0.2 °C with an electrical field strength of 30-35 V/cm. From the obtained electrophoretic mobility, the zeta-potential, ζ, was calculated by using the Smoluchowski equation as follows:
ζ ) 4πηu/ Here u is the electrophoretic mobility, η is the viscosity of the solvent, and is the dielectric constant of the solvent.
Results and Discussion Estimation of the Structure of PIC Micelles. A detailed analysis based on a cumulant method was carried out for the PIC micelles prepared at various mixing ratios (r ) 1.000, 1.600, 2.000, and 2.667) which included stoichiometric mixing ratios and nonstoichiometric mixing ratios with excess PEG-P(Asp). The results for the sample prepared at r ) 1.000 were shown for comparison, although they were already reported in previous paper.29 These h 2 in the range of 0.04-0.05, samples gave values of µ2/Γ suggesting a narrow size distribution.29 Figure 1a shows the relationship between an average characteristic line width (Γ h ) and a square of the scattering vector (q2). For (35) Koppel, D. E. J. Chem. Phys. 1972, 57, 4814.
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Harada and Kataoka
Table 1. Light Scattering Data for PIC Micelles Prepared at Various Mixing Ratios
c
mixing ratio
Rha (nm)
Rgb (nm)
Rg/Rh
Mw,appb (106 g/mol)
A2b [10-5 (mol‚mL)/g2]
1.000 1.600 2.000 2.667
23.63 27.06 29.35 32.87
17.10 18.65 19.93 21.75
0.724 0.689 0.679 0.662
1.668 1.848 2.051 2.296
2.514 2.506 2.500 2.493
association no.c lysozyme PEG-P(Asp) 56 46 44 40
62 84 101 122
a Determined from the diffusion coefficient at infinite dilution using the Stokes-Einstein equation. b Obtained from Zimm plots of SLS. Calculated from the Mw,app values on the basis of the assumption that the PIC micelles were formed at the loading ratio.
Figure 2. Relationship between the KC/∆R(0) values and the concentration for PIC micelles prepared at r ) 2.000 (detection angles, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, and 150°; temperature, 25.0 ( 0.1 °C). Table 2. ζ-Potential of PIC Micelles Prepared at Various Mixing Ratios
Figure 1. Estimation of PIC micelles using the cumulant analysis of DLS: (a) angular dependence; (b) concentration dependence. Key: b, r ) 1.000; 2, r ) 1.600; 9, r ) 2.000; 1, r ) 2.667; detection angles, 30, 60, 90, 120, and 150° in (a) and 90° in (b); temperature, 25.0 ( 0.1 °C.
the spherical particles, the Γ h /q2 ()D) values should be independent of the scattering vector because of the undetectable rotational motion.36 The correlation coefficients for all mixtures were 1.000, suggesting that the formed micelles may have a spherical shape, since the linearity of the plots of Γ h vs q2 reflect the dependence of 2 on the scattering vector. From the Γ h /q2 ()D) values, Γ h /q Rh of the PIC micelles at different mixing ratios was calculated on the basis of the Stokes-Einstein equation, and results are summarized in Table 1. There is observed an obvious increase in Rh with an increase in mixing ratio, being consistent with a trend of Mw,app and Rg determined by static light scattering as described in detail in a subsequent section. These results strongly suggest that the formation of PIC micelles may proceed in a noncooperative manner under the excess of PEG-P(Asp), and thus, the PIC micelles in this condition involve an excess number of PEG-P(Asp) compared to the stoichiometric PIC micelles formed at r ) 1.000. This is in a sharp contrast to the PIC micelle formation under the excess of lysozyme (r < 1.000), in which the micelle formation occurred in a (36) Xu, R.; Winnik, M. A.; Hallett, F. R.; Riess, G.; Croucher, M. D. Macromolecules 1991, 24, 87.
mixing ratio
ζ-potential (mV)
mixing ratio
ζ-potential (mV)
1.000 1.600
-0.06 ( 0.58 -1.02 ( 0.61
2.000 2.667
-0.97 ( 0.83 -1.21 ( 0.64
cooperative manner to be coexistent with free lysozyme and stoichiometric PIC micelles. Figure 1b shows the dependence of the diffusion coefficient (D) on the concentration. It was obvious that the D values were independent of the concentration. An increase in the concentration induced no formation of secondary aggregates (the cluster of PIC micelles), suggesting that the steric repulsions of the PEG segments are effectively preventing the aggregation of the PIC micelles. These results were consistent with a core-shell structure. Further, the values of the ζ-potentials for the PIC micelles were extremely small absolute values regardless of varying the mixing ratio as summarized in Table 2, indicating that the surfaces of the PIC micelles were surrounded by the PEG segments being electrically neutral. Estimation of the Critical Association Concentration (cac) Using SLS. The determination method of the cac used here was reported by Eisenberg et al.37 They reported the determination of the cac for the polymeric micelles from polystyrene-poly(sodium acrylate) block copolymer in tetrahydrofuran, polystyrene-poly(4-vinylpyridine) block copolymer in toluene, and polystyrenepolyisoprene block copolymer in n-hexadecane by using Debye plots of SLS expressed as the following equation:
KC/∆R(0) ) 1/Mw,app + 2A2C Figure 2 shows the relationship between the KC/∆R(0) and the concentration of PIC micelles prepared at r ) 2.000. A steep decrease in the KC/∆R(0) values with increasing concentration was observed at relatively low (37) Khougaz, K.; Gao, Z.; Eisenberg, A. Macromolecules 1994, 27, 6341.
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Langmuir, Vol. 15, No. 12, 1999 4211
Figure 3. Change in the critical association concentration (cac) with the mixing ratio: (O, cac of total concentration (lysozyme + P(Asp) + PEG); 4, cac converted to the concentration of charged segments (lysozyme + P(Asp)).
Figure 4. Zimm plots of PIC micelles prepared at r ) 2.000 (detection angles, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, and 150°; total concentration, 4.0, 6.0, 8.0, and 10.0 mg/mL; cac, 1.34 mg/mL; temperature, 25.0 ( 0.1 °C).
concentrations. A straight line with a moderate slope at relative high concentration was observed. This means that the A2 values have a negative value in the region of relatively low concentration and were positive at relatively high concentration. Similar plots were observed for samples prepared at the other mixing ratios. This change was a typical phenomenon for the polymeric micelles in selective solvents. Eisenberg et al. determined the cac by considering the polydispersity of the block copolymers and extrapolating to the KC/∆R(0) corresponding to the molecular weight of the block copolymers. Here, we defined the cac as the point of intersection of two straight lines in the relatively low concentration range (A2 < 0) and at higher concentration range (A2 > 0). Consequently, the cac value obtained here become a considerably higher than the cac value determined by the method of Eisenberg et al. Figure 3 shows the change in the total cac (lysozyme + PEG-P(Asp); open circles) thus determined as a function of the mixing ratio. The total cac values increased with an increase in the mixing ratio. However, the cac values converted to the concentration of charged segments (lysozyme + P(Asp) segment in the block copolymer; open triangles in Figure 3) remained constant (0.55 mg/mL). This suggests that the cac value of the PIC micelles formed from lysozyme and PEG-P(Asp) may be determined by the complexation power of the charged segments, lysozyme and P(Asp) segments. As determined by light scattering as well as laserDoppler electrophoresis measurements, the PIC micelles from lysozyme and PEG-P(Asp) had a spherical shape with narrowly size distribution, and their ζ-potentials were close to zero. These results strongly suggest that nonionic PEG segments surround the surface of PIC micelles to form a core-shell architecture. Further, the finding that cac values are determined by the concentration of the charged segments is also consistent with core-shell structure, which the polyion complexes formed from lysozyme and the P(Asp) segments were surrounded by PEG segments. Detailed Analysis of PIC Micelles Using Static Light Scattering. To estimate the Mw,app, Rg, and A2 of the PIC micelles, Zimm plots were made from the following equation, which considered the influence of the critical association behavior:
at r ) 2.000. Similar plots were obtained from PIC micelles prepared at the other mixing ratios. The obtained Mw,app, Rg, and A2 are summarized in Table 1. The hydrodynamic radius (Rh), which was calculated from the diffusion coefficient at infinite dilution (in Figure 1b) using the Stokes-Einstein equation, is also summarized in Table 1. The Rh, Rg, and Mw,app values increased with an increase in the mixing ratio. The A2 values were considerably small (ca. 2.5 × 10-5 (mol‚mL)/g2) compared with that of the polymer in good solvents, for which the A2 value is generally on the order of 10-4 (mol‚mL)/g2.38 Small A2 values for this PIC micelle system were consistent with the formation of polymeric micelles, because the polymeric micelles generally have quite small A2 values.39,40 Also, the ratio of Rg and Rh (Rg/Rh) decreased with an increase in the mixing ratio. It is known that the Rg/Rh value is theoretically 0.776 for a hard sphere.38 The values obtained here smaller than 0.776 can be explained by considering the formation of a core-shell architecture. In the case of particles with a core-shell architecture, the density decreases from the center to outer area in a radial direction and Rg may decrease compared to that of a hard sphere. Consequently, the Rg/Rh values for the PIC micelles summarized in Table 1 were reasonable. The reason for the decrease of the Rg/Rh values with an increase in the mixing ratio will be discussed later. The association numbers of PEG-P(Asp) and lysozyme were calculated from the Mw,app values by using the molecular weight of PEG-P(Asp) (14 600 g/mol) and lysozyme (14 300 g/mol), based on the assumption that the PIC micelles were formed at the loading ratio. The calculated association numbers of PEG-P(Asp) and lysozyme for different mixing ratios are also summarized in Table 1. Although the association number of PEGP(Asp) linearly increased with an increase in the mixing ratio, the association number of lysozyme slightly decreased with an increase in the mixing ratio. Further, the radius of the core and the thickness of the corona were determined from the density of P(Asp) and lysozyme. The densities of P(Asp) and lysozyme at 25.0 °C were determined to be 1.084 and 1.106 g/cm3, respectively, using a picnometer. Assuming that the core of the PIC micelles included no solvent (water) and the density in the core was homogeneous, the core size (rcore) could be
K(C - cac)/(∆R(0) - ∆R(0)cac) )
(38) Douglas, J. K.; Roovers, J.; Freed, K. F. Macromolecules 1990, 23, 4168. (39) Quintana, J. R.; Ja´nez, M. D.; Villacampa, M.; Katime, I. Macromolecules 1995, 28, 4139. (40) Villacampa, M.; Apodaca, E. D.; Quintana, J. R.; Katime, I. Macromolecules 1995, 28, 4144.
2
2
1/Mw,app(1 + q Rg /3) + 2A2(C - cac) Figure 4 shows Zimm plots of the PIC micelles prepared
4212 Langmuir, Vol. 15, No. 12, 1999
Figure 5. Change in the core size (rcore) and the corona thickness (rcorona) with the mixing ratio.
calculated from the Mw,app of PIC micelles and the densities of P(Asp) and lysozyme by using the following equation:
rcore ) [(3Mw,app/4πNA)(WP(Asp)/φP(Asp) + Wlysozyme/φlysozyme)]1/3 Here Wi and φi are the weight fractions and the densities of P(Asp) and lysozyme, respectively. The corona thickness (rcorona) was then calculated from the following equation:
rcorona ) Rh - rcore Figure 5 shows the change in the core size and the corona thickness with the mixing ratio. The rcore values of PIC micelles remained constant (ca. 7 nm), but the rcorona linearly increased with an increase in the mixing ratio. It should be noticed that the density of lysozyme in the core was constant, since both the association number of lysozyme and the core size were independent of the mixing ratio. Taking into account the formation of PIC micelles with core-shell structure, the distance from the center of core to the interface between core and corona, i.e., the core radius, has to be shorter than the end-to-end distance of the P(Asp) segment with fully expanded conformation, since the junction point of the PEG and P(Asp) segments needs to align around the interface between core and corona. Further, the density in the core should keep its homogeneity. In this respect, the obtained results of the core size (rcore) may be reasonable, since the end-to-end distance of the P(Asp) segment (DP ) 15) with fully expanded model was calculated to be 8.25 nm 41 and was longer than the rcore value (ca. 7 nm). Also, it was assumed in the calculation process of the rcore values that the density in the core was homogeneous. On the other hand, the Rg/Rh values decreased with an increase in the mixing ratio as summarized in Table 1. This can be explained from the results of the rcore and Rh values. That is, the Rg/Rh values decreased due to a larger increase in the Rh values as compared to the small increase in the Rg values, since the contribution of the densely packed core to the whole size decreased with an increase in the mixing ratio. (41) Pauling, L.; Corey, R. B. Proc. Int. Wool Text. Res. Conf. 1955, B, 249.
Harada and Kataoka
The thermodynamics of PEG segments constructing the corona may be also one of the important parameters in the formation of PIC micelles. Considering the results on the corona thickness shown in Figure 5, the PEG segments must take a more elongated conformation with increasing mixing ratio, which is thermodynamically unfavorable. The end-to-end distance of PEG was calculated on the basis of three models: meander, zigzag, and random coil models.42 The meander model assumes that the polymer chain is twisted into an expanded helical coil. The zigzag model is assuming that the chain takes a fully expanded conformation. In the case of the PEG with molecular weight of 12 000 g/mol (DP ) 273), the end-to-end distances were calculated to be 34.4-38.3, 95.5, and 5.8 nm on the basis of the meander, zigzag, and random coiled models, respectively. The experimental values of corona thickness (16.7-26.2 nm) shown in Figure 5 suggest that the PEG corona in PIC micelles may not take a fully elongated conformation, which is in line with the results reported for the other polymeric micelle systems with a core-shell structure.36 Thus, thermodynamic penalty due to an elongated conformation of PEG with increasing the mixing ratio may not become a major determination factor in the micellization of lysozyme with PEG-P(Asp) compared to the complexation power based on electrostatic interaction. Conclusions In this study, the characterization of PIC micelles formed from lysozyme and PEG-P(Asp) at nonstoichiometric mixing ratios including excess PEG-P(Asp) to lysozyme were carried out using light scattering techniques. PIC micelles prepared at various mixing ratios had a spherical shape and extremely low absolute values of ζ-potential, suggesting that the polyion complexes formed from lysozyme and P(Asp) segments were surrounded by nonionic PEG segments, i.e., the formation of a core-shell structure. The critical association concentration (cac), the association number, the core size, and the corona thickness were determined. The cac values converted to the concentration of charged segments (lysozyme + P(Asp) segment) were independent of the mixing ratio, although the total cac values (lysozyme + PEG-P(Asp)) increased with an increase in the mixing ratio. The association number of lysozyme and the radius of the core were also independent of the mixing ratio. The core of PIC micelles investigated here had a radius of ca. 7 nm, and ca. 50 molecules of lysozyme were packed in the condensed core. This might be interesting from the viewpoint of the application of this system as a nanoreactor. Indeed, we have already confirmed an acceleration of enzymatic reaction by the incorporation into PIC micelles, and the details of this will be reported in our forthcoming paper.43 Acknowledgment. The authors thank Dr. Henk Stapert, Twente University, Enschede, The Netherlands, for the critical reading of the manuscript. A.H. acknowledges the Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. LA981087T (42) Tanford, C.; Nozaki, Y.; Rohde, M. F. J. Phys. Chem. 1977, 81, 1555. (43) Harada, A.; Kataoka, K. Manuscript in preparation.
