Advertisement

Polyelectrolyte Complexes

Bridging the Ensemble Average: Single-Molecule Strategies
  • Rita S. Dias
  • Bjørn Torger StokkeEmail author
Chapter
  • 1.4k Downloads
Part of the Engineering Materials book series (ENG.MAT.)

Abstract

Polyelectrolyte complexation is mechanistic in formation of various biological structures as well as in technological applications. Such structure formation can be viewed as key in regulating biological functionality and designing functional soft materials. The formation of polyelectrolyte complexes depends on the interrelation between the counter ion exchange, entropic contribution, polymer properties, solution conditions, and process approach. Thus, a comprehensive description of the polyelectrolyte complex formation, their properties, and structures deem it necessary to apply various tools. The chapter provides a brief overview of representative polyelectrolyte complex examples from biology and man-made ones. In particular, we aim at combining information obtainable at the ensemble and single molecule level with numerical simulations to provide a more comprehensive description of the structure formation and resulting morphologies. A particular feature is the possible existence of kinetically trapped structures due to the flexible and long chain nature of the components. Possible impact of this particularity to this growing field is discussed.

Keywords

Isothermal Titration Calorimetry Persistence Length Polyelectrolyte Complex Polyelectrolyte Chain Complex Coacervation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Hud, N.V., Allen, M.J., Downing, K.H., Lee, J., Balhorn, R.: Identification of the elemental packing unit of DNA in mammalian sperm cells by atomic force microscopy. Biochem Biophys Res Commun 193(3), 1347–1354 (1993)Google Scholar
  2. 2.
    Ou, Z., Muthukumar, M.: Entropy and enthalpy of polyelectrolyte complexation: langevin dynamics simulations. J. Chem. Phys. 124, 145902–145901/145911 (2006)Google Scholar
  3. 3.
    Carlsson, F., Linse, P., Malmsten, M.: Monte Carlo simulations of polyelectrolyte–protein complexation. J. Phys. Chem. B 105(38), 9040–9049 (2001)Google Scholar
  4. 4.
    Arents, G., Moudrianakis, E.N.: Topography of the histone octamer surface: repeating structural motifs utilized in the docking of nucleosomal DNA. Proc. Natl. Acad. Sci. 90(22), 10489–10493 (1993)Google Scholar
  5. 5.
    Schiessel, H.: The physics of chromatin. J. Phys. Condens. Matter 15, R699–R774 (2003)Google Scholar
  6. 6.
    Dorigo, B., Schalch, T., Kulangara, A., Duda, A., Schroeder, R.R., Richmond, T.J.: Nucleosome arrays reveal the two-start organization of the chromatin fiber. Science 306, 1571–1573 (2004)Google Scholar
  7. 7.
    Mangenot, S., Leforestier, A., Vachette, P., Durand, D., Livolant, F.: Salt-induced conformation and interaction changes of nucleosome core particles. Biophys. J. 82, 345–356 (2002)Google Scholar
  8. 8.
    Mangenot, S., Raspaud, E., Tribet, C., Belloni, L., Livolant, F.: Interactions between isolated nucleosome core particles. Eur. Phys. J. E 7, 221–231 (2002)Google Scholar
  9. 9.
    Bertin, A., Leforestier, A., Durand, D., Livolant, F.: Role of histone tails in the conformation and interactions of nucleosome core particles. Biochemistry 43, 4773–4780 (2004)Google Scholar
  10. 10.
    Allahyarov, E., Löwen, H., Hansen, J.P., Louis, A.A.: Nonmonotonic variation with salt concentration of the second virial coefficient in protein solutions. Phys. Rev. E 67(051404), 051401–051413 (2003)Google Scholar
  11. 11.
    Boroudjerdi, H., Netz, R.R.: Interactions between polyelectrolyte-macroion complexes. Europhys. Lett. 64, 413–419 (2003)Google Scholar
  12. 12.
    Boroudjerdi, H., Netz, R.R.: Strongly coupled polyelectrolyte-macroion complexes. J. Phys. Condens. Matter 17, S1137–S1151 (2005)Google Scholar
  13. 13.
    Mühlbacher, F., Schiessel, H., Holm, C.: Tail-induced attraction between nucleosome core particles. Phys. Rev. E 74(3), 031919 (2006)Google Scholar
  14. 14.
    Korolev, N., Lyubartsev, A.P., Nordenskiöld, L.: Computer modeling demonstrates that electrostatic attraction of nucleosomal DNA is mediated by histone tails. Biophys. J. 90, 4305–4316 (2006)Google Scholar
  15. 15.
    Horn, P.J., Peterson, C.L.: Chromatin higher order folding: wrapping up transcription. Science 291, 1824–1827 (2002)Google Scholar
  16. 16.
    Tse, C., Sera, T., Wolffe, A.P., Hansen, J.C.: Disruption of higher-order folding by core histone acetylation dramatically enhances transcription of nucleosomal arrays by RNA polymerase III. Mol. Cell. Biol. 18, 4629–4638 (1998)Google Scholar
  17. 17.
    Müller, M.: Polyelectrolyte Complexes in the Dispersed and Solid State II: Application Aspects. Springer, Berlin (2014)Google Scholar
  18. 18.
    Bertin, A.: Polyelectrolyte complexes of DNA and polycations as gene delivery vectors. Adv. Polym. Sci. 256, 103–196 (2014)Google Scholar
  19. 19.
    Müller, M.: Sizing, shaping and pharmaceutical applications of polyelectrolyte complex nanoparticles. Adv. Polym. Sci. 256, 197–260 (2014)Google Scholar
  20. 20.
    Ankerfors, C., Wågberg, L.: Polyelectrolyte complexes for tailoring of wood fibre surfaces. Adv. Polym. Sci. 256, 1–24 (2014)Google Scholar
  21. 21.
    Petzold, G., Schwarz, S.: Polyelectrolyte complexes in flocculation applications. Adv. Polym. Sci. 256, 25–66 (2014)Google Scholar
  22. 22.
    Decher, G., Schlenoff, J.: Multilayer Thin Films, 2nd Edn. Wiley, Weinheim (2012)Google Scholar
  23. 23.
    Thünemann, A.F., Müller, M., Dautzenberg, H., Joanny, J.F., Löwen, H.: Polyelectrolyte complexes. Adv. Polym. Sci. 166, 113–171 (2004)Google Scholar
  24. 24.
    Bucur, C.B., Sui, Z., Schlenoff, J.B.: Ideal mixing in polyelectrolyte complexes and multilayers: entropy driven assembly. J. Am. Chem. Soc. 128(42), 13690–13691 (2006)Google Scholar
  25. 25.
    Plum, G.E., Arscott, P.G., Bloomfield, V.A.: Condensation of DNA by trivalent cations. 2. Effects of cation structure. Biopolymers 30, 631–643 (1990)Google Scholar
  26. 26.
    Spruijt, E., Van Den Berg, S.A., Cohen Stuart, M.A., Van Der Gucht, J.: Direct measurement of the strength of single ionic bonds between hydrated charges. ACS Nano 6(6), 5297–5303 (2012)Google Scholar
  27. 27.
    Gus’kova, O.A., Pavlov, A.S., Khalatur, P.G.: Complexes based on rigid-chain polyelectrolytes: computer simulation. Polym. Sci. Ser. A 48(7), 763–770 (2006)Google Scholar
  28. 28.
    Narambuena, C.F., Leiva, E.P.M., Chávez-Páez, M., Pérez, E.: Effect of chain stiffness on the morphology of polyelectrolyte complexes. A Monte Carlo simulation study. Polymer 51, 3293–3302 (2010)Google Scholar
  29. 29.
    Bloomfield, V.: DNA condensation. Curr. Opin. Struct. Biol. 6, 334–341 (1996)Google Scholar
  30. 30.
    Bloomfield, V.: DNA condensation by multivalent cations. Biopolymers 44, 269–282 (1997)Google Scholar
  31. 31.
    Guldbrand, L., Jönsson, B., Wennerström, H., Linse, P.: Electrical double-layer forces—a Monte-Carlo study. J. Chem. Phys. 80(5), 2221–2228 (1984)Google Scholar
  32. 32.
    Grosberg, A.Y., Nguyen, T.T., Shklovski, B.I.: The physics of charge inversion in chemical and biological systems. Rev. Mod. Phys. 74, 329–345 (2002)Google Scholar
  33. 33.
    Gelbart, W.M., Bruinsma, R.F., Pincus, P.A., Parsegian, V.A.: DNA-inspired electrostatics. Phys. Today 53, 38–44 (2000)Google Scholar
  34. 34.
    Khan, M.O., Jonsson, B.: Electrostatic correlations fold DNA. Biopolymers 49(2), 121–125 (1999)Google Scholar
  35. 35.
    Mel’nikov, S., Khan, M.O., Lindman, B., Jönsson, B.: Phase behavior of single DNA in mixed solvents. J. Am. Chem. Soc. 121, 1130–1136 (1999)Google Scholar
  36. 36.
    Matulis, D., Rouzina, I., Bloomfield, V.A.: Thermodynamics of DNA binding and condensation: isothermal titration calorimetry and electrostatic mechanism. J. Mol. Biol. 296(4), 1053–1063 (2000)Google Scholar
  37. 37.
    Priftis, D., Megley, K., Laugel, N., Tirrell, M.: Complex coacervation of poly(ethylene-imine)/polypeptide aqueous solutions: thermodynamic and rheological characterization. J. Colloid Interface Sci. 398, 39–50 (2013)Google Scholar
  38. 38.
    Ghai, R., Falconer, R.J., Collins, B.M.: Applications of isothermal titration calorimetry in pure and applied research—survey of the literature from 2010. J. Mol. Recogn. 25(1), 32–52 (2010)Google Scholar
  39. 39.
    Lohman, T.M., Dehaseth, P.L., Record, M.T.: Pentalysine-deoxyribonucleic acid interactions—a model for the general effects of ion concentrations on the interactions of proteins with nucleic-acids. Biochemistry 19(15), 3522–3530 (1980)Google Scholar
  40. 40.
    Mascotti, D.P., Lohman, T.M.: Thermodynamic extent of counterion release upon binding oligolysines to single-stranded nucleic acids. Proc. Natl. Acad. Sci. USA 87, 3142–3146 (1990)Google Scholar
  41. 41.
    Patel, M.M., Anchordoquy, T.J.: Contribution of hydrophobicity to thermodynamics of ligand-DNA binding and DNA collapse. Biophys. J. 88, 2089–2103 (2005)Google Scholar
  42. 42.
    Park, S.Y., Harries, D., Gelbart, W.M.: Topological defects and the optimum size of DNA condensates. Biophys. J. 75, 714–720 (1998)Google Scholar
  43. 43.
    Ainalem, M.-L., Carnerup, A.M., Janiak, J., Alfredsson, V., Nylander, T., Schillen, K.: Condensing DNA with poly(amido amine) dendrimers of different generations: means of controlling aggregate morphology. Soft Matter 5(11), 2310–2320 (2009)Google Scholar
  44. 44.
    Carnerup, A.M., Ainalem, M.-L., Alfredsson, V., Nylander, T.: Watching DNA condensation induced by poly(amido amine) dendrimers with time-resolved cryo-TEM. Langmuir 25(21), 12466–12470 (2009)Google Scholar
  45. 45.
    Lasic, D.D.: Liposomes in Gene Delivery. CRC Press, Boca Raton (1997)Google Scholar
  46. 46.
    Carlstedt, J., Lundberg, D., Dias, R.S., Lindman, B.: Condensation and decondensation of DNA by cationic surfactant, spermine, or cationic surfactant—cyclodextrin mixtures: macroscopic phase behavior, aggregate properties, and dissolution mechanisms. Langmuir 28(21), 7976–7989 (2012)Google Scholar
  47. 47.
    Pinto, M.F.V., Moran, M.C., Miguel, M.G., Lindman, B., Jurado, A.S., Pais, A.A.C.C.: Controlling the morphology in DNA condensation and precipitation. Biomacromolecules 10(6), 1319–1323 (2009)Google Scholar
  48. 48.
    Babak, V.G., Merkovich, E.A., Galbraikh, L.S., Shtykova, E.V., Rinaudo, M.: Kinetics of diffusionally induced gelation and ordered nanostructure formation in surfactant—polyelectrolyte complexes formed at water/water emulsion type interfaces. Mendeleev Commun. 10(3), 94–95 (2000)Google Scholar
  49. 49.
    Morán, M.C., Miguel, M.G., Lindman, B.: DNA gel particles: particle preparation and release characteristics. Langmuir 23(12), 6478–6481 (2007)Google Scholar
  50. 50.
    Lapitsky, Y., Kaler, E.W.: Formation of surfactant and polyelectrolyte gel particles in aqueous solutions. Colloids Surf. A 250(1), 179–187 (2004)Google Scholar
  51. 51.
    Lapitsky, Y., Eskuchen, W.J., Kaler, E.W.: Surfactant and polyelectrolyte gel particles that swell reversibly. Langmuir 22(14), 6375–6379 (2006)Google Scholar
  52. 52.
    Morán, M.C., Pais, A.A.C.C., Ramalho, A., Miguel, M.G., Lindman, B.: Mixed protein carriers for modulating DNA release. Langmuir 25(17), 10263–10270 (2009)Google Scholar
  53. 53.
    Morán, M.C., Laranjeira, T., Ribeiro, A., Miguel, M.G., Lindman, B.: Chitosan-DNA particles for DNA delivery: effect of chitosan molecular weight on formation and release characteristics. J. Dispersion Sci. Technol. 30(10), 1494–1499 (2009)Google Scholar
  54. 54.
    McManus, J.J., Rädler, J.O., Dawson, K.A.: Observation of a rectangular columnar phase in a DNA—Calcium—Zwitterionic lipid complex. J. Am. Chem. Soc. 126(49), 15966–15967 (2004)Google Scholar
  55. 55.
    Maurstad, G., Stokke, B.T.: Metastable and stable states of xanthan polyelectrolyte complexes studied by atomic force microscopy. Biopolymers 74, 199–213 (2004)Google Scholar
  56. 56.
    Lazutin, A.A., Semenov, A.N., Vasilevskaya, V.V.: Polyelectrolyte complexes consisting of macromolecules with varied stiffness: computer simulation. Macromol. Theory Simul. 21(5), 328–339 (2012)Google Scholar
  57. 57.
    Hud, N.V., Downing, K.H.: Cryoelectron microscopy of l-phage DNA condensates in vitreous ice: The fine structure of DNA toroids. Proc. Natl. Acad. Sci. USA 98, 14925–14930 (2001)Google Scholar
  58. 58.
    Boussif, O., Lezoualc’h, F., Zanta, M.A., Mergny, M.D., Scherman, D., Demeneix, B., et al.: A versatile vector for gene and oligonucleotide transfer into cells in culture and in vivo: polyethylenimine. Proc. Natl. Acad. Sci. USA 92, 7297–7301 (1995)Google Scholar
  59. 59.
    Petersen, H., Kunath, K., Martin, A.L., Stolnik, S., Roberts, C.J., Davies, M.C., et al.: Star-shaped poly(ethylene glycol)-block-polyethylenimine copolymers enhance DNA condensation of low molecular weight polyethylenimines. Biomacromolecules 3, 926–936 (2002)Google Scholar
  60. 60.
    Danielsen, S., Vårum, K.M., Stokke, B.T.: Structural analysis of chitosan mediated DNA condensation by AFM: influence of chitosan molecular parameters. Biomacromolecules 5, 928–936 (2004)Google Scholar
  61. 61.
    Kwoh, D.Y., Coffin, C.C., Lollo, C.P., Jovenal, J., Banaszczyk, M.G., Mullen, P., et al.: Stabilization of poly-L-lysine/DNA polyplexes for in vivo gene delivery to the liver. Biochim. Biophys. Acta 1444, 171–190 (1999)Google Scholar
  62. 62.
    Liu, G., Molas, M., Grossmann, G.A., Pasumarthy, M., Perales, J.C., Cooper, M.J., et al.: Biological properties of Poly-L-lysine-DNA complexes generated by cooperative binding of the polycation. J. Biol. Chem. 276(37), 34379–34387 (2001)Google Scholar
  63. 63.
    Akinc, A., Lynn, D.M., Anderson, D.G., Langer, R.: Parallel synthesis and biophysical characterization of a degradable polymer library for gene delivery. J. Am. Chem. Soc. 125, 5316–5323 (2003)Google Scholar
  64. 64.
    Sakaua, T., Yoshikawa, K.: Folding/unfolding kinetics of a semiflexible polymer chain. J. Chem. Phys. 117, 6323–6330 (2002)Google Scholar
  65. 65.
    Matsuzawa, Y., Yonezawa, Y., Yoshikawa, K.: Formation of nucleation center in single double-stranded DNA chain. Biochem. Biophys. Res. Commun. 225, 796–800 (1996)Google Scholar
  66. 66.
    Yoshikawa, K., Matsuzawa, Y.: Nucleation and growth in single DNA molecules. J. Am. Chem. Soc. 118, 929–930 (1996)Google Scholar
  67. 67.
    Shen, M.R., Downing, K.H., Balhorn, R., Hud, N.V.: Nucleation of DNA condensation by static loops: formation of DNA toroids with reduced dimensions. J. Am. Chem. Soc. 122, 4833–4834 (2000)Google Scholar
  68. 68.
    Conwell, C.C., Vilfan, I.D., Hud, N.V.: Controlling the size of nanoscale toroidal DNA condensates with static curvature and ionic strength. Proc. Natl. Acad. Sci. USA 100, 9296–9301 (2003)Google Scholar
  69. 69.
    Schnurr, B., MacKintosh, F.C., Williams, D.R.M.: Dynamical intermediates in the collapse of semiflexible polymers in poor solvents. Europhys. Lett. 51, 279–285 (2000)Google Scholar
  70. 70.
    Schnurr, B., Gittes, F., MacKintosh, F.C.: Metastable intermediates in the condensation of semiflexible polymers. Phys. Rev. E 65:161904-161161–161913 (2002)Google Scholar
  71. 71.
    Rackstraw, B.J., Martin, A.L., Stolnik, S., Roberts, C.J., Garnett, M.C., Davies, M.C., et al.: Microscopic investigations into PEG-cationic polymer-induced DNA condensation. Langmuir 17(11), 3185–3193 (2001)Google Scholar
  72. 72.
    Eickbush, T.H., Moudrianakis, E.N.: The compaction of DNA Helices into either continous supercoils or folded-fiber rods and toroids. Cell 13, 295–306 (1978)Google Scholar
  73. 73.
    Noguchi, H., Saito, S., Kidoaki, S., Yoshikawa, K.: Self-organized nanostructures constructed with a single polymer chain. Chem. Phys. Lett. 261, 527–533 (1996)Google Scholar
  74. 74.
    Noguchi, H., Yoshikawa, K.: First-order phase transition in stiff polymer chain. Chem. Phys. Lett. 278, 184–188 (1997)Google Scholar
  75. 75.
    Noguchi, H., Yoshikawa, K.: Folding path in a semiflexible homopolymer chain: a brownian dynamics simulation. J. Chem. Phys. 113, 854–862 (2000)Google Scholar
  76. 76.
    Noguchi, H., Yoshikawa, K.: Morphological variation in a collapsed single homopolymer chain. J. Chem. Phys. 109, 5070–5077 (1998)Google Scholar
  77. 77.
    Stevens, M.J.: Simple simulations of DNA condensation. Biophys. J. 80, 130–139 (2001)Google Scholar
  78. 78.
    Martin, A.L., Davies, M.C., Rackstraw, B.J., Roberts, C.J., Stolnik, S., Tendler, S.J.B., et al.: Observations of DNA-polymer condensate formation in real time at a molecular level. FEBS Lett. 480, 106–112 (2000)Google Scholar
  79. 79.
    Lappala, A., Terentjev, E.M.: Maximum compaction density of folded semiflexible polymers. Macromolecules 46(17), 7125–7131 (2013)Google Scholar
  80. 80.
    Hugel, T., Grosholz, M., Claussen-Schaumann, H., Pfau, A., Gaub, H., Seitz, M.: Elasticity of single polyelectrolyte chains and their desorption from solid supports studied by AFM based single molecule force spectroscopy. Macromolecules 34, 1039–1047 (2001)Google Scholar
  81. 81.
    Friedsam, C., Gaub, H.E., Netz, R.R.: Probing surfaces with single-polymer atomic force microscope experiments. Biointerphases 1(1), MR1–MR21 (2006)Google Scholar
  82. 82.
    Brown, A.: Analysis of cooperativity by isothermal titration calorimetry. Int. J. Mol. Sci. 10(8), 3457–3477 (2009)Google Scholar
  83. 83.
    Buurma, N.J., Haq, I.: Advances in the analysis of isothermal titration calorimetry data for ligand—DNA interactions. Methods 42(2), 162–172 (2007)Google Scholar
  84. 84.
    Priftis, D., Laugel, N., Tirrell, M.: Thermodynamic characterization of polypeptide complex coacervation. Langmuir 28(45), 15947–15957 (2012)Google Scholar
  85. 85.
    Boddohi, S., Moore, N., Johnson, P.A., Kipper, M.J.: Polysaccharide-based polyelectrolyte complex nanoparticles from chitosan, heparin, and hyaluronan. Biomacromolecules 10(6), 1402–1409 (2009)Google Scholar
  86. 86.
    Danielsen, S., Strand, S., Davies, C.L., Stokke, B.T.: Glycosaminoglycan destabilization of DNA—chitosan polyplexes for gene delivery depends on chitosan chain length and GAG properties. Biochim. Biophys. Acta 1721, 44–54 (2005)Google Scholar
  87. 87.
    Maurstad, G., Danielsen, S., Stokke, B.T.: Analysis of compacted semiflexible polyanions visualized by atomic force microscopy: influence of chain stiffness on the morphologies of polyelectrolyte complexes. J. Phys. Chem. B 107(32), 8172–8180 (2003)Google Scholar
  88. 88.
    Minagawa, K., Matsuzawa, Y., Yoshikawa, K., Matsumoto, M.: Doi M Direct observation of the biphasic conformational change of DNA induced by cationic polymers. FEBS Lett. 295, 67–69 (1991)Google Scholar
  89. 89.
    Takahashi, M., Yoshikawa, K., Vasilevskaya, V.V., Khokhlov, A.R.: Discrete coil-globule transition of single duplex DNAs induced by polyamines. J. Phys. Chem. B 101(45), 9396–9401 (1997)Google Scholar
  90. 90.
    von Hippel, P.H., McGhee, J.D.: DNA-protein interaction. Annu. Rev. Biochem. 41, 231–300 (1972)Google Scholar
  91. 91.
    Fant, K., Esbjorner, E.K., Lincoln, P., Norden, B.: DNA condensation by PAMAM dendrimers: self-assembly characteristics and effect on transcription biochemistry 47(6), 1732–1740 (2008)Google Scholar
  92. 92.
    Dias, R.S.: DNA-surfactant interactions. Encyclopedia of Surface and Colloid Science, 2nd edn. Taylor & Francis, London (2010)Google Scholar
  93. 93.
    Dias, R., Mel’nikov, S., Lindman, B., Miguel, M.G.: DNA phase behavior in the presence of oppositely charged surfactants. Langmuir 16(24), 9577–9583 (2000)Google Scholar
  94. 94.
    Dias, R.S., Magno, L.M., Valente, A.J.M., Das, D., Das, P.K., Maiti, S., et al.: Interaction between DNA and cationic surfactants: effect of DNA conformation and surfactant headgroup. J. Phys. Chem. B 112(46), 14446–14452 (2008)Google Scholar
  95. 95.
    Holmberg, K., Jönsson, B., Kronberg, B., Lindman, B.: Surfactants and Polymers in Aqueous Solution, 2nd edn. Wiley, West Sussex (2003)Google Scholar
  96. 96.
    Dias, R.S., Innerlohinger, J., Glatter, O., Miguel, M.G., Lindman, B.: Coil-globule transition of DNA molecules induced by cationic surfactants: a dynamic light scattering study. J. Phys. Chem. B 109(20), 10458–10463 (2005)Google Scholar
  97. 97.
    Sarraguça, J.M.G., Dias, R.S., Pais, A.A.C.C.: Coil-globule coexistence and compaction of DNA chains. J. Biol. Phys. 32, 421–434 (2006)Google Scholar
  98. 98.
    Prevette, L.E., Nikolova, E.N., Al-Hashimi, H.M., Banaszak Holl, M.M.: Intrinsic dynamics of DNA—polymer complexes: a mechanism for DNA release. Mol. Pharm. 9(9), 2743–2749 (2012)Google Scholar
  99. 99.
    Dias, R.S., Pais, A.A.C.C., Miguel, M.G., Lindman, B.: Modeling of DNA compaction by polycations. J. Chem. Phys. 119(15), 8150–8157 (2003)Google Scholar
  100. 100.
    Khan, M.O., Mel’nikov, S.M., Jönsson, B.: Anomalous salt effects on DNA conformation: experiment and theory. Macromolecules 32(26), 8836–8840 (1999)Google Scholar
  101. 101.
    Khan, M.O., Chan, D.Y.C.: Effect of chain stiffness on polyelectrolyte condensation. Macromolecules 38(7), 3017–3025 (2005)Google Scholar
  102. 102.
    Dias, R.S., Linse, P., Pais, A.A.C.C.: Stepwise disproportionation in polyelectrolyte complexes. J. Comput. Chem. 32, 2697–2707 (2011)Google Scholar
  103. 103.
    Uchman, M., Gradzielski, M., Angelov, B., Tosner, Z., Oh, J., Chang, T., et al.: Thermodynamic and kinetic aspects of coassembly of PEO-PMAA block copolymer and DPCl surfactants into ordered nanoparticles in aqueous solutions studied by ITC, NMR, and time-resolved SAXS techniques. Macromolecules 46(6), 2172–2181 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Biophysics and Medical Technology, Department of PhysicsThe Norwegian University of Science and TechnologyTrondheimNorway

Personalised recommendations