References
- Belmonte A, Shelley MJ, Eldakar ST, et al. Dynamic patterns and self-knotting of a driven hanging chain. Phys Rev Lett. 2001;87:114301.
- Klotz AR, Soh BW, Doyle PS. Motion of knots in DNA stretched by elongational fields. Phys Rev Lett. 2018;120:188003.
- Saitta AM, Soper PD, Wasserman E, et al. Influence of a knot on the strength of a polymer strand. Nature. 1999;399:46–48.
- Tubiana L, Rosa A, Fragiacomo F, et al. Spontaneous knotting and unknotting of flexible linear polymers: equilibrium and kinetic aspects. Macromolecules. 2013;46:3669–3678.
- Ko KT, Hu IC, Huang KF, et al. Untying a knotted SPOUT RNA methyltransferase by circular permutation results in a domain-swapped dimer. Structure. 2019;27:1224–1233.e4.
- Moorthi K, Kamio K, Ramos J, et al. Monte Carlo simulations of structure and entanglements in polymer melts. Mol Simul. 2014;41:993–995.
- Masubuchi Y, Takimoto J-I, Koyama K. Simulation study on effect of polymer entanglement on the strain hardening. Mol Simul. 1999;21:257–269.
- Rubinstein M, Colby R. H: polymer physics. New York: Oxford University Press; 2003. 361–422.
- Reifenberger JG, Dorfman KD, Cao H. Topological events in single molecules of E. coli DNA confined in nanochannels. Analyst. 2015;140:4887–4894.
- Yin S, Dhital B, Hou YM. How to untie a protein knot. Structure. 2019;27:1190–1191.
- Liu Y. Dynamic feature of incipient polymer collapse below the theta point. J Phys Chem B. 2017;121:9469–9475.
- Xu X, Gao X. Polymer knot in solution near the θ point. J Phys Chem B. 2020;124:2723–2729.
- Grosberg AY, Rabin Y. Metastable tight knots in a wormlike polymer. Phys Rev Lett. 2007;99:217801.
- Marcone B, Orlandini E, Stella AL, et al. Size of knots in ring polymers. Phys Rev E Stat Nonlinear Soft Matter Phys. 2007;75:041105.
- Zhang P, Alsaifi NM, Wang ZG. Revisiting the Θ point. Macromolecules. 2020;53:10409–10420.
- Imakaev MV, Tchourine KM, Nechaev SK, et al. Effects of topological constraints on globular polymers. Soft Matt. 2015;11:665–671.
- Millett K, Dobay A, Stasiak A. Linear random knots and their scaling behavior. Macromolecules. 2005;38:601–606.
- Tubiana L, Orlandini E, Micheletti C. Multiscale entanglement in ring polymers under spherical confinement. Phys Rev Lett. 2011;107:188302.
- Virnau P, Kantor Y, Kardar M. Knots in globule and coil phases of a model polyethylene. J Am Chem Soc. 2005;127:15102–15106.
- Metzler R, Hanke A, Dommersnes PG, et al. Equilibrium shapes of flat knots. Phys Rev Lett. 2002;88:188101.
- Hanke A, Metzler R, Dommersnes PG, et al. Tight and loose shapes in flat entangled dense polymers. Eur Phys J E. 2003;12:347–354.
- Dommersnes PG, Kantor Y, Kardar M. Knots in charged polymers. Phys Rev E. 2002;66:031802.
- Muthukumar M. 50th anniversary perspective: a perspective on polyelectrolyte solutions. Macromolecules. 2017;50:9528–9560.
- Tagliabue A, Izzo L, Mella M. Interface counterion localization induces a switch between tight and loose configurations of knotted weak polyacid rings despite intermonomer Coulomb repulsions. J Phys Chem B. 2020;124:2930–2937.
- Nedelcu S, Sommer JU. Molecular dynamics simulations of electrophoresis of polyelectrolytes in nano confining cylindrical geometries. J Phys Chem. 2013;138:104905.
- Plimpton S, Crozier P, Thompson A. LAMMPS: large-scale atomic/molecular massively parallel simulator. Sandia Natl Lab. 2007;18:43.
- Schlick T. Molecular modeling and simulation: an interdisciplinary guide. New York: Springer; 2010.
- Wei M, Xu PX, Yuan YZ, et al. Molecular dynamics simulation on the mechanical properties of natural-rubber-graft-rigid-polymer/rigid-polymer systems. Phys Chem Chem Phys. 2018;20:8228–8240.
- Toukmaji AY, Board Jr JA. Ewald summation techniques in perspective: a survey. Comput Phys Comm. 1996;95:73–92.
- Yu J, Jackson NE, Xu X, et al. Multivalent ions induce lateral structural inhomogeneities in polyelectrolyte brushes. Sci. Adv. 2017;3:eaao1497.
- Hao QH, Cheng J, Liu LX, et al. Surface morphologies of planar ring polyelectrolyte brushes induced by trivalent salts. Macromolecules. 2020;53:7187–7197.
- Kremer K, Grest GS. Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J Chem Phys. 1990;92:5057–5086.
- Aronovitz JA, Nelson DR. Universal features of polymer shapes. J Phys. 1986;47:1445–1456.
- Rudnick J, Gaspari G. The asphericity of random walks. J Phys A Math Gen. 1986;19:L191–L193.
- Auhl R, Everaers R, Grest GS, et al. Equilibration of long chain polymer melts in computer simulations. J Chem Phys. 2003;119:12718–12728.
- Dai L, Renner CB, Doyle PS. Metastable knots in confined semiflexible chains. Macromolecules. 2015;48:2812–2818.
- Tubiana L, Polles G, Orlandini E, et al. KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers.Eur. Phys J E. 2018;41:72.
- Dai L, Doyle PS. Universal knot spectra for confined polymers. Macromolecules. 2018;51:6327–6333.
- Shen K, Wang ZG. Polyelectrolyte chain structure and solution phase behavior. Macromolecules. 2018;51:1706–1717.
- Volk N, Vollmer D, Schmidt M, et al. Conformation and phase diagrams of flexible polyelectrolytes. In: Schmidt M, editor. Polyelectrolytes with defined molecular architecture II. Berlin: Springer. (Advances in Polymer Science; 166).
- Priftis D, Laugel N, Tirrell M. Thermodynamic characterization of polypeptide complex coacervation. Langmuir. 2012;28:15947–15957.
- Priftis D, Tirrell M. Phase behaviour and complex coacervation of aqueous polypeptide solutions. Soft Matter. 2012;8:9396–9405.
- Klos J, Pakula T. Computer simulations of a polyelectrolyte chain with a mixture of multivalent salts. J Phys: Condens Matter. 2005;17:5635–5645.