Effects of Cations on the Sorting of Oppositely Charged Microgels

May 6, 2009 - ... and Technology of China, Hefei, China, and Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong...
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J. Phys. Chem. B 2009, 113, 7457–7461

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Effects of Cations on the Sorting of Oppositely Charged Microgels Yi Hou,† Jing Ye,†,‡ Xiaoling Wei,†,‡ and Guangzhao Zhang*,† Hefei National Laboratory for Physical Sciences at Microscale, Department of Chemical Physics, UniVersity of Science and Technology of China, Hefei, China, and Department of Chemistry, The Chinese UniVersity of Hong Kong, Shatin, N.T., Hong Kong ReceiVed: March 20, 2009

Two kinds of thermally sensitive oppositely charged polymeric microgels, poly(N-isopropylacrylamide-cosodium acrylate) (NIPAM-co-SA) and poly(N-isopropylacrylamide-co-vinylbenzyl trimethylammonium chloride) (NIPAM-co-VT), have been prepared by dispersion polymerization. Their temperature-induced aggregation was studied by use of laser light scattering. In the absence of a salt, NIPAM-co-SA and NIPAMco-VT microgels in the mixture do not aggregate but shrink upon the heating. The addition of monovalent cations does not affect the aggregation. In the presence of divalent metal ions, the heating leads to the association of NIPAM-co-SA microgels via the complexation of metal ions and carboxyl groups on the microgel surface when the temperature approaches their lower critical solution temperature (LCST ∼ 32 °C). Further heating over the LCST results in the adsorption of NIPAM-co-VT microgels on the NIPAMco-SA aggregate via the electrostatic attraction so that a core-shell structure with a NIPAM-co-SA core and a NIPAM-co-VT shell forms, resembling the biological cell-sorting. Introduction As a fundamental issue in colloid science, aggregation of oppositely charged colloids is useful for our understanding the molecular interactions. It is also important in various applications such as paper-making, flotation, and water purification.1 Such an heteroaggregation has been investigated in the past years. Theoretically, the aggregation has been described by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory.2 Experimentally, the time evolution of the size and structure of oppositely charged colloids have been investigated.3 It has been demonstrated that the fractal structure and kinetics of heteroaggregates can be controlled by electrolyte concentration, which alters the range of electrostatic interactions between the colloidal particles.4 However, the formation and structure of the heteroaggregates need to be further examined. On the other hand, cell sorting usually occurs in tissue formation and repair, where unlike cells occupy different parts of the aggregate or separate each other.5-9 The sorting is actually a heteroaggregation. Steinberg10 proposed that the sorting depend on the adhesion between unlike cells. The hypothesis has been tested valid later by calculation.11,12 Monte Carlo simulations show that the less adhesive cells usually engulf the more adhesive ones when cell sorting occurs.13,14 Experiments about chicken embryonic tissues15 and hydra cells16-19 demonstrate that ectodermic cells are less adhesive than endodermic cells, so that endodermic cell dynamics is dominated by the adherent behavior of ectodermic cells. Studies on cell-cell interaction reveal that the connection of cadherin and calcium ion (Ca2+) is responsible for homophilic adhesion between cells.20-23 Considering that cell sorting depend upon the type and level of cadherins they express,24 the role of cadherin adhesion in cadherin-calcium binding with the cytoskeletal network has been investigated at the cellular level.25-28 Note that cell * To whom correspondence should be addressed. † University of Science and Technology of China. ‡ The Chinese University of Hong Kong.

adhesion may not be the only factor determining cell-sorting.29 Harries has proposed cortical tension between cells could also contribute to cell sorting.30,31 Because of the complexity of biological system, the mechanism of cell-sorting is also not clear yet. In this study, poly(N-isopropylacrylamide-co-sodium acrylate) (NIPAM-co-SA) and poly(N-isopropylacrylamide-co-vinylbenzyl trimethylammonium chloride) (NIPAM-co-VT) microgels with negative and positive charges, respectively, were prepared by dispersion polymerization. The microgels with concentrated polymer chains in them have similarities to a cell with crowded macromolecules inside. It is known that some metal ions can interact with carboxylic groups (COO-) on microgel surface and lead the microgels to aggregate.32,33 Because of the different ability to bind with cations, the oppositely charged microgels would express different adhesive ability so they are expected to sort. By use of laser light scattering (LLS) and high-resolution transmission electron microscopy (HRTEM), we have investigated the aggregation and structure of the unlike microgels. Our aim is to understand the role of ions on cell-sorting by using microgels as a simple model. Experimental Section Materials. N-isopropylacrylamide (NIPAM, Kohjin) was recrystallized three times from a benzene/n-hexane mixture prior to use. Sodium acrylate (SA) and vinylbenzyl trimethylammonium chloride (VT) from Aldrich were used as received. N,Nmethylenebisacrylamide (MBA) from Sinopharm was purified by recrystallization from methanol. Potassium persulfate (KPS) from Sinopharm was recrystallized from deionized water. CaCl2, MgCl2, NH4Cl, NaCl, were all AR grade (Sinopharm) and used without further purification. Other regents were all used as received. Preparation of Microgels. The preparation of microgels is detailed elsewhere.34 Typically, NIPAM (1.011 g, 0.009 mol), SA (0.094 g, 0.001 mol) or VT (0.212 g, 0.001 mol) and MBA (0.077 g, 0.0005 mol) were dissolved in deionized water (190

10.1021/jp902556m CCC: $40.75  2009 American Chemical Society Published on Web 05/06/2009

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Figure 1. Temperature dependences of the average radius of gyration 〈Rg〉 and average hydrodynamic radius 〈Rh〉 of NIPAM-co-SA, NIPAMco-VT microgels and their mixture (1/1, w/w). The inset shows the temperature dependence of weight-average molar mass (Mw), where the microgel concentration is 5.0 × 10-5 g/mL.

mL) in a 500 mL three-necked flask. After the reactor was purged with bubbling nitrogen for 30 min, 0.027 g of KPS in 10 mL of deionized water was introduced. The mixture was stirred under nitrogen bubbling at 70 °C for 8 h. The resultant solution was dialyzed for one week against deionized water using a semipermeable membrane with a molar mass cutoff of 3500 g/mol to remove the unreacted monomers. Microgel dispersions for all measurements were prepared with Millipore water. A buffer was not used to prepare the dispersion so that the effect of ions in the buffer could be avoided. ζ-potentials of NIPAM-co-SA and NIPAM-co-VT microgels measured on Malvern Zetasizer Nano ZS90 are -26.3 and 6.4 mV, respectively. Namely, they have opposite surface charges. Laser Light Scattering. A commercial spectrometer (ALV/ DLS/SLS-5022F) equipped with multi-τ digital time correlation (ALV5000) and a cylindrical 22 mW UNIPHASE He-Ne laser (λ0 ) 632 nm) as the light source was used. In static LLS,35 we can obtain the weight-average molar mass (Mw) and z-average root-mean-square radius of gyration (〈Rg〉) of particles in a dilute solution from the angular dependence of the excess absolute scattering intensity or Rayleigh ratio Rvv(q) by Zimm plot. For large aggregates, Mw and 〈Rg〉 were obtained by Guinier plot.36 In dynamic LLS,37 the measured intensity-intensity time correlation function G(2)(q,t) in the self-beating mode can transfer into line-width distribution G(Γ) by Laplace inversion. For a pure diffusive relaxation, G(Γ) is related to the translational diffusion coefficient D by (Γ/q2)Cf0,qf0 f D, and further to the hydrodynamic radius Rh via the Stokes-Einstein equation, Rh ) kBT/6ηπ0D, where kB, T, and η0 are the Boltzmann constant, absolute temperature, and solvent viscosity, respectively. The sample was stood for 2-3 h at each temperature so that the system was in equilibrium. The precision of temperature is (0.05 °C. High-Resolution Transmission Electron Microscopy. The morphology of the aggregates was observed on a JEOL2100 high-resolution transmission electron microscope operating at an acceleration voltage of 200 KV. The samples for the HRTEM measurements were prepared by deposition of one drop of dilute aqueous dispersion of mixture microgels with a concentration of 1.0 × 10-4 g/mL on a copper grid coated with thin films of carbon at a desired temperature. Some samples were stained

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Figure 2. Temperature dependences of the average hydrodynamic radius 〈Rh〉 and the weight-average molar mass (Mw) of NIPAM-coSA microgels at different [Ca2+], where the microgel concentration is 5.0 × 10-5 g/mL.

Figure 3. Temperature dependences of the average radius of gyration 〈Rg〉 and average hydrodynamic radius 〈Rh〉 of NIPAM-co-VT microgels in the presence of Ca2+, where the concentrations of microgels and Ca2+ are 5.0 × 10-5 g/mL and 0.03 M, respectively. The inset shows the temperature dependence of Mw.

Figure 4. Hydrodynamic radius distributions f(Rh) of NIPAM-co-SA, NIPAM-co-VT microgels and their mixture (1/1, w/w) in the presence of Ca2+ at 51 °C, where the concentrations of microgels and Ca2+ are 5.0 × 10-5 g/mL and 0.03 M, respectively.

by iodine vapor for 10 min before HRTEM observation to enhance the electron density contrast. Results and Discussion Figure 1 shows the temperature dependences of average radius of gyration (〈Rg〉) and average radius of hydrodynamic radius (〈Rh〉) of NIPAM-co-SA, NIPAM-co-VT microgels and their mixture without addition of salts, respectively. The ratio of NIPAM-co-SA to NIPAM-co-VT microgel in the mixture is

Effects of Cations on Sorting of Oppositely Charged Microgels

Figure 5. Temperature dependences of the average radius of gyration 〈Rg〉 and average hydrodynamic radius 〈Rh〉 of the mixture of NIPAMco-SA and NIPAM-co-VT microgels (1/1, w/w) in the presence of Ca2+, where the concentrations of microgels and Ca2+ are 5.0 × 10-5 g/mL and 0.03 M, respectively. The inset shows the temperature dependence of Mw.

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Figure 8. Temperature dependences of the average radius of gyration 〈Rg〉 and average hydrodynamic radius 〈Rh〉 of NIPAM-co-SA microgels in the presence of Na+, NH4+, and Mg2+, where the concentration of microgel and salts are 5.0 × 10-5 g/mL and 0.03 M, respectively. The inset shows the temperature dependence of Mw.

Figure 6. Temperature dependences of the ratio of 〈Rg〉/〈Rh〉 of the mixture of NIPAM-co-SA and NIPAM-co-VT microgels (1/1, w/w) in the presence of Ca2+, where the concentration of microgel is 5.0 × 10-5 g/mL.

Figure 9. Temperature dependences of the average radius of gyration 〈Rg〉 and average hydrodynamic radius 〈Rh〉 of the mixture of NIPAMco-SA and NIPAM-co-VT microgels (1/1, w/w) in the presence of Na+, NH4+ and Mg2+, where the concentration of microgel and salts are 5.0 × 10-5 g/mL and 0.03 M, respectively. The inset shows the temperature dependence of Mw.

Figure 7. HRTEM image of NIPAM-co-SA and NIPAM-co-VT microgel aggregates at 51 °C. The inset shows the image of the aggregates stained by I2 vapor.

1:1 in mass, and the charge ratio of the different microgels is also about 1:1, which can be calculated via the monomer composition of microgel. All the microgels exhibit a lower critical solution temperature (LCST) at ∼34 °C, higher than

that of PNIPAM homopolymer (LCST∼32 °C) because of the presence of hydrophilic moieties.38 As expected, 〈Rh〉 decrease as temperature increases, indicating that the microgels gradually shrink. At a temperature above 40 °C, the size of microgels no longer varies. The inset shows the weight-average molar mass (Mw) does not have temperature dependence, indicating that no aggregation occurs. This is because the repulsive electrostatic force from the charges on the microgel periphery can stabilize the microgel at a temperature above the LCST.39,40 Note that the oppositely charged microgels should associate after their mixing due to the attractive electrostatic force between them.41-43 However, the microgels can not associate because the present dispersion is dilute.44 In addition, the two kinds of microgels

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Figure 10. Schematic illustration of heteroaggregation of NIPAM-co-SA and NIPAM-co-VT microgels.

have similar size and temperature dependence of 〈Rh〉. Therefore, the effect of microgel size on the sorting behavior can be neglected. Figure 2 shows the temperature dependences of 〈Rh〉 and Mw of NIPAM-co-SA microgels as a function of [Ca2+], where the salt used is CaCl2. When [Ca2+] < 0.01 M, similar to the case in the absence of Ca2+ shown in Figure 1, 〈Rh〉 decreases with temperature in the range 32-45 °C, indicating that the microgels do not associate but shrink despite the presence of Ca2+. Further increase of [Ca2+] leads Mw and 〈Rh〉 to increase, particularly at a temperature above the LCST, indicating the association of microgels. Actually, the association is due to the complex between Ca2+ and carboxyls. As we know, in the absence of Ca2+, microgels separate far away at a temperature below the LCST, as temperature increases up to the LCST, the microgels would approach each other but do not form aggregates due to repulsive interaction of carboxyls. However, when [Ca2+] is high enough, Ca2+ would complex with carboxyls at different microgels, leading to the association of microgels. Moreover, as temperature increases, each microgel shrinks leading the density of carboxyls on the periphery to increase. Thus, more carboxyls can be complexed with Ca2+, forming larger aggregates at a higher temperature. In the following experiments, [Ca2+] is fixed at 0.03 M so that the aggregates can be well characterized by LLS in the range 34-51 °C. Figure 3 shows the temperature dependences of 〈Rg〉 and 〈Rh〉 of NIPAM-co-VT microgels in the presence of CaCl2, where [Ca2+] ) 0.03 M. Like the case in the absence of CaCl2, both 〈Rg〉 and 〈Rh〉 of NIPAM-co-VT microgels decrease with temperature, whereas Mw does not vary with temperature (the inset). In other words, NIPAM-co-VT microgels do not aggregate but shrink as temperature increases. This is understandable because Ca2+ cannot interact with trimethylammonium ([N(CH3)3]+) groups on the microgel surface. Note that the microgels are smaller than those in a salt-free dispersion. This is because the salts reduce the repulsive long-range Coulomb interaction between the charged groups and leads the microgels to shrink.33 Figure 4 shows the hydrodynamic radius distribution f(Rh) of NIPAM-co-SA, NIPAM-co-VT microgels and their mixture in the presence of CaCl2 at 51 °C. Their 〈Rh〉s are ∼40, 120, and 420 nm, respectively. The larger size of the mixture clearly indicates that the oppositely charged microgels form mixed aggregates. In addition, Figure 4 shows that such aggregates have a narrow size distribution.

Figure 5 shows that the 〈Rh〉 and 〈Rg〉 of the mixture of NIPAM-co-SA and NIPAM-co-VT microgels in the presence of CaCl2 slightly decrease at a temperature below LCST, indicating the shrinking of the microgels. As temperature increases up to the LCST, 〈Rh〉 and 〈Rg〉 sharply increase, indicating the association of the microgels. 〈Rh〉 and 〈Rg〉 level off at a temperature above ∼40 °C, indicating the formation of stable aggregates. Correspondingly, Mw significantly increase when temperature is close to the LCST and holds a constant at a temperature above the LCST (the inset), further indicating that the microgels form stable aggregates. Considering that the aggregates have a narrow distribution, the aggregate is a hybrid of NIPAM-co-SA and NIPAM-co-VT microgels. As discussed above, due to the interaction between Ca2+ and carboxyls, NIPAM-co-SA microgels shrink and form aggregates at a temperature above the LCST, which leads the local negative charge density to increase. Thus, the electrostatic attraction between the oppositely charged microgels increases. When the attraction is strong enough, NIPAM-co-VT microgels are expected to adhere to the surface of NIPAM-co-SA microgel aggregates forming a larger hybrid aggregate with the former and latter as the shell and core, respectively. Such a hybrid aggregate is stabilized by the positive charges on the shell.3,42 Figure 6 shows the temperature dependence of the ratio of 〈Rg〉/〈Rh〉. The ratio of 〈Rg〉/〈Rh〉 can describe the structure of the scattering object. For uniform nondraining spheres, hyperbranched clusters and random coils, 〈Rg〉/〈Rh〉 are ∼0.774, 1.0-1.2, and 1.5-1.8, respectively.45 In the presence of Ca2+, 〈Rg〉/〈Rh〉 slightly decreases from ∼0.77 to ∼0.75 with temperature at a temperature below the LCST, indicating the slight shrinking of microgels. At a temperature above the LCST, 〈Rg〉/ 〈Rh〉 increases from ∼0.80 to ∼1.10 in the range 32-37 °C, indicating that the microgels form loose aggregates. Subsequently, 〈Rg〉/〈Rh〉 decreases to ∼0.79, indicating that the aggregates have a denser spherical structure. The structure of the unlike microgel aggregates has been directly observed by HRTEM (Figure 7). Since metal ions can enhance the electron density contrast,46,47 the Ca2+ complexed with carboxyls makes a contrast between NIPAM-co-SA and NIPAM-co-VT domains. We can see that the aggregates have a core-shell structure. The inset shows the image of the aggregates stained by iodine vapor. A boundary can be clearly observed. It is formed by NIPAM-co-VT microgels because iodine can bind with [N(CH3)3]+ but can not with Ca2+. Clearly, NIPAM-co-SA and NIPAM-co-VT microgels form the core and

Effects of Cations on Sorting of Oppositely Charged Microgels shell of an aggregate, respectively. The core-shell structure indicates that the oppositely charged microgels exhibit sorting behavior during the aggregation, which is determined by the difference of Ca2+ adhesion between the unlike microgels. Note that the microgels are more collapsed in air than in an aqueous solution. That is why the size of aggregates measured by HRTEM is smaller than that by LLS. To understand the role of Ca2+, we also examined the effects of some other monovalent and divalent ions with the anions in all the salt being Cl-. As expected, Na+, NH4+, and Mg2+ do not lead NIPAM-co-VT microgels to associate (not shown). Figures 8 and 9 show the temperature dependences of 〈Rg〉 and 〈Rh〉 of NIPAM-co-SA microgels and the mixture with NIPAMco-VT microgels after the addition of Na+, NH4+, and Mg respectively. The insets show the temperature dependence of Mw. Similar to the case in the absence of salts, 〈Rg〉 and 〈Rh〉 decrease as temperature increase in the presence of monovalent cations (Na+ and NH4+), whereas Mw does not vary with the temperature. Namely, they cannot lead either the NIPAM-coSA microgels or the mixed microgels to aggregate. This is understandable because a monovalent cation cannot complex with more than one carboxyl at the surface of different microgels. In contrast, like the case in the presence of Ca2+, the addition of Mg2+ leads the NIPAM-co-SA microgels to associate and the mixed microgels to form larger aggregates. Therefore, the binding of a divalent metal ion with two carboxyls is essential for the sorting of the oppositely charged microgels. Figure 10 illustrates the heteroaggregation of NIPAM-co-SA and NIPAM-co-VT microgels. The above results show that the oppositely charged microgels aggregate in the presence of divalent ions or exhibit a sorting behavior. Belmonte et al.13 have investigated the sorting of two types of cells with different interaction intensity and demonstrated that even weak adherent motility facilitate cell-sorting. It has been suggested that the property of ion-adhesion is responsible for adhesive ability of cells.20-23 As a simple model, the results about the heteroaggregation of microgels reveal that the adhesive property plays an essential role in cell-sorting, which is determined by the interactions between cell and ions. The cells expressing high level of adhesion would stick together, and the association would enhance the local attractive interaction between the unlike cells such as Coulomb attraction. As a result, the cells expressing low level of cadherin adhere to the core via the locally enhanced attractive force, and the less adhesive cells engulf the more adhesive ones to form a shell. The electrostatic repulsion from the charges on the aggregates periphery stabilizes the aggregates. Conclusion The study on the aggregation of unlike thermosensitive microgels with opposite charges in the presence of different cations leads to the following conclusion. The adhesive property plays an important role in the sorting of oppositely charged microgels. Monovalent cations do not affect the aggregation of the microgels. Divalent metal ions (Ca2+ and Mg2+) lead NIPAM-co-SA microgels to express high adhesive probability via complexation with COO-. The high adhesive microgels would aggregate so that the low adhesive ones stick to the aggregates via locally enhanced attraction. As a result, the unlike microgels occupy different domains of the aggregates, namely, they exhibit sorting behavior. Our study should be useful for understanding the cell-sorting. Acknowledgment. The financial support of the National Distinguished Young Investigator Fund (20725414) and Ministry

J. Phys. Chem. B, Vol. 113, No. 21, 2009 7461 of Science and Technology of China (2007CB936401) is acknowledged. References and Notes (1) Ouali, I.; Pefferkorn, E.; Elaissari, A.; Pichot, C.; Mandrand, B. J. Colloid Interface Sci. 1995, 171, 276. (2) Behrens, S. H.; Borkovec, M. Phys. ReV. E 1999, 60, 7040. (3) Snoswell, D. R. E.; Rogers, T. J.; Howe, A. M.; Vincent, B. Langmuir 2005, 21, 11439. (4) Fernandez-Barbero, A.; Vincent, B. Phys. ReV. E 2000, 63, 011509. (5) Collier, C. P.; Vossmeyer, T.; Heath, J. R. Annu. ReV. Phys. Chem. 1998, 49, 371. (6) Weissman, I. L. Science 2000, 287, 1442. (7) Pick, M.; Nagler, A.; Grisaru, D.; Eldor, A.; Deutsch, V. Br. J. Heamatol. 1998, 103, 639. (8) Powles, R.; Mehta, J.; Kulkarni, S.; Treleaven, J.; Millar, B.; Marsden, J.; Shepherd, V.; Rowland, A.; Sirohi, B.; Tait, D.; Horton, C.; Long, S.; Singhal, S. Lancet 2000, 355, 1231. (9) Koh, M. B.; Prentice, H. G.; Corbo, M.; Morgan, M.; Cotter, F. E.; Lowdell, M. W. Br. J. Hamaetol. 2002, 118, 108. (10) Steinberg, M. S. Science 1963, 141, 401. (11) Brodland, M. S. Appl. Mech. ReV. 2004, 57, 47. (12) Belmonte, J. M.; Thomas, G. L.; Brunnet, L. G.; de Almeida, R. M. C.; Chate´, H. Phys. ReV. Lett. 2008, 100, 248702. (13) Graner, F.; Glazier, J. A. Phys. ReV. Lett. 1992, 69, 2013. (14) Rappel, W. J.; Nicol, A.; Sarkissian, A.; Levine, H.; Loomis, W. F. Phys. ReV. Lett. 1999, 83, 1247. (15) Foty, R. A.; Forgacs, G.; Pfleger, C. M.; Steinberg, M. S. Phys. ReV. Lett. 1994, 72, 2298. (16) Sato-Maeda, M.; Uchida, M.; Graner, F.; Tashiro, H. DeV. Biol. 1994, 162, 77. (17) Mombach, J. C. M.; Glazier, J. A.; Raphael, R. C.; Zajac, M. Phys. ReV. Lett. 1997, 75, 2244. (18) Phillips, H. M.; Steinberg, M. S. J. Cell Sci. 1978, 30, 1. (19) Rieu, J. P.; Kataoka, N.; Sawada, Y. Phys. ReV. E 1998, 57, 924. (20) Ringwald, M.; Schuh, R.; Vestweber, D.; Eistetter, H.; Lottspeich, F.; Engel, J.; Dolz, R.; Jahnig, F.; Epplen, J.; Mayer, S.; Mu¨ller, C.; Kemler, R. EMBO J. 1987, 6, 3647. (21) Nose, A.; Tsuji, K.; Takeichi, M. Cell 1990, 61, 147. (22) Koch, A. W.; Bozic, D.; Pertz, O.; Engel, J. Curr. Opin. Struct. Biol. 1999, 9, 275. (23) Troyanovsky, S. Eur. J. Cell Biol. 2005, 84, 225. (24) Takeichi, M. Curr. Opin. Cell Biol. 1995, 7, 619. (25) Ozawa, M.; Kemler, R. J. Cell Biol. 1990, 111, 1645. (26) Duguay, D.; Foty, R. A.; Steinberg, M. S. DeV. Biol. 2003, 253, 309. (27) Haussinger, D.; Ahrens, T.; Aberle, T.; Engel, J.; Stetefeld, J.; Grzesiek, S. EMBO J. 2004, 23, 1699. (28) Gumbiner, B. M. Nat. ReV. Mol. Cell Biol. 2005, 6, 622. (29) Jeremy, B. A. G. Nat. Cell Biol. 2008, 10, 375. (30) Harris, A. K. J. Theor. Biol. 1976, 57, 47. (31) Krieg, M.; Arboleda-Estudillo, Y.; Puech, P. H.; Ka¨her, J.; Graner, F.; Mu¨ller, D. J.; Heisenberg, C. P. Nat. Cell Biol. 2008, 10, 429. (32) Ben Jar, P. Y.; Wu, Y. S. Polymer 1997, 38, 2557. (33) Peng, S. F.; Wu, C. J. Phys. Chem. B 2001, 105, 2331. (34) Zhao, Y.; Zhang, G. Z.; Wu, C. Macromolecules 2001, 34, 7804. (35) Chu, B. Laser Light Scattering, 2nd ed.; Academic Press: New York, 1991. (36) Guinier, A.; Fournet, G. Small-angel Scattering of X-ray; John Wiley: New York, 1955. (37) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Plenum Press: New York, 1976. (38) Schild, H. G. Prog. Polym. Sci. 1992, 17, 163. (39) Deryaguin, B. V.; Landau, L. Acta Phys. Chem. 1941, 14, 633. (40) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (41) Dautzenberg, H.; Rother, G.; Hartmann, J. Macro-ion Characterization: From Dilute Solution to Complex Fluids; American Chemical Society: Washington, DC, 1994. (42) Schrage, S.; Sigel, R.; Schlaad, H. Macromolecules 2003, 36, 1417. (43) Andersson, T.; Holappa, S.; Aseyev, V.; Tenhu, H. Biomacromolecules 2006, 7, 3229. (44) Zhang, G. Z.; Wu, C. AdV. Polym. Sci. 2006, 195, 101. (45) Brown, W.; Burchard, W. Light Scattering Principles and DeVelopment; Clarendon Press: Oxford, 1996. (46) Trent, J. S.; Scheinbeim, J. I.; Couchman, P. R. Macromolecules 1983, 16, 589. (47) Hu, J. W.; Liu, G. J. Macromolecules 2005, 38, 8058.

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