Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction to Charged Macromolecules
- 2 Models of Uncharged Macromolecules
- 3 Water, Oil, and Salt
- 4 Charged Interfaces and Geometrical Objects
- 5 Dilute Solutions of Charged Macromolecules
- 6 Structure and Thermodynamics in Homogeneous Polyelectrolyte Solutions
- 7 Dynamics
- 8 Self-Assembly and Phase Behaviors
- 9 Adsorption, Complexation, and Coacervation
- 10 Gels
- 11 Epilogue
- Appendix 1
- Appendix 2
- Appendix 3
- Appendix 4
- Appendix 5
- Appendix 6
- Appendix 7
- Appendix 8
- Appendix 9
- Appendix 10
- References
- Index
- References
References
Published online by Cambridge University Press: 16 February 2023
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction to Charged Macromolecules
- 2 Models of Uncharged Macromolecules
- 3 Water, Oil, and Salt
- 4 Charged Interfaces and Geometrical Objects
- 5 Dilute Solutions of Charged Macromolecules
- 6 Structure and Thermodynamics in Homogeneous Polyelectrolyte Solutions
- 7 Dynamics
- 8 Self-Assembly and Phase Behaviors
- 9 Adsorption, Complexation, and Coacervation
- 10 Gels
- 11 Epilogue
- Appendix 1
- Appendix 2
- Appendix 3
- Appendix 4
- Appendix 5
- Appendix 6
- Appendix 7
- Appendix 8
- Appendix 9
- Appendix 10
- References
- Index
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Physics of Charged MacromoleculesSynthetic and Biological Systems, pp. 483 - 501Publisher: Cambridge University PressPrint publication year: 2023
References
Abramowitz, M. and Stegun, I. A. (1965). Handbook of Mathematical Functions. New York: Dover.Google Scholar
Acheson, N. H. (2007). Fundamentals of Molecular Virology. New York: John Wiley & Sons.Google Scholar
Adhikari, S., Leaf, M. A. and Muthukumar, M. (2018). Polyelectrolyte complex coacervation by electrostatic dipolar interactions. J. Chem. Phys., 149, 163308.CrossRefGoogle ScholarPubMed
Adhikari, S., Prabhu, V. M. and Muthukumar, M. (2019). Lower critical solution temperature behavior in polyelectrolyte complex coacervates. Macromolecules, 52, 6998–7004.Google Scholar
Alberts, B., Johnson, A., Lewis, J., Morgan, D., Raff, M., Roberts, K. and Walter, P. (2015). Molecular Biology of the Cell, 6th edn. New York: Garland Science.Google Scholar
Alexander, S. (1977). Adsorption of chain molecules with a polar head a scaling description. J. Phys. France, 38, 983–987.CrossRefGoogle Scholar
Alfrey, T., Berg, P. W. and Morawetz, H. (1951). The counterion distribution in solutions of rod-shaped polyelectrolytes. J. Polym. Sci. 7, 543–547.Google Scholar
Alfrey, T., Fuoss, R. M., Morawetz, H. and Pinner, H. (1952). Amphoteric polyelectrolytes. II. Copolymers of methacrylic acid and diethylaminoethyl methacrylate. J. Am. Chem. Soc., 74, 438–441.Google Scholar
Antipova, O. and Orgel, J. P. R. O. (2010). In situ D-periodic molecular structure of type II collagen. J. Biol. Chem., 285, 7087–7096.Google Scholar
Baker, T. S., Olson, N. H. and Fuller. S. D. (1999). Adding the third dimension to virus cycles: Three-dimensional reconstruction of icosahedral viruses from cryo-electron micrographs. Microbiol. Mol. Biol. Rev., 63, 862–922.Google Scholar
Baltimore, D. (1970). Viral RNA-dependent DNA polymerase: RNA-dependent DNA polymerase in virions of RNA tumour viruses. Nature, 226, 1209–1211.CrossRefGoogle ScholarPubMed
Banani, S. F., Lee, H. O., Hyman, A. A. and Rosen, M. K. (2017). Biomolecular condensates: organizers of cellular biochemistry. Nat. Rev. Mol. Cell Biol. 18, 285–298.Google Scholar
Banavar, J.R., Hong, T.X. and Maritan, A. (2005). Proteins and polymers. J. Chem. Phys. 122, 234910.CrossRefGoogle ScholarPubMed
Barthel, J. M. G., Krienke, H. and Kunz, W. (1998). Physical Chemistry of Electrolyte Solutions. New York: Springer.Google Scholar
Beer, M., Schmidt, M. and Muthukumar, M. (1997). The electrostatic expansion of linear polyelectrolytes: Effects of gegenions, co-ions, and hydrophobicity. Macromolecules, 30, 8375–8385.Google Scholar
Belyi, V. A. and Muthukumar, M. (2006). Electrostatic origin of the genome packing in viruses. Proc. Natl. Acad. Sci. USA., 103, 17174–17178.CrossRefGoogle ScholarPubMed
Bemporad, F., Calloni, G., Campioni, S., Plakoutsi, G., Taddei, N. and Chiti, F. (2006). Sequence and structural determinants of amyloid fibril formation. Acc. Chem. Res., 39, 620–627.CrossRefGoogle ScholarPubMed
Berne, B. J. and Pecora, R. (1976). Dynamic Light Scattering. New York: John Wiley & Sons.Google Scholar
Berry, R. S., Rice, S. A. and Ross, J. (2000). Physical Chemistry. Oxford: Oxford University Press.Google Scholar
Besteman, K., Eijk, K.V. and Lemay, S. G. (2007). Charge inversion accompanies DNA condensation by multivalent ions. Nat. Phys, 3, 641–644.Google Scholar
Bluhm, T. L. and Whitmore, M. D. (1985). Styrene /butadiene block copolymer micelles in heptane. Can. J. Chem. 63, 249.Google Scholar
Bockris, J. O. and Reddy, A. K. N. (1970). Modern Electrochemistry 1. New York: Plenum Press.Google Scholar
Dielectric spectroscopy and conductivity of polyelectrolyte solutions. J. Phys.: Condens. Matter, 16, R1423–R1463.Google Scholar
Borgia, A., Borgia, M. B., Bugge, K., Kissling, V. M., Heidarsson, P. O., Fernandes, C. B., Sottini, A., Soranno, A., Buholzer, K. J., Nettels, D., Kragelund, B. B., Best, R. B. and Schuler, B. (2018). Extreme disorder in an ultrahigh-affinity protein. Nature, 555, 61–66.CrossRefGoogle Scholar
Borisov, O. V. and Zhulina, E. B. (2002). Effect of salt on self-assembly in charged block copolymer micelles. Macromolecules, 35, 4472–4480.CrossRefGoogle Scholar
Boyd, R. H. and Phillips, P. J. (1993). The Science of Polymer Molecules. Cambridge: Cambridge University Press.Google Scholar
Bragg, W. L. and Williams, E. J. (1934). The effect of thermal agitation on atomic arrangement in alloys. Proc. Roy. Soc. London, 145A, 699–730.Google Scholar
Bragg, W. L. and Williams, E. J. (1935). The effect of thermal agitation on atomic arrangement in alloys. II. Proc. Roy. Soc. London, 151A, 540–566.Google Scholar
Brilliantov, N. V., Kuznetsov, D. V. and Klein, R. (1998). Chain collapse and counterion condensation in dilute polyelectrolyte solutions. Phys. Rev. Lett., 81, 1433–1436.Google Scholar
Brinkman, H. C. and Hermans, J. J. (1949). The effect of non-homogeneity of molecular weight on the scattering of light by high polymer solutions. J. Chem. Phys., 17, 574–576.CrossRefGoogle Scholar
Brinkers, S., Dietrich, H. R. C., de Groote, F. H., Young, I. T. and Rieger, B. (2009). The persistence length of double stranded DNA determined using dark field tethered particle motion. J. Chem. Phys., 130, 215105.CrossRefGoogle ScholarPubMed
Budkov, Y. A., Kolesnikov, A. L., Georgi, N., Nogovitsyn, E. A. and Kiselov, M. G. (2015). A new equation of state of a flexible-chain polyelectrolyte solution: Phase equilibria and osmotic pressure in the salt-free case, J. Chem. Phys., 142, 174901.Google Scholar
Buell, A. K., Blundell, J. R., Dobson, C. M., Welland, M. E., Terentjev, E. M. and Knowles, T. P. J. (2010). Frequency factors in a landscape model of filamentous protein aggregation. Phys. Rev. Lett., 104, 228101.CrossRefGoogle Scholar
Buell, A. K., Hung, P., Salvatella, X., Welland, M. E., Dobson, C. M. and Knowles, T. P. J. (2013). Electrostatic effects in filamentous protein aggregation. Biophys. Journal, 104, 1116—1126.Google Scholar
Buell, A. K., Galvagnion, C., Gasper, R., Sparr, E., Vendruscoio, M., Knowles, T. P.J. and Dobson, C. M. (2014). Solution conditions determine the relative importance of nucleation and growth processes in a-synuclein aggregation. Proc. Natl. Acad. Sci. (USA), 111,7671–7676.CrossRefGoogle Scholar
Bungenberg de Jong, H. G. and Kruyt, H. R. (1929). Coacerrvation (Partial miscibility in colloid systems). Proc. K. Ned. Akad. Wet., 32, 849–855.Google Scholar
Cadena-Nava, R. D., Comas-Garcia, M., Garmann, R. F., Rao, A. L. N., Knobler, C. M. and Gelbart, W. M. (2012). Self-assembly of viral capsid protein and RNA molecules of different sizes: Requirement for a specific high protein/RNA mass ratio,. Virol., 86, 3318–3326.Google Scholar
Calladine, C. R., Collis, C. M., Drew, H. R. and Mott, M. R. (1991). A study of electrophoretic mobility of DNA in agarose an polyacrylamide gels. J. Mol. Biol., 221, 981–1005.Google Scholar
Candau, S., Bastide, J. and Delsanti, M., (1982). Structural , Elastic, and Dynamic Properties of Swollen Polymer Networks. Adv. Polym. Sci., 44, 27–71.CrossRefGoogle Scholar
Carri, G. A. and Muthukumar, M. (1999). Attractive interactions and phase transitions in solutions of similarly charged rod-like polyelectrolytes. J. Chem. Phys. 111, 1765–1777.Google Scholar
Chandrasekhar, S. (1943). Stochastic processes in physics and astronomy. Rev. Mod. Phys., 15, 1–89.CrossRefGoogle Scholar
Chen, K., Jou, I., Ermann, N., Muthukumar, M., Keyser, U. F. and Bell, N. A. W. (2021). Dynamics of driven polymer transport through a nanopore. Nat. Phys., 17, 1043–1049.CrossRefGoogle Scholar
Chen, K. and Muthukumar, M. (2021). Entropic barrier of topologically immobilized DNA in hydrogels. Proc. Natl. Acad. Sci. USA., 118, https://doi.org/10.1038/s41567-021-01268-2.Google ScholarPubMed
Cherstvy, A. G. and Winkler, R. G. (2011). Polyelectrolyte adsorption onto oppositely charged interfaces: Unified approach for plane, cylinder, and sphere. Phys. Chem. Chem. Phys., 13, 11686–11693.CrossRefGoogle ScholarPubMed
Choi, J. M., Holehouse, A. S. and Pappu, R. V. (2020a). Physical principles underlying the complex biology of intracellular phase transitions. Annu. Rev. BioPhys., 49, 107–133.CrossRefGoogle Scholar
Choi, J. M., Hyman, A. A. and Pappu, R. V. (2020b). Generalized models for bond percolation transitions of associative polymers. Phys. Rev. E. 102, 042403.Google Scholar
Chremos, A. and Dougla, J. F. (2017). Communication : Counter-ion solvation and anomalous low-angle scattering in salt-free polyelectrolyte solutions. J. Chem. Phys., 147, 241103.Google Scholar
Cohen, J., Priel, Z. and Rabin, Y. (1988). Viscosity of dilute polyelectrolyte solutions. J. Chem. Phys., 88, 7111.CrossRefGoogle Scholar
Colby, R. H., Boris, D. C., Krause, W. E. and Tan, J. S. (1997). Polyelectrolyte conductivity. J. Polym. Sci. Part B: Polym. Phys., 35 2951–2960.Google Scholar
Conway, B. E., Bockris, J. O’ M. and Ammart, I. A. (1951). The dielectric constant of the solution in the diffuse and Helmholtz double layers at a charged interface in aqueous solution. Trans. Faraday Soc., 47, 756–766.Google Scholar
Conway, J. F. Steven, A. C. (1999). Methods for reconstructing density maps of “single” particles from cryoelectron micrographs to subnanometer resolution. J. Struct. Biol., 128, 106–118.Google Scholar
Cotton, J. P., Decker, D., Benoit, H., Farnoux, B., Higgins, J., Jannink, G., Ober, R., Picot, C., and des Cloizeaux, J. (1974). Conformation of polymer chain in the bulk. Macromolecules, 7, 863–872.Google Scholar
Crick, F. (1970). Central dogma of molecular biology. Nature, 227, 561–563.CrossRefGoogle ScholarPubMed
Dan, N. and Tirrell, M. (1993). Self -assembly of block copolymers with a strongly charged and a hydrophobic block in a selective, polar solvent. Micelles and adsorbed layers. Macromolecules, 26, 4310–4315.Google Scholar
Daoud, M., Cotton, J. P., Farnoux, B., Jannink, G., Sarma, G., Benoit, H., Duplessix, R., Picot, C. and de Gennes, P. G. (1975). Solutions of flexible polymers. Neutron experiments and interpretation. Macromolecules, 8, 804–818.Google Scholar
Dar, F. and Pappu, R. V. (2020). Phase separation: Restricting the sizes of condensates. Elife, 9, e59663.Google Scholar
Das, R. K. and Pappu, R. V. (2013). Conformations of intrinsically disordered proteins are influenced by linear sequence distributions of oppositely charged residues. Proc. Natl. Acad. Sci. USA., 110, 13392–13397.CrossRefGoogle ScholarPubMed
Das, R. K., Ruff, K. M. and Pappu, R. V. (2015). Relating sequence encoded information to form and function of intrinsically disordered proteins. Current Opinion in Structural Biology, 32, 102–112.CrossRefGoogle ScholarPubMed
Das, S. and Muthukumar, M. (2022). Microstructural organization in a-synuclein solutions. Macromolecules, 55, 4228–4236.Google Scholar
Dautzenberg, H., Jaeger, W., J. Kotz, B. P., Seidel, C. and Stscherbina, D. (1994). Polyelec-trolytes. New York: Hanser Publishers.Google Scholar
Debye, P. (1925). Marx ’ Handbuch der Radiologie. Akademische Verlagsgesellschaft, Liepzig, 6, 618, 680.Google Scholar
de Gennes, P. G. (1968). Statistics of branching and hairpin helices for the dAT copolymer. Biopolymers 6, 715–729.Google Scholar
de Gennes, P. G. (1971). Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys., 55, 572–579.Google Scholar
de Gennes, P. G. (1979). Scaling Concepts in Polymer Physics. Ithaca: Cornell University Press.Google Scholar
de Gennes, P. G., Pincus, P., Velasco, R. M. and Brochard, F. (1976). Remarks on polyelectrolyte conformation. J. Phys. France, 37, 1461–1473.Google Scholar
de Gennes, P. G. & Prost, J. (1993). The Physics of Liquid Crystals. Oxford: Clarendon Press.Google Scholar
de la Cruz, M. O., Belloni, L., Delsanti, M., Dalbiez, J. P., Spalla, O. and Drifford, M. (1995). Precipitation of highly charged polyelectrolyte solutions in the presence of multivalent salts. J. Chem. Phys., 103, 5781–5791.Google Scholar
des Closeaux, J. and Jannink, G. (1990). Polymers in Solution. Oxford: Clarendon Press.Google Scholar
Dobrynin, A. V., Colby, R. H. and Rubinstein, M. (1995). Scaling theory of polyelectrolyte solutions. Macromolecules, 28, 1859–1871.Google Scholar
Dobrynin, A. V., Colby, R. H. and Rubinstein, M. (2004). Polyampholyte s. J. Polym. Sci. Part B: Polym. Phys., 42, 3513–3538.CrossRefGoogle Scholar
Dobrynin, A. V. and Rubinstein, M. (2005). Theory of polyelectrolytes in solutions and at surfaces. Prog. Polym. Sci., 30, 1049–1118.Google Scholar
Doi, M. and Edwards, S. F. (1986). The Theory of Polymer Dynamics. Oxford: Clarendon Press.Google Scholar
Dou, S. and Colby, R. H. (2006). Charge density effects in salt-free polyelectrolyte solution rheology. Journal of Polymer Science: Part B: Polymer Physics, 44, 2001–2013.Google Scholar
Drifford, M. and Dalbiez, J P. (1984). Light scattering by dilute solutions of salt-free polyelec-trolytes, J. Phys. Chem., 88, 5368–5375.Google Scholar
Drifford, M. and Dalbiez, J. P. (1985). Effect of salt on sodium polystyrene sulfonate measured by light scattering. Biopolymers, 24, 1501–1514.Google Scholar
Dusek, K. and Patterson, D., (1968). Transition in swollen polymer networks induced by intramolecular condensation, J. Polym. Sci: Part A-2, 6, 1209–1216.Google Scholar
Dyson, H. J. and Wright, P. E. (2005). Intrinsically unstructured proteins and their functions. Nat. Rev. Mol. Cell Biol., 6, 197–208.Google Scholar
Edwards, S. F. (1966). The theory of polymer solutions at intermediate concentration, Proc. Phys. Soc., 88, 265–280.Google Scholar
Edwards, S. F. (1967). The statistical mechanics of polymerized material. Proc. Phys. Soc. (London), 92, 9–16.Google Scholar
Edwards, S. F. and Freed, K. F. (1974). Theory of the dynamical viscosity of polymer solutions. J. Chem. Phys., 61, 1189–1202.Google Scholar
Ehrlich, G. and Doty, P. (1954). Macro -ions. III. The solution behavior of a polymeric ampholyte. J. Am. Chem. Soc., 76, 3764–3777.Google Scholar
Einstein, A. (1956). Investigations on the Theory of Brownian Movement, New York: Dover.Google Scholar
Eisenberg, H. and Mohan, G. R. (1959). Aqueous solutions of polyvinylsulfonic acid: Phase separation and specific interaction with ions, viscosity, conductance and potentiometry. J. Phys. Chem. 63, 671–680.Google Scholar
Eisenberg, H. and Casassa, E. F. (1960). Aqueous solutions of salts of poly(vinylsulfonic acid). J. Polym. Sci. 47, 29–44.Google Scholar
Eisenberg, D., Nelson, R., Sawaya, M. R., Balbirnie, M., Sambashivan, S., Ivanova, M. I., Madsen, A. O. and Riekel, C. (2006). The structural biology of protein aggregation diseases: Fundamental questions and some answers. Acc. Chem. Res., 39, 568–575.Google Scholar
Ellison, W. J., Lamkaouchi, K. and Moreau, J. M. (1996). Water : A dielectric reference. J Mol. Liq., 68, 171–279.Google Scholar
England, J. L. and Haran, G. (2010). To fold or expand—a charged question. Proc. Natl. Acad. Sci. USA., 107, 14519–14520.CrossRefGoogle ScholarPubMed
Essafi, W., Lafuma, F. and Williams, C. E. (1995). Effect of solvent quality on the behavior of highly charged polyelectrolytes. J. Phys.ll France, 5, 1269–1275.Google Scholar
Everaers, R., Grosberg, A. Y., Rubinstein, M. and Rosa, A. (2017). Flory theory of randomly branched polymers. Soft Matter, 13, 1223–1234.Google Scholar
Faxen, H. (1922). Der widerstand gegen bewegung einer starren kugel in einer zaehen. Ann. Phys., 373, 89–119.Google Scholar
Ferry, J. D. (1936). Statistical evaluation of sieve constants in ultrafiltration. J. Gen. Physiol., 20, 95–104.CrossRefGoogle ScholarPubMed
Fink, A. L. (2006). The aggregation and fibrillization of αsynuclein. Acc. Chem. Res., 39, 628–634.CrossRefGoogle Scholar
Finkelstein, A. V. and Ptitsyn, O. B. (2002). Protein Physics. Amsterdam: Academic Press.Google Scholar
Firman, T. and Ghosh, K. (2018). Sequence charge decoration dictates coil-globule transition in intrinsically disordered proteins. J. Chem. Phys. 148, 123305.CrossRefGoogle ScholarPubMed
Fisher, M. E. and Levin, Y. (1993). Criticality in ionic fluids: Debye-Hückel theory, Bjerrum, and beyond. Phys. Rev. Lett. 71, 3826–3829.CrossRefGoogle ScholarPubMed
Fitzkee, N. Z. and Rose, G. D., (2004). Reassessing random-coil statistics in unfolded proteins, Proc. Natl. Acad. Sci. USA., 101, 12497–12502.Google Scholar
Fleer, G. J., Cohen Stuart, M. A., Scheutjens, J. M. H. M., Cosgrove, T. and Vincent, B. (1993). Polymers at lnterfaces, London: Chapma & Hall.Google Scholar
Flory, P. J. (1942). Thermodynamics of high polymer solutions. J. Chem. Phys., 10, 51–61.Google Scholar
Flory, P. J. (1949). The configuration of real polymer chains.J. Chem. Phys., 17, 303–310.Google Scholar
Flory, P. J. (1953a). Principles of Polymer Chemistry. Ithaca: Cornell University Press.Google Scholar
Flory, P. J. (1953b). Molecular configuration of polyelectrolytes. J. Chem. Phys. 21, 162–163.Google Scholar
Flory, P. J. (1956). Phase equilibria in solutions of rod-like particles. Proc. R. Soc. A234, 73–89.Google Scholar
Flory, P. J. (1969). Statistical Mechanics of Chain Molecules. New York: John Wiley & Sons.CrossRefGoogle Scholar
Flory, P. J. and Rehner, J. (1943). Statistical mechanics of crosslinked polymer networks ii. swelling, J. Chem. Phys., 11, 521.Google Scholar
Flory, P. J. and Krigbaum, W. R. (1950). Statistical mechanics of dilute polymer solutions. II. J. Chem. Phys., 18, 1086–1094.CrossRefGoogle Scholar
Förster, S., Schmidt, M. and Antonietti, M. (1990). Static and dynamic light scattering by aqueous polyelectrolyte solutions: Effect of molecular weight, charge density and added salt. Polymer 31, 781–792.CrossRefGoogle Scholar
Förster, S. and Schmidt, M. (1995). Polyelectrolytes in solution. Adv. Polym. Sci. 120, 51–133.Google Scholar
Fraden, S., Maret, G., Casper, D. L. D. and Meyer, R. B. (1989). Isotropic -nematic phase transition and angular correlations in isotropic suspensions of tobacco mosaic virus. Phys. Rev. Lett., 63, 2068–2071.CrossRefGoogle ScholarPubMed
Fraden, S., Maret, G. and Casper, D. L. D. (1993). Angular correlations and the isotropic-nematic phase transition in suspensions of tobacco mosaic virus. Phys. Rev. E, 48, 2816–2837.Google Scholar
Fredrickson, G. H. (2006). The Equilibrium Theory of Inhomogeneous Polymers. Oxford: Clarendon Press.Google Scholar
Freed, K. F. (1972). Functional integrals and polymer statistics. Adv. Chem. Phys. 22, 1–128.Google Scholar
Freed, K. F. (1987). Renormalization Group Theory of Macromolecules. New York: John Wiley & Sons.Google Scholar
Freed, K. F. and Edwards, S. F. (1974). Polymer viscosity in concentrated solutions. J. Chem. Phys., 61, 3626–3633.Google Scholar
Fuoss, R. M., Katchalsky, A. and Lifson, S. (1951). The potential of an infinite rod-like molecule and the distribution of the counterions. Proc. Natl. Acad. Sic. USA., 37, 579–589.Google Scholar
Ghosh, K., Carri, G. A. and Muthukumar, M. (2001). Configurational properties of a single semiflexible polyelectrolyte. J. Chem. Phys., 115, 4367–4375.Google Scholar
Gitlin, L., Carbeck, J. D. and Whitesides, G. M. (2006). Why are proteins charged? Net-works of charge-charge interactions in proteins measured by charge ladders and capillary electrophoresis. Angew. Chem. Int. Ed., 45, 3022–3060.Google Scholar
Gong, H., Hocky, G. and Freed, K. F. (2008). Influence of nonlinear electrostatics on transfer energies between liquid phases: Charge burial is far less expensive than Born model. Proc. Natl. Acad. Sci. USA., 105, 11146–11151.Google Scholar
Griffiths, D. J. (1999). Introduction to Electrodynamics. Upper Saddle River: Prentice Hall.Google Scholar
Grosberg, A. Y. and Khokhlov, A. R. (1994). Statistical Physics of Macromolecules. New York: AIP Press.Google Scholar
Grosberg, A. Yu., Nguyen, T. T., and Shklovskii, B. I., (2002). Colloquium : The physics of charge inversion in chemical and biological systems. Rev. Mod. Phys., 74, 329–345.Google Scholar
Gross, R. J. and Osterle, J. F. (1968). Membrane transport characteristics of ultrafine capillaries. J. Chem. Phys. 49, 228–234.Google Scholar
Gunton, J. D., Miguel, San, and Sahni, M., P. S. (1983). The dynamics of first-order phase transitions. Phase Transitions, 8, 267–482.Google Scholar
Gutin, A. M. and Shakhnovich, E. I. (1994). Effect of a net charge on the conformation of polyampholytes. Phys. Rev. E, 50, R3322-R3325.Google Scholar
Halperin, A. (1987). Polymeric micelles: A star model. Macromolecules, 20, 2943–2946.CrossRefGoogle Scholar
Hamada, F., Kinugasa, S., Hayashi, H. and Nakajima, A. (1985). Small -angle x-ray scattering from semidilute polymer solutions. I. Polystyrene in toluene. Macromolecules, 18, 22902294.CrossRefGoogle Scholar
Han, C. C., and Akcasu, A. Z., (2011). Scattering and Dynamics of Polymers. Singapore: John Wiley & Sons.Google Scholar
Hänggi, P., Talkner, P. and Borkovec, M. (1990). Reaction -rate theory: Fifty years after Kramers. Rev. Mod. Phys., 62, 251–341.Google Scholar
Harmon, T. S., Holehouse, A. S., Rosen, M. K. and Pappu, R. V. (2017). Intrinsically disordered linkers determine the interplay between phase separation and gelation in multivalent proteins. Elife, 6, e30294.CrossRefGoogle ScholarPubMed
Hendrix, R. W. (1999). Evolution : The long evolutionary reach of viruses. Curr. Bio., 9, R914–R917.Google Scholar
Henry, D. C. (1931). Cataphoresis of suspended particles. Part I. The equation of cataphoresis. Proc. R. Soc. London, Ser. A, 133, 106–129.Google Scholar
Hiemenz, P. C. and Rajagopalan, R. (1997). Principles of Colloid and Surface Chemistry. New York: Marcel Dekker, Inc.Google Scholar
Hiemenz, P. C. and Lodge, T. P. (2007). Polymer Chemistry. Boca Raton: CRC Press.CrossRefGoogle Scholar
Higgins, J. S. and Benoit, H. (1994). Polymers and Neutron Scattering. Oxford: Clarendon Press.Google Scholar
Higgs, P. G. and Joanny, J-F. (1991). Theory of polyampholyte solutions. J. Chem. Phys., 94, 1543–1554.Google Scholar
Hirotsu, S., Hirokawa, Y. and Tanaka, T. (1987). Volume-phase transitions of ionized n-isopropylacrylamide gels, J. Chem. Phys., 87, 1392–1395.Google Scholar
Hoagland, D., Arvanitidou, E. and Welch, C. (1999). Capillary electrophoresis measurements of the free solution mobility for several model polyelectrolyte systems. Macromolecules, 32, 6180–6190.Google Scholar
Hofmann, H., Soranno, A., Borgia, A., Gast, K., Nettels, D. and Schuler, B. (2012). Polymer scaling laws of unfolded and intrinsically disordered proteins quantified with single-molecule spectroscopy. Proc. Natl. Acad. Sci. USA., 109, 16155–16160.Google Scholar
Holm, C., Joanny, J. F., Netz, R. R., Reineker, P., Seidel, C., Vilgis, T. A. and Winkler, R. G. (2004). Polyelectrolyte theory. Adv. Polym. Sci. 166, 67–111.Google Scholar
Holmes, D. F. and Kadler, K. E. (2006). The 10+4 microfibril structure of thin cartilage fibrils. Proc. Natl. Acad. Sci. (USA), 103, 17249–17254.CrossRefGoogle Scholar
Horkay, F., Tasaki, I., and Basser, P. (2001). Effect of monovalent-divalent cation exchange on the swelling of polyacrylate hydrogels in physiological salt solutions, Biomacromolecules, 2, 195–199.Google Scholar
Horkay, F., Nishi, K., and Shibayama, M. (2017). Decisive test of the ideal behavior of tetra-PEG gels, J. Chem. Phys., 146, 164905.Google Scholar
Hu, Y., Zandi, R., Anavitarte, A., Knobler, C. M. and Gelbart, W. M. (2008). Packaging of a polymer by a viral capsid: The interplay between polymer length and capsid size, Biophys. J, 94, 1428–1436.Google Scholar
Hua, J., Mitra, M. K., and Muthukumar, M. (2012). Theory of volume transition in polyelectrolyte gels with charge regularization, J. Chem. Phys., 136, 134901.CrossRefGoogle Scholar
Huber, K. (1993). Calcium -induced shrinking of polyacrylate chains in aqueous solution. J. Phys. Chem., 97, 9825–9830.Google Scholar
Huggins, M. L. (1942a). Thermodynamic properties of solutions of long-chain compounds. Ann. N. Y. Acad. Sci., 43, 1–32.Google Scholar
Huggins, M. L. (1942b). Some properties of solutions of long-chain compounds. J. Phys. Chem. 46, 151–158.CrossRefGoogle Scholar
Huggins, M. L. (1942c). Theory of solutions of high polymers. J. Am. Chem. Soc., 64, 1712–1719.Google Scholar
Huihui, J., Firman, T. and Ghosh, K. (2018). Modulating charge patterning and ionic strength as a strategy to induce conformational changes in intrinsically disordered proteins. J. Chem. Phys. 149, 085101.Google Scholar
Huihui, J. and Ghosh, K. (2020). An analytical theory to describe sequence-specific inter-residue distance profiles for polyampholytes and intrinsically disordered proteins. J. Chem. Phys. 152, 161102.Google Scholar
Hulmes, D. J. S., Wess, T. J., Prockop, D. J. and Fratzl, P. (1995). Radial packing, order, and disorder in collagen fibril. Biophys. J., 68, 1661–1670.Google Scholar
Ikeda, Y., Beer, M., Schmidt, M. and Huber, K. (1998). Ca2+ and Cu2+ induced conformational changes of sodium polymethacrylate in dilute aqueous solution, Macromolecules, 31, 728–733.Google Scholar
Innes-Gold, S. N., Jacobson, D. R., Pincus, P. A., Stevens, M. J. and Saleh, O. A. (2021). Flexible , charged biopolymers in monovalent and mixed-valence salt: Regimes of anomalous electrostatic stiffening and of salt insensitivity. Phys. Rev., E, 104, 014504.Google Scholar
Isrealachvilli, J. N. (2011). Intermolecular and Surface Forces (Academic Press, London).Google Scholar
Izumrudov, V. A., Kargov, S. I., Zhiryakova, M. V., Zezin, A. B. and Kabanov, V. A. (1995). Competitive reactions in solutions of DNA and water-soluble interpolyelectrolyte complexes. Biopolymers, 35, 523–531.CrossRefGoogle Scholar
Jeon, B. J. and Muthukumar, M. (2014). Polymer capture by a-hemolysin pore upon salt concentration gradient. J. Chem. Phys. 140, 015101.CrossRefGoogle Scholar
Jia, D. and Muthukumar, M. (2018). Topologically frustrated dynamics of crowded charged macromolecules in charged gels. Nat. Commun., 9, 2248.Google Scholar
Jia, D. and Muthukumar, M. (2019). Effect of salt on the ordinary-extraordinary transition in solutions of charged macromolecules. J. Am. Chem. Soc., 141, 5886–5896.Google Scholar
Jia, D. and Muthukumar, M., (2020). Interplay between microscopic and macroscopic properties of charged hydrogels. Macromolecules, 53, 90–101.CrossRefGoogle Scholar
Jia, D. and Muthukumar, M. (2021a). Electrostatically driven topological freezing of polymer diffusion at intermediate confinements. Phys. Rev. Lett., 126, 057802.Google Scholar
Jia, D. and Muthukumar, M. (2021b). Theory of charged gels: Swelling, elasticity, and dynamics. Gels, 7, 49.Google Scholar
Joanny, J. F. and Leibler, L. (1990). Weakly charged polyelectrolytes in a poor solvent. J. Phys. France, 51, 545–557.Google Scholar
Johner, C., Kramer, H., Batzill, S., Graf, C., Hagenbüchle, M., Martin, C. and Weber, R. (1994). Static light scattering and electric birefringence experiments on saltfree solutions of poly(styrenesulfonate), J. Phys. II France, 4, 1571–1584.Google Scholar
Joosten, J. G. H., McCarthy, J. L., and Pusey, P. N., (1991). Dynamic and static light scattering by aqueous polyacrylamide gels. Macromolecules, 24, 6690–6699. 1991, 24, 6690.CrossRefGoogle Scholar
Kaji, K., Urakawa, H., Kanaya, T. and Kitamaru, R. (1988). Phase diagram of polyelectrolyte solutions, J. Phys. France, 49, 993–1000.CrossRefGoogle Scholar
Kanai, S. and Muthukumar, M. (2007). Phase separation kinetics of polyelectrolyte solutions. J. Chem. Phys. 127, 244908.Google Scholar
Kasianowicz, J. J., Brandin, E., Branton, D. and Deamer, D. W. (1996). Characterization of individual polynucleotide molecules using a membrane channel. Proc. Natl. Acad. Sci. U. S. A. 93, 13770–13773 (1996).Google Scholar
Katchalsky, A., Kunzle, O. and Kuhn, W. (1950). Behavior of polyvalent polymeric ions in solution. J. Polym. Sci. 5, 283–300.Google Scholar
Katchalsky, A., Lifson, S., and Eisenberg, H., (1951). Equation of swelling for polyelectrolyte gels, J. Polymer Sci., 7, 571–574.Google Scholar
Katchalsky, A., Shavit, N. and Eisenberg, H. (1954). Dissociation of weak polymeric acids and bases. J. Polym. Sci. 13, 69–84.Google Scholar
Kato, T., Miyaso, K., Noda, I., Fujimoto, T. and Nagasawa, M. (1970). Thermodynamic and hydrodynamic properties of linear polymer solutions. i. Light scattering of monodisperse poly(?-methylstyrene), Macromolecules, 3, 777–786.CrossRefGoogle Scholar
Kato, M., Han, T. W., Xie, S., Shi, K., Du, X., Wu, L. C., Mirzaei, H., Goldsmith E. J., Longgood, J, Pei, J., Grishin, N. V., Frantz, D. E., Schneider, J. W., Chen, S., Li, L., Sawaya, M. R., Eisenberg, D., Tycko, R and McKnight, S. L. (2012). Cell -free formation of RNA granules: Low complexity sequence domains form dynamic fibers within hydrogels. Cell, 149, 753–767.Google Scholar
Khokhlov, A. R. (1980). On the collapse of weakly charged polyelectrolytes. J. Phys. A, 13, 979–987.Google Scholar
Khokhlov, A. R. and Kramarenko, E. Y. (1994). Polyelectrolyte/ionomer behavior in polymer gel collapse. Macromol. Theory Simul., 3, 45–59.Google Scholar
Kim, H., Chang, T., Yohanan, J. M., Wang, L. and Yu, H. (1986). Polymer diffusion in linear matrices: Polystyrene in toluene. Macromolecules, 19, 2737–2744.Google Scholar
Kirkwood, J. and Riseman, J. (1948). The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J. Chem. Phys., 16, 565–573.Google Scholar
Kirkwood, J. G., and Goldberg, J. (1950). Light scattering arising from composition fluctuations in multi-component systems. J. Chem. Phys., 18, 54–57.CrossRefGoogle Scholar
Kirste, R. G., Kruse, W. A. and Ibel, K.. (1975). Determination of the conformation of polymers in the amorphous solid state and in concentrated solution by neutron diffraction. Polymer, 16, 120–124.Google Scholar
Kittel, C. (1996). Introduction to Solid State Physics. New York: John Wiley & Sons, Inc.Google Scholar
Kizilay, E., Kayitmazer, A. B. and Dubin, P. L. (2011). Complexation and coacervation of polyelectrolytes with oppositely charged colloids, Adv. Colloid Interface Sci., 167, 24–37.Google Scholar
Klein, J. (1996). Shear , friction, and lubrication forces between polymer-bearing surfaces. Annu. Rev. Mater. Sci., 26, 581–612.Google Scholar
Kleman, M. and Lavrentovich, O. D. (2003). Soft Matter Physics. New York: Springer-Verlag.Google Scholar
Klooster, N. T. M., Van der Touw, F. and Mandel, M. (1984). Solvent effects in polyelec-trolyte solutions. 2. Osmotic, elastic light scattering, and conductometric measurements on (partially) neutralized poly(acrylic acid) in methanol. Macromolecules, 17, 2078–2086.Google Scholar
Knipe, D. M. and Howley, P. M. (2001). Fundamental Virology, 4th edn. Philadelphia: Lippincott Williams & Wilkins.Google Scholar
Kohn, J. E., MilLett., I. S., Jacob, J., Zagrovic, B., Dillon, T. M., Cingel, N., Dothager, R. S., Seifert, S., Thiyagarajan, P., Sosnick, T. R., Hasan, M. Z., Pande, V. S., Ruczinski, I., Doniach, S. and Plaxco, K. W. (2004). Random-coil behavior and the dimensions of chemically unfolded proteins, Proc. Natl. Acad. Sci. USA., 101, 12491–12496.Google Scholar
Kozak, D., Kristan, J. Dolar, D. (1971). Osmotic coefficient of polyelectrolyte solutions. Z. Phys. Chem. Neue Folge, 76, 85–92.Google Scholar
Kremer, F. and Schönhals, A. (2003). Broadband Dielectric Spectroscopy. Berlin: Springer.Google Scholar
Kudaibergenov, S., Jaeger, W. and Laschewsky, A. (2006). Polymeric betaines: Synthesis, characterization, and application. Adv. Polym. Sci., 201, 157–224.CrossRefGoogle Scholar
Kudlay, A., Ermoshkin, A. V. and de la Cruz, M. O. (2004). Complexation of Oppositely Charged Polyelectrolytes: Effect of Ion Pair Formation, Macromolecules, 37, 9231–9241.Google Scholar
Kuhn, W., Hargitay, B., Katchalsky, A. and Eisenberg, H. (1950). Reversible dilation and contraction by changing the state of ionization of high-polymer acid networks. Nature 165, 514–516.Google Scholar
Kumar, R. and Muthukumar, M. (2007). Microphase separation in polyelectrolyte diblock copolymer melt: Weak segregation limit. J. Chem. Phys. 126, 214902.Google Scholar
Kumar, R. and Fredrickson, G. H. (2009). Theory of polyzwitterion conformations. J. Chem. Phys., 131, 104901.Google Scholar
Kundagrami, A. and Muthukumar, M. (2008). Theory of competitive counterion adsorption on flexible polyelectrolytes: Divalent salts. J. Chem. Phys., 128, 244901.Google Scholar
Kundagrami, A. and Muthukumar, M. (2010). Effective charge and coil-globule transition of a polyelectrolyte chain. Macromolecules, 43, 2574–2581.CrossRefGoogle ScholarPubMed
Lagueci, A., Ulrich, S., Labille, J., Fatin-Rouge, N., Stoll, S. and Buffle, J. (2006). Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment. Eur. Polym. J., 42, 1135–1144.Google Scholar
Lamm, G. and Pack, G. R. (1997). Calculation of dielectric constants near polyelectrolytes in solution, J. Phys. Chem. B, 101, 959–965.Google Scholar
Landau, L. D. and Lifshitz, E. M. (1980). Statistical Physics. Oxford: Pergamon Press.Google Scholar
Landau, L. D. and Lifshitz, E. M., (1986). Theory of Elasticity, Oxford: Pergamon Press.Google Scholar
Laschewsky, A. (2014). Structures and synthesis of zwitterionic polymers. Polymers, 6, 15441601.Google Scholar
Lee, C. L. and Muthukumar, M. (2009). Phase behavior of polyelectrolyte solutions with salt. J. Chem. Phys.130, 024904.Google Scholar
Leibler, L. (1980). Theory of microphase separation in block copolymers. 1980. Macro-molecules, 13, 1602–1617.CrossRefGoogle Scholar
Li, Y. and Tanaka, T. (1990). Kinetics of swelling and shrinking of gels, J. Chem. Phys., 92, 1365–1371.Google Scholar
Liaw, D-J. and Huang, C-C. (1997). Dilute solution properties of poly(3-dimethyl acryloy-loxyethyl ammonium propiolactone). Polymer, 38, 6355–6362.CrossRefGoogle Scholar
Lin, S. C., Lee, W. I. and Schurr, J. M. (1978). Brownian motion of highly charged poly(L-lysine). Effects of salt and polyion concentration. Biopolymers 17, 1041–1064.CrossRefGoogle Scholar
Lin, Y-H., Brady, J. P., Chan, H. S. and Ghosh, K. (2020). A unified analytical theory of het-eropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes. J. Chem. Phys. 152, 045102.Google Scholar
Liu, S. and Muthukumar, M. (2002). Langevin dynamics simulation of counterion distribution around isolated flexible polyelectrolyte chains. J. Chem. Phys., 116, 9975–9982.Google Scholar
Liu, S., Ghosh, K. and Muthukumar, M. (2003). Polyelectrolyte solutions with added salt: A simulation study. J. Chem. Phys., 119, 1813–1823.Google Scholar
Lodge, T. P. and Rotstein, N. A. (1991). Tracer diffusion of linear and star polymers in entangled solutions and gels. J. Non-Cryst. Solids, 131-133, 671–675.Google Scholar
Loh, P., Deen, R., Vollmer, D., Fischer, K., Schmidt, M., Kundagrami, A. and Muthukumar, M. (2008). Collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counterions? Macromolecules, 41, 9352–9358.Google Scholar
Lopez, C. G. (2019a). Entanglement properties of polyelectrolytes in salt-free and excess-salt solutions. ACS Macro Lett., 8, 979–983.CrossRefGoogle Scholar
Lopez, C. G. (2019b). Scaling and entanglement properties of neutral and sulfonated polystyrene. Macromolecules, 52, 9409–9415.Google Scholar
Lowe, A. B. and McCormick, C. L. (2002). Synthesis and solution properties of zwitterionic polymers. Chem. Rev., 102, 4177–4189.CrossRefGoogle ScholarPubMed
Luo, S., Jiang, X., Zou, L., Wang, F., Yang, J., Chen, Y. and Zhao, J. (2013). Resolving the difference in electric potential within charged macromolecule. Macromolecules, 46, 3132–3136.Google Scholar
Mahalik, J. P., Hildebrandt, B. and Muthukumar, M. (2013). Langevin dynamics simulation of DNA ejection from a phage. J. Biol. Phys., 39, 229–245.Google Scholar
Maier, W. and Saupe, A. Z. (1958). Eine einfache molekulare Theorie des nematischen kristallinflüssigen Zustandes. Z. Natureforsch., A13, 564–566.Google Scholar
Malmberg, C. G. and Maryott, A. A. (1956). Dielectric constant of water from 0° to 100°. J. Res. Nat. Bur. Stand. 56, 1–8.Google Scholar
Mandel, M. (1988). Polyelectrolytes. Encyclopedia of Polymer Science and Technology, 2nd Ed., 11, 739–829.Google Scholar
Mandel, M. (2000). The dielectric increments of aqueous polyelectrolyte solutions: A scaling approach. Biophys. Chem., 85, 125–139.Google Scholar
Mandel, M., Leyte, J. C. and Stadhouder, M. G. (1967). The conformational transition of poly(methacrylic acid) in solution. J. Phys. Chem. 71, 603–612.CrossRefGoogle Scholar
Manning, G. S. (1969). Limiting laws and counterion condensation in polyelectrolyte solutions. I: Colligative properties. II: Self-diffusion of the small ions. J. Chem. Phys. 51, 924–938.Google Scholar
Manning, G. S. (1975). Limiting law for the conductance of the rod model of a salt-free polyelectrolyte solution. J. Phys. Chem., 79, 262–265.Google Scholar
Manning, G. S. (1978). The molecular theory of polyelectrolyte solutions with application to the electrostatic properties of polynucleotides. Quarter. Rev. Biophys. bf 11, 179–246.CrossRefGoogle Scholar
Manning, G. S. (1981). Limiting laws and counterion condensation in polyelectrolyte solutions. 7. Electrophoretic mobility and conductance. J. Phys. Chem., bf 85, 1506–1515.CrossRefGoogle Scholar
Mao, A. H., Crick, S. L., Vitalis, A., Chicoine, C. L. and Pappu, R. V. (2010). Net charge per residue modulates conformational ensembles of intrinsically disordered proteins. Proc. Natl. Acad. Sci. USA., 107, 8183–8188.Google Scholar
Mark, J. E. and Erman, B., (1988). Rubberlike Elasticity A Molecular Primer, New York: John Wiley & SonsGoogle Scholar
Marko, J. F. and Rabin, Y. (1992). Microphase separation of charged diblock copolymers: Melts and solutions. Macromolecules, 25, 1503–1509.Google Scholar
Matsumoto, T., Nishioka, N. and Fujita, H. (1972). Excluded-volume effects in dilute polymer solutions. iv. Polyisobutylene, J. Polym. Sci.. A-2,10, 23–42.Google Scholar
Maxwell, J. C. (1875). On the dynamical evidence of the molecular constitution of bodies. Nature, 11, 357–359.Google Scholar
Mehler, A. and Eichele, G. (1984). Electrostatic effects in water-accessible regions of proteins. Biochemistry 23, 3887–3891.Google Scholar
Meller, A. (2003). Dynamics of polynucleotide transport through nanometre-scalepores. J. Phys. Condes. Matter, 15, R581–R607 (2003).Google Scholar
Miklavic, S. J. and Marc̃lja, S. (1988). Interaction of surface carrying grafted polyelectrolytes. J. Phys. Chem., 92, 6718–6722.Google Scholar
Milner, S. T., Witten, T. A. and Cates, M. E. (1988). Theory of the grafted polymer brush. Macromolecules, 21, 2610–2619.Google Scholar
Misra, S., Varanasi, S. and Varanasi, P. P. (1989). A polyelectrolyte brush theory. Macromolecules, 22, 4173–4179.Google Scholar
Miyaki, Y., Einaga, Y., Hirosye, T. and Fujita, H. (1977). Solution properties of poly(d-ji-hydroxybutyrate). 2. Light scattering and viscosity in trifluoroethanol and behavior of highly expanded polymer coils, Macromolecules, 10, 1356–1364.Google Scholar
Miyaki, Y., Einaga, Y. Fujita, H. (1978). Excluded-volume effects in dilute polymer solutions. 7. Very high molecular weight polystyrene in benzene and cyclohexane, Macromolecules, 11, 1180–1186.Google Scholar
Molliex, A., Temirov, J., Lee, J., Coughlin, M., Kanagaraj, A. P., Kim, H. J., Mittag, T. and Taylor, J. P. (2015). Phase separation by low complexity domains promotes stress granule assembly and drives pathological fibrillization. Cell, 163, 123–133.Google Scholar
Montiel-Garcia, D., Santoyo-Rivera, N., Ho, P., Carrillo-Tripp, M., Brooks III, C. L., Johnson, J. E. Reddy, V. S. (2021). VIPERdb v3. 0: a structure-based data analytics platform for viral capsids. Nucleic Acid Research, 49, D809-D816.Google Scholar
Morozova, S., Hu, G., Emrick, T. and Muthukumar, M. (2016). Influence of dipole orientation on solution properties of polyzwitterions. ACS Macro Lett., 5, 118–122.Google Scholar
Morozova, S. and Muthukumar, M. (2017). Elasticity of swelling equilibrium of ultrasoft poly-electrolyte gels: Comparisons of theory and experiments, Macromolecules, 50, 2456–2466.CrossRefGoogle Scholar
Morozova, S. Muthukumar, M. (2018). Electrostatic effects in collagen fibril formation. J. Chem. Phys., 149, 163333.Google Scholar
Müller-Späth, S., Soranno, A., Hirschfeld, V., Hofmann, H., Rüegger, S., Reymond, L., Nettels, D. and Schuler, B. (2010). Charge interactions can dominate the dimensions of intrinsically disordered proteins. Proc. Natl. Acad. Sci. USA., 107, 14609–14614.Google Scholar
Muthukumar, M. (1981). Viscosity of polymer solution. J. Phys. A: Math. Gen., 14, 2129–2148.Google Scholar
Muthukumar, M. (1984). Collapse transition of a stiff chain. J. Chem. Phys. 81, 6172–6276.Google Scholar
Muthukumar, M. (1987). Adsorption of a polyelectrolyte chain to a charged surface. J. Chem. Phys., 86, 7230–7235.Google Scholar
Muthukumar, M., (1989). Polyelectrolyte gels: Replica theory, Springer Proc. Phys., 42, 28–34.Google Scholar
Muthukumar, M. (1991). Entropic barrier model for polymer diffusion in concentrated polymer solutions and random media. J. Non-Cryst Solids, 131-133, 654–666.Google Scholar
Muthukumar, M. (1996a). Double screening in polyelectrolyte solutions: Limiting laws and crossover formulas. J. Chem. Phys., 105, 5183–5199.CrossRefGoogle Scholar
Muthukumar, M. (1996b). Localized structures of polymers with long-range interactions. J. Chem. Phys., 104, 691–700.Google Scholar
Muthukumar, M. (1997). Dynamics of polyelectrolyte solutions. J. Chem. Phys., 107, 2619–2635.Google Scholar
Muthukumar, M. (1999). Polymer translocation through a hole. J. Chem. Phys., 111, 10371–10374.Google Scholar
Muthukumar, M. (2001). Theory of viscoelastic properties of polyelectrolyte solutions. Polymer, 42, 5921–5923.Google Scholar
Muthukumar, M. (2002). Phase diagram of polyelectrolyte solutions: Weak polymer effect. Macromolecules, 35, 9142–9145.CrossRefGoogle Scholar
Muthukumar, M. (2004). Theory of counterion condensation flexible polyelectrolytes: Adsorption mechanism. J. Chem. Phys. 120, 9343–9350.Google Scholar
Muthukumar, M. (2010). Theory of capture rate in polymer translocation, J. Chem. Phys. 132, 195101.CrossRefGoogle Scholar
Muthukumar, M. (2012a). Counterion adsorption theory of dilute polyelectrolyte solution: Apparent molecular weight, second virial coefficient, and intermolecular structure factor. J. Chem. Phys. 137, 034902.Google Scholar
Muthukumar, M. (2014). Communication : Charge, diffusion, and mobility of proteins through nanopores. J. Chem. Phys., 141, 081104.Google Scholar
Muthukumar, M. (2016a). Electrostatic correlations in polyelectrolyte solutions, Polym. Sci. A, 58, 852–863.Google Scholar
Muthukumar, M. (2016b). Ordinary-extraordinary transition in dynamics of solutions of charged macromolecules, Proc. Natl. Acad. Sci. (USA), 113, 12627–12632.Google Scholar
Muthukumar, M. (2017). A Perspective on polyelectrolyte solutions. Macromolecules, 50, 9528–9560.Google Scholar
Muthukumar, M. (2019). Collective dynamics of semidilute polyelectrolyte solutions with salt. J. Polym. Sci. Part B: Polym. Phys., 57, 1263–1269.CrossRefGoogle Scholar
Muthukumar, M. (2021). Theory of ionic conductivity with morphological control in polymers. ACS Macro Lett., 10, 958–964.Google Scholar
Muthukumar, M. and Baumgärtner, A. (1989a). Effects of entropic barriers on polymer dynamics. Macromolecules, 22, 1937–1941.Google Scholar
Muthukumar, M. and Baumgärtner, A. (1989b). Diffusion of a polymer chain in random media. Macromolecules, 22, 1941–1946.Google Scholar
Muthukumar, M. and Edwards, S. F. (1982a). Extrapolation formulas for polymer solution properties, J. Chem. Phys., 76, 2720–2730.Google Scholar
Muthukumar, M. and Edwards, S. F. (1982b). Screening concepts in polymer solution dynamics. Polymer, 23, 345–348.Google Scholar
Muthukumar, M., Hua, J. and Kundagrami, A. (2010). Charge regularization in phase separating polyelectrolyte solutions. J. Chem. Phys., 132, 08490.Google Scholar
Muthukumar, M. and Nickel, B. G. (1984). Perturbation theory for a polymer chain with excluded volume interaction. J. Chem. Phys. 80, 5839–5850.CrossRefGoogle Scholar
Muthukumar, M. and Nickel, B. G. (1987). Expansion of a polymer chain with excluded volume interaction. J. Chem. Phys. 86, 460–476.Google Scholar
Muthukumar, M., Plesa, C. and Dekker, C. (2015). Single molecule sensing with nanopores. Physics Today 68, 32.Google Scholar
Naji, A., Kanduc, M., Forsman, J., Podgornik, R. Coulomb fluids -Weak coupling, strong coupling, in between and beyond. J. Chem. Phys. 2013, 139, 150901.Google Scholar
Nelson, D. L. and Cox, M. M. (2005). Lehninger Principles of Biochemistry. New York: W. H. Freeman and Company.Google Scholar
Nguyen, T. T., Rouzina, I. and Shklovskii, B. I. (2000). Reentrant condensation of DNA induced by multivalent counterions. J. Chem. Phys., 112, 2562–2568.Google Scholar
Nierlich, M., Williams, C. E., Boue, F., Cotton, J. P., Daoud, M., Farnoux, B., Jannink, G., Picot, C., Moan, M., Wolff, C., Rinaudo, M. and de Gennes, P. G. (1979). Small angle neutron scattering by semi-dilute solutions of polyelectrolyte, J. Physique, 40, 701–704.Google Scholar
Nishida, K., Kaji, K. and Kanaya, T. (2001). High concentration crossovers of polyelectrolyte solutions, J. Chem. Phys., 114, 8671–8677.Google Scholar
Nishida, K., Kaji, K., Kanaya, T. and Shibano, T. (2002). Added salt effect on the inter-molecular correlation in flexible polyelectrolyte solutions: Small-angle scattering study. Macromolecules, 35, 4084–4089.CrossRefGoogle Scholar
Niu, A., Liaw, D-J., Sang, H-C. and Wu, C. (2000). Light scattering study of a zwitterionic polycarboxybetaine in aqueous solution. Macromolecules, 33, 3492–3494.Google Scholar
Noda, I., Kato, N., Kitano, T. and Nagasawa, M. (1981). Thermodynamic properties of moderately concentrated solutions of linear polymers. Macromolecules, 14, 668–676.CrossRefGoogle Scholar
Norisuye, T., Miyata, Q. T., and Shibayama, M., (2004). Dynamic inhomogeneities in polymer gels investigated by dynamic light scattering, Macromolecules, 37, 2944–2953.Google Scholar
Nott, T. J., Petsalaki, E., Farber, P., Jervis, D., Fussner, E., Plochowietz, A., Craggs, T. D., Bazett-Jones, D. P., Pawson, T., Forman-Kay, J. D. and Baldwin, A. (2015). Phase transition of a disordered nuage protein generates environmentally responsive membraneless organelles. Molecular Cell, 57, 936–947.CrossRefGoogle ScholarPubMed
Odijk, T. (1977). Polyelectrolytes near the rod limit. J. Polym. Sci., Polym. Phys., 15, 477–483.CrossRefGoogle Scholar
Ohmine, I. and Tanaka, T. (1982). Salt effects on the phase transition of ionic gels, J. Chem. Phys., 77, 5725–5729.Google Scholar
Olvera de la Cruz, M., Belloni, M. L., Delsanti, M., Dalbiez, J. P., Spalla, O. and Drifford, M. (1995). Precipitation of highly charged polyelectrolyte solutions in the presence of multivalent salts. J. Chem. Phys., 103, 5781.Google Scholar
Onsager, L. (1949). The effects of shape on the interaction of colloidal particles. Ann. N. Y. Acad. Sci., 51, 627–659.Google Scholar
Oosawa, F. (1957). A simple theory of thermodynamic properties of polyelectrolyte solutions. J. Polym, Sci. 23, 421–430.CrossRefGoogle Scholar
Orkoulas, G., Kumar, S. K. and Panagiotopoulos, A. Z. (2003). Monte -Carlo study of coulombic criticality in polyelectrolytes. Phys. Rev. Lett. 90, 048303.Google Scholar
Ou, Z. and Muthukumar, M. (2005). Langevin dynamics of semiflexible polyelectrolytes: Rod-toroid-globule-coil structures and counterion distribution. J. Chem. Phys., 123, 074905.Google Scholar
Ou, Z. and Muthukumar, M. (2006). Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations. J. Chem. Phys., 124, 154902.Google Scholar
Pak, C. W., Kosno, M., Holehouse, A. S., Padrick, S. B., Mittal, A., Ali, R., Yunus, A. A., Liu, D. R., Pappu, R. V. and Rosen, M. K. (2016). Sequence determinants of intracellular phase separation by complex coacervation of a disordered protein. Mol. Cell, 63, 72–85.Google Scholar
Palmenberg, A. C. and Sgro, J-Y. (1997). Topological organization of picornaviral genomes: Statistical prediction of RNA structural signals. Semin. Virol., 8, 231–241.Google Scholar
Peng, B. and Muthukumar, M. (2015). Modeling competitive substitution in a polyelectrolyte complex. J. Chem. Phys., 143, 243133.Google Scholar
Pincus, P. (1991). Colloid stabilization with grafted polyelectrolytes. Macromolecules, 24, 2912–2919.Google Scholar
Prabhu, V. M., Muthukumar, M., Wignall, G. D. and Melnichenko, Y. B. (2001). Dimensions of polyelectrolyte chains and concentration fluctuations in semidilute solutions of sodium-poly(styrene sulfonate) as measured by small-angle neutron scattering, Polymer, 42, 8935–8946.Google Scholar
Prabhu, V. M., Muthukumar, M., Wignall, G. D. and Melnichenko, Y. B. (2003). Polyelectrolyte chain dimensions and concentration fluctuations near phase boundaries, J. Chem. Phys., 119, 4085–4098.Google Scholar
Prabhu, V. M., Amis, E. J., Bossov, D. P. and Rossov, N. (2004). Counterion associative behavior with flexible polyelectrolytes. J. Chem. Phys., 121, 4424–4429.CrossRefGoogle ScholarPubMed
Pum, D. and Sleytr, U. B. (2014). Reassembly of S-layer proteins. Nanotechnology, 25, 312001.Google Scholar
Rabin, Y. and Panyukov, S., (1997). Scattering profiles of charged gels: Frozen inhomogeneities, thermal fluctuations, and microphone separation, Macromolecules, 30, 301–312.Google Scholar
Raman, B., Chatani, E., Kihara, M., Ban, T., Sakai, M., Hasegawa, K., Naiki, H., Rao, C. M. and Goto, Y. (2005). Critical balance of electrostatic and hydrophobic Interactions Is required for yS2-microglobulin amyloid fibril growth and stability. Biochemistry, 44, 1288–1299.Google Scholar
Ray, S., Singh, N., Kumar, R., Patel, K., Pandey, S., Datta, D., Mahato, J., Panigrahi, R., Navalkar, A., Mehra, S., Gadhe, L., Chatterjee, D., Sawner, A. S., Maiti, S., Bhatia, S., Gerez, J. A., Chowdhury, A., Kumar, A., Padinhateeri, R., Riek, R., Krishnamorthy, G. and Maji, S. K. 2020. a-Synuclein aggregation nucleates through liquid-liquid phase separation. (2020). Nat. Chem., 12 , 705–716.Google Scholar
Renkin, E. M. (1954). Filtration , diffusion, and molecular sieving through porous cellulose membranes. J. Gen. Physiol, 38, 225–243.Google Scholar
Rice, S. A. and Nagasawa, M. (1961). Polyelectrolyte Solutions, New York: Academic Press.Google Scholar
Richards, R. W., Maconnachie, A. and Allen, G. (1978). Temperature dependence of chain dimensions. Polymer, 19, 266–270.CrossRefGoogle Scholar
Rotstein, N. A. and Lodge, T. P. (1992). Tracer diffusion of linear polystyrenes in poly(vinyl methyl ether) gels. Macromolecules, 25, 1316–1325.Google Scholar
Rouse, P. E. (1953). A theory of linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21, 1272–1280.Google Scholar
Rousseau, J., Drouin, G. and Slater, G. W. (1997). Entropic trapping of DNA during gel electrophoresis: Effect of field intensity and gel concentration. Phys. Rev. Lett., 79, 1945.Google Scholar
Routh, A., Domitrovic, T. and Johnson, J. E. (2012). Host RNAs, including transposons, are encapsidated by a eukaryotic single-stranded RNA virus. Proc. Natl. Acad. Sic. (USA), 109, 1907–1912.CrossRefGoogle ScholarPubMed
Rowghanian, P. and Grosberg, A. Y. (2012). Propagation of tension along a polymer chain. Phys. Rev. E, 86, 011803.Google Scholar
Rubinstein, M. and Colby, R. H. (2003). Polymer Physics, Oxford: Oxford University Press.Google Scholar
Sabbagh, I. and Delsanti, M. (2000). Solubility of highly charged anionic polyelectrolytes in presence of multivalent cations: Specific interaction effect. Eur. Phys. J. E, 1, 75–86.Google Scholar
Saha, S., Fischer, K., Muthukumar, M. and Schmidt, M. (2013). Apparent molar mass of a polyelectrolyte in an organic solvent in the low ionic strength limit as revealed by light scattering. Macromolecules, 46, 8296–8303.Google Scholar
Sakaue, T. (2007). Nonequilibrium dynamics of polymer translocation and straightening. Phys. Rev. E, 76, 021803.Google Scholar
Salehi, A. and Larson, R. G. (2016). A molecular thermodynamic model of complexa-tion in mixtures of oppositely charged polyelectrolytes with explicit account of charge association/dissociation. Macromolecules, 49, 9706–9719.Google Scholar
Samanta, H. S., Chakraborty, D. and Thirumalai, D. (2018). Charge fluctuation effects on the shape of flexible polyampholytes with applications to intrinsically disordered proteins. J. Chem. Phys. 149, 163323.Google Scholar
Sasaki, S. and Schipper, F. J. M., (2001). Coupled diffusion of segments and counterions in polyelectrolyte gels and solutions, J. Chem. Phys., 115, 4349–4354.Google Scholar
Sawle, L. and Ghosh, K. (2015). A theoretical method to compute sequence dependent configurational properties in charged polymers and proteins. J. Chem. Phys., 143, 085101.Google Scholar
Schiessel, H. (1999). Counterion condensation on flexible polyelectrolytes: Dependence on ionic strength and chain concentration. Macromolecules, 32, 5673–5680.Google Scholar
Schmitz, K. S. (1993). Macroions in Solution and Colloidal Suspensions, New York: VCH Publishers.Google Scholar
Schosseler, F., Ilmain, F., and Candau, S. J., 1991. Structure and properties of partially neutralized poly(acrylic acid) gels, Macromolecules, 24, 225–234.Google Scholar
Schuler, B., Soranno, A., Hofmann, H. and Nettels, D. (2016). Single molecule FRET spectroscopy and the polymer physics of unfolded and intrinsically disordered proteins. Annu. Rev. Biophys., 45, 207–231.CrossRefGoogle ScholarPubMed
Schuler, B., Borgia, A., Borgia, M. B., Heidarsson, P. O., Holmstrom, E. D., Nettels, D. and Sottini, A. (2020). Binding without folding -the biomolecular function of disordered polyelectrolyte complexes. Curr. Opin. Struct. Biol, 60, 66–76.Google Scholar
Schwarzenbach, G. (1936). Thermodynamick kinetik electrochemie eigenschaftslehre. Z. Phys. Chem. A 176, 133–153.Google Scholar
Sedlak, M. and Amis, E. J. (1992a). Dynamics of moderately concentrated salt-free polyelec-trolyte solutions: Molecular weight dependence. J. Chem. Phys., 96, 817–825.Google Scholar
Sedlak, M. and Amis, E. J. (1992b). Concentration and molecular weight regime diagram of salt-free polyelectrolyte solutions as studied by light scattering. J. Chem. Phys., 96, 826–834.Google Scholar
Severin, M. (1993). Thermal maximum in the size of short polyelectrolyte chains. A Monte Carlo study. J. Chem. Phys., 99, 628–633.CrossRefGoogle Scholar
Shew, C-Y. and Yethiraj, A. (1999). Monte Carlo simulations and self-consistent integral equation theory for polyelectrolyte solutions, J. Chem. Phys., 110, 5437–5443.Google Scholar
Shew, C-Y. and Yethiraj, A. (2000). Self-consistent integral equation theory for semiflexible chain polyelectrolyte solutions, J. Chem. Phys., 113, 8841–8847.Google Scholar
Shibayama, M. and Tanka, T. (1993). Volume phase transition and related phenomena of polymer gels, Adv. Poly. Sci., 109, 1–62.CrossRefGoogle Scholar
Shibayama, M., Ikkai, F., Shiwa, Y., and Rabin, Y., (1997). Effect of degree of cross-linking on spatial inhomogeneity in charged gels. I. Theoretical predictions and light scattering study, J. Chem. Phys., 107, 5227–5235.CrossRefGoogle Scholar
Shojaei, H. R. and Muthukumar, M. (2017). Adsorption and encapsulation of flexible polyelec-trolytes in charged spherical vesicles. J. Chem. Phys., 146, 244901.Google Scholar
Shoulders, M. D. and Raines, R. T. (2009). Collagen structure and stability. Ann. Rev. Biochemistry, 78, 929–958.Google Scholar
Shultz, A. R. and Flory, P. J. (1952). Phase equilibria in polymer-solvent systems. J. Amer. Chem. Soc. 74, 4760–4767.Google Scholar
Siber, A. and Podgornik, R. (2008). Nonspecific interactions in spontaneous assembly of empty versus functional single-stranded RNA viruses, Phys. Rev. E, 78, 05191.CrossRefGoogle Scholar
Siber, A., Bozic, A. L. and Podgornik, R. (2012). Energies and pressures in viruses: Contribution of nonspecific electrostatic interactions, Phys. Chem. Chem. Phys., 14, 3746–3765.Google Scholar
Skolnick, J. and Fixman, M. (1977). Electrostatic persistence length of a wormlike polyelec-trolyte. Macromolecules, 10, 944–948.Google Scholar
Slagowski, E., Tsai, B. and Mc Intyre, D. (1976.) The dimensions of polystyrene near and below the theta temperature. Macromolecules, 9, 687–688.Google Scholar
Slater, G. W. and Wu, S. Y. (1995). Reptation , entropic trapping, percolation, and rouse dynamics of polymers in “random” environments. Phys. Rev. Lett., 75, 164.CrossRefGoogle ScholarPubMed
Spruijt, E., Westphal, A. H., Borst, J. W., Stuart, Cohen, A. and van der Gucht, M., J. (2010). Binodal compositions of polyelectrolyte complexes. Macromolecules, 43, 6476–6484.Google Scholar
Srivastava, D. and Muthukumar, M. (1996). Sequence dependence of conformations of polyam-pholytes. Macromolecules, 29, 2324–2326.Google Scholar
Srivastava, S. and Tirrell, M. V. (2016). Polyelectrolyte complexation. Adv. Chem. Phys., 161, 499–543.Google Scholar
Stell, G., Wu, K. C., and Larsen, B. (1976). Critical point in a fluid of charged hard spheres. Phys. Rev. Lett. 37, 1369–1372.Google Scholar
Stellwagen, E., Lu, Y. and Stellwagen, N. (2003). Unified description of electrophoresis and diffusion for DNA and other polyions. Biochemistry, 42, 11745–11750.Google Scholar
Stevens, M. J., and Kremer, K. (1995). The nature of flexible linear polyelectrolytes in salt free solution: A molecular dynamics study. J. Chem. Phys., 103, 1669–1690.Google Scholar
Stockley, P. G., Twarock, R., Bakker, S. E., Barker, A. M., Borodavka, A., Dykeman, E., Ford, R. J., Pearson, A. M., Phillips, S. E. V., Ranson, N. A. and Tuma, R. (2013). Packaging signals in single-stranded RNA viruses: Nature’s alternative to a purely electrostatic assembly mechanism. J. Biol. Phys., 39, 277–287.CrossRefGoogle ScholarPubMed
Stockmayer, W. H. (1950). Light scattering in multi-component systems. J. Chem. Phys., 18, 58–61.Google Scholar
Störkle, D., Duschner, S., Heimann, N., Maskos, M. and Schmidt, M. (2007). Complex formation of DNA with oppositely charged polyelectrolytes of different chain topology: Cylindrical brushes and dendrimers. Macromolecules 40, 7998–8006.Google Scholar
Strauss, U. P., Helfgott, C. and Pink, H. (1967). Interactions of polyelectrolytes with simple electrolytes. II. Donnan equilibria obtained with DNA in solutions of 1–1 electrolytes. J. Phys. Chem., 71, 2550–2556.Google Scholar
Stroobants, A., Lekkerkerker, H. N. W. and Odijk, Th. (1986). Effect of electrostatic interaction on the liquid crystal phase transition in solutions of rodlike polyelectrolytes. Macromolecules, 19, 2232–2238.Google Scholar
Strzelecka, T. E. and Rill, R. L. (1990). Phase transitions of concentrated DNA solutions in low concentrations of 1:1 supporting electrolyte. Biopolymers, 30, 57–71.Google Scholar
Sung, W. and Park, P. J. (1996). Polymer translocation through a pore in a membrane. Phys. Rev. Lett., 77, 783–788.Google Scholar
Tanaka, T, Hocker, L. O., and Benedek, G. B., (1973). Spectrum of light scattered from a viscoelastic gel, J. Chem. Phys., 59, 5151–5159.Google Scholar
Tanaka, T. (1978). Collapse of gels and the critical point, Phys. Rev. Lett., 40, 820–823.CrossRefGoogle Scholar
Tanaka, T., Fillmore, D., Sun, S-T., Nishio, I., Swislow, G., and Shah, A., (1980). Phase transitions in ionic gels, Phys. Rev. Lett., 45, 1636–1639.Google Scholar
Temin, H. M. and Mizutani, S. (1970). Viral RNA-dependent DNA polymerase: RNA-dependent DNA polymerase in virions of Rous Sarcoma Virus. Nature, 226, 1211–1213.Google Scholar
Tihova, M., Dryden, K. A., Le, T. L., Harvey, S. C., Johnson, J. E., Yeager, M. and Schnee-mann, A. (2004). Nodavirus coat protein imposes dodecahedral RNA structure independent of nucleotide sequence and length. J. Virol., 78, 2897–2905.Google Scholar
Ting, C. L., Wu, J. and Wang, Z-G. (2011). Thermodynamic basis for the genome to capsid charge relationship in viral encapsidation, Proc. Natl. Acad. Sci. (USA), 108, 16986–16991.Google Scholar
Tohyama, K. and Miller, W. G. (1981). Network structure in gels of rod-like polypeptides. Nature, 289, 813–814.Google Scholar
Tokita, M. Tanaka, T. (1991). Friction coefficient of polymer network of gels. J. Chem. Phys., 95, 4613–4619Google Scholar
Tompa, P. (2010). Structure and Function of Intrinsically Disordered Proteins. Boca Raton: CRC Press.Google Scholar
Uversky, V. N. (2002). Natively unfolded proteins: A point where biology waits for physics. Protein Sci., 11, 739–756.Google Scholar
Uversky, V. N., Oldfield, C. J. and Dunker, A. K. (2008). Intrinsically disordered proteins in human diseases: Introducing the D2 concept. Annu. Rev. Biophys., 37, 215–246.Google Scholar
van der Lee, R., Buljan, M., Lang, B., Robert, J. Weatheritt, R. J., Gary W. Daughdrill, G. W., Dunker, A. K., Fuxreiter, M., Gough, J., Gsponer, J., David T. Jones, D. T., Kim, P. M., Kriwacki, R. W., Oldfield, C. J., Pappu, R. V., Tompa, P., Uversky, V. N., Wright, P. E. and Babu, M. M. (2014). Classification of intrinsically disordered regions and proteins. Chem. Rev., 114, 6589–6631.Google Scholar
Vink, H. (1982). Electrolytic conductivity of polyelectrolyte solutions. Makromol. Chem., 183, 2273–2283.Google Scholar
Viovy, J. L. (2000). Electrophoresis of DNA and other polyelectrolytes: Physical mechanisms. Rev. Mod. Phys., 72, 813.Google Scholar
Volk, N., Vollmer, D., Schmidt, M., Oppermann, W., and Huber, K. (2004). Polyelectrolyte theory, Adv. Polym. Sci., 166, 29–65.Google Scholar
von Goeler, F. and Muthukumar, M. (1994). Adsorption of polyelectrolytes onto curved surfaces. J. Chem. Phys., 100, 7796–7803.Google Scholar
Wallace, D. G. (1990). The relative contribution of electrostatic interactions to stabilization of collagen fibrils. Biopolymers, 29, 1015–1026.Google Scholar
Wandrey, C. (1999). Concentration regimes in polyelectrolyte solutions. Langmuir, 15, 40694075.Google Scholar
Wandrey, C., Hunkeler, D., Wendler, U. and Jaeger, W. (2000). Counterion activity of highly charged strong polyelectrolytes. Macromolecules, 33, 7136–7143.Google Scholar
Wang, J. and Muthukumar, M. (2011). Encapsulation of a polyelectrolyte chain by an oppositely charged spherical surface. J. Chem. Phys., 135, 194901.Google Scholar
Wang, Q. and Schlenoff, J. B. (2014). The polyelectrolyte complex/coacervate continuum. Macromolecules, 47, 3108–3116.Google Scholar
Wanunu, M. (2012). Nanopores : A journey towards DNA sequencing. Phys. Life. Rev. 9, 125–158.Google Scholar
Wanunu, M., Morrison, W., Rabin, Y., Grosberg, A. Y. and Meller, A. (2010). Electrostatic focusing of unlabelled DNA into nanoscale pores using a salt gradient. Nat. Nanotech. 5, 160–165.Google Scholar
Webb, T. J. (1926). The free energy of hydration of ions and the electrostriction of the solvent. J. Amer. Chem. Soc, 48, 2589–2603.Google Scholar
Wetzel, R. (2006). Kinetics and thermodynamics of amyloid fibril assembly. Acc. Chem. Res., 39, 671–679.Google Scholar
Wiegel, F. W. (1977). Adsorption of a macromolecule to a charged surface. J. Phys. A: Math. Gen., 10, 299–303.Google Scholar
Wiegel, F. W. (1986). Introduction to Path-Integral Methods in Physics and Polymer Science. Singapore: World Scientific.Google Scholar
Winkler, R. G., Gold, M. and Reineker, P. (1998). Collapse of polyelectrolyte macromolecules by counterion condensation and ion pair formation: A molecular dynamics simulation study. Phys. Rev. Lett., 80, 3731–3734.Google Scholar
Winkler, R. G. and Cherstvy, A. G. (2014). Strong and weak polyelectrolyte adsorption onto oppositely charged curved surfaces. Adv. Polym. Sci., 255, 1–56.Google Scholar
Wissenburg, P., Odijk, T., Cirket, P. and Mandel, M. (1995). Multimolecular aggregation of mononucleosomal DNA in concentrated isotropic solutions. Macromolecules 28, 23152328.Google Scholar
Wittmer, J., Johner, A. and Joanny, J. F. (1995). Precipitation of polyelectrolytes in the presence of multivalent salts. J. Phys. II France, 5, 635–654.Google Scholar
Yethiraj, A. (1998). Theory for chain conformations and static structure of dilute and semidilute polyelectrolyte solutions, J. Chem. Phys., 108, 1184–1192.Google Scholar
Yethiraj, A. (2009). Liquid state theory of polyelectrolyte solutions, J. Phys. Chem. B, 113, 1539–1551.Google Scholar
Young, H. D. and Freedman, R. A. (2000). University Physics, 10th edn. San Francisco: Addison-Wesley.Google Scholar
Zandi, R., Reguera, D., Rudnick, J. and Gelbart, W. M. (2003). What drives the translocation of stiff chains? Proc. Natl. Acad. Sci. USA., 100, 8649–8653.CrossRefGoogle Scholar
Zhang, J. and Muthukumar, M. (2009). Simulations of nucleation and elongation of amyloid fibrils. J. Chem. Phys., 130, 035102.Google Scholar
Zhou, K., Li, J., Lu, Y., Zhang, G., Xie, Z. and Wu, C. (2009). Re -examination of dynamics of polyeletrolytes in salt-free dilute solutions by designing and using a novel neutral-charged-neutral reversible polymer. Macromolecules, 42, 7146–7154.CrossRefGoogle Scholar
Zimm, B. H. (1956). Dynamics of polymer molecules in dilute solution: Viscoelasticity, flow birefringence and dielectric loss. J. Chem. Phys. 24, 269–278.CrossRefGoogle Scholar
Zimm, B. H. (1988). Size fluctuations can explain anomalous mobility in field-inversion electrophoresis of DNA. Phys. Rev. Lett. 61, 2965–2968.CrossRefGoogle Scholar
Zimm, B. H. (1991). “Lakes-straits” model of field-inversion gel electrophoresis of DNA. J. Chem. Phys. 94, 2187–2206.Google Scholar
Zimm, B. H. and Stockmayer, W. H. (1949). The dimensions of chain molecules containing branches and rings. J. Chem. Phys. 17, 1301–1314.Google Scholar
Zlotnick, A., Cheng, N., Stahl, S. J., Conway, J. F., Steven, A. C. and Wingfield, P. T. (1997). Localization of the C terminus of the assembly domain of hepatitis B virus capsid protein: Implications for morphogenesis and organization of encapsidated RNA. Proc. Natl. Acad. Sci. USA., 94, 9556–9561.Google Scholar